Nuclei Off the Line of Stability 9780841210059, 9780841211612

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Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.fw001

Nuclei Off the Line of Stability

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.fw001

ACS SYMPOSIUM SERIES 324 Nuclei Off the Line

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.fw001

of Stability Richard A . Meyer, E D I T O R Lawrence Livermore National Laboratory

Daeg S . Brenner, E D I T O R Clark University

Developed from a symposium sponsored by the Division of Nuclear Chemistry and Technology at the 190th Meeting of the American Chemical Society, Chicago, Illinois, September 8-13, 1985

A m e r i c a n C h e m i c a l Society, Washington, DC 1986

Library of Congress Cataloging-in-Publication Data Nuclei off the line of stability. ( A C S symposium series, ISSN 0 0 9 7 - 6 1 5 6 ; 324) Includes bibliographies and indexes.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.fw001

1. Nuclear structure. 2. Chemistry, Physical and theoretical. I. Meyer, Richard Α., 1 9 3 3 . II. Brenner, D a e g S., 1 9 3 9 . III. A m e r i c a n C h e m i c a l Society. Division of Nuclear Chemistry and Technology. IV. Series. QC793.3.S8N84 1986 ISBN 0 - 8 4 1 2 - 1 0 0 5 - 5

539.7'4

86-25905

Copyright © 1986 A m e r i c a n C h e m i c a l Society A l l Rights Reserved. T h e appearance o f the code at the bottom o f the first page o f each chapter in this volume indicates the copyright owner's consent that reprographic copies o f the chapter may be made for personal or internal use or for the personal or internal use o f specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc., 27 Congress Street, Salem, MA 01970, for copying beyond that permitted by Sections 107 or 108 o f the U.S. Copyright L a w . T h i s consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating a new collective work, for resale, or for information storage and retrieval systems. T h e copying fee for each chapter is indicated in the code at the bottom of the first page of the chapter. T h e citation o f trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS o f the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance o f any right or permission, to the holder, reader, or any other person or corporation, to manufacture, reproduce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. Registered names, trademarks, etc., used in this publication, even without specific indication thereof, are not to be considered unprotected by law.

PRINTED IN THE UNITED STATES OF AMERICA

ACS Symposium Series M . Joan Comstock, Series Editor

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.fw001

Advisory Board Harvey W. Blanch University of California—Berkeley

Donald E. Moreland USDA, Agricultural Research Service

Alan Elzerman Clemson University

W. H . Norton J. T. Baker Chemical Company

John W. Finley Nabisco Brands, Inc.

James C. Randall Exxon Chemical Company

Marye Anne Fox The University of Texas—Austin

W. D. Shults Oak Ridge National Laboratory

Martin L . Gorbaty Exxon Research and Engineering Co.

Geoffrey K . Smith Rohm & Haas Co.

Roland F. Hirsch U.S. Department of Energy

Charles S.Tuesday General Motors Research Laboratory

Rudolph J . Marcus Consultant, Computers & Chemistry Research

Douglas B. Walters National Institute of Environmental Health

Vincent D . McGinniss Battelle Columbus Laboratories

C. Grant Willson IBM Research Department

FOREWORD

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.fw001

T h e A C S S Y M P O S I U M S E R I E S was f o u n d e d i n 1974

to p r o v i d e a

m e d i u m for p u b l i s h i n g s y m p o s i a q u i c k l y i n b o o k f o r m . T h e format o f the Series parallels that o f the c o n t i n u i n g A D V A N C E S IN C H E M I S T R Y S E R I E S except that, i n order to save t i m e , the papers are not typeset but are reproduced as they are submitted by the authors i n c a m e r a - r e a d y f o r m . (The papers i n this b o o k were prepared w i t h a different text area, reference style, a n d format f r o m those usually used i n the A C S S Y M P O S I U M SERIES.) P a p e r s are r e v i e w e d under the s u p e r v i s i o n o f the E d i t o r s w i t h the assistance o f the Series A d v i s o r y B o a r d a n d are selected to m a i n t a i n the integrity o f the s y m p o s i a ; h o w e v e r , v e r b a t i m reproductions o f p r e v i o u s l y p u b l i s h e d papers are not accepted. B o t h reviews a n d reports o f research are acceptable, because s y m p o s i a m a y embrace both types o f presentation.

PREFACE

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.pr001

THE

F U N D A M E N T A L C O N S T I T U E N T S O F N U C L E I , protons a n d neutrons, a n d

their interactions w i t h each other a n d w i t h particles o f their o w n k i n d w i t h i n the atomic nucleus have been studied intensively f o r more than h a l f a century. In attempts to understand a n d e x p l a i n the structure o f the nucleus, scientists have b o r r o w e d proven concepts f r o m a t o m i c chemistry and physics a n d used these as points o f departure. T h u s , n u c l e i , e x t r a o r d i ­ narily s m a l l entities o f enormous density, have been characterized i n terms of shells, as analogous to the p e r i o d i c i t y o f atoms, a n d as h a v i n g p h y s i c a l properties such as shape a n d surface tension. E l e m e n t a r y m o d e s o f c o l l e c t i v e e x c i t a t i o n , rotations a n d v i b r a t i o n s , have been suggested as a n a l o g o u s to m o l e c u l a r systems. T h e s e concepts have served the n u c l e a r scientist w e l l ; l i k e b o r r o w e d clothes, they tend to be f a m i l i a r , e c o n o m i c a l , and w e l l - w o r n . U n f o r t u n a t e l y , these concepts do not fit n u c l e i quite as w e l l as they fit their o r i g i n a l owners. A m a j o r focus o f this b o o k is the recent e x c i t i n g progress t o w a r d f i n d i n g a new set o f " c l o t h e s " f o r the nucleus. T h e s y m p o s i u m upon w h i c h this b o o k is based w a s o r i g i n a l l y p l a n n e d as a t i m e l y snapshot o f an i n t e r d i s c i p l i n a r y field, one that has t r a d i t i o n a l l y i n v o l v e d both chemists and physicists. M a n y see o u r d i s c i p l i n e at a c r i t i c a l j u n c t u r e ; one path c o u l d lead to an e x c i t i n g future for a somewhat neglected discipline; the other c o u l d lead to l o w e r expectations. T h e nuclear structure research c o m m u n i t y as a w h o l e l o o k s t o w a r d a n e x c i t i n g future a n d w a s anxious to gather together f o r a c o m p r e h e n s i v e presentation o f recent research. U s u a l l y , a t w o - d a y s y m p o s i u m w o u l d have sufficed, but as w o r d spread a n d interest g r e w , the s y m p o s i u m expanded to four a n d o n e - h a l f days a n d n u m b e r e d nearly one h u n d r e d presentations. P a r t i c i p a n t s agreed that a very h i g h level o f excitement i n nuclear structure research has been brought about b y recent developments i n both theory and experiment. In o r g a n i z i n g this b o o k , w e d e c i d e d to arrange presentations i n four b r o a d categories: Section I, M o t i v a t i o n f o r F u r t h e r E x p l o r a t i o n ; Section II, E x p e r i m e n t a l E x p l o r a t i o n o f C u r r e n t Issues; Section III, N e w F a c i l i t i e s a n d Techniques; and Section I V : Survey o f C u r r e n t Research. Section I provides a r i c h but focused s u m m a r y o f m o t i v a t i o n s f o r future w o r k i n the field. R e v o l u t i o n a r y advances i n theory a n d s p a r k l i n g achievements i n e x p e r i ­ mentation describe the state o f nuclear structure research. T h e introduction o f symmetries a n d supersymmetries has e n c o u r a g e d experimenters to c o n f i r m some o f the n e w predictions that f l o w f r o m boson models. R e e x a m i n a t i o n o f the e x i s t i n g n u c l e a r structure data base has brought to light s i m p l i f y i n g correlations that i n turn promise to i m p r o v e o u r ability to accurately extrapolate nuclear parameters into regions not yet accessible to experimental exploration. In this regard, the region o f n e u t r o n - r i c h isotopes xiii

is especially significant because o f its i m p o r t a n c e to astrophysics a n d reactor technology. S e c t i o n II provides an e x a m i n a t i o n o f the current status o f n u c l e a r structure research a n d presents but a s a m p l e o f the m a n y e x c i t i n g a n d c l e v e r experiments u n d e r w a y or c o m p l e t e d recently. F o u r topics are h i g h l i g h t e d : intruder states i n n u c l e i , octupole modes i n n u c l e i , h i g h - s p i n state investigations using heavy ions, a n d nuclear moments. T h i s selection reflects the o p i n i o n o f independent reviewers and our belief that these four

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.pr001

areas provide a comprehensive set o f new data for testing new theories. In m a n y instances, c r i t i c a l testing o f new theories w i l l be possible only i f new facilities a n d techniques are f o r t h c o m i n g . S e c t i o n III contains discussions o f m a j o r new f a c i l i t i e s — s o m e under c o n s t r u c t i o n , some i n intensive design stages, and s o m e still i n the idea stage. These and other m a j o r facilities are c r i t i c a l to m a i n t a i n i n g the r a p i d p a c e o f a d v a n c e m e n t i n n u c l e a r structure research a n d represent, for the most part, a history o f m u l t i n a t i o n a l p a r t i c i p a t i o n . T h e c o o r d i n a t i o n a n d phased development o f new facilities a v o i d d u p l i c a t i o n o f effort a n d enhance o v e r a l l productivity o f the w o r l d w i d e research c o m m u n i t y . Section III also l o o k s at a selection o f new techniques a n d s m a l l e r facilities that p r o v i d e a s a m p l e o f i m a g i n a t i v e a p p r o a c h e s to c u r r e n t a n d future experiments. T h r e e very different approaches to the study o f a p a r t i c u l a r nucleus, S m , are i n c l u d e d to illustrate the c o m p l e m e n t a r i t y o f different facilities a n d techniques i n a p p r o a c h i n g the study o f specific cases. F i n a l l y , the c a l l for papers for the s y m p o s i u m p r o v i d e d us w i t h a b r o a d s e l e c t i o n o f v e r y fine m a n u s c r i p t s . U n f o r t u n a t e l y , because o f space requirements we c o u l d p u b l i s h i n full o n l y a portion o f those presentations. Abstracts o f the other papers are i n c l u d e d i n Section I V . These papers c a n be obtained by w r i t i n g to R i c h a r d A . M e y e r or D a e g S. Brenner. M a n y i n d i v i d u a l s c o n t r i b u t e d to the success o f the s y m p o s i u m upon w h i c h this b o o k is based. W e especially thank R i c h a r d W . Hoff, C h a i r , and J o s e p h R . P e t e r s o n , T r e a s u r e r , o f the D i v i s i o n o f N u c l e a r C h e m i s t r y a n d T e c h n o l o g y o f the A m e r i c a n C h e m i c a l Society for their valuable assistance and t r o u b l e - s h o o t i n g . W e also gratefully a c k n o w l e d g e f i n a n c i a l support f r o m the N a t i o n a l Science F o u n d a t i o n , the D i v i s i o n o f N u c l e a r C h e m i s t r y and T e c h n o l o g y , a n d A p t e c N u c l e a r , Inc., i n presenting the s y m p o s i u m . T h e i r support e n h a n c e d s i g n i f i c a n t l y the q u a l i t y a n d scope o f the s y m ­ posium. 1 3 8

RICHARD A. MEYER

DAEG S. BRENNER

Division of Nuclear Chemistry Lawrence Livermore National Laboratory Livermore, C A 94550

Office of Academic Affairs Clark University 950 Main Street Worcester, M A 01610

August 25, 1986 xiv

INTRODUCTION

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.pr001

By Richard A . Meyer and Daeg S. Brenner

^N^UCH R E S E A R C H O N N U C L E A R S T R U C T U R E and d y n a m i c s i n recent years has investigated the behavior of nuclear matter under extreme conditions. F o r e x a m p l e , the study o f r a p i d l y rotating n u c l e i has l e d to a s i m p l e understanding o f h o w a nucleus adjusts its structure i n order to carry h i g h angular m o m e n t u m . B y e x a m i n i n g the deexcitation process, scientists have g a i n e d detailed k n o w l e d g e o f shape changes that a c c o m p a n y a loss o f e x c i t a t i o n energy. A n o t h e r w a y o f stressing n u c l e i is to produce them i n such a w a y as to create an unstable i m b a l a n c e i n v o l v i n g constituent protons and neutrons. Studies o f decay processes o f these f a r - f r o m - s t a b i l i t y nuclides have r e v e a l e d i m p o r t a n t subtleties i n n u c l e a r structure. " I n t r u d e r " states, nuclear configurations that arise f r o m an exchange of particles (holes) w i t h an adjacent shell or subshell, are one such discovery. T h e coexistence o f n o r m a l and intruder states i m p l i e s a coexistence o f different shapes w i t h i n a given nucleus. F o r m a n y years researchers have k n o w n that nuclei can be excited into v i b r a t i o n a l modes o f m o t i o n that are not reflection symmetric. T h e simplest o f these a s y m m e t r i c modes, the octupole v i b r a t i o n , has been charted extensively. O n l y recently, however, has new evidence suggested that some nuclei have reflection a s y m m e t r i c , or pear-shaped, ground-state c o n f i g u r a ­ tions. A l t h o u g h there is disagreement as to whether these n u c l e i are pearshaped or p i m p l e d , it is b e c o m i n g clear that a m o r e detailed m a p p i n g o f the nuclear surface is necessary to e x p l a i n both the spectroscopic properties a n d the masses o f heavy elements. T h e field o f nuclear structure and d y n a m i c s has developed for p r a c t i c a l as w e l l as esoteric reasons. T w o o f our most i m p o r t a n t customers for nuclear k n o w l e d g e , nuclear engineers and astrophysicists, have longstand­ i n g interests i n nuclear data and suggestions for nuclear spectroscopists. O n the p r a c t i c a l side, we often study properties o f nuclides of p a r t i c u l a r interest to the n u c l e a r p o w e r industry. U n f o r t u n a t e l y , o u r w a y o f studying these n u c l e i does not often lead to results useful to scientists c o n c e r n e d w i t h i m p r o v i n g our k n o w l e d g e o f the reactor source t e r m , w h i c h predicts the b u i l d u p o f heat i n a reactor f o l l o w i n g a loss-of-coolant accident. A s t r o p h y s i c i s t s are also a v i d customers for nuclear i n f o r m a t i o n a n d theories. C a l c u l a t i o n s o f e l e m e n t a l abundances resulting f r o m r-process nucleosynthesis a n d related m e c h a n i s m s depend o n the systematics o f xv

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.pr001

n u c l e a r properties. N u c l e a r properties such as masses, h a l f - l i v e s , a n d d e l a y e d neutron e m i s s i o n p r o b a b i l i t i e s affect these predictions i n c o m p l i ­ cated ways. In the absence o f data very far f r o m stability, models are used to extrapolate relevant parameters. T h i s uncomfortable situation w o u l d be eased i f more data were available for n e u t r o n - r i c h nuclides. T h u s , we have two very important reasons—one c o s m i c , one p r a c t i c a l — t o pursue studies o f nuclear properties to the frontier of spontaneous nuclear disintegration. In our o p i n i o n , however, the o v e r r i d i n g reasons for renewed excitement in the nuclear structure c o m m u n i t y are the successes i n theory arising f r o m formulations o f nuclear interactions i n terms o f pairs o f interacting bosons, or, i n the case o f o d d - A n u c l e i , b o s o n - f e r m i o n interactions. These new a p p r o a c h e s to u n d e r s t a n d i n g a n d c a l c u l a t i n g n u c l e a r structures a n d b e h a v i o r have b o r r o w e d the concepts o f s y m m e t r y f r o m h i g h - e n e r g y physics and f r o m crystallography. A l t h o u g h these algebraic models provide less o f a sense o f the tangible than older geometric models, they have t w o very important advantages: they are readily e m p l o y e d by experimenters as w e l l as theorists, and they c a n be applied to regions o f shape transition i n a natural w a y . T h e second advantage is extremely i m p o r t a n t because the interacting boson m o d e l ( I B M ) is the only m o d e l o f nuclear structure that provides a g l o b a l f o r m a l i s m for c a l c u l a t i n g nuclear structure. T h e c o m p u ­ t a t i o n a l successes o f the m o d e l have s t i m u l a t e d a r e e x a m i n a t i o n o f the systematic patterns o f n u c l e a r structure. E x a m i n a t i o n o f the trends o f a variety o f n u c l e a r data as a function o f the product o f the n u m b e r o f valence neutrons and protons appears to provide an i m p r o v e d f r a m e w o r k for r e l i a b l e e x t r a p o l a t i o n o f n u c l e a r properties into regions far f r o m stability. F i n a l l y , because models such as the I B M consider o n l y valence p a r t i c l e s — t h o s e b e y o n d the nearest closed shell or, i n some instances, s u b s h e l l — r e s e a r c h e r s are interested i n m a p p i n g , e x p e r i m e n t a l l y , the locations o f shells and subshells into regions far f r o m stability. A n i m p r o v e d k n o w l e d g e o f shell a n d subshell gaps at the extremes o f n u c l e a r stability w i l l provide important b e n c h m a r k s for testing nuclear models.

xv i

1 Supersymmetry in Nuclei Recent Developments

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch001

F. Iachello A. W. Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06511

Recent developments in applications of supersymmetry to the study of complex spectra are discussed. In particular, extensions of supersymmetry to nuclei with an odd number of protons and neutrons are presented. 1.Introduction Since its introduction in nuclear physics in 1980 [IAC80], supersymmetry has been extensively used to describe properties of complex nuclei [BAL81a,BAL81b,BAL83,SUN83a,SUN83b,CAS84,IAC85]. In its original formulation, supersymmetry was used to link properties of nuclei with an even number of protons and neutrons (even-even nuclei) with those of nuclei with an odd number of protons and an even number of neutrons (odd-even nuclei) or viceversa (even-odd nuclei). This formulation was based on a description of properties of nuclei in terms of a set of collec­ tive variables (bosonic in nature) and a set of single particle variables (fermionic in nature). In treating the collective vari­ ables, no distinction was made between protons and neutrons (interacting boson model-1). It has been recognized since, that the proton-neutron degree of freedom plays an important role in the description of some properties of nuclei and thus i t must be explicitly introduced (interacting boson model-2). In addition to providing a better understanding of the properties previously described, the introduction of the proton-neutron degree of freedom leads to the possibility of describing properties of nuclei with an odd number of protons and neutrons (odd-odd nuclei). In this lecture, I w i l l discuss some properties of oddodd nuclei as obtained from supersymmetry. 0097-6156/ 86/ 0324-0002S06.00/ 0 © 1986 American Chemical Society

1.

Supersymmetry in Nuclei

IA C H E L L O

2.The

model In

the

states

interacting

of nuclei

[ARI77,OTS78 ] , and

neutron

have

I t

(μ=±2,±1,0)

and

and

(ν) degrees

annihilation s

^ν,μ^'

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch001

proton

bosons

neutron

v^*

i s

o

t

,

r

s

a

tors

by t >

tion

operators

able

ρ i s called neutron

neutrons. number

the (

)

When

(

(s-boson)

introduce

creation

operators.

of freedom assume

an

a r e added,

extra

label

I shall

bosons

The s i x p r o t o n

When

a n d J=2 ( d ^ *, s * ) proton

(π)

the creation

and

(π,ν),

denote

d^

s_*,

t h e 12

opera­

ρ=ττ,ν. T h e c o r r e s p o n d i n g

will

be d e n o t e d

by b p . T h e t w o - d i m e n s i o n a l

F-spin.

correspond

)

nucleus, (neutron)

i s built

B

V

noting

to correlated

collective

annihila­ vari­

a

I t i s worthwhile

f o r each

only

U

to

dynamical

bosons. J=0

(dy,s)

simplicity,

of proton

ν

(6) ®

f

momentum

12

collective

α = 1,...,6;

Hamiltonian Β

π

o

of

lying

where

Thus,

π

e

low

i n terms

angular

convenient

bosons

Ν (Ν )

shells.

ϋ

a p

k

model-2,

and s i xn e u t r o n

annihilation

operators

F

boson

are described

s i x

(d-boson).

and

3

their pairs

degrees

that

pairs

number outside

of protons

and

i s fixed

to the

t h e major

closed

of freedom

o u t o f t h e 36+36

the proton

are considered,

generators

of t h e group

(6),

(B) 1 u

G a„ ρ , · α ρ- ~b " a p b„ a ',p_ J

and

n

Λ

1ft

i s given

by

(Β) Η

( 1 )

u

(B) = Ε

+ 0

Χ L

(ρ)

(Β)

ε

α,α',ρ

G α,α'

αρ,α'ρ

(ρ,τ)

2

In U

this (

V

B

)

u α , α ' ,β,β ' ,ρ, τ

equation,

(6).

B

E^ ^

0

G α,α',β,Β'

i s assumed

(Β)

(Β)

G αρ,βρ

t o be i n v a r i a n t

(2) α'τ,β'τ

under

Β

υ" ^ ^(6)< π

4

N U C L E I O F F T H E LINE O F STABILITY

In single

addition

ticles.

The

c o l l e c t i v e degrees

ticle

unpaired

levels.

The

angular

momentum

several

single

^ (2j +1). i

to

p a r t i c l e degrees

is

p a r t i c l e s are

fermions

is

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch001

for of

protons

to

is

label

introduce

the

an

extra isospin

The

fermions ( π

Π

can

( Ω ) β (F)

be

υ

(

Γ

)

ν

G

=

written

in

terms

with

the

Ω

occupy is

a

.

Ω and

If

the

creation

and

a

label,

Hamiltonian

of

level

label

2

υ

par­

creation

(ί=1,...,Ω),

i

single

degeneracy

i s the

neutrons.

also par­

p a r t i c l e can

considered,

acquire

has

unpaired

particle

total

a^

one

the

occupying

single

here

freedom

are

unpaired

the

also

extra

from

a the

fermions,

operators

( i = 1 ,...,Ω ; r = 1 , 2 ) . T h e

of If

levels,

convenient

degree

annihilation

tinguishes

(2j+1).

operators

proton-neutron

freedom,

. These

degeneracy

j

of

freedom

particle

It

i

annihilation

of

^ i r

which

dis­

describing

the

generators

of

2 +

Ω

(Ω), a

f

a

i r i

ir

a,

i

1f n

(3)

r

ΙΓ,ΓΓ

and

i s given

by

(F)

(F)

H

=

Ε

Λ +

X

0

1

2

Q

U

v

the

' ( Ω ) .

States

in

number

denoted

by

of

unpaired for

This

one

ir , i' r

to

nucleus

fermions

protons has

interaction

(F) G ir,kr

1

assumed

each

M^

Finally, neutrons.

1

is

(r) G

(r,t) ν ii'kk

i ,i ,k ,k ,r ,t

E

The quantity ( F)

(r) ^ε i ,i' ,r ii'

be can

they for

thus

an

interaction

is written

be

contain.

M

(ii)

1

invariant

and

v

(F) G i· t,k t

under

;

char a c t er i zaed This

number

will

( Ω ) ® by be

neutrons.

as

between

protons

and

1.

(BF)

Υ

V

(ρ,r) w αα'ϋ'

L

=

1

1

α ,α ,i , i , ρ , r

The

algebraic

Η

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch001

is

.

structure

H< > B

then

5

Supersymmetry in Nuclei

IACHELLO

H< >

that

+

F

+

of

υ

( Β ) π

of

V
™> ™ and R' a r e compared i n T a b l e 2 w i t h t h e e x p e r i m e n t a l d a t a . ee oo oe oe R

R

r

These models t h u s o f f e r and 1 , r e s p e c t i v e l y ,

r

possible explanations

of these 4 q u a n t i t i e s ,

t o the d e v i a t i o n s from 2, 2, 1

in p a r t i c u l a r

These r e s u l t s may be c o n s i d e r e d as e x p e r i m e n t a l of a f i n i t e

R

Q e

evidences f o r the

number o f bosons i n t h e r e l e v a n t n u c l e i .

between t h e e x p e r i m e n t a l

for

A detailed

and

R^.

influence comparison

v a l u e s and t h e p r e d i c t i o n s o f t h e v a r i o u s v e r s i o n s

t h e boson models c o n s i d e r e d h e r e , e s p e c i a l l y

f o r t h e a c c u r a t e l y known R

tios, yields

the f o l l o w i n g c o n c l u s i o n s .

experimental

u n c e r t a i n t i e s , between t h e e x p e r i m e n t a l

Q e

There i s a good a g r e e m e n t , w i t h i n d a t a and t h e

of

ra­ the

parameter-

f r e e p r e d i c t i o n s o f t h e s y m m e t r i e s S U ( 5 ) , SU(5) χ 1/2 and U ( 6 / 2 ) , w h i c h have been a p p l i e d t o t h e s e n u c l e i

previously

[ V E R 8 2 ] , e x c e p t , maybe, f o r

R

in

24

N U C L E I O F F T H ELINE O F STABILITY

Table 2

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch003

Nuclei Ν R

R

e e

oo

1 0 2

Ru 7

1 0 3

Rh 6

1 0 6

Pd 7

-

1 0 7

Ag 6

1 0 8

Pd 8

-

1 0 9

Ag 7

1.81(26)

exp.

1.49(21)

1.72(23)

SU(5)

1.714

1.714

1.750

0(6)

1.336

1.336

1.354

1.60(12)

1.66(23)

1.78(22)

1.667

1.714

e

x

p

'

SU(5) χ

1/2

1.667

0(6) χ

1/2

1.310

1.310

1.336

SU(5) x 1 / 2 , 3 / 2 , 5 / 2

1.714

1.714

1.750

0 ( 6 ) χ 1/2, 3 / 2 , 5/2

1.336

1.336

1.354

xp. oe U ( 6 / 2 ) SU(5) χ

0.888(32)

0.857(48)

0.812(47)

1/2

0.857

0.857

0.875

0(6) χ

1/2

0.779

0.779

0.802

R

e

U(6/12) ' S U ( 5 ) , 0 ( 6 ) χ

fe =e b

f

1/2,3/2,5/2(e =0 f

1

1

1

0.735

0.735

0.766

xp. oe U ( 6 / 2 ) SU(5) χ

0.96(15)

0.83(15)

0.80(15)

1/2

0.833

0.833

0.857

0(6) χ

1/2

0.764

0.764

0.791

R

€

U(6/12) ' S U ( 5 ) , 0 ( 6 ) χ 1/2,3/2,5/2

fe =e b

(e =0 f

f

1

1

1

0.735

0.735

0.766

3. 1f)ft , u o

25

Coulomb Excitation

LOISELET ET AL.

10Q

Pd -

*Ag ; t h i s

i s n o t t h e case f o r 0 ( 6 ) and 0 ( 6 ) χ 1 / 2 ,

t i o n s are s y s t e m a t i c a l l y

lower than the experimental

results.

whose It

predic­

has been

s u g g e s t e d t h a t t h e e v e n - e v e n Ru and Pd i s o t o p e s can be d e s c r i b e d by an m e d i a t e s i t u a t i o n between SU(5) and 0 ( 6 )

inter­

[ S T A 8 2 ] , and t h a t t h e odd-A Rh i s o t o ­

pes s i m i l a r l y c o r r e s p o n d t o an i n t e r m e d i a t e s i t u a t i o n between SU(5) χ 1 / 2 , 5 / 2 and 0 ( 6 ) χ 1 / 2 ,

3/2,

5/2

[VAN84b].

shows t h a t t h e p r e d i c t i o n s o f such d e s c r i p t i o n s c o u l d be made t o a g r e e the experimental

d a t a by a s u i t a b l e c h o i c e o f t h e p a r a m e t e r ξ w h i c h

t h e SU(5) t o 0 ( 6 ) t r a n s i t i o n charges, e

b

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch003

points w i l l

and e , f

[ S T A 8 2 ] , and o f t h e boson and f e r m i o n

respectively

[VAN84b].

More s p e c i f i c

p r o b a b l y be made when o t h e r B ( E 2 ) ' s

tion

with

governs effective

s t a t e m e n t s on t h e s e

i n t h e odd-A n u c l e i w i l l

d e t e r m i n e d , r e s u l t i n g p a r t l y f r o m a more d e t a i l e d a n a l y s i s o f t h e r e p o r t e d i n t h e p r e s e n t paper

3/2,

The c o m p a r i s o n p e r f o r m e d i n T a b l e 2

be

experiments

[ L 0 I 8 5 ] , in p a r t i c u l a r of the angular

distribu­

measurements.

References [ALE78] [ARI76] [ARI79] [BAL81]

T.K. Alexander, and J.K. Forster, Adv. Nucl. Phys. X Ch. 3 (1978). A. Arima, and F. Iachello, Ann. Phys. (N.Y.) 99 253 (1976). A. Arima, and F. Iachello, Ann. Phys. (N.Y.) 123 468 (1979). A.B. Balantekin, I. Bars, and F. Iachello, Phys. Rev. Lett. 47 19 (1981) ; Nucl. Phys. A370 284 (1981). [BIJ84] R. Bijker, and V.K.B. Kota, Ann. Phys. (N.Y.) 156 110 (1984). [BIJ85] R. Bijker, and F. Iachello, Ann. Phys. (N.Y.) 161 360 (1985). [BOC79] A. Bockisch et al., Zeits. f. Phys. A292 265 (1979). [DES61] A. de-Shalit, Phys. Rev. 122 1530 (1961). [FAE83] A. Faessler, Nucl. Phys. A396 291c (1983). [HIR82] J.H. Hirata, and O. Dietzsch, Proc. Int. Conf. Nucl. Struct., Amster­ dam, 1982, vol. I. 131 (1982). [IAC81] F. Iachello, and S. Kuyucak, Ann. Phys. (N.Y.) 136 19 (1981). [LAN80] S. Landsberger et al., Phys. Rev. C21 588 (1980). [LOI80] M. Loiselet et al., Phys. Lett. 146B 187 (1984). [LOI85] M. Loiselet et al., to be published. [NDS85] Nuclear Data Sheets, last issues on the relevant mass chains as to September 1 (1985). [STA82] J. Stachel, P. Van Isacker, and K. Heyde, Phys. Rev. C25 650 (1982).

26

NUCLEI OFF T H E LINE OF STABILITY

[SUN84] H . Z .

Sun e t a l . , P h y s . Rev. C29 352

[ V A N 8 4 a ] P . Van I s a c k e r , A . F r a n k , and H.Z.

(1984). Sun, Ann. Phys.

(N.Y.)

JJ57

(1984). [ V A N 8 4 b ] P . Van I s a c k e r e t a l . , P h y s . L e t t . [VER82] J . V e r v i e r ,

and R . V . F . J a n s s e n s ,

[VER83] J . V e r v i e r ,

Phys. L e t t .

JJ33B

[VER85] J . V e r v i e r e t a i . , P h y s . Rev.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch003

R E C E I V E D A p r i l 11, 1986

J49B

26

(1984).

Phys. L e t t .

JI08B

135 ( 1 9 8 3 ) . ( t o be p u b l i s h e d ) .

1 (1982).

183

4 Manifestations of Fermion Dynamical Symmetries in Collective Nuclear Structures Da Hsuan Feng

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

Department of Physics and Atmospheric Science, Drexel University, Philadelphia, PA 19104

A Fermion dynamical symmetry model which can account for both the low as well as high spin nuclear collective phenomena is presented.

The phenomenological Interacting Boson Model (IBM), introduced about a decade ago by Arima and Iachello , has linked the collective phenomena in the low energy region 1

for nuclei (E < 2 MeV and J < 10, say) with the concept of dynamical symmetries. The profound program of the IBM is remarkably simple and can be understood as follows. By simulating the L=0 and 2 valence coherent nucléon pairs as s and d bosons, the IBM has the highest symmetry U ( 6 ) which, together with the lowest symmetry 0 ( 3 ) B

B

physically demanded by rotational invariance, resulted in three limiting dynamical symmetries: U ( 5 ) , S U ( 3 ) and 0 ( 6 ) . B

B

multi-chain

Using the generalized coherent

B

states of Perelomov and G i l m o r e ( See also the book recently edited by Klauder and 2

3

S k a g e r s t a m ) , one can show that each of these chains depicts a particular type of 4

geometrical motion (vibrational: U ( 5 ) , rotational: S U ( 3 ) and y-soft: 0 ( 6 ) ) . It should B

B

B

5

be mentioned that everyone of these dynamical symmetries of the IBM is realized in nuclear structure. This point is well discussed by the many talks in this symposium, especially the overview talk of Iachello . Hence, the IBM treats all the collective 1

motions on equal footing:

each has its own characteristics and its own set of

eigenstates and more importantly, its own geometrical interpretation. For example, a special characteristic of the 0 ( 6 ) limit is to predict the staggering of the states in the B

γ-band while the S U ( 3 ) limit does not. Clearly, the multi-chain concept of the IBM, B

which is perhaps the most important

lesson

one learns from the model, is a clear

0097-6156/ 86/ 0324-0027506.00/ 0 © 1986 American Chemical Society

N U C L E I O F F T H EL I N E O F STABILITY

28

departure from the conventional usage of dynamical symmetry of Elliott and its many subsequent

d e v e l o p m e n t s where there is only one 6

dynamical symmetry chain

( S U ( 3 ) or pseudo-SU (3)). F

F

Although the multi-chain dynamical symmetries concept of the IBM is successful in anchoring the various types of collective structures, the full microscopic justification for each chain is still not entirely transparent. Thus, on a purely theoretical level, we deem it important to know whether the multi-chain dynamical symmetries of the IBM are:

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

(a) merely a fortuituous consequence of the boson assumption for the coherent valence fermion pairs; or (b) inherent in the "raw" fermionic shell structure, i.e. the most general shell model hamiltonian with one and two body interactions, simplified only by the same "physics input" of the IBM. Also, there are experimental reasons as to why these questions require serious consideration. For example, it was recently noted by Casten and von Brentano that nuclei with A«130 (a large number of the Xe and Ba isotopes), just as the previously studied A« 196 system (Pt isotopes) , are very well described by the IBM's 0 ( 6 ) limit. Of course, the boson assumption of the IBM prevents an obvious way to explore the reason (or reasons) why these two mass regions should possess the same dynamical symmetry even though they manifestly have different underlying shell structures. Thus, such experimental observations clearly hasten the necessity to seek answers to the above raised questions. 7

8

B

There is another equally important reason as to why it is necessary to seek the dynamical symmetries from the fermionic point of view. One knows that the physics of nuclei in states of large angular momentum constitutes an important branch of nuclear structure physics as well. Experiments are now routinely done yielding detailed spectroscopy of states in the range of J = 35 ~ 45 (typically Ε is about 10 MeV or so) No comprehensive theory of nuclear structure can ignore these facts - such a theory must adequately address both the low as well as the high spin phenomena. Therefore, to propose a fermionic dynamical symmetry model of collective nuclear structure which is only applicable in the low energy, low spin region must be inadequate by definition. 9

Motivated by these considerations, we have recently proposed a multi-chain fermionic dynamical symmetry model (FDSM) which was developed to specifically address the above raised questions. Our starting point is the Ginocchio SO(8) model ( s i n c e from now on only fermion groups will be mentioned, we shall drop the use of the F superscript to denote them). In our opinion, Ginocchio was the first person to seriously pursue the concept of multi-chain dynamical symmetries from a fermionic viewpoint. The main ingredients of the Ginocchio model can be summarized as follows. If one were to take the fermion pair ( i.e. a a type of operators) with X=0(S) and 2(D) and certain multipole operators (i.e. a a type of operators), both types are constructed from 10

+

+

+

4.

29

Fermion Dynamical Symmetries

FENG

recoupling the single particle j's into pseudo-spin (i ) and pseudo-orbit (k), then we will obtain either the Sp(6) or SO(8) algebras. The SO(8) and Sp(6) algebras have the following group chains : SO(8) 3 SO(5)xSU(2) 3 SO(5) z>SO(3)

(1 a)

DSO(6)

DSO(5)DSO(3)

(1b)

=>SO(7)

z>SO(5) 3 S 0 ( 3 )

(1c)

and

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

Sp(6) => SU(3) 3 SU(2)xSO(3)

3S0(3)

(2a)

=>SO(3)

(2b)

The eigenstates of (1a) and (1b) are identical with the U(5) vibrational and 0 ( 6 ) γ-soft limits of the IBM respectively, while (1c) has no IBM counterpart. The eigensates of (2a) and (2b) are identical with the SU(3) rotational and U(5) vibrational limits of the IBM respectively. There are many interesting features of the Ginocchio model which we do not have the space to cover here. The two most notable ones are: (a) the S 0 ( 8 ) => S 0 ( 6 ) has similar characteristics of the 0 ( 6 ) limit of the IBM. This is the first fermionic (dynamical symmetry) description of the γ-soft collective mode in nuclei. This mode has so far not been understood microscopically, (b) Although there exists a "rotational" chain Sp(6) => SU(3), it was ruled out on the grounds that the most important representation (2N,0) (where Ν is the pair number) is disallowed due to the Pauli principle (more about this later when we get into the description of our model). What is perhaps most lacking in the Ginocchio model is how one might link such algebraic structures to the shell structures, without which the model cannot be used for the study of real nuclei(i.e. toy model) The model which we have developed is called the Fermion Dynamical Symmetry Model ( F D S M ) which is the subject matter of two recent preprints. The FDSM begins with a shell model Hamiltonian in one major valence shell. 1 1

H = Xjejiij + Vp + V

(3)

q

where V ( q j is the pairing (multiple) part of the residual interaction. Our model makes p

three assumptions, (a) The dominant parts of the pairing interaction V and quadrupole. (b) The two body matrix elements of V ( ) p

q

p

are monopole

are proportional to the

degeneracy of each major valence shell, (c) Terms involving the single particle energies and the multipole interactions are approximated so that the Hamiltonian is a

N U C L E I O F F T H E LINE O F STABILITY

30

function of the generators of a tractable Lie algebra. Clearly, the first assumption is a result of the successes of the IBM which we have used as input physics. The second assumption is the simple generalization of the usual pairing assumption in nuclear physics and the third is derived from the belief that a dynamical symmetry in the Hamiltonian corresponds to a certain collective mode of the system, which is perhaps the most important lesson one learns from the IBM. As a result of our assumption (a), we can reclassify all the single particle levels in the major valence shell (see F i g . 1) in terms of the pseudo orbit (k) and pseudo spin (i), thus allowing us to make contact with the Ginocchio model for symmetry classifications. The result is that for the normal parity levels, we will have either the Sp(6) or SO(8) symmetry and for the "intruder" level, it is an SU(2) algebra, meaning that for the

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

intruder, only monopole pair is allowed in the lowest energy levels.

Thus we have

either Sp(6)xSU(2) or SO(8)xSU(2), depending on which major shell we are referring to.

For example, for the major shell with normal single particle levels s

g

(k=2, i=3/2) and intruder single particle h

7 / 2

(uniquely) SO(8)xSU(2).

1 1 / 2

(

k = 0

- 3 / 2 » 5/2» D

1 / 2

D

» i=11/2) level, the symmetry is

Let me mention in passing that this is fully consistent with

the experimental observation of a large number of stable 0 ( 6 ) nuclei for this mass region . 7

As we have mentioned earlier, although one could construct an Sp(6) 3

SU(3) chain in the Ginocchio model, it was nevertheless discarded because the (2N.0) representation is ruled out for most deformed nuclei due to the Pauli principle ( Ν < Ω/3 where Ω , the full degeneracy of a major physical shell, was nebulously specified). This so-called "major flaw" of the model was also reiterated by H e c h t . 6

However, in our

model, the Pauli restriction applies only for the normal parity levels, i.e. where

and

< Ω^3

are the pair number and the total degeneracy of the normal levels,

respectively. There is no requirement in our model that the total number of pairs in one major physical shell, defined as Ν = NQ + N j must be < Ω/3.

Hence Ν can be

approximately Ω/2 (a condition for most deformed nuclei) while N j £ Ω^β. this means that the Pauli principle squeezes out the remaining N

0

Physically,

pairs to the unique

parity levels. In a forthcoming paper, we will discuss in detail an analysis based on the Nilsson scheme. The result indicates that for the strongly deformed nuclei, N-j is generally < û j / 3 thus eliminating the reason for rejecting the Sp(6) chain. Thus, we now have, within the context of the FDSM, a handle on how the multi-chain dynamical symmetries, all treated on equal footing just as ther IBM, can manifest themselves. As we have emphasized earlier, any comprehensive theory of nuclear structure must adequately address the high spin phenomena. By simulating the coherent fermion pairs as bosons, the IBM essentially ruled out the possibility of discussing high spin p h e n o m e n a without additional ingredients. In our m o d e l , however, this is accomplished in a rather simple fashion. Note that the S 0 ( 8 ) [Sp(6)] and the SU(2)

4.

31

Fermion Dynamical Symmetries

FENG

possess the quantum numbes u and υ

0

where they denote the generalized seniority

(for S and D pairs in the normal levels) and seniority (for the S pairs in the intruder level) respectively. For u = υ = 0, one can find a one to one association with the IBM 0

dynamical symmetries for the FDSM. For example, in the SU(3) limit, for the ground band, one can obtain the usual rigid rotation situation. On the other hand, when either u * 0 or υ φ 0 or both, we have the possibility of broken (either generalized or S) 0

pair(s) which corresponds to the well known phenomena in high spin physics, i.e. rotational alignment, Coriolis antipairing, multiple band crossing and the associated backbendings. The ability to incorporate such features is a consequence of this being a fermion (not boson) model! We present, as an example of this work, the results for the nucleus T h as predicted by the FDSM. It is of course known that for this nucleus, the neutrons occupy the 8th major shell while the protons occupy the 7th major shell. Since our results are based on dynamical symmetries, no interband mixing is introduced. In Fig. 2, the results of the yrast states plotted as a function of J(J+1) (although only the J value is indicated) are given. It is seen very clearly that roughly between J=10 to 12, the band switches from the ground band (with u = υ = 0) to the i = 7/2 pair band ("broken" proton normal

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

2 3 2

0

pairs with u=2 and υ = 0). Similarly, another band crossing occurs between J=18 to 20. The new band is the i=9/2 pair band ("broken" neutron normal pairs with u=2 and υ = 0). Finally, for a much higher J (24 or so), the new band is associated with the "breaking" of the proton S pair in the j=i=13/2 orbit. These band crossing phenomena is even more transparent in the B(E2)s\ plotted as a function of J , as can be seen from Fig. 3. (The data is joined by the dash line to guide the eye). For the j=13/2 band crossing, there is a sharp drop of the B(E2) values. The physical reason for this to occur is quite clear, whenever there is a band crossing (i.e., the breaking of a pair of coherent fermions), the "core" of the rotor will slow down because of angular momentum conservation. This slowing down of the core (the core is the primary contributor of the B(E2)s) is reflected in the data. For the FDSM, the same physics applies also for the low J band crossing phenomena. Our B(E2) calculations, which ignore band mixing, show very clearly this predicted behavior, i.e., whenever band crossing occurs, there is a reduction of the B(E2) (The dotted line in Fig. 3). The reduction is in fact zero when there is no band mixing and with just a small amount of band mixing, the B(E2) can be fitted rather well. Also, whether these primordial structures can remain depends very much on the strength of band mixing. For the actinides ( T h , U isotopes, for example), such structures prevail. Hence, since the FDSM incorporates fermion degrees of freedom, it gives a better description of high-spin B(E2) values than the algebraic boson model. 0

0

1 2

2 3 2

So far, we have concentrated only on the even-even nucleus. Of course, our model encompass the even-odd as well as odd-odd nuclei as well (by the study of other seniority states).

N U C L E I O F FT H E LINE O F STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

Th

2 3 2

E(MeV)

F i g u r e 1. Dynamical s y m m e t r i e s o f t h e s h e l l m o d e l . be f o u n d i n R e f s . 10-11.

F i g u r e 2. 12.

Yrast states of

Th.

D e t a i l s may

The d a t a a r e t a k e n f r o m R e f .

Fermion Dynamical Symmetries

No

1

2

3

4

η

0

1

2

3

5 4

4

1

0

1

0

i

1/2

1/2

3/2

7/2

3/2

9/2

3/2 11/2

1/2

Pi/2

S

9/2

s h 1/2 11/2

P3/2

d

3/2

d

5/2

f

CONFIGURATION

1

1/2

f

7/2

P

1/2

9

b

r,

P3/2

d

3/2

5/2

d

5/2

5

1

0

0

S

5

5

2

8

7

6

3

k

1

1/2

P

1/2

6

6

6

7

0

1

1

0

7/2 13/2

f

5/2 'l3/2

P3/2 7/2 f

h

9/2

3/2

9/2 15/2

1/2

9

d

3/2

9

d

5/2

S

7/2 15/2 J

9/2 'l1/2

9?/2

SYM

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

FENG

G

6

G

8

G

3

G

6

G

8

G

3

G

8

G

6

G

6

0

0

0

0

5

6

7

8

Qi

1

3

6

4

6

10

15

21

Ω

1

3

6

4

11

16

22

29

126

184

il

2

G = 6

G

3

8

20

50

28

(SpgXS0 ) χ ( S & 2 3

X

82

S6> ) 3

= (SU3X SOg) x ( S ^ x S6> ) 2

3

G = (SOgX SO3) x ( S ^ x S6>) 8

2

3

F i g u r e 3. The t h e o r e t i c a l are taken from Ref. 12.

and e x p e r i m e n t a l

B(E2) v a l u e s .

The d a t a

34

NUCLEI O F F T H E LINE O F STABILITY

In conclusion, just as the IBM, the FDSM contains, for each low energy collective mode, a dynamical symmetry. For no broken pairs, some of the FDSM symmetries correspond to those experimentally known and studied previouly by the IBM. Thus all the IBM dynamical symmetries are recovered. In addition, as a natural consequence of the Hamiltonian, the model describes also the coupling of unpaired particles to such modes. Furthermore, since the model is fully microscopic, its parameters are calculable from effective nucleon-nucleon interactions. The uncanny resemblance of these preliminary results to well-established phenomenology leads us to speculate that fermion dynamical symmetries in nuclear structure may be far more pervasive than has commonly been supposed.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch004

Acknowledgments

This work is supported by the National Science Foundation. It is indeed a pleasure for me to thank my colleagues and collaborators in China and the US in this work. They are C h e n g - L i W u of Jilin University, X u a n - G e n C h e n of the Nanjing Military College, J i n - Q u a n C h e n of Nanjing University and M i c h a e l W . G u i d r y of the University of Tennessee, all of whom I have known and learned from for a number of years. It must also be mentioned that during the development of this work, J o e G i n o c c h i o of the Los Alamos Scientific Laboratory has played the role of a "knowledge provider" and critical evaluator of our ideas. Finally, I must thank the two organizers of this symposium, Dr. R. A. Meyer and Prof. Daeg Brenner, for inviting me to participate in my first (and hopefully not last) ACS meeting.

References 1. A. Arima and F. Iachello, see Professor Iachello's contribution in this volume. 2. A. M. Perelomov, Commun. Math. Phys. 26, 222 (1972). 3. F. T. Arecchi, E. Courtens, R. Gilmore and H. Thomas, Phys. Rev. A6, 2211(1972); R. Gilmore, Rev. Mex. de Fisica 23, 143 (1974). 4. J. N. Ginocchio and M. W. Kirson, Phys. Rev. Lett. 44, 1744(1980); A. E. L Dieperink, O. Scholten and F. Iachello, Phys. Rev. Lett 44, 1747(1980); D. H. Feng, R. Gilmore and S. R. Deans, Phys. Rev. C23, 1254(1981). 5. COHERENT STATES, ed. by J. R. Klauder and B.-S. Skagerstam, World Scientific, Singapore, 1985. 6. J. P. Elliott, Proc. Roy. Soc. A245, 128(1958); A245, 562(1958); Κ. T. Hecht, Lectures delivered at the VIIIth symposium on Nuclear Physics, Oaxtepec, Mexico, Jan. 1985 and Phys. Rev. C (to be published). J. P. Draayer, Lectures delivered at the VIIIth symposium on Nuclear Physics, Oaxtepec, Mexico, Jan. 1985. 7. R. F. Casten and P. von Brentano, Phys. Lett. B152 , 22(1985). 8. J. A. Cizewski et al., Phys. Rev. Lett. 40, 167(1980). 9. For a comprehensive discussion, see R. Bengtsson and J. D. Garrett in COLLECTIVE PHENOMENA IN ATOMIC NUCLEI, edited by T. Engeland, J. Rekstad and J. S. Vaagen (World Scientific, Singapore, 1985). 10.J. N. Ginocchio, Ann. of Phys. 126, 234(1980). 11.C.-L. Wu, D. H Feng, X.-G. Chen, J.-Q. Chen and M. W. Guidry, Preprint, 1985. Submitted to Phys. Lett. and Ann. of Phys. 12. This is the so-called "GSI catastrophe" which shows that as a function of J, the IBM predictions of the B(E2) values will eventually drop off. See H. Ower, Ph.D. thesis, University of Frankfurt, 1980. RECEIVED May 2, 1986

5 On the Microscopic Theory of the Interacting Boson Model M. Sambataro Istituto Nazionale di Fisica Nucleare-Sez. di Catania, Corso Italia 57, Catania, Italy

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch005

We present a new mapping procedure from fermion onto boson spaces. The procedure is based on the Generator Coordinate Method. We show an applica­ tion of this technique to systems of nucleons moving in a single j - o r b i t . The extension of this microscopic investigation to many j-orbit systems is also examined. One o f t h e m o s t i n t Boson Model concerns i t s s p a c e . The u n d e r s t a n d i n g l i k e f e a t u r e s a r i s e from i n f a c t , a way t o r e l a t e tion.

eresting aspects of the Interacting connections with the underlying fermion o f t h e mechanism through which boson­ effective nuclear hamiltonians provides, c o l l e c t i v e s p e c t r a t o t h e f e r m i o n mo­

Since t h e o r i g i n a l study o f Otsuka, Arima and I a c h e l l o (OTS78), much w o r k h a s b e e n c a r r i e d o u t o n t h i s s u b j e c t . I n s p i t e of t h a t , u n t i l now, t h e d e s c r i p t i o n o f w e l l d e f o r m e d n u c l e i c a n n o t b e c o n s i d e r e d s a t i s f a c t o r y . We p r e s e n t h e r e a n e w m a p p i n g technique which i s d i r e c t e d toward t h e treatment o f these s y s t ems. The m i c r o s c o p i c d e r i v a t i o n o f a b o s o n h a m i l t o n i a n f r o m a f e r m i o n one i s b a s i c a l l y a two s t e p p r o c e s s . I n t h e f i r s t step, one h a s t o s e l e c t t h e c o l l e c t i v e s u b s p a c e o f t h e s h e l l m o d e l s p a c e . F o r t h e IBM t h i s means t r u n c a t i n g t h e s h e l l m o d e l s p a c e t o t h e s p a c e o f c o l l e c t i v e S-D p a i r s . I n t h e s e c o n d s t e p , t h i s space has t o be mapped onto t h e s - d boson space. I n t h e r e a l i s t i c c a s e o f nucléons m o v i n g i n many j - o r b i t s , the f i r s t step i m p l i e s t h e n o n - t r i v i a l task o f f i x i n g t h e i n t e r ­ nal s t r u c t u r e o f t h e c o l l e c t i v e p a i r s . I n o r d e r t o focus on t h e m e c h a n i s m o f t h e m a p p i n g , t h e n , we w i l l f i r s t d i s c u s s t h e c a s e of nucléons i n a s i n g l e j - o r b i t , w h e r e t h i s p r o b l e m does n o t e x i s t . The d i s c u s s i o n c o n c e r n i n g more r e a l i s t i c s y s t e m s w i l l be postponed t o t h e second p a r t o f t h i s contribution. The The rator the

mapping

procedure

Coordinate

Schrodinger

procedure we

are going

Method equation

(GCM).

t o expose

i s based

T h e GCM l o o k s

on t h e Gene­

f o rsolutions

of

o f t h e form (1)

0097-6156/ 86/ 0324-0035S06.00/ 0 © 1986 American Chemical Society

36

NUCLEI O F F T H E LINE O F STABILITY

|φ(*)>, t h e

where \*.]

, the

generating

generator

determined

by

f u n c t i o n s , depend

coordinates.

The

on

some

condition leads

to

=°

the

(2)

Hill-Wheeler

equation

^ ( < * ( α ) ΐ « ι φ ( * ) > - ί < 4 ( * ) Ι φ ( ' » ) JC*) α

The one.

basic

1ψ(β)> "be b o s o n

Let

us

suppose

Let

us

ρ

suppose,

fermion

the

mapping

one

can

,i.e. find

furthemore,

hamiltonian

Η

also

we

F

this

case, are

As

an

generating

establish

a relation

between

a

f u n c t i o n (&»F(pt) , s u c h

that

i n correspondence

a boson

Hill-Wheeler

example

and

j=23/2.

application

which

boson

we

and

ρ =

overlaps 1

shown

similarly

but

ferent

values.

We

case ;

this

>

one,

l e t us

discuss

overlap

a

Η

so

Β

given that

(5)

fermion

choose

refers

to

and

boson

as

fermion

the

case

N=3

choose

(^*N*°) =

we

to

(τ)

M l o >

a relation

the

that

eigenvalues.

and

i n f i g . 1;

so

va­

states

to

' O T ?

i n the

identical

method

I *V(«0>

get

relation,

fermion

W

equations

f u n c t i o n we

i n the

C^M

the

4

.

the

β

to

this

going

hamiltonian

(3

intrinsic


~

4

9 /

(III)

*[f /2r

P3/2r P l / 2 ) "

2

5

2

9

4 2

f

+

l +2

99/2 J

o

r

1

w

w

h

h

i

i

c

c

h

h

"max n

a

s

J

max

β

v[g / " db/2 1 + 2

9

2

1

8

a

n

d

1

2

s

β

8

which was J a x 24. Computational r e s t r i c t i o n s were such that J j . and 12 f o r ( I I ) and ( I I I ) , r e s p e c t i v e l y . Odd-parity s t a t e s were described i n the model space wtf^, P 3 , Ρ ι ) ~ 9 / 2 1 ' η • 1 or 3 . C a l c u l a t e d even- and odd-parity l e v e l s are compared with experiment i n Becker, et a l . [BEC84]· An adequate d e s c r i p t i o n of s t a t e s with J > 10 r e q u i r e s c o n t r i b u t i o n s from Models II and I I I . T e c h n i c a l l y , Model II and I I I c a l c u l a t i o n s r e q u i r e a s h i f t i n main frame computers and are not complete. The agreement ( w i t h i n the model space I r e s t r i c t i o n ) between experimental energy l e v e l s i s reasonable f o r the even-parity s t a t e s . The model p r e d i c t s the l e v e l s p i n sequence c o r r e c t l y . S e l e c t e d electromagnetic moments and t r a n s i t i o n r a t e s are presented i n Tables I I I and IV, r e s p e c t i v e l y . Agreement i s good f o r the f i r s t 8 i s t a t e f o r both quadrupole and magnetic moments. The electromagnetic t r a n s i t i o n strengths p r e d i c t e d by Model I are i n accord with the f r a y branching r a t i o s observed f o r the 1 0 a n d 9]+ s t a t e s ; agreement i s not good f o r the decay of the 82 state. Experimentally the 1 0 i * 8 i and the 9 χ • 8y γ-ray branches are 100%. The p o s s i b l e l O ^ 8 and 9i+ * 8 branches are not observed. m

m

η

+ η

9

+

+

+

+

+

+

2

+

2

n

80

NUCLEI OFF THE LINE OF STABILITY

T h i s i s i n accord with the t r a n s i t i o n branching l i s t e d i n Table IV. The experimental γ-ray branching of the 82"*" s t a t e i s [ B . R . ( 8 ·* 8 )]/[B.R.(8 * 6 ) ] « 43.67, while the c a l c u l a t i o n p r e d i c t s 27/1. 2

+

X

2

Table I I I .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch012

° 8

2

Quadrupole (e fm*) and magnetic moments ( μ

+

0

) for

Q(E2)

A

Jftf

+

+

+

90

Theory -53.4

90

+ 18.8

88

+25.6

88

-72.9

μ Theory +12.31

Exp. 151(6)1*

a

Exp. +10.85(5)

b

+ 0.31

2

+

+

151(6) I

-1.808(4)

-3.09

3

+ 12.0

2

a b c

P. Raghavan, p r i v a t e communication. O. Hausser, e t a l . , Nucl. Phys. A293, 248 (1977). T. Faesterman, e t a l . , Hyperfine I n t e r a c t i o n s 4, 196 (1978).

Table IV.

Branching R a t i o (BR) Comparison f o r

9 0

*

8 8

Zr.

THEORY BRj/BR2

EXP. A

J

10] +

90

J

f l

f

BR

2

8

2

8

2

X

BR 2

+

100

N.O.

15650/1

+

100

N.O.

26570/1

a

8l

+

8l

+

90

8l

+

6l

+

43(6)

57(6)

88

8l

+

8

+

1.8(3)

98.2(3)

1/50

2

8

+

1.8(5)

94.4(9)

1/23

2

8

+

3.8(8)

94.4(9)

1/411

2

90

88 8B 88 a

8 8

C

«2

+

8l

+

8l

+

100

27/1

134/1

N.O.

N.O. denotes not observed e x p e r i m e n t a l l y .

zr,

z r has a f u l l l f / * l 5 / 2 ' P 3 / 2 ' P l / 2 s h e l l f o r protons and 8 neutrons i n the g / o r b i t a l . We d e s c r i b e the low l y i n g even p a r i t y s t a t e s of Z r i n the model space i r v [ ( f / 2 / P 3 / 2 ' P l / 2 ' ^ " g 9 ) 2 l , which has J * 2 0 . Odd-parity s t a t e s a r e d e s c r i b e d f o r 8 8

f

7

2

2

2

9

2

8 8

5

m

a

x

2

12.

81

Shell-Model Calculations

BECKER ET AL.

J > 0 i n t h e model space I T T V [ ( f / , Pz/2' Pl/2* 9 9 / 2 " while f o r J >^ 12 the model space I I was 7 T V [ ( f 5 / , P3/2* P l / 2 ^ " 9 9 / 2 1 · models have J - 15 and 24, r e s p e c t i v e l y . R e s u l t s f o r e x c i t a t i o n energies are given i n Becker, e t a l . [BEC84]· The p o s i t i v e p a r i t y energy l e v e l spectrum i s i n good agreement with experiment. Note Ε ( 9 ) > E ( 1 0 ) as i s observed experimentally. The spectrum of negative p a r i t y s t a t e s i s compressed r e l a t i v e t o experiment. S e l e c t e d electromagnetic moments a r e presented i n Tables I I I . Agreement f o r the e l e c t r i c quadrupole moment and magnetic moment f o r the 8]+ s t a t e i s not very good f o r Z r ( 8 i ) . There a r e s e v e r a l electromagnetic t r a n s i t i o n s r a t e s t h a t can be compared: The c a l c u l a t e d value B(E2; 8 ] + 6 i + ) « 0 . 8 6 Wu i t too small by a f a c t o r 6 . A strong Ml t r a n s i t i o n 12 * + 12}+ i s measured; the model p r e d i c t s B(M1) • 3.10 Wu while the experimental value i s 0.95 Wu. The model a l s o p r e d i c t s B(E2; 10]+ -»> 8 ) * 7.56 Wu; the experimental observation i s B(E2) > 15.4 Wu. The 8 • 8 t r a n s i t i o n has B(M1) » 8.1(6) χ 10" ; the c a l c u l a t i o n p r e d i c t s Β(Ml) « 6.3 χ 1 0 " . Some γ-ray branching can a l s o be compared with c a l c u l a t e d values (see Table I V ) . The l O ^ * 83+ decay i s observed with a 1.8(3)% branch. The model p r e d i c t s a 2% branch r e l a t i v e t o the IOJL" " + 8 decay. The 9^ s t a t e i s observed t o decay t o the ΙΟ}*, 8 , and 8}+ s t a t e s with branching r a t i o s 1.8(5), 94.4(9), and 3.8(8)%. The model p r e d i c t s t h a t t h e r a t i o o f branching r a t i o s , [ B . R . ( 9 •+· 10 )]/[B.R.(9 + 8 ) ] » 1/23 and [ Β . Κ · ^ * + β ^ ) ] /[B.R.(9i 8 ) ] « 1/411. The 8 s t a t e i s observed t o decay 100% 8 8 j * with no reported 8 -»· 6 i branch. The c a l c u l a t i o n p r e d i c t s [ B . R . ( 8 + 8 ) ]/[B.R.(8 6 ) ] » 134/1. 5

2

3

9

T

n

e

s

e

2

n

a

x

+

χ

+

1

x

1

8 8

+

2

2

+

+

+

2

3

X

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch012

5

+

4

+

2

+

2

+

1

+

+

1

+

1

2

+

+

+

2

2

+

+

2

90

+

2

+

+

2

+

x

+

2

X

Y 9 0

Y has a f u l l g / s h e l l f o r neutrons and one neutron i n the d 5 / s h e l l , and one proton-hole i n the f-p s h e l l . We d e s c r i b e Y i n the model space 9

2

2

9 0

^[(f

5 / 2

p)"

( n + 1 )

(g

n

9 / 2

) ]V[(d

1

5 / 2

) ];n-0,2}

f o r o d d - p a r i t y and

{ir[(£

5 / 2

P)-

< n + 2 ,

(g

»

9 / 2

n + 1

]V (d [

1

5 / 2

) ];n.0,2}

f o r even-parity l e v e l s . The p r e d i c t e d energy l e v e l s a r e compared with t h e experimental r e s u l t s i n P i g . 1. S u f f i c i e n t l e v e l s i n the r i g h t region o f e x c i t a t i o n a r e p r e d i c t e d , however, t h e energy s c a l e f o r the p o s i t i v e p a r i t y l e v e l s appears t o be too expanded. The l a r g e gap between t h * 7 and 8 l e v e l s i s reproduced by the c a l c u l a t i o n . +

+

88

Y

The model space f o r ^V[(f

5 / 2

p)"

( n + 1 )

(g

8 8

9 / 2

Y was

)

9 + n

;n-0,2]}

f o r o d d - p a r i t y s t a t e s and

{wv[(£

5 / 2

p)-

( n + 2 )

(g

9 / 2

)

1 0 + n

;n-0,2]}

NUCLEI OFF THE LINE OF STABILITY

+

12

6195

+

5685

+

5048

13

11

4519

+

[12 ] 13"

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch012

4213

+

(11 )

9" io8" 12"

3560

+

10 / /

ir

3098/

+

(10 )

9 /

2455/

+

(9) 8 5"

/

2970

+

/

2217

+

8

2217 [-216.06]

+

1900

1343

1298

+

(6 )

1023 r

682 \ \

3"

?M

\

\

241

7 7+

38 [-218.24] π=-

exp

π=+

90γ F i g u r e 1. 9 0

Experimental and c a l c u l a t e d Y l e v e l schemes. Only the lowestl y i n g (or s e v e r a l l o w e s t - l y i n g ) l e v e l s of a given s p i n and p a r i t y are included i n the c a l c u l a t e d s p e c t r a . The experimental and c a l c u l a t e d s p e c t r a are matched a t the 8 (π=+) and 3"(π=*-) l e v e l s . The c a l c u l a t e d b i n d i n g energies o f these two l e v e l s are given i n brackets. Only c a l c u l a t e d l e v e l s are shown with J >6(TP +) and J ·>2(π=-). ~ +

s

Shell-Model Calculations

BECKER ET AL.

+

17

6901

15+ 6294

16+

6260 +

5898

+

5302

+

4151

+

3509

14 [15]

/

/

s

15"

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch012

/

12" 10­ Ι 3" 11"

4107/ /

13

[14]

/

14"

/

5558

r

4824 -

/ 4178

(13~)

3964

χΛΐ2-)

\

12

(11")

3652 11

(10)

3257

+

(10)

2444

[9 ]

2312

+

1477

+

9

(7') /

\

A~ π

230

5^

[-199.93]

4^

=

-

+

2649 2469

+

1581

+

1462

675

ET

3171

10 ' 9

9 1423

+

10

675 [-199.82]

232 0 exp

π=+

88 γ F i g u r e 2. Experimental and c a l c u l a t e d Y l e v e l schemes. Only the lowestl y i n g (or s e v e r a l lowest-lying) l e v e l s of a given s p i n and p a r i t y are included i n the c a l c u l a t e d s p e c t r a . The experimental and c a l c u l a t e d s p e c t r a are matched a t the 8 (π=+) and 4~(π*-) l e v e l s and only l e v e l s with spins greater than these are shown. The c a l c u l a t e d b i n d i n g energies ( i n Mev) o f these two s t a t e s are given i n brackets. 8 8

+

84

NUCLEI OFF THE LINE OF STABILITY

f o r even p a r i t y s t a t e s . The r e s u l t s are compared t o experiment i n F i g . 2. Again, s u f f i c i e n t energy l e v e l s a r e generated a t the r i g h t e x c i t a t i o n energy. The c a l c u l a t i o n s make the apparent switch between even and odd p a r i t y f o r the Y r a s t s t a t e s a t E • 3.5 MeV i n Y seem q u i t e p l a u s a b l e . 8 8

x

III.

SUMMARY A s h e l l model c a l c u l a t i o n o f ' z r and » y has been done with a " r e a l i s t i c " two-body i n t e r a c t i o n . A l a r g e model space which however does not allow E l γ-ray t r a n s i t i o n s was used. For * 8 8 g j accounts of t h e observed electromagnetic moments and t r a n s i t i o n s o f the lower l y i n g p o s i t i v e p a r i t y l e v e l s are obtained, i n p a r t i c u l a r the decay o f the 1 0 i states f o r both n u c l e i . For Z r , the strong 1 2 •* 12^ i s i d e n t i f i e d c o r r e c t l y . Our c a l c u l a t i o n p r e d i c t s that the model space required f o r zr high s p i n even p a r i t y s t a t e s ( J >^ 11) requires the breaking o f the 9^/2 neutron s h e l l . For 90,88 d e l space employed generates s u f f i c i e n t energy l e v e l s as approximately the c o r r e c t e x c i t a t i o n . The competition between odd-and even-parity Y r a s t l e v e l s i s p r e d i c t e d , and f o r Y , t h e l a r g e energy gap between the J « 7 and 8 l e v e l i s reproduced. 9 0

8 8

9 0

8 8

9 0

Z r

0 0
..y-.. ^

1

2+5+

5+

I

3

^

+

^

-j- 3

+

+ :

4 +

-p—3^-i:_ -[- '"" ^

M 1

J

3

1 0.8 0.6 4.8

5.0

5.2

5.4

5.6

5.8

6.0

6.2

Ε (MeV) γ

Figure 9.

C o m p a r i s o n of the calculated and measured [HOF85b] reduced transition intensities for

primary gamma rays f o l l o w i n g 2-keV neutron capture b y

1 7 5

Lu.

obtained from the estimated number of radiating states. The bars indicate experimental values and their error limits, with some showing spin and parity assignments. A l l measurements and calculations are normalized to the single indicated transition. Originally, the comparison showed that our calculated M l / E l ratio was low by a factor of 3. In order to preserve the total radiation width value that had given agreement with experiment, and also match the M l / E l ratio from the A R C measurements, we had to increase our M l strength function by a factor of 3 and decrease our E l strength in the region around 5 to 6 MeV. Figure 10 compares the newly derived strength functions (the solid curves) with those predicted by our original systematics (the dashed curves). We revised the E l strength function downward around 5 MeV, while still maintaining continuity with the photonuclear region, by changing the value of the one free parameter in our systematics, E , from 5 to x

11 MeV, as indicated by the arrows in the figure. This parameter, E , is the energy at which our energyx

dependent Breit-Wigner line shape[GAR84b] has the same value as that for the Lorentzian line shape (the dotted curve), both defined with the same giant dipole resonance parameters. A s seen in Fig. 11, when we applied the new E l systematics in the mass-90 region, we obtained excellent agreement with experimental measurements for Y[AXE70] and Zr[SZE79]. Our original sys­ 89

90

tematics had predicted E l strengths that were about 30% higher. We are continuing this work in other mass regions to verify and further improve our systematics.

15.

GARDNER AND GARDNER

10 i-5 .

1

I

1

1 . ι . • ι ι j τ 1 7 6

>

Ά

io-

a

10.·,

111

The Importance of Level Structure

τ ;

Γ

Lu

···*' s

M1 jj. y. ζ»/ lit ' ι 1 i 1 . 1 . 1 . 1 , 1, -9 10 0 2 4 8 10 12 14

10"

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch015

ο α

E

(MeV)

7

Figure 10. Recently derived absolute dipole strength functions for L u (solid curves), com­ pared w i t h those predicted b y our original sys­ tematics (dashed curves). T h e arrows indicate the value assigned to the one free parameter, E . In our recent derivation, E = 11 M e V , and i n our original systematics, E = 5 M e V . 1 7 6

x

x

x

Figure 11. E l strength functions for Y a n d " Z r , calculated using our revised systematics, compared w i t h measurements from [AXE70, SZE79], 8 9

Use of Discrete Levels i n A n a l y s i s of Primary G a m m a - R a y Spectra Another interesting utilization of Hoff's modeled discrete levels for L u is presented in Fig. 12, where we show calculated primary dipole transitions to the L u modeled levels with energies in the range of 0.40 to 0.82 M e V following 2-keV neutron capture by L u . Also shown are the positions of the accessible levels and their spins and parities. The spectrum was constructed by smearing the calculated transition intensities with a unit Gaussian line shape with a 6-keV resolution. Note these features of the plot: (a) fcr gamma rays from 5.5 to 5.9 M e V we see 5 doublets, 1 triplet, and 1 quadruplet, all unresolved, more than expected on statistical grounds[HOF85b]; (b) the 2 " + 5 " doublet just below 0.44 M e V excita­ tion appears to have the same shape and intensity as the singlet 4" peak at 0.466 MeV, while the triplet, quadruplet, and doublet peaks at 0.66, 0.75, and 0.77 MeV, respectively, also show a close resemblance in shape and intensity; (c) the true singlet E l peaks, due to transitions to 4" levels at 0.82, 0.60, and 0.47 MeV, show a pronounced increase in intensity because of the energy dependence of the E l strength function itself, in addition to the expected E energy dependence. This kind of plot should be quite useful in interpreting the experimental data, particularly where unresolved multiple peaks occur. 1 7 6

1 7 6

1 7 5

3

112

NUCLEI OFF T H E LINE OF STABILITY

Level energy (MeV) 0.80

O70

τ — j — ι — ι

·

ι

j

0.60 ι

ι

ι—j

ι

0.50 ι

ι

ι

ι

ι

0.40 ι

ι

ι

ι

ι

I

2+4" 4

f Tf Γ

4

ill

+

I

4" 3+ 5"

+

5 I

I I I

4

+

2

+

I I

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch015

cc

/ ν 5.5

/I

5.6

5.7

λ

M,

M

5.8

/u 5.9

E (MeV) 7

Figure 12. A portion of the calculated primary gamma-ray spectrum for the Lu(n,/) reaction. 175

Conclusion It is evident from the above examples that the use of complete sets of discrete levels is an essential key in making accurate statistical-model Hauser-Feshbach calculations. Since these level sets must include both the observed and modeled information for completeness, additional personnel and expertise are required to produce them. It should also be pointed out that the use of large discrete-level sets in calcula­ tions usually requires significant increases in computer time. We see that many problems still need to be solved in order to obtain accurate results in HauserFeshbach calculations. Some examples are the energy dependence of rotational enhancement of levels in deformed nuclei, the energy and mass dependence of M l gamma-ray transitions, the importance of E2 transitions, and better estimates of fission barriers. Work in each of these areas will benefit greatly from a better understanding of the discrete levels, particularly in nuclei away from stability.

Acknowledgments The authors are grateful to M . N . Namboodiri of the Lawrence Livermore National Laboratory for presenting this paper at the Symposium. This work was performed under the auspices of the U.S. Depart­ ment of Energy by Lawrence Livermore National Laboratory under contract N o . W-7405-ENG-48.

15.

GARDNER AND GARDNER

113

The Importance of Level Structure References

[AXE70] [BAR83]

P. Axel et al., Phys. Rev. C 2, 689 (1970). D. W. Barr, S. A. Beatty, M. M . Fowler, J. S. Gilmore, R. J. Prestwood, Ε. N . Treher, and J. B. Wilhelmy, "(p,xn) Measurements on Strontium Isotopes," Nuclear Chemistry Division Annual Report FY 82, Los Alamos National Laboratory, Los Alamos, NM, LA-9797-PR (1983). [BAY75] B. P. Bayhurst et al., Phys. Rev. C 12, 451 (1975). [BEE80] H. Beer, F. Kappeler, and K. Wisshak, "The Neutron Capture Cross Sections of Natural Yb, Yb, Lu, and W in the Energy Range from 5 to 200 keV for the Lu-Chronometer," Proc. Int. Conf. Nuclear Cross Sections for Technology, Knoxville, TN, 1979, National Bureau of Stan­ dards, Gaithersburg, MD, NBS Special Publication 594 (1980), p. 340. [BOL77] J. W. Boldeman et al., Nucl. Sci. Eng. 64, 744 (1977). [COO67] J. L. Cook, H. Ferguson, and A. R. Musgrove, Nuclear Level Densities in Intermediate and Heavy Nuclei, Australian Atomic Energy Commission, AAEC/TM-392 (1967). [GAR84a] M. A. Gardner, " Tm(n,3n) Tm Cross-Section Calculations Near Threshold," Nuclear Chem­ istry Division FY 84 Annual Report, Lawrence Livermore National Laboratory, Livermore, CA, UCAR-10062-84/1 (1984). [GAR84b] D. G. Gardner, "Methods for Calculating Neutron Capture Cross Sections and Gamma-Ray Energy Spectra," Neutron Physics and Nuclear Data in Science and Technology, Volume 3, Neu­ tron Radiative Capture (Pergamon Press, New York, 1984), Chapter III. [GAR85a] M. A. Gardner, Calculational Tools for the Evaluation of Nuclear Cross-Section and Spectra Data, Lawrence Livermore National Laboratory, Livermore, CA, UCRL-91947 (1985); to be published in Proc. Int. Conf. Nuclear Data for Basic and Applied Science, Santa Fe, NM, May 13-17, 1985. [GAR85b] D. G. Gardner, M. A. Gardner, and R. W. Hoff, "Absolute Dipole Gamma-Ray Strength Func­ tions for Lu," Proc. Conf. Capture Gamma-Ray Spectroscopy and Related Topics, Knoxville, TN, American Institute of Physics, New York, NY, AIP Conf. Proc. #125 (1985), p. 513. [GIL65] A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43, 1446 (1965). [HAN83] G. Hansen and A. S. Jensen, "Energy Dependence of the Rotational Enhancement Factor in the Level Density," IAEA Advisory Group Meeting on Basic and Applied Problems of Nuclear Level Densities, Brookhaven National Laboratory, Upton, NY, BNL-NCS-51694 (1983), p. 161. [HEN77] E. A. Henry, Lawrence Livermore National Laboratory, Livermore, CA, private communication (1977). [HEN85] E. A. Henry, Lawrence Livermore National Laboratory, Livermore, CA, private communication (1985). [HOF84] R. W. Hoff and W. R. Willis, "Level-Structure Modeling of Odd-Mass Deformed Nuclei," Nuclear Chemistry Division FY 84 Annual Report, Lawrence Livermore National Laboratory, Livermore, CA, UCAR 10062-84/1 (1984). [HOF85a] R. W. Hoff, J. Kern, R. Piepenbring, and J. B. Boisson, "Modeling Level Structures of Odd-Odd Deformed Nuclei," Proc. Conf. on Capture Gamma-Ray Spectroscopy and Related Topics, Knox­ ville, TN, American Institute of Physics, New York, NY, AIP Conf. Proc. #125 (1985), p. 274. [HOF85b] R. W. Hoff et al., Nucl. Phys. A437, 285 (1985). [KAT78] S. Kataria et al., Phys. Rev. C 18, 549 (1978). [MAC78] R. L. Macklin, D. M. Drake, and J. J. Malanify, Fast Neutron Capture Cross Sections of Tm, Ir, Ir, and Lu for 3 < E < 2000 keV, Los Alamos National Laboratory, Los Alamos, NM, LA7479-MS (1978). [MEY85] R. A. Meyer, Lawrence Livermore National Laboratory, Livermore, CA, private communication (1985). [MUG84] S. F. Mughabghab, Neutron Cross Sections, Vol. 1, Part Β (Academic Press, New York, 1984). [MYE75] W. Myers et al., J. Inorg. Nucl. Chem. 37, 637 (1975). [NET72] D. R. Nethaway, Nucl. Phys. A190, 635 (1972); also, unpublished (n,3n) cross-section measure­ ments, Lawrence Livermore National Laboratory, Livermore, CA (1972). [NET76] D. R. Nethaway, unpublished (n,2n) cross-section measurements, Lawrence Livermore Na­ tional Laboratory, Livermore, CA (1976). [REF80] G. Reffo, "Phenomenological Approach to Nuclear Level Densities," Theory and Applications of Moment Methods in Many-Fermion Systems (Plenum Press, New York, 1980). 170

175

184

176

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch015

169

167

176

169

193

175

11

191

114 [SZE79] [UHL70] [VEE77] [VOI83]

NUCLEI OFF THE LINE OF STABILITY

G. Szeflinska et al., Nucl. Phys. A323, 253 (1979). M. Uhl, Acta Phys. Austriaca 31, 245 (1970). L. R. Veeser et al., Phys. Rev. C 16, 1792 (1977). J. Voignier, S. Joly, and G. Grenier, "Mesure De La Section Efficace De Capture Radiative Du Lanthane, Du Bismuth, Du Cuivre Naturel et De Ses Isotopes Pour Des Neutrons D'Energie Comprise Entre 0,5 et 3 MeV," Proc. Int. Conf. Nuclear Data for Science and Technology, A Belgium (1983), p. 759.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch015

RECEIVED May 8, 1986

16 Distribution of Electromagnetic Transition Amplitudes 1

2

P. J. Brussaard and J. J. M. Verbaarschot 1

Fysisch Laboratorium, Rijksuniversiteit te Utrecht, P.O. Box 80.000, 3508 TA Utrecht, the Netherlands Max-Planck-Institut für Kernphysik, Postfach 103980, D-6900 Heidelberg, Federal Republic of Germany

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch016

2

The present-day shell-model computer programmes of nuclear physics can handle very large model spaces, and often in practice the upper bounds on dimensionalities are set by the capacity of the computer. However, still larger configuration spaces can be treated successfully by the methods of statistical spectroscopy to obtain average properties of many-particle systems. These methods are based on the use of distribution functions with parameters that can be evaluated without the explicit calculation and diagonalization of a high-dimensional hamiltonian matrix. The basic philosophy behind this method is that the average properties depend on the particular model at hand, whereas the fluctuations about the average are universal. The latter remark means that the fluctuations can be described by the gaussian orthogonal ensemble. Of course, the results are less detailed than those one would obtain, if possible, from the explicit diagonalization of the energy matrix and the use of the resulting many-dimensional wave functions. The most familiar example is the energy spectrum of a nuclear hamiltonian that can be described by a gaussian distribution. It must be remarked that for a system of many, say N, noninteracting particles the gaussian distribution of the eigenvalues is a direct consequence of the central limit theorem for large values of N. For interacting particles, to the contrary, not every hamiltonian will lead to a gaussian energy spectrum. For example, the square of a traceless one-body operator as a hamiltonian will produce a x -distribution. Proper ensemble averaging of the energy density, however, will then generate the gaussian distribution of eigenvalues, as it is also obtained by many largescale shell-model calculations that have been performed with a wide variety of realistic interactions. In a proper ensemble the influence of the unwanted hamiltonians is essentially eliminated. Let the k-body hamiltonian be given by 2

f

H=I H. a a αβ " rt H rr ft

- |a> represents the k - p a r t i c l e s t a t e |. In the corresponding

gaussian orthogonal ( i . e . , showing orthogonal invariance) ensemble the d i s t i n c t matrix elements Η β are independently d i s t r i b u t e d as gaussian α

v a r i a b l e s according to the r e l a t i o n s 2

< Η > = 0 and < ( Η ) > = ( 1 + δ ) ν α β

α β

2

(2)

α β

where the acute brackets denote ensemble averaging

[BR081; POR651 .

When these matrices are a p p l i e d i n an N - p a r t i c l e c o n f i g u r a t i o n space (N»k)

the moments of the hamiltonian behave on ensemble averaging i n

the l i m i t of large d i m e n s i o n a l i t y as i n the case of n o n i n t e r a c t i n g p a r t i c l e s without averaging. This r e f l e c t s the dominance of binary c o r r e l a t i o n s i n the

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch016

operator products H 'dilute

1

p

when the ensemble averaging i s performed i n the

system (k «

N)·

For a space of eigenvectors of matrices of the gaussian

orthogonal

ensemble (k = N) the d i s t r i b u t i o n of values of matrix elements of electromagnetic t r a n s i t i o n operators i s gaussian, as f o l l o w s from the c e n t r a l l i m i t theorem. The ensemble averaging of hamiltonians

guarantees

that no c o r r e l a t i o n s e x i s t between the hamiltonian s t r u c t u r e and the p a r t i c u l a r t r a n s i t i o n operator that i s considered. However, we are concerned with a many-body system that i s described by a p a r t i c u l a r one- and two-body i n t e r a c t i o n . For each eigenvalue p a r t i c l e e i g e n f u n c t i o n ψ^, obeying

Ηψ

1

= Ε ψ ±

(3)

±

can be expanded i n a s e t of basis s t a t e s φ

•i

=

Σ ' a

1

the many-

the Schrôdinger equation

α

φ

α

as

4

α

or i n v e r s e l y Φ

= y c* ψ, ι

(5)

where the basis s t a t e φ^ i s expanded i n terms of the eigenstates ψ.^. The values of |

c i a

|

2 f

o

r

a

given s t a t e ψ.^ turn out to show a s e c u l a r

v a r i a t i o n as a f u n c t i o n of the diagonal matrix elements Α

The s e c u l a r behaviour

itself

[VER79].

depends on the energy Ej^ which r e f l e c t s a

c o r r e l a t i o n between the hamiltonian and the t r a n s i t i o n operator. Thus one should expect

the d i s t r i b u t i o n of the e l e c t r o m a g n e t i c - t r a n s i t i o n amplitudes

to be gaussian only f o r a small energy range of the energies W and W i n i t i a l and f i n a l many-particle s t a t e s , r e s p e c t i v e l y . The square

of the

of the

16.

Electromagnetic Transition Amplitudes

BRUSSAARD A N D VERBAARSCHOT

absolute values of the t r a n s i t i o n amplitudes f o r the operator 0, isospin,

117

single-particle

|W> I2-,--between spaces of f i x e d angular momentum,

| and thus are expected to

define gaussian d i s t r i b u t i o n functions [FRE71] 2

n (W'-E') Pu< ) - — e x p [ =—] σ»/2π 2σ· w W with the parameters being the moments f o r ρ - 0,1,2 w

wl

w

(9)

2

defined i n eq. ( 8 ) .

S i m i l a r l y the many-body eigenvalue d i s t r i b u t i o n f o r a two-body interaction

i s very c l o s e to gaussian [FRE71; MON75]. The d i s t r i b u t i o n of

f i n a l s t a t e s |W> i s given by (wt_-pt\2

p . 0

(

w

. ) . - i L

e

σ^/2π

x

p

[

-

(

w

V

2σ^

2

]

ao)

NUCLEI OFF T H E LINE OF STABILITY

118 where the parameters

are derived from the moments (p - 0,1,2)

-fco

/ -»

W'V(W)dW

- — I « 1 - T r ( H ) d α d Ρ

f

α

α

P

(11)

f

2

The s e c u l a r behaviour of o (W*,W), defined i n eq. ( 7 ) , can now be expressed i n terms of the d i s t r i b u t i o n s (9) and (10) as P (W) a (W\W) = | I n ( 1 ) Gamow-Teller t r a n s i t i o n s . Lows e n i o r i t y e x c i t a t i o n s are a l l o w e d w i t h i n the (1g,2d,3s,1h) s h e l l , which are m i x e d by t h e K a l l i o - K o l l t v e i t [ K A L 6 4 ] two-body e f f e c t i v e i n t e r a c t i o n . The s i n g l e - p a r t i c l e e n e r g i e s a r e t a k e n f r o m a d e t a i l e d a n a l y s i s [ S T 0 8 5 ] o f one-, two-, and t h r e e - q u a s i - p a r t i c l e n u c l e i n e a r t h e Z=50, N=82 c l o s e d s h e l l s w i t h t h e same two-body f o r c e . l 3 0

1 3 0

+

l 3 0

+

20.

TAKAHASHI ET AL.

147

Shell-Model Calculations of β-Decay Rates

The resultant β-strength functions are displayed in Fig. 2 as a sequence in the number of Lanczos iterations. As for the absolute values, we have assumed a quenching factor of 0.5 for the GT sum-rule. I t can be understood that the h a l f - l i f e i t s e l f converges very quickly. For the predicted groundstate β-decay Q-value of 6.4 MeV ([LIR76], [JAN76], [C0M76]), the calculated C d h a l f - l i f e i s 0.08 sec as shown in Fig. 3 in comparison with the TDA calculations with a GT residual interaction [KLA84]. l30

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch020

Cd

Strength

Function

Cd

Strength

Energy (MeV)

Function

Energy (MeV) I30

F i g . 2. Calculated GT-strength function for the C d ground-state (0 ) decays to the low-lying 1 (T=16) states i n I n as a sequence of the number of Lanczos iterations. The abscissa i s the excitation energy in I n . For convenience of drawing, the minimum width i s chosen to be 100 keV. +

1 3 0

1 3 0

I0'

Cd

10' ο : p r e s e n t work

I0

l

l30

F i g . 3. Calculated C d h a l f - l i f e i n comparison with the TDA predictions for Cd isotopes by Klapdor et a l . [KLA84], The squares represent known experimental data.

120 130 HO

150 160 170

Mass Number A

American Chemical Society Library 1155 16th St., N.W. Washington, D.C. 20036

148

N U C L E I O F F T H E LINE O F STABILITY

As a t e s t o f o u r p r e d i c t i o n f o r C d , we have c a l c u l a t e d t h e 8~decay r a t e s f o r t h e GT t r a n s i t i o n s f r o m t h e l o w e s t 1 s t a t e o f I n t o t h e ground ( 0 ) and f i r s t - e x c i t e d ( 2 ) s t a t e s o f Sn. The r e s u l t a n t I n total halfl i f e i s 0.26 s e c f o r t h e assumed Q«=10.2 MeV, w h i c h i s c o m p a r a b l e w i t h t h e r e p o r t e d v a l u e ( 0 . 3 3 s e c ) f o r t h e l o w - s p i n (1 , 3 ) s t a t e [RUD85]. More s y s t e m a t i c c a l c u l a t i o n s w i t h t h e p r e s e n t method w i l l c e r t a i n l y h e l t o c l a r i f y o u r u n d e r s t a n d i n g o f t h e β-decay p r o p e r t i e s o f s p h e r i c a l n u c l e i f a o f f t h e l i n e o f s t a b i l i t y , which a r e needed i n r - p r o c e s s s t u d i e s . I n p a r t i c u l a r , a s t u d y o f t h e e f f e c t s o f t h e β-decay o f l o w - l y i n g s t a t e s t h e r m a l l y p o p u l a t e d i n t h e h i g h t e m p e r a t u r e r - p r o c e s s e n v i r o n m e n t i s due. S u e e f f e c t s have n o t been i n c l u d e d i n any r - p r o c e s s m o d e l y e t a t t e m p t e d . Finally we m e n t i o n t h a t a d i f f e r e n t a p p r o a c h ( i . e . RPA) i s p r o b a b l y c a l l e d f o r i n o r d e r t o d e a l w i t h d e f o r m e d n u c l e i e f f e c t i v e l y [BRA85] . l 3 C

+

+

+

1 3 0

1 3 0

1 3 0

+

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch020

Acknowledgments

Work p e r f o r m e d u n d e r a u s p i c e s o f t h e U.S. D e p a r t m e n t o f E n e r g y b y t h e L a w r e n c e L i v e r m o r e N a t i o n a l L a b o r a t o r y u n d e r c o n t r a c t number W-7405-ENG-48, and s u p p o r t e d i n p a r t b y t h e LLNL I n s t i t u t e f o r G e o p h y s i c s a n d P l a n e t a r y Science.

References [BEK81] S.A.Becker, in Physical Processes in Red Giants, eds. I.Iben, Jr. and A.Renzini (Reidel, 1981), p.141 [BRA85] B.S.Meyer, W.M.Howard, G.J.Mathews, P.Möller and K.Takahashi, this meeting [CAM59] A.G.W.Cameron, Astrophys.J. 130 452 (1959) [COM76] E.Comay and I.Kelson, Atm.Nucl.Dat.Tables 17 463 (1976) [COS84] K.R.Cosner, K.H.Despain and J.W.Truran, Astrophys.J. 283 313 (1984) [FOW75] W.A.Fowler, G.R.Caughlan and B.A.Zimmerman, Ann.Rev.Astron.Astrophys. 13 69 (1975) [HAU76] R.F.Hausman, J r . , Ph.D. thesis, University of California Radiation Laboratory Rept. UCRL-52178 (1976) [IBE77] I.Iben, J r . , Astrophys.J. 217 788 (1977) [JAN76] J.Jänecke, Atm.Nucl.Dat.Tables 17 455 (1976) [KAL64] A.Kallio and K.Kolltveit, Nucl.Phys. 53 87 (1964) [KLA84] H.V.Klapdor, J.Metzinger and T.Oda, Atm.Nucl.Dat.Tables 31 81 (1984) [LIR76] S.Liran and N.Zeldes, Atm.Nucl.Dat.Tables 17 431 (1976) [MAT85a] G.J.Mathews and R.A.Ward, Rept.Prog.Phys., in press [MAT85b] G.J.Mathews, K.Takahashi, R.A.Ward and W.M.Howard, Astrophys.J., in press [RUD85] G.Rudstam, P.Aagaard and H.-U. Zwicky, The Studsvik Science Research Laboratory Rept. NFL-42 (1985) [SCH83] D.N.Schramm, in Essays in Nuclear Astrophysics, eds. C.A.Barnes, D.D.Clayton and D.N.Schramm (Cambridge Univ., 1983) p.325 [SMI83] V.V.Smith and G.Wallerstein, Astrophys.J. 273 742 (1983) [STO85] C.A.Stone, W.B.Walters, S.D.Bloom and G.J.Mathews, this meeting [TAK83] K.Takahashi and K.Yokoi, Nucl.Phys. A404 578 (1983) [TAK85a] K.Takahashi, G.J.Mathews and S.D.Bloom, Phys.Rev. C, submitted [TAK85b] K.Takahashi, G.J.Mathews, R.A.Ward and S.A.Becker, in Proc.5th Moriond Meeting on Nucleosynthesis and its Implications to Nuclear and Particle Physics, Les Arcs, 1985 (Reidel) in press [WHI80] R.R.Whitehead, in Moment Method in Many Fermion System, eds. B . J . Dalton, S.S.Grimes, J.D.Vary and S.A.Williams (Plenum, 1980), p.235 [YOK85] K.Yokoi and K.Takahashi, Kernforschungszentrum Karlsruhe Rept. KfK-3849 (1985) RECEIVED May 16,

1986

21 β-Delayed Fission Calculations for the Astrophysical r-Process B. S. Meyer, W. M . Howard, G. J . Mathews, P. Möller, and K. Takahashi Lawrence Livermore National Laboratory, University of California, Livermore, C A 94550

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch021

We discuss RPA calculations of the Gamow-Teller properties of neutron-rich nuclei to study the effect of β-delayed fission and neutron emission on the production of Th, U and Pu chronometric nuclei in the astrophysical r-process. We find significant differences in the amount of β-delayed fission when compared with the recent calculations of Thielemann et a l . (1983). In the simplest case of a constant abundance along the r-process path, however, the inferred production ratios in both calculations are similar. The s t u d y o f t h e decay o f n u c l e i f r o m t h e r - p r o c e s s p a t h back t o t h e βs t a b i l i t y l i n e i s an a r e a o f a s t r o p h y s i c s w h i c h r e q u i r e s k n o w l e d g e o f βs t r e n g t h f u n c t i o n s o f f the l i n e of b e t a s t a b i l i t y . T h i s knowledge i s e s p e c i a l l y i m p o r t a n t f o r the d e t e r m i n a t i o n o f the abundances o f the p r o g e n i t o r s o f t h e Th-U-Pu c h r o n o m e t e r s s i n c e β-delayed f i s s i o n and n e u t r o n e m i s s i o n d u r i n g d e c a y back t o t h e s t a b i l i t y l i n e may s i g n i f i c a n t l y a f f e c t t h e f i n a l abundance d i s t r i b u t i o n o f t h e s e n u c l e i ( [ B E R 6 9 ] , [WEN75], [ K 0 D 7 5 ] , [ K R U 8 1 ] ) . The β-strength f u n c t i o n f o r n u c l e i a l o n g t h e d e c a y b a c k p a t h s [coupled with neutron separation energies ( S ) , f i s s i o n b a r r i e r heights (B ) and β-decay Q - v a l u e s ( Q g ) ] d e t e r m i n e s t h e amount o f β-delayed f i s s i o n and n e u t r o n e m i s s i o n t h a t o c c u r s d u r i n g t h e c a s c a d e back t o t h e β-stability l i n e . A r e c e n t a n a l y s i s by T h i e l e m a n n e t a l . [THI83] o f t h e e f f e c t s o f βd e l a y e d p r o c e s s e s on t h e p r o g e n i t o r s o f t h e Th-U-Pu c h r o n o m e t e r s showed t h a t these processes (delayed f i s s i o n i n p a r t i c u l a r ) d i d indeed s i g n i f i c a n t l y i n f l u e n c e the f i n a l abundances o f the chronometer p r o g e n i t o r s . T h i s l e a d s t o a l o n g age f o r t h e G a l a x y . I n view o f the importance of t h i s r e s u l t , i t i s u s e f u l t o r e - e x a m i n e t h e c a l c u l a t i o n w i t h a n u c l e a r model t h a t i n c l u d e s t h e e f f e c t s o f n u c l e a r d e f o r m a t i o n on t h e β-decay r a t e s , f i s s i o n b a r r i e r s , and neutron s e p a r a t i o n energies s e l f - c o n s i s t e n t l y . S i n c e many o f t h e n u c l e i i n v o l v e d a r e p r e s u m a b l y h i g h l y - d e f o r m e d , we have u s e d t h e N i l s s o n RPA c o d e o f K r u m l i n d e and Môller [ K R U 8 4 ] , w h i c h c a l c u l a t e s β-strength f u n c t i o n s , u s i n g an i n f i n i t e - r a n g e r e s i d u a l (GamowT e l l e r ) i n t e r a c t i o n w i t h a s t r e n g t h x j = 23/A MeV. W i t h t h i s c o d e , we have c a l c u l a t e d β-strength f u n c t i o n s f o r 1ΐέ n u c l e i l y i n g i n t h e mass r a n g e f r o m A=232 t o A=255 and f r o m t h e l i n e o f β-stability t o t h e r - p r o c e s s p a t h g i v e n by T h i e l e m a n n e t a l . [THI83] ( s e e F i g . 1 ) . T h e s e 118 n u c l e i s a t i s f i e d t h e c r i t e r i a f o r p o s s i b l e β-delayed f i s s i o n (Q^ o f p r e c u r s o r έ of emitter) a n d / o r p o s s i b l e β-delayed n e u t r o n e m i s s i o n ( Q o f p r e c u r s o r 2 S of emitter) as d e t e r m i n e d f r o m t h e v a l u e s g i v e n i n [H0W80.,. The r e q u i r e d i n p u t v a l u e s a r e t h e d e f o r m a t i o n p a r a m e t e r s £ 2 and ε·» and t h e numbers κ and μ w h i c h d e t e r m i n e t h e s i z e o f t h e 1-s f o r c e and l t e r m s f o r the harmonic o s c i l l a t o r . We a d o p t e d t h e v a l u e s κ = 0.0577 and μ = 0.650 f o r p r o t o n s and κ = 0.0635 and μ = 0.325 f o r n e u t r o n s o v e r t h e e n t i r e r a n g e s t u d i e d , i n a c c o r d a n c e w i t h [H0W80]. The v a l u e s o f ε and επ f o r e a c h n u c l e u s were t a k e n f r o m t h e same s o u r c e . n

f

G

g

n

2

η

η

2

0097-6156/ 86/ 0324-0149S06.00/ 0 © 1986 American Chemical Society

150

NUCLEI OFF T H E LINE OF STABILITY

From o u r β-strength d i s t r i b u t i o n s , we t h e n c a l c u l a t e d r a t e s a s a f u n c t i o n o f e x c i t a t i o n energy i n t h e daughter n u c l e u s . These r a t e s and the Qg, B , and S v a l u e s [H0W80] g i v e t h e amount o f β-delayed f i s s i o n a n d n e u t r o n e m i s s i o n f o r each daughter nucleus. Our r e s u l t s a r e shown i n F i g . 1 . The numbers i n t h e s q u a r e s i n F i g . 1 ( a ) g i v e t h e p e r c e n t a g e o f d e c a y s r e s u l t i n g i n a daughter n u c l e u s e x c i t a t i o n energy g r e a t e r than o r equal t o t h e f i s s i o n b a r r i e r h e i g h t . The numbers i n t h e s q u a r e s i n F i g . 1(b) g i v e t h e p e r c e n t a g e of decays r e s u l t i n g i n an daughter nucleus e x c i t a t i o n energy g r e a t e r than o r equal t o t h e neutron s e p a r a t i o n energy but l e s s than t h e f i s s i o n b a r r i e r height. I n o r d e r t o d e t e r m i n e t h e maximum p o s s i b l e e f f e c t o f d e l a y e d f i s s i o n , we t a k e t h e number f r o m ( a ) a s t h e amount o f β-delayed f i s s i o n and t h e number f r o m ( b ) a s t h e amount o f β-delayed n e u t r o n e m i s s i o n i n t h e d a u g h t e r nucleus. T h i s undoubtedly l e a d s t o an overestimate o f delayed f i s s i o n p r o b a b i l i t i e s i n some c a s e s . F o r t h e p u r p o s e o f s i m p l e c o m p a r i s o n w i t h [THI83], we assume c o n s t a n t a b u n d a n c e s (1.0 p e r i s o b a r ) a l o n g t h e r - p r o c e s s p a t h shown i n F i g . 1 . A f t e r βd e l a y e d f i s s i o n and n e u t r o n e m i s s i o n d u r i n g decay b a c k , t h e f i n a l a b u n d a n c e s a r e t h o s e shown i n T a b l e 1. C l e a r l y β-delayed f i s s i o n p l a y s a l a r g e r o l e i n d e c a y back a t Α ί 2 5 0 . On t h e o t h e r h a n d , β-delayed n e u t r o n e m i s s i o n d o e s n o t a f f e c t t h e a b u n d a n c e s t o o much, s i n c e l o s s f r o m c h a i n A i s more o r l e s s c o m p e n s a t e d f o r by g a i n f r o m c h a i n A+1, e x c e p t i n a few c a s e s (A = 234, 236, 239, 2 4 4 , 2 4 8 , a n d 2 4 9 ) . O f c o u r s e , a more s i g n i f i c a n t e f f e c t o f d e l a y e d , n e u t r o n e m i s s i o n w i l l be s e e n i f we t a k e more r e a l i s t i c i n i t i a l a b u n d a n c e s a l o n g t h e r - p r o c e s s p a t h , which u s u a l l y e x h i b i t a s t r o n g even-odd e f f e c t .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch021

f

n

—

—

λ —a •¥-\-*-

I I • I * / I* V /

V

! À-

1

I

+•

1

>'*' β X •

1 23

m

l

I I)

18

17 72 46

150

7

25

2

μ -

1

1

18

*

>

—

I I

I 145

10

29 1

140

22

Ι

5

1

6

I I

f v

1 1

155

160

165

Ν

—-

Fig. 1(a). C a l c u l a t e d maximum p o s s i b l e v a l u e s o f β-delayed f i s s i o n p r o b a b i l i t i e s ( i n %) shown f o r t h e p r e c u r s o r n u c l e i . The a r r o w f o l l o w s t h e r - p r o c e s s p a t h g i v e n i n [THI833. The c r o s s e s i n d i c a t e β-stable n u c l e i , and t h e d a s h e d l i n e s i n d i c a t e α decays. The r - p r o c e s s n u c l e a r c o s m o - c h r o n o m e t e r s a r e c i r c l e d .

21.

β-Delayed Fission Calculations

MEYER ET AL.

Ζ

+'

/

,+

V *s V x' S V @

,@

A

7

A

•jr

s

V

/

*\

151

*-

+'

/

& •«

3

12

14 15 35 26 37

45

1

1

3

4

η

4

1

ι/Μ

7

27

15

f?

ni

1

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch021

r

lu

1

17 20 15 44

1

1

1

51 50 41 72

1

55 67 "5

14

4

- r i !57 1 145

150

155

160

165

N

—

F i g - K b ) . C a l c u l a t e d minimum p o s s i b l e v a l u e s o f β-delayed n e u t r o n e m i s s i o n p r o b a b i l i t i e s ( i n % ) . See t h e c a p t i o n t o F i g . 1 ( a ) .

T a b l e 1. I s o b a r i c a b u n d a n c e changes d u r i n g t h e cascade from t h e i n i t i a l v a l u e o f 100 % a t t h e r - p r o c e s s p a t h shown i n F i g . 1 down t o t h e β-stable n u c l e i marked by c r o s s e s .

A

%

A

%

232 233 234 235 236 237 238 239 240 241 242 243

78 102 70 118 133 92 97 67 115 111 103 94

244 245 246 247 248 249 250 251 252 253 254 255

47 112 110 124 64 64 47 32 67 18 11 6

From t h e r e s u l t s i n T a b l e 1, we c a n f i n d t h e r - p r o c e s s p r o d u c t i o n r a t i o s of i n t e r e s t t o n u c l e a r cosmo-chronology: Th/ U, U/ U , and * P u / U . T h e s e a r e o b t a i n e d by summing t h e α-decay p r o g e n i t o r s f o r e a c h i s o t o p e and c o n s i d e r i n g t h e l e a k due t o s p o n t a n e o u s f i s s i o n . Our r e s u l t s a r e 32 238 23 5U/ 2 3 8U 2*»p /*i*\j = 0.57. Our v a l u e f o r Th/ U r a t i o i n t h i s a p p r o x i m a t i o n o f c o n s t a n t r - p r o c e s s abundances would i m p l y a l o w e r l i m i t o n t h e G a l a x y ' s age o f 8.8 G y r . However, i t i s i m p o r t a n t t o n o t e t h a t t h e f i n a l p r o d u c t i o n r a t i o s w i l l be d e p e n d e n t on t h e e x p l i c i t r 2 3 2

2l+,

2

2 3 2

2 38

T n /

2 3 8

U

m

1 e 6 Q

=

u

2 3 8

2 3 5

2 3 8

152

NUCLEI OFF THE LINE OF STABILITY

process calculation employed [ F O W 8 5 ] . (See also [ M E Y 8 5 ] , [ T H I 8 3 ] and [ Y O K 8 3 ] for further details on nuclear cosmo-chronology.) For comparison, we give the values for the chronometer production ratios determined by Thielemann et a l . [ T H I 8 3 ] for constant abundances along the rprocess path: T h / U = 1 . 6 3 , U / U = 1 . 2 1 , and --Pu/ U = 0.13. To our surprise, our T h / U ratio agrees well with [ T H I 8 3 ] , despite the large difference between the two calculations in the amount of β-delayed f i s s i o n (compare Fig. 1(a) with Fig. 2 of [ T H I 8 3 ] ) . This result suggests that βdelayed processes do indeed significantly affect the abundances of the progenitors of the r-process chronometers. The other two sets of ratios d i f f e r rather strongly, however. These differences are not surprising because of the different β-strength functions and adopted mass formulae (for Qg and S ) , although both sets of calculations used the same f i s s i o n barrier heights. I t i s worth emphasizing that the virtue of our calculations are that a l l input data were taken from a single source [H0W80], i.e., the effects of nuclear deformations on the f i s s i o n barriers and β-strength functions were treated self-consistently. We understand that many uncertainties s t i l l exist in this calculation and, therefore, that further work i s s t i l l required. We hope to pursue this study in the near future and w i l l be aided by improvements in the code used for calculating the β-strength functions (e.g., the inclusion of the first-forbidden decay) and in the set of Qg, B and S values. We w i l l also include a more r e a l i s t i c determination of the competition between delayed f i s s i o n and delayed neutron emission. These improvements should lead to a better understanding of decay back to the β-stability line and help in the search for the astrophysical site(s) for the r-process. 232

238

232

235

238

2

238

238

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch021

n

f

n

Acknowledgment s

We express our thanks to Prof. William A.Fowler for useful discussions and encouragement. Work performed under auspices of the U.S.Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48, and supported in part by the LLNL Institute for Geophysics and Planetary Science. One of us (BSM) acknowledges the support of National Science Foundation Graduate Fellowship. References [BER69] E.Yu.Berlovich and Yu.N.Novikov, Phys.Lett. 29B 155 (1969) [FOW85] W.A.Fowler and C.C.Meisel, in Proc.Symp. on Cosmogonical Processes, Boulder, Colorado, 1985, in press [HOW80] W.M.Howard and P.Möller, Atm.Nucl.Dat.Tables 25 219 (1980) [KOD75] T.Kodama and K.Takahashi, Nucl.Phys. A239 489 (1975) [KRU81] J.Krumlinde, P.Möller, C.-O.Wene and W.M.Howard, in Proc.4th Int.Conf. on NUclei Far From Stability, Helsingør, 1981; CERN Rpt. 81-09, p.260 [KRU84] J.Krumlinde and P.Möller, Nucl.Phys. A417 419 (1984) [MEY85] B.S.Meyer and D.N.Schramm, in Proc.5th Moriond Astrophysics Meeting on Nucleosynthesis and its Implications on Nuclear and Particle Physics, Les Arcs, 1985 (Reidel) in press [THI83] F.-K.Thielemann, J.Metzinger and H.V.Klapdor, Astron.Astrophys. 123 162 (1983) [WEN75] C.-O.Wene, Astron.Astrophys. 44 233 (1975) [YOK83] K.Yokoi, K.Takahashi and M.Arnould, Astron.Astrophys. 118 6 (1983) RECEIVED April 11, 1986

Shell-Model Plus Pairing Calculations of β-Delayed Neutron Emission Properties at A ≡90-100

22

Shaheen Rab and Adnan Shihab-Eldin

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch022

Kuwait Institute for Scientific Research, P.O. Box 24885 Safat, Kuwait

Expressions a r e d e r i v e d f o r reduced t r a n s i t i o n p r o b a b i l i t i e s o f allowed Gamow-Teller beta decay using S e n i o r i t y Truncated Exact D i a g o n a l i z a t i o n (STED) method w i t h i n the framework o f shell-model plus p a i r i n g . When expressed i n terms o f f r a c t i o n a l occupation p r o b a b i l i t y parameters U and V, the d e r i v e d formulae a r e i d e n t i c a l t o those of BCS method. These expressions a r e used t o c a l c u l a t e beta-delayed neutron emission p r o b a b i l i t y and beta decay h a l f life o f Br and Rb isotopes. The r e s u l t s are found t o be s e n s i t i v e to p a i r i n g strength parameter G and optimum agreement with experimental values a r e obtained f o r G(n) = 0.25. The c a l c u l a t e d values f o r these q u a n t i t i e s a r e in agreement with the o v e r a l l trend o f experimental r e s u l t s . Moreover, they show better agreement with experimental values than s i m i l a r c a l c u l a t i o n using BCS p a i r i n g method.

Introduction The beta delayed neutron emission properties of neutron rich nuclei have attracted a lot of interest recently because of advancements in experimental techniques. The information on neutron spectrum, beta decay half-life t½, delayed neutron emission probability p for nuclei far from the n

line of stability are important in nuclear reactors, nuclear physics and astrophysics. These properties, for nuclei around mass A — 9 0 — 100, have been studied previously by statistical theory [HAR78] [GJ078] and Gross theory [TAK69] [YAM70]. Application of shell model (SM) plus pairing was first suggested in the mid seventies [SHI77]. The SM plus pairing model [OLI80] gave better overall agreement with experimental results for ty and p . The pairing forces are usually treated in BCS 2

n

quasi particle theory [KIS63] [LAN64]. Inclusion of Gamow Teller force in SM plus pairing (BCS) improved the fit better [OLI80]. The deviation from the experimental curve is still large compared to uncertainties and the odd-even fluctuation is the main problem we are concerned with here. The problem of particle non-conservation in BCS introduces an averaging effect on the properties of neighbouring isotopes.

Furthermore, the blocking effect is not taken into account in these

calculations. To overcome these BCS limitations, we propose to handle pairing force in SM using Seniority Truncated Exact Diagonalization (STED) scheme. Expressions are derived for reduced transition probability Β in STED to calculate beta strength function, S, ty , and p . The overall n

2

agreement with the experimental results of ti^, p

n

in STED for " 9 2

1 0 2

Rb and

8 7 - 9 2

Br is found

to be better than the BCS results.

Seniority Truncated Exact Diagonalization (STED) Scheme Only Gamow Teller (GT) allowed β-decay is studied in this work as it plays the dominant role

in the specified mass range.

The experimentally studied nuclei are assumed to be

0097-6156/86/0324-0153$06.00/0 © 1986 American Chemical Society

NUCLEI OFF T H E LINE OF STABILITY

154

spherical and hence we use spherical shell model basis. The number conserving and conceptually simpler STED scheme developed by John [JOH68] is used t o deal w i t h the pairing force. The usual fermion creation and destruction operators C , C are used t o define pair creation (destruction) +

operator a

(a).

+

~l

^ ( - D ^ C ^ C ^

ι

V2(2i+1)

(1)

m>0

The Hamiltonian is written as:

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch022

(2) where ej is the single particle energy, nj is the occupation number, G is the pairing force constant, Ω{ = 1/2 (2i + 1 ), the pair degeneracy. The truncated basis wave functions are:

Seniority Zero State = | p j > =

(a|)

p

| >

(3)

0

w i t h 77j (p) being the normalization constant.

Seniority One State = |ρ,> =

( a | ) C+ P

m

|θ>

(4)

w i t h ρ pairs + 1 particle, again, fjj(p) is the normalization constant.

Seniority Two State = |P:>=

-=77

( a j ) 7=

ajj ( J M ) |θ> , J ^ O

P

V j CP)

V

(5)

2

w i t h ρ pairs + 2 odd particles in orbital j , !?j(p) the normalization constant. The anticommutation rules of C , C and the commutation of a , a together w i t h Wick's theorem, are repeatedly used +

+

in diagonalizing the Hamiltonian.

Reduced Transition Probability for β Decay—Β The |3-decay strength function S^ is proportional t o the square of the matrix elements of 0-operator between final and initial states. So is Β and is defined by:

B(GT;. .,)= r

| < ' , M |Tl 11, > | X - T - T ι-μ | i f

MjM M

M j

2

= -gfc |f 2lj+1 Ρ ' M M " I T

(6)

f

IJ] = Σ LOO -

(10)

II. (i)

u (ii)

III.

.

Β = ( ψ

2

( ι - φ-J

(ι)

I *c Pi 3 »-*

^ * p > - ^{'-ïf*Hf

(ii)

|*CPiJ " C q j ) ) -

*«,>(5=ϊ>,>

°(0

n

d ι>

.

(12)

8 = ^ ( 1 - ^ ^ " ° (13) V

I'CUP r

^(ψ»(*$

cp*i>,*i)),B=

(ii) [ l ^ C P i J X K q i ^ ^ l "CPi) "Cqj5> -

2

vlin

'(1-4.)

2

ι Ι ^ - Ο , Κ Π » .

ν

(14)

B = \/

ι | - C W * « , » -

°

B=

IV.

(iii)

2

k(Pi)Kqj)>rty

(i)

v

2

ίτ ΐ - g J L 1

B =

2

/ V (E±l-]f

U ( l v ) [ | ' < W x ^ > H ^ J ^ ^ , B = ( T

1

l ) « ( i - - ^ ] f

V / (

P

V* ^

2

0

J

2

(16)

V

* ( ο ^ τ ) Γ

All these expressions for Β agree with those of earlier BCS calculations [SAK64] [OLI80].

2

°

(17) [RAN72]

156

NUCLEI OFF THE LINE OF STABILITY

Applications to

8

7

9

2

Br and

9

2

1

0

Rb Precursors

2

The model calculations are carried out for

B 3

r

5

- ^ 3

K 6

r

- * 3 6

K

r

+

n

a

n

d

37

R

b

^38

S

r

"

,

>

38

S

r

+

n

transitions assuming the core with Ζ =28 and Ν = 50. The single particle energies are taken from experiments when available, otherwise from systematics. The j3-decay half life of the parent is given by: C

1

=

ESsCEiHCQg-Ej)

(18)

where

V E , ) =

, , D(g /g ) 1

n

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch022

with D = 6260 ± 60 sec., g

v

B(GT, E,)

2

v

A

2

(19)

g , are the vector and axial vector constants of γ-current. The delayed A

neutron emission probability p

n

is defined as the fraction of j3-decays to intermediate levels in the

emitter which finally leads to neutron emission. Assuming no γ-ray emission above B , p is defined n

n

as: Sg(Ej) fjCQg-E,)

Σ P„ % =

'· "„'* Ρ Β

X 100%

0

2

(20)

Sç (Ej) fCQc-Ej)

Results and Discussions The calculated half-lives (ty ) for Br and Rb isotopes are shown in Figs. 1 and 2. We also 2

show in the same figures the calculated half-lives using the BCS method [OLI80] and the experimental values. Similarly in Figs. 3 and 4, we show the delayed neutron branching ratios, p and n

compare them again with those obtained using BCS method and the experimental values. It can be concluded from these figures that the STED method gives a better overall agreement with the experimental results than the BCS method, for both ty and p . The noticeable odd-even fluctuation 2

n

in the ty values for the BCS method is not present in the STED results, which follow very closely 2

the experimental trends. The calculations for Br isotopes were repeated for different values of G(n) and were found sensitive to it. The best fit was at G(n) = 0.25, G(p) = 0.3 for both ty and p . 2

n

Preliminary analysis of the energy distributions and strengths of the configurations responsible foF the GT-beta decay indicate that this difference in the two sets of calculations is due to the fact that STED takes account of the blocking effect

while BCS ignores it completely. As a result of these

encouraging results, we are currently extending this work to include a GT-type residual interaction

22.

RAB AND SHIHAB-ELDIN

β-Delayed Neutron Emission Properties

157

Half Lives for Rb Isotopes

1

1

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch022

S ι2

- I 4

ft(sec)




2

Thus t h e e x p e r i m e n t a l v a l u e f o r t h e above m a t r i x may be o b t a i n e d . t h a t f o r t h e above t r a n s i t i o n ^ ±

It

χ ρ

We f i n d

s 0.04

is pointed out in r é f .

[B0H75] t h a t a p u r e d e f o r m e d o s c i l l a t o r

0097-6156/ 86/ 0324-0159506.00/ 0 © 1986 American Chemical Society

model,

160

NUCLEI OFF THE LINE OF STABILITY

assuming good a s y m p t o t i c quantum numbers, w o u l d y i e l d t h e v a l u e 1 f o r t h e above m a t r i x e l e m e n t . W i t h N i l s s o n wave f u n c t i o n s we o b t a i n 0 . 8 6 . The s m a l l

- -

9

r e d u c t i o n i s due t o t h e m i x i n g o f o r b i t a l s due t o t h e £«s and £ t e r m s i n t h e s i n g l e - p a r t i c l e p o t e n t i a l and a s m a l l amount o f distortions. Now, w i t h t h e a d d i t i o n o f p a i r i n g , t h e i n c r e a s i n g c o m p l e x i t y o f t h e wave f u n c t i o n s r e d u c e s the c a l c u l a t e d value o f the t r a n s i t i o n m a t r i x element t o 0 . 3 7 . According t o [B0H75] one can e x p e c t a r e d u c t i o n by a b o u t a f a c t o r o f 4 due t o p a i r i n g f o r l e v e l s c l o s e t o t h e Fermi s u r f a c e , because t h e r e d u c t i o n i s u u o r ν ν and u ρ η ρ η and ν a r e ^ Fermi s u r f a c e . T h a t we o b t a i n e d a s m a l l e r r e d u c t i o n i n 1

a

t

t

n

e

t h i s p a r t i c u l a r case i s due t o t h e f a c t t h a t t h e e n t e r i n g p a i r i n g f a c t o r s 1 2 l a r g e r than

An a d d i t i o n a l

r e d u c t i o n o f +

i n t h e model

oped by [KRU84] comes a b o u t f r o m t h e a d d i t i o n o f a r e s i d u a l

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch023

s p e c i f i c t o GT d e c a y , VQ-|. = : β

1 -

·β

1 +

:,

i n t h e RPA a p p r o x i m a t i o n . With t h i s m a t r i x element i s reduced t o

±

2

treated

i n c l u d e d , t h e square o f

the

= 0.09

The V -p r e s i d u a l G

devel­

interaction,

t o t h e H a m i l t o n i a n , w h i c h was

interaction

are

interaction

i s introduced t o account f o r the

retardation

o f l o w - e n e r g y GT decay r a t e s , and as we saw i n o u r example a b o v e , t h e s t r e n g t h was r e d u c e d by a b o u t a f a c t o r o f f o u r . The c a l c u l a t e d s t r e n g t h i s s t i l l a b o u t a f a c t o r o f 2 l a r g e r than the observed s t r e n g t h . The c a l c u l a t e d s t r e n g t h c o u l d be f u r t h e r r e d u c e d by i n c r e a s i n g f u r t h e r t h e s t r e n g t h χ o f t h e V* j G

i n t e r a c t i o n , w h i c h i s s e t a t χ = 23/A MeV by [KRU84] as i s a l s o done by most other investigators. However, t h e s t r e n g t h χ i s d e t e r m i n e d by t h e r e q u i r e m e n t t h a t t h e c a l c u l a t e d p o s i t i o n o f t h e g i a n t Gamow-Teller resonance agrees w i t h the experimental r e s u l t s . T h u s , t h e mechanism b e h i n d t h e r e m a i n i n g f a c t o r - o f two d i s c r e p a n c y between t h e e x p e r i m e n t a l and c a l c u l a t e d s t r e n g t h i s t h o u g h t t o be o f a d i f f e r e n t o r i g i n . Two mechanisms t h a t a r e b e i n g i n v e s t i g a t e d a r e c o u p l i n g s t o 2p2h s t a t e s [BER82] and t h e Δ ( 1 2 3 2 ) i s o b a r [ B 0 H 8 1 ] . To a c c o u n t f o r t h e m i s s i n g s t r e n g t h i n h a l f - l i f e c a l c u l a t i o n s we d i v i d e t h e c a l c u l a t e d s t r e n g t h by 2 f o r such a p p l i c a t i o n s . The c a l c u l a t e d s t r e n g t h s shown i n t h i s c o n t r i b u t i o n a r e n o t d i v i d e d by 2 however. We have added some new f e a t u r e s t o t h e model d e s c r i b e d a b o v e , w h i c h was d e v e l o p e d by [KRU84]. I n p a r t i c u l a r we have o b s e r v e d t h a t t h e p e r t u r b a t i o n e x p r e s s i o n s f o r t h e Δν = 0 t r a n s i t i o n s f o r odd-mass and odd n u c l e i used by [KRU84] ( e q s . ( 4 3 ) - ( 4 7 ) i n t h a t p a p e r ) b r e a k down o c c a s i o n a l l y . Similar e x p r e s s i o n s have a l s o been used e a r l i e r by [HAL67] and [RAN73]. When t h e e x p r e s s i o n s b r e a k down, a s i n g l e Δν = 0 t r a n s i t i o n may have a s t r e n g t h t h a t i s many t i m e s t h e sum r u l e S" - s t = 3 ( N - Z ) f o r t h e Δν = 2 t r a n s i t i o n s . However, Ρ Ρ t h e e q u a t i o n s ( 4 3 ) - ( 4 7 ) o f r é f . [KRU84] can be m o d i f i e d somewhat t o remove this difficulty. The e q u a t i o n s f o r t h e Δν = 0 s t r e n g t h c o n t a i n sums o v e r t e r m s w i t h a m p l i t u d e s A (nu>) = l / ( E " " )· q u a n t i t i e s u> a r e t h e r o o t s o f t h e RPA e q u a t i o n s and a r e " c l o s e " t o t h e a s y m p t o t e s E + E but not E

p

p

ω

T

n

e

n

p

n >

c l o s e enough t o cause any s i n g u l a r i t y i n t h e Δν = 2 t r a n s i t i o n s t r e n g t h s . By " a c c i d e n t " t h e y may be so c l o s e t o t h e q u a n t i t y E - E t h a t t h e p e r t u r b a t i o n p

e x p a n s i o n b r e a k s down and a s i n g u l a r i t y o c c u r s .

R

T h i s s i n g u l a r i t y can be

23.

Calculations of β-Strength Functions

KRATZ ET AL.

161

removed by i n t r o d u c i n g a w i d t h d , and m o v i n g t h e p o l e Ε plane. T h u s , we r e p l a c e Α ( η ω ) =

Ε i n t o t h e complex η Λ

p

ρ

by

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch023

V ™

0

2 [ E

=

p

-

id -

+

id

"]

=

(E,

E

- u>) + d 2

n

2

I n f i g s , l a - l b we show t h e r e s u l t s f o r t h e o r i g i n a l model ( a ) w h i c h e x h i b i t s a p r o n o u n c e d s i n g u l a r i t y and f o r d = 0 . 1 MeV and d = 1.0 MeV ( b ) . In f i g . l b we have i n d i c a t e d t h e d = 0 . 1 MeV r e s u l t s w i t h dashed l i n e s . We see t h a t d i f f e r e n c e s between t h e d = 0 . 1 MeV and d = 1.0 MeV r e s u l t s a r e m i n o r and t h a t t h e r e s u l t s t h e r e f o r e a r e i n s e n s i t i v e t o t h e w i d t h d , as s h o u l d b e . We have s e l e c t e d d = 0 . 1 MeV f o r o u r c a l c u l a t i o n s . 1

*

·

1

1

1

1

i

·

·

1

Pm+r :200

.100

I

•

•

•

ι

Ι

ι

ι

ι

i

l

10

l

ENERGY CIWV) ENERGY (MeV) Fig. lb Fig. la I n f i g . 2 we e x h i b i t some r e s u l t s f o r a sequence o f Rb n u c l e i w i t h t h i s modification included. We have a l s o c o r r e c t e d an e r r o r t h a t o c c u r e d i n an e a r l i e r v e r s i o n o f t h e c o m p u t e r code f o r some Δν = 0 t r a n s i t i o n s i n t h e s p h e r ­ i c a l case. The e r r o r was u s u a l l y s m a l l . Compared t o [KRU84] f i g . 2 c o n t a i n s o n l y t h e s e two m o d i f i c a t i o n s and t h e d i f f e r e n c e s r e l a t i v e t o t h e e a r l i e r r e s u l t s are s m a l l . However t h e i n t r o d u c t i o n o f t h e w i d t h d i s v e r y i m p o r t a n t i n some o t h e r cases as can be seen i n f i g . 1 . The c a l c u l a t e d r e s u l t s a r e d i s c u s s e d e x t e n s i v e l y i n [ K R U 8 4 ] , t o w h i c h we r e f e r f o r a more c o m p l e t e d i s c u s s i o n . H e r e , l e t us j u s t n o t e t h a t f o r t h e t o p f o u r s p e c t r a i n f i g . 2 we used t h e p a r a m e t e r s e t "A = 1 0 0 " and f o r t h e l o w e r f o u r f i g u r e s we used t h e p a r a m e t e r s e t "N = 6 0 " . The Ν = 60 s e t r e p r o d u c e s b e s t t h e l a r g e i n c r e a s e i n s t r e n g t h o f t h e l o w - e n e r g y peak t h a t i s seen e x p e r i ­ mentally in Rb r e l a t i v e to Rb. The Ν = 60 s i n g l e - p a r t i c l e p a r a m e t e r s e t was a d j u s t e d t o r e p r o d u c e r e s u l t s i n t h e v i c i n i t y o f t h e Ν = 56 s u b s h e l l [ A Z U 7 8 ] , so i t i s t o be e x p e c t e d t h a t t h i s s e t g i v e s t h e b e t t e r d e s c r i p t i o n o f some f e a t u r e s i n t h i s r e g i o n . One m a j o r d i f f i c u l t y i n t h e N i l s s o n model i s t h e d e t e r m i n a t i o n o f t h e s i n g l e - p a r t i c l e p a r a m e t e r s κ and μ f o r v a r i o u s r e g i o n s o f n u c l e i . Usually t h e s e p a r a m e t e r s a r e d e t e r m i n e d by a d j u s t i n g c a l c u l a t e d s i n g l e - p a r t i c l e l e v e l s t o experimental data. S i n c e κ and μ can v a r y r a t h e r u n p r e d i c t a b l y f r o m r e g i o n t o r e g i o n , t h e model i s t h e r e f o r e somewhat u n s u i t a b l e f o r e x t r a p o l a t i o n s t o unknown r e g i o n s o f n u c l e i . W i t h t h e aim o f b e i n g a b l e t o c a l c u l a t e p r o p e r t i e s f o r such n u c l e i more r e l i a b l y we a r e now d e v e l o p i n g t h e code t o a c c e p t wave § 5

9 3

162

NUCLEI OFF THE LINE OF STABILITY

j

10h

— -

5

5 -

\n_is.. ,

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch023

»Ί

,

.

.

:

0 0

i

1

1

1

A

Ππ 1

1

• • • ΓΤ

5.0

so x

t

S

R2 5

S 0.0

InJLrJ 0 0

of nuclei. See f o r example t h e s t u d i e s [ M 0 L 8 1 a ] , [M0L81b] and [BEN84] o f t h e folded-Yukawa p o t e n t i a l , which covers the e n t i r e p e r i o d i c system. In t h i s i n i t i a l s t u d y we s h a l l use Woods-Saxon wave f u n c t i o n s , m a i n l y because such a

164

NUCLEI OFF THE LINE OF STABILITY

code has been made a v a i l a b l e t o us by [NAZ84] i n a f o r m t h a t r u n s on VAX and NORSK DATA c o m p u t e r s . The f o l d e d - Y u k a w a code c u r r e n t l y r u n s o n l y on CDC computers. The Woods-Saxon model i s d e s c r i b e d i n [DUD82]. F i g u r e 3 shows β - s t r e n g t h f u n c t i o n s c a l c u l a t e d w i t h Woods-Saxon wave f u n c t i o n s f o r a sequence o f Rb n u c l e i . Above a l l b u t t h e l a s t o f t h e c a l c u ­ l a t e d s t r e n g t h f u n c t i o n s , w h i c h have t h e words BETA STRENGTH a l o n g t h e v e r t i ­ c a l a x i s , t h e r e a r e p l o t s o f e x p e r i m e n t a l r e s u l t s f r o m [KRA83] and [ K R A 8 1 ] . The e x p e r i m e n t a l r e s u l t s have t h e l a b e l B ' ( G T ) a l o n g t h e v e r t i c a l a x i s . The r e s u l t s w i t h Woods-Saxon w a v e - f u n c t i o n s a r e s i m i l a r t o t h e r e s u l t s o b t a i n e d w i t h t h e o s c i l l a t o r m o d e l , and a l s o a g r e e f a i r l y w e l l w i t h e x p e r i m e n t . Here we s h a l l j u s t comment on two a s p e c t s o f t h e r e s u l t s . F i r s t , the l a r g e i n c r e a s e i n s t r e n g t h seen e x p e r i m e n t a l l y when g o i n g f r o m R b t o R b i s s l i g h t l y l e s s w e l l r e p r o d u c e d w i t h t h e Woods-Saxon w a v e - f u n c t i o n s , t h a n w i t h t h e N i l s s o n wave f u n c t i o n s w i t h t h e Ν = 60 s e t . However, t h e s e t Ν = 60 was o p t i m i z e d t o r e p r o d u c e t h e Ν = 56 s u b s h e l l c o n d i t i o n s . The Woods-Saxon c a l c u ­ l a t i o n was p e r f o r m e d w i t h a " u n i v e r s a l parameter s e t [DUD82], which should i n g e n e r a l be more r e l i a b l e f o r e x t r a p o l a t i o n s f a r f r o m s t a b i l i t y . Second, f o r t h e d e f o r m e d R b and R b r e s u l t s t h e r e i s v e r y l i t t l e s t r e n g t h a t low e n e r g y , i n c o n t r a s t t o t h e e x p e r i m e n t a l s i t u a t i o n and t h e m o d i f i e d o s c i l l a t o r results. However, t h e Woods-Saxon c a l c u l a t i o n was r u n f o r a d e f o r m a t i o n t h a t was somewhat s m a l l e r t h a n t h e a p p r o p r i a t e v a l u e f o r R b and R b . Due t o c i r c u m s t a n c e s beyond o u r c o n t r o l , we have o n l y been a b l e t o p r e ­ s e n t v e r y few i n i t i a l r e s u l t s w i t h t h e Woods-Saxon wave f u n c t i o n s h e r e . We hope, h o w e v e r , t o e x p l o r e t h e model more f u l l y i n t h e n e a r f u t u r e , i n p a r t i c u ­ l a r t o r u n R b and R b w i t h a more a p p r o p r i a t e v a l u e o f β and t o e x p l o r e 9 3

9 5

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch023

1 1

9 7

9 9

9 7

9 7

9 9

9 9

2

a d d i t i o n a l regions o f n u c l e i f a r from s t a b i l i t y , f o r which a p p l i c a t i o n s the Woods-Saxon s i n g l e - p a r t i c l e model s h o u l d be advantageous compared t o t h e Nilsson model, which i s less r e l i a b l e f o r e x t r a p o l a t i o n s . Acknowledgments We a r e g r a t e f u l t o J . Dudek and W. N a z a r e w i c z Woods-Saxon code a v a i l a b l e t o u s .

f o r making a copy o f

their

References [AZU78] R.E. Azuma, G. L. Borchert, L.C. Carraz, P.G. Hansen, B. Jonson, S. Mattson, O.B. Nielsen, G. Nyman, I. Ragnarsson and H.L. Ravn, Phys. Lett. 80B 4 (1978). [BEN84] R. Bengtsson, P. Möller, and J.R. Nix, Phys. Scr. 29 402 (1984). [BER82] G.F. Bertsch, and I. Hamamoto, Phys. Rev. C26 1323 (1982). [BOH75] A. Bohr, and B.R. Mottelson, Nuclear Structure, vol. II (Benjamin, New York, 1975) pp. 306, 307. [BOH81] A. Bohr and B. R. Mottelson, Phys. Lett. 100B 10 (1981). [DUD82] J. Dudek, Z. Szymanski, T. Werner, A. Faessler, and C. Lima, Phys. Rev. C26 1712 (1982). [HAL67] J.A. Halbleib, S r . , and R.A. Sorensen, Nucl. Phys. A98 542 (1967). [KRA81] K.L. Kratz, H. Ohm, A. Schröder, H. Gabelmann, W. Ziegert, H. V. Klapdor, J . Metzinger, T. Oda, B. Pfeiffer, G. Jung, L. Alquist and G.I. Crawford, Proc. 4th Int. Conf. on nuclei far from s t a b i l i t y , Helsinger, 1981 (CERN 82-09, Geneva, 1981) p. 317. [KRA83] K.L. Kratz, Priv. comm. (1983). [KRU84] J . Krumlinde, and P. Möller, Nucl. Phys. A417 419 (1984). [MOL81a]P. Möller, and J.R. Nix, Nucl. Phys. A361 117 (1981). [MOL81b]P. Möller, and J . R. Nix, At. Data Nucl. Data Tables 26 165 (1981). [NAZ84] W. Nazarewicz, and J . Dudek, Priv. com. (1984). [RAN73] J . Randrup, Nucl. Phys. A207 209 (1973). RECEIVED August 20, 1986

24 Identifying Nilsson States in A β-Decay Properties 1

1

1

≡100 Nuclei by Investigating Gross 1

2

2

K.-L. Kratz , H. Gabelmann, W. Ziegert , V. Harms , J. Krumlinde , and P. Möller 1

Institut für Kernchemie, Universität Mainz, D-6500 Mainz, Federal Republic of Germany Department of Mathematical Physics, Lund Institute of Technology, Lund University, Box 118, S-22100 Lund, Sweden

2

Since most nuclei in the region of deformation at A~ 100 can only be produced with rather low yields which makes detailed spectroscopic studies d i f f i c u l t , we have examined p o s s i b i l i t i e s of extracting nuclear structure information from easily measurable gross β-decay properties. As examples, comparisons of recent experimental results on Rb-Y and Rb-Y to RPA shell model calculations using Nilsson-model wave functions are presented and discussed.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch024

99

101

The existence of strong deformation for neutron-rich A~100 nuclei was already extablished 15 years ago [CHE70], and data continue to collect on this region up to now. They revealed a rather complex picture indicating rapid nuclear shape changes and shape coexistence [BEN84,MEY85] which can be related to the occurrance of several (quasi-) spherical and deformed subshells for both Ζ and Ν (see Fig.1). While in the past years spec­ troscopic studies were mainly restricted to even-even nuclei, more recent investigations have turned towards odd-mass nuclei which allowed f i r s t conclusions on individual Nilsson orbitals as well as the determination of the Nilsson Hamiltonian in theA~100mass region (see e.g. [SIS84]). Usually, characterization of nuclear structures in transitional nuclei requires rather sophisticated spectroscopic investigations, e.g. measure­ ments of level life-times, γ - t r a n s i t i o n multipolarities and magnetic mo­ ments. Unfortunately, most of the nuclei of interest in the A-100 mass region are fission products far from β - s t a b i l i t y which - at present - can only be produced with rather low yields. This makes detailed spectroscopic studies very time-consuming, and in a number of cases even impossible. Therefore, we have examined p o s s i b i l i t i e s of determining shape transitions and Nilsson states in very-neutron-rich nuclei via correlated changes in easily measurable gross β-decay properties, such as the h a l f - l i f e (T1/2), the delayed neutron emission probability ( P ) , or the gross β-brancning pattern in terms of the β-strength function (Sg). To be more specific, we thoroughly compare existing experimental data on these quantities with shell model [KRU84] expectations for different nuclear structures, and from agreement, respectively disagreement between measurements and predictions information on Nilsson parameters (χ, μ, odd-particle states) and deformation is deduced. n

The trigger for this attempt was the observation of strong variations in the shape of Sg of neutron-rich odd-mass Rb isotopes [KRA81,83,84] which could be related to the spherical N=56 subshell closure and to the sudden onset of strong deformation at the deformed N=60 shell gap (see F i g . l ) . In 0097-6156/86/ 0324-0165506.00/ 0 © 1986 American Chemical Society

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch024

166

NUCLEI OFF THE LINE OF STABILITY

F i g . l . S i n g l e - p a r t i c l e l e v e l s f o r p r o t o n s and n e u t r o n s i n t h e A=100 r e g i o n f o r t h e m o d i f i e d o s c i l l a t o r p o t e n t i a l o f t h e N i l s s o n model as a f u n c t i o n o f p r o l a t e d e f o r m a t i o n . t h e case o f t h e N=60 i s o t o n e R b , t h e shape o f S$ l e a d t o t h e n [ 4 3 1 3 / 2 ] assignment f o r the ground s t a t e ( g . s . ) o f t h i s n u c l e u s , which c o n s t i t u t e d some o f t h e f i r s t e v i d e n c e f o r e s t a b l i s h i n g d e f o r m a t i o n i n medium-mass o d d n u c l e o n i s o t o p e s . To g i v e an example f o r t h e p o s s i b l e s e n s i t i v i t y o f s h e l l s t r u c t u r e on g r o s s β - d e c a y p r o p e r t i e s , i n F i g . 2 t h e s i t u a t i o n f o r 9 7 R is shown i n a s i m p l i f i e d , s c h e m a t i c way. As i s d i s c u s s e d i n some d e t a i l in [ K R A 8 3 , 8 4 ] , d e p e n d i n g on t h e v a l e n c e - p r o t o n N i l s s o n o r b i t a l , q u i t e d i f f e r e n t shapes o f 5β w i l l o c c u r . W i t h t h e π [ 3 0 1 3 / 2 ] c o n f i g u r a t i o n , Sg w i l l have a d i s t r i b u t i o n s i m i l a r t o t h a t shown i n t h e u p p e r p a r t o f F i g . 2 , w i t h t h e l o w e s t G a m o w - T e l l e r (GT) t r a n s i t i o n ( v g-//2 - * - n g g / 2 ) a t medium e x c i t a t i o n e n e r g y . T h i s w i l l r e s u l t i n a ' l o n g ' Τ χ / 2 and a ' h i g h ' P - v a l u e . For t h e c o n n e c t i o n o f b o t h q u a n t i t i e s t o S R , see [ K R A 8 4 ] . On t h e o t h e r h a n d , when assuming t h e odd p r o t o n in the [431 3 / 2 ] N i l s s o n o r b i t a l , p a r t o f the 97/2-* 9?/2 strength w i l l be s h i f t e d down t o ( n e a r ) t h e g . s . o f Sr, r e s u l t i n g i n an S$ d i s t r i b u t i o n s i m i l a r t o t h a t i n t h e l o w e r p a r t o f F i g . 2 . T h i s w i l l g i v e a ' s h o r t ' Τχη and a ' l o w ' P . I t i s r e a s o n a b l e t o assume t h a t such d i f f e r e n c e s i n β-decay p r o p e r t i e s w i l l o c c u r a l s o f o r o t h e r o d d p a r t i c l e n u c l e i i n t h e A-100 mass r e g i o n , t h u s p r o v i d i n g a new and s i m p l e method f o r an i d e n t i f i c a t i o n o f N i l s s o n s t a t e s . 9 7

d

n

ν

π

9 7

n

MOT [ 1

Fig. 2. Schematic m o d e l - S ^ ' s f o r t h e decay o f a f a r - u n s t a b l e n u c l e u s , as e . g . R b , and t h e i r i n f l u e n c e on Τ χ / 2 and P . F o r d i s c u s s i o n , see t e x t . 9 7

n

3

2-10

T

A good example f o r t e s t i n g t h e a p p l i c a b i l i t y o f o u r approach i s t h e β-decay o f t h e o d d - p r o t o n (Z=37) n u c l e u s R b t o t h e o d d - n e u t r o n (N=61) daughter S r . As was shown i n Î P F E 8 4 ] , even f r o m a r a t h e r t i m e - c o n s u m i n g spectroscopic i n v e s t i g a t i o n of 99R decay a t OSTIS, r e s u l t i n g i n g . s . band properties considerably improved over those reported in an earlier 9 9

9 9

d

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch024

24.

167

Identifying Nilsson States

KRATZ ET AL.

p u b l i c a t i o n [W0H83], an unambiguous N=61 N i l s s o n o r b i t a l a s s i g n m e n t was n o t possible since both calculated (gK"9R)/Qo curves f o r ν [ 4 1 1 3 / 2 ] and v[541 3 / 2 ] overlapped w i t h the experimental value f o r deformations of ε>0.3. However, we were able to demonstrate^ t h a t , when including β - i n t e n s i t y arguments f o r t h e decays o f m o t h e r and d a u g h t e r n u c l e u s ( i n p a r t i c u l a r l o g f t - v a l u e s f o r t h e Rb-^Sr and S r - * Y g . s . t o g . s . t r a n s i t i o n s ) , and w i t h a d d i t i o n a l c o m p a r i s o n t o s h e l l model p r e d i c t i o n s u s i n a t h e N=60 N i l s s o n p a r a m e t e r s e t [KRU84], t h e v [ 5 4 1 3 / 2 ] o r b i t a l f o r t h e ^ S r g r o u n d band c o u l d be r u l e d o u t . I n t h i s w a y , a l s o two e x c i t e d r o t a t i o n a l bands built on the v[413 5/2] and v [ 4 2 2 3 / 2 ] Nilsson configurations were i d e n t i f i e d (see F i g . l o f [ P F E 8 4 ] ) . I t s h o u l d be p o i n t e d o u t i n t h i s c o n t e x t , t h a t good agreement between e x p e r i m e n t a l e n e r g i e s and l o g f t - v a l u e s f o r t h e d i f f e r e n t band heads w i t h s h e l l model p r e d i c t i o n s can be o b t a i n e d , p r o v i d e d an a p p r o p r i a t e c h o i c e o f N i l s s o n p a r a m e t e r s and d e f o r m a t i o n i s made. As i s d e m o n s t r a t e d i n [KRU84] f o r n e u t r o n - r i c h Rb i s o t o p e s and as w i l l be more g e n e r a l l y discussed f o r the A = 80-110 r e g i o n i n [KRA85], N i l s s o n parameters fitting experimental data o f spherical nuclei near s t a b i l i t y , l i k e the s t a n d a r d A=100 s e t o f [ L A R 7 6 ] , t e n d t o become i n a p p r o p r i a t e f o r f a r - u n s t a b l e deformed n u c l e i . T h i s may, f o r e x a m p l e , be t h e r e a s o n f o r some i n c o r r e c t p r o t o n o r b i t a l a s s i g n m e n t s t o band heads i n Y [W0H85] w h i c h were based on BCS+pairing p r e d i c t i o n s using N i l s s o n parameters a d j u s t e d t o s i n g l e - p a r t i c l e levels of near-stable Y isotopes. 9 9

I n p r i n c i p l e , t h e same c o n c l u s i o n on t h e N i l s s o n o r b i t a l o f t h e Sr g . s . as o b t a i n e d by t h e above m e n t i o n e d γ - s p e c t r o s c o p i c work can a l r e a d y be drawn from a comparison of easily measurable g r o s s β-decay features (requiring ~ 5 h m e a s u r i n g t i m e f o r β- and n - m u l t i s c a l i n g , compared t o ~ 3 weeks f o r γ - s p e c t r o s c o p y ) t o p r e d i c t i o n s o f o u r RPA s h e l l m o d e l . I n t h e 9 9

Nilsson states 37th7T

61st ν

[3013/ ] - [413 s/ ] 2

2

[ 3 0 1 -

[541 /2] 3

Shell model

TVzlms]

©

190

39

205

66

420

59

[312 3/2] - [404*2]

P

n

[%]

Shell model [440 >2] - [411 3/2] 1

[431 3/ ] - [411 3/ ] 2

2

®

[431 4] - [532 /2] 3

5

I 59*1 I

I

20 *

21

Energy [MeV]

Fig.3. Comparison o f t h e e x p e r i m e n t a l d i s t r i b u t i o n o f R b decay w i t h RPA s h e l l model p r e d i c t i o n s ( m i d d l e p a r t ) i n v o l v i n g d i f f e r e n t o d d - p a r t i c l e N i l s s o n s t a t e s l y i n g near t h e Fermi l e v e l ( l e f t p a r t ) . I n t h e r i g h t p a r t , t h e c o r r e s p o n d i n g Λ\ιι and P v a l u e s a r e l i s t e d . 9 9

n

168

NUCLEI OFF THE LINE OF STABILITY

middle p a r t o f F i g . 3 , the β - s t r e n g t h p a t t e r n f o r R b decay o b s e r v e d i n e x p e r i m e n t i s compared t o ( s c h e m a t i c a l ) Sg p r e d i c t i o n s i n v o l v i n g t h e o d d p a r t i c l e N i l s s o n s t a t e s shown i n t h e l e f t p a r t o f t h e f i g u r e . Two d i f f e r e n t types of strength distributions are c a l c u l a t e d : (a) w i t h o u t low-lying G T - s t r e n g t h , and ( b ) w i t h g . s . t o ( n e a r ) g . s . G T - t r a n s i t i o n s . I n t h e r i g h t p a r t o f F i g . 3 , t h e c o r r e s p o n d i n g m o d e l - Τ χ / 2 and P a r e l i s t e d t o g e t h e r w i t h o u r e x p e r i m e n t a l v a l u e s . C l e a r l y , f r o m b o t h t h e shape o f as w e l l as f r o m Τ χ / 2 and P , t h e N i l s s o n o r b i t a l c o m b i n a t i o n s f o r t y p e ( a ) decay p a t t e r n s can be e x c l u d e d . F u r t h e r m o r e , f o r t y p e ( b ) s t r e n g t h f u n c t i o n s t h e n [ 4 4 0 1 / 2 ] - v [ 4 1 1 3 / 2 ] c o m b i n a t i o n can be r u l e d o u t - a l t h o u g h h a v i n g t h e c o r r e c t S$ shape - because t h e e s t i m a t e d P v a l u e i s a f a c t o r 2 . 5 t o o l o w . W i t h t h i s , t h e [ 4 3 1 3 / 2 ] o r b i t a l can be a s s i g n e d t o t h e 3 7 t h p r o t o n i n Rb, while for t h e 6 1 s t n e u t r o n no d i s t i n c t i o n between t h e N i l s s o n s t a t e s [ 4 1 1 3 / 2 ] and [532 5 / 2 ] i s p o s s i b l e f r o m t h e g r o s s β-decay p r o p e r t i e s o f t h i s i s o t o p e . However, a s i m i l a r c o m p a r i s o n o f t h e o r e t i c a l Τ χ / 2 and P w i t h e x p e r i m e n t a l data f o r S r decay (see T a b . l ) a l l o w s t h e unambiguous a s s i g n m e n t o f t h e v[411 3 / 2 ] o r b i t a l t o the g . s . of S r and, moreover, c o n f i r m s the e a r l i e r assignment o f the π[422 5 / 2 ] o r b i t a l f o r the Y g r o u n d band [M0N82]. 9 9

n

n

n

9 9

n

9 9

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch024

9 9

9 9

Tab.l. Comparison o f e x p e r i m e n t a l T l / 2 and P f o r S r t o s h e l l model predictions f o r d i f f e r e n t odd-par­ t i c l e N i l s s o n o r b i t a l s near the Fermi l e v e l

N i l s s o n states 61st ν 39th π

L

l / 2 [ms]

9 9

n

413 411 411 541 532 [411

550 431 3/2 5/2 177 431 3/2 3/2 190 301 3/2 3/2 1065 431 3/2 3/2 1172 422 5/2 5/2 3/2] - [422 5/2] 275 Experiments 285-15

0.29 0.03 0.03 0.34 1.21 0.20 0.19*0.10 1

The second example i s r e l a t e d t o t h e p o s s i b l e i d e n t i f i c a t i o n o f N i l s s o n s t a t e s i n o d d - n u c l e o n A=101 i s o t o p e s . I n t h e case o f ^ R b , t h e 3 7 t h p r o t o n may occupy t h e [ 3 0 1 3 / 2 ] , [ 4 3 1 3 / 2 ] o r [312 3 / 2 1 N i l s s o n o r b i t a l , and s i m i l a r l y t h e 6 3 r d n e u t r o n i n t h e d a u g h t e r n u c l e u s ^ S r may be i n d i f f e r e n t s t a t e s n e a r t h e Fermi s u r f a c e (see F i g . l ) . The c o r r e s p o n d i n g o d d - p a r t i c l e N i l s s o n o r b i t a l c o m b i n a t i o n s may a g a i n y i e l d d i f f e r e n t S3 d i s t r i b u t i o n s a n d , consequently, different Τχ/2 and P (see F i g . 4 ) . From a v e r y recent e x p e r i m e n t p e r f o r m e d a t CERN-ISOLDE, a r a t h e r s h o r t β-decay h a l f - l i f e o f T i / 2 = ( 3 2 ± 5 ) ms and a r e l a t i v e l y low P - v a l u e o f (24+5) % were o b t a i n e d . Com­ p a r i s o n o f t h e s e ( p r e l i m i n a r y ) r e s u l t s w i t h o u r s h e l l model predictions favours an S$ of type (b) and thus suggests the τι[431 3 / 2 ] g.s. c o n f i g u r a t i o n f o r the precursor ^ R b , b u t i t c a n n o t d e t e r m i n e t h e N=63 Nilsson assignment f o r S r . However, as i n t h e A=99 c a s e , t h i s a m b i g u i t y can be removed by c o n s i d e r i n g g r o s s β-decay p r o p e r t i e s o f t h e l a t t e r n u c l e u s to levels in * Y (see F i g . 5 ) . A p a r t f r o m an o l d e r measurement a t ISOLDE w h i c h y i e l d e d a Τχ/2 o f a b o u t 180 ms, t h e o n l y o t h e r i n f o r m a t i o n on Sr decay comes f r o m r e c e n t s t u d i e s a t TRISTAN. Wohn e t a l . [W0H83] have e s t a b l i s h e d two r o t a t i o n a l bands i n Y , and Reeder e t a l . [REE85] have measured Τ χ / 2 and P f o r t h e Sr p r e c u r s o r . As can be seen f r o m F i g . 5 , a c o m p a r i s o n o f t h e s e e x p e r i m e n t a l d a t a w i t h o u r s h e l l model p r e d i c t i o n s f o r d i f f e r e n t N i l s s o n o r b i t a l c o m b i n a t i o n s f o r t h e 6 3 r d n e u t r o n and t h e 3 9 t h proton suggests the [411 3 / 2 ] assignment f o r the S r g . s . and c o n f i r m s t h e n[422 5 / 2 ] c o n f i g u r a t i o n f o r the Y g r o u n d band [W0H83]. F u r t h e r m o r e , d e f o r m a t i o n s o f ε = 0 . 3 5 ΐ 0 . 0 3 can be deduced f o r b o t h i s o t o p e s . n

n

1 0 1

1 0

1 0 1

1 0 1

n

1 0 1

1 0 1

24.

KRATZ ET AL.

169

Identifying NUsson States

Nilsson states 37th7r

63rdv

^

[3013/i ] - [413 5/ ]

1

[31234] - [411 3/]

^

2

2

[43134]- [532 54]

f

[4313/2] - [411 3/]

~

2

I Shell model |

®^

TMms]

W

®

\

219

100

46

29

48

28

a

Exp.: [32^51 1

1

1

θ"

5 Energy [MeV]

10

[%]

n

83

1 Shell model |

"ou CO

P

108

Γ24±Π

F i g . 4 . S h e l l model p r e d i c t i o n s o f Sg d i s t r i b u t i o n s o f Rb decay ( m i d d l e p a r t ) i n v o l v i n g d i f f e r e n t o d d - p a r t i c l e N i l s s o n o r b i t a l s ( l e f t p a r t ) . In the r i g h t p a r t , the corresponding m o d e l - Τ χ / 2 and P a r e l i s t e d and compared t o e x p e r i m e n t a l d a t a . 1 U i

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch024

n

Nilsson states 39th π

TV [ms]

Shell model

63 rd ν

2

[4313/2] - [4135/2]

232

[43134] - [541 4] 3

[301 34] - [532 54] [422 54] - [532 54]

ι*

P

[%]

n

1.6

Shell model

338

1.85

®

546

4.3

473

3.8

Shell model [422 4 ] - [4113/ ] 5

2

©

160

10

1115/180 I I 2.5±0.3 |

Energy [MeV]

F i g . 5. S h e l l model p r e d i c t i o n s o f Sg d i s t r i b u t i o n s o f 1 0 1 decay ( m i d d l e p a r t ) i n v o l v i n g d i f f e r e n t o d d - p a r t i c l e N i l s s o n s t a t e s n e a r t h e Fermi s u r f a c e ( l e f t p a r t ) . I n t h e r i g h t p a r t , t h e c o r r e s p o n d i n g m o d e l - Τ χ / 2 and P a r e compared t o e x i s t i n g experimental data.

S r

n

So f a r , we have c o n s i d e r e d β-decay m o t h e r - d a u g h t e r p a i r s w i t h ( a l m o s t ) i d e n t i c a l g . s . d e f o r m a t i o n s , s i n c e o u r s h e l l model i m p l i c i t l y c o n t a i n s t h i s c o n s t r a i n t [KRU84]. C o n s e q u e n t l y , i n case o f d i f f e r e n t g . s . d e f o r m a t i o n s f o r m o t h e r and d a u g h t e r , o r i n case o f shape c o e x i s t e n c e , o u r method i s l e s s conclusive. Nevertheless, by c a l c u l a t i n g Sp w i t h b o t h d e f o r m a t i o n s and t a k i n g i n a sense t h e ' a v e r a g e ' o f b o t h p r e d i c t i o n s , we can a t l e a s t deduce some i n f o r m a t i o n on t h e e f f e c t i v e structure p r o p e r t i e s o f such n u c l e i . F o l l o w i n g t h i s l i n e , we c a n , f o r e x a m p l e , d e m o n s t r a t e t h a t t h e g e n e r a l shape o f S$ as w e l l as Τ χ / 2 and P o f ^ R b ]y u n d e r s t o o d when assuming a g.s. deformation of ε » 0 . 3 f o r t h e p r e c u r s o r and ε < 0 . 2 f o r t h e g . s . o f t h e d a u g h t e r . Moreover, i n o r d e r t o reproduce the magnitude o f the e x p e r i m e n t a l S(3, we have t o assume a change i n d e f o r m a t i o n t o ε ^ 0 . 3 f o r l e v e l s above 0 . 5 MeV i n S r . This observation is c o n s i s t e n t w i t h the i n t e r p r e t a t i o n of n

9 7

c

a

n

o n

D e

170

NUCLEI OFF T H E LINE OF STABILITY

shape c o e x i s t e n c e i n t h i s N=59 i s o t o n e [PFE81,KRA83,MEY85] and d e t e r m i n e s t h e g . s . c o n f i g u r a t i o n o f ^Sr t o be [ 4 1 1 3 / 2 ] , i n c o n t r a s t t o o u r e a r l i e r assignment o f J = l / 2 [PFE81]. In summary, we have d e m o n s t r a t e d that the comparison o f present generation shell model predictions for very-neutron-rich odd-nucleon i s o t o p e s i n t h e A - 100 r e g i o n w i t h e x p e r i m e n t a l gross β-decay p r o p e r t i e s may serve to identify, within limits, nuclear shape changes and Nilsson parameters, and t o d e t e r m i n e n u c l e a r d e f o r m a t i o n . However, in order to deduce r e l i a b l e i n f o r m a t i o n c a r e must be e x c e r c i s e d when s e l e c t i n g the s i n g l e - p a r t i c l e p a r a m e t e r s i n t h e models used i n t h e c a l c u l a t i o n o f β-decay p r o p e r t i e s . W i t h t h i s , t h e o r e t i c a l e s t i m a t e s o f Τ χ / 2 and decay p a t t e r n s may s e r v e as a v a l u a b l e g u i d e t o t h e s e l e c t i o n o f e x p e r i m e n t s f o r i n v e s t i g a t i n g e x o t i c i s o t o p e s o f unknown p r o p e r t i e s , and - more g e n e r a l l y - may r e s u l t i n more r e l i a b l e e x t r a p o l a t i o n s up t o t h e n e u t r o n d r i p l i n e . For e x a m p l e , w i t h r e g a r d t o a s t r o p h y s i c a l a p p l i c a t i o n , o u r s h e l l model p r e d i c t i o n s o f Τ χ / 2 , b e i n g on t h e average a f a c t o r o f two l o n g e r t h a n t h o s e e s t i m a t e d by K l a p d o r e t a l . [KLA84], might (again) r a i s e questions about the p l a u s i b i l i t y of r-process nucleosynthesis in He-burning environments.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch024

n

+

Acknowledgment Thanks a r e due t o t h e o r g a n i z e r s o f t h i s symposium and t o t h e ACS. Withoul t h e i r s u p p o r t , K . - L . K r a t z and P. M o l l e r c o u l d n o t have p a r t i c i p a t e d . This work was s u p p o r t e d by t h e German BMFT and by t h e Swedish NSRC.

[BEN84] [CHE70] [KLA84] [KRA81] [KRA83] [KRA84] [KRA85] [KRU84] [LAR76] [MEY85] [MON82] [PFE81] [PFE84] [REE85] [SIS84] [WOH83] [WOH85]

References R. Bengtsson et a l . , Phys. Scripta 29 402 (1984). E. Cheifetz et a l . , Phys. Rev. Lett. 25 38 (1970). H.V. Klapdor et a l . , At. Data Nucl. Data Tables 31 81 (1984). K.-L. Kratz et a l . , Proc. 4th Int. Conf. on Nuclei Far From Stabi­ l i t y , Helsingør, Denmark, CERN 81-09 317 (1981). K.-L. Kratz et a l . , Z. Physik A312 43 (1983). K.-L. Kratz, Nucl. Phys. A417 447 (1984). K.-L. Kratz et a l . , 'Beta-Strength Function Systematics of A = 100 Nuclei', to be published. J. Krumlinde and P. Möller, Nucl. Phys. A417 419 (1984). S.E. Larsson et a l . , Nucl. Phys. A261 77 (1976). R.A. Meyer, Hyperfine Interactions 22 385 (1985), and Refs. therein. E. Monnand et a l . , Ζ. Physik A306 183 (1982). Β. Pfeiffer et a l . , Proc. 4th Int. Conf. on Nuclei Far From Stabi­ l i t y , Helsingør, Denmark, CERN 81-09 423 (1981). Β. Pfeiffer et a l . , Z. Physik A317 123 (1984). P.L. Reeder et a l . , these proceedings. K. Sistemich et a l . , Proc. Int. Symp. on In-Beam Nuclear Spectros­ copy, Debrecen, Hungary, Vol. I 51 (1984), and Refs. therein. F.K. Wohn et a l . , Phys. Rev. Lett. 51 873 (1983). F.K. Wohn et a l . , Phys. Rev. C31 621 and 634 (1985),and these proceedings.

RECEIVED August 20, 1986

25 New Delayed-Neutron Precursors from TRISTAN 1

1

2

3

3

P. L. Reeder , R. A. Warner , M. D. Edmiston , R. L. Gill , and A. Piotrowski 1

Pacific Northwest Laboratory, Richland, WA 99352 Bluffton College, Bluffton, OH 45817 Brookhaven National Laboratory, Upton, NY 11973

2

3

Recent development of reliable, high intensity ion sources for the TRISTAN on-line mass separator facility has greatly expanded the number of very neutron-rich fission products available. Half-lives and delayed neutron emission probabilities are being measured for these nuclides with a high efficiency neutron counter. During the past year, previously unknown P values have been measured for 11 precursors; Cu, Rb, Sr, Y, Cs, Ba, and La. For Rb,

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch025

n

75

100

100-102

100-102

148

149

149

combining our P value with the previously measured ratio of P /P gives a P

100

n

2n

n

2n

of 0.14 ±0.04%.

The TRISTAN on-line mass separator facility at Brookhaven National Laboratory provides mass separated beams of delayed neutron precursors at over 52 mass numbers. Many of these mass numbers include several isobars which are precursors. In addition, some of the nuclides have two or more beta decaying isomers which may or may not be precursors. We have engaged in a series of experiments to measure the half-lives and delayed neutron emission probabilities (P ) of as many of these precursors as possible [REE83-1 .REE83-2]. Because delayed neutron emission can be detected with high sensitivity in the presence of large intensities of beta and gamma radiations, we have used neutron counting to search for new isotopes among the very neutron-rich fission products [REE83-1 ,REE85]. We report here our recent half-life and P measurements among the low-yield fission products. The P values for precursors around mass 100 are unusually low, which may be a manifestation of ground state deformation in this vicinity. We also describe our observations on the three new isotopes Cu, Ag,and Ba. n

n

n

75

124

H9

Mass separated beams of fission products from TRISTAN were deposited on an aluminized Mylar tape in the center of a high efficiency neutron counter. The neutron counter contained 40 He filled counter tubes embedded in polyethylene and surrounded by Cd, boral, and polyethylene shields. Experiments were done with two alternative arrangements of the counter tubes. For higher efficiency (s 50$) and flat neutron energy response, the tubes were arranged in three concentric rings. This arrangement gave a neutron residence half-time of 25 JJLS. For beta-neutron coincidence experiments, it is desirable to have an even shorter residence time. This was achieved by arranging the counter tubes in four quadrants and packing them as close as possible to the beam deposition point. The residence half-time was 11 with this configuration but the neutron counting efficiency was« 34$. 3

0097-6156/86/0324-0171$06.00/ 0 © 1986 American Chemical Society

172

NUCLEI OFF THE LINE OF STABILITY

Beta particles at the deposition point passed through the Mylar tape and a 0.0075 cm thick Al vacuum window and were counted with a 450 mm totally depleted surface barrier Si detector 1000 2

μπ\ thick. The geometric solid angle for a point source under these conditions was estimated to be 17% ; however, the measured efficiency was about 14$. The experiments consisted of simultaneous multiscaler measurements of growth and decay curves for the beta counting rate, neutron counting rate, beta-neutron coincidence rate, and accidental coincidence rates. Data were stored in four 128 channel multiscalers. The ion beam was switched by upstream electrostatic deflection. Cycle times were chosen to give about 2 half-lives of beam-on and 14 half-lives of beam-off. Each cycle included a 1 s period during which the tape was moved about 2 cm. This distance was sufficient to completely remove long-lived beta activity from the beta counter.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch025

However, if there were long-lived neutron activities in a short cycle time experiment, these neutrons were still counted in successive cycles. These neutrons were corrected for in the data analysis. To simplify the analysis of background components, the multiscalers were turned on for several channels before the start of each beam-on pulse. The residence time was determined for our neutron counter by measuring the time intervals between beta start signals and neutron stop signals. With a residence half-time of 11 μ ε and a coincidence resolving time of 40 M S . 92$ of the true coincidence events were included. The fraction of true events not detected does not influence the present results because we normalize the P

n

measurements to a known P value measured under identical conditions. The coincidence rate was n

measured by a simple overlap coincidence module where the beta pulse Input was stretched to 40 jxs by a gate and delay generator. To measure the accidental coincidence rate, the same beta pulse was sent to a second coincidence module and overlapped with neutron pulses which had been delayed 45 JAS. After correcting each coincidence rate for deadtime effects, the difference was the true coincidence rate. The beta singles, neutron singles, and coincidence growth and decay curves were analyzed by the least square fitting program MASH [W0H78]. This program explicitly includes parent, daughter, and granddaughter relationships. Delayed neutron branching to the one-unit-lower mass chain as well as branching to isomeric states can be included in the beta decay curve analysis. The program outputs the saturation counting rate of each component present In the sample. Half-lives can be varied by an iterative procedure to find the best fits. The determination of P values is based on the bete saturation counting rate (cPg^), the neutron n

saturation counting rate ( C ^ ) , the beta-neutron coincidence saturation counting rate ( C P ^ ) , the 0

0

beta counting efficiency (ep), and the neutron counting efficiency ( € ) . The usual relation for the n

delayed neutron emission probability is

25.

Delayed-Neutron Precursors

REEDER ET AL.

P

n

173

=

(1)

By measuring the coincidence rate, we can obtain P from n

^

sat

P =

(2)

n

^sat^n If one could reproduce the neutron and beta efficiencies from one mass to the next, one could use a known P value to determine the ratio of beta efficiency to neutron efficiency and then calculate all other P n

n

values using Eq. 1. With our present apparatus, the neutron efficiency is insensitive to changes from Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch025

one mass number to the next, but the beta efficiency depends more critically on how the beam is tuned. We thus use Eq. 2 to calculate P because the beta efficiency does not appear in the expression. In some n

mass chains with several precursors (either isomers or isobars) It Is possible to determine the beta efficiency for one of the prominent precursors from the ratio of the coincidence counting rate to the neutron counting rate. We then calculate P values for the other precursors in that mass chain by use of n

Eq. 1. In all cases we use the neutron counting efficiency determined for ^ R b by use of Eq. 2 and the P value of 13.6 ± 0.9$. The half-lives and P values are presented in Table I. These results differ slightly from a n

previous report of this work [WAR85] due to additional experiments performed at masses 81 -83, 98-100,131-132, and 147-149. The latest experiments used the ring configuration for the neutron counter, whereas the previous experiments used the quadrant configuration. We have assumed equal neutron counting efficiencies for all precursors. The uncertainties shown on the P values include all n

the statistical uncertainties plus a systematic uncertainty of 10% on the neutron efficiency for data taken with the ring configuration or a systematic uncertainty of 20% for data taken with the quadrant configuration. These systematic uncertainties account for the energy dependence of the neutron counter efficiency and for our lack of knowledge of the neutron energy spectra of these precursors. Upper limits are based on twice the uncertainty when the error on the P exceeded the value. n

Table I also shows recommended P values from a recent compilation [MAN84]. The present n

results include 11 precursors for which no P values have been reported previously. The

1 0 0

n

~

1 0 2

Y

P values are significant in that these precursors were expected to contribute a large fraction of the n

unmeasured total delayed neutron yield in microscopic summation calculations [ΕΝΘ83, REE84]. If one comperes the experimental P values to estimated values using the prescription given in [MAN84], one n

observes a number of low ratios In the vicinity of mass 100. In Fig. 1 where the ratio of experimental P to calculated P is plotted versus neutron number, one sees a group of unusually low P values for n

n

n

Rb, Sr, and Y precursors with neutron number just above the shell closure at 60. These low P values n

may be another manifestation of the region of deformed nuclides around mass 100 which has been Identified by gamma spectoscopy experiments.

n

174

NUCLEI O F F T H ELINE O F STABILITY

Table I. Half-lives and delayed neutron emission probabilities a Half-life (s) P (%)

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch025

Precursor

a

n

P (%) (Mann)

75 Cu

1.3

±0.1

3.5

±0.6

79 6a 80 6a 81 6a 82 6a 83 6a

2.85 1.69 1.218 0.609 0.308

±0.01 ±0.01 ±0.004 ± 0.003 ± 0.004

0.055 0.69 11.7 20.9 62.8

±0.012 ±0.16 ± 1.2 ±2.2 ±6.3

0.10 0.86 12.2 21.9 44.

±0.01 ± 0.08 ± 1.2 ±2.6 ±8.

95 Rb 97 Rb 98 Rb 99 Rb 100 Rb

0.377 0.169 0.106 0.059 0.059

±0.001 ±0.001 ±0.001 ±0.001 ±0.010

9.0 26.1 13.6 20.7 5.0

± 1.1 ±5.4 ±0.9 ±2.3 ι 1.0

8.59 26.9 13.4 13.1

± 0.60 ± 1.9 ±0.9 ± 1.8

97 Sr 98 Sr 99 Sr 100 Sr 101 Sr 102 Sr

0.429 0.653 0.269 0.201 0.115 0.069

± 0.005 i 0.002 ±0.001 ±0.001 ±0.001 ±0.015

97 (precursors Rb-93-->97). Results are in reasonable agreement with values obtained with the formulas of Gilbert and Cameron.

A f r e q u e n t decay mode o f v e r y n e u t r o n - r i c h n u c l i d e s such as f i s s i o n p r o d u c t s i s t h e t w o - s t a g e cascade i n w h i c h a p r e c u r s o r n u c l i d e (PR) b e t a decays t o an e x c i t e d s t a t e o f a n e u t r o n - e m i t t e r n u c l i d e (NE) w i t h enough e x c i t a t i o n e n e r g y t o f o r m a g r a n d c h i l d n u c l i d e (GC) i n g r o u n d o r e x c i t e d states. T h i s phenomenon a f f o r d s u n i q u e e m p i r i c a l c l u e s t o n e u t r o n c r o s s sections of far-unstable nuclides. The key p o i n t i s t o e x p l o i t t h e i n v e r s e r e l a t i o n s h i p between n e u t r o n e m i s s i o n and a b s o r p t i o n by c o m p o u n d - n u c l e a r l e v e l s above t h e n e u t r o n b i n d i n g e n e r g y . Data o f s u f f i c i e n t q u a l i t y and q u a n t i t y t o a l l o w c o n s t r u c t i o n o f e m p i r i c a l l y based c r o s s s e c t i o n s f o r v e r y n e u t r o n - r i c h n u c l i d e s w o u l d be o f i n t e r e s t f o r a s t r o p h y s i c s and f o r n u c l e a r t h e o r y . Such c r o s s s e c t i o n s w o u l d i n some cases be d o m i n a t e d by i n d i v i d u a l i s o l a t e d resonances and i n o t h e r s w o u l d be v i e w e d as averages o v e r a number o f c l o s e l y spaced r e s o n a n c e s . I n e i t h e r case, delayed neutron s p ec t r a are a unique source o f data f o r n u c l i d e s t h a t are completely i n a c c e s s i b l e t o d i r e c t measurement. The v a l i d i t y o f t h i s approach has been d e m o n s t r a t e d r e c e n t l y by K r a t z _et _ a l - [KRA83a] who a p p l i e d i t i n t h e case o f two p r e c u r s o r s , B r - 8 7 and K - 5 0 , and has been d i s c u s s e d f u r t h e r by W i e s c h e r e t al_. [ W I E 8 5 ] . 0097-6156/ 86/0324-0177$06.00/ 0 © 1986 American Chemical Society

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch026

178

NUCLEI OFF THE LINE OF STABILITY

Over t h e p a s t s e v e r a l y e a r s we have c o n d u c t e d a program t o d e v e l o p a h i g h r e s o l u t i o n t i m e - o f - f l i g h t (TOF) s y s t e m f o r d e l a y e d n e u t r o n s p e c t r a below 100 keV and t o e x p l o r e i t s a p p l i c a t i o n t o m a s s - s e p a r a t e d f i s s i o n p r o d u c t p r e c u r s o r s a t t h e TRISTAN f a c i l i t y a t t h e High F l u x Beam R e a c t o r a t Brookhaven N a t i o n a l L a b o r a t o r y . The o r i g i n a l goal was a system w i t h s u f f i c i e n t r e s o l u t i o n , e f f i c i e n c y , and b a c k g r o u n d r e j e c t i o n t o o b t a i n n a t u r a l l i n e w i d t h s o f a s t a t i s t i c a l l y u s e f u l number o f l e v e l s ; i n t e r p r e t a t i o n o f such d a t a t o o b t a i n l e v e l d e n s i t i e s and c r o s s s e c t i o n s w o u l d r e q u i r e a minimum o f a d d i t i o n a l a s s u m p t i o n s . Although t h a t goal proved t o be u n f e a s i b l e , s p e c t r a have been o b t a i n e d w i t h v e r y c o n s i d e r a b l y i m p r o v e d r e s o l u t i o n ( b e l o w 100 keV) o v e r t h a t i n e a r l i e r ones t a k e n w i t h C u t t l e r S h a l e v i o n chambers ( K r a t z e t a K [ K R A 8 3 b ] , Reeder e t a]_. [ R E E 8 0 ] , Rudstam [RUD79]) and w i t h p r o t o n r e c o i l c o u n t e r s (Greenwood and C a f f r e y [ G R E 8 3 ] ) . The TOF s p e c t r a t h e r e f o r e e x h i b i t many more r e s o l v e d peaks and make p o s s i b l e more r e l i a b l e d e d u c t i o n s o f l e v e l d e n s i t i e s . We r e p o r t h e r e n e a r l y f i n a l r e s u l t s f o r n e u t r o n - e m i t t e r s S r - 9 3 t h r o u g h S r - 9 7 , w h i c h have h a l f - l i v e s o f seconds o r l e s s and have ( r e s p e c t i v e l y ) f o u r t o e i g h t more n e u t r o n s t h a n t h e h i g h e s t mass S r i s o t o p e t h a t can be s t u d i e d by n e u t r o n c a p t u r e on s t a b l e Sr i s o t o p e s . Experimental

Method

The b a s i c e x p e r i m e n t a l method has been d e s c r i b e d i n e a r l i e r r e p o r t s [CLA83, MCE85]. B r i e f l y , t h e TOF a p p a r a t u s c o n s i s t s o f a p l a s t i c s c i n t i l l a t o r telescope t o d e t e c t betas t h a t feed n e u t r o n - e m i t t i n g l e v e l s and a L i - 6 g l a s s s c i n t i l l a t o r t o d e t e c t t h e e m i t t e d n e u t r o n s . A fast c o i n c i d e n c e between t h e two b e t a d e t e c t o r s p r o v i d e s t h e s t o p p u l s e f o r a t i m e - t o - a m p l i t u d e c o n v e r t e r (TAC); the s t a r t pulse i s from the neutron detector. The o b s e r v e d FWHM o f t h e TOF peak due t o b e t a s i n t h e t e l e s c o p e and gammas i n t h e n e u t r o n d e t e c t o r was t y p i c a l l y a b o u t 2 . 9 ns u n d e r r u n n i n g conditions. The s l o w s i g n a l s f r o m t h e n e u t r o n and t h i c k b e t a d e t e c t o r s a r e d i g i t i z e d and r e c o r d e d i n t h r e e - p a r a m e t e r e v e n t mode. The n e u t r o n d e t e c t o r p u l s e h e i g h t i s used t o e l i m i n a t e many o f t h e p u l s e s due t o gammas. The t h i c k b e t a d e t e c t o r p u l s e h e i g h t can be used t o o b t a i n t h e spectrum o f betas t h a t are i n coincidence w i t h s e l e c t e d neutron time ( e n e r g y ) g a t e s and t h e r e b y a i d i n d e c i d i n g w h i c h p a r t s o f t h e n e u t r o n s p e c t r u m f e e d d i f f e r e n t l e v e l s i n t h e f i n a l (GC) n u c l i d e . The n e u t r o n s c i n t i l l a t o r i s o f t y p e NE912 g l a s s , 0 . 9 5 mm t h i c k and 127 mm d i a m e t e r , s h i e l d e d on i t s f a c e by 6 . 7 mm o f B o r a l and 14 mm o f l e a d and on i t s s i d e s by 6.4-mm b o r o n - l o a d e d p l a s t i c . Path l e n g t h s o f 5 0 , 7 1 , and 120 cm have been u s e d , and i n l a t e r r u n s as many as f o u r d i f f e r e n t n e u t r o n d e t e c t o r s were used a t t h e same t i m e , i n e f f e c t r u n n i n g f o u r q u a s i - i n d e p e n d e n t simultaneous experiments. Time dependent and e q u i l i b r i u m gamma s i n g l e s s p e c t r a o f t h e a c t i v e d e p o s i t were a l s o r e c o r d e d i n most r u n s . The most i m p o r t a n t p a r a m e t e r o f t h e d e t e c t i o n system i s i t s r e s p o n s e function. We have s t u d i e d t h i s e x t e n s i v e l y i n Monte C a r l o and o t h e r calculations. The c a l c u l a t e d t i m e - s p e c t r u m r e s p o n s e t o m o n o e n e r g e t i c n e u t r o n s i s composed o f a Gaussian t i m i n g c u r v e ( 2 . 9 7 - n s FWHM), a t r a p e z o i d a l c o n t r i b u t i o n f r o m d e t e c t o r t h i c k n e s s and n o n - a x i a l p a t h s , and an e x p o n e n t i a l t a i l , c a l c u l a t e d by Monte C a r l o , f r o m m u l t i p l e s c a t t e r i n g i n t h e n e u t r o n scintillator. ( S p e c t r u m d i s t o r t i o n due t o n e u t r o n s m u l t i p l y s c a t t e r e d by s t r u c t u r a l and o t h e r p a r t s o f t h e a p p a r a t u s and a r r i v i n g a t t h e n e u t r o n

26.

CLARK ET AL.

Level Densities near the Neutron Separation Energy

179

d e t e c t o r w i t h i n c o r r e c t f l i g h t t i m e s was a l s o e s t a b l i s h e d by Monte C a r l o and f o u n d t o be n e g l i g i b l e . ) The t i m e - s p e c t r u m r e s p o n s e i s a v e r y c l e a n , n e a r l y s y m m e t r i c peak w i t h a FWHM r e s o l u t i o n i n t h e e n e r g y s p e c t r u m o f 2% t o 4% f o r t h e f l i g h t p a t h s t h a t were u s e d . The o n l y f e a s i b l e check o f t h i s c a l c u l a t e d response f u n c t i o n i s measuring the spectrum o f B r - 8 7 and c o m p a r i n g t h e a n a l y z e d r e s u l t s w i t h an e x p e c t e d s p e c t r u m d e r i v e d f r o m t h e p r e c i s e l y known r e s o n a n c e e n e r g i e s and w i d t h s f o u n d by Raman e t à]_. [RAM83] i n c r o s s s e c t i o n measurements. We p l a n such a c a l i b r a t i o n o f o u r system when t h e a p p r o p r i a t e i o n s o u r c e i s a v a i l a b l e t o us a t TRISTAN.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch026

Data R e d u c t i o n and A n a l y s i s The t h r e e - p a r a m e t e r e v e n t mode d a t a were scanned w i t h v a r i o u s s o f t w a r e windows and t h e r e s u l t s were p r o c e s s e d i n s t a n d a r d f a s h i o n . A brief outline follows. The raw TOF s p e c t r a showed a d e l a y e d - n e u t r o n r e g i o n , a n a r r o w peak due t o t r u e beta-gamma c o i n c i d e n c e s , and on t h e o t h e r s i d e o f t h e peak a " n o n - p h y s i c a l " r e g i o n due t o " e v e n t s " i n w h i c h t h e s t o p s i g n a l o c c u r r e d b e f o r e t h e s t a r t s i g n a l ; t h i s r e g i o n was u s e f u l f o r c o r r e c t l y s u b t r a c t i n g random c o i n c i d e n c e s . The n e u t r o n p u l s e h e i g h t s p e c t r u m had t h e c h a r a c t e r i s t i c appearance f o r L i - 6 g l a s s - - a b r o a d n e u t r o n peak on a s l o p i n g gamma p l a t f o r m . The gamma-only p o r t i o n s were used as s o f t w a r e g a t e s i n s c a n n i n g t h e TOF s p e c t r a t o d e t e r m i n e a r e a l i s t i c shape f o r t h e random c o i n c i d e n c e p l a t f o r m l y i n g u n d e r t h e d e l a y e d n e u t r o n s . A l a r g e number o f d e l a y e d - n e u t r o n peaks were d i s c e r n i b l e i n t h e TOF s p e c t r a g a t e d by t h e n e u t r o n p o r t i o n ; many o f t h e s e were f i t t e d t o a c o n v o l u t i o n o f t h e c a l c u l a t e d system r e s p o n s e f u n c t i o n w i t h L o r e n t z i a n shapes o f various widths. However, o n l y t h e two p r o m i n e n t peaks i n Rb-95 showed s t a t i s t i c a l l y s i g n i f i c a n t n a t u r a l l i n e w i d t h s [MCE85], T h e r e f o r e t h e use o f a l e v e l w i d t h d i s t r i b u t i o n as a m i s s i n g - l e v e l i n d i c a t o r was n o t p o s s i b l e and an i n t e n s i t y d i s t r i b u t i o n a p p r o a c h was a d o p t e d . The i n t e n s i t y method r e q u i r e s a c a r e f u l a n a l y s i s o f t h e e n t i r e TOF s p e c t r u m because i t compares t h e summed i n t e n s i t i e s i n r e s o l v e d peaks w i t h the t o t a l i n t e n s i t y i n c l u d i n g the unresolved continuum. L i - 6 glass e x h i b i t s a number o f s c a t t e r i n g resonances w h i c h add e x p o n e n t i a l t a i l s o f v a r y i n g s i z e s and decay l e n g t h s t o t h e s p e c t r a l peaks w h i l e r e d u c i n g t h e i r primary s i z e . Monte C a r l o c a l c u l a t i o n s were c a r r i e d o u t f o l l o w i n g a method o f K i n n e y [ K I N 7 6 ] t o d e t e r m i n e t h e r e d u c t i o n and t a i l p a r a m e t e r s as a f u n c t i o n o f i n c i d e n t n e u t r o n e n e r g y . Using t h e s e , a p a r t i a l spectrum s t r i p p i n g was p e r f o r m e d t o remove t h e t a i l s and c o r r e c t t h e s p e c t r u m s h a p e . These c o r r e c t i o n s can be s i g n i f i c a n t t o as low a n e u t r o n e n e r g y as 70 keV. As p a r t o f t h e same u n f o l d i n g o p e r a t i o n t h e L i - 6 ( n , a l p h a ) c r o s s s e c t i o n was used t o p r o v i d e t h e system e f f i c i e n c y . The f l u c t u a t i o n s i n n e u t r o n peak i n t e n s i t i e s a r i s e f r o m t h e P o r t e r - T h o m a s d i s t r i b u t e d b e t a decay w i d t h s t o l e v e l s i n t h e NE n u c l i d e . In the simplest case o n l y a s i n g l e s t a t e i n t h e GC n u c l i d e can be f e d and o n l y one n e u t r o n p a r t i a l wave i s s i g n i f i c a n t . The o b s e r v e d l e v e l s w i l l be a s u b s e t o f l e v e l s i n t h e NE n u c l i d e and w i l l be d i s t r i b u t e d i n e n e r g y f o l l o w i n g a Wigner d i s t r i b u t i o n . I n a t y p i c a l GC n u c l i d e , h o w e v e r , t h e r e w i l l be a number o f a c c e s s i b l e f i n a l s t a t e s and t h e d e l a y e d n e u t r o n s p e c t r u m w i l l be a s u p e r p o s i t i o n o f t r a n s i t i o n s f r o m s e v e r a l p a r t s o f t h e NE n u c l i d e level structure.

180

NUCLEI OFF THE LINE OF STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch026

I n t h e case where a s i n g l e f i n a l s t a t e i s a c c e s s i b l e i n t h e GC n u c l i d e t h e l e v e l s p a c i n g may be e s t i m a t e d r a t h e r s i m p l y . A s u i t a b l e energy i n t e r v a l i s chosen by c o n s i d e r i n g t h e system r e s o l u t i o n and t h e s p a c i n g o f observed peaks. The r a t i o o f t h e summed i n t e n s i t y i n d i s c r e t e peaks t o the t o t a l neutron i n t e n s i t y i s simply r e l a t e d through the Porter-Thomas d i s t r i b u t i o n t o t h e average l e v e l spacing i n t h e energy i n t e r v a l . For each o f t h e Sr n u c l i d e s i n t h i s s t u d y more t h a n one s t a t e i s a v a i l a b l e and n e u t r o n peaks must be a s s i g n e d t o p a r t i c u l a r f i n a l s t a t e s and p a r t i a l n e u t r o n b r a n c h i n g r a t i o s must be d e t e r m i n e d . T h i s i s t h e most d i f f i c u l t part of the a n a l y s i s . Each i s o t o p e i s t r e a t e d s e p a r a t e l y , b u t i n g e n e r a l s i n c e t h e l e v e l d e n s i t y i s an e x p o n e n t i a l l y i n c r e a s i n g f u n c t i o n o f e x c i t a t i o n e n e r g y t h e a v e r a g e i n t e n s i t y o f peaks w i l l d r o p s h a r p l y as h i g h e r f i n a l s t a t e s i n t h e GC n u c l i d e a r e c o n s i d e r e d . To o b t a i n a t o t a l l e v e l d e n s i t y f o r a l l s p i n s t a t e s r e q u i r e s s p i n and p a r i t y a s s i g n m e n t s f o r t h e PR and GC n u c l i d e s and t o deduce a l e v e l d e n s i t y p a r a m e t e r a t h e n e u t r o n b i n d i n g e n e r g y Β i n t h e NE n u c l i d e must be known. These and o t h e r v a l u e s a r e given i n Table 1 .

R e s u l t s and C o n c l u s i o n s The r e s u l t s o f t h e s e s t u d i e s a r e p r e s e n t e d i n T a b l e 2 and compared w i t h v a l u e s c a l c u l a t e d w i t h t h e f o r m u l a s o f G i l b e r t and Cameron [ G I L 6 5 ] . I n Rb-93 and Rb-94 i t was assumed t h a t any t r a n s i t i o n s t r o n g enough t o

Table 1 .

A

PR n u c l i d e Spin Ρ

NE n u c l i d e Β Spins

%

MeV

General

Data

Neutron spectra GC n u c l i d e KE No. o f d i s - S p i n range c r e t e peaks η p

keV

%

93

5/2"

1.4

5.46

3/2"

36-156

9

94

3"

10.2

6.83

2,3,4"

12-100

16

95

5/2"

8.6

4.36

3/2" 3/2,5/2,7/2"

9-100

10 16

96

2"

14.2

5.89

l/2

97

3/2

26.9

4.01

+

+

—

l/2 , 3/2,5/2 1/2* +

3-40

0

+

7/2

0 10

+

8 5 .,2

[a]

73

[a]

42 ± 4 49 ± 4 l/2

—

+

* T h i s work [ a ] R e f e r e n c e KRA83b

i

i

+

24

* * [a]

0 ± 20 * 50 ± 9 * [ a ]

26.

CLARK ET AL.

Level Densities nearthe Neutron Separation Energy

181

be o b s e r v e d f e e d s t h e g r o u n d s t a t e . The p a r t i a l n e u t r o n b r a n c h i n g was used t o c a l c u l a t e an a v e r a g e s p a c i n g . For Rb-95 i t was p o s s i b l e by u s i n g t h e b e t a l e g o f t h e d a t a a c q u i s i t i o n system t o d e t e r m i n e w h i c h peaks f e d t h e ground s t a t e . Hence s e p a r a t e l e v e l d e n s i t i e s were o b t a i n e d f o r t h e two s t a t e s . I n Rb-96 t h e s t a t i s t i c s were p o o r and t h e e f f e c t i v e l e v e l d e n s i t y t o o h i g h t o i s o l a t e any p e a k s . I n Rb-97 t h e u s a b l e e n e r g y range was l e s s t h a n 40 keV and i t was assumed t h e r e i s no peak f e e d i n g the ground s t a t e i n t h a t range. I t was n o t p o s s i b l e t o s e p a r a t e t h e s p e c t r a by f i n a l s t a t e s i n t h e GC n u c l i d e . The r e s u l t s a r e c o n s i s t e n t w i t h t h o s e p r e d i c t e d by t h e G i l b e r t and Cameron f o r m u l a f o r t h e two e x c i t e d states taken t o g e t h e r .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch026

Table 2.

Nuclide PR

B

n

Level

MeV

D e n s i t y Parameters f o r

L e v e l D e n s i t y , MeV" calc.[a]

expt.

Sr-93-->97

a , MeV"

NE

MeV

Rb-93

Sr-93

5.25

5.35

185

Rb-94

Sr-94

6.83

6.87

1278

Rb-95

Sr-95 4.36

4.41

81

92

5.22

972

1390

5.89

5.95

365

14.67

4.01

4.03 4.84 5.26

42 607 296

15.26

Rb-96

13.2

560 ± 250

13.36

11.8

+0.7 -1.0

13.98

14.3

+1.2 0.5

14.7

+0.4 -0.3

14.7

+0.7 -0.9

+ 70 - 20 + 305 - 190

Sr-96

Sr-97 g.s. 1st e.s. 2nd e . s . 1 s t & 2nd

[ a ] R e f e r e n c e GIL65

903

+0.6 •0.6

12.76

e.s.

Rb-97

expt.

240 ± 80

g.s.

1st

calc.[a]

690 ± 245

182

NUCLEI OFF THE LINE OF STABILITY

The e x p e r i m e n t a l v a l u e s i n T a b l e 2 a g r e e r e a s o n a b l y w i t h i n s t a t i s t i c a l e r r o r s w i t h t h e G i l b e r t and Cameron v a l u e s , w h i c h can be e x p e c t e d t o p r e d i c t l e v e l d e n s i t i e s w i t h i n a f a c t o r o f 2 . The n u c l i d e s s t u d i e d have f o u r t o e i g h t a d d i t i o n a l neutrons than Sr isotopes f o r which l e v e l parameters can be o b t a i n e d by c o n v e n t i o n a l n e u t r o n c r o s s s e c t i o n m e t h o d s . However, no t r e n d s away f r o m v a l u e s f o r t h e l i g h t e r i s o t o p e s can be seen i n t h e present r e s u l t s . E x t e n s i o n o f t h e e x p e r i m e n t s t o l a r g e r n e u t r o n excess o r t o o t h e r ranges o f Ζ and A m i g h t t u r n up r e s u l t s showing d e v i a t i o n s .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch026

The main s t u m b l i n g b l o c k f o r t h e TOF system i s t h e e f f i c i e n c y o f the L i - 6 glass d e t e c t o r s ; t h e low neutron counting r a t e s r e s t r i c t both t h e r e s o l u t i o n and t h e i s o t o p e s a v a i l a b l e t o s t u d y . A more e f f i c i e n t d e t e c t o r w i t h equal g e o m e t r i c a l and e l e c t r o n i c r e s o l u t i o n w o u l d make t h e system a v e r y p o w e r f u l t o o l i n i n v e s t i g a t i n g n u c l i d e s f a r o f f t h e line of stability.

Acknowledgments The v e r y c o n s i d e r a b l e p a t i e n c e and a s s i s t a n c e o f t h e TRISTAN s t a f f i s g r a t e f u l l y acknowledged. S p e c i a l t h a n k s a r e due t o H. E. J a c k s o n o f Argonne N a t i o n a l L a b o r a t o r y f o r p r o v i d i n g t h e L i - 6 d e t e c t o r s . R. E. C h r i e n and Taun-Ran Yeh were o f v e r y g r e a t h e l p i n t h e i n i t i a l phases o f t h e program. T h i s work was s u p p o r t e d i n p a r t by t h e U . S . D e p a r t m e n t o f Energy.

References [CLA83] D. D. Clark, R. D. McElroy, T. R. Yeh, R. E. Chrien, R. L. Gill, BNL-51778, p. 449 (1983). (NEANDC Specialists Meeting,BNL, October, 1983) [GIL65] A. Gilbert, A.G.W.Cameron, Can. J. Phys. 43, 1466 (1965). [GRE83] R.C.Greenwood, A.J.Caffrey, BNL-51778, p. 365 (1983). [KIN76] W.E.Kinney, private communication, in J.A.Harvey, N.W.Hill, Nucl. Instr. Methods 162, 507 (1979). [KLA83a] K.-L.Kratz et al., Astron. Astrophys. 125, 381 (1983). [KLA83b] K.-L.Kratz et al., Z. Phys. A 312, 43 (1983) and references therein. [MCE85] R.D.McElroy, D.D.Clark, R.L.Gill, A.Piotrowski, AIP Conference Proceedings No. 125, p. 912 (1985) (Capture Gamma-Ray Symposium, Knoxville, September 1984) [RAM83] S.Raman et al., Phys. Rev. C28, 602 (1983) [REE80] P.L.Reeder et al., Nucl. Sci. & Engr. 75, 140 (1980) [RUD79] G.Rudstam, private communication quoted in [GRE83] [WIE85] M.Wiescher et.al., AIP Conference Proceedings No. 125, p. 908 (1985) (Capture Gamma-Ray Symposium, Knoxville, September 1984) RECEIVED

June 5, 1986

27 Toward a Shell-Model Description of Intruder States and the Onset of Deformation 1

1

2

3

K. Heyde, P. Van Isacker, R. F. Casten , and J. L. Wood 1

Institute for Nuclear Physics, Proeftuinstraat 86, B-9000 Gent, Belgium Brookhaven National Laboratory, Upton, NY 11973 School of Physics, Georgia Institute of Technology, Atlanta, GA 30332

2 3

Basing on the nuclear shell-model and concentrating on the monopole,pairing and quadrupole corrections originating from the nucleon-nucleon force,both the appearance of low-lying 0 intruder states near major closed shells(Z=50, 82)and sub-shell regions (Z=40,64) can be described.Moreover,a number of new facets related to the study of intruder states are presented.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch027

+

In a nucleus,the major part of the nucleonic motion is determined by the average single-particle field.This field approximation implies the existence of magic numbers i.e. 20,28,50,82,126 ,determining extra stability for the par­ ticular nuclei having proton and/or neutron number equal to such a magic num­ ber.The energy separation between the last filled single-particle orbitals and the lowest,unfilled orbitals varies from ~6 MeV(light nuclei) to~3.5 MeV(Z=82 gap).Besides,a number of subshell closures have by now been established i.e. Z=40,64.In these cases,a much smaller energy gap of 1 and 2.5 MeV,respectively results.It is precisely the existence of particular configurations that makes the study of nuclear structure approximate tractable.Most nucleons can be con­ sidered to contribute to the "core" nucleus and thus to the average field lea­ ving only a small number of nucleons,called valence nueleons(particles or holes) outside closed shells(see fig.1).In region I,few valence nucleons are present

Figure 1. Schematic divisions of nuclei in three major regions: (I) region near doubly closed shells; (II) region of strongly deformed nuclei; (III) region of intruder states.

ζ

AO

50 Ν

60

70

0097-6156/86/0324-0184$06.00/0 © 1986 American Chemical Society

27.

and t h e n u c l e a r s h e l l - m o d e l

techniques[SHA63Jal

l y i n g nuclear excited s t a t e s . I n cal

nucléons are p r i m o r d i a l

til!

this

region

case,the

(or s p i n - o r b i t

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch027

of the v a r i a t i o n

r

a

detailed

properties

II

study of between

[B0H75]) moving i n

o r b i t a l s [bHA53,FED79]

interaction

of shell

are

i s t h e dominant

1,11 v e r y much r e l i e s

shell configurations.Since

gaps can be shown t o be A d e p e n d e n t ( s e e analysis

o

low-

identi-

identical

present.In

contribution

nuclei.

i n two r e g i o n s

defined closed

(region

partner)

strong proton-neutron

The s e p a r a t i o n

f

and s t r o n g l y c o l l e c t i v e m o t i o n does n o t d e v e l o p u n -

and l e a d s t o p e r m a n e n t l y deformed

a set of well

l o w

I,the pairing

many v a l e n c e p r o t o n s and n e u t r o n s

single-particle

185

Shell-Model Description of Intruder States

H E Y D E ET AL.

sect.2

on t h e e x i s t e n c e

the value o f tne

[GU077,S0R84]) ,a more

gaps as a f u n c t i o n

of A w i l l

of

shell

detailed

have t o be s t u -

died. T h e r e now a l s o e x i s t s

an i d e a l i z e d r e g i o n

o f nucléons i s near a closed s h e l l and t h e o t h e r has a maximal

configuration(very

i n such n u c l e i , t h e

lyinq particle-hole

(p-h)excitations

in detail

f o r odd-A n u c l e i

vered i n d e t a i l . I n

closed shell

nucléons)

result(lp-2h

first,a

or Zp-lh

in

larqer excitation

i n odd-A n u c l e i

"intruder"

studied

regions are co-

even-even

approach f o r d e s c r i b i n g both t h e small

ha-

statesfor

e n e r g y , h a v e been

[HEY83] ,where most c l o s e d - s h e l l

and t h e p a r t i c u l a r Α-dependence o f such i n t r u d e r

situation).It

can be e x c i t e d and l o w -

the present d i s c u s s i o n ( s p e c i f I C f o r

present a shell-model

where one t y p e

few v a l B n c e

l h or Ip outside a closed shell).These

w h i c h one w o u l d e x p e c t , a t

fig.l)

number o f v a l e n c e nue I e o n s ( m i d - s h e l 1

has been shown t h a t

ving o r i q i n a l l y

III(see

nuclei),we

excitation

states throughout

energy

region

III

nuclei. 2.She!1-model

description

In a schematic we t a k e as t h e l o w e s t

of

intruder

presentation(see intruder

state

fig.2)

states of a single-closed shell

(0 state) +

a proton

( π ) 2p-2h

nucleus,

configuration

Figure 2. Schematic representation of a proton (π) intruder 2p-2n 0 configuration where denotes the regular o r b i t a l , the intruder orbital and j the neutron orbitals f i l l e d i n a BCS way ( v ) +

v

#

186

NUCLEI OFF THE LINE OF STABILITY

w i t h the valence neutrons tals.The

d i s t r i b u t e d over the a v a i l a b l e s i n g l e - p a r t i c l e

unperturbed energy then

We now s h o r t l y

discuss the d i f f e r e n t

pairing correlations

both

2p-2h c o n f i g u r a t i o n s

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch027

in

BCS o c c u p a t i o n p r o b a b i l i t i e s

energies

= 2(fc = l

of the j

-ΐ

results

)-2(ε

A

Z

effects

become m o d i f i e d due t o t h e

proton-

2 energy[TAL63]

and ν

neutron orbitals.because of

these

energy v a r i a t i o n s , a f i r s t

intruder configurations

ΔΕ

due t o c o r e p o l a r i z a t i o n

t h e f o l l o w i n g way

π ν ν ) the average p r o t o n - n e u t r o n

single-particle

in­

binding

correction

The p r o t o n s i n g l e - p a r t i c l e

,j

e n e r g i e s and t h e

+

neutron i n t e r a c t i o n ii

strong

0 core.

2 . 1 Monopole f i e l d

with E(j

due t o o o t n t h e

and t n e p r o t o n - n e u t r o n

the proton s i n g l e - p a r t i c l e

energy o f these i n t r u d e r o f the underlying

energy c o r r e c t i o n s

i n t h e 2p and 2h c o n f i g u r a t i o n s

teraction affecting

orbi­

becomes

interaction

correction

to the unperturbed

.

the

proton

as

-ε

)

[E(J;.J )-E(J,.J )] V

(3)

V

ν T h i s monopole c o r r e c t i o n shell

has been s t u d i e d i n some d e t a i l

Z = b 0 , « 2 and t h e s u b s n e l l

Z=40,b4 r e g i o n s [ H E Y 8 5 ] . i t shell

for

both tne

large

t h e r e b y becomes

that f o r the large spherical

single-particle

m o d i f i c a t i o n o f the o r i g i n a l

gap r e s u l t s . O n t h e c o n t r a r y , f o r

the subshell

gions,when Ν i n c r e a s e s , a n almost complete e r a d i c a t i o n o f t h e subshell ( f o r Z=40 n e a r N = b 8 , b 0 ; f o r Z=b4 n e a r IM=88,9U) r e s u l t s c a s e s , w e end up w i t h n u c l e i

similar

to the region

II

and t h u s , i n

field

the l o w e s t - l y i n g states

A E

A

P

E

(similar

=

A E

p a i r W

0

l

e

S

>

=

a r t

-)

+

A E

case.

coupled c o n f i g u r a t i o n s

+

using the residual

pairing(

h o l e s

nucleon-nucleon

p

a

r

n

a r t

- ) ) »where

gain.

as

)


-> | 0 β 0 > + ct|2 fi 2 > + . . . . (6) π ν π ν π ν U s i n g p e r t u r b a t i o n t h e o r y and t h e l o w e s t s e n i o r i t y s h e l l - m o d e l d e s c r i p t i o n o f the 0 p a i r d i s t r i b u t i o n , o n e c a l c u l a t e s a quadrupole p o l a r i z a t i o n energy gain +

+

+

1

+

+

1

+

1

+

ΔΕ where ( K

$ m

Q η


6"J" t r a n s i t i o n i s at 691 keV, e s t a b l i s h ­ ing the 8* l e v e l at 2018 keV. The 655-keV γ ray, assigned by Koenig et a l . as

192

NUCLEI OFF THE LINE OF STABILITY

00 CO CO

( 8 ) £ i co

2318.5

+

F i g . 2. Level scheme of P d determined from ( t , ργγ) s t u d i e s . Previous studies are beta decay (circles), fission frag­ ment decay (squares), and (t,p) t r i a n g l e s .

2002.6

H

I

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch028

2

+

Τ ro ^ *t In ^

'

«~ i"* !> r> r> OÎ σ>

+

0

+

^^1125.7

SES»© ii) CO 03 R SΛ ^ oo 3

+

2

1 1 2

1550.3 (6 ) /1362.3

| < CM

924.0 882.9 736.8 348.7

•

A A

•

•

A

•

•

A

the e^^oj t r a n s i t i o n , a c t u a l l y feeds the 4Ϊ l e v e l d i r e c t l y from a new l e v e l at 1397 keV. We suggest that t h i s new l e v e l has a J value of 4 . 1 7

+

Gamma rays with energies of 398 and 401 keV are known from previous studies and are observed as a m u l t i p l e t i n the (ί,ργ) data. These γ rays depopulate the 2"£ and 0* l e v e l s , r e s p e c t i v e l y . However, a gate on these γ rays reveals coincidences with a l l the members of the yrast band, not just the 2"}+0"£ t r a n s i t i o n as expected. A narrower gate set at about 399 keV reveals weak coincidences with the 8"J"-»-6~J\ 6"j^4"j\ and 4*-»·2* t r a n s i t i o n s . Though the s t a t i s t i c s are poor, the i n t e n s i t i e s f o r these t r a n s i t i o n s i n the coincidence spectrum are c o n s i s t e n t with the 399-keV γ ray feeding the 8* l e v e l . We suggest that t h i s t r a n s i t i o n may be the 10*+8"[ yrast t r a n s i t i o n . If this assignment i s confirmed, i t w i l l be the f i r s t experimentally observed backbend i n the neutron r i c h n u c l e i near A=100. A backbend at the 10~|" l e v e l would agree with the c a l c u l a t i o n by T r i p a t h i et a l . [TRI84] of a pronounced backbend at the 10+ l e v e l i n M o . 102

112 Pd. L i t t l e has been known experimentally about the l e v e l s t r u c t u r e of Pd. Previous studies are i n agreement only f o r the J assignment of the 2^ l e v e l at 349 keV [CAS72,CHE70]. We have e s t a b l i s h e d f i v e new l e v e l s i n Pd see F i g . 2 ) , and have been able to propose J assignments f o r some of the Pd l e v e l s from decay patterns. The coincidence r e s u l t s e s t a b l i s h e d a ground s t a t e t r a n s i t i o n depopulating the 736 keV l e v e l , i n d i c a t i n g that i t i s a 2 level. The l e v e l at 924 keV has a t r a n s i t i o n to the 2+ l e v e l , and a γ ray seen i n the proton gated s i n g l e s i s probably the ground s t a t e t r a n s i t i o n , suggesting a J value of 2 f o r that l e v e l a l s o . Our data confirm that the 4+ l e v e l occurs at 882 keV, i n agreement with the r e s u l t s of the f i s s i o n fragment decay s t u d i e s , but that the previous t e n t a t i v e assignment of the 6+ l e v e l was incorrect. Instead, we e s t a b l i s h the 6+ l e v e l at 1550 keV, and have evidence that suggests that the 8+ l e v e l occurs at 2319 keV. New l e v e l s at 1096, 1362, and 2002 keV are based on the coincidence r e s u l t s . 7 1

1 1 2

7 r

+

1 1

+

28.

In-Beam Spectroscopy

H E N R Y E T AL.

193

S t a c h e l et a l . [STA82] have i n t e r p r e t e d the s t r u c t u r e of Ru and Pd n u c l e i i n t e r m s o f the t r a n s i t i o n between t h e SU(5) ( v i b r a t i o n a l ) and 0(6) (γunstable) l i m i t s of the I n t e r a c t i n g Boson Model ( I B M ) . The e n e r g y r a t i o s 4 / 2 6 / 2 s i s t e n t w i t h t h o s e of the 0 ( 6 ) l i m i t f o r t h e h e i v i e i Pd and *Ru \ i u c l e i . S t a c h e l e t a l . p o i n t out t h a t the e n e r g y r a t i o E2 /E2 i s not w e l l r e p r o d u c e d i n t h e i r c a l c u l a t i o n . Experimentally, that r a i i o hs c l o s e r t o the SU(5) l i m i t t h a n the 0(6) l i m i t , even f o r Pd. However, i f the s u g g e s t e d 2^ l e v e l a t 924 keV i n Pd i s i n s t e a d the 2"£ l e v e l w i t h i n the model s p a c e , the E 2 / E r a t i o i s j u s t above t h a t of the 0(6) limit. In Pd the E Q / E energy r a t i o i s h i g h e r t h a n f o r the l i g h t e r Pd n u c l e i , but s t i l l o n l y mldwaV between t h e SU(5) and the 0(6) l i m i t s . Stachel e t a l . s u g g e s t t h a t the 0 l e v e l i s an i n t r u d e r l e v e l s i m i l a r t o t h o s e known i n n e a r b y Cd n u c l e i . Taken t o g e t h e r , t h i s e v i d e n c e i n d i c a t e s t h a t Pd c a n ­ not be d e s c r i b e d by the s i m p l e 0 ( 6 ) l i m i t of IBM a l o n e . Recent c a l c u l a t i o n s show t h a t c o m p l e t e s t r u c t u r e s r e s u l t i n g f r o m i n t r u d e r s t a t e s must be i n c l u d e d w i t h a l a r g e degree of m i x i n g o c c u r r i n g between the two configurations [KUS85]· E

+

E

+

a n d

E

+

E

+

a r e

c o n

1 1 2

1 1 2

+

+

2

1 1 2

+

+

1

2

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch028

2

3. S y s t e m a t i c s of p j n e a r A=100. R e s u l t s 102-106 Pd Mo, Ru, and from l i t e r a t u r e d a t a .

Fig.

0.16

h

2

9 6

0.12

h

H

0.08

h-

—\

i U Z

and for are

0.06

0.04

h-

0.02

h

CM

X

0.04

h

54

56

58

60

62

Neutron number

64

66

54

56

58

60

62

Neutron number

64

66

194

NUCLEI OFF THE LINE OF STABILITY

su red EO t r a n s i t i o n s i n the neutron r i c h n u c l e i We have 'Mo, R u , and ~ ^ P d using the (t,p) reactions and coincidence techniques. L i s t e d i n Table 1 are the values f o r the EO(K) branching r a t i o s from our measurements. Where h a l f - l i f e information and E2 branching: r a t i o s are a v a i l a b l e from our own measurements or from the l i t e r a t u r e , ρ and 1X values have been determined (see F i g . 3 ) . The P J and X values f o r MZr. Near closed major s h e l l s , such as N=50, nuclear shapes are s p h e r i c a l . A gradual t r a n s i t i o n from s p h e r i c a l to deformed shape i s expected to take place as neutron number increases, with maximum deformation at m i d - s h e l l , as observed i n both even—even [CHE70] and odd—mass [MON82] n u c l e i near A~100. However, the Z=40 proton s u b s h e l l closure i n t h i s region leads to the appearance of i n t r u d e r c o n f i g u r a t i o n s which c o e x i s t with the ground-state configuration. The i n f l u e n c e of t h i s c o n f i g u r a t i o n mixing on the l e v e l s t r u c t u r e of t r a n s i t i o n a l Mb n u c l e i was described by recent neutron-proton interacting boson model (IBM-II) c a l c u l a t i o n s which took i n t o account e x p l i c i t l y the t w o - p a r t i c l e , two-hole proton e x c i t a t i o n s across the Z=40 s u b s h e l l [SAM82]. A s p e c i a l s i t u a t i o n occurs at ^^Zr (Z=40), where the neutron s u b s h e l l closure (N=56) gives t h i s nucleus a double s u b s h e l l c l o s u r e . Thus, p a r t i c l e hole pair e x c i t a t i o n s across both s u b s h e l l gaps are p o s s i b l e . This could produce s i t u a t i o n s much l i k e those i n doubly closed s h e l l l^O, i n which the lowest-lying intruder deformed band has been shown to a r i s e due to such e x c i t a t i o n s [BR064]. The f i r s t excited state of 9 6 z ^ Q+ s t a t e , as i n doubly closed s h e l l 0 or closed s h e l l / s u b s h e l l 9°Zr. Support f o r the i d e n t i f i c a t i o n of the 0+ state i n 9 6 z as an intruder deformed state comes from p a r t i c l e t r a n s f e r +

r

s a

1 6

r

0097-6156/ 86/0324-0196$06.00/ 0 © 1986 American Chemical Society

29.

MOLNÂR ET AL.

Possible Evidence for a-Clustering (α)

197

1.0

4oZr(Oj)

D 1 I

(t,p)(p,t)( C, 0) (d, Li)|

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch029

l4

Π. A: 96 N 54

l6

6

Γί

ri

J

98 56

100 58

102 60

I 104 62

Fig. 1. a) R e l a t i v e cross sections f o r t r a n s f e r r e a c t i o n s populating the f i r s t two 0 states of Zr n u c l e i . A l l cross sections are normalized to the ground state cross s e c t i o n of 9oZr. fc) Percentage composition of the ground states of the target Mo n u c l e i . Unshaded bars: c o n f i g u r a t i o n with one proton boson; shaded bars: " i n t r u d e r " c o n f i g u r a t i o n with three proton bosons. +

data. Figure 1(a) summarizes the r e s u l t s of two-proton [MAY82], two-neutron [BAL71] and a l p h a - p a r t i c l e [VAN84] t r a n s f e r r e a c t i o n s t u d i e s ; Figure 1(b) shows the admixtures of the basic s p h e r i c a l and the " i n t r u d e r " deformed boson c o n f i g u r a t i o n for the ground state wavefunctions [SAM82] for the Mo targets used i n some of these s t u d i e s . The most s t r i k i n g feature i s the unusually high alpha-pickup strength to the 0+ state of ^ Z r [VAN84]· Even though some of the two-particle t r a n s f e r cross sections do not c o r r e l a t e e x a c t l y with the alpha-transfer cross s e c t i o n s , which may be due to i n t e r f e r e n c e e f f e c t s , the high value of the cross s e c t i o n r a t i o i n favor of the state i s a common feature. Apparently, t h i s state d i f f e r s markedly i n nature from the supposedly s p h e r i c a l ground s t a t e ; we suggest that t h i s i s due to i t s character as a f o u r - p a r t i c l e , four-hole deformed s t a t e , l i k e the 0* state of doubly closed s h e l l * 0 [BR064]. In order to e l u c i d a t e the nature of the 0 e x c i t a t i o n s i n 9©Zr j search for associated s t r u c t u r e s , we have performed (η,η'γ) r e a c t i o n s t u d i e s . Gamma-ray s i n g l e s and angular d i s t r i b u t i o n measurements were f i r s t c a r r i e d 6

6

+

a n c

t 0

198

NUCLEI OFF THE LINE OF STABILITY

out at the reactor neutron beam f a c i l i t y of the I n s t i t u t e of Isotopes i n Budapest. These measurements l e d to the i d e n t i f i c a t i o n of s e v e r a l h i t h e r t o unknown t r a n s i t i o n s from previously unplaced l e v e l s [FAZ84]. Excitation f u n c t i o n measurements performed at the U n i v e r s i t y of Kentucky pulsed neutron beam f a c i l i t y have shown that a 644.2-keV t r a n s i t i o n , also i d e n t i f i e d i n the Budapest experiments, populates the 0+ s t a t e . P a r a l l e l beta decay studies [MEY85] i n d i c a t e that the c o r r e c t energy of the l a t t e r i s 1581.4 +0.5 keV, hence the 644-keV t r a n s i t i o n deexcites the w e l l known 2225-keV s t a t e . These r e s u l t s have also been confirmed by p a r a l l e l in-beam (t,py-y) studies [HEN85]· The angular d i s t r i b u t i o n s of the 2225-keV and 644-keV gamma rays d e e x c i t i n g t h i s l e v e l to the f i r s t and second 0 s t a t e s , r e s p e c t i v e l y , have been measured at the Kentucky f a c i l i t y . As F i g . 2 shows, they are i d e n t i c a l and give a unique 2 s p i n - p a r i t y assignment, i n contrast with the p r e v i o u s l y suggested value of 3" [FLY70,SAD75]. We a s s o c i a t e the 2225-keV 2+ s t a t e with the t h i r d l a r g e s t peak observed i n the ( d , L i ) Z r r e a c t i o n study by van den Berg et a l . [VAN84] · Although these authors prefer a 5" assignment, t h e i r angular d i s t r i b u t i o n data are also c o n s i s t e n t with spin 2 which gives about 60 percent alpha-pickup strength with respect to the ground state strength. We have searched f o r a p o s s i b l e doublet at t h i s energy with the (η,η'γ) r e a c t i o n which should lead to s i g n i f i c a n t population of a 5~ s t a t e , but found no evidence for a second s t a t e . Hence the ( d , ^ L i ) r e a c t i o n leads to strong population of the 2+ s t a t e as w e l l . The measured B(E2;2+->0+)/B(E2;2+->0+) r a t i o of 10 demonstrates a strong p r e f e r e n t i a l decay to the 0+ s t a t e . These two f a c t s suggest the 2225-keV state as the 2 member of an i n t r u d e r deformed band b u i l t on the 0+ f i r s t excited state i n 9 6 According to the angular d i s t r i b u t i o n pattern of the 1107-keV t r a n s i t i o n depopulating the 2857-keV s t a t e (see F i g . 3) t h i s l e v e l i s an obvious candidate f o r the 4 band member. It can be associated with the 2.87-MeV peak i n the ( d , L i ) spectrum of van der Berg et a l . [VAN84] even though t h e i r p a r t i c l e angular d i s t r i b u t i o n i s best f i t t e d with L-3. In F i g . 4 we summarize our r e s u l t s , emphasizing the proposed band s t r u c t u r e . It i s important to understand what gives r i s e to the established c o e x i s t i n g i n t r u d e r band i n doubly closed subshell 9©Zr. 6 0 .

intensities higher

+

o f t h e scheme t h e r e 2

states

Y i s a very

[GRU72] and has r e g a i n e d i n several served

part

+

Q

rotational

isomer

neutron p a r t i c l e

7 9 2 , 912 and 990 keV a g r e e +

these s h e l l

9 8

9 8

is

2 7 / 2 " and t h e 162 keV t r a n s i t i o n

and one p r o t o n i n t h e g y

Y , although t h i s

Shape c o e x i s t e n c e

Its

for a

be u n d e r s t o o d

The i s o m e r

Ζ = 40 ( o r 38) and Ν = 56 w h i c h

Apparently, 9 7

1.00(19).

characteristic

can b e s t

o f a hn/2

of

t h e new l e v e l s

at

is

Fig. 1.

of the 6 , 4 , 2

A ~ 1 0 0 . An example

concluded

S r . Re­

Y has been d i s c o v ­

o f the two-neutron c o r e . Thus, t h e energies

of the g g / 2 ®

beyond t h e Ν = 50 s h e l l is

9 7

with higher spins i n ­

proceeds t h r o u g h a s e r i e s

intense γ t r a n s i t i o n s

Zr.

9 8

in

and p a r i t y

average energy d i f f e r e n c e s

Sr

of

of E 3 > =

units

and i t s d e p o p u l a t i o n are

9 9 / 2 Photon i s c o u p l e d t o s t a t e s the

particle

consists of the conversion

neutron hole.

all

o f 144 ms i n

9 7

[BL085].

which

state

s p i n s up t o 9 / 2 had

a t 3523 keV and i s d e p o p u l a t e d t h r o u g h a

2 single

state

configurations

quasiparticle

9 6

with

o f t h e β " decay

o f 162 keV w i t h a p r o b a b l e m u l t i p o l a r i t y

particle-to-hole

of

levels

[LHE85] w h i c h decays t h r o u g h a sequence o f l e v e l s

the g /

transition

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch030

Y which contains

9 7

[M0N76, PFE81] f r o m t h e s t u d y

of

for a

rota­

the γ t r a n s i ­

between t h e l e v e l s

times

of

l e v e l s was

of the

K forbiddenness

degree o f

in

1

/ 2

u*

9 7

2

Y

are populated

schemes o f t h e

π p 1/

β-decay

2

Tt g 9 / ® 2*

2

π g 9/ ®

2

ν

97 39'58

[MEY85].

[ R 0 E 7 8 ] . h = l o g ( H ) / n , where H i s

from

are taken

+

2

2

πς9/ ® v(h11/2.g7/2) π g 9/ β v(d5/ - g7 )

level

2

(21/ )

(27/f)

Ut. ms

(the hatched l e v e l s

1: Those p a r t s

isomers

Fig.

1 *.27.9 1336.3 1 319.6

3 3 6 1 .1

3523.3

=

283.8

«2.2

(9/2Ί

« M .

706.,''M.

975

the hindrance

of

the t r a n s i t i o n s

and η =

/ 2

=8.6us 2

2

-

K

f

- λ

the

coefficients

of

5

-TT.U22/]

]v[^113/ ][40^2]

v

99 39'60

i n t h e decay

5

f ;/2 tx[^22

conversion

Ν ~ 60, which are observed

0.83ns

,('321

['7/2*1

i n t h e β" d e c a y ) . The t h e o r e t i c a l

at

2

tl,

200 keV energy

Y isotones

100 Transition

v

98 39'59

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch030

Η

> 00

30.

Structure Transition in Heavy Y Isotopes

LHERSONNEAU ET AL. A reasonable

obtained with

fit

t o the energies

the rotational

the parameters

Κ = 2, E

A considerably

better

Ε = E

Although ed, of

o f t h e band

+A [ l ( I + l ) - K j

Q

the value

however,

possible

2

[PEK84] w i t h

o f A = 1 7 . 2 keV i s s m a l l

o f about

the

90 % o f t h e r i g i d

neighbour

with the classical result

rotor

( i t corresponds

value)

it

t o a mo­

i s not unexpect­

A = 9 9 . I f Κ = 1 o r Κ = 3 were used

rotational

formula then values

which are not compatible w i t h

The the

parity

with

ground

its

own

state

of

ground

of

decay

t h e members 9 8

into

[BEC83,SIS76]. tions

of

the available Y

o f t h e band

information.

since sight

state

of

indicate

9 8

the conversion

1 2 1 , 2 0 4 , 51 and 119 keV w h i c h

state

from

multipolarities

connect

nuclei unambi­

are assigned

+

into

are

this

probably

level

to

and

allowed

of the γ t r a n s i ­

t h e band

o f Ml a n d / o r

other Y.

head w i t h

the

E2 a n d , h e n c e , no p a r i t y

parity.

But i t c a n n o t be r u l e d o u t t h a t t h e 121 keV t r a n s i t i o n has a m u l t i p o ­ o f E l w i t h a s m a l l a d m i x t u r e o f M2 i n s t e a d o f M1/E2. A m i x i n g p a r a 2 9

larity meter

of δ

= 4 · 1 0 " ^ would a c c o u n t

transition

factors the

Sr

1

coefficients

c h a n g e . Thus t h e band head s h o u l d have p o s i t i v e

this

Zr

9 8

9 8

be d e t e r m i n e d

and p a r i t y

t h e β" decays

t h e ground

At f i r s t

cannot

Spin

band

for the f i t

o f A ~ 27 keV and ~ 12 keV

t h e knowledge a b o u t

i n t h i s mass r e g i o n . Hence, Κ = 2 i s proposed f o r t h e band i n guously

if

2

formula

s i n c e a v a l u e o f A = 1 8 . 0 keV has been deduced f o r t h e ground s t a t e t h e odd-mass

would

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch030

can be

+ Β [I(1+1)-K ]

2

Q

+ al.

2

ment o f i n e r t i a

o f t h e members

E=E

= 4 5 5 . 3 k e V , A = 1 7 . 2 keV and Β = - 2 2 eV a r e u s e d .

fit is,

+ A [l(I+l)-K ]

Q

formula

205

of

f o r both

and f o r t h e h a l f - l i f e

4.6 · 1 0

121 keV l i n e

the conversion

o f t h e 495 keV l e v e l

and 3 . 3 f o r t h e E l and M2 f r a c t i o n ,

7

has t h i s

character,

then the p a r i t y

coefficient (with

of

hindrance

respectively).

If

o f t h e band members

is

negative. Calculations nuclei ties,

namely

both

have

this

intruder

9 7

Sr

and

of the excitation

i n t h e A = 100 r e g i o n

and

9 9

{π[422 5 / 2 ] v [ 4 0 4

the

same

Zr,

see b e l o w .

the neutron

bital

f o r the 2

driving

neutron

configuration

+

alternative

proton-neutron While

band w h i c h

there

is

9/2]}2

+

o f t h e band heads o f odd-odd f o r both

pari­

and { π [ 3 0 3 5 / 2 ] v [ 4 0 4 9 / 2 ] } 2 "

which

configuration.

candidates

There

is

evidence

[MEY84]

causes a l s o i s o m e r i s m i n t h e odd-mass

Another

configuration

energies

[H0F84, MEY84] o f f e r

fact

of interest

originate with

from

i s , that

the ggy

the p o s s i b i l i t y

2

that

isotones

both the proton

single

particle

or­

of a strong deformation

-

interaction. little

doubt

about

the rotational

i s based upon t h e 495 keV s t a t e ,

the nature

properties

of the

of the levels

below QO

the is

band head and o f t h o s e w h i c h a r e o n l y not c l e a r .

able

that

though

most

These l e v e l s

populated

do n o t show a membership t o bands and i t

o f them a r e n o t o f r o t a t i o n a l

t h e energy

of

i n t h e β" decay o f

119 keV o f t h e f i r s t

character.

excited

state

is

In p a r t i c u l a r , is similar

yo

Sr

prob­ al­

to the

206

NUCLEI OFF THE LINE OF STABILITY

energy

of

the

odd-mass exists

first

nuclei

in

Y.

9 8

e x c i t e d members o f

it If

is

so t h e n

l y i n g members was f e d to

choose

strong

improbable in

a convenient

hindrance

of

it

rotational

that

would

an

be a s t o n i s h i n g

t h e decay o f t h e

value

of

more t h a n

a t 495 keV i n t o t h e ground

Κ for

10

bands o f t h e

unperturbed

for

1 0

that

state

none o f

i s o m e r s . Moreover

such

neighbouring

ground it

the is

band higher

difficult

a band w h i c h w o u l d e x p l a i n

the

direct

decay

from the

the

band

head

state. QQ

The

ground

corresponding

and

levels

first

excited

in the

isotones

character of the p a r t i c l e - v i b r a t o r The

lowest

levels

similarity

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch030

clei ond

of

of

the

these

9 7

are

9 9

may r a t h e r

Zr

for

due

depicted

be r e l a t e d

which a J-2

in

probabilities

in spite

possibly

*°Y

and

are

observed t r a n s i t i o n

states

Sr

of

fig.

a low

lying

J-l

[MEY84].

The

indicates

of the differences to

2.

to

and

c o u p l i n g t y p e has been proposed

isotones

have t h e same s t r u c t u r e excited

states

striking

that

both

nu­

i n e n e r g y . The s e c ­

intruder

configuration

f r o m a deformed s h a p e . The s y m m e t r i c

rotor

The l e v e l 9 9

Sr

[PFE81,PET85] and

which the

" γ

scheme o f

9 9

Y

via

has been s t u d i e d b o t h t h r o u g h t h e β" decay

an

is

directly

populated

most

extended

rotational

isomeric

in

fission

symmetric

properties rotor.

accordance

with

deformation the

bands

nuclei.

Thus, the

of ε can

The

of

be

9 9

Y

suggest

the

accounted

half-life

of

for

the

keV

has been f o u n d that

configurations Also

2142

with

in

high

of spin

nucleus

contains

an odd-A

nucleus

s i d e bands have been o b s e r v e d .

predictions

0.3.

at

[M0N82,MEY85]. T h i s

band w h i c h

a t A ~ 1 0 0 . In a d d i t i o n , s e v e r a l The

state

of

can the

mixing in

this

Nilsson ratios

the

nucleus

be a s s i g n e d model

δ for

classical

isomer

at

2142

on

three

to

is

for

classical

the

bands

A ~ 100

in

and

t h e ΔΙ = 1 members picture

keV

a

all

is

of

a of

rotational

obviously

due

to

Κ

forbiddenness. Conclusions^ The

available

knowledge

t o p e s o f Y shows t h a t t h e s e n u c l e i 9 7

Y

has

properties

nucléons

which

beyond t h e c o r e

three-quasiparticle

9 6

the

neighbouring

have v e r y d i f f e r e n t

are

basically

determined

Zr

(or

The e x i s t e n c e o f t h e i s o m e r

character

9

^Sr).

indicates

that

Y

most

rotational

probably

has c o e x i s t i n g

band on t h e

rather of vibrational 9 9

Y

is

characterized

the investigated

nuclear

495 keV l e v e l

through

there

s o f t n e s s a g a i n s t d e f o r m a t i o n even a t h i g h e x c i t a t i o n 9 8

neutron-rich

is

the

no

valence of

particular

energy.

shapes w i t h

and o t h e r

iso­

structures:

a well

developed

l e v e l s w h i c h seem t o

be

nature. through t h e occurence o f

rotational

bands a l l

r e g i o n o f e n e r g i e s up t o 2 MeV as a s y m m e t r i c

over

rotor.

30.

Structure Transition in Heavy Y Isotopes

LHERSONNEAU ET AL.

These

results

demonstrate

considerable study

of

details

change

the of

isotopes

the

be even more still

of

shape

rapid at

vestigations

of

the

of

only

nuclei

at

one

neutron

A ~ 100

odd n u e l e o n numbers can p r o v i d e

in

shapes

the

The t r a n s i t i o n

in

the

Sr and Zr c h a i n s where t h e

and where t h e s h e l l - m o d e l

high e x c i t a t i o n

energies

has n o t y e t

of

the

level

schemes

of

the

causes

and t h a t

insight

Y isotopes Ν = 60

character

into seems

Y isotopes

and

to

a

the the to

isotones

of the Ν =

been t e s t e d . F u r t h e r

a r e , h o w e v e r , needed i n o r d e r t o c o n f i r m i n d e t a i l

interpretation similarly

with

a difference

nature

transition.

than

have c o e x i s t i n g

58 i s o t o n e s

that

the

207

the see

in­

proposed whether

r a p i d s t r u c t u r e changes o c c u r i n t h e Rb and Nb i s o t o p e s a t Ν ~ 6 0 .

F i g . 2: The lowest l e v e l s of the isotones of Y . The v a l u e s o f

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch030

9 8

i 2 f e x c i t e d s t a t e s and o f 60.

One should thus also expect Y,

deformed rare earths, and this can be inter­

which i s Intermediate In Ζ between Sr and Zr,

preted as a consequence of an unusually low

to have a similarly sharp onset of deformation

strength of the pairing interaction [PET85J.

leading to a rotational structure for Ν > 60.

A third, and quite intriguing, feature of deformed A=100 nuclei i s the apparent coexis­ tence of spherical and highly deformed shapes. A l l of the N=60 isotones ^ S r , 10

«Suand

106

1 0 0

Zr,

102

H>,

+

P d have an "extra" 0 state (the

0^ state) that cannot be reproduced in col­ lective models as a simple collective excita­ tion of the core. 98

The very low-lying 0^

1 0 0

level in S r and Z r , which lies at 215 and 331 keV respectively, can best be understood as +

shape coexistent 0 states with the ground state being dominantly a symmetric rotor and 46

44*"

W

42*°

+

+

40

7 7

Fig. 2. Ε(4 )/Ε(2 ) systematics. Ί

Ί

w

5 7

"

+

the 02 state being dominantly a spherical, or nearly spherical, shape [W0H86J. In contrast,

NUCLEI O F F T H E LINE O F STABILITY

210

the heavier Mo and Ru isotopes were inter­

tion probabilities.

preted as asymmetric rotors with non-zero

the 5 singlenquasiparticle band calculations

values of the geometric asymmetry parameter γ

of [W3H85] are presented. Other levels, such

[SHI83], [SIM80].

as particle-vibration (3 quasiparticle) states

In terms of the three limiting group sym­

in "Y are discussed in [PET95]. Since so l i t t l e was known about the

metries used in the interacting boson model

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch031

In the following, only

(IBM), the shape transition of Ru or Pd nuclei

single particle structure of deformed A=100

can be explained as a SU(5) to 0(6) transition

nuclei, our approach in [W0H85] was to use a

[STA82]. The transition of Sr or Zr nuclei

textbook version of the particle-rotor model,

is characterized instead as SU(5) to SU(3).

as outlined by [BUN71], that had been system­

For Mo nuclei, the shape transition appears to

atically used to study deformed rare earths. The model parameters f a l l into two clas­

be more complicated than the above and has not yet been adequately described. The unusual features of the A=100 nuclei briefly reviewed above continue to stimulate

ses, an "energy" class and a "transition" class. The energy class includes

(the

proton pairing gap), the 3 Nilsson parameters

strong interest in the structure of these

(κ, μ, and 6), the inertia! parameter

nuclei. Theoretical studies, including poten­

of the axially symmetric deformed core, and

t i a l energy and microscopic shell model calcu­

the Coriolis attenuation parameter k. Fig. 4

lations, as well as a more detailed review of

shows the Nilsson parameters and

here permits, are discussed in [PET85].

we used.

For a l l bands we used δ = 0.34 and an in-

the features of the A=100 region than space

ertial parameter of 21.8 keV. The bandheads were calculated, not arbitrarily set [VJ0H85].

II.

DEFORMED ODD-A Y ISOTOPES A clear gap in the study of this region

was a lack of information on single-particle

5.50

states in deformed nuclei with Ν > 60. Only

5.25

recently, since we began our first Y study with

5.00

has such information emerged. The f

status through the end of 1984 was recently summarized ty [PET85].

4.50

From studies of the decay of an 8.6-ys isomer in "Y [M3N82] and our study [PET85] 99 of the decay of

4.25 4.00

Sr, we have identified 5

rotational bands i n « I .

[ΡΕΓ85] gives the

QQ

details of our

4.75

Id

Sr decay study and [W3H85]

gives details of a particle-rotor calculation of the rotational band structure and transi­

Fig. 4. δ Nilsson diagram for protons with κ = 0.067 and μ = 0.53; BCS model Fermi level for Y with Δ = 0.69 MeV i s indicated by dots.

31.

Rotational Structure of Y Nuclei

W O H N E T AL.

211

Of the energy parameters, k was determined by our

parity and k - 1.35 for normal-parity bands. The transition class of parameters were g' (the ratio of the spin g-factor and the free

Experiment

Calculation

Bandhead

data. We found k = 0.77 for unique-

-

5/2[303]

26 ps

3/2[301]

33 ps

1/2[431]

49 ps

5/2[303]

4.8 ns

4.7±0.5 ns

3/2[301]

1.9 ns

2.0±0.6 ns

-

proton g-factor) and H (the enhancement factor 103

Nb

of the Δ Κ Ο E l Nilsson matrix elements). We found g' = 1.0 for the unique-parity bands and g

1

In order to test our calculation against

= 0.7 for the normal-parity bands. An H

103

absolute transition rates, we turned to Nb.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch031

of 3.0 was found to give good reproduction of the relative El and Ml rates for the Coriolis-

since the same 3 lowest bands were seen and

mlxed 5/2[303] and 3/2(301] bands. The bands

El transitions from the 5/2[303] and 3/2[301I

and transition rates are given in Fig. 5.

bandheads i n

103

Nb had measurable half-lives [SE084]. We did not change the Nilsson El matrix elements but

3 S 1595

'»2*

E x p e ^ m e n t o l Bonds ι

( o )

Transitions: MI + E 2 •

correction (due to the different • W W j T

,

1220

, ^ Ι Isa

1

5/£pl

and

i-

eCfrS 656 7 -'2£ /r>

407

-- ^ - r r E

J25_ [301

5/2

[303]

5/2[422]

: : - i J : : 1/2

103

Nb). We obtained the

lifetimes given in the table above, which clearly shows that H=3.0 works remarkably well

ALL . . V f i y l zea. .

Η-VI-

Λ 3/2

£

9 9

quasiparticle energies for Y

^

3^ΠΤΤΠθ09

_ V l Hi _ J-i_ _ _

changed only the pairing factor

[43l]

also for 3/2 [431]

1

0

3

Nb.

The "adjustment" factors (k, g \ H) of our "textbook" version of the particle-rotor

Tronsitions Ml • E2 •

model are much closer to unity for "Y than i s typical for the rare earth nuclei.

It is inte­

resting to speculate i f this can be simply a consequence of the lower density of single-particle states and lower pairing energy for the neutron-rich A-100 nuclei. Figure 5. N i l s s o n bands and r e l a t i v e t r a n s i t i o n i n t e n s i t i e s f o r Y . For ease of comparison the exp. i n t e n s i t i e s are given i n (a) and (b). 9 9

Our study of

1 0 1

Y levels

from the decay of ^ S r i s not

NUCLEI OFF THE LINE OF STABILITY

212

yet complete, hit the 4 bands shown in Fig. 6

III. DEPOBMED CCD-ODD Y ISOTOPES

1C1

are definite. In Y the 3/2[431] band lies

As mentioned above, deformed A*100 nuclei

lower and the 1/2[431] band lies higher in

have unusually weak pairing, as indicated by

energy than i n « I . hence identification of

moments of inertia of 70% of the moment of a π

rigid spheriod (see Fig. 3) for the Κ = 0

101

the latter band is more difficult for Y.

+

ground bands of e-e nuclei. With the addition of 1 quasi-

Tronsitions M l * E2 I Q

^

particle, the deformed odd-A

.1027 '996

nuclei have moments of inertia

«2 S -622 5/ -

that increase to -85%. With 2

.114. .

---j3

.V!

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch031

2

unpaired quasiparticles, the •8-3JQ- -"/* - «

'z

.494A.

Λ-

deformed oro nuclei could thus have moments nearly equal to the rigid moment of inertia.

3. Fig.

Nuclei in which the effec­

3/,[«'l

[422]

M

tive neutron and proton pairing

6.

gaps have vanished are referred

Nilsson bands and relative transition Intensities for The similarity between the level structures of 101

"Y and Y i s striking. and

(Also, both

101

Nb

have the same 3 lowest bands [SE084]

with very similar level spacings.) Indeed, a l l known odd-A deformed A=100 nuclei appear to have very similar deformed cores. As stated earlier, coexistence of deformed

1 0 1

Y

to as "pairing-free" nuclei.

The deformed odd-odd A=100 nuclei thus present a unique opportunity to observe the pairingfree nuclear phase at conditions of low angu­ lar momentum and low excitation energy. [EED77] proposed that the unusually weak pairing for A=100 nuclei i s associated with the very strong coupling between gg/2 protons

and spherical shapes i s characteristic of the

and g-ji2 neutrons. For o-o nuclei, we expect

lighter deformed A=100 nuclei. Both "Y and

the deformed states with the strongest p-n

101

coupling would be most likely to approach the

Y have anomalous states (at 599 and 890 keV

respectively) that are not associated with the

pairing-free phase. Thus cro nuclei having

lower energy bands. These states decay only

low-lying Nilsson orbitals with strong ïïg^

to the 3/2 [301] bandhead, hence could be the

and Vg^2 components should have the required

p

strong p-n coupling.

l/2

s t a t e

expected for the 3 9 ^ proton i n a

spherical potential. Spherical A=100 nuclei +

have a 2^ energy of -800 keV, and the anoma­

Odd-odd Y and Nb nuclei with Ν > 60 are ideal candidates, since the odd proton state

lous states are fed only by -800 keV γ rays,

5/2 [422] has a large

which supports our speculation that they may

or 63 nuclei have a 3/2 [411] ground band with

be

a large gyy component.

particles coupled to a spherical core.

2

component and N=61

These orbitals

31.

WOHN ETAL.

Rotational Structure of Y Nuclei π

should couple to form a low-lying Κ * 1

213

band

that should be strongly fedtythe β decay of the e-e parent. π

+

Figure 7 gives our proposed Κ • 1 bands. +

The lower 1 bands we propose to be nearly "pairing free" bands and their moments of inertia (shown in Fig. 3) range from 88% to

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch031

94% of the rigid value. Our TRISTAN data was

these proceedings gives additional arguments. REFERENCES

[BEN84] R. Bengtsson, P. Moller, J.R. Nix and J. Zhang, Phys. Scripta 29, 402 (1984). [BUN71] M.E. Bunker and C.W. Reich, Rev. Mod. Phys. 43, 348 (1971). [CAS81] R.F. Casten, D.D. Warner, D.S. Brenner and R.L. Gill, Phys. Rev. Lett. 47, 1433 (1981). [CHE71] E. Cheifetz, R.C. Jared, S.G. Thompson and J.B. Wilhelmy, Phys. Rev. C 4, 1913 (1971). [FED77] P. Federman and S. Pittel, Phys. Lett. 69B, 385 (1977) and 77B, 29 (1978). [MEY84] R.A. Meyer, R.W. Hoff, and K. Sistemich, FY 1984 Annual Report of Nuclear Chemistry Division, LLL, UCAR 10062-84/1, p. 41. [MON82] E. Monnand, J.A. Pinston, F. Schussler, B. Pfeiffer, H. Lawin, G. Battistuzzi, K. Shizuma, and K. Sistemich, Z. Phys. A 306, 183 (1982). [PEK86] L.K. Peker, F.K. Wohn, John C. Hill, and R.F. Petry (to be published). [ΡΕΓ85] R.F. Petry, H. Dejbakhsh, J.C. Hill, F.K. Wohn, M. Schmid, and R.L. Gill, Phys. Rev. C 31, 621 (1985). [SEO84] T. Seo, A. Schmitt, H. Ahrens, J.P. Bocquet, N. Kafrell, H. Lawin, G.Lhereonneau,R.A. Meyer, K. Shizuma, K. Sistemich, G. Tittel, N. Trautmann, Z. Phys. A 315, 251 (1984). [SHI83] K. Shizuma, H. Lawin, and K. Sistemich, Z. Phys. A 311, 71 (1983). [STA82] J. Stachel, N. Kaffrel, E. Grosse, H. Emling, H. Folger, R. Kulessa, and D. Schwalm, Nucl. Phys. A383, 429 (1982). [SUM80] K. Summerer, N. Kaffrell, E. Stender, N. Trautmann, K. Broden, G. Skarnemark, T. Bjornstad, I. Haldorsen, and J. A. Maruhn, Nucl. Phys. A339, 74, (1980). [WOH83] F.K. Wohn, John C. Hill, R.F. Petry, H. Dejbakhsh, Z. Berant, and R.L. Gill, Phys. Rev. Lett. 51, 873 (1983). [WOH85] F.K. Wohn, John C. Hill, and R.F. Petry, Phys. Rev. C 31, 634 (1985). [WOH86] F.K. Wohn, John C. Hill, C.B. Howard, K. Sistemich, R.F. Petry, R.L. Gill, and H. Mach, Phys. Rev. C (submitted August 1985). RECEIVED May 2, 1986

32 Coexistence in the C d Isotopes and First Observation of a U(5) Nucleus A. Aprahamian Department of Chemistry, Clark University, Worcester, MA 01610 118,120

The Cd nuclei were studied from the decay of Ag produced from the fission of U. The resulting systematics of the cadmium nuclei show that the intruding configuration bandheads have in fact risen in excitation energy relative to those observed in Cd and are well-separated from the two­ -phonon triplet of states. These results also led to the identification of a set of five states, in Cd whose close-spacing in excitation energy and decay transition probabilities seem to qualify Cd as the first example of a U(5) nucleus. 235

112,114

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch032

118

118

The presence of intruder states near the Z=50 closed shell has been well documented and tested [HEY82] for Cd, whose structures showed an anomalous grouping of five states with a centroid at approximately 1.2 MeV instead of the expected vibrational triplet of states. The low-lying excitation structure of these nuclei and their E2 transition probabilities have been successfully interpreted in terms of the mixing of an intruding rotational configuration with the normally expected vibrational configuration where the intruder states are described as particle-hole excitations resulting from the excitation of a pair of protons across the Z=50 major oscillator shell gap. 112,114

Detailed descriptions of the model is given elsewhere [ΗΕΥ82], [ΗΕΥ83]· The basic idea, however, is to calculate two sets of states where one corresponds to the vibrational states and the other corresponds to the rotation-like intruder states which arise from the particle-hole excitations, and then to mix the two resulting configurations. The hamiltonians for both configurations are esssentially the same: H

VIB ROT

=

6

π "d

+

E

v "d "

K

% '%

where and ε^ are the proton and neutron boson energies and the KQ^.Q^ is the neutron-proton quadrupole interaction. The main difference between the two configurations arises from the n(n-l) particle number dependence of the quadrupole interaction where η is the effective number of valence particles. The particle number dependence of the KQ^.Q^ term results in the prediction of a "V" shaped systematics for the excitation energies of the intruding 0097-6156/ 86/0324-0214S06.00/ 0 © 1986 American Chemical Society

32.

215

Coexistence in the Cd Isotopes

APR AH AMI AN

c o n f i g u r a t i o n for a given

i s o t o p i c chain where the i n t r u d e r states decrease i n

energy towards the middle of the neutron s h e l l and comparisons

of

excitation

i n Cd n u c l e i near

the

engeries

the

predicted

rise

in

rise

thereafter.

transition

Although

branching

ratios

2,

neutron midshell

with the above mentioned model, not test

and

(^* *^Cd) show very good agreement

enough data e x i s t e d away from m i d s h e l l excitation

energy

for

the

to

intrudering

11 ft 170

configuration. known

Cd

Studies

ii0

of

systematics,

and

> ^cd A

to

were undertaken

determine

the

i n order to extend

evolution

of

the

the

intruding

configuration. These n u c l e i were studied from the decay of Ag produced i n the f i s s i o n of J J

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch032

enriched National the

U

at

the

Laboratory

measurements

γ-γ

on-line

isotope

separator,

several

standard

spectroscopic

by

of

angular

and

3-γ

The

systematics of the

coincidence,

correlations

and

by

a

TRISTAN,

s t a t e s of the Cd

the

new

r e s u l t s from the

that

the

the

same as 0+

third KeV

centroid

of

that

state has

in

Cd.

the

of

present

quintuplet

the

0+,

gone up

2+,

study of

4+

states

that

in

triplet

i n energy to

It i s c l e a r

x l o

for

in

1615

the

KeV

intruder

observed

increase

confirms

the

nuclei.

A good signature

the of

B(E2) R,

in

i n e x c i t a t i o n energy of the

coexistence

mixing

of

the

n u c l e i are shown along

u

^ Cd.

This

r e s u l t s from the

1,

range

large

9 ^cd i

1 1 2

1 1 8 > 1 2 0

1 1 8

in

in Fig.

*Cd

However,

[APR84] and has

interpretation for

in R

i s due

between the

the 1745

risen in This

intruder c o n f i g u r a t i o n bandhead the

structure

of

Cd

i s given

by

i n the top p o r t i o n of F i g . 1.

decrease

Note

is essentially

Cd.

Cd

1.

the neutron m i d s h e l l .

from a maximum of

l a r g e r distances

»

1 1 Z

extent of c o n f i g u r a t i o n mixing

r a t i o R which i s defined

shown i n F i g . 1

and

system,

states.

configuration

energy r e l a t i v e to the **^Cd case which represents

including

detector

1?n

lift

with

Brookhaven

techniques,

fixed-four

l i f e t i m e s of some excited

low-lying

at

5.3X10^ i n

to

two

the

The

values

**^Cd

to

CO CVJ

•H

6

Ό

*J M-l

o

CO

υ

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch032

"cVi 6*8£2I

1 [6j>_;

•

•H

rH

CO CD 4J CO

CO Cl) >->

φ

Z'LZW

ν

CO

C

1

CO

ο


2* and 2j •> 2* t r a n s i t i o n s were c a l c u l a t e d using π

π

π

p

6 = 0.00832 χ E^ where Ε

(MeV)

3

p

2

χ [efm ]/(ju^]

i s the photon energy of the t r a n s i t i o n involved. Results f o r B(E2) and B(M1) p r o b a b i l i t y r a t i o s , as w e l l as the mixing r a t i o δ, i n v o l v i n g 0$ and 2* l e v e l s i n > - T e show considerably c l o s e r agreement with experiment as compared with c a l c u l a t i o n s without mixing. For the sake of s i m p l i c i t y , e i = e3 = 12.4 efm and gi = g (g = + 1.1 μ , g (N) v a r i e d with Ν w i t h i n -0.10 to -0.15 UJJ) was taken i n a l l c a l c u l a t i o n s . The lack of data i n the energy region of i n t e r e s t does not allow such comparison for » T e . Experimental information i s also rather l i m i t e d f o r l l > l l T and does not provide a s o l i d b a s i s f o r mixing c a l c u l a t i o n despite rather reasonable r e s u l t s without mixing. Examination of the two l i g h t e r Te i s o ­ topes would be very important f o r understanding of v a r i a t i o n s i n the i n t r u d e r c o n f i g u r a t i o n e i t h e r side of the middle of the neutron 50-82 s h e l l . The present s i t u a t i o n regarding p o s s i b l e mixing i n Te isotopes high­ l i g h t s s e v e r a l experimental questions, e s p e c i a l l y the uncertainty about the 1517 and 1845 keV l e v e l s i n T e . More complete data on a l l l e v e l s above 2 MeV i s needed i n > Te. In T e a search f o r a l l 0 s t a t e s , and i n the other n u c l e i , for EO t r a n s i t i o n s between O 3 and 0 j s t a t e s , by e l e c t r o n conversion measurement would be valuable. The T e (η,η'γ) r e a c t i o n should be another u s e f u l source of information on excited 0 states i n Te. However even the present stage of the i n v e s t i g a t i o n shows a p o s s i b i l i t y of understanding the problem of i n t r u d e r configurations i n even Te isotopes. γ

118

L20

2

3

1 2 2

TT

Ν

1 2 1 +

v

4

6

e

1 1 8

1 2 0

1 2 2

1 2 0

+

1 2 0

+

1 2 0

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch034

232

NUCLEI OFF THE LINE OF STABILITY

References [CHO82] P. Chowdhury, W.F. Piel, J r . , and D.B. Fossan, Phys. Rev. C25 813 (1982). [DUV81] P. Duval and B.R. Barrett, Phys. Lett. 100B 223 (1981). [FIE78] H.W. Fielding, R.E. Anderson, P.D. Kunz, D.A. Lind, C.D. Zafiratos and W.P. Alford, Nucl. Phys. A304 520 (1978). [GRE85] V.R. Green, J . Rikovska, T.L. Shaw, N.J. Stone, I.S. Grant, P.M. Walker and K.S. Krane, Annual Report, Daresbury Laboratory, 1984/85. [HEY82] K. Heyde, P. Van Isacker, M. Waroquier, G. Wenes and M. Sambataro, Phys. Rev. C25 3160 (1982). [HEY83] K. Heyde, P. Van Isacker, M. Waroquier, J.L. Wood and R.A. Meyer, Phys. Reports, 102 291 (1983). [HEY85] K. Heyde, P. Van Isacker, R.F. Casten and J.L. Wood, Phys. Lett. 155B 303 (1985). [ΜΕΥ77] R.A. Meyer and L. Peker, Z. Phys. A283 379 (1977). [MHE84] A. Mheemeed et a l . , Nucl. Phys. A412 113 (1984). [ROB83] S.J. Robinson, W.D. Hamilton and D.M. Snelling, J . Phys. G: Nucl. Phys. 9 961 (1983). [SHA85a]T.L. Shaw, V.R. Green, N.J. Stone, J . Rikovska, P.M. Walker, S. Collins, S.A. Hamada, W.D. Hamilton and I.S. Grant, Phys. Lett. 153B 221 (1985). SHA85b]T.L. Shaw, private communication, (1985). [WEN81] G. Wenes, P. Van Isacker, M. Waroquier, K. Heyde and J. Van Maldeghem, Phys. Rev. C23 2291 (1981).

[

RECEIVED May 12, 1986

35 Spectroscopy of Light Br and Rb Isotopes Onset of Large Quadrupole Deformation 1,2

1

1

K. P. Lieb , L. Lühmann , and B. Wörmann Universität Göttingen, D-3400 Göttingen, Federal Republic of Germany State University of New York, Stony Brook, NY 11794 1

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch035

2

1. Introduction Among the nuclei off the line of stability, the Ν ≡Ζ = 34-40 region offers some very interesting and unique features: large quadrupole deformations, triaxiality, shape coexistence and trans­ itions, and reductions of pairing correlations leading to rigid body ro­ tation |BEN84, LIS84a, LIE84, HAM85|. We have performed over the last years at the University of Göttingen a systematic study of level energies and lifetimes of rotational bands in this mass region. In particular, we have investigated the effects which one or several aligned g proton(s) or neutron(s) have on the collective parameters; we present here recent results in the odd-A proton nuclei Br and Rb |PAN82, LUH85, LUH86, WOR85|. 2. Experiments These nuclei have been studied via the heavy ion fu­ sion evaporation reactions with C, O, F, Ar and Ca beams provi­ ded by the tandem accelerators at Cologne, Daresbury and Brookhaven and the VICKSI cyclotron at Berlin. Besides the conventional γ-spectroscopic techniques (γγ-coincidences, excitation functions, angular distributions) we also employed neutron and charged particle gating and Compton suppres­ sion in order to enhance the channels and γ-ray lines of interest and to clean the spectra from Coulomb excitation, inelastic scattering and βdecay processes. Lifetimes in the 10~ - 10" sec range have been measu­ red with the Doppler shift attenuation, recoil distance and electronic timing methods, as described in detail in |PAN82, LUH85|. In two of the reactions studied, we have been able to measure the spin dependence of the side feeding time τ* namely for the reaction Ni( 0,p2n) Br at 60 MeV beam energy (LUHèôI and the reaction Ca( Ca,3p) Rb at 122 MeV beam energy |LUH861· A summary of the experiments is given in Table 1. Table 1: Reactions and techniques used to study the Br and Rb Nucleus Reaction Ε (MeV) I (h) Technique ^ 9/2

73,75

12

77,79

16

19

13

36

40

7

62

1+0

lt0

16

75

77

0

maY

73

Br

75

Br

77

79

Rb Rb

0

36

" Ca( Ar,3p) *°Car°Ca,a3p) Ni( 0,p2n) Zn( C,p2n) ^Cai^Ca^p) Cu( F,p2n) Ge( C,p2n)

62

16

66

12

63

19

70

12

105 155, 170 45-65 35-55 120-170 45-65 35-45

33/2

ΎΎι ΡΎ, RD, AD, PT

33/2

YYi ηγ, RD, AD, DSA

37/2 29/2

ΎΎ» ΡΎ, RD, AD, DSA ΎΎ 5ηγ, RD, AD, DSA, PT

a) RD=recoil distance method, DSA=Doppler shift attenuation method, AD=angular distributions, PT=pulsed beam electronic timing 0097-6156/ 86/ 0324-O233$06.00/ 0 © 1986 American Chemical Society

234

NUCLEI OFF THE LINE OF STABILITY

3 . Quadrupole d e f o r m a t i o n p a r a m e t e r s Before d i s c u s s i n g the i n d i v i ­ d u a l n u c l e i l e t us l o o k a t t h e d e f o r m a t i o n p a r a m e t e r s 62 deduced f r o m t h e measured t r a n s i t i o n a l q u a d r u p o l e moments | Q+J = ( 1 6 π / 5 B ( E 2 , I - * 1 - 2 ) ) / < I K 2 0 | l - 2 Κ > : As a s t a r t i n g p o i n t we assumed a x i a l symmetry (γ = 0 ) and a f i x e d Κ v a l u e s u g g e s t e d by t h e N i l s s o n scheme, t h u s n e g l e c t i n g Κ m i x i n g due t o t r i a x i a l i t y and r o t a t i o n . I n T a b l e 2 , t h e s e | ffe I v a l u e s a r e compa­ r e d w i t h t h e r e s u l t s o f S t r u t i n s k y Bogolyubov c a l c u l a t i o n s w i t h a d e f o r ­ med Saxon Woods p o t e n t i a l p e r f o r m e d by Nazarewicz e t a l . | N A Z 8 5 | . T a b l e 2 : E x p e r i m e n t a l and p r e d i c t e d d e f o r m a t i o n p a r a m e t e r s 62 ,d) b) Therory Experiment a ) C o n f i g u ration P2 R e f . S p i n range IM

Nucleus

7 2

Se

2

+

6 -10 +

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch035

7 3

7

Br

0.20(2) 0.31(2)

HAM74 LIE77I

1/2

0.40(2)

|W0R85|

0.28(1)

|BAR74|

0.35(2) 0.36(2) 0.29(2) 0.29(2)

I LUH85I

21/2*,25/2 19/2--27/2"

1/2 3/2 1/2 3/2 0

0.35(2)

KEM84I |W0R84|

+0.35/-0.31

+

2 -10 +

Br

0 0

0

9/2 13/2

*Se

7 5

+

+

+

c)

9/2 ,13/2 +

+

+

+0.31/-0.25 431 3 / 2 312 3 / 2 " +

+0.35 +0.33

7 6

Kr

2 -8

7 7

Rb

9/2 -25/2 9/2"-21/2"

3/2 3/2

0.40(2) 0.45(2)

| L I S 8 4 b | 431 3 / 2 ' I LUH86| 312 3 / 2 "

+0.35 +0.38

7 8

Kr

2 -8

0

0.31(1)

|HEL79| IWIN851

+0.30/-0.25

7 9

Rb

3/2 3/2 3/2

0.36(2) 0.41(3) 0.24(2)

IPAN82I

+

+

+

+

+

+

9/2 - 2 1 / 2

431 3 / 2 312 3 / 2 "

+

+0.33 +0.36

a ) Assumed f i x e d Κ and γ=0 ; t h e d e f o r m a t i o n p a r a m e t e r s a r e t h e w e i g h t e d a v e r a g e v a l u e s deduced f r o m t h e B(E2) o f s t r e t c h e d E2 t r a n s i t i o n s i n t h e s p i n range g i v e n b) I n e v e n - e v e n n u c l e i , d e f o r m a t i o n s o f p r o l a t e and o b l a t e minima |NAZ85| c) B ( E 2 , 6 + 4 ) not included d) " S e , B r from |LUH85|; a l l o t h e r s f r o m |NAZ85|. +

7

7 5

The f o l l o w i n g c o n c l u s i o n s can be drawn f r o m t h i s c o m p a r i s o n : ( 1 ) The n u c l e i show c o n s i s t e n t l y l a r g e d e f o r m a t i o n s o f β = 0 . 3 5 0 . 4 5 . I t t h u s can be i n f e r r e d t h a t t h e p r e d i c t e d p r o l a t e t o o b l a t e shape t r a n s i t i o n i n t h i s mass r e g i o n |BEN84, NAZ85| o c c u r s by a change o f γ r a t h e r t h a n by l a r g e v a r i a t i o n s o f β . ( 2 ) The o v e r a l l agreement between t h e e x p e r i m e n t a l and c a l c u l a t e d β values i s good. E x t r a p o l a t i o n s t o the c o n j e c t u r e d l a r g e deformations o f t h e N = Z = 3 4 - 4 0 n u c l e i i n t h e i r g r o u n d s t a t e s t h e r e f o r e seem t o be w e l l j u s t i f i e d |BEN84, M 0 L 8 1 | . T h i s agreement a l s o i m p l i e s t h a t a l l odd-A n u c l e i discussed h e r e are p r o l a t e . - F u r t h e r m o r e , i t appears t h a t t h e p o ­ s i t i v e and n e g a t i v e y r a s t bands have v e r y s i m i l a r β v a l u e s . I n t h e i r band head w a v e f u n c t i o n s t h e |431 3 / 2 | and |312 3 / 2 " | components d o m i n a t e , t h e i r energies being n e a r l y degenerate. 2

2

2

2

+

35.

Onset of Large Quadrupole Deformation

LIEBETAL.

235

( 3 ) I n a l l cases t h e a d d i t i o n a l p r o t o n i n d u c e s a s u b s t a n t i a l i n c r e a se o f t h e c o r e d e f o r m a t i o n by some 1 5 - 3 0 %. T h i s " p o l a r i z a t i o n " e f f e c t i s s t r o n g e r f o r t h e S e - B r i s o t o p e s t h a n f o r K r - R b . The most d r a m a t i c p o l a r i ­ z a t i o n o c c u r s between S e and B r as i l l u s t r a t e d i n F i g . 1b: due t o t h e p r o l a t e - o b l a t e shape c o e x i s t e n c e a t low s p i n , t h e d e f o r m a t i o n i n Se s t a r t s a t o n l y β = 0 . 2 0 ( 2 ) and t h a n i n c r e a s e s t o = 0 . 3 1 i n t h e r e g i o n where t h e g r o u n d band has r e a c h e d a w e l l d e f o r m e d ( p r o l a t e ) shape |HAM77, LIE77I The r e c e n t l y measured l i f e t i m e s o f t h e 9 / 2 and 1 3 / 2 l e v e l s i n B r d e t e r m i n e β = 0 . 4 0 ( 2 ) , n e a r l y d o u b l e t h a t o f t h e S e ground s t a t e |W0R85|. ( 4 ) The dependence o f t h e t r a n s i t i o n a l moment |Q+J o f t h e g g ^ bands in B r and R b i s p l o t t e d i n F i g . 2 and 3 as f u n c t i o n o f t h e r o t a t i o n a l frequency ηω. W i i l e | Q | is e s s e n t i a l l y constant in R b , i t drops i n Rb and » * B r above s p i n 1 7 / 2 · S e v e r a l e x p l a n a t i o n s h a v e been p r o p o s e d t o e x p l a i n t h i s r e d u c t i o n o f Q : i n t h e I n t e r a c t i n g Boson i(Fermion) model IIAC79 I, t h e f i n i t e boson number l e a d s t o r e d u c t i o n s o f t h e B ( E 2 ) , as f o r example s u g g e s t e d f o r R b | P A N 8 2 | ; a l t e r n a t i v e l y , changes o f β* and γ a s s o c i a t e d w i t h t h e a l i g n m e n t o f g o / 2 n u c l é o n s have been c o n s i d e r e d . C a l culations in B r s u g g e s t t h a t Q d e c r e a s e s a t H u ) = 0 . 4 5 MeV as γ changes s i g n due t o g g / 2 p r o t o n a l i g n m e n t | L U H 8 5 | . 7 2

7 3

7 2

2

+

7 3

7 2

2

7 5

7 7

7 7

7 9

t

7 3

7

+

t

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch035

7 9

7 5

t

4 . Shape s t a b i l i s a t i o n i n Br So f a r t h e g q / 2 band up t o s p i n 3 3 / 2 h ( s i g n a t u r e α = 1/2) has been i d e n t i f i e d |W0R85|. The g / proton n o t o n l y d r a m a t i c a l l y i n c r e a s e s t h e d e f o r m a t i o n o f t h e c o r e as m e n t i o n e d b e f o r e , b u t a l s o s t a b i l i z e s t h e c o l l e c t i v e s h a p e . F i g . 1a i l l u s t r a t e s t h e Ι χ ( ω ) p l o t f o r t h e y r a s t bands i n Se, K r and B r |HAM74, L I E 7 7 , ROT 8 4 1 . P r o l a t e - o b l a t e shape c o e x i s t e n c e below 0 . 4 Me V and ( g g / 2 ) alignment a t 0.55 MeV p r o d u c e i r r e g u l a r i t i e s i n t h e g r o u n d bands o f t n e e v e n - e v e n c o r e s . The g g ^ b a n d i n Br i n c o n t r a s t f e a t u r e s a n e a l y c o n s t a n t moment o f i n e r t i a 2 ? π = 21 M e V c l o s e t o t h e r i g i d body v a l u e . The d i s a p p e a ­ r a n c e o f t h e f i r s t backbend i n B r proofs t h e gq/2 (2qp) proton charac­ t e r o f t h e s-band i n K r . A s i m i l a r i n t e r p r e t a t i o n based on t h e b l o c k i n g o f t h e s - b a n d by t h e g proton also applies to K r |PAN82, LUH86|. 7 3

9

7 2

7 1 t

2

7 3

2

2

1

7 3

7 1 t

/ 6 , 7 8

9

/

2

5. Rigid r o t a t i o n i n R b Among t h e f o u r odd-A n u c l e i d i s c u s s e d Ί h e r e , " R b o f f e r s a s u r p r i s i n g l y simple r o t a t i o n a l s t r u c t u r e |LIS84b, LUH86I. As shown i n F i g . 3 , both t h e q u a d r u p o l e and i n e r t i a l moments o f t h e y r a s t bands w i t h s i g n a t u r e α = 1/2 v a r y l i t t l e o v e r a l a r g e f r e q u e n ­ cy r a n g e . For t h e g b a n d , we f i n d j i ) ^ = 7( )/h a t 15ω = 0 . 4 - 0 . 7 MeV, i n d i c a t i n g r i g i d r o t a t i o n . I f we assume equal t r i a x i a l l y shaped n e u ­ t r o n and p r o t o n d i s t r i b u t i o n s , we can deduce t h e d e f o r m a t i o n p a r a m e t e r s β = 0 . 3 7 ( 2 ) and γ = - 2 5 ( 7 ) ° f r o m t h e measured v a l u e s | Q | = 3 . 1 3 ( 1 2 ) b and 7 / r i = 2 1 . 1 ( 4 ) M e V " . T h i s γ - v a l u e i s s u p p o r t e d by t r i a x i a l r o t o r plus q u a s i p a r t i c l e c a l c u l a t i o n s ]T0K76|. The a v e r a g e t r a n s i t i o n a l q u a d r u ­ p o l e moment o f t h e n e g a t i v e p a r i t y b a n d , | Q . | = 3 . 5 2 ( 1 2 ) b , i s i n e x c e l ­ l e n t agreement w i t h t h a t o f t h e 3 / 2 " ground s t a t e , Q = 3 . 4 8 ( 1 6 ) b , d e t e r ­ mined by l a s e r s p e c t r o s c o p y | T H I 8 1 | . — The s u p p r e s s i o n o f p a i r i n g c o r r e ­ l a t i o n s as e v i d e n c e d by r i g i d r o t a t i o n can be q u a l i t a t i v e l y e x p l a i n e d by t h e s i n g l e p a r t i c l e s t r u c t u r e a t β = 0 . 4 . The Ν= Ζ = 3 8 e n e r g y gap o f 2 MeV i s c o n s i d e r a b l y l a r g e r t h a n t h e p a i r i n g gap p a r a m e t e r s Δ = 1.4 MeV and Δ = 1 . 1 MeV ( a t β = 0 ) r e s p . Δ = 0 . 6 MeV a t β = 0 . 4 |HEY84, N A Z 8 5 I . P r o t o n p a i r i n g c o r r e l a t i o n s seem t o be s u p p r e s e d because t h e |431 3 / 2 | N i l s s o n o r b i t i s b l o c k e d and t h e 1422 5/2+1 o r b i t i s t o o f a r away e n e r g e ­ t i c a l l y . A t β = 0 . 4 , t h e d e n s i t y o f s i n g l e p a r t i c l e l e v e l s near t h e 7 7

1

Q

/

2

2

2

2

2

t

2

1

2

π

2

ρ

2

+

2

NUCLEI O F FT H ELINE O F

STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch035

236

F i g . 1 : Spin p r o j e c t i o n Ι ( a ) and t r a n s i t i o n a l q u a d r u p o l e moment | Q J ( b ) of t h e g band i n B r |W0R85j and t h e g r o u n d bands i n S e |LIE77| χ

7 3

9

/

2

7 2

and

7 t +

Kr

| ROT841.

F i g . 2 : ( a ) Cranked s h e l l model a n a l y s i s o f y r a s t bands i n Br. (b) Aligned s i n g l e p a r t i c l e angular momentum ί ( ω ) o f t h e s e b a n d s . Reproduced w i t h p e r m i s s i o n f r o m LUH85. C o p y r i g h t 1985 American Physical Society. 7 5

χ

LIEB ET AL.

237

Onset of Large Quadrupole Deformation

Rb

TRIAX ^ = 0 4 ,

]

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch035

y»-20

76KJ

r

; ; - · · • *

TRIAX 0 = 0.4, X » - 2 0 " RS

F i g . 3 : Dynamical monent of i n e r t i a ( ) / h ( a ) and t r a n s i t i m a l quadrupole moment Q ( b ) o f t h e y r a s t bands i n R b |LUH861. 2

2

t

7 7

a) 0.2

0.4 ΐιω

0.8

0.6

(MeV)

t h e Fermi e n e r g y i s r e d u c e d by a f a c t o r o f 2 - 3 r e l a t i v e t o β = 0 . We f i n a l l y l i k e t o p o i n t o u t t h a t r i g i d r o t a t i o n sets i n a t r a t h e r low s p i n . 2

6 . The t r a n s i t i o n a l n u c l e u s Br I n t h i s n u c l e u s we have e x t e n d e d t h e y r a s t bands up t o s p i n 3 3 / 2 and have d e t e r m i n e d 17 l i f e t i m e s | L U H 8 5 | . A c r a n k e d s h e l l model a n a l y s i s o f t h e bands i s p r e s e n t e d i n F i g . 2 a . The g o / 2 band shows a l a r g e s i g n a t u r e s p l i t t i n g w i t h n e a r l y c o n s t a n t a l i g n e d s i n g l e - p a r t i c l e a n g u l a r momenta i ( a = + 1 / 2 ) = 3 . 0 h and i ( a = - 1 / 2 ) = 1.7 h . The c a l c u l a t e d t o t a l e n e r g y s u r f a c e shows a w e l l pronounced minimum a t β = 0 . 3 5 , γ = - 1 5 ° . The n e g a t i v e p a r i t y band has v e r y l i t t l e s i g n a t u r e s p l i t t i n g ( γ = 0 ° ) , here i i n c r e a s e s g r a d u a l l y and r e a c h e s 4 . 0 h a t ηω = 0 . 5 teV. T h i s i n d i c a t e s s t r o n g m i x i n g between t h e P3/2 ( 1 q p ) and t h e s p i n a l i g n e d ( g o / ? ) P3/2 ( 3 q p ) s - b a n d , a c c o p a n i e d by a d r o p o f B(E2) v a ­ l u e s ( s e e F i g . 2 D ) . A d e t a i l e d d i s c u s s i o n o f t h e γ - d r i v i n g f o r c e s and c o e x i s t e n c e phenomena i n B r has been g i v e n i n | L U H 8 5 | . 7 5

x

2

x

7 5

x

238

N U C L E I O F F T H ELINE O F STABILITY

7. Conclusions We have e s t a b l i s h e d t h a t t h e l i g h t Br and Rb i s o t o ­ pes p r e s e n t e d h e r e have v e r y l a r g e q u a d r u p o l e d e f o r m a t i o n s o f 82 0 . 4 and moments o f i n e r t i a c l o s e t o t h e r i g i d body v a l u e s . The odd p r o t o n i n t h e 1431 3 / 2 | N i l s s o n o r b i t p o l a r i z e s and s t a b i l i z e s t h e γ - s o f t , shape c o e x ­ i s t e n t Se and Kr c o r e s i n t o d e f i n i t e p r o l a t e t r i a x i a l s h a p e s . T h i s e f f e c t s e t s i n a t r a t h e r l o w s p i n and seems t o be i n t i m a t e l y c o n n e c t e d w i t h t h e s u p p r e s s i o n o f p a i r i n g c o r r e l a t i o n s n e a r t h e Ν = Ζ = 38 gap d e v e l o p i n g a t 82 = 0 . 4 . We t h u s f a c e a c u m u l a t i v e s u p p r e s s i o n o f b o t h p r o t o n and n e u t r o n p a i r i n g c o r r e l a t i o n s i n t h e same o s c i l l a t o r s h e l l , a f a i r l y u n i q u e feature in the periodic t a b l e . s

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch035

+

Acknowledgments The e x p e r i m e n t s r e p o r t e d h e r e have been p e r f o r m e d i n c o l l a b o r a t i o n w i t h J . Heese, F. R a e t h e r ( G o t t i n g e n ) , D. A l b e r , H. G r a we, B. SpelTmeyer ( B e r l i n ) , C. J . L i s t e r , B. J . \ a r l e y ( M a n c h e s t e r ) , H. G. P r i c e ( D a r e s b u r y ) , J . E b e r t h ( K b l n ) and J . W. Olness ( B r o o k h a v e n ) . I t i s a p l e a s u r e t o acknowledge t h e e x c e l l e n t s p i r i t o f team work and d e d i c a ­ t i o n . D i s c u s s i o n s w i t h R. B e n g t s s o n , K. H. B h a t t , F. I a c h e l l o , W. N a z a r e ­ w i c z and T . Otsuka have been s t i m u l a t i n g . One o f t h e a u t h o r s (KPL) acknow­ l e d g e s t h e h o s p i t a l i t y o f t h e S t a t e U n i v e r s i t y o f New York a t S t o n y Brook w i e r e t h i s a r t i c l e has been p r e p a r e d . T h i s work has been a l s o f u n d e d by t h e German BMFT.

References |BAR74| J. Barrette, et al., Nucl. Phys. A235 154 (1974) |BEN84| R. Bengtsson, et a l . , Phys. Scr. 29 402 (1984) H | AM74| J. H. Hamilton, et a l . , Phys. Rev. Lett. 32 239 (1974) H | AM85| J. H. Hamilton, P. G. Hansen and E. F. Zganjar, Rep. Progr. Phys. 48 631 (1985) |HEL79| H. P. Hellmeister, e t a l . , Nucl. Phys. A332 241 (1979) |HEY84| K. Heyde, J. Moreau and M. Waroquier, Phys. Rev. C29 679 (1984) |IAC79| F. Iachello and O. Scholten, Phys. Rev. Lett. 43 679 (1979) K | EM84| P. Kemnitz, et a l . , Nucl. Phys. A425 493 (1984) |LIE77| K. P. Lieb and J. J. Kolata, Phys. Rev. C15 939 (1977) |LIE84| K. P. Lieb, XIX Winter School on Physics, Zakopane/Poland (1984) |LIS84a| C. J. Lister, et al., "Nuclera Physics with Heavy Ions", P. Braun Minzinger, ed. (Harwood Acad. Publ. Chur, 1984) p. 257 |LIS84b| C. J. Lister, et a l . , "Atomic Masses and Fundamental Constants" O. Klepper, ed. (THD Schriftenreihe, Darmstadt, 1984) p.300 |LUH85| L. Lühmann, et a l . , Phys. Rev. C31 828 (1985) |LUH86| L. Lühmann, et al., Europhys. Lett. 1 623 (1986) |NAZ85| W. Nazarewicz, et a l . , Nucl. Phys. A435 397 (1985) |PAN82| J. Panqueva, et a l . , Nucl. Phys. A389 424 (1982) |PIE76| R. B. Piercey, et a l . , Phys. Rev. Lett. 37 496 (1976) R | OT84| J. Roth, et al., J. Phys. G10 L25 (1984) |THI81| C. Thibault, et a l . , Phys. Rev. C23 2720 (1981) |TOK76| H. Toki and A. Faessler, Phys. Lett. 63B 121 (1976) W | IN85| G. Winter, et al., J. Phys. G11 277 (1985) W | OR84| Β. Wörmann, et al., Nucl. Phys. A431 170 (1984) W | OR85| Β.Wörmann,et al., Z. Phys. A321 171 (1985 RECEIVED July 16, 1986

36 Intruder States in Highly Neutron-Deficient Pt Nuclei Evidence from Lifetime Measurements?

1

1

1

1

1

24 ,

U. Garg , M. W. Drigert , A. Chaudhury, E. G. Funk , J. W. Mihelich , D. C. Radford , H. Helppi , R. Holzman, R. V. F. Janssens, T. L. Khoo , A. M. Van den Berg, and J. L. Wood3 25 ,

2

2

2

26,

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch036

1

Physics Department, University of Notre Dame, Notre Dame, IN 46556 Physics Division, Argonne National Laboratory, Argonne, IL 60439 School of Physics, Georgia Institute of Technology, Atlanta, GA 30332

2 3

The recoil distance technique has been employed following the 154

34

184

Sm( S,4n) Pt reaction to measure the lifetimes of states in the ground state band (GSB) of the highly neutron deficient nucleus Pt. Lifetimes have been extracted for up to the 18 state in the GSB. The B(E2) values exhibit a marked increase between spins 2 and 10, suggesting a strong mixing between the GSB and a less collective band at low spin and, thus, providing indirect evidence for an "intruder" (6h-2p)O ground state. This is further confirmation of the shape coexistence occuring at low energy in this region. 184

+

+

The structure of very neutron-deficient Pt isotopes is most unusual and needs to be better clarified for a number of reasons: (1) There is an emerging picture of an extensive occurence of shape coexistence at low energy in the region near Z=82 and N=104 (see, for example,[HEY83,DUP84] and the references therein). This region needs to be carefully mapped away from closed shells to determine the systematics of bandhead energies and mixing matrix elements for the coexisting bands. The present view [WOO81] 4

Current address: Chalk River Nuclear Laboratories, Chalk River, Ontario K0J 1J0, Canada Permanent address: Lappeenranta University of Technology, Finland Current address: Rijks Universiteit Utrecht, Utrecht, the Netherlands

5 6

0097-6156/ 86/ 0324-0239506.00/ 0 © 1986 American Chemical Society

240

NUCLEI OFF THE LINE OF STABILITY The

in Table data.

lifetimes obtained from a p r e l i m i n a r y analysis a r e summarized

1 which also includes the B ( E 2 ) values e x t r a c t e d from the lifetime

F i g . 2 s h o w s a plot of B ( E 2 ) ' s

depopulating

( i n W e i s s k o p f U n i t s ) v s . s p i n of t h e

state.

TABLE I Ε

I.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch036

Ύ (keV)

τ

*

B(E2) §

B(E2)t

f

1

(W.U.)

(ps)

163

2+ •> 0+

272

4

+

363

6

+

-> 4

+

433

8

+

+

+ 2

Theory

(W.U.)

85.3

582±50

112±10

39± 3

200±17

96.5

9± 2

220±49

107.8

-> 6

+

3.2±0.5

261±41

115.8

-

8

+

1.7±0.4

309±73

120.7

+ 10

+

2.310.4

184±33

122.3

476

10

+

497

12

+

522

14

+

+ 12

+

2.0±0.4

166±34

104.6

555

16

+

+ 14

+

l-6±0.5

153±47

106.2

586

18

+

+ 16

+

1.3±0.8

144±90

107.8

* E r r o r s a r e c o n s e r v a t i v e estimates. f l n t e r n a l conversion has been taken values. §From

into account i n calculating B ( E 2 )

(KUM80) It i s clear from F i g . 2 that t h e r e i s a s i g n i f i c a n t i n c r e a s e i n t h e

B(E2)

values between spins 2

+

+

a n d 1 0 ( b y a f a c t o r o f >2.5). T h i s

vides an unequivocal

c o n f i r m a t i o n of t h e b e h a v i o r

mixing

+

between the 0

states a n d between the 2

bands and, thus, provides strong evidence 184 existence i n

pro­

b e c a u s e of t h e

states i n the coexisting

f o r t h e p r e s e n c e of s h a p e c o -

P t . A s e p a r a t e a n d i n t r i g u i n g a s p e c t of o u r m e a s u r e m e n t s +

is t h e d e c l i n e i n B ( E 2 ) v a l u e s b e y o n d s p i n 1 0 . of t h e o n s e t of t r i a x i a l i t y . in

+

expected

This might be indicative

I tcoincides with thebeginning

t h e G S B a n d i s , p o s s i b l y , t h e r e s u l t of a l a r g e i n d u c e d

to t h e a d d i t i o n of a p a i r o f 1-^3/2 ° ±

uas

n

of b a c k b e n d i n g triaxiality due

i eutrons· S u c h b e h a v i o r

has recently

been observed

i n the deformed r a r e - e a r t h nuclei [FEW85]. Also, a possible 186 e m e r g e n c e of t r i a x i a l i t y h a s b e e n r e p o r t e d f o r Hg [ J A N 83]. Finally, 184

our B ( E 2 ) values i n calculated conserving

P t can be comoared

(Table

1) w i t h B ( E 2 ) v a l u e s

[KUM80] u s i n g a microscopic a p p r o a c h of v a r i a t i o n w i t h n u m b e r projection from a p a i r i n g - p l u s - q u a d r u p o l e

Hamiltonian.

36.

241

Intruder States in Highly Neutron-Deficient Pt Nuclei

GARG ET AL.

of t h e e v e n - m a s s

Os, P t , H g a n d Pb isotopes i s v e r y

p u z z l i n g i n that the

more deformed b a n d i s an e x c i t e d b a n d i n P b , H g a n d O s a n d a p p e a r s to be the g r o u n d b a n d i n P t ( f o r A 0^ t r a n s i t i o n . T h i s i n d i c a t e s t h a t t h e i n t e n s i t y r a t i o I + _^ Q+ /1^+ _^ Q ^ J Q - 3 Thus, the expected electron-gamma c o i n c i d e n c e 2 1 / 1 1 i n t e n s i t y i s a b o u t a f a c t o r 1 0 s m a l l e r t h a n t h e γ-γ c o i n c i d e n c e i n t e n s i t y f o r t h e s t r o n g e s t γ-ray t r a n s i t i o n s , t a k i n g i n t o a c c o u n t a ε = 0 . 0 3 f o r t h e e l e c ­ t r o n spectrometers. For P b t h i s f a c t o r i s even 3. 1 0 . F i g . 2 shows t h e r e s u l t s f o r P b (the data a n a l y s i s f o r Pb i s i n p r o g r e s s ) . I n a d d i t i o n t o t h e 288, 307 and 754 keV t r a n s i t i o n s w h i c h h a v e a l s o b e e n o b s e r v e d by Van Duppen e t a l . i n t h e 3-decay o f B i i s o t o p e s we have f o u n d e v i d e n c e f o r a 413 keV and a 563 keV t r a n s i t i o n . These γ-rays a r e c l e a r ­ l y v i s i b l e i n t h e c o i n c i d e n c e s p e c t r u m b e t w e e n d e l a y e d γ-rays and d e l a y e d c o n ­ v e r s i o n e l e c t r o n s . T h i s does n o t e x c l u d e t h a t t h e y a r e a l s o p r e s e n t i n t h e prompt-prompt s p e c t r u m . I f t h e i n t e n s i t y i n t h e l a t t e r s p e c t r u m w o u l d a p p r o x i ­ m a t e l y be t h e same as i n t h e d e l a y e d s p e c t r u m t h e s e γ-rays w o u l d have b e e n e s ­ caped f r o m o u r o b s e r v a t i o n due t o t h e h i g h e r b a c k g r o u n d i n the prompt s p e c t r u m . We have t e n t a t i v e l y a s s i g n e d t h e 413 keV and t h e 565 keV t r a n s i t i o n s t o t h e d e c a y o f a J^=b and J =6" " l e v e l s o f t h e r o t a t i o n a l band b u i l t on t h e J =0 i n t r u d e r s t a t e on t h e b a s i s o f t h e c o i n c i d e n c e i n t e n s i t y and t h e t r a n s i t i o n e n e r g i e s ( c f . F i g . 3 ) . The r e g u l a r i n c r e a s i n g t r a n s i t i o n e n e r g i e s b e t w e e n t h e members o f t h e p r o p o s e d band a g r e e w i t h t h o s e o f t h e g r o u n d s t a t e band i n P t . A s i m i l a r o b s e r v a t i o n has b e e n made f o r t h e Sn i s o t o p e s . It w i l l be very d i f f i c u l t to o b t a i n f u r t h e r evidence f o r the r o t a t i o n a l band on t h e J™=0 state i n P b . Α γ-γ c o i n c i d e n c e measurement t o e s t a b l i s h t h e c o i n c i d e n c e r e l a t i o n s b e t w e e n t h e p r o p o s e d i n t r a b a n d t r a n s i t i o n s seems 1 9 6

+

+

Q

2

1 9 l +

2

1 9 6

+

7T

t

1 9 2

+

1 9 6

1 9 1 +

+

254

NUCLEI O F F T H ELINE O F STABILITY

1 9 8

H g ( a, 6nY

2.

Time spectrum showing the decay of the 40.0-keV l e v e l i n Ac. S t a r t s i g n a l s included 80-300 keV e l e c t r o n s and stop s i g n a l s were 20-40 keV e l e c t r o n s .

H a l f - l i f e of the 31.6-keV s t a t e In

Ra

2 2 3

225

— The h a l f - l i v e s of l e v e l s i n Ra were measured by α-e delayed coincidence technique. The α - p a r t i c l e s were detected with a 6-mm diameter Au-Si surface b a r r i e r detector and the e l c t r o n s were detected with the 1 mm t h i c k p i l o t Β d e t e c t o r , α - p a r t i c l e s i n g l e s [Bar70, He185] and coincidence [Hel85] s t u d i e s show that only < 0.2% alpha i n t e n s i t y occurs a t the 31.6-keV l e v e l . Therefore the s t a r t s i g n a l s were obtained from the c c peak (the 236 keV l e v e l p a r t l y decays v i a the 31.6-keV l e v e l ) . The time spectrum obtained i n coincidence with c*23 peak and 15-25 keV e l e c t r o n s contained three main components. The longest component i n the spectrum was not present when the e l e c t r o n gate was set above 35 keV. T h i s c l e a r l y i n d i c a t e s that the longest l i f e t i m e belongs to the 25.4 or 31.6 keV l e v e l . The h a l f - l i f e of the 25.4-keV l e v e l was obtained by measuring the TAC spectrum i n coincidence with a and 15-25 keV e l e c t r o n s 2

3

6

6

2 5

41.

AHMAD

Fast Electric Dipole Transitions

275

and was found to be 0.88 ± 0.04 ns. Therefore, the longest component i n the spectrum belongs to the 31.6 keV l e v e l . A least-squares a n a l y s i s gave a h a l f l i f e of 2.1 -k 0.2 ns.

3.3

H a l f - l i f e of

the 27.4 keV s t a t e i n 227 A C

We have performed coincidence measurements to e s t a b l i s h that the 38 ns h a l f - l i f e p r e v i o u s l y measured [Led78] belongs to the 27.4 keV l e v e l . The r e l e v a n t p o r t i o n of the ^ P a decay scheme i s shown i n Fig.3. The major alpha t r a n s i t i o n s populate the 29.9 and 46.4 keV l e v e l s ; very l i t t l e i n t e n s i t y occurs at the 27.4 keV l e v e l . The 29.9 keV l e v e l decays to the ground state by a f a s t highly converted Ml t r a n s i t i o n and the 46.4 keV l e v e l decays v i a the 27.4 keV l e v e l . Both the 29.9 and 18.9 (46.4-27.4) keV t r a n s i t i o n s generates Ac L X-rays. 2 3

231

P a 3.28 χ 10

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch041

1/2, 3/2"

5/2

3/2,

Energy (keV)

I, π +

y

7 ^

Κ,

4

46.4

a

α-intensity ^25.4%

/

< 20%

/

2.5%

/Ίι.ο%

3/2" 227 F i g . 3.

P a r tr i a9Ac l decay scheme of

z 3 L

Pa.

An α-γ coincidence experiment was performed using a cooled S i ( L i ) detector f o r the d e t e c t i o n of photons and a S i detector f o r the d e t e c t i o n of exparticles. Three parameter events were c o l l e c t e d on tape and one dimensional spectra were l a t e r generated i n coincidence with various gates. The spectra showed that the and OL^Q prompt coincidence with L X-rays and the delay occurs a t the 27.4 keV l e v e l . The a n a l y s i s of the time spectrum between the o t group and the 27.4 keV photopeak gave a h a l f - l i f e of 38.3 ± 0.3 ns, i n agreement with previous measurements. a r e

i n

4 6

Discussion From the measured l e v e l h a l f - l i f e , ^i/2> t i o n p r o b a b i l i t i e s , T , of the E l γ-rays. e x

w e

have derived the gamma t r a n s i ­ These are given by the equation

276

NUCLEI OFF THE LINE OF STABILITY 0.693.f l

(1)

l/2

where f i s the f r a c t i o n of the t o t a l decay from the p a r t i c u l a r l e v e l which occurs by the given t r a n s i t i o n , and C Is the square of the appropriate Clebsch-Gordon c o e f f i c i e n t between the two l e v e l s . In cases, where a s i n g l e t r a n s i t i o n deexcites the l e v e l , f (1 + α ) , α being the t o t a l conversion c o e f f i c i e n t . The above t r a n s i t i o n rate was divided by the Weisskopf estimate (w.u.) to o b t a i n an energy-independent q u a n t i t y . We have p l o t t e d t h i s quantity f o r a l l known ΔΚ-0 E l t r a n s i t i o n s i n heavy elements a g a i n s t the mass number i n F i g . 4. The values f o r ^ A c , Ac, and *Ra are from the present work; other data are taken from l i t e r a t u r e [Led78, Asa60]. In F i g . 4 there i s 225 225 2 Pa n u c l e i . a d e f i n i t e enhancement i n the E l rate f o r the Ac, Ra, and β

τ

τ

Z 2

10

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch041

8

_ 10'

Pa

Ac* °Ac

a

S 10 φ

5

2 3 5

s iff

4

Νρ·

l7

·Ι 220

Am«

Ac"

10

ισ

2 4 3

Np

.

.

230

240

1

Mass Number

F i g . 4.

Known t r a n s i t i o n rates of the ΔΚ = 0 E l t r a n s i t i o n s i n odd-mass heavy n u c l e i .

T h e o r e t i c a l c a l c u l a t i o n s [Cha77] i n d i c a t e that the E l matrix elements do not change much with the decreasing $ deformation between a given p a i r of s t a t e s . One, therefore, expects that the E l rate should not change with mass number. Thus the large enhancement i n E l rates f o r n u c l e i with A6.4 8.8±1.2 0.48±0.06 3610!)

2

58.0 8.4 17.2 0.52 12.3 2.0 11.0 7.3 1.5 1.4

C*E2 84.0 34.0 20.4 1.1 13.6 3.2 12.0 74 1.1 1.0

c*El 13.9 1.9 4.2 0.11 3.0 0.40 2.7 1.8 0.38 0.34

' C a l c u l a t e d f r o m NUT 21.225-230 (1978). EXPERIMENTAL RESULTS The l o w - e n e r g y p o r t i o n o f t h e l e v e l scheme deduced f o r i s shown i n figure 2. A s a t u r a t e d sample o f t h e A=145 i s o b a r s was c o l l e c t e d and c o u n t e d t o d e t e r m i n e t h e a b s o l u t e i n t e n s i t y o f t h e 175.4 k e V ^ - r a y ( 1 9 . 8 ± 2.4/100 decays). T h i s v a l u e , a l o n g w i t h t h e yt and c - e i n t e n s i t i e s , was u s e d t o c a l c u l a t e t h e 3 " f e e d i n g t o t h e g . s . and e x c i t e d l e v e l s i n ^Ba. The l a r g e u n c e r t a i n t y i n t h e 3 " f e e d i n g t o t h e 198.9 keV l e v e l i s a d i r e c t r e s u l t o f t h e l a r g e u n c e r t a i n t y i n t h e r e l a t i v e i n t e n s i t y o f t h e 198.9 keV γ-ray. 5 c g has a 12% d e l a y e d n e u t r o n b r a n c h [ R I S 7 9 ] and t h e m a j o r t r a n ­ sition in B a i s a 199 keV - r a y . As a r e s u l t , t h e i n t e n s i t y o f t h e 198.9 keV t r a n s i t i o n i n ^^Ba c o u l d o n l y be d e t e r m i n e d f r o m t h e c o i n c i d e n c e data. Our v a l u e o f 54.7 f o r I199 i s l o w e r t h a n t h e 68.5 v a l u e p r e v i o u s l y r e p o r t e d by R a p p a p o r t e t . a l . [ R A P 8 2 ] , As n o t e d a b o v e , t h e g . s . s p i n o f ^ B a has been measured t o be 5 / 2 . The n e g a t i v e p a r i t y a s s i g n m e n t f o r t h e g . s . i s based upon t h e s y s t e m a t i c s o f t h e N=89 i s o t o n e s and t h e Z=56 i s o t o p e s . The g . s . J" o f b o t h N d and 51sm i s 5 / 2 " . The g . s . o f J * o f t h e odd-A Ba i s o t o p e s i s : 3 9 B a = 7 / 2 ~ , 4 l B a = 3 / 2 ' , and From t h e i n t e r n a l c o n v e r s i o n c o e f f i c i e n t s g i v e n i n t a b l e 2 , t h e f o l l o w i n g gammas were d e t e r m i n e d t o be M1/E2 t r a n s i t i o n s i n agreement w i t h 1 4

1 4 4

5

1 4 9

1

1

1

g?

Η- If (M 00

ο

it ο

— ο — — OS —

ο

MK)

co in \US0 I* M— O σ»

* — N) N)

Ο - (Λ Ο — * sD * If It M- If — — O O o k ) * σ>

W

U

-

* 6* V0 « 4k Ο Μ· It It Μ Ν) Ο M * so

σ»

IN IN IN

0 3 9 1 . 2 1.1 3 6 7 . 7 5.3 2 4 6 . 9 2.5 5 4 7 . 1 23.6 4 3 4 . 7 5.7 348.2 1 1 2 2 7 . 4 3.4 4 9 2 . 1 13.8 2 1 4 . 5 1.2 4 5 4 . 8 10.6 3 4 1 . 7 0.6 2 7 9 . 5 4.0 2 5 5 . 9 2.5 3 8 . 2 1.8 4 3 5 . 6 24.3 3 2 3 . 3 5.2 2 6 0 . 3 0.9 416.55.1 3 0 4 . 5 2.4 2 4 1 . 0 28.9 319.8 7 6 2 0 7 . 1 16.2 1 2 1 . 0 0.4 277.1 2 1 164.67.5 1 9 8 . 9 54.7 8 6 . 3 5.8 1 7 5 . 4 100.0 54.1

•W

-

*-W +W +

UIUI

* UI +

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch043

7 8 5 . 3 0.4 5 8 6 . 6 1.8 3 6 9 . 2 0.9 238.4 7 9 753.311.2 5 7 8 . 1 7.6 5 5 4 . 7 5.2 3 1 7 . 6 3.0 7 2 4 . 3 8.1 5 4 8 . 9 5.8 5 2 5 . 8 3.7 3 0 8 . 0 2.0 559.94.5 3 9 5 . 1 5.6 1 0 5 . 9 0.8 6 6 3 . 5 1.9 4 8 7 . 2 6.9 4 6 4 . 8 1.0

W

2 452 429.1 13 172.0 4 3 611.2 54 4 3 5 . 7 1 0 2j 1 9 4 . 6 3.4 1 1 5 6 . 3 2.4

315 J17

1112.5 1

I I

•g -g

-•g W N is)* uiw œ01 -W M* M * 01 I V 13 N0S1H3H0H

£t7

288

NUCLEI OFF THE LINE OF STABILITY

the e a r l i e r work: 112.4, 175.4, 198.9, 241.0, and 454.7. Rappaport also reports t h a t the 86.3 and 238.4 3-rays are M1/E2 t r a n s i t i o n s . The non-zero A44 values f o r both the 368-199-0 cascade and the 155-455-0 cascade r u l e s out the p o s s i b i l i t y t h a t J* of the 199 keV level or the 455 keV level i s 3 / 2 " . In a d d i t i o n , the A22/A44 values f o r the 368-199-0 cascade l i m i t the spin of the 567 level to e i t h e r 1/2 or 3/2 once J* of the 199 level i s known not to be 3 / 2 " . The large A22 value of 0.24 f o r the 323-112-0 cascade, coupled w i t h the f a c t t h a t the 435 level i s 5 / 2 , rules out the p o s s i b i l i t y t h a t the 112 level has ϋ = 3 / 2 " ; the l a r g e s t A22 can be f o r a 5 / 2 * - 3 / 2 " - 5 / 2 " cascade i s 0.08. The only t r a n s i t i o n t h a t was determined to be El by the measured conversion c o e f f i c i e n t s was the 435.7 k e V y - r a y . Setting an upper l i m i t on the area expected f o r the 547.1 K-conversion peak in the electron spectrum indicates t h a t the 547 i s also an El t r a n s i t i o n . Likewise, an upper l i m i t of 0.064±0.008 f o r α f o r the 207.1 keV t r a n s i t i o n can also be established by s e t t i n g the mixing of the 175.4 keV t r a n s i t i o n to zero. This low α value suggests t h a t the 207.1 γ - r a y i s an El t r a n s i t i o n . A spin of 3/2" f o r the 435 level i s ruled out by the large negative A22 value f o r the 317-435-0 cascade. In a d d i t i o n , a l o g ( f t ) of approximately 6 f o r the 435 keV level makes the 3~ decay to t h i s level an allowed t r a n s i t i o n . Because the g . s . spin of C s i s 3 / 2 , t h i s rules out the p o s s i b i l i t y t h a t the spin of the 435 level i s 7 / 2 and subsequently l i m i t s the spin of the 435 level to 5 / 2 . +

π

κ

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch043

κ

1 4 5

+

+

+

CONCLUSION Clearly the r o t a t i o n a l band s t r u c t u r e observed i n the l i g h t odd-A a c t i ­ nides i s not seen i n the s t r u c t u r e of B a . Like the N-89 isotones N d [ P I N 7 7 ] and Sm[C0076], the negative p a r i t y states in B a can not be grouped i n t o any obvious r o t a t i o n a l bands and seem to be very hard to explain i n the framework of the Nilsson model. The l e v e l s a t 319.8, 547.1, and 785.5 keV might be members of a strongly perturbed p o s i t i v e - p a r i t y r o t a t i o n a l band, but both the 319 and 547 appear to be 5/2 l e v e l s . Aparently the 435.7 keV level can not be a member of the p o s i t i v e p a r i t y band including the 547 and 785 because neither of these p o s i t i v e p a r i t y l e v e l s decay to i t . The absence of any c l e a r l y defined n e g a t i v e - p a r i t y r o t a t i o n a l bands in B a suggests that i t i s not strongly quadrupole deformed. The clear r o t a t i o n a l s t r u c t u r e observed in l**(àû 1 5 5 completely dissapears as the N=89 isotones cross the Z=64 s h e l l . This conclusion i s also supported by the 32 values calculated from the l i f e t i m e s of the f i r s t 2 states in B a and B a . The r a t i o 3 / 3 p · r e s p e c t i v e l y . This i s compared to the r a t i o of 12.2 and 10.7 observed in the quadrupole deformed nuclei G d and D y . Thus, although B a does not have the p a r i t y doublets expected for an octupole deformed nucleus, i t i s possible t h a t (because $2 * small) i t s s t r u c t u r e i s determined by higher orders of deformation; i . e . the s t r u c t u r e i s very dependent on 3 3 , 3 Δ , e t . . The great s i m i l a r i t y between the s t r u c t u r e of Ba, C e , and N d added to our i n a b i l i t y to understand these N=89 (and N=87) nuclei in the framework Nilsson model points to the need f o r extended t h e o r e t i c a l and experimental work in t h i s t r a n s i t i o n a l r e g i o n . 1 4 5

149

151

1 4 5

1 4 5

a n d

ΰν

+

1 4 4

1 4 6

f

2

o

r

1 4 4 β ά

a n d

1 4 6 β ά

i s

6

8

a n d

7

5

2 s

1 5 4

s

1 5 6

1 4 5

s o

1 4 5

1 4 7

1 4 9

ACKNOWLEDGMENTS We would l i k e to thank Dr. Leander f o r his helpful discussions. work has been supported by the U.S. Department of Energy.

This

43. ROBERTSON ET AL.

Decay of Cs to Levels of Ba 145

145

289

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch043

REFERENCES [LEA82] G.A. Leander, R.K. Sheline, P. Moller, P. Olanders, I. Ragnarsson, and A.J. Sierk, Nucl. Phys. A388 452 (1982). [IAC82] F. Iachello and A.D. Jackson, Phys. Lett. 108B 151 (1982). [GAI83] M. Gai, J.F. Ennis, M. Ruscev, E.C. Schloemer, B. Shivakumar, S.M. Sterbenz, N. Tsoupas, and D.A. Bromley, Phys. Rev. Lett. 51 646 (1983). [NAZ84] W. Nazarewicz, P. Olanders, I. Ragnarsson, J. Dudek, G.A. Leander, P. Moller, and E. Ruchowska, Nucl. Phys. A429 269 (1984). [LEA84] G.A. Leander and R.K. Sheline, Nucl. Phys. A413 375 (1984). [LEA85] G.A. Leander, W. Nazarewicz, P. Olanders, I. Ragnarsson, and J. Dudek, Phys. Lett. 152B 284 (1985). [MOL72] P. Moller, S.G. Nilsson, and R.K. Sheline, Phys. Lett. 40B 329 (1972). [MUE83] A.C Mueller, F. Buchinger, W. Klempt, E.W. Otten, R. Neugart, C. Ekstrom, and J. Heinemeier, Nucl. Phys. A403 234 (1983). [RAG83] I. Ragnarsson, Phys. Lett. 130B 353 (1983). [RAP82] M.S. Rappaport, G. Engler, A. Gayer, and I. Yoresh, Z. Physik. A305 359 (1982). [DEJ85] H. Dejbakhsh, private communication. [GIL84] R.L. Gill, M.L. Stelts, R.E. Chrien, V. Manzella, H. Liou, and S. Shostak, Nucl. Instr. and Meth. 186 243 (1981). [PIO84] A. Piotrowski, R.L. Gill, and D.C. McDonald, Nucl. Instr. and Meth. 22 1 (1984). [RIS79] C. Ristori, J. Crancon, K.D. Wunsh, G. Jung, R. Decker, and K.L.Kratz, Z. Physik. A290 311 (1979). [PIN77] J.A. Pinston, R. Roussille, G. Sadler, W. Tenten, J.P. Bocquet, B. Pfeiffer, and D.D. Warner, Z. Physik. A282 303 (1977). [COO76] W.B. Cook, M.W. Johns, G. Louhoiden, and J.C. Waddington, Nucl. Phys. A259 461 (1976). RECEIVED

August 1, 1986

44 Spectroscopic Consequences of Shape Changes at High Angular Momenta Ingemar Ragnarsson and Tord Bengtsson

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch044

Department of Mathematical Physics, Lund Institute of Technology, P.O. Box 118, S-22100 Lund, Sweden We discuss so called terminating states which occur because of the finiteness of rotational bands and which are associated with a gradual shape change until the rotation takes place around a symmetry axis. Predictions on terminating configurations in nuclei with 10-12 valence particles outside the Gd core are compared with recent experimental data. Observed and calculated spectra show a remarkable similarity, at least for Er and Er which nuclei are discussed in detail here. 146

156

It

158

i s by

spin

now w e l l - e s t a b l i s h e d that substantial shape changes occur a t high

for nuclei

changes out

with a few p a r t i c l e s o u t s i d e the ^ 5 4 ^ 3 2

-

Such shape

appear t o be a s s o c i a t e d with so c a l l e d band terminations as pointed

a few years ago [BEN83] and r e c e n t l y some experimental

occurence The

c o r e

of

states

experiment

terminating

which appear

average

trend

way

localise

to

systematics

f o r the

[BAK85, RAG85, STE85].

a band and which one could hope t o observe i n

t o be very favoured e n e r g e t i c a l l y , i . e . r e l a t i v e t o some

they

at

bands have been presented

terminate

evidence

are e x c e p t i o n a l l y l o w - l y i n g . Indeed, a s t r a i g h t f o r w a r d

band high

terminations

seems

t o be

to

analyse the energy

s p i n and compare with the general trends p r e d i c t e d by

calculât i o n s . With

many

becomes

enough

possible

configuration. follow

axis.

in a

The

typically

from

leads

to

alignment

(and holes) b u i l d i n g an a l i g n e d s t a t e , i t also a

at

collective

structures

within

the

terminating band where i t i s p o s s i b l e t o

o f the s p i n vectors u n t i l f u l l alignment i s

process

i s accompanied

by

a gradual shape change,

p r o l a t e a t lower spins over t r i a x i a l t o o b l a t e shape a t the

( f i g . 1). The deformation

rotation

spins

form

s t a t e where a l l s p i n v e c t o r s a r e quantised along a symmetry

alignment

termination to

This

the gradual

achieved

particles to

f i x e d deformation.

changes give an energy g a i n

relative

Many terminating bands a r e p r e d i c t e d a t 1 4

1=40-60

f o r n u c l e i with 10-12 nucléons outside the ^ G d c o r e . Note 20 a l s o that t h i s alignment process i s s i n c e long known i n Ne [BOH75, RAG81]. ICO

Let between

us

now consider

particle-hole

Er as an i l l u s t r a t i v e example o f the competition states

c o l l e c t i v e a t low spins with a

and

collective

deformation

bands.

This

corresponding

to

0097-6156/ 86/ 0324-0292S06.00/ 0 © 1986 American Chemical Society

nucleus

is

ε=0.20-0.25.

44.

Spectroscopic Consequences of Shape Changes

RAGNARSSON AND BENGTSSON TERMINATING

293

BAND A - 150

I

prolate — t r i a x i a l —

oblate* I ax = ^ 0 - 5 0 t l

0

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch044

m

i *

m

I = 46*

I~30*

m

I max

2 * 3* m

F i g . l . Schematic i l l u s t r a t i o n o f a band terminating c o n f i g u r a t i o n and i t s e v o l u t i o n with s p i n .

Fig.2. Schematic i l l u s t r a t i o n of c a l c u l a t e d (unpaired) bands i n the y r a s t region o f Er.

Reproduced with permission from [RAG85] . Copyright 1985 NorthHolland Physics P u b l i s h i n g Company.

Reproduced with permission from [RAG85] . Copyright 1985 NorthHolland Physics P u b l i s h i n g Company.

With

p a i r i n g neglected,

i r i d

g

5/2 7/2 alignment)

)

4

(

h

)

the ground s t a t e c o n f i g u r a t i o n would be described as

V ( f

h

ll/2 7/2 9/2 the deformation

) 6 ( i

) 2

13/2 decreases

W

i

t

h

and

a

increasing s p i n (and band with the proton

comes lower i n energy [BEN85a]. For even ^11/2 spins and a t a deformation c l o s e t o s p h e r i c a l , i t becomes favourable

configuration higher to

8

1 5 e

Tr(dcy ) 2

( h

π

close

η

the Z=64 core leading t o the ( ι ι / 2 )

4

proton c o n f i g u r a t i o n while 6 · 2 n

I

n

t n

s

the neutron c o n f i g u r a t i o n remains unchanged, V(f7/2 9/2' ^ 1 3 / 2 ' * * configuration, the maximum s p i n i s Ι , - l £ L + l J J = 16+30=46. T h i s band max max max Λ

structure of The

full

experiment cranking spin

1 5 8

Er

i s schematically

calculational

result

v

ν

e v

i l l u s t r a t e d i n f i g . 2. [BEN83]

for

Er

i s compared

with

i n f i g . 3. The c a l c u l a t i o n s are based on the N i l s s o n - S t r u t i n s k y method

where

we f o l l o w i n d i v i d u a l c o n f i g u r a t i o n s as f u n c t i o n s o f

γ, energy and ε . oThe c a l c u ls at ta te ed bands denoted bywith 1, 2respect and 3 are [BEN85 ]. ε , The f each i s minimised to 4

ir Similarly, a 35*

respectively. V(h,9/2 strong

way

that cannot

also given

theoret i c a l l y .

40*-*38* and

given be

note in

i n réf.

then the 38

i n t h i s 40*

s t a t e can be understood

s t a t e . T h i s however

38*-*36* gamma rays come i n reversed

réf.

the

order

[STE85]. Indeed, the o r d e r i n g of these

determined [STE85a] from the present

that

requires

low-lying [STE85]

38*

seems

experiment

two and

s t a t e which r e s u l t s from the very

difficult

to

explain

44.

Spectroscopic Consequences of Shape Changes

RAGNARSSON AND BENGTSSON The

to

1=34, 35, 36, 40 and 42 s t a t e s e s s e n t i a l l y exhaust the p o s s i b i l i t i e s

form

low-lying

particles

of

1 5 6

p o s i t i v e p a r i t y s t a t e s with 12:30 w i t h i n the ten valence

E r . The most l o w - l y i n g f u l l y a l i g n e d negative π

are c a l c u l a t e d f o r Ι f

ν

7/2* ^

with and

n

**13/2

= 38~, 39~ corresponding

negative

this

indeed,

s p i n observed f o r negative

^

2

state,

p a r i t y i s a t 1=38

33~, i s observed

relatively

low i n energy, and

the c a l c u l a t i o n s give a low-lying a l i g n e d 33~ s t a t e which compared +

summary

evolution

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch044

1 3

e n e r g e t i c a l l y ( f i g . 5 ) . One more

f

to the 4 2 s t a t e i s formed by the rearrangement ^ ( ^ 1 3 / 2 11/2 In

V(i

9/2* r e l a t i v e t o the 4 2 s t a t e . T h i s seems c o n s i s t e n t

38~ s t a t e i s very favoured

parity

parity states

t o the rearrangements +

the f a c t that the highest that

such

297

of

we

finite

terminating

particles lations,

have

7/2-7/2^'

the shape t r a n s i t i o n a s s o c i a t e d with the

r o t a t i o n a l bands t o t h e i r p o i n t s o f t e r m i n a t i o n . Many

bands

(and holes) the very

discussed

a r e p r e d i c t e d i n c o n f i g u r a t i o n s with 10-12 valence relative

low energy

to a of

1 4 6

G d c o r e . According

the terminating

t o the c a l c u ­

s t a t e s i s a prominent 158

feature 1 5 6

Er,

recent

i n these

c o n f i g u r a t i o n s . For the n u c l e i discussed

i t i s found experiments

that

E r and

not o n l y the p r e d i c t e d trends a r e confirmed by

but a l s o

l a t i o n s appear t o be present

here,

many

o f the d e t a i l e d f e a t u r e s

i n the observed h i g h - s p i n

i n the c a l c u ­

spectra.

References [BAK85] C. Baktash et al., Phys. Rev. Lett. 54 (1985)978. [BEN83] T. Bengtsson and I. Ragnarsson, Phys. Scripta T5 (1983)165. [BEN85] T. Bengtsson and I. Ragnarsson, Nucl. Phys. A436 (1985)14. [BEN85a] T. Bengtsson and I. Ragnarsson, Phys. Lett. B, to appear. [BOH75] A. Bohr and B.R. Mottelson, Nuclear Structure, vol. II (Benjamin, New York, 1975) [DIA85] R.M. Diamond, these proceedings. [RAG81] I. Ragnarsson, S.Åbergand R.R. Sheline, Phys. Scripta 24(1981)215 [RAG84] I. Ragnarson and T. Bengtsson, Proc. 1984 INS—RIKEN Int. Symp. on Heavy Ion Physics, Mt. Fuji, Aug. 1984, J. Phys. Soc. Jpn 54 (1985) Suppl. II, p. 495. [RAG85] I. Ragnarsson et al., Phys. Rev. Lett. 54 (1985)982. [SIM84] J. Simpson et al., Phys. Rev. Lett. 53 (1984)648; [STE85] F.S. Stephens et al., Phys, Rev. Lett. 54 (1985)2584. [STE85a] F.S. Stephens, priv. comm., June 1985. [TJO85] P. Tjøm et al., subm. to Phys.Rev. Lett. [RAG85] I. Ragnarsson and T. Bengtsson, Nucl. Phys. A447 (1985) 253c-255c. RECEIVED July 21, 1986

45 Evolution of Nuclear Shapes at High Spins Noah R. Johnson

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch045

Oak Ridge National Laboratory, Oak Ridge, TN 37831 Outstanding progress has been made during the past ten years on an understanding of the properties of nuclei excited into states of high angular momentum. Much of the experimental progress has resulted from γ-γ coin­ cidence measurements u t i l i z i n g complex detector arrays. Many of the proper­ ties of the yrast and near-yrast bands in nuclei revealed in these measure­ ments have become reasonably well explained by current theory. Both cranked shell model (CSM) and cranked Hartree-Fock Bogoliubov (CHFB) calculations have enjoyed considerable success in accounting for many aspects of high spin behavior. However, for a detailed understanding of the structure of these high spin states and for a stringent test of these models, i t is necessary to resort to measurements of their static and dynamic electromagnetic multipole moments. During the past few years we at Oak Ridge have concentrated on stu­ dies of the latter quantity, the dynamic electric quadrupole (E2) moments which are a direct reflection of the collective aspects of the nuclear wave functions. For t h i s , we have carried out Doppler-shift lifetime measurements u t i l i z i n g primarily the recoi1-distance technique. The nuclei with neutron number Ν « 90 possess many interesting proper­ t i e s . These nuclei have very shallow minima in their potential energy sur­ faces, and thus, are very susceptible to deformation driving influences. It is the evolution of nuclear shapes as a function of spin or rotational fre­ quency for these nuclei that has commanded much of our interest in the l i f e ­ time measurements to be discussed here. There is growing evidence that many deformed nuclei which have prolate shapes in their ground states conform to t r i axial or oblate shapes at higher spins. Since the E2 matrix elements along the yrast line are sensitive indicators of deformation changes, mea­ surements of lifetimes of these states to provide the matrix elements has become the major avenue for tracing the evolving shape of a nucleus at high spin. Of the several nuclei we have studied with Ν « 90, those to be dis­ cussed here are i60,i6i [FEW82], [J0H82], [FEW82], [FEW85] and Er [0SH84a], [0SH84b]. In addition, we will discuss briefly the preliminary, but interesting and surprising results from our recent investigation of the Ν = 98 nucleus, W [RA085]. 1 5 8

Yb

172

0097-6156/ 86/0324-0298S06.00/ 0 © 1986 American Chemical Society

45.

Nuclear Shapes at High Spins

JOHNSON

II.

Experimental Both

its

1 6 0

inverse

case.

Aspects

Yb

^Ti (

and 1 1 6

1 6 1

and Data

It

C d , x n ) , at a c e n t e r - o f - m a s s

which a c t s

p o s s i b l e t o g a t e on g i v e n

channel.

puter

p r o g r a m , LIFETIME [WEL85] w h i c h i n c l u d e s

population

γ-ray

intensities

lifetimes

fits

each

is discussed

In t h i s

in

a 25-cm χ way i t

was

e n e r g y s p e c t r u m and g e t a

by t h e

o f t h e usual

corrections

features

of the level

scheme, one

t o account

The program t h e n s o l v e s t h e

lifetimes

and i n i t i a l

t o t h e decay c u r v e s .

are used i n t h e f i t t i n g

com­

all

cascade s i d e f e e d i n g t o each l e v e l

from undefined t r a n s i t i o n s .

o b t a i n the best

145 MeV i n

r e s u l t i n g decay c u r v e s

Knowing t h e g e n e r a l

equations while adjusting the to

γ-ray

and

8

times.

were e x t r a c t e d f r o m t h e

[STU76] t o t h e d a t a .

C d ( ** Ti , x n )

S p e c t r a were o b t a i n e d f o r

of

u s u a l l y models a t w o - s t e p

filter.

of the t o t a l

reaction

total

Lifetimes

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch045

as a t o t a l - e n e r g y

flight

1 1 6

i n s i d e t h e annular opening of

regions

enhancement o f t h e d e s i r e d 17 d i f f e r e n t

energy of

d e v i c e used i n t h e measurements

was d e s i g n e d t o f i t

25-cm Nal c r y s t a l

Analyses

Y b were p r o d u c e d by t h e r e a c t i o n s

The r e c o i 1 - d i s t a n c e

[J0H81].

299

populations

Both t h e s h i f t e d

procedure.

of the and

levels

unshifted

Uncertainties

were d e t e r m i n e d by t h e method o f t h e s u b r o u t i n e

for

Bateman

in

the

MINOS, d e s c r i b e d

in

[JAM75]. Excited 1 2 8

Te(

large tors

3 4

S,4n)

1 5 8

at

Er

nuclei

f o r t h e s e s t u d i e s were p r o d u c e d v i a t h e

a bombarding e n e r g y o f

155 MeV.

In these experiments

Nal d e t e c t o r was removed i n o r d e r t o p l a c e an a r r a y o f a t 90° w i t h

t o the t a r g e t .

r e s p e c t t o t h e beam d i r e c t i o n T h i s was done i n o r d e r t o t e s t

c i d e n c e measurement tation

could o f f e r

of the experimental

analyses

problems a s s o c i a t e d w i t h

contribution

of

if

separations

statistical

i n t h e 0° d e t e c t o r Lifetimes different

quality

is

158Ε

γ

a

t

f o r the y r a s t

(6 cm) coin­

and

interpre­

respect t o s i m p l i f y i n g Direct

the

s i d e f e e d i n g makes no

g a t e d by band members

a

total

of

14 t a r g e t - s t o p p e r

spectra taken at f o u r of

shown i n F i g . 1 .

and r e v e a l

as a r e s u l t

with

the spectrum i s

A p o r t i o n of the t o t a l - p r o j e c t e d

target-stopper

a high-efficiency

in the analysis

the

Ge d e t e c ­

interest.

Measurements were t a k e n on tances.

if

side f e e d i n g .

t o a γ-ray t r a n s i t i o n

higher than the t r a n s i t i o n

cellent

especially

five

and a t c l o s e geometry

simplifications

data,

reaction

These s p e c t r a a r e o f

a favorable

peak-to-background

o f u s i n g t h e Compton s u p p r e s s i o n sequence o f

sets of coincidence d a t a :

1) t h a t

1 5 8

Er

ex­ ratio

shield.

were d e t e r m i n e d f r o m

f r o m g a t i n g on t h e

dis­

the

first

four

300

NUCLEI OFF THE LINE OF STABILITY ORNL-DWG 8 5 - 9 8 9 2

ORNL-DWG 89-9602

d=20/xm 30,000

h 1 6

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch045

10,000

Π

1 4

n

20,000 | -

n

12*

π

-Π Π II L

Fig. 1. Illustrative " t o t a l p r o j e c t e d " coincidence spectra of E r c o v e r i n g t h e 400-650 keV r e g i o n f o r f o u r o f t h e f o u r t e e n d i s t a n c e s measured. 1 5 8

transition 2) t h a t

above t h e one o f

f r o m t h e sum o f a l l

below t h e t r a n s i t i o n 4) t h a t

1 5 8

interest; gates

from t h e t o t a l - p r o j e c t e d

cidences.

Although side feeding

the state of i n t e r e s t

40

F i g . 2 . Decay c u r v e s f o r mem­ b e r s o f t h e y r a s t sequence i n Er. The p o i n t s r e p r e s e n t the experimental data w i t h the appropriate corrections. The s o l i d curves are t h e f i t t e d time d i s t r i b u t i o n s determined by t h e program LIFETIME.

interest;

of i n t e r e s t ;

20

FLIGHT TIME (pe)

f r o m g a t i n g on t h e second

transition 3) t h a t

above t h e one o f

0

and coin­ to

i s n o t e l i m i n a t e d i n t h e l a s t two t y p e s o f d a t a ,

have an advantage i n b e i n g o f e x c e l l e n t

statistical

quality.

they

I n f a c t , we

f o u n d t h a t t h e program LIFETIME h a n d l e d t h e i r more complex s i d e f e e d i n g ditions data. fits

quite well,

based on c o m p a r i s o n s o f l i f e t i m e s

I n F i g . 2 a r e shown e x p e r i m e n t a l t o these For t h e

from a l l

con­

four sets

of

d a t a f o r each s t a t e and t h e program

data. 1 7 2

W studies, the

beam energy o f E|_

aD

= 230 MeV.

12i

*Sn

(

5 2

C r , 4n) r e a c t i o n was u t i l i z e d

The e x p e r i m e n t a l

arrangement was s i m i l a r

at a to

45. that

for

tors

a t 90° f o r c o i n c i d e n c e g a t i n g .

1 5 8

distances

Er

measurements, e x c e p t here we used s i x l a r g e volume Ge d e t e c ­ Data were c o l l e c t e d f o r

r a n g i n g f r o m 16un t o 7mm.

analyses are a v a i l a b l e

To t h i s

only f o r the t o t a l

t h e sums o f g a t e s below t h e t r a n s i t i o n III.

transition

t h e reduced e l e c t r i c t o the

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch045

these Q

of

interest.

of Q

t

=

^

probabilities,

B(E2),

2

Q

2 t

states

values f o r the y r a s t

g r o u n d band o f tunately,

stretching

The d a t a f o r 1 6 0

Yb are,

effect

In F i g .

t

trend

with

values

somewhat s i m i l a r l y the rotational

^

r

^

of

Q

t

1

dif­

bands,

21/2*

Û

γ*

1

f 1

with

values

Γ

ι

25/2

\

+

I

29/2+

behaving

as a f u n c t i o n

of

Likewise,

rather

similar

As seen i n F i g . 4 ,

J

L_ 0.2

0.3

In f a c t ,

(MeV)

the

v a l u e s a l s o show a d r o p o f f

i n the s band.

I

17/2*

Λω

behavior.

an

increasing

frequency.

bands w i t h

d a t a show c l e a r

of

Y b shows o n e - and t h r e e - q u a s i ­

particle

The l a t t e r

i n t h e ground band as e x p e c t e d f o r

Yb

1 6 0

Y b t h e r e are t h r e e

each showing Q

for

F i g u r e 4 shows a p l o t

the

bands i n b o t h

two-quasiparticle

Er.

Yb.

there

feature

Y b show an o v e r a l l

1 6 0

1 5 8

1 6 1

unfor­

A most i n t e r e s t i n g

For

Y b and

the

is present

loss of c o l l e c t i v i t y

1 6 0

3,

frequency

indicate

the data in F i g . 3 i s t h a t quasiparticle

in

sequence o f

too l i m i t e d to

whether t h i s

Er

according

,

i s a Clebsch-Gordon c o e f f i c i e n t .

and n e a r - y r a s t

Ν = 90 n u c l e u s .

ferent

from

t

< I 2 0 0 | 1-2 0 >

evidence of c e n t r i f u g a l

1 6 1

q u a d r u p o l e moments, Q , were o b t a i n e d

v a l u e s are p l o t t e d as a f u n c t i o n o f t h e r o t a t i o n a l

t

some y r a s t

1 5 8

lifetime

p r o j e c t e d c o i n c i d e n c e s p e c t r a and

quadrupole t r a n s i t i o n

where t h e t e r m i n b r a c k e t s

1 6 1

p o i n t , the preliminary

flight

expression B(E2:I-I-2)

ω.

18 r e c o i l

Discussion Experimental

and

301

Nuclear Shapes at High Spins

JOHNSON

the

f o r t h e 8 " , 9" and s bands

F i g . 3. T r a n s i t i o n quadrupole moments o f some y r a s t and n e a r y r a s t s t a t e s o f 160, i e i r o t a t i o n a l frequency. Y b

v s

302 of

NUCLEI OFF THE LINE OF STABILITY 158£

s

Γ

n

o

w

r e d u c i n g t r e n d when p l o t t e d as a f u n c t i o n o f r o t a t i o n a l

a

quency, although

i t i s l e s s pronounced t h a n i s t h e d a t a o f F i g . 3 .

mon a l i g n e d q u a s i p a r t i c l e orbital

with parity

bands i n

1 6 0

(ττ,α) = ( + , + 1 / 2 ) .

and ( - , - 1 / 2 )

h

9

/

Y b and t h e 8 " and 9 " bands i n

behavior of Q (+,+1/2)

i n a l l o f t h e s e bands i s t h e l o w e s t energy i

and s i g n a t u r e

coupled t o t h e ( - , + 1 / 2 )

with

t

2

orbitals 1 5 8

Er.

influence

x

3

/

This q u a s i p a r t i c l e

2

is

t o f o r m t h e 6 " and 9 " s i d e The s i m i l a r i t i e s

ω f o r t h e s e bands s u g g e s t t h e p o s s i b i l i t y

q u a s i n e u t r o n has a dominant

fre­

The com­

in the

that the i 1 3 / 2

on t h e c o r e .

A d d r e s s i n g t h e i d e a s d i s c u s s e d a b o v e , t h e group a t Lund has r e p o r t e d [BEN83] r e s u l t s

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch045

calculations

of self-consistent

o f t h e shape o f

1 6 0

f i n d t h a t t h e 1 1 3 / 2 alignment

c r a n k e d H a r t r e e - F o c k - B o g o l i u b o v (HFB)

Y b as a f u n c t i o n o f a n g u l a r momentum.

produces a quadrupole d e f o r m a t i o n

near t h e g r o u n d - s t a t e v a l u e and w h i c h remains a p p r o x i m a t e l y spin. about tion, tive

However, t h e t r i a x i a l i t y

p a r a m e t e r γ shows a s t e a d y

10° by I = 1 8 , t h e h i g h e s t

spin they

+

of a prolate

with

increase,

reaching

( I n t h e Lund c o n v e n ­

ellipsoid

and γ = 60° c o r r e s p o n d s t o n o n c o l l e c rotations

o f an o b l a t e

Another t h e o r e t i c a l

and i t i n v o l v e s

ORNL-DWG 8 5 - 1 1 3 6 3

Ί

Γ

ellipsoid.) approach

has a l s o been t a k e n [LEA83]

cal

2

constant

γ = 0° c o r r e s p o n d s t o c o l l e c ­ rotations

tive

reported.

They

ε which i s

O g BAND

[FRA83]

•

s BAND

a more p h e n o m e n o l o g i -

examination of the e f f e c t s

of the

γ degree o f freedom on t h e e n e r g y o f the quasiparticles cranked s h e l l

and t h e c o r e .

model

The

"5 *

(CSM) i s used t o

calculate the quasiparticle

energies

w h i c h a r e added t o t h e e n e r g y o f t h e r o t a t i n g c o r e as a f u n c t i o n o f γ . t h e N~90 t r a n s i t i o n quasiparticles

region, the i

qualitatively,

consistent CSM r e s u l t s but w i l l

3

/

2

drive the equilibrium

v a l u e o f γ t o around 5 ° . least

x

In

results

So, at

both t h e s e l f -

for

1 6 0

L

SPIN

Y b and t h e

(calculated f o r

be v e r y s i m i l a r

J 12

for

1 6 0

Yb,

1 5 8

Er)

F i g . 4 . T r a n s i t i o n quadrupole moments o f y r a s t s t a t e s i n Er. 1 5 8

45.

Nuclear Shapes at High Spins

JOHNSON

303

a r e seen t o be i n agreement w i t h o u r e x p e r i m e n t a l l y tivity

at high r o t a t i o n a l

we p o i n t

out t h a t

frequencies

should a l l

of the loss of c o l l e c t i v i t y

be a t t r i b u t e d t o t r i a x i a l i t y , o f 20° a t s p i n

observed l o s s of

in the q u a s i p a r t i c l e

it

is

bands.

i n t h e s e two

necessary t o invoke values of

If

is strongly

it

lies

l o w e s t energy f o r

low i n t h e s h e l l , t h e n t h e h i g h - j γ > 0.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch045

to collective

rotations

n e u t r o n Fermi

surface

When t h e Fermi giving

surface

excess

mation d r i v i n g

it

lies

potential

resistant

of

has γ

conforming

a n u c l e u s whose

near t h e m i d d l e o f t h e 1*13/2 s h e l l

i s e x p e c t e d t o be r e l a t i v e l y

surface

near mid s h e l l ,

Admittedly,

w e l 1 - d e f o r m e d r o t o r w i t h a pronounced minimum i n i t s and, t h e r e f o r e ,

deformation

quasiparticle

rise to t r i a x i a l i t y

o f an o b l a t e e l l i p s o i d .

lies

the

a f f e c t e d by t h e l o c a t i o n o f t h e Fermi

t e n d s t o move t o t h e n e g a t i v e s e c t o r ,

s h o u l d be a energy

to t r i axial

surface defor­

influences.

I n measuring t h e l i f e t i m e s is

nuclei

+

An i n t e r e s t i n g a s p e t o f t h e CSM approach above i s t h a t

its

γ in

18 .

d r i v i n g tendency a nucleus.

collec­

However,

of h i g h - s p i n

states

in

1 7 2

W

(N = 9 8 , w h i c h

near t h e m i d d l e o f t h e i 1 3 / 2

s h e l l ) , we d i d not a n t i c i p a t e

a

significant

collec­

tivity

difference

at spins

18-20 i n t h e

sequence f r o m t h a t ground band.

in the

yrast

f o u n d low i n

At t h i s

[RA085] have o n l y p a r t i a l l y

completed

t h e d a t a a n l a y s e s , but t o o u r p r i s e , the Q

t

values of

in Fig. 5 display

1 7 2

a very

W

very

This

sur­ shown

similar

b e h a v i o r t o t h e much s o f t e r near Ν = 9 0 .

the

p o i n t we

result

nuclei

raises

i n t e r e s t i n g questions

some

relating

t o w h i c h degrees o f freedom a r e c h a n g i n g t o produce t h i s viously,

additional

ments o f n u c l e i important;

effect.

lifetime

Ob­

measure­

near Ν = 96-100 a r e

but t h e search f o r

better

t o a c c o u n t f o r such p h e __ nomena i s e q u a l l y demanded.

2 + 6 8 10

16 18 20

SPIN

theories

F i g . 5. T r a n s i t i o n quadrupole moments of y r a s t s t a t e s i n W. 1 7 2

304

NUCLEI OFF THE LINE OF STABILITY

Acknowledgments The f o l l o w i n g c o l l a b o r a t o r s a r e t o be t h a n k e d f o r t h e i r r o l e s i n c a r r y i n g out the research discussed here: Hattula,

I.Y.

M.P. F e w e l l , F.K. McGowan, J . H .

L e e , C. B a k t a s h , Y. S c h u t z , J.W. J o h n s o n , J . C . W e l l s ,

L.L.

R i e d i n g e r , M.W. G u i d r y , S . C . P a n c h o l i , M. Oshima, R.V. R i b a s , M.N. Rao, K. E r b , J.W. McConnell and A. L a r a b e e .

References

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch045

[BEN83] R. Bengtsson, Y-D. Chen, J-S. Zhang and S. Aberg, Nucl. Phys. A405, 221 (1983). [FEW82] M.P. Fewell, J . Hattula, D.R. Haenni, N.R. Johnson, J.W. Johnson, I.Y. Lee, F.K. McGowan, L . L . Riedinger, J.C. Wells, and S.C. Pancholi, B u l l . Am. Phys. Soc. 27, 522 (1982). [FEW82] M.P. Fewell, J.S. Hattula, N.R. Johnson, I.Y. Lee, F.K. McGowan, H. Ower, S.C. Pancholi, L . L . Riedinger, and J.C. Wells, in Proc. of the Conf. on High Angular Momentum Properties of Nuclei, Oak Ridge, TN, Nov. 1982, ed. by N.R. Johnson, Nuclear Science Research Conf. Series, Vol. 4 (Harwood Academic, New York, 1983), p. 69. [FEW85] M.P. Fewell, N.R. Johnson, F.K. McGowan, J.S. Hattula, I.Y. Lee, C. Baktash, Y. Schutz, J.C. Wells, L . L . Riedinger, M.W. Guidry, and S.C. Pancholi, Phys. Rev. C, 31, 1057 (1985). [FRA83] S. Frauendorf and F.R. May, Phys. Lett. 125B, 245 (1983). [JAM75] F. James and M. Roos, Comput. Phys. Commun. 10, 343 (1975). [JOH81] N.R. Johnson, J.W. Johnson, I.Y. Lee, J . E . Weidley, D.R. Haenni, and J.R. Tarrant, ORNL Phys. Div. Prog. Report No. ORNL-5787, 1981, p. 147. [JOH82] N.R. Johnson, in Proc. of the 1982 Inst. for Nuclear Study Intnl. Symposium on Dynamics of Nuclear Collective Motion, ed. by K. Ogawa and K. Tanahe (Inst. for Nuclear Study, Univ. of Tokyo, 1982), p. 144. [LEA83] G.A. Leander, S. Frauendorf and F.R. May, Proc. Conf. on High Angular Momentum Properties of Nuclei, Vol. 4, Nuclear Science Research Conf. Series, ed. by N.R. Johnson (Harwood Academic Publishers, New York, 1983) p. 281. [OSH84a] M. Oshima, N.R. Johnson, F.K. McGowan, I.Y. Lee, C. Baktash, R.V. Ribas, Y. Schutz, and J.C. Wells, B u l l . Am. Phys. Soc. 29, 1043 (1984). [OSH84b] M. Oshima, N.R. Johnson, F.K. McGowan, I.Y. Lee, C. Baktash, R.V. Ribas, Y. Schutz, and J . C . Wells, ORNL Phys. Div. Prog. Report, ORNL-6120 (1984) p., 77. [RAO85] M.N. Rao, N.R. Johnson, C. Baktash, F.K. McGowan, I.Y. Lee, K. Erb, J.W. McConnell, M. Oshima, J.C. Wells, A. Larabee and L . L . Riedinger, unpub. [STU76] R . J . Sturm and M.W. Guidry, Nucl. Instrum. Methods 138, 345 (1976). [WEL85] J.C. Wells, M.P. Fewell and N.R. Johnson, ORNL/TM-9105 (1985). RECEIVED July 15, 1986

46 Signature Splitting in 1

Pr

135

1

1

1

2

2

T. M. Semkow, D. G. Sarantites, K. Honkanen, V. Abenante, C. Baktash, Noah R. Johnson, I. Y. Lee , M. Oshima , Y. Schutz , C. Y. Chen , O. Dietzsch, J. X. Saladin , A. J. Larabee, L. L. Riedinger, Y. S. Chen , and H. C. Griffin 2

2

2

4

3

5

3

3

4

6

1

Washington University, St. Louis, MO 63130 Oak Ridge National Laboratory, Oak Ridge, TN 37831 University of Pittsburgh, Pittsburgh, PA 15260 University of Tennessee, Knoxville, TN 37996-1200 Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831 University of Michigan, Ann Arbor, MI 48109

2

3 4 5

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch046

6

135

120

19

In-beam spectroscopic study of Pr was made using 91 MeV Sn( F,4n) reaction. A strong negative parity proton band based on the h - 3/2[541] configuration with (π,α)=(-,-1/2) was observed. (-,+1/2) unfavored band i s probably observed. Also two positive parity proton bands are observed and are based on the g + 3/2[422] configuration with (π,α)=(+,±1/2). In the case of π(+) bands the backbending i s caused by the alignment of two h 3/2[541] protons. For the (-,-1/2) band the backbending is caused by the alignment of two h - protons: 3/2[541] and 1/2[550]. This is considerably different than i n Ce core, where the h neutron-holes are aligning. 11/2

7/2

11/2

11/2

134

11/2

Nuclei i n the v i c i n i t y of La, Ce, Pr are predicted to be soft i n γ­ -deformation [CHE83]. An investigation was undertaken to study the signature s p l i t t i n g between rotational bands i n Pr, which i s related to γ-deforma­ tion. Pr was produced by the Sn( F,4n) reaction at 91 MeV using the tandem accelerator at the Brookhaven National Laboratory. Coincidence data were recorded between 4 Compton-suppressed Ge detectors at ~ 40° relative to the beam and 2 unsuppressed Ge detectors at ~ 85°. In addition an array of 11 NaI detectors around the target were used as a m u l t i p l i c i t y selector. 135

135

The

1 3 5

120

19

P r decay scheme i s shown i n F i g . 1 and i t was constructed from γ γ -

0097-6156/86/0324-0305506.00/0 © 1986 American Chemical Society

(47/2TV

Fig.

1 . Decay scheme o f

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch046

Pr.

Η

r

DO

Η >

τι &ο

Ο

m r ζ en

Η 3C

τη τι

η r Ξ ο

G

ζ

Os

Ο

SEMKOW ET AL.

46.

coincidence, of

1 3 5

Pr

Signature Splitting in

intensity,

Pr

307

135

and a n g u l a r c o r r e l a t i o n i n f o r m a t i o n .

f r o m i n - b e a m and r a d i o a c t i v e decay work

Low-spin

were v a l u a b l e i n a s s i g n i n g s p i n s and p a r i t i e s o f h i g h - s p i n s t a t e s . t h e i n t e n s i t y goes t o t h e p r o t o n band w h i c h i s based on h n / 2 " f i g u r a t i o n , with signature a = - l / 2 . a = + l / 2 unfavored band.

d e c o u p l e d because o f t h e K = 3 / 2 band h e a d . 1 3 / 2 " l e v e l moves below 1 5 / 2 " l e v e l i n γ f r o m 21° t o 34° ( s l i g h t l y o b l a t e , bands a r e based on i r g 7 / 2

+

3/2[422]

necting t r a n s i t i o n s observed.

the

1 3 9

[ K 0 R 8 5 ] , o v e r more

The two bands a r e

strongly

However, by a d d i n g 4 n e u t r o n s Pr

[PII80]

due

see F i g . 2 ) . The a = + l / 2 p o s i t i v e configuration.

f r o m f a v o r e d band

i n agreement w i t h B ( M 1 ) / B ( E 2 ) s y s t e m a t i c s f o r c o n n e c t e d r o t a t i o n a l [HAG82].

Above t h e b a c k b e n d i n g most o f t h e i n t e n s i t y goes t o band s i m i l a r l y as i t

tran­

f r o m t h e u n f a v o r e d t o f a v o r e d band

a r e so weak, t h a t t h e y can be seen o n l y f r o m t h e f a v o r e d band b e l o w .

(π,οϋ=(-,-1/2)

of

parity

There a r e s e v e r a l Ml c o n ­

The Ml b r a n c h i n g f r a c t i o n s

On t h e o t h e r hand t r a n s i t i o n s

the

to the increase

0 . 0 5 f o r t h e 274 k e V , 0 . 1 2 f o r t h e 260 keV, and 0 . 9 1 f o r 204 keV

sitions.

of con­

The p a t h t h r o u g h t h e 8 4 3 , 7 2 5 , and 482 keV cascade

i n t e n s e p a t h t h r o u g h 796 and 726 keV c a s c a d e .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch046

Most

3/2 [541]

There i s a l s o some e v i d e n c e f o r

was chosen because t h e 482 keV t r a n s i t i o n was known b e f o r e

are:

studies

[K0R85, WIS75, C0N73, EKS72]

i s observed i n

1 3 3

Pr

This

is

bands

the

[HIL85].

19/2"

Fig.

2. Systematics

levels pes.

i n odd-A Pr References:

[ H I L 8 5 ] , A=135 A=137

A=I35

A = 137

A=I39

A=l33

[K0R85] ,

[KLE75] , A=139

[PI 180].

A = 133

of

n(-

isoto­

308

NUCLEI OFF THE LINE OF STABILITY Changes o f γ - d e f o r m a t i o n i n r o t a t i o n a l n u c l e i a r e caused by t h e

balance

between d r i v i n g f o r c e s r e s u l t i n g f r o m t h e q u a s i - p a r t i c l e p r o p e r t i e s

before

backbending, the behavior o f a l i g n i n g q u a s i - p a r t i c l e s a t the backbend, the s o f t n e s s o f t h e c o r e , and t h e c o l l e c t i v e r o t a t i o n BEN84].

γ-

[LEA82, FRA83, CHE83,

These changes i n γ - d e f o r m a t i o n a r e t h u s o b s e r v e d as changes o r even

inversions

[BEN84] o f s i g n a t u r e s p l i t t i n g .

The c o r e i s e x p e c t e d t o be d r i v e n

by r o t a t i o n t o w a r d s γ - - 3 0 ° ( i n t h e Lund c o n v e n t i o n

[AND76, L E A 8 2 ] ) . Q u a s i ­

p a r t i c l e s o c c u p y i n g h i g h - j s h e l l cause t h e d r i v i n g f o r c e t o w a r d s γ>0° when t h e Fermi l e v e l i s a t t h e b e g i n n i n g o f t h e s h e l l , towards γ = 0 . 3 2 MeV.

3/2[541]

were done w i t h Z2 = 0 . 2 5 , tics,

protons at η ω

= 0.02,

Δ

ρ

= Δ

and t h e c r o s s i n g was f o u n d a t γ = 0 ° .

0 . 4 6 MeV w i t h a l i g n m e n t o f ~ 10 h .

π

Α Β

= 0 . 3 MeV.

upbend.

The

the

calculations

The i r ( - ) band c r o s s e s a t hu> = c

Using b l o c k i n g arguments t h e protons:

calculation 1/2[550]

and

A t t h e h i g h e r f r e q u e n c i e s b o t h t h e i r ( + ) and i r ( - ) bands show an T h i s may be due t o t h e B C - a l i g n m e n t o f p r o t o n s i n i r ( + ) bands and t h e

A B - a l i g n m e n t o f n e u t r o n s i n ττ(-) b a n d s , w i t h t h e i n c r e a s e o f t h e being r e l a t e d to higher i n t e r a c t i o n strengths. tons i n

Pr.

= 1.2 MeV t a k e n f r o m s y s t e m a ­

g i v e s η ω ^ = 0 . 4 6 MeV w i t h t h e a l i g n m e n t o f two h n / 2 " 3/2[541].

1 3 5

Preliminary

c

c a l c u l a t i o n s show t h a t t h i s i s c o n s i s t e n t w i t h

a l i g n m e n t o f two h n / 2 ~

shift

spectrosco­

3 shows t h e a l i g n e d a n g u l a r momentum f o r t h e t h r e e bands i n

cranking-shell-model

to

1 3 5

Pr

i s s u r p r i s i n g i n comparison w i t h

a t t h e d i f f e r e n t γ * s a r e i n p r o g r e s s t o see i f s i s t e n t w i t h the Pr d a t a . the a> 's are s l i g h t l y c

backbend.

1 3 3

Pr

[HIL85]

frequency

The a l i g n m e n t o f h n / 2 1 3

^ C e and f u r t h e r

pro­

calculations

a n o t h e r p i c t u r e w o u l d be c o n ­

behaves s i m i l a r l y

to

1 3 5

Pr,

except

l o w e r and t h e ( - , - 1 / 2 ) band shows upbend r a t h e r t h a n

the

Signature Splitting in

S E M K O W E T AL.

309

Pr

135

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch046

46.

Πω Fig.

(MeV)

5. Energy i n the r o t a t i n g vs.

rotational

I frame

frequency.

(fi)

F i g . 6 . E n e r g y between l e v e l s and 1 - 1 / 2

vs. middle

1+1/2 spin.

310

NUCLEI OFF THE LINE OF STABILITY Experimental energies i n the r o t a t i n g

and 5 f o r

f r a m e , E * , a r e p l o t t e d on F i g s , 4

t h e τ τ ( - ) and ττ(+) b a n d s , r e s p e c t i v e l y .

The s i g n a t u r e s p l i t t i n g

d e f i n e d as t h e d i f f e r e n c e between E* f o r o p p o s i t e s i g n a t u r e s .

The

s p l i t t i n g decreases w i t h i n c r e a s i n g ω f o r

signature

splitting

the π ( - )

bands.

f o r t h e i r ( + ) bands can be i l l u s t r a t e d b e t t e r

The

i n F i g . 6 , where

e n e r g y d i f f e r e n c e between Δ Ι = 1 l e v e l s i s p l o t t e d v s . m i d d l e s p i n f o r signatures after

[RIE83].

Large s i g n a t u r e s p l i t t i n g b e f o r e the backbending

the backbending.

signature s p l i t t i n g

This behavior i s d i f f e r e n t

i s s m a l l e r and does n o t

than i n

1 3 3

Pr,

is

signature

the both

inverts

where

the

invert.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch046

Acknowledgments The a u t h o r s w i s h t o acknowledge L . A. A d l e r and 0 . El-Ghazzawy f o r t h e computer codes a v a i l a b l e .

T h i s work i s s u p p o r t e d by t h e U. S.

o f Energy, D i v i s i o n o f Nuclear

Physics.

making

Department

References [AND76] [BEN84] [CHE83] [CON73] [EKS72] [FRA83] [HAG82] [HIL85] [KLE75] [KOR85] [LEA82]

G. Andersson et al., Nucl. Phys. A268 205 (1976) R. Bengtsson et al., Nucl. Phys. A415 189 (1984) Y. S. Chen et al., Phys. Rev. C 28 2437 (1983) T. W. Conlon, Nucl. Phys. A213 445 (1973) C. Ekström et al., Nucl. Phys. A196 178 (1972) S. Frauendorf and F. R. May, Phys. Letters 125B 245 (1983) G. B. Hagemann et al., Phys Rev. C 25 3224 (1982) L. Hildingsson et al., private communication (1985) H. Klewe-Nebenius et al., Nucl. Phys. A240 137 (1975) M. Kortelahti et al., Ζ. Phys. A 321 417 (1985) G. A. Leander et al., Proceedings of the Conference on High Angular Momentum Properties of Nuclei, Oak Ridge (1982), p. 281 [MUL78] M. Müller-Veggian et al., Nucl. Phys. A304 1 (1978) [MUL84] M. Müller-Veggian et al., Nucl. Phys. A417 189 (1984) [PII80] M. Piiparinen et al., Nucl. Phys. A342 53 (1980) [RIE83] L. L. Riedinger, Phys. Scripta 15 36 (1983) [WIS75] K. Wisshak et al., Nucl. Phys. A247 59 (1975) [ZEM82] A. Zemel et al., Nucl. Phys. A383 165 (1982) RECEIVED July

17, 1986

47 Massive Transfer Reactions and the Structure of Transitional A ~ 100 Nuclei D. R. Haenni, H. Dejbakhsh, and R. P. Schmitt Cyclotron Institute, Texas A&M University, College Station, TX 77834 Band crossings and other features of the mass 100 transitional Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch047

nuclei have been studied with massive transfer and fusion reaction based γ-ray spectroscopy.

Experimental blocking

argument results and calculations agree that υh 2 alignment is responsible for the band crossing in Ru. 11/2

102

soft core of

The

103

Rh is influenced by the configuration of the

odd proton; however, the mechanism for this is not clear. High-spin features of the t r a n s i t i o n a l ( Z < 5 0 , N>50) a r e i n t e r e s t i n g

but not well

change between 58 and 60 n e u t r o n s . three d i f f e r e n t

closed o r b i t a l

B a c k b e n d i n g i s known f o r w i t h cranked s h e l l

model

present discussion w i l l

1

0

4

,

1

0

configurations 6

pd

T h e r e i s an a b r u p t

c e n t e r around

1 0 2

comparisons

have been made [ S T A 8 4 ] .

R u and

1 0 3

The

R h w h i c h bave N=58 and a r e

closures.

Most o f t h e n u c l e i

The i n v e s t i g a t i o n o f h i g h - s p i n

v i a in-beam γ - r a y spectroscopy w i t h the usual h i n d e r e d by t h e l a c k o f s u i t a b l e

to

( Z = 4 0 , Z = 5 0 , and N = 5 0 ) .

t o s t u d y s i n c e t h e y l i e on t h e n e u t r o n

side o f the v a l l e y o f s t a b i l i t y .

shape

are a l s o t r a n s i t i o n a l

[GRA76] b u t o n l y s c h e m a t i c

midway between t h e 40 and 50 p r o t o n o r b i t a l

i n general

i n t h e mass 100 r e g i o n

studied.

These n u c l e i

(CSM) p r e d i c t i o n s

t h i s mass r e g i o n a r e d i f f i c u l t

nuclei

(ΗΙ,χηγ)

in

rich

phenomenon

fusion reactions

is

targets.

P a r t o f t h e s p e c t r o s c o p y program a t TAMU i s t h e d e v e l o p m e n t o f t h e so c a l l e d massive t r a n s f e r structure

studies.

of a projectile

(MT) o r b r e a k - u p f u s i o n r e a c t i o n s f o r

B a s i c a l l y these heavy-ion r e a c t i o n s

discrete-line

involve the

transfer

fragment t o the t a r g e t w i t h the remaining energetic

fragment

being emitted i n the forward d i r e c t i o n .

W i t h MT r e a c t i o n s one t e n d s

to

o b s e r v e a b e t t e r p o p u l a t i o n o f h i g h - s p i n s t a t e s when compared t o t h e corresponding fusion r e a c t i o n . also provide a sort of e x i t the study o f nuclei

D e t e c t i o n o f t h e e m i t t e d l i g h t f r a g m e n t can

channel

filter.

These f e a t u r e s can be u s e f u l

in

w h i c h a r e more n e u t r o n r i c h t h a n n o r m a l l y a c c e s s i b l e by 0097-6156/86/0324-0311$06.00/ 0 © 1986 American Chemical Society

312

NUCLEI OFF THE LINE OF STABILITY

( H I , χηγ) r e a c t i o n s , , Further d e t a i l s concerning γ-ray spectroscopy MT r e a c t i o n s can be f o u n d e l s e w h e r e [HAE82] .

with

E x p e r i m e n t a l l y p a r t i c l e - γ and p a r t i c l e - γ - γ c o i n c i d e n c e s a r e m e a s u r e d . W i t h beams h e a v i e r t h a n L i a γ - r a y m u l t i p l i c i t y select high-multiplicity energetic particles measurement i t

filter

i s needed t o

MT e v e n t s f r o m o t h e r r e a c t i o n s w h i c h r e s u l t

b u t low m u l t i p l i c i t i e s .

in

From a s i n g l e MT s p e c t r o s c o p y

i s p o s s i b l e t o s i m u l t a n e o u s l y o b t a i n much o f t h e

usual

4803 4052 -(25/2*)

3431

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch047

3214

3109

2704

21/2* 19/2*

2318

1874-

1554

2

4

1

8

1716-

1400 1332 642 590

2802

-

*

2680-

-23/2*

2804

-17/2*

2132-

-19/2*

2 I / 2

2

93 - L - L 9/2*

^

3 / 2

1

774 -

i /2-

2

9/2* Τ 772*

-

5

1.

Partial

102

level

10 - (A) 1 0 4

Pd GSB

Τ

l04

Ru

0 "

l 0 2

l 0 0

excita­

t i o n f u n c t i o n , c r o s s bombardment,

angular

lcÎ2

R u GSB

its

Ru

" ^ " ^

( ίι,χηγ) 7

Rh9/2*

1 0 1

R u GSB 0.2

03 0.4 0.5 h ω (MeV)

These

Each

results

MT r e a c t i o n s 1 0 0

Mo

t a r g e t a t 49

and 77 MeV, r e s p e c t i v e l y and c o n v e n t i o n a l

T c 9/2*

, 0 2

and

i n d u c e d on a m e t a l l i c

l 0 l

l 0 3

Ru and

neighbors are given i n F i g . 1 .

Institute with \ i

s

5 - RuH/2l0l

schemes f o r

were o b t a i n e d a t t h e TAMU C y c l o t r o n

I T ^ R u 7/2* Ru5/2* _ l0,

l 0 3

level

band c o n t a i n s new l e v e l s .

2

' (C)

several

channels. 102

Partial

Ru7/ **V

Rhi/2>^

for

R u GSB"

\

5 l03

2.

nuclei.

G S B / ^

'

l 0 3

Fig.

-15/2-

' -

experimental γ - r a y data ( s i n g l e s ,

RuGSB"V^

10

0

-I9/2"

4

Ru and n e i g h b o r i n g

adjacent e x i t

0 10

-23/2"

d i s t r i b u t i o n , and c o i n c i d e n c e )

5

M

-27/2"

2132

,443-

i — l 9/ «

Fig.

3080-

0.6

P a r t i c l e alignment

vs

r o t a t i o n a l f r e q u e n c y f o r bands 102 Ru and n e i g h b o r i n g n u c l e i .

s p e c t r o s c o p y a t 45 MeV.

For

R u o t h e r bands were a l s o p o p u l a t e d

but

t h e y c o u l d n o t be e x t e n d e d t o h i g h e r s p i n s than p r e v i o u s l y r e p o r t e d [KLA82]. The 104 Ru l e v e l

scheme a g r e e s w i t h

Coulomb e x c i t a t i o n work

recent

[STA84].

Massive Transfer Reactions

47. HAENNI ET AL.

313 102

The y r a s t cascade i n ι

π—

1

backbend w i t h a c r o s s i n g f r e q u e n c y o f

1

l 0 2

Ο.370ω and an a l i g n m e n t g a i n o f 9 . 5 t f . The u s u a l a l i g n m e n t p l o t s [BEN79] i n F i g . 2a 102 compare Ru w i t h a d j a c e n t e v e n - e v e n 104 nuclei. Except f o r Pd t h e r e f e r e n c e 102 band f o r Ru i s used t o g e n e r a t e t h e s e plots. Both R u [VOI76] and R u show upbends w i t h t h e f o r m e r a t a h i g h e r 102 frequency than Ru. The e x p e r i m e n t a l in?

Ru

w V\ v\ V

\\

\

^ \* \

Ii_ _y_ Neutron

-0.5

0°

B

0.14

10°

C

0.20

-10°

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch047

D

\

2

0.17

Proton ~

i/hn, ll/

A

\

Y

-

1 0 0

wai 0.05

w

-60°

A

\ -

04 ticu

1 0 4

R o u t h i a n [BEN79] f o r

(MeV)

w i t h CSM p r e d i c t i o n s Fig.

3. in?

for

Experimental

Ru shows a

routhian

u

Ru i s compared

(triaxial

version)

[FRA83] i n F i g . 3 assuming e i t h e r t h e vh or ïïg alignment. From t h e s e LL/ά via 1 0 2 1

Ru compared w i t h CSM.

1

/

0

Q/0

c a l c u l a t i o n s t h e backbend i n

Ru s h o u l d

a r i s e from v h ^ ^ alignment w i t h a small positive ε

d e f o r m a t i o n and perhaps a

2

s l i g h t l y positive γ deformation. T h i s c o n c l u s i o n s h o u l d be t e s t e d t h r o u g h b l o c k i n g arguments based on t h e s i n g l e q u a s i p a r t i c l e bands i n t h e a d j a c e n t odd-A n u c l e i . 102 been o b t a i n e d t h r o u g h t h i s work f o r a l l t h e n e i g h b o r s o f bands based on v d ^ f r e q u e n c y as

1 0 2

2

, vg^

a 2

n

d

π

>

Ρι/2

x

n

i

D

1

t

Ru.

I n F i g . 2b

c r o s s i n g s a t a b o u t t h e same

R u and t h u s a r e n o t t h e cause o f t h e o b s e r v e d a l i g n m e n t . 1Ω2

Bands based on t h e v h ^ n

2

o r b i t a l , F i g . 2c, block the

p r e t a t i o n o f the results f o r the π g first

e

New d a t a has

Ru b a c k b e n d .

Inter­

bands i s n o t as s t r a i g h t f o r w a r d . To ' 101 103 order a p l o t of the favored states f o r Tc and Rh i n d i c a t e t h a t

this orbital

Q / 9

a l s o b l o c k s t h e backbend.

In other t r a n s i t i o n a l

odd-A n u c l e i , h o w e v e r , band c r o s s i n g s a r e known

t o change t h e s i g n a t u r e s p l i t t i n g unfavored s t a t e s )

( s t a g g e r i n g between t h e f a v o r e d and

and t h e B ( M 1 ) / B ( E 2 )

ratios.

T h i s o c c u r s when t h e odd

n u c l é o n and t h e a l i g n i n g p a i r a r i s e f r o m t h e u n i q u e p a r i t y o r b i t s i n respective shells.

In both

8 1

K r [FUN83] and

1 5 9

Tm

their

[LAR84] f o r example t h e

s i g n a t u r e s p l i t t i n g i s r e d u c e d above t h e band c r o s s i n g and t h e B ( M 1 ) / B ( E 2 ) r a t i o s are enhanced.

Frauendorf

[FRA84] has e x p l a i n e d t h e s e f e a t u r e s

with

t h e a s s u m p t i o n t h a t t h e u n p a i r e d n u c l é o n s p r o d u c e c o n f i g u r a t i o n dependent γ deformations o f the s o f t t r a n s i t i o n a l

core.

For t h e mass 100 r e g i o n an odd

314

π 9

9/2

NUCLEI OFF THE LINE OF STABILITY w

o

u

l

g e n e r a t e a n e g a t i v e γ d e f o r m a t i o n and l a r g e s i g n a t u r e

d

splitting.

A l i g n i n g a v h ^ ^ p a i r w i t h i t w o u l d push γ t o n e a r 0 ° and remove t h e ^ ~ _ ~ J-. .

l ^ j - x ^

signature ïïg

Ατ

Λ

ι

ι

ι

£

ι_

j.1

1 η / o"^~

ο ι

J

/

ι

Ί _

_c

splitting Α Δ Ι = 1 band f e e d s t h e 1 9 / 2 and 2 1 / 2 l e v e l s o f t h e 103 . . 2 band i n Rh and may r e p r e s e n t such a ^ 9 / 2 ^ 1 / 2 b a n d . T h i s band Λ

D U

9/2

3Q/9

has l e v e l s a t 3 3 9 6 , 3 6 3 0 , 3 9 3 7 , 4 3 2 0 , 1

1

1

1

4 7 0 5 , 5 1 9 5 , 5 6 6 2 , and 6205 keV w i t h

I

23/2

10

^9/2 F i g . 4 . A back­ bend o c c u r s a t a f r e q u e n c y c o n s i s t e n t 102

π R

l 0 2

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch047

0

h

Trg9£

RuGSB

ι

O.I

ι ·1

) 0

R u GSB

0.2 0.3 Q4 Q5 *w (MeV)

-

b

with

06

a

n

d

1 S

Ru.

s

n

o

w

n

i

n

The π ς ^ 9

b

a

n

d

i

observed

s

2

above t h e band c r o s s i n g r e g i o n . Fig. 4.

P a r t i c l e a l i g n m e n t vs

rotational πg

frequency f o r the

band i n

spins

An a l i g n ­

+

ment p l o t f o r t h i s band c r o s s i n g w i t h t h e

V\

'x

to 37/2 , respectively.

+

R h assuming a 9/2 change i n s i g n a t u r e s p l i t t i n g . 1 0 3

The s t a r t

o f an up-bend i s f o u n d above 0.5Ηω. present level

scheme f o r ^ T c

e x t e n d h i g h enough t o show a s i m i l i a r c r o s s i n g band. The c o m p l e x i t y o f o u r a n g u l a r t r i b u t i o n s p e c t r a do n o t p e r m i t

extraction o f mixing r a t i o s

The

does n o t

f o r the I + I - l

transitions

i n the

dis­

reliable b

a

n

d

-

Assuming t h a t t h e s e a r e p u r e M l , a 10 f o l d i n c r e a s e i n t h e e x p e r i m e n t a l B(M1)/B(E2)

i s o b s e r v e d between t h e one and t h r e e q u a s i p a r t i c l e

Donau and F r a u e n d o r f

bands.

[D0N83] have s u g g e s t e d t h a t s i n c e t h e r o t a t i o n a x i s

is

n o t t h e same as t h e a l i g n m e n t a x i s i n a h i g h Κ b a n d , p a r t i c l e a l i g n m e n t can enhance Ml t r a n s i t i o n r a t e s .

T h i s o c c u r s when t h e g f a c t o r

opposite sign f o r the i n i t i a l

and t h e a l i g n i n g q u a s i p a r t i c l e s .

semi c l a s s i c a l 9

e x p r e s s i o n f o r the B(M1)/B(E2)

ratios.

r a t i o o v e r t h e same range o f

R

has an

They gave a

With a s t r o n g

9 / 2 proton (K=9/2) t h i s expression gives a f a c t o r o f 3

B(M1)/B(E2)

(g^-g )

coupled

increase i n the

spin.

The s i g n a t u r e s p l i t t i n g o b s e r v e d i n t h e g ^ g

b

a

n

d

d

o

e

s

2

n

o

t

necessarily

i m p l y c o n f i g u r a t i o n dependent γ d e f o r m a t i o n s as p r o p o s e d by F r a u e n d o r f .

A

similiar splitting in A g was r e p r o d u c e d [P0P79] w i t h a q u a s i p a r t i c l e p l u s - r o t o r (SR) model i n c l u d i n g a VMI t r e a t m e n t o f t h e s o f t c o r e . The l e v e l 103 scheme f o r Rh shows many o f t h e same f e a t u r e s as t h e Ag i s o t o p e s b u t i s 103 1 0 5 , 1 0 7

more c o m p l e t e .

To e x p l o r e t h i s f u r t h e r t h e l e v e l s

in

c a l c u l a t e d u s i n g t h e SR, IBFM-1 [ J 0 L 8 5 ] , and t r i a x i a l models.

Rh have been rotor

(AR) [MAY 7 5 ]

P a r a m e t e r s f o r t h e SR model were chosen i n a manner s i m i l i a r

to the

47.

315

Massive Transfer Reactions

HAENNI ET AL.

(A)

4.0 L 2 5 / 2 ' -

(B)

21/2'3.0

h

17/2'-

21/219/2-

15/2"-

2

ω

2.0

17/2-

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch047

11/2"

1.0

15/2-

9/2" 5/2Ί 7/2"

13/2— 11/2(o) 5 / 2 -

5/2". 3/2'" "•g9/2Bo

0.0 IBFM-I

EXR S.R. T r p i / 2 Band

Fig.

5.

parity model

EXP

Comparison o f t h e n e g a t i v e 103 "Rh w i t h d b a n

i

Fig.

6 . Comparison o f t h e p o s i t i v e 103 Rh w i t h parity '

n

n

D

calculations.

Ag i s o t o p e s

[P0P79]

model

b u t u s i n g an a v e r a g e

n

d

Ί

J

η

n

calculations.

Ru -

parameters are from a recent c a l c u l a t i o n

a

Pd c o r e .

The IBFM-1

[ J 0 L 8 5 ] f o r o d d - A Rh i s o t o p e s

assuming t h a t Rh i s a h o l e i n t h e c o r r e s p o n d i n g Pd c o r e . Parameters f o r 102 104 AR model were a g a i n based on an a v e r a g e Ru Pd c o r e . 103 R e s u l t s o f t h e s e c a l c u l a t i o n s a r e compared t o

the

Rh i n F i g s . 5 , 6 .

For

t h e n e g a t i v e p a r i t y l e v e l s t h e SR and IBFM-1 models p r o d u c e a r e a s o n a b l e agreement w i t h t h e d a t a . sets

The f i t s

to the g

g

^

D

a

n

d

w

l

t

n

t h e same p a r a m e t e r

[ ( A ) f o r t h e SR m o d e l ] a r e n o t as good and a p p e a r t o i n d i c a t e a

core than observed.

softer

The AR model p r e d i c t s s i g n a t u r e s p l i t t i n g f o r t h e g ^ g

band as do t h e o t h e r models b u t i t s a s s u m p t i o n o f a r i g i d r o t o r c o r e i s appropriate for a transitional can be improved (B) i f parameter C i s

nucleus.

the deformation ε

The SR model f i t

i s decreased ( 0 . 2 - 0 . 1 5 )

2

increased (0.006-0.02 MeV ).

d i r e c t i o n o f a s t i f f e r more s p h e r i c a l

to the g ^

3

core.

These changes a r e i n

g

b

2

not a

n

d

2

and t h e VMI the

316

N U C L E I OFF T H E LINE OF STABILITY

With core parameters d e r i v e d from n e i g h b o r i n g even-even n u c l e i t h e SR and IBFM-1 models g e n e r a t e a s i m i l i a r p a t t e r n o f r e s u l t s . band i s more o r l e s s r e p r o d u c e d w h i l e t h e g 103 provides evidence t h a t the s o f t core i n proton.

It

results

g

i s not c l e a r .

/

9

band i s c o m p r e s s e d .

band t h a n t h e p ^

2

2

This i n t e r a c t i o n

The

perhaps

has a l r e a d y been shown

[FED79] t o be t h e d e f o r m a t i o n d r i v i n g f o r c e i n t h i s mass r e g i o n w i t h ^9g/2

a

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch047

orbital

n

d

v g

7/2

o

r

D

l

t

would l i k e l y

a

l

s

playing

show e f f e c t s

particularly

transition

transitional

odd-A n u c l e i

key r o l e s . from t h i s

r a t e s f o r the g ^ g

2

Bands based on t h e interaction.

^9g/2

More d a t a ,

b a n d / b e t t e r models f o r

a r e needed t o draw more d e f i n i t e

the

such

conclusions.

References [BEN79] R.Bengtsson and S. Frauendorf, Nucl. Phys. A327 139 (1979). [DON83] F. Dőnau and S. Frauendorf, High Angular Momentum Properties of Nuclei edited by N. R. Johnson (Harwood Academic, New York) 281 (1983). [FED79] P. Federman and S. Pittel, Phys. Rev. C 20 820 (1979). [FRA83] S. Frauendorf and F. R. May, Phys. Lett. 125B 245 (1983). [FRA84] S. Frauendorf, International Symposium on In-Beam Nuclear Spectroscopy, Debrecen, Hungary (1984). [FUN83] L. Funke et a l . , Phys. Lett. 120B 301 (1983). [GRA76] J. A. Grau et al., Phys. Rev. C 14 2297 (1976). [HAE82] D. R. Haenni et al., Phys. Rev. C 25 1699 (1982). [JOL85] J. Jolie et al., Nucl. Phys. A438 15 (1985). [KLA82] W. Klamra et al., Nucl. Phys. A376 463 (1982). [LAR84] A. J. Larabee et al., Phys. Rev. C 29 1934 (1984). [MAY75] J. Mayer-ter-Vehn, Nucl. Phys. A249 111 (1975). ibid. 141. [POP79] Rakesh Popli et al., Phys. Rev. C 20 1350 (1979). [STA84] J. Stachel et al., Nucl. Phys. A419 589 (1984). [VOI76] M. A. J. de Voight et al., Nucl. Phys. A270 141 (1976). RECEIVED July

14, 1986

1

This

band.

I t may a r i s e f r o m γ d e f o r m a t i o n o r

f r o m n-p i n t e r a c t i o n s .

p

Rh i s i n f l u e n c e d by t h e odd

i s more a p p a r e n t f o r t h e g ^

cause f o r t h i s

Q

both

The

48 High-Spin Structure of 1

Lu

163

2

1

1

1

3

K. Honkanen, H. C. Griffin , D. G. Sarantites, V. Abenante, L. A. Adler , C. Baktash, Y. S. Chen , O. Dietzsch, M. L. Halbert, D. C. Hensley, Noah R. Johnson, A. J. Larabee , I. Y. Lee , L. L. Riedinger, J. X. Saladin , T. M. Semkow, and Y. Schutz 6

4

3

3

5

3

3

4

1

5

3

1

Washington University, St. Louis, MO 63130 University of Michigan, Ann Arbor,MI48109 Oak Ridge National Laboratory, Oak Ridge, TN 37831 University of Pittsburgh, Pittsburgh, PA 15260 University of Tennessee, Knoxville, TN 37996-1200 Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831

2

3

4 5

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch048

6

The π9/2-[514] ground band structure of

163

Lu shows a large signa­

ture splitting with inversion above the backbend suggesting a shape change associated with the triaxiality degree of freedom.

The π1/2-[541]

band shows no backbending up to ћw = 0.4 MeV indicating a more deformed structure.

Recently,

t h e c r a n k e d s h e l l model h a s been v e r y s u c c e s s f u l i n

t h e s p e c t r a o f t h e deformed n u c l e i a t h i g h s p i n s . n u c l e u s i s assumed t o have an i n t r i n s i c adiabatically

nonspherical

a r o u n d a space f i x e d a x i s . [ B E N 7 9 ]

interpreting

In this picture, the shape and t o r o t a t e

Traditionally,

most e x p e r i -

m e n t a l a n d t h e o r e t i c a l e f f o r t s were f o c u s e d on t h e a s p h e r i c i t y p a r a m e t e r Z2 and i t s i n f l u e n c e on t h e r o t a t i o n a l

spectra.

In contrast,

a t t e n t i o n h a s been d i r e c t e d t o t h e t r i a x i a l i t y

only very

recently

p a r a m e t e r γ , w h i c h p l a y s an

i m p o r t a n t r o l e on t h e e v o l u t i o n o f shapes a s a f u n c t i o n o f s p i n .

More

t h o r o u g h i n v e s t i g a t i o n s a r e needed t o p r o v i d e a d e t a i l e d u n d e r s t a n d i n g o f t h e b e h a v i o r o f n u c l e i a t h i g h s p i n s as a f u n c t i o n o f γ . It

h a s been p o i n t e d o u t by s e v e r a l a u t h o r s t h a t

tionally

a l i g n i n g h i g h - j o r b i t a l s may p r o v i d e a s e n s i t i v e p r o b e o f t h e

triaxiality

p a r a m e t e r γ , and c o u l d be used t o t r a c e t h e e v o l u t i o n o f γ w i t h

a n g u l a r momentum [ B E N 8 3 ] , .the f a c t

the population of rota-

that a particle

[FRA83], (hole)

[LEA83].

in a high-j

These o b s e r v a t i o n s a r e based on orbital polarizes

0097-6156/ 86/ 0324-0317$06.00/ 0 © 1986 American Chemical Societv

the core

toward

318

NUCLEI OFF THE LINE OF STABILITY

oblate (prolate)

shapeι w h e r e a s , a q u a s i - p a r t i c l e

o r b i t a l s h e l l generates the intermediate shape.

in a half-filled

s i t u a t i o n leading to a

These e x p e c t a t i o n s where c o n f i r m e d i n a c r a n k e d s h e l l - m o d e l

calcula­

te

t i o n by L e a n d e r

[ L E A 8 3 ] , who c o n c l u d e d t h a t i n a γ - s o f t n u c l e u s t h e

of a h i g h - j q u a s i - p a r t i c l e with favored signature w i l l t h e n u c l e u s a t a γ v a l u e t h a t depends i n i t i a l l y l e v e l i n the s h e l l .

F o r non γ - s o f t

i s more t h a n h a l f

s t a t e s a r e much l e s s s e n s i t i v e Fermi l e v e l

i n the s h e l l .

presence

t h e shape

on t h e p o s i t i o n o f t h e

exerts a driving

p o s i t i v e γ v a l u e s when t h e s h e l l i s l e s s t h a n h a l f v a l u e s when i t

stabilize

full.

force

mini­

toward

f u l l or toward negative γ

I n c o n t r a s t the unfavored

t o v a r i a t i o n s o f γ and λ ,

This r e s u l t s

of

Fermi

n u c l e i t h a t have a p o t e n t i a l - e n e r g y

mum a t some o t h e r γ v a l u e t h e q u a s i - p a r t i c l e

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch048

high-j

triaxial

signature

the p o s i t i o n of

in signature s p l i t t i n g s

the

t h a t become a

s e n s i t i v e measure o f t h e v a r i a t i o n o f γ - d e f o r m a t i o n w i t h s p i n and λ . I n v e r s i o n o f s i g n a t u r e s p l i t t i n g above t h e backbend i n ^ y H o ^ 1

69

T m

90

C

RIE83

]

e

^

i n

7 r 7

/2~[523]

i n f l u e n c e o f t h e t w o 113/2

[HAG82] and

band was e x p l a i n e d by t h e p o s i t i v e

driving

n e u t r o n s above t h e backbend w h i c h r e s u l t s

change f r o m n e g a t i v e t o s l i g h t l y

o f such e f f e c t s

i n t h e γ p l a n e as a

f u n c t i o n o f t h e p r o t o n number we have s t u d i e d t h e h i g h s p i n s t r u c t u r e w h i c h has two p r o t o n s and two n e u t r o n s more t h a n

the π9/2"[514] lated.

and p o s s i b l y

in a

p o s i t i v e γ above t h e b a c k b e n d .

I n order to explore the p o s s i b i l i t y

^ L u ^

in

the π7/2 [404] +

1 5 9

Tm.

of

In t h i s

case

o r b i t a l s w o u l d be p r e d o m i n a n t l y

The f o r m e r o f t h e s e may be a new c a n d i d a t e f o r such a s i g n a t u r e

popu­

inver­

sion. The h i g h s p i n s t a t e s i n

1 6 3

L u were p o p u l a t e d v i a t h e

1 2 2

Sn(^ Sc,4n)

t i o n a t 192 MeV w i t h t h e tandem a c c e l e r a t o r a t t h e H o l i f i e l d Facility.

A stack of

used as a t a r g e t . lar

four

(250 y g / c m

2

each)

A short run w i t h a t h i c k e r

e n e r g y r e s o l u t i o n i n t h e Ge γ - r a y e n e r g y The γ - r a y

1 2 2

Sn

reac­

5

Heavy-Ion

self-supporting

foils

( 1 . 2 m g / c m ) t a r g e t gave

were simi­

2

spectra.

s p e c t r o s c o p i c i n f o r m a t i o n was o b t a i n e d u s i n g an a r r a y o f

five

Ge d e t e c t o r s w i t h p e n t a g o n a l N a l a n t i - C o m p t o n s h i e l d s l o c a t e d a t 63° t o beam and t h r e e a d d i t i o n a l Ge d e t e c t o r s a t 2 4 ° . e v e n t s f r o m t h e s e d e t e c t o r s were used t o t r i g g e r Spin Spectrometer t o r o f 3.5 f o r

(SS) a t ORNL.

the

a t 2 0 . 8 cm f r o m t h e

6 0

[JAA83]

coincident

t h e 72 N a l d e t e c t o r s o f

An a v e r a g e Compton s u p p r e s s i o n

C o s p e c t r u m was o b t a i n e d . target.

Two-fold or higher

the

The Ge d e t e c t o r s were

the fac­

placed

48.

High-Spin Structure of

HONKANEN ET AL.

319

Lu

163

The e v e n t t a p e s were p r o c e s s e d i n o r d e r t o ( 1 ) l i n e a r i z e and match gains o f the Nal d e t e c t o r s , SS, and ( 3 ) c o n s t r u c t

the

( 2 ) separate the n e u t r o n from the γ pulses i n

the t o t a l pulse h e i g h t ,

the

H, and t h e c o i n c i d e n c e f o l d

The p r o c e s s e d e v e n t s were t h e n s o r t e d by p l a c i n g 2 - d i m e n s i o n a l g a t e s i n

k.

(H,k)

space i n o r d e r t o s e p a r a t e t h e c a s c a d e s a s s o c i a t e d w i t h t h e 4n f r o m t h e 5n channel.

This procedure reduces the background from the competing

by a f a c t o r o f 2 o r m o r e .

channels

The g a t e d e v e n t s were s o r t e d i n t o an Εγ-Εγ

w h i c h was c o r r e c t e d f o r Ge d e t e c t o r e f f i c i e n c y .

A two-dimensional

matrix,

background

s u b t r a c t i o n p r o c e d u r e was d e v e l o p e d t o s u b t r a c t t h e Compton-Compton and peak-Compton b a c k g r o u n d s f r o m each g a t e on t h e o b s e r v e d p e a k s .

Angular

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch048

c o r r e l a t i o n i n f o r m a t i o n was o b t a i n e d f r o m a m a t r i x w i t h t h e 2 4 ° and 6 3 ° d e t e c t o r s on s e p a r a t e a x e s . I n F i g . 1 a r e shown t h r e e band s t r u c t u r e s b e l i e v e d t o be a s s o c i a t e d E n e r g y s y s t e m a t i c s i n t h e h e a v i e r odd A Lu i s o t o p e s show t h a t π9/2"[514] rapidly 1 6 5

band w o u l d be t h e y r a s t b a n d , a l t h o u g h t h e π 1 / 2 [ 4 1 ΐ ]

L u and

1 6 3

the present work.

it

The t r a n s i t i o n s

c i a t e d w i t h CH,k) d i s t r i b u t i o n s t h u s were a s s i g n e d t o

In

significant

Lu

1 6 3

Lu

[XN84]

the

1 6 3

from a l l

t h e s e s t r u c t u r e s have y i e l d s of the (

4 5

Sc,4n)

reaction

the 9/2"[514]

signature s p l i t t i n g

between some o f t h e bands i n

band was seen up t o I [J0N84].

1 6 3

Lu

= 4 3 / 2 " and i t

A second band was a s s i g n e d as π 1 / 2 " [ 5 4 1 ]

i n analogy w i t h

Lu.

a p a r t o f the 7/2 [404] +

and

has a

Based on s y s t e m a t i c s f r o m t h e odd-A

w h i c h p l a c e s t h e b a c k b e n d i n g a t a b o u t 12 u n i t s o f r o t a t i o n a l

1 6 5

asso­ and

Lu.

The b a c k ­

b e n d i n g i n t h i s r e g i o n i s due t o b r e a k i n g and a l i g n m e n t o f an 113/2

momentum.

in

further

s t r u c t u r e s based on o b s e r v e d

L u i s o t o p e s , we have a s s i g n e d t h i s y r a s t band as t h e π 9 / 2 ~ [ 5 1 4 ] .

pair,

the

π9/2"[514]

i s a l s o t h e s t r o n g e s t band p o p u l a t e d

characteristic

There i s a s t r i k i n g s i m i l a r i t y Lu.

In

i s i n progress to connect the d i f f e r e n t

1 6 5

s t a t e and i n

The decay scheme shown i n F i g . 1 i s p r e l i m i n a r y and

coincident γ-rays.

1 6 5

to the π 7 / 2 [ 4 0 4 ] +

L u may become t h e g r o u n d s t a t e .

band i s t h e y r a s t band and i n

analysis

decreases

+

i n energy w i t h decreasing A r e l a t i v e

with

the

neutron angular

based on s y s t e m a t i c s

A t h i r d band s t r u c t u r e shown i n F i g . 1 i s most

and

likely

band.

The f a v o r e d and u n f a v o r e d bands Cot = ~

and ^ ) g a i n 7 . 2 and 8 . 2 u n i t s

a n g u l a r momentum above t h e b a c k b e n d , r e s p e c t i v e l y

(Fig. 2a).

This i s

con-

of

320

NUCLEI OFF THE LINE OF STABILITY

6637 5131

-445/2")

5 | / 2

-6l80

805 4326

163, 71

U

-441/2")

49/2" 47/2

752

92

45/2"

3574

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch048

53/2"

-437/2")

43/2

696 2878

{33/2*) 638

2240

39/2

-429/2") 35/2

1663

577

502

—Î25/2") 31/2-

2

7

1

33/2"

3

513 1150 616 699

569 510 463

399

327

259

421/2") 27/2 450

-(Ι7/2Ί 385 314 — 0 3 / 2 " ) 23/2' 314 OfY (9/2") 19/2 15/2 11/2

7ΓΙ/2" Fig.

1

Tentative 1

6

\ u .

decay scheme f o r

The s p i n 9 / 2 "

for

band was assumed based on

[541]

9/2" ITS/2'

[514]

t h e t h r e e band s t r u c t u r e s a s s i g n e d the lowest observed l e v e l systematics.

in

the

to

π9/2"[514]

48.

High-Spin Structure of

H O N K A N E N ET AL.

30

Lu

321

163

- Γ - Τ ^--Ρ , ! ! I ! ! . . ,

(α)

(b)

7 Γ 9 / 2 " [514]

— 20

• α

=-1/2

- - - ο α =+1/2 —

Α77Ί/2"

[541]

-0.5

MeV*

3 7Γ 9/2"

1514]

• — • α = -1/2 Γ — - ο α = • ι/2

10

;

Α 7 Γ Ι / 2 " [541]

h b

. .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch048

0.0

0.1

0.2 hbi

Fig.

2.

0.3

0.4

0.5

0.0

I

;

.

I

.1

0.1

(MeV)

0.2

;

I

0.3

0.4

0.5

fuj (MeV)

Panels a and b show the aligned angular momentum and the energy in 9

the rotating frame (E

= ^Level - ^ ω Ι ) χ

for the bands indicated.

sistent with the decoupling and alignment of an 113/2 neutron pair.

The

crossing frequencies for the a=~ and a=-i bands are 0.263 and 0.280 MeV, respectively, as is seen from Fig. 2 b .

Below the backbend the π9/2"[514]

band shows a large negative signature splitting which increases with ω from ~ 55 to 120 keV (Fig. 2b), but above the backbend a signature inversion occurs with a splitting of 10 keV which remains constant with increasing ω .

This is

seen in detail in Fig. 3. Fig.

3 Signature splitting

indicated by the d i f ­ ferences in Ε γ (I+I-l) values for transitions starting from the ot=~ levels (open squares) and the a=| levels (open circles).

The corres­

ponding f u l l points give the B(M1,I-*I-1)/B(E2, I+1-2) ratios obtained from branching ratios assuming 6=0.

322

NUCLEI OFF THE LINE OF STABILITY A cranked shell-model c a l c u l a t i o n f o r

signature s p i t t i n g MeV.

1 6 5

L u gave a ~ 80 keV n e g a t i v e

f o r t h e q u a s i - p r o t o n s f o r a γ v a l u e o f - 1 0 ° a t ηω = 0 . 2 4

A signature inversion i s predicted for the quasi-proton

at γ - 0°.

Above t h e backbend t h e two 113/2

toward p o s i t i v e γ v a l u e s .

configuration

quasi-neutrons are

driving

When t h e r o u t h i a n s f o r t h e s e 3 - q u a s i p a r t i c l e s

added and t h e e f f e c t o f t h e c o r e i s i n c l u d e d , a γ v a l u e f o r t h i s f i g u r a t i o n can be o b t a i n e d .

Qualitatively,

shape change f r o m n e g a t i v e t o s l i g h t l y case.

it

appears t h a t a

t o t h a t observed i n

1 5 5

H o on

1 5 9

band i s q u i t e

T m where t h e 7 / 2 " [523] q u a s i - p r o t o n

f i g u r a t i o n was pushed t o w a r d s l i g h t l y p o s i t i v e γ v a l u e s by t h e

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch048

significant

p o s i t i v e γ values i s present i n

Thus, the s i g n a t u r e i n v e r s i o n i n the π9/2~[514]

d r i v i n g i n f l u e n c e o f t h e two s t r o n g l y a l i g n i n g 113/2 The g r a d u a l g a i n i n a l i g n m e n t o f t h e i r l / 2 ~ [ 5 4 1 ]

are

con­

this similar

con­

positive

quasi-neutrons. band w i t h i n c r e a s i n g ω

( F i g . 2a) suggests t h a t e i t h e r the a l i g n i n g q u a s i p a r t i c l e s e x h i b i t a s t r o n g i n t e r a c t i o n , o r t h a t a l a r g e r €2 v a l u e compared t o 0 . 2 f o r t h e i r 9 / 2 " [ 5 1 4 ] band and p o s s i b l y a d i f f e r e n t γ v a l u e a r e needed i n o r d e r t o e x p l a i n

its

behavior. Acknowledgments Work s u p p o r t e d by t h e U. S . D e p a r t m e n t o f E n e r g y , D i v i s i o n o f

Nuclear

Physics.

References [BEN79] [BEN83]

[FRA83] [LEA83] [HAG82] [JÄÄ83]

[JON84] RECEIVED

R. Bengtsson and S. Frauendorf, Nucl. Phys. A 314, 27 (1979); A314, 139 (1979). R. Bengtsson, et al. Bormio, 1982 p. 144; and in "High Angular Momentum Properties of Nuclei", Ed. N. R. Johnson (Harwood, New York, 1983) p. 161. S. Frauendorf and F. R. May, Phys. Lett. 125B, 245 (1983). G. A. Leander, et al. in "High Angular Momentum Properties of Nuclei", Ed. N. R. Johnson (Harwood, New York, 1983), p. 281. G. B. Hagemann, et al. Phys. Rev. 25C, 3324 (1982). M. Jääskeläinen et al., Nucl. Instr. 204, 385 (1983). S. Jonsson et al. Nucl. Phys. A422, 397 (1984). April 11, 1986

49 Shape Competition and Alignment Processes in Light A u and Pt Nuclei 1

1

2

L. L. Riedinger , A. J. Larabee , and J.-Y. Zhang 1

University of Tennessee, Knoxville, TN 37996-1200 Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch049

2

Calculations are presented and data are reviewed on the properties of the high-j states in the light Au nuclei. Both prolate and oblate structures are observed in this region. It is found that the collective model describes well the band- head and the high-spin properties of the h9/2 and i13/2 proton states, without resort to an "intruder state" phenomenology. There has been m u c h discussion at this and other conferences about the existence o f nuclear intruder states, i.e. levels outside the m o d e l space f o r a g i v e n nucleus. There is ample evidence [ H E Y 8 3 ] f o r the existence o f intruder states at o r near closed shells, w h i c h demonstrates the importance o f the v a r y i n g particle-hole c o m p o s i t i o n o f these states. A s one proceeds away f r o m the closed shell b y a d d i n g o r subtracting nucléons, at some point there occurs n o r m a l deformed n u c l e i adequately described b y the N i l s s o n m o d e l , i n w h i c h case the s h e l l - m o d e l particle-hole structure o f states becomes irrelevant. O n e important question is f o r h o w m a n y nucléons beyond a closed shell does the intruder description o f certain states g i v e w a y to the collective description. W e pursue here this question f o r the Ζ = 7 9 isotopes o f g o l d and describe experiments and calculations performed o n both the bandhead energies o f h i g h - j states (occasion­ a l l y c a l l e d intruders) and the bands built o n these states. W e f i n d that the c o l l e c ­ tive picture adequately describes these levels i n a transition region o f competing nuclear shapes. W h i l e oblate structures o c c u r i n the heavier g o l d isotopes, the lighter ones are dominated b y prolate bands. O u r group has performed measurements o n a n u m b e r o f P t and A u n u c l e i . H i g h - s p i n states i n ' A u [ L A R 8 5 ] and i n P t [ W A D 8 5 ] have been studied at the M c M a s t e r U n i v e r s i t y T a n d e m A c c e l e r a t o r w i t h F i n d u c e d reactions. A n array o f 5 G e and 6 N a l counters was used to collect g a m m a - g a m m a coincidence data. A n g u l a r distribution measurements were also performed. B a n d s i n 183,184^ d i e d [CAR85] with a induced reaction at the H o l i f i e l d H e a v y Ion Research F a c i l i t y . T h e S p i n Spectrometer was used w i t h 9 G e counters, six o f w h i c h were C o m p t o n suppressed w i t h N a l annuli. T h e systematics o f the prolate and oblate states observed i n the light 1 8 5

1 8 6

1 8 5

1 9

w

e

r

e

s t u

0097-6156/ 86/0324-0323506.00/ 0 © 1986 American Chemical Society

324

NUCLEI OFF THE LINE OF STABILITY

Ε

Ε (MeV)

( MeV )

1-5 +

0.5+

l.o

+

9/2 -.191

in

Au

-;·.?· -.1β7

0*

0.5 + .238

1.5+

Η —

2.0 τ Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch049

233 — Η

163 185 187 189 191 193 ^05 _. -.196 1Β7

-.210

.205

-.201

ΕΧΡ

1-5 + 0.5+

1.0

+

257

1 3 / 2 " ^ in

Au

0.5 +

0+

0 +

102

106 110

A Η

Η

183 185 187 189 191 193

F i g . 2. N i l s s o n c a l c u l a t i o n o f b a n d head energies f o r the I19/2 and 113/2 proton states i n the A u isotopes. A prolate (solid line) and a n oblate (dashed line) solution is g i v e n for most. E q u i l i b r i u m deformations are g i v e n for each. T h e experimental energies are g i v e n for c o m p a r i s o n .

1 14

F i g . 1. E x p e r i m e n t a l systematics o f some prolate (closed squares) and oblate (open squares) states i n H g (Z=80), A u (79), and Pt (78) n u c l e i . H g , A u , and P t n u c l e i are shown i n F i g . 1. T h e first 2 state o f the H g isotopes is remarkably constant i n energy and has been described as a slightly deformed oblate state. A s mapped i n detail i n U N I S O R measurements [ H A M 7 5 ] , there exist r a p i d l y f a l l i n g prolate states i n H g . T h e heavy P t isotopes are evidently s i m i l a r i n ground properties to the H g n u c l e i , but the isotopes b e l o w Ν = 110 m a y be prolate i n shape, j u d g i n g b y the structure o f the 113/2 b a n d i n adjacent o d d - N P t isotopes. A s summarized b y W o o d [ W 0 0 8 1 ] , l o w - l y i n g 0 states i n P t m a y be the oblate states s i m i l a r i n structure to the H g ground configuration. T h u s , Ζ = 79 around Ν = 106 appears to be the point o f crossing +

1 8 4

1 8 8

+

1 8 2

1 8 6

49.

RIEDINGER E T AL.

Shape Competition and Alignment Processes

for the oblate and prolate m i n i m a . A s seen i n F i g . 1, the π1ΐ9/2 and πίΐ3/2 states f a l l r a p i d l y i n the l i g h t A u n u c l e i , w h i c h suggests the intruder description, i.e. a different b e h a v i o r o f the n o r m a l 3-hole states (hi 1/2, d3/2, sm) c o m p a r e d to the 1-particle 4-hole levels (I19/2,113/2). T h e structure o f the bands b u i l t o n these states suggests the prolate or oblate nature described i n F i g . 1. A Strutinsky-type N i l s s o n c a l c u l a t i o n o f the bandhead energies for the A u isotopes is s h o w n i n F i g . 2. T h e parameters used i n this N i l s s o n c a l c u l a t i o n were those suggested b y the L u n d group [ B E N 8 5 ] , except for μ = 0.52 for the Ν = 5 and Ν = 6 proton shells. T h i s value better describes levels i n this r e g i o n and became necessary i n order to e x p l a i n i n A u the n e w l y found l / 2 [ 5 3 0 ] band, based partially o n the fia shell state [ L A R 8 5 ] . A s seen i n F i g . 2, there are both prolate and oblate m i n i m a calculated for each o f the quasiparticle states. W h i l e the oblate hm and 113/2 states are rather constant i n energy as a f u n c t i o n o f N , the prolate m i n i m u m falls r a p i d l y , b e c o m i n g l o w e r a t A u for the f o r m e r and at A u for the latter. These calculations m a t c h rather w e l l the observed trend (see F i g . 1), and suggest that it is changing deformation w h i c h is responsible for the " i n t r u d i n g " h i g h - j states, as opposed to the d i f f e r i n g particle-hole character. T h i s c o l l e c t i v e explanation requires a deformation o f -0.173 for the lowest I19/2 state i n A u , but unfortunately the b a n d structure built o n this state is u n k n o w n and thus it is d i f f i c u l t to surmise i f this deformation is reasonable. C a l c u l a t i o n s w i t h a W o o d s - S a x o n potential give results very s i m i l a r to those s h o w n i n F i g . 2 [NAZ85]. It is clear f r o m the calculations o f F i g . 2 that the b a n d structures seen i n the light A u n u c l e i should be dominated b y prolate shapes, as is observed e x p e r i ­ m e n t a l l y i n A u [ L A R 8 5 ] . R o t a t i o n - a l i g n e d bands are b u i l t o n I19/2,113/2, and f7/2 N i l s s o n states, indicative o f Κ = 1/2 bands and prolate shapes. H o w e v e r , the stucture b u i l t o n the h i 1/2 bandhead is more c o m p l e x , as s h o w n i n the partial l e v e l scheme o f F i g . 3. T h e 2 2 0 - k e V bandhead is k n o w n [ B E R 8 3 ] to be a 26 ns isomer, e x p l a i n e d as due to an oblate h i 1/2 to prolate I19/2 transition. T h e sequence of E 2 transitions to the right i n F i g . 3 is s i m i l a r to that seen i n the heavier o d d - A A u n u c l e i [ G O N 7 9 ] , and is explained as the w e a k c o u p l i n g o f the h i 1/2 h o l e state to the slightly oblate H g core. H o w e v e r , the sequence of levels b e g i n n i n g at 1210 k e V is different f r o m anything seen i n the heavier isotopes. T h e strongly-coupled nature o f this n e w band suggests a prolate h i 1/2 structure, w h i c h is expected to lie close i n energy to the oblate band according to the calculations. T h e c o m p l i c a t e d structure s h o w n i n F i g . 3 is therefore quite compatible w i t h the predicted near degeneracy o f prolate and oblate bands i n Au. 1 8 5

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch049

325

1 8 9

1 8 7

1 9 3

1 8 5

1 8 5

F o u r bands are observed to h i g h spins i n

1 8 5

A u and are s h o w n i n the

326

NUCLEI OFF THE LINE OF STABILITY

Δ 7rh9/2 α 1/2 s

A

7rh

9 / 2

α = -1/2

+ 7rf7/ α « -1/2 Ο iri a*1/2 2

1 3 / 2

3365.0327.7 •205.7

2831.6-

269.9,

—

3037.3

476 —

2561.7

259 2 •

1B

2302.5-

* P 1 - yrast band

ο vi a = 1/2 1185pt • ^'13/2 " 2 J ν 7Γη ι/ϊ 2 ο =1 Ί • 7rh i/i a = 0j

536.5 277.3,

1 3 / 2

a

9 / 2

s

1 3 /

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch049

1263.9

1 β 6

A

9 / 2

2025.2

541.2

1 /

u

1761.2

1 3 / 2

—

212.4J

551.51

(23/2Ί

476

1548.8 338.7

1

628.0 1397.2 19/2"

1210.1714.9

682.3 15/2" 462.3 • ο _Ο Δ

184 w 5

220.0

Pt-yrast band Pt IM Au iri / Au Trh

11/2-

1 3 / 2

185

1 3

, e 5

cj (irh

2

c

9 / 2

)

9 / 2

185

79 106 A u

F i g . 3. A partial l e v e l scheme f o r A u e m p h a s i z i n g the structure b u i l t u p o n the h i i/2 state [ L A R 8 5 ] . T h e 2 2 0 - k e V state has an isomeric decay o f 26 ns to the h9/2 l e v e l . 1 8 5

0.1 Τΐω

0.2 (MeV)

0.3

04

F i g . 4. I n the top t w o panels, the experimental alignment (i) as a function o f rotational frequency f o r bands i n ' A u [ L A R 8 5 ] , P t [ C A R 8 5 ] , and P t [ W A D 8 5 ] . Reference parameters o f JLC= 2 2 * / M e V and «0, = 110 * / M e V are used. I n the bottom panel, the second moment o f inertia is plotted versus frequency f o r selected bands. 1 8 5

1 8 6

1 8 4

2

1 8 5

4

3

alignment v s . rotational frequency graph o f F i g . 4. T h e ol = - 1 / 2 negative parity bands cross a n d interact around I = 2 3 / 2 , w h i c h explains the perturbations i n those t w o bands i n F i g . 4. A l i g n m e n t gains o f different magnitudes are observed i n each o f these bands, suggesting differing alignment processes taking place.

49.

RIEDINGER ET AL.

327

Shape Competition and Alignment Processes

B y comparison, the yrast band o f the core nucleus, P t , is s h o w n i n the second panel o f F i g . 4, as are the two signatures o f the 9/2[624] 113/2 b a n d i n P t . It was previously thought b y some (e.g. [ B E S 7 6 ] ) that the crossing i n P t resulted f r o m the alignment o f in/2 neutrons, as is the case throughout the N = 9 0 to 106 deformed region. O n the other h a n d , our earlier measurements o n Au [ K A H 7 8 ] suggested that the crossing i n P t h a d to result f r o m nhm alignment. It is n o w apparent f r o m the data s h o w n i n F i g . 4 that both o f these quasiparticle alignments take place at nearly the same frequency. T h e third panel i n F i g . 4 contains a plot o f the second moment of inertia versus frequency, w h i c h more sensitively shows crossings for these bands. T h e yrast b a n d o f P t and the πΐΐ3/2 b a n d o f A u have two peaks i n this second-moment plot. T h e Vii3/2band o f P t shows o n l y the first peak, w h i l e the π1ΐ9/2 band o f A u displays the second. These data thus indicate the existence o f a nhm crossing at i w = 0.25 M e V w i t h a Δί = 5.111, and a V113/2 crossing at 1Ι= 0.31 M e V w i t h a Δί = 5 . 7 * . T h e yrast b a n d o f P t is affected b y both crossings, w h i c h explains the large alignment g a i n (9.7-fi) compared to the neighboring o d d - A n u c l e i . O u r measurements o n A u [ L A R 8 5 ] indicate a 7ch9/2vii3/2 b a n d w h i c h shows no crossing, since b o t h alignment processes are b l o c k e d (see F i g . 4). 1 8 4

1 8 5

1 8 4

1 8 5

1 8 4

1 8 4

1 8 5

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch049

1 8 5

1 8 5

1 8 4

1 8 6

.20 +

( MeV

F i g . 5. C r a n k e d S h e l l M o d e l frequency f o r the proton I19/2 crossing m i n u s that f o r the neutron 113/2 crossing plotted as a function o f neutron number f o r the Pt isotopes.

)

.10

.05

C r a n k e d S h e l l M o d e l calculations have been performed to learn i f these two c l o s e - l y i n g band crossings c a n be explained w i t h reasonable shape para­ meters. T h e difference i n the calculated crossing frequencies is s h o w n i n F i g . 5 as a function o f neutron number for the P t isotopes. V a l u e s o f £ a n d tfy were obtained f r o m a potential-energy-surface calculation ( w i t h κ and μ values as g i v e n above) and then used i n the C S M calculation. T h e m i n i m u m i n the curve occurs for P t , i n agreement w i t h the data. N o attempt has yet been made to exactly reproduce these experimental crossing frequencies, since other parameters such as pairing gaps are p o o r l y k n o w n i n this region. Nevertheless, x

1 8 4

328

NUCLEI OFF THE LINE OF STABILITY

the calculations do show that it is reasonable for the nhm and ν in/2 crossings, rather w i d e l y split i n other n u c l e i , to be very close i n frequency i n P t . In c o n c l u s i o n , our data o n h i g h - s p i n states i n » A u and i n » P t are mostly indicative o f band structures and alignment processed i n prolate n u c l e i . T h e oblate h i 1/2 b a n d is observed, but is crossed at intermediate spin b y what is probably a prolate h i 1/2 structure. C o l l e c t i v e m o d e l (Nilsson) calculations o f bandhead properties o f the A u isotopes agree w e l l w i t h the observed systematics of the " i n t r u d i n g " hm and 113/2 proton states, c a l l i n g into question the p a r t i c l e hole interpretation o f these states. 1 8 4

1 8 5

1 8 6

184

185

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch049

Acknowledgments

T h e authors w i s h to thank W i t e k N a z a r e w i c z and J i m W a d d i n g t o n f o r many h e l p f u l discussions. Research at the U n i v e r s i t y of Tennessee is supported b y the U . S . Department o f E n e r g y under contract N o . D E - A S 0 5 - 7 6 E R O - 4936. T h e Joint Institute for H e a v y Ion Research has as member institutions the U n i v . of Tennessee, V a n d e r b i l t U n i v . , and the O a k R i d g e N a t i o n a l L a b o r a t o r y ; it is supported b y the members and b y the U . S . D O E .

References [BEN85] T. Bengtsson and I. Ragnarsson, Nucl. Phys. A436 14 (1985). [BER83] V. Berg, Z. Hu, J. Oms, and C. Ekstrom, Nucl. Phys. A410 445 (1983). [BES76] S. Beshai, K. Fransson, S.A. Hjorth, A. Johnson, T. Lindblad, and J. Szarkier, Z. Physik A277 351 (1976). [CAR85] M.P. Carpenter, C.R. Bingham, L.H. Courtney, S. Juutinen, A.J. Larabee, Z.M. Liu, L.L. Riedinger, C. Baktash, M.L. Halbert, N.R.Johnson, I.Y.Lee, Y. Schutz, A. Johnson, J. Nyberg, K. Honkanen, D.G. Sarantites, Bull. Am. Phys. Soc. 30 762 (1985). [GON79] Y. Gono, R.M. Lieder, M . Muller-Veggian, A. Neskakis, C. Mayer-Böricke, Nucl. Phys. A327 269 (1979). [HAM75] J.H. Hamilton etal., Phys. Rev. Lett. 35 562(1975). [HEY83] K. Heyde, P. Van Isacker, M . Waroquier, J.L. Wood, and R.A. Meyer, Phys. Rpts. 102 291 (1983). [KAH78] A.C. Kahler, L.L. Riedinger, N.R. Johnson, R.L. Robinson, E.F. Zganjar, A. Visvanathan, D.R. Zolnowski, M.B. Hughes, and T.T. Sugihara, Phys. Lett. 72B 443 (1978). [LAR85] A.J. Larabee, M.P. Carpenter, L.L. Riedinger, L.H. Courtney, J.C. Waddington, V.P. Janzen, W. Nazarewicz, J.Y. Zhang, R. Bengtsson, and G.A. Leander, submitted to Phys. Lett. [NAZ85] W. Nazarewicz et al., to be published. [WAD85] J.C. Waddington, S. Monaro et al., to be published. [WOO81] J.L. Wood, 4th International Conference on Nuclei Far From Stability, Helsingør, 1981, pg 612. RECEIVED July 31, 1986

50 Rotational Bands in Deformed Odd-Odd Nuclei William C. McHarris, Wen-Tsae Chou, Jane Kupstas-Guido, and Wade Olivier

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch050

National Superconducting Cyclotron Laboratory and Departments of Chemistry and of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 In-beam γ-ray studies of deformed odd-odd nuclei in the neutron­ -deficient Re region produce simpler spectra than expected. Almost all of the deexcitation feeds through a few rotational bands based on high-Ω proton and/or neutron states (Κ itself is not necessarily large). A similar phenomenon is found with high-spin bands in the near-closed­ -shell Sb nuclei. This can be explained on the basis of highly-aligned single-particle states being most efficient at sharing large amounts of angular momentum with the collective core modes: Once locked into such states, the nucleus tends to deexcite through related, highly-aligned states, thus picking out a select subset of possible states. In addition, such odd-odd nuclei tend to have multi-particle states at lower energies than other nuclei, often with the particles forming a sort of oblate girdle about the prolate core -- these can be thought of as oblate-|| pseudo-rotational bands. Very-heavy-ion beams are necessary to bring in enough angular momentum to excite much in the way of high-spin collective modes in these odd-odd nuclei. U n t i l r e c e n t l y in-beam Ύ-ray s p e c t r o s c o p y unrewardingly mostly

cumbersome.

o f odd-odd n u c l e i was t h o u g h t t o be

Spectra were unduly messy, and the r e s u l t i n g l e v e l schemes were

l i s t s o f numbers, f o r i t was d i f f i c u l t

m e a n i n g f u l c o n f i g u r a t i o n s t o the s t a t e s .

t o a s s i g n quantum n u m b e r s , much l e s s

During the l a s t s e v e r a l years, however, a number

of experimental groups have discovered t h a t , under c e r t a i n c o n d i t i o n s , in-beam Ύ-ray s t u d i e s o f odd-odd n u c l e i produce f a r s i m p l e r s p e c t r a t h a n e x p e c t e d , schemes y i e l d i n g a c o n s i d e r a b l e amount o f worthwhile structure.

The necessary

with the resulting level

i n f o r m a t i o n about d e t a i l s o f n u c l e a r

c o n d i t i o n s appear t o be deformed n u c l e i and/or h i g h - s p i n s t a t e s .

I n F i g . 1 we show t h e l e v e l scheme p r o d u c e d by t h e ® T a ( o , 3 η Ύ ) 1

[SLA8M] .

1

1 8 2

Re r e a c t i o n

T h i s r e a c t i o n b r i n g s i n only a moderate amount o f angular momentum; yet most o f

the d e e x c i t a t i o n proceeds through only two h i g h - s p i n r o t a t i o n a l bands, the remainder through two a d d i t i o n a l low-spin but high-Ω bands.

A l l f o u r bands show c o n s i d e r a b l e d i s t o r t i o n — i n

p a r t i c u l a r , a compressed Α-term and a n o n - n e g l i g i b l e p o s i t i v e B-term when t h e i r energies are f i t t e d t o the standard

Ej - E

equation,

2

Q

2

• A J ( J • 1) • B J ( J • I ) .

T h i s t y p e o f d i s t o r t i o n i s c h a r a c t e r i s t i c o f C o r i o l i s c o u p l i n g , where the matrix elements have the form, 0097-6156/86/ 0324-0329506.00/0 © 1986 American Chemical Society

330

NUCLEI OFF THE LINE OF STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch050

A β C Û

Neutron Y t/2*|*24»]

5/2* 1*02 •] 9/2" [514·] T/2-(525»j 1/2-[941 •]

Fig.

-M /23*CJ(J D " Ω(β ± D] +

1

CJ(J • D " K(K ± l ) ]

1

Thus, a p e r t u r b a t i o n expansion r e s u l t s i n a n e g a t i v e Α - t e r m ( e f f e c t i v e l y i n c r e a s i n g moment of i n e r t i a , so that Y?/2$

appears s m a l l e r than normal) and a p o s i t i v e B-term.

examine the s i n g l e - p a r t i c l e s t a t e s i n v o l v e d i n these bands, we f i n d t h a t the f o r a l l o f them i s t h e

9/2*[624] N i l s s o n s t a t e , which o r i g i n a t e s from the i

s t a t e and has very l a r g e C o r i o l i s m a t r i x elements; a l s o , t h r e e o r i g i n a t e f r o m the &

o r 11/2

n

9/

2

1

3

/

2

state

spherical

four proton

states

s p h e r i c a l s t a t e s and have l a r g e C o r i o l i s matrix elements.

I t i s these s t a t e s that decouple and a l i g n t h e i r s p i n s w i t h produce "backbending" [STE72].

of the

neutron

the

I f we

t h a t o f the

r o t a t i n g core

to

In other words, an e f f i c i e n t mechanism f o r c a r r y i n g l a r g e

amounts o f angular momentum i s f o r i t to be shared between R* of the core and j of the s i n g l e nucléons.

In even-even n u c l e i t h i s r e q u i r e s the uncoupling o f a p a i r , but i n odd-odd n u c l e i

i t merely r e q u i r e s the s e l e c t i v e p o p u l a t i o n of a l i g n e d s i n g l e - p a r t i c l e s t a t e s . i l l u s t r a t i o n o f t h i s e f f e c t i s given i n F i g . 2.

A whimsical

[Such s t a t e s can be designated " k l o k a s t "

( c l e v e r e s t ) s t a t e s , i n the " y r a s t " s p i r i t of misusing Swedish words.]

Once such s t a t e s

are

p o p u l a t e d i n t h e h i g h l y - e x c i t e d n u c l e u s , normal Ύ-ray s e l e c t i o n r u l e s tend to keep the d e e x c i t a t i o n locked i n t o r e l a t e d s t a t e s , the r e s u l t being t h a t o n l y p o s s i b l e s t a t e s are

seen.

t i e d up i n the s i n g l e - p a r t i c l e modes. value of R i s only moments of i n e r t i a .

a small

For example, i n the

l 8 2

R e l e v e l scheme the

10 ( i n the Κ - 2 band), not enough to produce any It will

subset of

the

T h i s mechanism means that a great d e a l o f angular momentum i s

r e q u i r e much h e a v i e r

largest

d r a s t i c s h i f t s i n the

beams t o b r i n g i n l a r g e r amounts o f

angular momentum before phenomena such as backbending can be s t u d i e d i n odd-odd systems.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch050

50. McHARRIS ET AL. Deformed Odd-Odd Nuclei 331

NUCLEI OFF THE LINE OF STABILITY

332 core.

C l a s s i c a l l y , an oblate spheroid rotating about i t s symmetry axis (oblate-||) has the

largest moment of inertia and consequently produces the l o w e s t - l y i n g i.e.,

i s the most e f f i c i e n t in handling high angular momentum.

rotational

states,

Quantum mechanically, such

rotations are not defined, of course, but i t should be possible [BOH75] to produce pseudor o t a t i o n a l o b l a t e - I | bands by having each successive "member" r e s u l t coupling or combination of single particles.

The 15* state in

l 8 2

from a different

R e could be the beginning

of such a band. Because so much angular momentum is tied up in single-particle motion, heavier beams are needed to extend the studies.

1

® R e is d i f f i c u l t to produce by heavier beams, but the 14 2

lighter Re nuclei can easily be produced by beams such as

Ν on Er t a r g e t s .

Preliminary

r e s u l t s [LIE85] for R e are shown in Fig. 4, and an example of a 182Ύ - r a y spectrum for ^ R e [OLI85] i s shown in Fig. 5. Both are somewhat more complex than Re; yet they i n d i c a t e l 8 0

(19)

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch050

(16)·

Fig. 5

Deformed Odd-Odd Nuclei

McHARRIS ET AL.

the same sort of behavior:

333

Most of the deexcitation occurs through a select few bands,

which are composed of highly-aligned odd-odd states. Although odd-odd r o t a t i o n a l bands are best understood in well-deformed nuclei, for quite some time they have also been known to exist, based on excited states, in n u c l e i very close to closed s h e l l s [SAM77]. odd-odd Sb isotopes.

Rather intriguing examples of this occur in many of the

The high-spin level scheme of

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch050

reaction [BEN85], is shown in Fig. 6.

bands based on states at 1001 and 1193 keV. straightforward 5/2

) -

T

h

e

p

r

o

^Sb, resulting from the

1 1 5

Ιη(α,3ηΎ)

The former can be characterized as a relatively

strongly-coupled rotational band, with the proton in the 9/2*[404] orbital

(originating from the g ^ d

11

It contains at least two rotational bands, the J - 7

t

o

n

s

t

a

t

spherical state) and the neutron in the 5/2*[402] o r b i t a l (from

/2

again i s associated with large C o r i o l i s matrix elements.

e

The

second band is a bit more complicated, but i t can be explained in a fashion silimar to that 198 by which bands were explained in in the g g

/2

Tl [T0K77].

The proton can be taken basically as being

o r b i t a l , which i s deformation aligned (but s p l i t into the proper deformed

s t a t e s ) , while an h

n

/

2

neutron s p l i t s away from the core to become rotationally aligned.

Calculations reproduce the observed spacings remarkably w e l l , even down to the squashed appearance of the f i r s t

several members of the band.

That these rotational bands figure

prominently in the deexcitation pattern is again consistent with our proposed mechanism of populating

"klokast" s t a t e s .

Less can be said about the most prominent high-spin

d e e x c i t a t i o n pattern (at the l e f t side of F i g . 6 ) , for there are too many p o s s i b l e constructs.

However, oblate-1 | pseudo-rotation and rotationally-aligned particles could

certainly play major roles.

And the other odd-odd Sb show remarkably parallel behavior.

This paper i s necessarily a very abbreviated survey, but we hope we have demonstrated by these few examples that Coriolis coupling and rotational alignment play an important part i n h i g h - s p i n structures of odd-odd n u c l e i .

This can be true for n u c l e i near closed

334

NUCLEI OFF THE LINE OF STABILITY s h e l l s , as w e l l as f o r n u c l e i In well-deformed regions. o p e r a t i o n a c t u a l l y s i m p l i f i e s r a t h e r than complicates spectroscopy.

T h i s , coupled

S e l e c t i v i t y c a u s e d by t h e i r

s p e c t r a obtained

w i t h t h e abundance o f r e l a t i v e l y

i n in-beam Ύ-ray

low-lying multi-particle

s t a t e s , makes odd-odd n u c l e i a f e r t i l e f i e l d f o r f u r t h e r study.

Acknowledgment s T h i s work was supported i n part by the U. S. N a t i o n a l S c i e n c e

F o u n d a t i o n under G r a n t No.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch050

PHY-83-12245.

References [BEN85] W. H. Bentley, R. A. Warner, Wm. C. McHarris, and W. H. Kelly, submitted to Phys. Rev. C (1985). [BOH75] A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, Reading, Mass., 1975), Vol. II, pp. 43ff, 72ff. [LIE85] R. M. Lieder, XXIII International Winter Meeting on Nuclear Physics, Bormio, Italy, Proceedings, p. 276 (1985). [OLI85] W. A. Olivier, W.-T. Chou, J. Kupstas-Guido, and Wm. C. McHarris, work in progress (1985). [SAM77] L. Ε. Samuelson, W. H. Bentley, W. H. Kelly, R. A. Warner, F. M. Bernthal, and Wm. C. McHarris, Phys. Rev. C 15, 821 (1977). [SLA84] M. F. Slaughter, R. A. Warner, T. L. Khoo, W. H. Kelly, and Wm. C. McHarris, Phys. Rev. C 29, 114 (1984). [STE72] F. S. Stephens and R. Simon, Nucl. Phys. A183, 257 (1972). [TOK77] H. Toki, H. L. Yadav, and A. Faessler, Phys. Lett. 71B, 1 (1977). RECEIVED July 14, 1986

51 Heavy-Ion-Induced Transfer Reactions A Spectroscopic Tool for High-Spin States P. D. Bond

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch051

Brookhaven National Laboratory, Upton, NY 11973

One of the early hopes of heavy ion induced transfer reactions was that new states in nuclei would be preferentially populated. The fact that this hope diminished was due primarily to insufficient understanding of the reaction mechanism, but also to the generally poorer energy resolution ob­ tained with heavy ions as compared to light ions. In this paper, I hope to demonstrate that with the proper kinematical conditions there is a remarkable selectivity which can be obtained with a proper choice of the reaction and that these reactions can be valuable spectroscopic tools. The data in this talk have been taken using beams from the Brookhaven National Laboratory double MP tandem facility with particles identified in the focal plane of a QDDD spectrometer. Shown in Fig. 1 are spectra for three single neutron transfer reac­ tions leading to known states in the same final nucleus Sm. The ( C, C) in reaction in Fig. 1 populates final states much as the (d,p) reaction and because of the worse energy resolution this heavy ion reaction is thus not very useful for spectroscopic purposes. The ( C, C) and ( 0, 0) reactions on the other hand show a very strong selectivity for high spin states with the latter reaction also showing a strong preference for j»£,+l/2 final states. The reasons for this selectivity are discussed else­ where [B0N83], the purpose here is to use this selectivity for spectroscopic studies. Shown in Fig. 2 is a schematic representation of the shell model states for the region near * Gd. There has been a great deal of interest in this mass region since it was proposed [OGA78] that a shell closure occurs for Z-64. 2ηο As in the *"°Pb region high spin single particle states are available so that simple configurations are likely to con­ tribute to the structure of high spin states. In particular, near *^ Gd the proton hjj/2 orbital and the neutron i / 2 orbital should play an important role, however, there is little direct evidence about the states based on these orbitals. For the Nd isotopes considered Fig. 1. Single neutron transfer here the protons have partially filled reaction for Sm the 87/2*^5/2 levels and the neutrons * Sm for three dif­ are beginning to f i l l orbitals above ferent projectiles. N-82. Reproduced with permission from [B0N83]. Copyright 1983 Gordon & Breach Science Publishers. 149

12

11

16

13

15

1!

6

6

13

lif8

1J

9

0097-6156/ 86/ 0324-0335S06.00/ 0 © 1986 American Chemical Society

12

NUCLEI OFF THE LINE OF STABILITY

336

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch051

KVI 3146

Fig.

2.

Schematic r e p r e s e n t a t i o n

of s h e l L model o r b i t a l s near

ll

6

* Gd.

We f i r s t focus on the p r e v i o u s l y unknown i / neutron strength i n the N=84 nucleus ^ S ï d . An e a r l i e r (d,p) study [RAM76] observed no 1χ3/2 strength except i n the low l y i n g 3" s t a t e . Gamma ray experiments f o l l o w i n g compound nucleus formation [BER76, GEE76, QUA82] found s e v e r a l negative p a r i t y states but a l l with odd spin ( n a t u r a l p a r i t y ) . The f i n d i n g s are con­ s i s t e n t with the supposition that the negative p a r i t y states are formed by a 3~ core e x c i t a t i o n coupled to two f / 2 neutrons producing spins of 3~, 5~, 7~, 9~. S i n g l e nucléon t r a n s f e r would only weakly populate these states through m u l t i s t e p processes. I f , on the other hand, these negative p a r i t y states were due p r i m a r i l y to v f / * ^ 1 3 / 2 c o n f i g u r a t i o n s the ordering of the n a t u r a l p a r i t y s t a t e s would be the same but t r a n s f e r to these states should be strong. In a d d i t i o n , the unnatural p a r i t y states ( J * 4~,6",8", 10") of t h i s m u l t i p l e t should a l s o be seen with the strongest state i n the t r a n s f e r spectrum being the unnatural p a r i t y s t a t e J ^ I O " . This state would not be e a s i l y seen i n the xn experiments because i t i s not y r a s t . The s e l e c t i v i t y shown i n F i g . 1 demonstrates the ( 0 , 0 ) t r a n s f e r s t r o n g l y favors t r a n s f e r to states of f 7 / 2 i-13/ 2 character. In bom­ bardment of a * Nd t a r g e t , which has J «7/2~, the states i n *Nd which should be populated are therefore ( vf / ) 0 , 2 , 4 , 6 and v f / * v i / 2 = 3~,...,10~. In F i g . 3 the spectrum of the * Nd( 0 , 0 ) *Nd r e a c t i o n [COL85] i s shown with the l o c a t i o n of known states i n d i c a t e d on the f i g u r e . For e x c i t a t i o n energies up to about 1.5 MeV there i s no ambiguity i n assign­ ments since other states are not present. However, above that e x c i t a t i o n energy the r e s o l u t i o n of roughly 100 keV i s not s u f f i c i e n t to uniquely iden­ t i f y the s t a t e s . In order to help determine the spin and e x c i t a t i o n of the l e v e l s , gamma rays i n coincidence with the p a r t i c l e peaks have been measured with an i n t r i n s i c Ge detector. 1

3

2

7

7

2

β

16

o

ll

3

ir

ltfi

2 a

7

15

r

+

+

+

+

2

7

1J

3

16

15

2

1 3

ul

Shown i n F i g . 4 are two gamma ray spectra [C0L85] one f o r the peak l a b e l e d 9" i n F i g . 3 and one for the p a r t i c l e peak at about 3.8 MeV, which was p r e v i o u s l y unknown. The upper gamma ray spectrum i n F i g . 4 confirms that the peak at 2.902 MeV i s indeed the 9~ state seen i n previous work [BER76, GEE76, QUA82]. The p a r t i c l e peak at 3.8 MeV shows a nearly i d e n t i c a l gamma ray spectrum with the a d d i t i o n of one gamma ray o f 900 keV, j u s t the d i f f e r ­ ence i n energy between the 9" state and t h i s s t a t e . Since t h i s peak i s so

51.

Heavy-Ion-Induced Transfer Reactions

BOND

200

1

— ι l 4 3

Nd('60,'50)

Γ l 4 4

τ

Nd

Γ

6

120 M e V

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch051

337

+

ILL

Ο» ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι 4 3 2 EXCITATION ENERGY ( M e V ) F i g . 3.

ll+3

Spectrum of the

1 6

1 5

Nd( 0 , 0 ) ^ N d r e a c t i o n .

Reproduced with permission from [BON83]. & Breach Science P u b l i s h e r s .

Copyright 1983 Gordon

s t r o n g l y populated i n p a r t i c l e t r a n s f e r and decays p r i m a r i l y to the 9" state i t i s almost c e r t a i n l y the p r e v i o u s l y unobserved 10" s t a t e . Gamma rays i n coincidence with the other labeled peaks i n the spectrum confirm they are indeed the s t a t e s i n d i c a t e d on F i g . 3.

Τ

'«*Nd(' 0. Oy> e

l 9

, 4 4

Nd

'm

(b)

120

bat

160

CHANNEL

F i g . 4.

200

L ?' 240

280

320

NUMBER

Gamma rays i n coincidence with a) the state at 2.9 MeV and b) the s t a t e at 3.8 MeV.

Reproduced with permission from [BCN83]. & Breach Science P u b l i s h e r s .

Copyright 1983 Gordon

338

NUCLEI OFF THE LINE OF STABILITY 11+l

The l e v e l scheme of states i n *Nd seen i n t h i s experiment i s shown i n F i g . 5. The s t r u c t u r e of the negative p a r i t y states i s as f o l l o w s . The low l y i n g 3" and 5~ states appear to be rather complicated as t h e i r population does not follow the (2J+1) population expected for a simple m u l t i p l e t . In c o n t r a s t , the 7~, 9" and 10" appear to have equivalent f / 2 * *l3/2 strength and thus have rather simple s t r u c t u r e . On the ^other hand, no e v i ­ dence i s found f o r the 4~ or 8" states and only weak evidence that the s t a t e at 3.3 MeV i s a 6~ s t a t e . Configuration mixing i s a p o s s i b l e , though not a c e r t a i n , reason for the absence of these s t a t e s . In any case, there does not appear to be a simple v f / * v / multiplet. For the p o s i t i v e p a r i t y s t a t e s , the population of the 0 • 6 states follows (2J+1) which i n d i c a t e s that these states are consistent with being an ( f / ) m u l t i p l e t . As can be seen i n F i g . 1, the spectrum of the ( C C) r e a c t i o n leading to *Nd enhances h / t r a n s f e r . Comparison of the ( 0 , 0 ) and ( C , C ) spectra c l e a r l y shows that the 8+ state at 2.709 MeV i s p r i m a r i l y an f / * h / c o n f i g u r a t i o n . Unfortunately, there are no extensive s h e l l model c a l c u l a t i o n s with which to compare these r e s u l t s . We turn now to the proton l e v e l s i n the Ν-82 nucleus Nd. S i m i l a r spectra to those of F i g * 1 f o r proton t r a n s f e r demonstrate that the ( 0 , N ) r e a c t i o n s t r o n g l y enhances t r a n s f e r to d / and h n / 2 proton o r b i t a l s . ι ι Since the ground state of ** Ϋτ i s 5/2 the ( 0 , N ) r e a c t i o n on that nu­ cleus s t r o n g l y enhances f i n a l states i n * Nd of ( i f d / ) - 0 + , 2+, 4+ and i r d / * *hn/ 2 • 3". ...8". The s i n g l e proton t r a n s f e r spectrum [B0N85] to Nd i s shown i n F i g . 6. Gamma rays i n coincidence with these p a r t i c l e peaks have been measured and lead to the l e v e l scheme shown i n F i g . 5. 7

7

2

1 3

2

+

+

2

7

l2

2

ll

9

llf
.

are

P™

new i s t h e n a t u r e

of

t h e band between t h e 9 . 6 MeV 30 t h e 1 4 . 4 MeV 4 2 ' i s most l i k e l y configuration

( f

7

/

2

)

2

( i

s t a t e of this

1

/

2

)

2

oblate

]

2

] ] / 2

) ]-,

6

.

a

shape.

state to the 3 0

+

3.

Level

scheme f o r

1 5 6

Er.

aligned

the

v 6

[(

h 9

/ )

2

2

non-collective But decay

of

level

proceeds

six

stretched

Fig. 4. Energy l e v e l s o f Er, - · - , and E r , - Θ - , minus a r i g i d - r o t o r energy v s . s p i n , I . 1 5 6

1 5 8

and

latter

predicted

4

m a i n l y by a cascade o f

Fig.

to

Gd c o r e ) ir[(h

3

The

the maximally

(relative 146

doubly-magic by t h e o r y ,

levels.

+

52.

345

Berkeley High Energy Resolution Array

DIAMOND

E2 t r a n s i t i o n s ,

and s u g g e s t s a band s t r u c t u r e .

An i n t e r p r e t a t i o n

w i t h t h e s e f e a t u r e s and w i t h c u r r e n t t h e o r e t i c a l a triaxial

r e l a t i v e t o those of a r i g i d

rotor,

+

state.

The e n e r g i e s o f

these

as shown i n F i g . 4 , s u p p o r t

this

rotor or

the weakly p r o l a t e l y - d e f o r m e d

of

bands below 2 4 * i s c h a r a c t e r i s t i c

particularly population

in a fully-aligned

low e n e r g y o f t h e 4 2 * s t a t e r e s u l t s

(10% o f t h e 4

+

-> 2

+

transition)

state.

r a r e l y seen a t h i g h

The o t h e r new f e a t u r e o b s e r v e d i s t h e l a r g e number o f transitions

that

All

spin.

interband

f o u r bands t a k e p a r t i n t h i s c r o s s - f e e d i n g ,

c o n s i d e r a b l e m i x i n g o f t h e bands and s u g g e s t i n g a s t r u c t u r a l

the

large

seen a t t h e backbends ( p r o b a b l y BC) o f t h e n e g a t i v e - p a r i t y

around s p i n 2 2 * .

to

In a d d i t i o n ,

in a r e l a t i v e l y

is

and

i d e a , as t h e i r d e c r e a s e i n e n e r g y w i t h s p i n compared t o a r i g i d

c a l c u l a t e d f o r a band t e r m i n a t i n g

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch052

consistent

is that this

band, w i t h the parameter γ i n c r e a s i n g w i t h i n c r e a s i n g s p i n ,

t e r m i n a t i n g i n t h e f u l l y a l i g n e d and o b l a t e 4 2 levels

calculations

bands

indicating

change.

I t may

be r e l a t e d t o t h e f a c t t h a t f o u r o f t h e s i x v a l e n c e n e u t r o n s have become a l i g n e d and so have t o a l a r g e e x t e n t quenched t h e n e u t r o n correlations.

e x p l a i n the extensive mixing of s t a t e s this

pairing

T h i s c o u l d cause some change i n s h a p e , b u t r e a l l y does i n v o l v i n g both s i g n a t u r e s .

Y e t above

r e g i o n t h r e e o f t h e bands c o n t i n u e i n a somewhat l e s s r e g u l a r

but s t i l l

i n v o l v i n g o n l y s t r e t c h e d E2 t r a n s i t i o n s

increasing energy. s t r u c t u r e of these

of roughly

not

fashion,

monotonically

C l e a r l y , much remains t o be l e a r n e d a b o u t t h e

detailed

bands.

In a study of

Er l e v e l s , o f w h i c h o n l y t h e p o s i t i v e - p a r i t y

yrast

band i s c o m p l e t e d , two i n t e r e s t i n g f e a t u r e s , one new, a g a i n were f o u n d . The 40 r e a c t i o n used was 175 MeV Ar f r o m t h e 8 8 " C y c l o t r o n on s e v e r a l backed and 2 122 unbacked - 1 mg/cm Sn t a r g e t s . W i t h t h e f u l l 2 1 - d e t e c t o r a r r a y we 8 8 r e c o r d e d - 2 χ 10 t r i p l e c o i n c i d e n c e s ( c o r r e s p o n d i n g t o 6 χ 10 d o u b l e s ) i n a two-day run.

A p a r t o f t h e s p e c t r u m ( 7 0 0 - 1 4 0 0 keV) o b t a i n e d w i t h

unbacked t a r g e t

i n c o i n c i d e n c e w i t h a g a t e on t h e 1058 keV, 3 8

transition

i s shown i n F i g . 5 a .

The f i v e h i g h e r t r a n s i t i o n s

+

same t r a n s i t i o n b u t f o r a g o l d - backed t a r g e t .

that

in

addition

F i g u r e 5b shows t h e same r e g i o n g a t e d by t h e

a r e m i s s i n g , and we b e l i e v e t h i s shifts,

+

observed

[ S I M 8 4 ] a t 8 2 7 , 1 0 3 1 , 1 2 0 3 , 1 2 1 0 , and 1280 keV can be s e e n , and i n t h e r e i s a weak 971 keV l i n e .

the

•* 3 6

The 1203 and 1210 keV

lines

i s because t h e y a r e smeared o u t by D o p p l e r

i s , t h e y have l i f e t i m e s

mean s l o w i n g t i m e ( 0 . 5 p i c o s e c o n d ) .

(plus feeding times)

shorter than

the

On t h e o t h e r h a n d , f o r t h e 8 2 7 , 9 7 1 ,

346

NUCLEI OFF THE LINE OF STABILITY

1 0 3 1 , and 1280 keV l i n e s t o be s h a r p means t h a t an i n t e r v a l

o f a few p i c o s e c o n d s .

1017 keV, 3 6

+

-» 3 4

transition

+

is

The most i n t e r e s t i n g

yrast result

f e e d i n g components i n t o t h e 3 8

+

studies

give the level

band shown i n F i g .

spherical

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch052

rare-earth nuclei

of

(»1

In c o n t r a s t ,

( 9 0 < Ν < 110) a p p e a r t o have f a s t

t h o u g h t t o be due t o s t r o n g l y c o l l e c t i v e

rotational

top

f a s t and

slow

nuclei

having

p s ) have been

regions of n o n - c o l l e c t i v e

shapes) a l o n g t h e decay p a t h w a y s .

the

scheme f o r t h e

Among t h e r a r e - e a r t h

n e u t r o n numbers between 82 and 8 8 , s l o w f e e d i n g t i m e s o b s e r v e d , p r e s u m a b l y because o f

the

6.

is the i d e n t i f i c a t i o n

level.

after

i s observed i f

used as a g a t e , and a l t o g e t h e r

c o i n c i d e n c e and a n g u l a r c o r r e l a t i o n p a r t of the p o s i t i v e - p a r i t y

t h e y have been e m i t t e d

A weak 1276 keV l i n e

behavior

(oblate

the well

deformed

feeding times bands.

It

is

(«1

or

ps),

therefore

"I C O

n o t so s u r p r i s i n g t h a t regions,

Er, which l i e s

on t h e boundary between

has b o t h f a s t and s l o w f e e d i n g c o m p o n e n t s .

time resolved

lines

have been i d e n t i f i e d

feed i n t o the y r a s t

But t h i s

the

is the

first

f o r b o t h branches and shown how t h e y

band.

1200

800

400

§

Γ·

^^°°

r

ί ο

Ο 32+-

800

30

+

-

28+-

400

26+24+22+-

n 1J L r t f 700

1000

1300

Ey(KEV) F i g . 5. P a r t i a l spectrum of t r a n s i ­ tions in 158£ - j coincidence with 1058 keV, 38+ -* 36+ l i n e f o r unbacked t a r g e t , u p p e r s p e c t r u m , and g o l d - b a c k e d one, lower spectrum. r

n

F i g . 6. P a r t i a l l e v e l scheme t h e t o p o f t h e y r a s t band i n

for Er.

1 5 8

52.

DIAMOND

Berkeley High Energy Resolution

The o t h e r p o i n t o f

interest

Array

347

r e l a t e s t o the nature of the highest

s t a t e o b s e r v e d , t h a t d e c a y i n g by t h e 971 keV t r a n s i t i o n . keV l i n e s a r e s t r e t c h e d E2 t r a n s i t i o n s , one t h a t the 4 2

+

Er,

1 5 6

Er.

for

F i g u r e 4 shows t h e l e v e l

state

is the

If

lifetimes

higher in

46

But i t

a r e q u i t e weak ( i n

sequence

f o r t h e slow b r a n c h ,

1 5 8

to

in

though

spin.

i s t r u e i n general

1-5% o f t h e 4

+

nature

f o r the states at high spin

s h o u l d be remembered t h a t t h e d i s c r e t e Er,

+

rigid-

can be m e a s u r e d , much more can be s a i d a b o u t t h e

o f t h e s e s t a t e s , and t h i s other n u c l e i .

e n e r g y (minus a

Er compared t o t h e b e t t e r e s t a b l i s h e d

and t h e r e i s a r e m a r k a b l e s i m i l a r i t y

displaced four units

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch052

as we s u s p e c t , t h i s

spin

t h e 971 and 1031

i s t h e m a x i m a l l y a l i g n e d s t a t e p r e d i c t e d by t h e o r y and a n a l o g o u s state in

r o t o r energy) 1 5 6

If

-> 2 * t r a n s i t i o n ) ,

lines

and i f

in

involved we want

t o know what most o f t h e s t a t e s a r e l i k e a t t h e s e h i g h s p i n s we must d e v e l o p o u r t e c h n i q u e s t o s t u d y c o n t i n u u m s p e c t r a , and i n p a r t i c u l a r t o d e t e r m i n e effects

o f e x c i t a t i o n above t h e y r a s t

line.

a r r a y s a r e s u r e l y g o i n g t o h e l p us do t h a t , dimension i n d i s c r e t e - l i n e

the

The new Compton-suppressed Ge as w e l l as g i v e us a new

spectroscopy. Acknowledgments

A l a r g e number o f p e o p l e c o n t r i b u t e d t o t h e s u c c e s s f u l c o m p l e t i o n o f t h e 2 1 - m o d u l a r a r r a y ; space l i m i t a t i o n s a l l o w o n l y t h e naming o f R. B e l s h e , A. Dancosse, F. G i n , D. L a n d i s , and M.K. Lee. The two e x p e r i m e n t s d e s c r i b e d were p e r f o r m e d by P.O. Tjrim, F . S . S t e p h e n s , J . C . B a c e l a r , E.M. Beck, M.A. D e l e p l a n q u e , J . E . D r a p e r , and A . O . M a c c h i a v e l l i . T h i s work was s u p p o r t e d by t h e D i r e c t o r , O f f i c e o f Energy R e s e a r c h , D i v i s i o n o f N u c l e a r P h y s i c s o f t h e O f f i c e o f High Energy and N u c l e a r P h y s i c s o f t h e U.S. Department o f Energy under C o n t r a c t DE-AC03-76SF00098.

References [BEN83] T. Bengtsson and I. Ragnarsson, Phys. Scripta T5, 165 (1983). [DIA81] R.M. Diamond and F.S. Stephens, The High Resolution Ball (proposal) (unpublished 1981). [SIM84] J. Simpson et al., Phys. Rev. Lett. 53, 648 (1984). [STE85] F.S. Stephens et al., Phys. Rev. Lett. 54, 2584 (1985). [TWI83] P.J. Twin et al., Nucl. Phys. A409, 343e (1983). RECEIVED

September 2, 1986

53 On-Line Nuclear Orientation N. J . Stone Clarendon Laboratory, Parks Road, Oxford ΟΧ2 3PU, United Kingdom

A brief survey is given of the technique and its limiting parameters. Recent results on moments of proton rich iodine isotopes show shape coexistence and the presence of the g [404] intruder orbital for A ≥ 118. Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch053

9/2

As a t e c h n i q u e f o r m e a s u r i n g n u c l e a r moments and i n v e s t i g a t i n g n u c l e a r l e v e l s t r u c t u r e , low temperature n u c l e a r o r i e n t a t i o n has long been k e p t from a r e a s o f c u r r e n t a c t i v i t y i n l o w e n e r g y n u c l e a r p h y s i c s by t h e h a l f l i f e l i m i t a t i o n c a u s e d b y needs o f sample p r e p a r a t i o n and c o o l i n g t o b e l o w 1 K. The d e v e l o p m e n t o f He/ He d i l u t i o n r e f r i g e r a t o r s c a p a b l e o f c o n t i n u o u s l y m a i n t a i n i n g t e m p e r a t u r e s o f o r d e r 10 mK i n t h e p r e s e n c e o f h e a t f l u x o f o r d e r 1 opened up t h e p o s s i b i l i t y o f u s i n g t h e method o n - l i n e t o s o u r c e s o f a c t i v e i s o t o p e s . The m a g n e t i c h y p e r f i n e i n t e r a c t i o n e x p e r i e n c e d by n u c l e i o f a l l e l e m e n t s when p r e s e n t as d i l u t e i m p u r i t i e s i n f e r r o m a g n e t i c m e t a l s i s a q u a s i - u n i v e r s a l method o f p r o d u c i n g a p p r e c i a b l e p o l a r i z a t i o n a t s u c h t e m p e r a ­ t u r e s . More r e c e n t l y s i n g l e c r y s t a l s o f n o n - c u b i c m e t a l s have come t o t h e f o r e as s u i t a b l e s o u r c e s f o r e l e c t r i c q u a d r u p o l e a l i g n m e n t , a l t h o u g h t h e t e m p e r a t u r e r e q u i r e d i s o f t e n l o w e r t h a n 10 mK. A f i n a l n e c e s s a r y i n n o v a t i o n has b e e n t h e d e v e l o p m e n t o f i m p l a n t a t i o n t e c h n i q u e s t o i n t r o d u c e n u c l e i o f many e l e m e n t s , w h e t h e r c h e m i c a l l y c o m p a t i b l e o r n o t , i n t o h o s t l a t t i c e s s u c h t h a t a m a j o r p r o p o r t i o n o f t h e i m p l a n t s come t o r e s t i n e s s e n t i a l l y undamaged s u b s t i t u t i o n a l s i t e s and e x p e r i e n c e l a r g e h y p e r f i n e i n t e r a c t i o n s . Such samples a r e t h i n , w i t h l i t t l e s e l f - a b s o r p t i o n f o r a l p h a - and b e t a particles . The c o m b i n a t i o n o f t h e s e t h r e e d e v e l o p m e n t s h a s l e d t o t h e o n - l i n e n u c l e a r o r i e n t a t i o n method (OLNO). A f u r t h e r advance o f t h e t e c h n i q u e h a s b e e n t h e c o m b i n a t i o n w i t h NMR, w h i c h u s e s r e s o n a n t r f p e r t u r b a t i o n o f t h e n u c l e a r p o l a r i z a t i o n , y i e l d i n g moment v a l u e s t o a f e w p a r t s i n 10 . The w i d e r a n g e o f e l e m e n t s i n w h i c h m a g n e t i c p o l a r i z a t i o n and e l e c t r i c a l i g n m e n t o f r a d i o a c t i v e n u c l e i have b e e n o b s e r v e d i s shown i n f i g u r e 1, w h i c h g i v e s a l s o t h e number o f i s o t o p e s i n w h i c h NMR/ON h a s b e e n d e t e c t e d . As w i t h c o n v e n t i o n a l n u c l e a r o r i e n t a t i o n , o n - l i n e work c a n y i e l d t h e s t r e n g t h o f t h e h y p e r f i n e i n t e r a c t i o n , deduced f r o m t h e t e m p e r a t u r e depen­ dence o f t h e r a d i a t i o n a n i s o t r o p y . F o r t h e m a j o r i t y o f e l e m e n t s i n F i g . 1 h o s t m e t a l s may be c h o s e n i n w h i c h t h e m a g n e t i c f i e l d , o r e l e c t r i c f i e l d g r a d i e n t , i s k n o w n , a l l o w i n g e x t r a c t i o n o f t h e n u c l e a r moment. T y p i c a l l y e x t r a c t e d moments a r e a c c u r a t e t o 5-10%, p o s s i b l y s u b j e c t t o v a r i o u s s y s t e m a t i c e r r o r s . By c o n t r a s t , NMR/ON g i v e s p r e c i s e unambiguous r e s u l t s . S i m u l t a n e o u s l y t h e d i f f e r e n t d e g r e e s o f a n i s o t r o p y shown b y d i f f e r e n t t r a n s i ­ t i o n s i n t h e same d e c a y c o n t a i n i n f o r m a t i o n on t h e s p i n s o f t h e n u c l e a r l e v e l s and t h e m u l t i p o l a r i t i e s and m i x i n g r a t i o s o f t r a n s i t i o n s l i n k i n g them. T h i s s e p a r a t i o n c a n be s e e n i n t h e f a m i l i a r e x p r e s s i o n f o r t h e a n g u l a r d i s t r i b u t i o n f r o m an a x i a l l y o r i e n t e d ensemble 3

l+

4

W(0,T) = 1 + Z B ( T ) A P ( c o s 6 ) À

À

x

where Β (Τ) a r e t h e t e m p e r a t u r e dependent o r i e n t a t i o n p a r a m e t e r s o f t h e 0097-6156/ 86/ 0324-0350506.00/ 0 © 1986 American Chemical Society

53.

On-Line Nuclear Orientation

STONE

H

li

It

Ni

Mg

/

Magnetic

4

Number of resonated isotopes and isomers

/ Κ

Co

/

/

Ti

Sc

V

Rb

/

Sr

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch053

/

Y /

α

Bo

Fr

R*

/

/

Zr

/

3

U 1

Hi

Ac

Rl

Tc

4

R«

w4

3

/

/

/

Ht

/

Co

5

Ni

Cu

1

/ \ Cd

Pd

Rh

3

Ot

lr

4

1

/ \ Zn

Al

Si

G*

Go

N

0

P

s

/

/

As

Pt

4

/ \ ta

1

Au

10

6

Sb

5 /

?

ΤΙ

Pb

li

1

Nt

Cl

Ar /

Ir

1

/

St

F

/

St

3

/

Ru

c

Β

/ Tt

Kr /

/

4

1

Xt

6 / \ Po

\ At

R

Tm

Yb

lu

r

2

3

Ho

/

Ct

1

Th

Fig.

1

Electric

Ft

2

/

Mb

Nb

/

Mn

Cr

1

1 /

/

\

351

/

Pr

/

Pa

/ Nd

U

/

Pm

/

Sm

/ Hp

/ Eu

/ Pu

An

/ Gd

Cm

/

Tb

Ik

/

/

Ci

/

Ho

/

Es

/

Er

1

/

Fm

Md

No

Ir

1. Elements studied by low temperature nuclear o r i e n t a t i o n (magnetic and e l e c t r i c ) and by NMR/ON.

parent state and are d i r e c t i o n a l d i s t r i b u t i o n c o e f f i c i e n t s d e s c r i b i n g the decay sequence pKRA7 Q . A schematic OLNO experiment i s shown i n F i g . 2. The primary a c c e l e r a ­ tor beam s t r i k e s a target incorporated i n the i o n source of an isotope separator, where heavy i o n beams can produce a wide range of isotopes pre­ dominantly on the proton r i c h side of the N/Z s t a b i l i t y l i n e . Alternatively a s p a l l a t i o n source or a neutron beam can be used with advantage to reach a d d i t i o n a l neutron r i c h isotopes. The a c t i v i t i e s desorb from the target, are i o n i s e d , and enter the separator. Ions of a chosen mass are focussed and pass through a s l i t i n the f o c a l plane. Leaving the separator, having been accelerated through a p o t e n t i a l of 50 - 100 kV, they enter a cold (4 K) beam tube and are implanted i n t o a target f o i l , u s u a l l y of i r o n , attached by a copper c o l d f i n g e r to the mixing chamber of a d i l u t i o n r e f r i g e r a t o r and main­ tained close to 10 mK. The target f o i l i s magnetised to provide an axis of p o l a r i z a t i o n f o r the implanted n u c l e i which are oriented i n the magnetic hyperfine f i e l d . What are the c r i t i c a l parameters of such a system? C l e a r l y we are concerned with the a t t a i n a b l e temperature, the e f f e c t i v e n e s s of the low temp­ erature implantation, the required p a r t i c l e f l u x and the c o n d i t i o n that the n u c l e i , i n i t i a l l y random, become p o l a r i z e d before they decay. Each of these i s b r i e f l y considered. The current lowest f u l l y o n - l i n e temperature i s 10 mK, but, f o r some­ what longer h a l f - l i v e s , c l o s i n g o f f the r e f r i g e r a t o r a f t e r implantation can give r e s u l t s to ^ 7 mK i n about 30 m (see F i g . 4 ) . The Bonn group, who were

352

NUCLEI OFF THE LINE OF STABILITY

ACCELERATOR BEAM

ill

TARGET ION SOURCE B, applied SEPARATOR

t

TARGET T=0 01K

T=tK

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch053

DETECTORS

Fig.

2.

Schematic o n - l i n e n u c l e a r

o r i e n t a t i o n experiment.

the f i r s t t o o p e r a t e o n - l i n e t o a n i s o t o p e s e p a r a t o r , have shown f o r many s y s t e m s t h a t i m p l a n t a t i o n b e l o w 4K i s a t l e a s t as e f f e c t i v e i n p r o d u c i n g h i g h l y s u b s t i t u t i o n a l i m p l a n t s as room t e m p e r a t u r e i m p l a n t a t i o n [HER78]. NMR/ON i n f u l l y OLNO i m p l a n t e d s y s t e m s h a s b e e n o b s e r v e d i n L e u v e n [VAN85ajj . A c r u c i a l parameter i n implanted source p r e p a r a t i o n i s the t o t a l i m p l a n t d o s e . F o r o n - l i n e work t h e f l u x o f i m p l a n t i o n s i s v e r y low as we a r e f a r f r o m any s t a b l e beam. E v e n a f l u x o f 1 0 i o n s s~ g i v e s o n l y 1 0 i o n s / d a y , w e l l b e l o w t h e l i m i t i n g c o n c e n t r a t i o n o f o r d e r 0.1 a t o m i c p e r c e n t i f i m p l a n t a t i o n i s a t 50 KeV o r a b o v e . A v a l u a b l e f e a t u r e o f OLNO i s t h a t a sequence o f i s o t o p e s may be s i m u l t a n e o u s l y s t u d i e d as t h e p r i m a r y i m p l a n t decays towards the s t a b i l i t y l i n e . T h i s f r e q u e n t l y makes a c c e s s i b l e i s o t o p e s of e l e m e n t s w h i c h do n o t r e a d i l y f o r m i o n beams. Nuclear o r i e n t a t i o n i s a s i n g l e s counting technique i n which the measured e f f e c t s a r e t y p i c a l l y o f o r d e r 10 p e r c e n t ( b u t may be much l a r g e r ) . I n d i v i d u a l measurements a c c u r a t e t o 1 p e r c e n t w i l l g e n e r a l l y g i v e u s e f u l results. T h i s r e q u i r e s p e r h a p s 3 x 1 0 ^ c o u n t s t o be r e c o r d e d , i f some a l l o w ­ ance i s made f o r b a c k g r o u n d s u b t r a c t i o n . I t i s s i m p l e t o mount f o u r l a r g e G e ( L i ) d e t e c t o r s , i n p a i r s , a t θ = 0 and θ = π/2 r e l a t i v e t o t h e p o l a r i s a t i o n a x i s and a b o u t 7 cm. f r o m t h e s o u r c e . The combined p h o t o p e a k e f f i c i e n c y i s t h e n a p p r o x i m a t e l y 3 p e r c e n t a t each a n g l e , so t h e d e s i r e d r e c o r d e d c o u n t r e q u i r e s 10 d i s i n t e g r a t i o n s feeding the observed t r a n s i t i o n . An i m p l a n t a ­ t i o n r a t e o f ΙΟ* n u c l e i p e r s e c o n d , t h a t i s , a s s u m i n g a 1 p e r c e n t s e p a r a t o r e f f i c i e n c y , a r e a c t i o n y i e l d o f 10 n u c l e i p e r second, w i l l give the r e q u i r e d c o u n t s i n 100 s e c o n d s f o r a t r a n s i t i o n f e d i n 100 p e r c e n t o f d e c a y s . It is c l e a r n o t o n l y t h a t measurements c a n be made by OLNO when i m p l a n t a t i o n r a t e s f a l l as l o w as 100 n u c l e i p e r s e c o n d f o r s t r o n g l y f e d t r a n s i t i o n s , b u t a l s o t h a t a t h i g h e r r a t e s weak t r a n s i t i o n s c a n be s t u d i e d w i t h a d e q u a t e a c c u r a c y to y i e l d u s e f u l i n f o r m a t i o n . NMR/ON r e q u i r e s t h a t r e s o n a n t d e s t r u c t i o n o f t h e a n i s o t r o p y be detected. The f a c t t h a t a sequence o f c o u n t s as a f u n c t i o n o f c h a n g i n g f r e ­ quency i s n e c e s s a r y means t h a t t h i s p r e c i s i o n method w i l l be r e s t r i c t e d t o n u c l e i w i t h i m p l a n t a t i o n r a t e s g r e a t e r than 10 per second, although a l l t r a n s i t i o n s i n t h e d e c a y o f t h e r e s o n a t e d i s o t o p e c a n be combined t o g i v e t h e t o t a l resonance s i g n a l . 6

6

4

6

3

l

1 1

53.

On-Line Nuclear Orientation

STONE

353

1

On implantation i n t o the cold f o i l the n u c l e i are i n i t i a l l y 'hot i . e . u n p o l a r i s e d . They approach thermal e q u i l i b r i u m with the f o i l l a t t i c e tempera­ ture through the Korringa r e l a x a t i o n mechanism v i a the conduction e l e c t r o n s . A r e l a t i o n s h i p of the form T i T ( h v ) = C where C i s a constant f o r a s p e c i f i c host and hv i s the Zeeman s p l i t t i n g has been e s t a b l i s h e d to give estimates of T i to about a f a c t o r of two. T y p i c a l values at 10 mK l i e i n the range Is-1000s. The h a l f l i f e T i must be _> T i . The leading o r i e n t a t i o n parameter B 2 i s given approximately f o r low degrees of p o l a r i s a t i o n by B 2 = 1 (hv/kT) /5. U s e f u l NO measurements r e q u i r e t y p i c a l l y B2(min) = 0.2, g i v i n g a maximum use­ f u l temperature of Τ(max) = Ihv/k, f o r which T i = C/[(hv) T(max)] = C k / I ( h v ) = 2 χ lO'+C/KhvP where C i s i n MHz sK and hv i n MHz. For i r o n host C = 5 χ 10 . The average value of B 2 , taking the s i m p l i f y i n g assumption of a nuclear s p i n temperature % approaching the l a t t i c e temperature T as (1/T)^(t) = 1/T ( l - e / i ) is B = B ( T ) [2X /(1 + 3X + 2X2)j where X = Ti/Ti£n2 and B ( T ) i s the f u l l e q u i l i b r i u m l i m i t . For cases with higher degrees of p o l a r i s a t i o n a b e t t e r approximation i s B α 1/T and we have B 2 = B2(Τγ)[x(1+X)] . Results f o r B 2 / B 2 ( T ^ ) are shown i n f i g u r e 2 as a f u n c t i o n or X. These r e l a t i o n s allow estimates to be made of the mean p o l a r i s a t i o n achieved f o r any combination of host C values, hyperfine s p l i t t i n g and h a l f l i f e . The l i m i t i n g case i s found by p u t t i n g Τ(max) equal to the lowest a t t a i n a b l e temperature. This gives hv(min), hence Ti(min) and Τχ(min). For d i f f e r e n t elements the hyperfine f i e l d v a r i e s from 100 T, and with v a r y i n g nuclear spins and moments each case must be considered s e p a r a t e l y . 2

2

2

3

2

2

4

_ t

L

T

L

2

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch053

2

2

L

2

L

2

Fig. 3 . Mean value of B 2 as a f u n c t i o n of T i / T i r a t i o . Upper curve f o r large a n i s o t r o p i e s (>10%), lower f o r s m a l l . The r e s u l t s of these c o n s i d e r a t i o n s l i m i t current methods of OLNO. Representative estimates of lower l i m i t h a l f - l i v e s are given i n Table 1, assuming i r o n host and taking I=g=l. These should be taken as a guide only, v a r i a t i o n s with I and g being i n d i c a t e d . I t i s seen that, f o r many elements, l i m i t i n g l i f e t i m e s are less than 1 minute. In e f f e c t t h i s means a range of 15-25 isotopes per element above Ζ ^ 30. Comparison of OLNO with other methods of moment and l e v e l s t r u c t u r e study has been given b r i e f l y i n [ST085]. Most a l t e r n a t i v e moment measurements require considerably higher count r a t e s . When working f u r t h e r from s t a b i l i t y decay schemes are o f t e n poorly e s t a b l i s h e d and, as Q values f o r decay i n ­ crease, they become more complex. The occurrence of isomers i s r e l a t i v e l y frequent, which has the advantage of populating s t a t e s of a wide range of s p i n values and the drawback of producing complicated parentage f o r t r a n s i ­ tions lower i n the daughter decay scheme. The over a l l r e s u l t i s that nuclear

354

NUCLEI OFF THE LINE OF STABILITY

TABLE 1 L i s t i n g f o r each element of the temperature at which B 2 = 0.2 i n i r o n host, the estimated Ύ\ a t that temperature and hence the minimum h a l f - l i f e a c c e s s i b l e . In Table, I = g = 1 i sassumed, see footnotes • Element

B

hf (T)

Τ

T i1

max (mK) +

at Τ max = T, (min)

Element

B

hf (T)

2

T i1

Τ max (mK) +

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch053

seconds* 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I

-13.2 -12.2 -8.7 -6.6 -22.8 -33.9 -28.7 -23.4 -21.8 -19. 1 -9.4 6.0 34.4 69 84 66 5.4 -10 -22.6 -27.4 -26.6 -25.6 -31.7 -49 -55.7 -54.7 -44.7 -39.2 -28.7 8.5 23.4 68. 1 1 14.6

4.8 4.5 3.2 2.5 8.4 12.4 10.5 8.5 8.0 7.0 3.4 2.2 12.6 25.2 30.7 24 1.9 3.7 8.3 10.0 9.7 9.4 11.6 17.9 20.4 20.0 16.3 14.3 10.5 3.1 8.5 24.9 41.9

3

1.0 χ 10 1.3 χ 10 3.5 10 7.8 χ 10 194 59 97 179 222 330 2.8 χ 10 1.1 χ 10 57 7 4 8 1.4 χ 10 2.3 χ 10 200 112 122 137 72 20 13 14 26 38 97 3.8 χ 10 180 7 1.5

3

3

3

3

3

3

3

3

3

54 55 56 57 58 62 63 65 66 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 88 90 92 94 96

Xe Cs Ba La Ce Sm Eu Tb Dy Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Ra Th U Pu Cm

160 27.6 8.5 -46 41 314 148 380 610 768 625 125 61 -63 -64 -69 -75 -109 -147 -128 -115 -84 -18.5 26.2 119.1 238 254 170 12.7 31 56 1 13

S b based on c o m p a r i s o n o f t h e i r measured g - f a c t o r s w i t h c a l c u l a t i o n s b a s e d on n e i g h b o u r i n g odd-A n u c l e i w h i c h y i e l d g = 1.06(3) f o r t h e f o r m e r c o n f i g u r a ­ t i o n and g = 0 . 8 2 ( 3 ) f o r t h e l a t t e r . The p r e s e n t i m p r e c i s e measurement, g = ± 0.87(9) i n S b needs t o be i m p r o v e d u s i n g t h e NMR/ON t e c h n i q u e , b u t 1 2 2

1 1 6

v s

1 2 0

l l S

356

STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch053

NUCLEI O F FT H E LINE O F

F i g . 4.

T e m p e r a t u r e dependence

o f γ-anisotropy f o r o r i e n t e d I i s o t o p e s .

53.

357

On-Line Nuclear Orientation

STONE

f a v o u r s t h e CI5/2 p r o t o n s t a t e , f o u n d as g r o u n d s t a t e i n a l l odd-A i s o t o p e s lll-121

S b e

I_. I n g | l ç a n d 5 3 1 5 7 we h a v e r e s u l t s o n two i s o m e r s f o r e a c h mass number. The h i g h s p i n i s o m e r ( a s s i g n e d 7" o n t h e b a s i s o f l e v e l s f e d i n d e c a y ) h a s μ = ± 4.2(2)nm i n b o t h c a s e s . This i s d i s t i n c t i v e of the d i s t o r t e d π (404) 9/2"*" o r b i t a l w h i c h , c o u p l e d t o ν (532) 5 / 2 " w o u l d g i v e Ι = 7"", μ = 4.8nm. The o c c u r r e n c e o f t h i s o r b i t a l a t l o w e x c i t a t i o n i s d i r e c t l y i n d i c a t i v e of large e q u i l i b r i u m deformation associated with the s o f t m i d - s h e l l n e u t r o n number. The l o w s p i n i s o m e r ( 2 ~ ) shows a moment i n I , ± 1.9(3)nm, w h i c h i s c l e a r l y l a r g e r t h a n f o u n d f o r l e v e l s o f t h e same Ι in I ± 1.23(3)nm and I ± 1.14(8)nm |])EJ83] . A p o s s i b l e e x p l a n a t i o n for this v a r i a t i o n i s that i n l S we a r e c l o s e t o t h e s h e l l m o d e l c o n ­ figuration |jg /2,vhi1/2J2" ^schmidt -2.5nm) w i t h r e l a t i v e l y s m a l l e q u i ­ l i b r i u m d e f o r m a t i o n , s u g g e s t i n g t h a t t h i s i s o t o p e i s a d r a m a t i c example o f i s o m e r i s a t i o n w i t h m a r k e d l y d i f f e r e n t d e f o r m a t i o n i n t h e two i s o m e r s . The same c o n f i g u r a t i o n Qrg7/2> h l l / 2 ] 2 " h a s b e e n p r o p o s e d f o r ^ f S b y ! (^meas ~1·9 nm) and C a l l a g h a n e t a l h a v e shown t h a t d e t a i l e d c o r r e c t i o n s t o t h e S c h m i d t moment r e d u c e t h e c a l c u l a t e d v a l u e t o - 1 . 9 5 ( 5 ) n m [CAL74] . The moment o f I ( 1 ) a t ± 0.93(9)nm l i e s c l o s e r t o t h e d e f o r m e d analogue C s ( l ) Q r ( 4 2 0 ) | , v ( 4 1 1 ) i ] μ = 0.67 nm, t h a n t o t h e s p h e r i c a l S b ( l ) Qrds/2, v d ] μ = + 2.3(2)nm. 1

1

5

π

1

1

8

π

1

2

0

1 2 i +

1

1

8

=

7

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch053

v

=

1 2 2

1 2 I +

1 2 0

+

+

+

3 / 2

References [CAL74] P.T. Callaghan et al. Nuclear Physics A221 1 (1974). [DEJ83] J. de Jong and H. Postma, Hyp. Int. 15/16 69 (1983). [HER78] P. Herzog et al. Nucl. Inst. and Meth. 155 421 (1978). [KRA71] K. Krane, Los Alamos Report LA4677 (1971). [STO85] N.J. Stone, Hyp. Int. 22 3 (1985). W [ OU85] J. Wouters et al. Hyp. Int. 22 527 (1985). [VAN85a]D. Vandeplassche et al. Hyp. Int. 22 483 (1985). [VAN85b]E. Van Walle et al. Hyp. Int. 22 507 (1985). RECEIVED July

18, 1986

54 Spins and Moments Determined by On-Line Atomic-Beam Techniques Curt Ekström

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch054

The Studsvik Science Research Laboratory, S-611 82 Nyköping, Sweden

Hyperfine structure measurements using on-line atomic-beam techniques are of great importance in the systematic study of spins and moments of nuclei far from beta-stability. We will discuss the atomic-beam magnetic resonance (ABMR) method, and laser spectroscopy methods based on crossed-beam geometry with a collimated thermal atomic-beam and collinear geometry with a fast atomic-beam. Selected results from the extensive measurements at the ISOLDE facility at CERN will be presented. Nuclear spins and moments of ground and isomeric states are b a s i c prop e r t i e s probing the s t r u c t u r e and shape of atomic n u c l e i . The systematic experimental study of these q u a n t i t i e s along i s o t o p i c and i s o t o n i c chains thus allows a mapping of the nuclear behaviour, to be compared with the p r e d i c tions of d i f f e r e n t nuclear models. The main experiments s p e c i f i c a l l y aimed a t r e v e a l i n g the nuclear s t r u c ture by measuring nuclear spins and moments are those i n v e s t i g a t i n g the hyp e r f i n e s t r u c t u r e (hfs) o f f r e e atoms using radio-frequency and o p t i c a l spectroscopy techniques. Although a large amount of data has been obtained i n o f f l i n e experiments, i t i s only through the i n t r o d u c t i o n of o n - l i n e techniques at d i f f e r e n t I S O L - f a c u i t i e s that s h o r t - l i v e d n u c l i d e s f a r from s t a b i l i t y , and thus long i s o t o p i c chains, have come w i t h i n reach f o r study. The e x p e r i ments performed at the ISOLDE f a c i l i t y , CERN, by the Gothenburg-Uppsala, Orsay and Mainz groups c o n s t i t u t e a main e f f o r t i n t h i s d i r e c t i o n . C e r t a i n l y , these experiments p r o f i t from the e x c e l l e n t performance of the ISOLDE massseparator and from the wide range of elements a v a i l a b l e i n high production y i e l d s [RAV79, RAV84]. The h f s experiments at ISOLDE may be d i v i d e d into techniques employing atomic-beams and resonance-cells. Here, we w i l l concentrate on the d i f f e r e n t atomic-beam experiments performed by the groups mentioned above. The present subject has been discussed i n some d e t a i l i n [EKS85], g i v i n g e.g. a f u l l r e ference l i s t on the atomic-beam works at ISOLDE. In the o p t i c a l spectroscopy experiments, data on the isotope s h i f t s (IS) may be obtained i n a d d i t i o n to those on the h f s . The important nuclear i n formation on the changes of mean square charge r a d i i , deduced from the IS r e s u l t s , w i l l be discussed by Kluge at t h i s symposium [KLU85].

NOTE:

The author of this chapter worked with members of the I S O L D E Collaboration, C E R N , C H - 1 2 1 1 Geneva 23, Switzerland. 0097-6156/ 86/0324-0358506.00/ 0 © 1986 American Chemical Society

54.

Spins and Moments

EKSTRÔM

359

Atomic-Beam Experiments a t ISOLDE In t h i s s e c t i o n we w i l l b r i e f l y discuss the d i f f e r e n t atomic-beam methods used i n hfs measurements a t ISOLDE, and give information on the i s o t o p i c chains studied. The d e s c r i p t i o n , although c l a s s i f i e d according to the t e c h n i que used, f o l l o w to a large extent the c h r o n o l o g i c a l order. The atomic-beam magnetic resonance (ABMR) apparatus of the GothenburgUppsala group, connected o n - l i n e to the ISOLDE mass separator, i s given schem a t i c a l l y i n F i g . 1. A d e t a i l e d d e s c r i p t i o n of the design and operation may be found i n [EKS78, EKS81]. The ABMR method has been a p p l i e d to s e v e r a l d i f ferent elements a t ISOLDE f o r measurements mainly of nuclear spins and magnet i c d i p o l e moments. The main r e s u l t s have been obtained i n the a l k a l i e l e ments 3 7 R b , 5 5 C S and 8 7 > ^ i - 7 9 A U . Shorter sequences have been studied i n 3 5 B r , i+gln, 5 3 I , 6 3 E U , ggTm and Q\TI. References to the ABMR works are g i ven i n [EKS85]. The ABMR p r o j e c t at ISOLDE i s , i n i t s present form, now ess e n t i a l l y terminated. The p o s s i b i l i t i e s f o r p r e s i c i o n hfs measurements to get information on the hyperfine anomaly, probing the d i s t r i b u t i o n of nuclear magnetism, are under d i s c u s s i o n .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch054

F

r

a n c

n

Laser spectroscopy i n crossed-beam geometry with a c o l l i m a t e d thermal atomic-beam was introduced at ISOLDE by the Orsay group [THl81a, T0U81] ( c f . F i g . 1). With t h i s method, a considerable extension of the ABMR measurements i n the a l k a l i elements, mentioned above, was obtained. The nuclear spectroscopic quadrupole moments could be reached by studying the hfs of the P 3 2 e x c i t e d atomic s t a t e , as w e l l as the IS i n the i s o t o p i c sequences. A number of nuclear spins and magnetic moments was a l s o added. The Orsay works on the a l k a l i elements 3 7 R b , C s and 8 7 ISOLDE have been presented i n [HUB78, LIB80, THl81b, THI81c, C0C85]. The atomic-beam l a s e r spectroscopy, i n the Orsay v e r s i o n , i s mainly r e s t r i c t e d to the a l k a l i elements, where, however, future double-resonance experiments, g i v i n g accurate hfs constants, w i l l be of i n t e r e s t . 2

F

a

r

t

5 5

At present, the most powerful method f o r hfs and IS measurements i s c o l l i n e a r fast-beam l a s e r spectroscopy," developed and introduced a t ISOLDE by the Mainz group [NEU81] ( c f . F i g . 2). During the few years of operation, t h i s experiments has produced a vast amount of data on nuclear spins, moments and mean square charge r a d i i of long i s o t o p i c chains throughout the nuclear chart. The s e n s i t i v i t y of the method w i l l probably be f u r t h e r increased by the i n t r o d u c t i o n of n o n - o p t i c a l d e t e c t i o n techniques. The f i r s t measurements a t ISOLDE were made i n a long sequence of barium isotopes, " B a [MUE83], covering both sides of the Ν = 82 n e u t r o n - s h e l l c l o s u r e . S i m i l a r l y , the che­ mical analogue radium has been studied i n the mass range 208 - 232 [AHM83], i . e . on both sides of Ν = 126. A systematic i n v e s t i g a t i o n o f the r a r e - e a r t h n u c l i d e s , with s p e c i a l emphasis on those i n the t r a n s i t i o n a l region above Ν = 82, i s i n progress. At present, the measurements include 0" 53 [AHM85], li+2-160 146-164 150-170 156-176 [ UC82, NEU85]. Recently, radon isotopes i n the mass range 202 - 222 and indium isotopes between ^ I n and I n were i n v e s t i g a t e d [NEU85], the l a t t e r extending the sequence " In studied by the same method at GSI [ULM85]. In a d d i t i o n to these systematic measurements, point e f f o r t s on n u c l e i of p a r t i c u l a r i n t e r e s t are made, l i k e i n the cases H g and T 1 [NEU85]. Furthermore, the o p t i c a l l i n e s connect­ ing the 7s atomic ground s t a t e with the 8p e x c i t e d states i n francium were discovered by c o l l i n e a r l a s e r spectroscopy, and the f i r s t hfs measurements on the heavy francium isotopes were made [NEU85]. 1 2 2

l t +

G d j

D y j

E r

a

n

d

Y b

1 1 + 6

1

E u

B

1

i 2 7

1 0 7

1 8 2

2 0 7

1 1 1

360

NUCLEI OFF THE LINE OF STABILITY

ATOMIC-BEAM

ATOMIC-BEAM MAGNETIC RESONANCE

LASER SPECTROSCOPY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch054

COLLECTOR DETECTOR

MAGNETIC F I E L D

122

.) —

r~Ï2kHz

I-

Cs Λ"

1

/\ RADIO FREQUENCY

LASER

Fig.

FREQUENCY

1

S c h e m a t i c v i e w o f t h e atomic-beam m a g n e t i c r e s o n a n c e and atomic-beam l a s e r s p e c t r o s c o p y s e t - u p s a t ISOLDE. I n b o t h e x p e r i m e n t s , t h e 60 keV ion-beam f r o m ISOLDE i s c o n v e r t e d t o g i v e a c o n t i n u o u s f l o w o f t h e r m a l atoms t h r o u g h t h e m a c h i n e s . Resonances a r e o b s e r v e d i n t h e ABMR e x p e r i ­ ments when r f - t r a n s i t i o n s a r e i n d u c e d i n t h e a t o m i c g r o u n d - s t a t e h f s , c h a n g i n g t h e atoms f r o m a f o c u s i n g ( M j > 0) t o a d e f o c u s i n g ( M j < 0) s t a t e . The AF = 1 r e s o n a n c e t r a n s i t i o n s i n C s ( I = 1) a r e g i v e n a t t h e b o t t o m l e f t : a) ( F = 3/2, M = 1/2) + ( 1 / 2 , -1/2) and ( 3 / 2 , -1/2) + (1/2, 1 / 2 ) , b) ( 3 / 2 , 3/2) ( 1 / 2 , 1 / 2 ) . The s m a l l l i n e - w i d t h s , d e t e r ­ m i n e d m a i n l y b y t h e t r a n s i t t i m e o f t h e atoms t h r o u g h t h e r f - f i e l d , s h o u l d be n o t e d . They g i v e t h e d i p o l e - c o n s t a n t i n t h i s p a r t i c u l a r c a s e w i t h a p r e c i s i o n o f 5 ppm. I n t h e atomic-beam l a s e r e x p e r i m e n t s , t h e r e s o n a n c e s a r e r e c o r d e d a f t e r s t a t e s e l e c t i o n w i t h a s i x - p o l e magnet; n e g a t i v e s i g n a l s a r e o b t a i n e d when t h e p o p u l a t i o n o f a s t a t e w i t h M j > 0 i n t h e s t r o n g - f i e l d l i m i t i s r e d u c e d b y o p t i c a l pumping w i t h l a s e r l i g h t v i a an e x c i t e d a t o m i c s t a t e , and p o s i t i v e s i g n a l s when t h e p o ­ p u l a t i o n i s i n c r e a s e d ( c f . t h e l a s e r - f r e q u e n c y s c a n i n C s ( I = 1) at t h e bottom r i g h t ) . 1 2 2

F

1 3 0

Reproduced with permission from [EKS85] · Copyright 1985 J . C. B a l t z e r A3 S c i e n t i f i c Publishing Company.

EKSTROM

Spins and Moments

COLL IN E A R

F A S T - B E A M

L A S E R

CHARGE EXCHANGE CELL

ELECTROSTATIC DEFLECTOR LENS

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch054

SPECTROSCOPY

Fig. 2 S i m p l i f i e d drawing of the c o l l i n e a r fast-beam l a s e r experiment a t ISOLDE. The ion-beam i s d e f l e c t e d i n t o t h e a p p a r a t u s and p a s s e s , s u p e r i m p o s e d o n a l a s e r beam, a l o n g t h e o p t i c a l a x i s . The i o n s a r e n e u t r a l i z e d i n a c h a r g e - e x c h a n g e c e l l t o g i v e a beam o f f a s t atoms. These a r e e x c i t e d b y t h e l a s e r l i g h t and t h e d e t e c t i o n o f t h e r e s o ­ n a n c e s a r e made b y r e c o r d i n g t h e e m i t t e d f l u o r e s c e n c e p h o t o n s i n a p h o t o m u l t i p l i e r . The r e s o n a n c e s a r e scanned by k e e p i n g t h e l a s e r f r e q u e n c y a t a f i x e d v a l u e and v a r y i n g t h e D o p p l e r s h i f t o f t h e a b s o r p t i o n l i n e by an a d d i t i o n a l v o l t a g e p u t on the r e t a r d a t i o n and c h a r g e - e x c h a n g e s y s t e m s . The p h o t o n s p e c t r u m o f D y ( I = 7/2) as a f u n c t i o n o f a c c e l e r a t i o n v o l t a g e i s g i v e n a t t h e b o t t o m . The AF = 1 and AF = 0 r e s o n a n c e s o b s e r v e d i n t h e 4212 Â t r a n s i t i o n a r e i n d i c a t e d i n the energy l e v e l diagram. 1 4 9

Reproduced with permission from [EKS85]. Copyright 1985 J . C. Baltzer PC S c i e n t i f i c Publishing Company.

362

NUCLEI OFF THE LINE OF STABILITY Discussion of Selected Results

The elements i n which long i s o t o p i c chains have been subject to hfs and IS measurements at ISOLDE are i n d i c a t e d i n F i g . 3. Here, we w i l l choose two nuclear regions f o r short comments; the rare-earth region and the "heavyradium" region.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch054

As discussed i n the preceeding s e c t i o n , an extensive i n v e s t i g a t i o n of the r a r e - e a r t h region i s being performed by c o l l i n e a r l a s e r spectroscopy. I t includes a two-dimensional mapping of the (Ν, Z)-plane, covering not only scattered i s o t o p i c sequences but isotopes of a range of elements. The information on nuclear deformation from the IS-data i n d i c a t e s that the steep increase, observed between Ν = 88 and 90, i s r e s t r i c t e d to a few elements around gadolinium (Z = 64). The e f f e c t becomes l e s s pronounced i n the l i g h t e r as w e l l as heavier elements. In barium (Z = 56) and ytterbium (Z = 70) the step vanishes completely and there i s a smooth t r a n s i t i o n from s p h e r i c a l to s t r o n g l y deformed shapes above Ν = 82. This behaviour i n d i c a t e s that the Ζ = 64 proton s u b s h e l l c l o s u r e , with i t s s t b i l i z i n g e f f e c t f o r sphe­ r i c a l shapes, plays an important r o l e .

20

40

60

80

100

120

140

160

Ν Fig.

3

Nuclear chart i n c l u d i n g the major s h e l l closures and approximative isodeformation curves f o r ε = 0.2. Hfs and IS measurements have been performed at ISOLDE i n long i s o t o p i c chains of the elements i n d i c a t e d by arrows. Shorter sequences of the elements 3 s B r , 5 3 I , ggTm and 81^1» not i n d i c a t e d here, have also been studied at ISOLDE.

54.

EKSTROM

Spins and Moments

363

The p i c t u r e above i s supported by the r e s u l t s on nuclear spins and mo­ ments. Here, an i n t e r p r e t a t i o n w i t h i n the p a r t i c l e - r o t o r model gives a rather complete mapping of the ground-state s i n g e l - p a r t i c l e s t r u c t u r e i n the Ν = 82 region. The model c a l c u l a t i o n s reproduce w e l l the t r a n s i t i o n from e s s e n t i a l l y shell-model states close to Ν = 82 to strongly coupled almost pure N i l s s o n states i n the region of strong nuclear deformation [EKS85]. The n u c l i d e s i n the "heavy-radium" region above Ν = 126 have a l o c a t i o n on the nuclear chart s i m i l a r to that of the rare-earths above Ν = 82. How­ ever, because of the presence of extremely s h o r t - l i v e d n u c l i d e s j u s t above Ν = 126, the systematic i n v e s t i g a t i o n s of radon, francium and radium have been l i m i t e d to n u c l i d e s above Ν = 131.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch054

As mentioned above, the radon and radium sequences have been i n v e s t i g a ­ ted by c o l l i n e a r fast-beam l a s e r spectroscopy, whereas i n francium a l l three atomic-beam methods, ABMR, atomic-beam l a s e r spectroscopy and c o l l i n e a r l a s e r spectroscopy, have c o n t r i b u t e d . The "heavy-radium" region i s c h a r a c t e r i z e d by an i n c r e a s i n g quadrupole deformation with i n c r e a s i n g neutron number. This i s evidenced by the IS-data as w e l l as by previous B(E2)-data. In a d d i t i o n , there i s evidence f o r the occurence of the t h e o r e t i c a l l y p r e d i c t e d [LEA84, NAZ84] octupole deformation i n t h i s region. The IS-data i n radium i s much b e t t e r reproduced by i n c l u d i n g an octupole deformation of 33 — 0.1. S i m i l a r values are obtained from the magnetic moments i n radium [AHM83, LEA84, RAG83] and i n francium [COC85]. Acknowledgments F r u i t f u l d i s c u s s i o n s with members of the d i f f e r e n t h f s groups at ISOLDE, and i n p a r t i c u l a r those with Dr. R. Neugart, are g r a t e f u l l y acknowledged.

References S.A. Ahmad et al., Phys. Lett. 133B(1983)47. S.A. Ahmad et al., Ζ. Phys. A321(1985)35. F. Buchinger et al., Nucl. Instr. and Meth. 202(1982)159. A. Coc et al., submitted to Phys. Lett. Β. C. Ekström et al., Nucl. Instr. and Meth. 148(1978)17. C. Ekström, Nucl. Instr. and Meth. 186(1981)261. C. Ekström, Hyp. Int. 22(1985)65. G. Huber et al., Phys. Rev. Lett. 41(1978)459. H.-J. Kluge, contribution to this symposium. G.A. Leander and R.K. Sheline, Nucl. Phys. A413(1984)375. S. Liberman et al., Phys. Rev. A22(1980)2732. A. Mueller et al., Nucl. Phys. A403(1983)234. W. Nazarewicz et al., Nucl. Phys. A429(1984)269. R. Neugart, Nucl. Instr. and Meth. 186(1981)165. R. Neugart et al., to be published. I. Ragnarsson, Phys. Lett. 130B(1983)353. H.L. Ravn, Phys. Rep. 54(1979)201. H.L. Ravn, Proc. On-Line in 1985 and Beyond, Workshop on the ISOLDE Programme, Zinal, Switzerland (1984) p. D9. [THI81a] C. Thibault et al., Nucl. Instr. and Meth. 186(1981)193. [THI81b] C. Thibault et al., Phys. Rev. C23(1981)2720. [THI81c] C. Thibault et al., Nucl. Phys. A367(1981)1. [TOU81] F. Touchard et al., Nucl. Instr. and Meth. 186(1981)329. [ULM85] G. Ulm et al., Ζ. Phys. A321(1985)395.

[AHM83] [AHM85] [BUC82] [COC85] [EKS78] [EKS81] [EKS85] [HUB78] [KLU85] [LEA84] [LIB80] [MUE83] [NAZ84] [NEU81] [NEU85] [RAG83] [RAV79] [RAV84]

RECEIVED July 4, 1986

55 UNISOR Collinear Laser Facility First Results

1

1

2

2

H. K. Carter, G. A. Leander, J. A. Bounds, and C. R. Bingham 1

UNISOR, Oak Ridge Associated Universities, Oak Ridge, TN 37831 Physics Department, University of Tennessee, Knoxville, TN 37996-1200

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch055

2

The hyperfine structure and isotope shifts of 189m,191m,193m,193g,Tl have been measured by means of collinear fast-beam/laser spectro­ scopy. Deformations for the 9/2 isomers are determined to be larger than for the l/2 ground state and increase with decreasing neutron number. Despite different deformations, rotational pro­ perties are nearly identical in Tl. Microscopic theory ascribes this to a systematic balance between changing deformation and neutron pairing. -

+

185-199

P r i o r t o about application electric

1955 much o f t h e n u c l e a r

o f atomic p h y s i c s .

i n f o r m a t i o n was o b t a i n e d

moments and changes i n mean-squared c h a r g e r a d i i

measurement o f t h e a t o m i c h y p e r f i n e a r e o b t a i n e d i n a n u c l e a r model

structure

are derived

( h f s ) and I s o t o p e S h i f t

independent way.

The scheme o f c o l l i n e a r

[KAU76] p r o m i s e d t o be u s e f u l

laser/fast-beam

The l i g h t

results

f r o m t h e UNISOR l a s e r

s t a t e s and t h e bands b u i l t

the

l/2

facility.

paper

deformation of t h i s

9/2" state.

9

2

on i t , d r o p s i n e n e r g y w i t h r e s p e c t t o mass 1 8 9 . A t

This suggests a r a p i d l y

changing

However, t h r o u g h o u t t h i s , t h e s t a t e s b u i l t on

t h e 9 / 2 * s t a t e m a i n t a i n n e a r l y c o n s t a n t energy l e v e l t h a t t h e bands b u i l t

series of

documented [ H E Y 8 3 ] .

g r o u n d s t a t e as t h e n e u t r o n number Ν d e c r e a s e s u n t i l

mass 187 and l o w e r t h e s t a t e t h e n r i s e s .

describes

The b e h a v i o r o f t h e h /

on them has been w e l l

T h i s l e v e l , and t h e band s t r u c t u r e b u i l t +

The p r e s e n t facility.

t h a l l i u m i s o t o p e s were chosen t o be t h e f i r s t

i s o t o p e s t o be s t u d i e d a t t h e UNISOR l a s e r intruder

f i e l d has

spectroscopy

f o r a wide v a r i e t y o f e l e m e n t s , t h u s UNISOR

began i n 1980 t o d e v e l o p t h i s t y p e o f f a c i l i t y . some o f t h e f i r s t

from ( I S ) and

W i t h t h e development o f t h e

t u n a b l e dye l a s e r and i t s use w i t h t h e o n l i n e i s o t o p e s e p a r a t o r t h i s been r e j u v e n a t e d .

from

The n u c l e a r s p i n , n u c l e a r m a g n e t i c and

s p a c i n g s . This

on t h e 9 / 2 " s t a t e have r e l a t i v e l y

unchanging

suggests

deformation

as a f u n c t i o n o f n e u t r o n number. Thus t h a l l i u m appeared t o be a good c a n d i d a t e 0097-6156/ 86/ 0324-0364S06.00/ 0 © 1986 American Chemical Society

55.

365

UNISOR Collinear Laser Facility

C A R T E R E TAL.

f o r measurement o f IS s i n c e we c o u l d t h e n d e t e r m i n e changes i n q u a d r u p o l e moments and rms c h a r g e

radii.

Experimental

A p p a r a t u s and Procedure

F i g u r e 1 shows s c h e m a t i c a l l y The c o l l i n e a r

used.

o f 535 nm e x c i t e s t h e 6 P /

Laser l i g h t

level.

fiber

3

optic

collector source.

The r e s o n a n t

2

metastable state to the

i s d e t e c t e d by t h e 377 nm t r a n s i t i o n

light

c o l l e c t o r which i s 1 0 . 8 cm l o n g .

A c o l l i n e a r magnetic nance u n t i l

field

is 7 S / 2

L

2

to the

i s c o l l e c t e d and c h a n n e l l e d t o t h e PMT by a With t h e c y l i n d r i c a l

i s e s t i m a t e d t o a c c e p t 44% o f t h e l i g h t Colored glass f i l t e r s

o n l i n e t o t h e UNISOR

l a s e r / f a s t - a t o m beams t e c h n i q u e [KAU76] 2

The r e s o n a n t c o n d i t i o n

ground s t a t e .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch055

the laser f a c i l i t y

isotope separator.

a r e used t o reduce t h e l a s e r

i s used t o Zeeman s h i f t

t h e atom reaches t h e d e t e c t i o n

mirror the

e m i t t e d by an o n - a x i s light

the t r a n s i t i o n

point

background. out of

reso-

region.

Charge Exchange

Iter I Filter Photomulti

1

0

Fig.

V l

2

Saturated Absorption

1.

Schematic o f t h e l a s e r

system o n l i n e t o UNISOR i s o t o p e separator.

The d a t a r e c o r d e d as t h e l a s e r f r e q u e n c y i s scanned c o n s i s t s fluorscence signal

f r o m t h e PMT, a D o p p l e r - f r e e

markers from t h e é t a l o n . scan.

The D o p p l e r - f r e e

used t o c o r r e c t

The é t a l o n p r o v i d e s I

f o r small

2

spectra provides laser

I

2

a calibration

of the frequency

an a b s o l u t e f r e q u e n c y

frequency d r i f t s ,

separator

shift

first

corrections.

f o r t h e Doppler

We a r e t h u s a b l e t o r e c o r d d a t a o v e r l o n g p e r i o d s o f t i m e ,

3 h o u r s , and m a i n t a i n a r e a s o n a b l e o n l i n e data recorded w i t h t h i s

detection efficiency

reference

v o l t a g e d r i f t s and

t o determine the absolute a c c e l e r a t i o n voltage of the separator

e.g.

of the

s p e c t r u m and f r e q u e n c y

r e s o l u t i o n o f 100 MHz.

has been measured t o be 1 / 1 0 0 0 ,

per 1000 a t o m s , f o r t h e l a r g e s t

Some o f t h e

system i s shown i n F i g u r e 2 .

transition

The o v e r a l l

i . e . one d e t e c t e d

in the nuclear

s p i n 1/2

photon

isotopes.

366

NUCLEI OFF THE LINE OF STABILITY Results W h i l e d a t a were o b t a i n e d on i s o t o p e s

moments and i s o t o p e problem o u t l i n e d teristic sitions 9/2

above.

Examination of

three hfs t r a n s i s t i o n s due t o t h e 9 / 2

i s o m e r has f a l l e n

t o permit

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch055

s h i f t s , the data w i l l

isomeric

f r o m mass 189 t o

be d i s c u s s e d o n l y

Figure

due t o t h e 1/2 state

2 reveals that

relation both the

to

T1.

1 9 3

and i s o m e r i c

tran-

I n 189,191JI

decay i s

in the

charac-

ground s t a t e and t h e s i x

are observed i n

below t h e 3/2 s t a t e

o b s e r v a t i o n o f t h e ground

193 r e s u l t i n g

in

the

insufficient

state.

Fig.

2.

Sample o f

hfs

recorded in present I93g,my|

experiment

The upper p o r t i o n

e

t h e atomic t h e two

data

hyperfine

levels

of

shows for

spins.

Laser Frequency

The change i n m e a n - s q u a r e d - c h a r g e shift is

using standard techniques [ H E I 7 4 ] ,

approximately

error.

The r e s u l t i n g

good a p p r o x i m a t i o n , t o an e l e c t r o n i c

same f o r

all

factor

is

mation f o r 2 0 7 J ]

in Figure

one p r o t o n

model [MYE83]

D r o p l e t model

zero deformation

proportionality

(which i s

t h e n use t h e d r o p l e t

lines

factor

not d i r e c t l y

from the

isotope

field

mass s h i f t

shift

is

times 6 < r > .

shift

smaller

proportional, For t h e case o f

2

calculable

is

b u t s h o u l d be v i r t u a l l y

to Tl the

isotopes.

To deduce t h i s

shifts.

is obtained

8 MHz between masses and t h e s p e c i f i c

than the experimental

the e l e c t r o n i c

radius

For t h a l l i u m t h e normal mass

for

Tl we assumed z e r o

to extract

2

2

for different

08Pb)

deformations

values of 6 < r > w i t h 3 = 0 are f i t

and p r e d i c t i o n s 3.

factor

f r o m d o u b l e magic

and

2 0 0

from the

deforT1.

We

field

t o t h e two p o i n t s

deformations

a r e shown as

of

solid

55.

189

191 I

193 I

195

197

199

201

y\

ι

y

^3/2» % and l l / 2 c o n f i g u r a t i o n s outside the closed S n core. The r e s u l t i n g c o n f i g u r a t i o n mixed wave functions were used to c a l c u l a t e the g - f a c t o r s i n Table 1, and using two sets of elemental proton g - f a c t o r s . The f i r s t set c o n s i s t s of the f r e e values of g^ and g . The c a l c u l a t e d g - f a c t o r s are s i g n i f i c a n t l y smaller than the experimental values[BER85b] This i s due to the neglect of core p o l a r i z a t i o n e f f e c t s , as was discussed i n d e t a i l for T e [W0L76]. In order to account f o r these e f f e c t s , we c a l c u l a t e d a set of e f f e c t i v e elemental proton g - f a c t o r s from the ground s t a t e g - f a c t o r s of L a and P r . The r e s u l t i n g values, g^=1.12 and gg=4.12 were then again combined with the shell-model wave functions to c a l c u l a t e g ( 4 J " ) and g(6"f) . The r e s u l t s , given i n column 4 of Table 1, are i n e x c e l l e n t agreement with the measured values. Thus, a s i n g l e set of e f f e c t i v e g-factors i s s u f f i c i e n t to account f o r core p o l a r i z a t i o n e f f e c t s i n the four N=82 isotones discussed here. Moreover, a c l o s e i n s p e c t i o n of the c o n t r i b u t i o n of various components of the wave-functions to the r e s p e c t i v e g - f a c t o r s , reveals that i n a l l cases a s i n g l e component of the wave f u n c t i o n contributes s i g n i f i c a n t l y (more than 75%) to the g - f a c t o r . More s p e c i f i c a l l y , t h i s component i s ( g 7 / 2 ) th > 4,6 f o r Te, Xe, B a respectively. 1 3 6

1 3 8

X

1 3 4

a n

T e

2 5 2

X e

1 3 8

ll+

+

l t + 0

+

1 3 8

8 2

1 3 3

ll+8

g

d

s

h

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch058

1 3 2

s

1 3 l +

1 3 9

l i + 1

n

1 3 l +

1 3 6

w i

n = 2

1 3 8

4. g - f a c t o r s of 2* states at the onset of deformation The magnetic moments of c o l l e c t i v e s t a t e s are mainly determined by the proton motion. The simple hydrodynamical model p r e d i c t s g=Z/A f o r such s t a t e s . S i g n i f i c a n t d e v i a t i o n s from t h i s r e l a t i o n were found experimentally. These d e v i a t i o n s are due to: a) d i f f e r e n t p a i r i n g forces of protons and neutrons; t h i s e f f e c t causes a reduction of about 15% with respect to Z/A, but does not a f f e c t the smooth behavior of g vs. A; b) changes i n the number of protons that a c t u a l l y take part i n the c o l l e c t i v e motion. This l a t t e r e f f e c t , which i s p a r t i c u l a r l y important i n the v i c i n i t y of s u b s h e l l c l o s u r e s , causes s i g n i f i c a n t s t r u c t u r e i n the dependence of g vs. A. Such s t r u c t u r e was observed f o r neutron-rich Nd and Sm isotopes C K O L 8 4 ] . These n u c l e i are i n the region A=150 where a t r a n s i t i o n from v i b r a t i o n a l to r o t a t i o n a l s t r u c t u r e takes place around N=88. This onset of deformation causes the e l i m i n a t i o n of the Z=64 s u b s h e l l c l o s u r e , which means that around N=8S d r a s t i c changes i n the number of a c t i v e protons are expected to occur. A d d i t i o n a l n u c l e i i n t h i s region are the neut r o n - r i c h Ba, Ce, Gd and Dy isotopes. The A=100 region i s s i m i l a r to the A=150 r e g i o n . The onset of deformation i s observed here i n Sr, Zr, Mo and Ru i s o t o p e s , when the number of neutrons increases beyond N=5R. A l s o , the Z=40 s u b s h e l l i s eliminated f o r N*60. We mentioned i n the I n t r o d u c t i o n that neutron-rich n u c l e i around A=100 and A=150 are produced by f i s s i o n . The PAC method was used to measure

58.

Magnetic Moments of Excited States

WOLF ET AL.

389

g - f a c t o r s o f 2 i s t a t e s i n some o f t h e s e n u c l e i . g ( 2 i ) for Zr, Mo were measured a t JOSEF [wOL80, MEN85U, and f o r Ba, C e w e r e mea­ s u r e d a t TRISTAN [w0L83a,W0L85a]. The e x p e r i m e n t a l r e s u l t s a r e summarized i n T a b l e 2. 1 0 0

l h k

, l t + 6

1 0 2 , 1 0 l +

l l t 6 , 1 I + 8

4.1.

S y s t e m a t i c s o f g (2 χ) i n t h e A=150 r e g i o n . I n F i g u r e 2 we p l o t t e d t h e e x p e r i m e n t a l g ( 2 i ) v a l u e s v s . A, f o r t h e n e u t r o n - r i c h Ba - Gd i s o t o p e s . The d a t a was t a k e n f r o m T a b l e 2, [KOL84] Table 2 and [ L E D 7 8 ] . We s^e t h a t w h i l e f o r Experimental v a l u e s of g ( 2 ) f o r t r a n ­ s i t i o n a l n u c l e i , f r o m JOSEF and TRISTAN Ba and Gd t h e g ( 2 j ) v a l u e s s l o w l y d e c r e a s e as a f u n c t i o n o f A, as e x ­ Nucleus ~ ^(2Ï) ' T p e c t e d f o r a n o r m a l Z/A d e p e n d e n c e , (nsec) ι oo Z r 0.22(5) t h e b e h a v i o r f o r Ce, Nd and Sm i s 0.71(3) 102 0.42(7) 0.114(13) d i f f e r e n t . I n f a c t , a pronounced i n ­ 10«+] Mo 0.19(11) 0.91(3) crease of g 11+4 Ba 0.34(5) 0.70(3) l»+6 Ba 0.85(6) 0.28(7) 1«*6, Ce v s . A i s observed f o r 0.25(3) 0.24(5) H+8 Ce these i s o t o p e s . 1.01(6) 0.37(6) We now p r o c e e d t o a n a l y z e t h e v a l u e s o f g(2^) i n terms o f IBA-2. t r o n d e g r e e s o f f r e e d o m can be w r i t t e n [SAM84] The g - f a c t o r o f a s t a t e w h i c h i s p u ­ r(2) e l y s y m m e t r i c i n t h e p r o t o n and n e u g(2Î> 8 f V t SvV *' +

N

Λ

N

g(2Î)

M o

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch058

+

(21)

N

n

N

+

where g f l , g a r e t h e p r o t o n b o s o n , n e u t r o n b o s o n g - f a c t o r s , N^,N a r e t h e num­ b e r o f p r o t o n , n e u t r o n b o s o n s , and N =N^j+N . When we u s e e q u a t i o n ( 2 ) , t h e q u e s t i o n o f c o u n t i n g N^,N a r i s e s . The c o u n t i n g o f N i s s t r a i g h t f o r w a r d be­ yond N=82. The c o u n t i n g o f N^ i s somewhat c o m p l i c a t e d by t h e e l i m i n a t i o n o f t h e Z=64 s u b s h e l l f o r N^90. T h u s , % s h o u l d be c o u n t e d i n t h e 50-64 s u b s h e l l f o r N$88, and i n t h e m a j o r 50-82 s h e l l f o r N^90. A c c o r d i n g t o t h i s c o u n t i n g p r o c e d u r e , t h e Sm i s o t o p e s h a v e N ^ - l f o r N$88 and % = 6 f o r N^90, i . e . a d r a s ­ t i c change ΔΝ^ =5 o c c u r s as we add n e u t r o n s beyond N=88. F o r Ce, Nd t h i s e f ­ f e c t i s s m a l l e r , i . e . ΔΝ^=1,3 r e s p e c t i v e l y , w h i l e f o r Ba ΔΝΐϊ=0 s i n c e Ba i s b e l o w m i d s h e l l f o r b o t h 50-64 and 50-82 s h e l l s . From (2) i t i s o b v i o u s t h a t f o r Ce, Nd and Sm, g(2"f) w i l l s u d d e n l y i n c r e a s e a t N=90, due t o t h e change ΔΝιι i n t h e number o f a c t i v e p r o t o n b o s o n s . We h a v e h e r e a q u a l i t a t i v e e x p l a ­ n a t i o n f o r t h e s t r u c t u r e o b s e r v e d i n F i g u r e 2, and a l s o f o r t h e d i f f e r e n t b e h a v i o r o f B a , where Δ % = 0 and no d r a s t i c e f f e c t i s e x p e c t e d . The above c o u n t i n g p r o c e d u r e assumes a sudden d i s s i p a t i o n o f t h e Z=64 v

V

t

v

V

v

• ο • • •

Bo Nd Sm Gd Dy

ti

1

g ( 2 | ) = g„ N „ / N + q » N / N t

0.63

w

t

(4)

=0.05(5) x

U4

U6

H8

150

152

154

A F i g u r e 2. g(2|") s y s t e m a t i c s a r o u n d A = 150.

2

=0.80

156

F i g u r e 3. P l o t of g(2+)N /N v s . Ν^/Ν · Reproduced w i t h p e r m i s s i o n from [W0L85bL C o p y r i g h t 1985 NorthHolland Physics Publishing Company, t

ν

390

NUCLEI OFF THE LINE OF STABILITY

Table 3 Values of N ^ i n the A^lSO^region Nucleus Hjff

s u b s h e l l at N=90. A c t u a l l y , I t i s reasonable to expect that t h i s d i s s i p a t i o n should be gradual. The experimental g(2"{") values f o r Ce, Nd and Sm isotopes can be used to e x t r a c t e f f e c t i v e values of N^y ( N f f ) across the region of i n t e r e s t ( i . e . N=86-92). One 1.5(6) can thus f o l l o w the d i s s i p a t i o n process of the subCe 148 4.9(21) s h e l l . N Ç f can be determined by using equation (2) l^Nd 0.2(1) and the experimental values of g (2"}") . In order to do t h i s , we need the values of g^, g . We r e w r i t e equa1.6(5) t i o n (2) : 5.0(15) "•tod Nd 6.7(18) g ( 2 t ) N / N = (gv+gflNfl/Nv) (3) "*Sm If we assume g^,gv to be constant i n the region of 1.5(3) A=150, then from (3) i t follows that a l i n e a r r e l a 4.0(8) t i o n s h i p e x i s t s between g(2J")N /N and N^/Ny. To Sm 6.8(13) t e s t t h i s we use experimental values of g(2 ) f o r 7.0(9) l^'l^Ba. Nd, ' S m , ^ " l ^ G d , and 160-16*+ . For a l l these isotopes % i s counted i n the major 50-82 s h e l l . The r e s u l t s are shown i n Figure 3. We see that the l i n e a r r e l a t i o n s h i p p r e d i c t e d by equation (3) i s very w e l l confirmed by the data, with g =0.63±0.04, g =0.05±0,05. These values of g^,g can now be used together with the e x p e r i mental g(2i) from Table 2 and [K0L84]to obtain N Ç f o r the t r a n s i t i o n a l Ce, Nd, and Sm i s o t o p e s . The r e s u l t s are given i n Table 3 [W0L85b]. Although some of the e r r o r bars are l a r g e , we c l e a r l y observe an i n c r e a s e of NÇ^f across the region N=86-92, thus confirming the gradual d i s s i p a t i o n of the Z=64 s u b s h e l l . A s i m i l a r r e s u l t was obtained by Casten [CAS85a]from an a n a l y s i s of energy l e v e l systematics. Another i n t e r e s t i n g r e s u l t of the above a n a l y s i s i s the r e l a t i v e l y low value of g^, much l e s s than the expected g^=l.0. D e t a i l e d microscopic c a l c u l a t i o n s are needed to e x p l a i n t h i s f a c t . Moreover, when we use g^=0.63, g^O.05 to c a l c u l a t e the Β (Ml) strength of the r e c e n t l y observed i s o v e c t o r 1 states [BOH84], we o b t a i n B ( M 1 ) = 0 . 9 - 1 . 3 u , f o r the Gd,Dy,Er, Yb i s o t o ­ pes. This value i s i n e x c e l l e n t agreement with the experimental r e s u l t s 5yjj. N . However, when we use g^=1.0, g =0.0, we o b t a i n B(Ml)exp=0.8-l.5y B ( M l ) i = 2 . 7 - 3 . 8 y N , i . e . much l a r g e r than the experimental values. e

f

1 1 , 6

f

Ce

v

1 5 0

t

v

1 5 2

t

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch058

1 5 0

1?2

v

151+

Dy

1f

v

v

f f

+

2

calc

N

2

v

2

ca

c

4.2.

g(2i") r e s u l t s i n the A=100 r e g i o n . The experimental data i n the t r a n s i t i o n a l r e g i o n A=100 i s scarce. A s y s ­ tematic study l i k e i n F i g s . 2,3, i s not p o s s i b l e here. The Z=40 s u b s h e l l i s eliminated f o r N^60. Sr, Kr and Se are 1,2,3 bosons away from Z=40 and thus are analogous to Sm, Nd and Ce. I n t e r e s t i n g isotopes are: Sr, Kr, e t c . Unfortunately, no g(2t) data i s a v a i l a b l e f o r these n u c l e i . The only e x i s t i n g r e s u l t s are f o r Z r and » M o . (Table 2). The value of g(2f) for Z r i s q u i t e s m a l l , and suggests, i n analogy with the A=150 r e g i o n , that a r e l a t i v e l y small number of protons take part i n the c o l l e c t i v e motion. I t i s therefore of i n t e r e s t to c a l c u l a t e N Ç for Z r . To that purpose we need the values of gu,g . Because of i n s u f f i c i e n t d a t a , a best f i t procedure as i n Figure 3 is_ not p o s s i b l e . However, i f we assume g v 0 , then g^ can be extracted from g(2\) of * » M o . provided N^ ,N f o r t h i s nucleus are known. We use %=3, and N =5,6 f o r » M o , obtained from IBA-2 c a l c u l a tions [SAM82], and c a l c u l a t e g^ using equation (2). The r e s u l t i n g value, g i p l . 0 0 ( 2 3 ) , i s l a r g e r than g^ i n the A=150 r e g i o n . With g^=1.0 and g =0.0, the experimental g(2J") of ^ Z r g i v e s : NÇ = 1.5±0.6 This value i s much smaller than %=5, which would be expected i f the Z=40 9 I +

1 Ô 0

1 0 2

1 0 0

9 2 _ 9 8

1 0 4

1 0 0

f f

1 0 0

v

=

0 2

1 0 l f

V

I 0 2

1 0 1 +

v

v

1 0

f f

58.

391

Magnenc Moments of Excited States

WOLF ET AL.

s u b s h e l l were e l i m i n a t e d . We c o n c l u d e t h a t t h e v i b r a t i o n a l - r o t a t i o n a l t r a n s i ­ t i o n h a s n o t b e e n c o m p l e t e d i n Z r , and t h a t t h e Z=40 s u b s h e l l p e r s i s t s e v e n f o r N=60. A s i m i l a r r e s u l t f o r Z r was r e c e n t l y r e p o r t e d b y C a s t e n [ C A S 8 5 - i »from e n e r g y l e v e l s y s t e m a t i c s . C a s t e n f i n d s % = 3 . 3 f o r Z r , also l e s s t h a n 5, and t h u s i n q u a l i t a t i v e agreement w i t h o u r c o n c l u s i o n . 1 0 0

1 0 0

a

1 0 0

5.

Conclusions We have shown t h a t g - f a c t o r s o f e x c i t e d s t a t e s i n n u c l e i f a r f r o m s t a b i ­ l i t y can provide important n u c l e a r s t r u c t u r e i n f o r m a t i o n , such as: p u r i t y o f wave f u n c t i o n s , c o n f i g u r a t i o n - m i x i n g , number o f a c t i v e p r o t o n s , d i s s i p a t i o n of s h e l l c l o s u r e s , values o f g^,g . F u r t h e r experiments should c o n c e n t r a t e towards t h e double magic Sn, n u c l e i a r o u n d Z r , and t r a n s i t i o n a l e v e n - e v e n n u c l e i a r o u n d A=l(j)0. Open q u e s t i o n s a r e , f o r example: what a r e t h e v a l u e s o f g(4J") and g ( 6 i ) f o r Sn and what i s t h e s t r u c t u r e o f t h e r e s p e c t i v e s t a t e s ? I s t h e d i s s i p a t i o n o f t h e Z=40 s u b s h e l l s i m i l a r t o t h a t o f t h e Z=64 s u b s h e l l ? I s g^ i n t h e A=100 r e g i o n r e a l l y d i f f e r e n t f r o m t h a t i n t h e A-150 r e g i o n ? A l s o , t h e t r a n s i t i o n a l n u c l e i a r o u n d A=130 and 190, r e c e n t l y d i s c u s s e d b y C a s t e n [ C A S 8 5 b ] , s h o u l d a l s o b e e x p l o r e d and w i l l c e r t a i n l y p r o v i d e a l o t o f i n t e r e s t i n g d a t a . v

1 3 2

9 6

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch058

1 3 2

References [BER85a] Z. Berant et al., Phys. Lett. 156B, 159 (1985). [BER85b] Z. Berant et al., Phys. Rev. C31, 570 (1985). [BOH84] D. Bohle et al., Phys. Lett. 148B, 260 (1984) [CAS85a] R.F. Casten, Phys. Lett. 152B, 145 (1985) [CAS85b] R.F. Casten, Phys. Rev. Lett. 54, 1991 (1985) [CHE76] Ε. Cheifetz and A. Wolf, Cargese Conf., CERN 76-13 p.471 (1976) [FRA66] H. Frauenfelder and R.M. Steffen, in : Alpha-, Beta- and Gamma-ray Spectroscopy, ed. K. Siegbahn (1966). [GIL81] R.L. Gill et al., Nucl. Instr. Methods 186, 243 (1981) [IKE76] H. Ikezoe et al., Hyp. Int. 2, 331 (1976). [KOL84] N. Benczer-Koller et al., Ann. Israel Phys. Soc. 7, 133 (1984). [LAW76] H. Lawin et al., Nucl. Instr. Methods 137, 103 (1976). [LEP78] C.M. Lederer and V.S. Shirley eds., Table of isotopes, 7th Ed. [ΜΕΝ85] G. Menzen et al., Z. Physik A 321, 593(1985). [PEK79] L.K. Peker, Nucl. Data Sheets 28, 267 (1979). [SAM82] M. Sambataro and G. Molnar, Nucl. Phys. A376, 201 (1982). [SAM84] M. Sambataro et a l . , Nucl. Phys. A423, 333 (1984). [WOL76] A. Wolf and Ε. Cheifetz, Phys. Rev. Lett. 36, 1072 (1976). [WOL80] A. Wolf et al., Phys. Lett. 97B, 195 (1980). [WOL83a] A. Wolf et al., Phys. Lett. 123B, 165 (1983) [WOL83b] A. Wolf et al., Nucl. Instr. Methods 206, 397 (1983). [WOL85a] A. Wolf et al., to be published [WOL85b] A. Wolf, D.D. Warner and N. Benczer-Koller, Phys. Lett. 158B 7 (1985) RECEIVED

September 5, 1986

59 Spectroscopy and Measurement of Electromagnetic Moments in Po 198,200,210

Κ. H . Maier Hahn-Meitner-Institut Berlin, D-1000 Berlin 39, Glienicker Str. 100, Federal Republic of Germany 210

π

+

-

-

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch059

-

The quadrupole coupling constants for the Po Ι =8 , 11 , 13 isomers in Bi have been measured, and Q(11 ) = 82(2) fm and Q(13 ) = 90(2) fm normalized to Q( Po8 ) = 57 fm are deduced. In beamγ-spectroscopyof Po showed the (πh 9/2 8 ) π(h9/2i13/2 11 ) and (vi 13/2 12 ) isomers. TheB(E28 ->6 )and Q(8 ) in Po to Po are discussed, a sudden drop is found for the B(E2) in Po. TheB(E3,11 ->8 )rises very steeply in the light Po isotopes. -

2

210

+

198,200

-

198

2

2

2

2

+

+

+

+

+

210

198

-

+

This c o n t r i b u t i o n covers work done with the Nuclear S t r u c t u r e Group a t Lawrence Livermore N a t i o n a l Laboratory and a t the Hahn-Meitner-Institut a t B e r l i n . The former uses the t r i t o n beam of the Los Alamos tandem f o r γ-spectroscopy i n beam t o measure f a i r l y b a s i c p r o p e r t i e s of simple few p a r t i c l e 208 states very c l o s e t o Pb. There are s t i l l many gaps i n our knowledge, p a r t i c u l a r l y on neutron p a r t i c l e and proton hole states, a few of these could be f i l l e d by t h i s unique setup f o r γ-spectroscopy with n e u t r o n r i c h t r i t o n p r o j e c t i l e s . Here I w i l l cover recent measurements of the quadrupole moments +

2 1

f o r the 8 , 11" and 13" isomers i n ° P o . At HMI we use the heavy i o n beams 208 from VICKSI f o r spectroscopy of n u c l e i f u r t h e r away from Pb t o observe the gradual t r a n s i t i o n from pronounced s i n g l e p a r t i c l e s t r u c t u r e t o i n c r e a s i n g l y 19 8 20 0 c o l l e c t i v e behaviour. As example spectroscopy of * Po i s presented 210 here. We can then look i n t o the systematics of Po-isotopes from magic

Po

with N=126 down t o N=114 with a few holes i n the 1 1 3 / 2 neutron s h e l l and t h e r e f o r e diminished s t a b i l i t y of s p h e r i c a l shape. 209 A s i n g l e c r y s t a l of t r i t o n s with about

B i metal was struck by a p u l s e d beam of 15 MeV

1 ns pulsewidth. The bismuth

c r y s t a l was heated t o 478±5 Κ

to avoid e f f e c t s from r a d i a t i o n damage. I t s c-axis p o i n t e d a t t o the beam i n the plane of the two detectors a t 15e and 90°. F i g . 1 gives the r e l e v a n t 210 0097-6156/ 86/the 0324-0392506.00/ p a r t of the Po l e v e l scheme. For high energy0 l i n e s from the 11 and 3

© 1986 American Chemical Society

59.

Spectroscopy and Measurement of Electromagnetic Moments

MAIER

4372 4324

-13"

yf

393

93ns

-11" R(t)

2

1

0

P o

1 =

13"

E

y

=

1473

KeV

0.20

1522.9*

1475.1* 0.00 -0.20

>'

2849

0.20

yf

•11"

20.4ns

o.oo

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch059

-0.20

1292.2*

0.20 0.00 -0.20 300

1557

y

1473

\,83.7*

1427

\ ,46.5

1181

yr

•8*

96.0ns

•6

+

42.6ns

•4

+

1.53ns

time[ns]

Fig. 2

245.3

Measured quadrupole modulation p a t t e r n s

1181.4

210

Fig. 1

Isomers i n

Po. *used

f o r measuring Q

yf

•o*

13" l e v e l s c o a x i a l Ge-detectors with 6 mm +

+

f o r the 83.7 keV 8 -*6 t r a n s i t i o n ,

l e a d absorbers were used, whereas

l y i n g between the B i - and Po- K

a

and

Κβ X-rays, p l a n a r detectors were employed. F i g . 2 shows the quadrupole modulation p a t t e r n s 1/2[N(158° ,t)/N(90°,t)-1] and the r e s u l t s are presented 17

i n the t a b l e . The f i e l d gradient f o r Po i n B i eq(PoBi) = 11.7·10 normalized by c a l c u l a t i n g Q ( P o 8 ) = 57 f m from the measured 2 1 0

+

2

2

V/cm [l]

is

210 +

+

B(E2,8 ->·6 ) assuming pure h9/2 c o n f i g u r a t i o n s . As the s t r u c t u r e of q u i t e pure t h i s i s the best n o r m a l i z a t i o n a v a i l a b l e . Mahnke e t a l .

Po i s [ 2 ] got

394

NUCLEI OFF THE LINE OF STABILITY

14.5(15)· 10

17

V/cm

2

from the same procedure f o r

208

Po which i s l e s s safe on

the nuclear model assumption. 210 Table 1: Quadrupole

moments i n

Po. The c o u p l i n g constants are f o r PoBi a t +

+

478(5) K. * C a l c u l a t e d as reference from B(E2,8 -*6 ) |Q|(ref.

57*

57*

e Qq/h

8+

160.7(10) MHz

11"

229(4)

13"

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch059

JQ|present

2

level

MHz

253(4)

MHz

81(2) fm

2

90(2) fm

2

3)

82(19) fm

2

62(11) fm

2

In d e t a i l the time d i s t r i b u t i o n of the 83.5 keV l i n e at e a r l y times i s not reproduced by the f i t ,

due to feeding from the 11" isomer. However, the

d i s t a n c e t o the next pronounced

s t r u c t u r e , a t which a l l n u c l e a r spins are i n

phase again i s p r a c t i c a l l y independent of t h i s . Feeding from 13" i n t o 11" i s weak and spread out i n time and t h e r e f o r e unimportant. V a r i a t i o n s of the f i t t e d range and other parameters

changed the r e s u l t s f o r the frequencies by

'*"**^v-^_.

Gd( Ar,4n).

Using a r e c o i l separation technique,

^^^*

V

V

s

( F i g . 4b) could be obtained. The >

1 9 2

(b)

^^

however, [STE85] very clean spectra

1 9 0

.

v

3 6

B(E2) values extracted

^

,

^^ * * ^^ 4

1

0

!

ΐ

| [llTO

2

for

P b p e r f e c t l y extend the

10 i

-

Q

-

trend observed in the heavier

^—L

timers]

isotopes ( F i g . 3 ) .

F i

9-

4

:

D

e

c

a

y

c

u

r

v

e

s

f

o

r

1

2

+

i

s

o

m

e

r

s

The dominating tendency of the quadrupole moments toward a zero c r o s s i n g about f i l l e d ii3/2

s

1 8 9

n

e

1

P b may be d i r e c t l y understood as a consequence of a h a l f 1

a

t

t

n

i

point.

s

In the q u a s i - p a r t i c l e model the parameter

( u - v ) i s used a measure of the subshell f i l l i n g .

We have extended

t h e o r e t i c c a l c u l a t i o n s [PAU73] in the Tamm-Dancoff

approximation using a

2

2

previous 2

2

surface d e l t a i n t e r a c t i o n to the l i g h t e r Pb isotopes. The values of (u -v obtained are shown in F i g . 3. They permit us to c a l c u l a t e the charge e f f / e associated with an 1*13/2 neutron in the e

i s o t o p e s . It extract

)

effective

different

i s t h i s parameter, also graphed in F i g . 3 , that allows to

information about c o n t r i b u t i o n s of the core to the E2 moments. It

is

seen to increase sharply between A = 206 and 200 and then to l e v e l o f f at e f f / e - 2 . 5 . This value corresponds to a p r o l a t e core deformation of e

β = 0.04 f o r the 12"* states in 1

theoretical

1 9 0

-

2 0 0

pb

9

- j q u a l i t a t i v e agreement with the n

expectations.

Magnetic Moments: The g - f a c t o r s f o r the ( i i 3 / 2 ) measured by ( α , χ η ) f o r (**°Ar,4n) f o r Typical

1 9 2

1 9 6

-

2 0 6

P b [STE83b], ( 0 , 4 n ) f o r 16

s t a t e s have been

2

Pb

l9k

[STE85] and

p b [STE83a] with the PAD technique to high p r e c i s i o n .

r e s u l t s are displayed in F i g . 5. For the matrices employed, Hg and

Pb, Knight s h i f t and diamagnetic s h i e l d i n g c o r r e c t i o n s could be a p p l i e d .

60.

From the data shown in c ^ + · 6 one can see t h a t , in

r. Fig.

403

Electromagnetic Properties

HAAS ET AL.

omr" 1

P

b

020 -

contrast to previous data [R0U77], these r e s u l t s e x h i b i t a very c l e a r trend: The (negative) magnetic

0

moments remain constant between

j

A = 206 and 200 and then show a

j

continuous increase in magnitude

2

Y

ΓΤ/* y

0

-0.20 I

0

E =337 keV * «à A

W \/ V f

*

iff

Y

Α

jk

λ

k

Μ

ifiï

if

τ

IP

I

| BPl '

Γ

\

Λ .I

ft

A

-0 20

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch060

* V V nf τ

' * ^ ; 2oo

of the Ml core p o l a r i z a t i o n

pb

t i v e agreement. For

2 0 6

^_

0.20 ! q

o

""°-

.

777keV

ji

||

j

illfl

i l l j

Γ |

|r|'t n

m 1 L |J |Il

»

j '

20

III

Ë |J|

il ' l| I'll llllBtll

I l llll ψ

J

cated theory [ SPE77] was able to

\

A A i\ Pk |f|Mf Μ ΜΙΜΒΙJ Iftlfli I \ f y Ή 1/ fj/li ΜΤ'^ϊΙ |H IH I R I H fH

o

P b , on the

other hand, a much more s o p h i s t i -

\J. il

' ,*

ever, f a i l i n g to y i e l d a u a n t i t a -

I

«]f f Tim

p a r t l y predicted by c a l c u l a t i o n s [R0U77], the c a l c u l a t i o n s , how-

^lii

ill J)

toward the Schmidt value. Q u a l i t a - 0.00 t i v e l y such a trend has been

ffi

mm

il

*

Pb E =541keV

il Liu II g Κ ' I

«Λ ^

198

Α

0

y

I J it I

Hi

A Af\AK

A 0

'

— %

reproduce the q-factor c o r r e c t l y

I1111I11H111

timers]

with an e f f e c t i v e Ml operator. We

F i

9-

5 :

T

W

i c a 1

s p l n r o t a t l o n curves

have scaled the core p o l a r i z a t i o n c a l c u l a t i o n s with t h i s operator to get a d e s c r i p t i o n of the

1*13/2

c o n t r i b u t i o n to the g - f a c t o r s . Such a treatment

( s o l i d l i n e in F i g . 6) y i e l d s complete agreement f o r the l i g h t e r i s o t o p e s , while near to the closed s h e l l small admixtures to the 13/2 wave f u n c t i o n coming from 3" and 5" core e x c i t a t i o n s can account f o r the remaining discrepancies.

-0.1st, • I Fig.

M •} .

6: g - f a c t o r s for ( i i

3/2)

isomers. Theory

^

J

£ |

x

n

ο Pb

[SPE77] 3",5~ admixtures

*T 0

subtracted Effect of core polarization

)s

£

1

| " '

ι 206

1 202

.

1

1

198

m a s s number

» 194

1

Λ

404

NUCLEI OFF THE LINE OF STABILITY As a b y p r o d u c t

several

lower-lying

obtained.

In general

by t h e use o f

predict

the

Furthermore,

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch060

states

particularly

these Fig.

+

isomers 6,follow

state

range o f

in the

in

(α,χη)

Pb.

for

is properly

as

determined in

possibly

9

»

6

1

9

8

p

D

connected

region

[DUP84],

(29/2,

The v i r t u a l l y

by t h e f a c t

with

thick

n

quasiparticle by t h e

Hg t a r g e t s

that

33/2) pure

+

states

(i13/2)

their

n

1

12

+

+

i n t h e t h e o r y o f Speth e t

to

isomers

'

1 9 9

is

Pb

of in

clearly

and can be

induced core

1 8 8

if

Pb

halflife and

t h e s e have

isomers

a l . [SPE77]

deforma­

in the

for

identify

(113/2)°

1 9 7

included

isomers

are e x p e c t e d f r o m e x t r a p o l a t i o n s experiments

'

5

well.

the 12

a small

Pb i s o t o p e s .

9

character

nature of these states

assumption of

initial

in

g-factors, very

many

The e x p l a n a t i o n

are

core

1 8 6

Pb,

not

quanti­ polarization

for.

[ALB78] [AND78] [DUP84] [MAH79] [PAU73] [ROU77] [SPE77] [STE83a] [STE83b] [STE85] [ZYW81]

References G. Albouy et a l . , Nucl.Phys. A303 521 (1978) C.G. Andersson et a l . , Nucl.Phys. A309 141 (1978) P. van Duppen et a l . , Phys.Rev.Lett. 52 1974 (1984) H.-E. Mahnke et a l . , Phys.Lett. 88B 48 (1979) M. Pautrat et a l . , Nucl.Phys. A201 449 (1973) C. Roui et et a l . , Nucl.Phys. A285 156 (1977) J. Speth, E. Werner, W. Wild, Phys.Reports 33C 127 (1977) Ch. Stenzel et a l . , Hyperfine Interactions 15/16 97 (1983) Ch. Stenzel et a l . , Nucl.Phys. A411 248 (1983) Ch. Stenzel et a l . , Z.Phys. A322 83 (1985) S. Zywietz et a l . , Hyperfine Interactions 9 109 (1981)

RECEIVED

July 15,

1986

1

configurations

in t h i s

are a l s o e x c i t e d .

The m a g n e t i c moments o f t h e

accounted

admixture,

The measured E2 moments f o r

Unfortunately

explained

neutron

seen i n t h e even i s o t o p e s

explained

been s u c c e s s f u l .

all

also

can be r e a c h e d

are t h e 5" s t a t e s

discovered

reactions

the

t h e more n e u t r o n d e f i c i e n t

respectively.

tatively

2 0 5

(i13/2)

10 μ$ and 1

the values

low s p i n o r b i t a l s

A collective

recently

for

for

i s o t o p e s were

discrepancy.

the trend

demonstrate the

for

states

is supported

quantitatively

the

exception

i n t h e odd Pb i s o t o p e s

Conclusions:

tion

explanation

for

g-factors.

straightforward

and t h e 3 3 / 2

e x p e r i m e n t s m a g n e t i c moments

i n the even-even

v a l u e s were f o u n d , w h i l e

intruder

account f o r

isomeric

g-factors

negative

with the proton could

states

[STE85]. A noteworthy

positive

small

the present

a satisfactory

effective

experimentally where s m a l l

of

isomeric

61 ISOLDE Today and Tomorrow B. W. Allardyce

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

ISOLDE, CERN, CH-1211 Geneva 23, Switzerland Isolde is known throughout the world as the on-line isotope separator at the 600 MeV synchrocyclotron at CERN, Geneva. Work has been going on there since 1967 on many topics includino nuclear physics, solid state, atomic physics, etc. There have been great improvements made over the years but it became clear that the physics output could only be i n ­ creased i f there were to be an expansion of the facility. It was decided to build a second on-line separator to be used a l ­ ternately with the existing Isolde, thus doubling the poten­ tial. The new separator is under construction, called Isolde 3, and is scheduled for first operation next year. 1.

Evolution of Isolde

The Isolde separator started to work on-line to the CERN 600 ?«eV synchrocyclotron (SO as long aoo as 1967, when the accelerator was already 10 years old. In those days the SC could produce an extracted proton beam of up to about 50 nA which, combined with the early taroet/ion sources used by Isolde at that time, resulted in on-line ion beams of, for example, Hp isotopes with a maximum intensity of 10 ions/sec. However, this was adequate for the experiments planned then, and Isolde ran successfully for about C* years with Gradually improving techniques. Finally, about 12% of the SC* s beam time was devoted to Isolde physics, or about 800 hours per year. In 1973/4 the lone-awaited SC improvement programme was implemented, and in parallel with it the Isolde group upgraded their installation, from then on labelled Isolde 2. This upgrade converted what had been a fertile series of experiments into an experimental facility. On the accelerator side, the Improvement Programme consisted of fitting a new radiofrequency system, improving the beam optics from the ion source through to extraction, and increasing the extraction efficiency by an order of magnitude with a septum magnet. As a result the SC could deliver beam intensities of 2μΑ to the Isolde target, an increase by a factor of more than 40. 7

0097-6156/86/0324-0406$06.00/0 © 1986 American Chemical Society

61.

407

ISOLDE Today and Tomorrow

ALLARDYCE

In the underground Isolde zone the changes were e q u a l l y dramatic.

The

zone was completely reshuffled so as to gain space, and the separator magnet was moved close to the production target 3m through

:

previously the ion beams d r i f t e d

a concrete s h i e l d i n g wall before reaching the magnet.

The r e s u l t

was a doublinc of the experimental area a v a i l a b l e for p h y s i c s , which could now be

fully

exploited

switchyard

with

four

a f t e r the magnet.

separate

beam l i n e s

from

the

Targets were another area of

the i n t r o d u c t i o n of disposable, s e l f - c o n t a i n e d target/ion

electrostatic

improvement

with

source u n i t s and a

remote target change mechanism, which permitted the f u l l proton i n t e n s i t y be used on a target of thickness of order 100 gm/cm . 2

to

The f i r s t targets to be

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

used were the highly successful a l k a l i producing t a r g e t s . Demand for

beam time at IS2 s t e a d i l y increased a f t e r

the upgrading,

reachinq 1900 hours of physics i n 1980, or 35% of the SC's beam time.

An

a d d i t i o n a l experimental zone of 120 m at ground level was opened in 1978, fed 2

by a v e r t i c a l extension of one of the beam l i n e s in the underaround zone.

In

1982 an i n d u s t r i a l robot was introduced as a more f l e x i b l e way of exchanging target

units.

reliability

Meanwhile

a great

deal

of

work

the

to

of the f a c i l i t y and the l i f e t i m e of the t a r g e t s ,

extend the range of elements a v a i l a b l e as beams. with

was done

303 MeV/amu

3

He

+ +

beam of

the

improve as well

the

as to

Encouraging t e s t s were made

SC which

showed that

for

certain

elements (and e s p e c i a l l y for the isotopes on the n e u t r o n - d e f i c i e n t side of the y i e l d curve), there were considerable gains to be made compared to using 600 MeV protons. results.

The

Beams of 86 MeV/amu main

l i m i t a t i o n in

C were also t r i e d , with l e s s encouraging

l2

both cases was the

i n t e n s i t y , which the SC Group promised to r e c t i f y ,

lack of primary

beam

given s u f f i c i e n t d e v e l -

opment time. By the e a r l y saturated

at

the

1980's i t

level

of

about

became c l e a r 2000 hours

thought had to be given to the f u t u r e . s i z e of the experimental

that of

the

Isolde

was also a l i m i t a t i o n from the manpower occupied keeping the f a c i l i t y

was

and some

Isolde was l i m i t e d by the p h y s i c a l

zones, by the primary proton i n t e n s i t y ,

need to service the equipment in the h i g h l y r a d i o a c t i v e target fully

facility

physics per year,

side,

running,

and by the

zone.

There

since the s t a f f were already developing

new techniques and

producing the roughly 30 consumable target/ion source u n i t s needed each year.

408

NUCLEI OFF THE LINE OF STABILITY Various

to but

SIN where the

scenarios

very

proposal

separator

(IS3)

much

finally

at

future

proton

accepted

in

were

investigated,

intensities December

A c u t - a w a y view o f

1983

accelerator how t h e

including

would have was

been

to

build

primarily

complete

for

facility

a move

available, a

second

Isolde will

for look

1.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

shown i n F i g .

the

t h e SC and t o r u n t h e

4000 h o u r s per y e a r . is

for

higher

Fig.

2.

Present

status of

Currently the

facility

is

there used

1

The S C - I s o l d e

facility

IS2

are

about

by almost

30 e x p e r i m e n t s

200 p h y s i c i s t s .

in

progress

A detailed

at

Isolde,

catalogue

of

and the

61.

beams

available

(Ra84),

409

ISOLDE Today and Tomorrow

ALLARDYCE

at

Isolde

was

presented

last

year

at

the

and a summary o f w h i c h e l e m e n t s can be produced i s

Zinal

workshop

shown i n F i g .

2.

PERIODIC TABLE OF THE ELEMENTS 1A

vaiA

H T

HA

u

B.

Ψ Mg nm

\ T.

B c • Si

\

Gt

ï.

ιν· «· «· vw . »w . ι· Η· Al v Cr τ F t Co Ni i» V la

l e Ti

It \a

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

VA VIA VIIA

T

V

To

MIA IVA

Tr la

T

V

Zr

Nb Mo

La

Hf

Ta

Mn Tc Ru

Rh

Pd

Rt

Ir

Pt

W

Os

W

*

?

F

0

P

s l

pu I.

î,

l T,

Sn ^ b

J . Tl, Ti t b ς.

^. « In r

,

T

Ac

CTiwocs-j-Th j Ρα j U | Np | Pu | Am| Cm| Bk | Cf | E t | Fm|Md | No | Lr |

Elomontt

ΓΠ

Fig.

Of

2

o v a l l o b l o a l ISOLDE

Summary o f t h e e l e m e n t s a v a i l a b l e

t h e 66 e l e m e n t s which may be p r o d u c e d ,

from the t a r g e t ,

which means ~ 1 0

for

a 1 μΑ p r o t o n

for

these

could

beam,

and

e l e m e n t s no f u r t h e r

benefit

from

source

has

Isolde

;

target/ion being this

it

found

recently

been

results ;

direct

in

for

in

in

in

order

there

example,

source many

at

Isolde

and

being

is

will

several

different

cases

the

the

the

in

the

different

yield

The

release

of

the

the of

developed

version

become

cathode

versions

;

source.

latest

different

curve

remainder

plasma source

and/or

yield

selectivity

of

standard

surface.

to the p a r t i c u l a r

yield

require

or

gradually of

the

necessary.

The

has t o be t a i l o r e d optimise

of

i n t o the ion

laboratories.

heating

peak

have a h i g h

good c h e m i c a l is

selectivity

completed

to

the

work

resistive

source c o m b i n a t i o n

performed,

source

ion

sources

has

development

at with

from the t a r g e t m a t e r i a l

The most p o p u l a r FEBIAD

available

improvements

desired r a d i o a c t i v i t y

from

are

Isolde

r o u g h l y one h a l f

atoms/sec

n

at

at The

experiment

selectivity, the

this

and

target/ion

temperatures

in

the

410

NUCLEI OFF THE LINE OF STABILITY

transfer source

tube

are

positive units

between

also

target

frequently

and n e g a t i v e .

which

was

task

in

its

source.

the

in

effect

improvement

to the f a c i l i t y

This

on

production of

other

than

ionisation of

the

the

plasma

source,

both

target/ion

source

manpower.

development

doses

to

the

has been t h e

has

been

very

personnel.

addition

the underground area t o the experimental

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

surface

are exchanged by means o f t h e i n d u s t r i a l

1982.

especially

3.

Sources

the

and r e q u i r e s a l o t

source u n i t s

purchased

ion

notably

Consequently

i s not a t r i v i a l Target/ion

and

used,

of

robot

successful,

Another

recent

a second beam l i n e

a r e a a t ground f l o o r

from

level.

P r o g r e s s on IS3

The near t o cost

to

location

an a c c e p t a b l e

on t h i s

basis that

target that

ideal

for

IS3 would

I S 2 , but t h e c o s t e x c l u d e d t h i s

had this

to

be

situated

could

in

two

alternately

from

to maintain

the

be housed separate the

planned t o use t h e

was f i n a l l y

inside

and

SC,

been

was t o make use o f

the p r o j e c t

implied,

experiments results

level

have

solution.

the

the

Isolde with

(Ce83). spite

to

be

a switch-over source

line

for

of

of

for

was the

of

the t a r g e t s

can

an hour

the

two

the

and i t

the

Hall"

which

time

pots

zone

As a r e s u l t

inconvenience

designed

"Proton

installations

same t a r g e t / i o n

o n l y one p r o d u c t i o n

in

had

existing

a new u n d e r g r o u n d

existing buildings,

accepted

SC v a u l t

separator in

in

The o n l y way o f k e e p i n g

so

that

the

the

SC.

This

receive

beam

or

so.

It

separators,

is

so as

and t h u s keep c o s t s t o a

minimum. The new s e p a r a t o r optical be

throughout,

beam e n v e l o p e the

design. wall

to

normal

Isolde

a focus

to

formance o f

beams the

Auxiliary

the

will

be

;

coils

the

are

and in

order

to

intention

is

to

able

to

8m t h r o u g h

separator

magnet,

an e l e c t r o s t a t i c the

measure

be

source d e v e l o p e d

optics

t o be r e a l i s e d .

used

Electrostatic in

transported 90°

in the t a b l e ,

(14 cm)

and a s l i t

first

aberrations

separator

aperture

source

sources

ion

before

correct

magnet

a wide

from a s l i t

field.

used

first

with

Unseparated

uniform be

listed

p r o p e r t i e s o f t h e beam are shown i n F i g . 3 .

used

both

has t h e c h a r a c t e r i s t i c s

and

The f o c a l the

beam

the

which

permit

plane

lenses

accomodate to

run

from the

multipole to

and t h e

the with

Isocelle

SC

shielding

has

a

highly

element the

chamber

properties,

will

and

will

best

per-

after to

the

select

61.

the d e s i r e d 60°

Proton

Fig.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

isotope.

magnet,

and

A second stage o f

the

beam

3 C a l c u l a t i o n s of in

plane

the

finally

s e p a r a t i o n then f o l l o w s , distributed

to

the

via a

experiments

similar in

the

from

the

source

through

focus

the

after

bending

the

horizontal

bottom r i g h t

at

to

a

second

magnet.

Table

Two-stage

-

;

to

power o f

t o r e a c h ~30,000 w i t h

be t r a n s p o r t e d

to

the

first

~5000 a t

high

slits. magnet

:

3mA u s i n g

a

source.

-

Acceleration

-

Dispersion

v o l t a g e 60 kV maximum. after

beam; t h e f i r s t Enhancement factor

a combined r e s o l v i n g

possibility

Maximum c u r r e n t slit

Parameters of the I s o l d e 3 s e p a r a t o r

separation with

transmission

-

is

Hall.

beam

-

411

ISOLDE Today and Tomorrow

ALLARDYCE

of 1 0

the f i r s t focal

factor 2

to 10

"ΙΟ * f o r 1

4

magnet

> 12 mm per %, p e r p e n d i c u l a r

p l a n e t o c o v e r a mass range o f the

first

stage,

to

the

± 10%.

increasing

i n t h e second s t a g e and by t u n i n g .

by a f u r t h e r

412

NUCLEI OFF THE LINE OF STABILITY The

power

supplies

for

the

Faraday cage i n t h e P r o t o n H a l l , high

voltage

designed

for

tube

of

very

high

low c a p a c i t y . stability

t h e s u p p l i e s f r o m a commercial as at

IS2,

cations.

is

generated

in

the e f f e c t has

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

which

of

have o v e r

Control

of

the

in t h i s pared,

domain. much o f

made on t h e

several

the

i s not

at

commercial

(1 in 1 0 ) .

ease o f

especially

One o t h e r

be

by

room, c l o s e is

a

to

the

high

to

energy

minimise

computers. advantage

voltage

sup-

zone.

microprocessor

and work

is

based

progressing

t o t h e SC c o n t r o l available

are

fed

specifi-

important

a highly radioactive

will

a

The h i g h v o l t a g e , 60 kV

e q u a l l y demanding

access

in

and

Power i s

5

equipment,

IS2.

CERN i n t e r f a c e s ,

CAMAC hardware

room,

already,

is

serial rapidly

being

and a s t a r t

pre-

has been

software.

The s e p a r a t o r

is

participating

laboratories.

have a l r e a d y a r r i v e d and a l l

experimental

separator

A control

are

housed

i s being paid t o keeping the stored

problem

IS2 i s

standard

the

supplies

be

specially-designed

s h i e l d i n g and Faraday cages i n o r d e r t o

since the Proton Hall

CAMAC system u s i n g

the

a home-made s u p p l y w i t h

a considerable

IS3 w i l l

plies,

All

will by a

isolation transformer.

s p a r k i n g on o t h e r

been

source

t o the t a r g e t

and low r i p p l e

A g r e a t deal o f a t t e n t i o n

t o a minimum and t o i n t r o d u c e

This

target/ion

joined

the c i v i l

Most

in

a collaborative

pieces

; t h e magnets t h e m s e l v e s

part

Proton

to

prior

of

the separator

mounting

it

in

its

in

way by CERN and

are d e s i g n e d

and

are t o be d e l i v e r e d

e n g i n e e r i n g work has been c o m p l e t e d .

assemble t h e f i r s t Hall

being constructed

the

correct

near

It

in

items

October,

i s our i n t e n t i o n

future

place

some

for

during

tests the

in

Spring

to the of

1986.

4.

Future

possibilities

Although exotic i o n s or t h e i r

storage

p l a n s t o proceed i n

possibilities in

a storage

t h i s way.

a w a i t o n l y t i m e and manpower.

such as t h e a c c e l e r a t i o n

ring

However,

of

radioactive

have been d i s c u s s e d t h e r e are no two development

areas

are c l e a r ,

firm and

61.

ISOLDE Today and Tomorrow

ALLARDYCE

The use o f a

3

He

beam o f 303 MeV/amu has a l r e a d y

+ +

an advantage i n c e r t a i n c a s e s , e s p e c i a l l y a beam i s a l s o the

advantageous

SC v a u l t .

sufficient compared

However,

intensity

t h e SC's i o n

factor

3 or

He

+ +

in that

the

3

make

4 to

intensity

source

to

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch061

Ion

sources

the

are a l s o

on-line

sources

elements

include

available

ECR sources

the

an

been

produced

interesting

intensity

proposition

an i n t e n s i t y

> 10

1 3

system

gain

has n o t been t e s t e d . (i.e.

in

with

have been made t o t h e r . f .

this

as Such

induced r a d i o a c t i v i t y

so f a r

now p e r m i t

so f a r

proton

use

been mentioned

f a r from s t a b i l i t y .

less

has n o t

frequent

but

of If

ions/sec),

a

the this

I s o l d e p r o d u c t i o n beam o f t h e f u t u r e .

an a r e a where i t

i s p l a n e d t o make

and manpower

laser

source

but w i l l

(where t h e p r o b l e m w i l l

high-temperature,

produces

beam

should

i s working

to Isolde

for nuclei

Improvements

beam c o u l d become t h e p r e f e r r e d

once t h e new s e p a r a t o r

it

+ +

which

be a c h i e v e d ,

rises

He its

t o 600 MeV p r o t o n s .

and t o

3

to

413

is

(which

certainly

liberated. will

probably

improvements, New i d e a s

for

n o t make new

improve t h e s e l e c t i v i t y ) ,

and

be t o adapt e x i s t i n g ECR t e c h n o l o g y t o t h e

high r a d i a t i o n environment of the Isolde

separator).

References

[Ra84] H. Ravn in "Zinal 1984, Workshop on the Isolde Programme beyond 1985". Also as an Appendix in Proceedings of TRIUMF-ISOL Workshop, Mont Gabriel, June 1984, TRI-84-1. [Ce83] CERN PSCC-83-27: The Isolde Project. RECEIVED

July 18, 1986

62 A New Heavy-Ion Facility at Chalk River J. C. Hardy

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch062

Atomic Energy of Canada, Limited, Chalk River Nuclear Laboratories, Chalk River, Ontario K0J 1J0, Canada

The Tandem Accelerator Superconducting Cyclotron facility at Chalk River, which is nearing completion of phase 1, will be cap­ able of accelerating a l l ions to at least 10 MeV/u. Together with the on-line isotope separator it will provide a powerful means of studying exotic nuclei. D u r i n g phase 1 o f c o n s t r u c t i o n o f t h e Tandem A c c e l e r a t o r S u p e r c o n ­ d u c t i n g C y c l o t r o n (TASCC) f a c i l i t y a t C h a l k R i v e r , t h e e x i s t i n g tandem a c c e l ­ e r a t o r was r e v e r s e d , a s u p e r c o n d u c t i n g c y c l o t r o n b u i l t and some 60 m e t r e s o f b e a m - t r a n s p o r t l i n e i n s t a l l e d t o c o n n e c t t h e two and t o d e l i v e r beams t o an "interim target l i n e " . The r e s u l t , w h i c h r e q u i r e d an a p p r e c i a b l e b u i l d i n g e x t e n s i o n , i s shown i n f i g u r e 1, As o f e a r l y September, 1985, t h e f a c i l i t y i s b e i n g c o m m i s s i o n e d . C a r ­ bon, n i t r o g e n and o x y g e n beams f r o m t h e tandem have r e a c h e d t h e i n t e r i m t a r ­ get l o c a t i o n s v i a t h e b y p a s s l i n e , and an i o d i n e beam has been i n j e c t e d i n t o the c y c l o t r o n . F i r s t attempts to a c c e l e r a t e i o d i n e i n the c y c l o t r o n a r e imminent. Some e x p e r i m e n t a l e q u i p m e n t , i n c l u d i n g t h e o n - l i n e i s o t o p e s e p a r ­ a t o r [SCH81J, i s a l r e a d y s e t up and u n d e r g o i n g t e s t s w i t h tandem beams.

PATH OF BEAM UNE TO TARGET ROOMS (PHASE 2)

INTERNA TARGET UNE (PHASE 1)

TANDEM ACCELERATOR SUPERCONDUCTING CYCLOTRON (TASCC PHASE 1)

Fig.

1. Artist'8 impression of phase 1 of the TASCC f a c i l i t y . Shown in dashed l i n e s is the beam delivery system to 11 target locations, planned for phase 2. This second phase, which is not yet funded, u t i l i z e s e x i s t i n g target rooms. 0097-6156/86/0324-0414S06.00/ 0 © 1986 American Chemical Society

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch062

62.

HARDY

Heavy-Ion Facility at Chalk River

415

When i t reaches i t s f u l l c a p a b i l i t y , TASCC w i l l a c c e l e r a t e a l l ions between l i t h i u m and uranium to energies up to 50 MeV/u and 10 MeV/u, respec­ tively. I t w i l l feed some major pieces of apparatus: the Q3D magnetic spec­ trometer, the isotope separator, a growing array of gas and s o l i d - s t a t e detectors housed i n a 1,5 m diameter s c a t t e r i n g chamber, and the "8π" γ-ray spectrometer [AND 84], A l l are c u r r e n t l y o p e r a t i o n a l except the 8 π s p e c t r o ­ meter, which i s being b u i l t by a consortium of Canadian u n i v e r s i t i e s and AECL Chalk R i v e r , with completion scheduled f o r l a t e 1986. It w i l l comprise two subsystems: i ) a s p i n spectrometer of 72 bismuth germanate (BGO) d e t e c t o r s , and i i ) an array of 20 Compton-suppressed hyperpure (HP) Ge d e t e c t o r s . At the completion of phase 2, these devices and others w i l l be served by the beam l i n e s shown dashed i n f i g u r e 1. However, phase 2 i s not yet funded, so i n the meantime somewhat r e s t r i c t e d conditions w i l l p r e v a i l . The Q3D, which i s already s i t e d at T10, w i l l be i n a c c e s s i b l e , the isotope separ­ ator w i l l only be on-line v i a a He-jet coupling and the remaining experimen­ t a l equipment w i l l be strung end-to-end at the i n t e r i m target l i n e to o f f e r as broad a scope as p o s s i b l e f o r u t i l i z i n g the new beams as they appear. Although TASCC i s not the f i r s t i n i t s energy range, i t j o i n s a very s e l e c t group of f a c i l i t i e s worldwide with v e r s a t i l e c a p a b i l i t i e s at t r a n ­ s i t i o n a l energies. As such, TASCC opens up many e x c i t i n g experimental possibilities. For the purposes of t h i s symposium, I s h a l l focus on those i n the f i e l d of n u c l e i f a r from s t a b i l i t y . Accelerator F a c i l i t y The a c c e l e r a t i o n process begins with negative ion generation i n the 300 kV i n j e c t o r followed by a c c e l e r a t i o n i n the tandem at voltages up to 13 MV. The beam i s bunched into timed pulses by passing i t through a gridded-gap prebuncher be­ fore the tandem and a twogap drift-tube buncher between the tandem and the cyclotron. The l a t t e r pro­ duces a time focus when the beam bunches reach a s t r i p ­ per f o i l located i n a mag­ n e t i c v a l l e y near the center of the K=520 c y c l o t r o n (see f i g u r e 2). The f o i l , whose position i s radially adjust­ able, i n t e r c e p t s the beam j u s t where i t becomes tan­ gent to the radius appro­ p r i a t e f o r i t s energy and resulting charge state. Once the beam has been accelerated to a radius of 650 mm, turn separation i s increased and i t enters an e l e c t r o s t a t i c channel where it i s deflected into the magnetic e x t r a c t i o n channel. Fig. 2. Cutaway Chalk River cyclotron.

view of the superconducting

416

NUCLEI OFF THE LINE OF STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch062

The c y c l o t r o n i t s e l f IHUL85] forms a s i n g l e 4-dee resonant s t r u c t u r e . Because the c e n t r a l axis i s not required f o r i o n sources, i t accommodates two c o a x i a l - l i n e tuners, each supporting a pair of dees located i n the magnetic valleys. Tne magnet i s excited by two superconducting niobium-titanium c o i l s , which are copper s t a b i l i z e d . Fine tuning of the f i e l d i s accomplished by a d j u s t i n g the p o s i t i o n s of 104 s a t u r a t e d - s t e e l trim rods, which penetrate through the upper and lower magnetic h i l l s . Small superconducting c o i l s are used i n the magnetic e x t r a c t i o n channel. So f a r , beams have not yet been a c c e l e r a t e d i n the c y c l o t r o n , although that should happen w i t h i n days. A beam of 127χ7+ been i n j e c t e d to the s t r i p p e r f o i l and the r e s u l t i n g charge states were d i s t i n g u i s h e d on a r a d i a l probe by t h e i r d e f l e c t i o n i n the c y c l o t r o n magnetic f i e l d . At 71 MeV, the most probable charge state was observed to be 23, i n reasonable agreement with expectation [HEI85]. The Οα-liae Isotope Separator The Chalk River isotope separator has been operating o n - l i n e with the tandem a c c e l e r a t o r since A p r i l 1979. When the tandem shut down i n 1982, the separator was completely dismantled and reassembled with some improved com­ ponents at i t s present l o c a t i o n , where i t w i l l be o n - l i n e with TASCC (see f i g u r e 1). It i s now working again and, although recommissioning i s not yet complete, i t has already achieved some of the e x c e l l e n t performance char­ a c t e r i s t i c s met before the move. A p i c t u r e of the relocated instrument appears as f i g u r e 3. L i k e most other o n - l i n e isotope separators (ISOLs), the Chalk River device was p r e v i o u s l y operated with i t s i o n source e s s e n t i a l l y i n l i n e with the primary a c c e l e r a t o r beam so that n u c l e i produced by reactions i n a target would r e c o i l d i r e c t l y into the ISOL i o n source. We used a FEBIAD i o n source [KIR76], which was characterized by long cathode l i f e t i m e and good e f f i c i e n c y for a wide v a r i e t y of elements.

Fig.

à. View of a portion of the relocated ISOL. The vmage plane of the V6b° inhomogeneous magnet is in the large central chamber; the selected beam is deflected H0° and conveyed through the beam line at the top left to a counting area.

62.

HARDY

Heavy-Ion Facility at Chalk River

417

Fig. 4. The C0-N doublet at mass 28 mea­ sured with the Chalk River ISOL and a FEBIAD ion source; the resolving power is 20,000. With a slit-geometry source 16,000 has been obtained. (The separ­ ation between the two peaks is 10.5 MeV.) 2

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch062

VOLTAGE (VOLT)

For the time being with TASCC, such a d i r e c t coupling i s impossible since phase 1 does not provide magnetic beam transport elements to the ISOL ion source. Instead, a He-jet system, i n which r e c o i l n u c l e i are thermalized i n helium gas, has been coupled by c a p i l l a r y to an ion source through a skimmer LHAR84] · A s p e c i a l source has been b u i l t f o r the purpose with an e x t r a c t i o n s l i t of 1 mm χ 30 mm ( c f . a 1 mm d i a . hole f o r the FEBIAD), which allows f o r the n e c e s s a r i l y high throughput of helium. The ISOL i t s e l f was o r i g i n a l l y designed to accommodate s l i t geometry, high beam currents and a large gas l o a d . Preliminary tests of t h i s system before the tandem shut down i n d i c a t e d that e f f i c i e n c y of a few percent i s achievable. The q u a l i t y of separated beams from the Chalk River ISOL has always been very high. Both the 40 kV a c c e l e r a t i n g voltage and the f i e l d i n the 135° inhomogeneous magnet are highly s t a b i l i z e d ( 0 . 1 5 % ) , dc beam f r o m t h e ISOL, w i t h good e f f i c i e n c y . T h i s i s b e s t a c c o m p l i s h e d by some f o r m o f r a d i o f r e q e n c y q u a d r u p o l e (RFQ) s u c h as one b u i l t a t GSI f o r q/A > 1/130 [MTJL84] , o r a low f r e q u e n c y v e r s i o n (~23 MHz) o f the Los Alamos f o u r vane s t r u c t u r e . A p r e l i m i n a r y d e s i g n o f t h e l a t t e r v e r s i o n , done a t CRNL f o r q/A > 1/40, a peak f i e l d o f 1.5 K i l p a t r i c k s , and an o p e r a t i n g f r e q u e n c y o f 23 MHz, has a c a l c u l a t e d c a p t u r e e f f i c i e n c y o f a b o u t 86% f o r a 0.1 π cm/mrad ( n o r m a l i z e d e m i t t a n c e ) ISOL beam [BUC85]. At some p o i n t between 60 and 100 keV/amu the beam may be s t r i p p e d and i n j e c t e d i n t o a p o s t - s t r i p p e r section. T h i s l a t t e r s e c t i o n can be b a s e d on e x i s t i n g LINAC d e s i g n s s u c h as the UNILAC, HILAC o r RILAC. As an i l l u s t r a t i o n o n l y , a p o s s i b l e p o s t - a c c e l e r a t o r l a y o u t , i n i t i a t e d f o l l o w i n g d i s c u s s i o n s w i t h H. K l e i n [ K L E 8 4 ] , i s shown i n F i g . 4, a l o n g w i t h the a s s o c i a t e d experimental area. A f o i l s t r i p p e r i s i n s e r t e d at 100 keV/amu t o i n c r e a s e the c h a r g e - t o - m a s s r a t i o and m i n i m i z e the l e n g t h o f t h e a c c e l e r a ­ tor. The s i n g l e gap s e c t i o n s shown can be s w i t c h e d on o r o f f i n d i v i d u a l l y as w e l l as a d j u s t e d by t h e i r r e l a t i v e RF p h a s e s t o g i v e the r e q u i r e d i o n e n e r g y variation. A d e b u n c h e r i s a l s o p r o v i d e d t o t a i l o r t h e beam t o meet the 2

436

NUCLEI OFF THE LINE OF STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch065

required energy r e s o l u t i o n . This system, operating at CW, would require an estimated 4 MW of RF power. Other s i m i l a r s o l u t i o n s can be envisaged which use less power but may not meet a l l of the s p e c i f i c a t i o n s . A more complete d i s c u s s i o n of such i n i t i a l concepts of the TRIUMF-ISOL p o s t - a c c e l e r a t o r i s found elsewhere [PR085], [DAU85]

V A U L T W A L L

Fig.

4.

A p o s s i b l e RFQ LINAC Post-Accelerator layout and experimental area.

At present, a d e t a i l e d examination of the LINAC c o n f i g u r a t i o n i s being c a r r i e d out. This includes a r e a l i s t i c estimate of the RFQ a c c e l e r a t o r e f f i ­ ciency, the d e t a i l e d arrangement of the subsequent LINAC sections i n c l u d i n g intertank matching, the p o s i t i o n i n g ( i n energy), the type and e f f i c i e n c y of the s t r i p p e r , and the energy r e s o l u t i o n that can be expected. This w i l l be followed by preparation of r e a l i s t i c cost estimates and an implementation schedule. The r e s u l t s of t h i s study, supplemented by the proceedings of the r e c e n t l y completed TRIUMF Radioactive Beams Workshop held i n September 1985, w i l l be a v a i l a b l e as a f u l l proposal l a t e t h i s year 1985. It i s expected that the e n t i r e TRIUMF-ISOL proposal w i l l be reviewed f o r funding i n 1986. TISOL The f i n a l s e l e c t i o n of the appropriate target and ion source f o r the ISOL to produce such intense beams of the i n i t i a l p r o j e c t i l e s of i n t e r e s t , namely N, 0, F , Ne, and Na, requires considerable research and development. In general these species have not been of i n t e r e s t at present ISOL f a c i l i t i e s and conditions to optimize t h e i r y i e l d s require i n v e s t i g a t i o n . Table II presents the highest y i e l d s observed along with t a r g e t / i o n source (TIS) combinations used [RAV85]. Tests are presently underway to develop new TIS systems f o r these s p e c i e s . Due_ to the rather n o n - s p e c i f i c nature of t h e i r decay emissions, and the absence of any l o n g - l i v e d isotopes of these elements to be used as t r a c e r s , a small ISOL i s being i n s t a l l e d at TRIUMF t o perform such development studies, along with other proposed uses. This i s scheduled for commissioning i n the summer of 1986. The system w i l l be used f o r l i m i t e d beam current (1 μΑ)/target thickness ( 50% and can reach l e v e l s as high as 70%. Therefore, allowing f o r s i m i l a r chemistry l o s s e s , we expect that i n those s e l e c t e d cases where isotope separation r e c o v e r i e s are ~ 50%, the amount of i n i t i a l m a t e r i a l required to make a reasonable number of usuable targets can be as low as ~ 100 ug. The amount of i n t i a l m a t e r i a l required can also be reduced somewhat by paying more a t t e n t i o n to i n c r e a s i n g the e f f i c i e n c i e s of the wet-chemistry y i e l d s . Proposed future work i n our group w i l l continue to i n v o l v e the need f o r special targets. In p a r t i c u l a r , we are i n v e s t i g a t i n g techniques to prepare r a d i o a c t i v e targets of Eu (30y) and Ac (22y) f o r charged-particle spectroscopy work. Each of these targets present s p e c i a l problems which are outside our range of experience and o f f e r considerable t e c h n i c a l challenge. Beyond that, we have begun a program to measure l i g h t - i o n c h a r g e d - p a r t i c l e cross sections by a c t i v a t i o n and in-beam techniques. A c t i v a t i o n studies require the use of many separate target f o i l s . Moreover, each f o i l must be homogeneous and each must have a thickness known a c c u r a t e l y to a few percent. 1 5 0

2 2 7

NUCLEI OFF THE LINE OF STABILITY

Table I I . Yield summary for Original material Mass (ug) Relative yield Cumulative yield

170 (%) (%)

—

3

148

G d target preparation.

Electro­ Initial cleanup . deposition

Isotope separation

132

99

4

78

75

4

78

58

2

0

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch072

The i n i t i a l amount of Gd was determined by alpha-counting a small aliquot from the new sample. The chemical yields were determined by gamma-counting techniques. The sample contained a number of radioactive isotopes of gadolinium prior to Isotope separation. c

The assay of the f i n a l targets was obtained by back alpha-counting and xray fluorescence techniques.

We are experimenting with two schemes to prepare targets for cross-section measurements. The f i r s t is forming a self-supporting "ceramic" target which can be prepared from a metal oxide. This procedure has been used by Quinby, who prepared self-supporting oxide targets with thicknesses i n the range 1502500 ug/cm from several materials. An alternate technique involves producing thin Kapton plastic sheets (1-2 mil) which contain accurately known amounts of any material. The only requirement for the target material i s that i t i s in the form of a powder and that the natural particle size is small enough so that i t can be homogeneously mixed (coated) with the liquid plastic base before spreading and curing. Both techniques show considerable promise for making cheap, high quality targets- for light-ion studies when low-Z element contamination can be tolerated. Acknowledgment s This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. I am grateful to Mr. David Sisson for his work with the electro­ deposition procedures and to Mr. Thomas Massey for conducting the f i n a l purification chemistries.

References 1. C. M. Jensen, W. M. Buckley, R. G. Lanier, G. L. Struble, S. G. Prussin, and D. H. White, Nuclear Instrum. and Methods 135, 21 (1976). 2. C. M. Jensen, R. G. Lanier, G. L. Struble, L. G. Mann, and S. G. Prussin, Phys. Rev. C 15, 1972 (1977). 3.

S. G. Prussin, R. G. Lanier, G. L. Struble, L. G. Mann, and Schoenung, Phys. Rev. C 16, 1001 (1977).

S. M.

72.

LANIER

481

Nuclear Reaction and Spectroscopic Studies

4. R. J . Dupzyk, C. M. Henderson, W. M. Buckley, G. L. Struble, R. G. Lanier, and L. G. Mann, Nuclear Instrum. and Methods 153, 53 (1978). 5. Jean Kern, University of communication (1985).

Fribourg, Fribourg,

Switzerland,

private

6. See H. E. Martz, R. G. Lanier, G. L. Struble, L. G. Mann, R. K. Sheline, and W. Stöffl, Nucl. Phys. A439, 299 (1985) and references therein. 7. D. Mueller, R. T. Kouzes, R. A. Naumann, G. L. Struble, R. G. Lanier, and L. G. Mann, Bull. Am. Phys. Soc. 23, 91 (1978). 8. R. A. Dewberry, R. T. Kouzes, R. A. Naumann, R. G. Lanier, H. Börner and R. W. Hoff, Nucl. Phys. A399, 1 (1983). Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch072

9. Κ. E. Thomas, Radiochimica Acta 34, 135 (1983). 148

10. A preliminary target of Gd was prepared earlier with a somewhat less rigorous technique. Experimental studies with this target have been published in E. R. Flynn, J . van der Plicht, J . B. Wilhelmy, L. G. Mann, G. L. Struble, and R. G. Lanier, Phys. Rev. C 28, 97 (1983). 11.

"Fabrication of Self-Supporting Oxide Targets by Cationic Adsorption in Cellulosic Membranes and Thermal Decomposition," Thomas C. Quinby in Proceeding of Workshop 1983 of the International Nuclear Target Develop­ ment Society, Argonne National Laboratory, Argonne, IL, Sept. 7-9, 1983. ANY/PHY-84-2.

12. Trademark Ε. I. Du Pont de Nemours & Co. (Inc.) Wilmington, DL 19898. RECEIVED

July

15, 1986

73 Rapid, Continuous Chemical Separations J. V. Kratz, N. Trautmann, and G. Herrmann

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch073

Institut für Kernchemie, Universität Mainz, D-6500 Mainz, Federal Republic of Germany

We report on a number of on-line chemical procedures which were developed for the study of short-lived fission products and products from heavy-ion interactions. These techniques combine gas-jet recoi1-transport systems with I) multistage solvent extraction methods using high-speed centrifuges for rapid phase separation and II) thermochromatographic columns. The formation of volatile species between recoil atoms and reactive gases is another alternative. We have also coupled a gas-jet transport system to a mass separator equipped with a hollow cathode- or a high temperature ion source. Typical applications of these methods for studies of short-lived nuclides are described. 1. Introduction Nuclear reactions producing exotic nuclei at the limits of stability are usually very non-specific. For the fast and efficient removal of typically several tens of interferring elements with several hundreds of isotopes from the nuclides selected for study mainly mass separation [Han 79, Rav 79] and rapid chemical procedures [Her 82] are applied. The use of conventional mass separators is limited to elements for which suitable ion sources are available. There exists a number of elements, such as niobium, the noble metals etc., which create problems in mass separation due to restrictions in the diffusion-, evaporation- or ionization process. Such limitations do not exist for chemical methods. Although rapid off-line chemical methods are s t i l l valuable for some applications, continuously operated chemical procedures have been advanced recently since they deliver a steady source of activity needed for measurements with low counting efficiencies and for studies of rare decay modes. The present paper presents several examples for such techniques and reports briefly actual applications of these methods for the study of exotic nuclei. 0097-6156/ 86/ 0324-0482$06.00/ 0 © 1986 American Chemical Society

73.

Rapid, Continuous Chemical Separations

KRATZ ET AL.

483

2. Combination o f a g a s - j e t w i t h the s o l v e n t e x t r a c t i o n

N u c l e a r r e a c t i o n p r o d u c t s r e c o i l i n g o u t o f a t h i n s o l i d t a r g e t are s t o p p e d

in

nitrogen

to

these are

gas

containing

aerosols

(usually

inorganic

aerosols used)

chamber

are

transported

through

dissolution solvent

of

a

the

extraction

Η-centrifuges

along

capillary clusters in

in

at

the

thermalised

clusters with

to

static

operated

and

like

the

the

carrier

SISAK

attached

gas

system.

out

of

The

latter

the

20000

with

rpm.

separation

Fig.

FP

3

of

the

system SISAK I I

0.7MNQ0H

2ΜΗΝΟ3ΟΓ 0.8H HNO3

multistage

two

1 shows s c h e m a t i c a l l y

stopping provides

an aqueous s o l u t i o n and subsequent mixers

0.1M HN0 0.1 M KB1-O3

Fig.

products

p o t a s s i u m c h l o r i d e [ Ste 80]

f o r the i s o l a t i o n o f technetium w i t h the c e n t r i f u g e

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch073

system SISAK

phases the

in

set-up

[Ska 80] .

0.1M HN0

3

1 Flow-sheet f o r the continuous separation o f technetium [ Bro 8 1 ] f r o m f i s s i o n p r o d u c t s w i t h t h e c e n t r i f u g e system SISAK I I . DG = d e g a s s i n g u n i t , D i , D2 = d e t e c t o r p o s i ­ t i o n s , C I , C2, C3 = m i x e r - c e n t r i f u g e u n i t s , C = c o l u m n , FP = f i s s i o n p r o d u c t s 239

The

reaction

(700 μg static

2 3 9

Pu;

6 χ 10

mixer

potassium

oxidation

with

bromate.

dissolution

into

products

of

of

technetium molybdenum,

1 1

induced

consisting

solution

is

of

heated

together

with

80°

the

0.1 M

products

the

and

the fed

removed

and

and

accelerate

are

extracted

zirconium

acid

C to

reaction

by

suction.

into

0.05

and n i o b i u m

In

the

first

M Alamine-336 are

in

co-extracted.

t e c h n e t i u m i s back e x t r a c t e d w i t h 2 M o r 0 . 8 M n i t r i c (C3)

Pu

are d i s s o l v e d i n a

0.1 M n i t r i c to

of

where t h e c a r r i e r gas and t h e f i s s i o n n o b l e gases

is

the p e r t e c h n e t a t e .

fission

The g a s - l i q u i d m i x t u r e i s

and

zirconium

neutron

2

clusters

unit

thermal

n / c m - s ) c a r r i e d by a K C l / N - j e t

solution

The

the

the 2

technetium to

a degassing

separated

a

from

niobium

contaminations

are

mixer-centrifuge

unit

chloroform.

Traces

In

step

the

acid. removed

next

In a t h i r d by

of (C2)

stage

extraction

NUCLEI OFF THE LINE OF STABILITY

484 into

di(2-ethylhexyl)

orthophosphoric

acid

(HDEHP).

phase c o n t a i n s o n l y t e c h n e t i u m n u c l i d e s , t h e i r

The

outgoing

aqueous

d a u g h t e r p r o d u c t s and a s m a l l

c o n t a m i n a t i o n o f molybdenum. The

decay o f

36-s

even i s o t o p e s spin 108

1 0 6

Ru were

these

s e v e r a l models

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch073

Recently,

the

neutron-rich 136

1 0 8

5-s

1 0 8

Tc

into

excited

R u was s t u d i e d i n d e t a i l .

multipole

obtained. of

and o f

R u and

assignments,

structure

Tc

1 0 6

With

mixing this

ratios

rather

transitional

and

B(E2)

complete

nuclei

could

SISAK

Xe p r o j e c t i l e s

the

technique

set

has been a p p l i e d

isotopes

and t a r g e t s

centrifuge with

reaction

TiCl^.

is

formed 244

of

products

With

pumped

of

in

for

direct

^ R u

and

the

collective

in detail

the

separation

with

of

transfer reactions

new,

between

accelerator.

u n i t s and a d e g a s s e r .

dissolved in a s t a t i c

neptunium

the

products

in

the

is

degassing

reduced unit

and

a c i d causes

this

is

it

mixer-centrifuge. the

are e x t r a c t e d

into

the

m i x e r i n 0 . 6 M HC1

to

the

3

is

fed

into

organic

state.

+

a

The

mixer-

together

phase

the o x i d a t i o n o f neptunium t o the 4

extracted

into

HDEHP

7%

in

CCI

in

4

Complexing a g e n t s keep t h e f i s s i o n p r o d u c t s

last

with

whereas

aqueous p h a s e . The aqueous phase i s mixed w i t h 6 M

HNO^. The n i t r i c

In

for

Pu a t t h e UNILAC h e a v y - i o n

are

Ti C l ^

through

fission

neptunium remains

phase.

data

even-

schemes,

and c o n t a c t e d w i t h 5% HDEHP i n C C I ^ . T h o r i u m and u r a n i u m

several

form

the

step o f the separation procedure the KC1-clusters together

attached

mixture

values

be c o n f r o n t e d

The SISAK system c o n s i s t e d o f t h r e e m i x e r - c e n t r i f u g e

containing

of

S t a 84 .

neptunium

In the f i r s t

levels

Extended l e v e l

step

the

organic

phase

is

pumped i n t o

c e n t r i f u g e , where n e p t u n i u m i s b a c k - e x t r a c t e d w i t h H^PO^

+

state.

the in the

the

In

second aqueous

third

mixer

T e t 85 .

I n t h e γ - r a y s p e c t r a f o u r new γ - l i n e s t h a t f i t i n t o t h e known l e v e l schemes 243 244 of Pu and Pu have been o b s e r v e d . The h a l f - l i f e o f t h e new i s o t o p e 243 , 244 Np was d e t e r m i n e d as 61 τ 7 s . The decay c u r v e s o f Np a r e c o m p l e x 244 and

can be e x p l a i n e d by two i s o m e r s o f

140 + 20 s . tions

These

[Kla 84]

should of

195 s

for

2 4 3

Np

[Tak 7 3 ] p r e d i c t s

25 min and 3 m i n .

So

chemical

far

on-line

developed Pd, I ,

and

applied

Np w i t h h a l f - l i v e s

be compared w i t h

for

and

separations short-lived

theoretical 8 s

for

with

the

isotopes

of

2 4 4

of 7 : 4 s

(microscopic) Np.

SISAK As,

The

gross

system

Br,

Zr,

and

predic­ theory

have

been

Nb, T e ,

Ru,

L a , Ce, P r , and Np [ S k a 8 0 , Bro 8 1 , Ska 8 3 , Rog 8 4 , Aro 7 4 , T e t 8 5 ] .

73.

Rapid, Continuous Chemical Separations

KRATZ ET AL.

485

3. C o m b i n a t i o n o f a g a s - j e t w i t h t h e r m o c h r o m a t o g r a p h i c In

thermochromatography

reactive the

gases

less

and a r e

volatile

volatile

species

gas-jet

with

separation on-line

deposited

species in

a

of

volatile

the

in

species in

high

temperature

temperature

thermochromatographic

the

reaction

separation

of

products.

fission

formed

in

reactions

with

a column w i t h a t e m p e r a t u r e g r a d i e n t

the

low

are

methods

region. column

This

products

region The

forming

the

the

was

volatile

-

more

combination

allows

approach

and

of

a

continuous

applied nalides

for

the

[Hie

80,

Hie 8 4 ] .

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch073

It Hg,

was

also

Tl,

applied

Pb, B i ,

synthesize Arm 8 5 ] . column,

for

Po, A t

see

were r o t a t e d α-particles

2,

stepwise

in

case t h e

and were

isolation

of

volatile

metals

such as

n o b l e gases i n a r e c e n t , r i g o r o u s a t t e m p t 48 248

elements

latter

Fig.

on-line

and o f

superheavy

In the

the

the

Ca +

volatile

condensed

between p a i r s

and s p o n t a n e o u s - f i s s i o n

of

Cm

species

surface

[ Sum 8 4 ,

reaction

were a l l o w e d t o l e a v e

on u l t r a - t h i n

nickel

barrier

to

foils.

detectors to

the

These detect

fragments.

ACTINIDE ELEMENTS etc.

Fig.

2 : O n - l i n e gas phase c h e m i s t r y procedure f o r the separation o f v o l a t i l e superheavy e l e m e n t s [Sum 8 4 ] .

4 . C o n t i n u o u s s e p a r a t i o n s by c h e m i c a l r e a c t i o n s Instead

of

using

a

reaction

products

to

chemical

reactions

of

are

stopped

which

are

compounds

in

cluster-jet the the

a reactive

continuously are

formed

by

for

chemistry recoils gas

swept

in

where out

thermal

of

the

i n the c a r r i e r

transportation

apparatus, the

carrier

highly the

synthesis.

it

gas:

volatile stopping The

is

gas

of

Either products

chamber,

volatile

the

nuclear

possible

to

the

recoils

are or

species

use

formed volatile

are

then

486

NUCLEI OFF THE LINE OF STABILITY

separated

by

compounds

in

selective a

short-lived

tellurium

mixture

nitrogen

of

absorbents.

gas-jet

was

used

and s e l e n i u m and

The

thermal

the

separation

for

isotopes

hydrochloric

acid

[Zen 8 1 ] . N i t r o g e n

and

separation of arsenic 5. O n - l i n e mass

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch073

The

HELIOS

facilities fully

to

volatile

volatile

chlorides

are

a b s o r p t i o n . This

were

used

for

formed

technique

o f s h o r t - l i v e d germanium

acid

separator a gas-jet

at

v

the

elsewhere

Mainz

Details

separator

[Maz

studies

the

of

TRIGA

transportation

separator.

sources,

isotopes

the

on-line

80,

Maz

reactor

of

the

gas-jet

and

its

collector

81].

neutron-rich

is

one

of

the

system has been c o u p l e d

Recently,

isotopes

system,

the

integrated

facilities

HELIOS

was

have

for

o f praseodymium [ B r u 85]

and

sources

c o u p l e d p_lasma

successful to

ion

source

(ICP).

c o u p l i n g o f t h e g a s - j e t w i t h t h e ICP s o u r c e i t

ionize

any e l e m e n t

in

the

periodic

table

been

applied

i n progress i n order to replace the e x i s t i n g

an j n d u c t i v e l y

few

success­

neodymium [ Kar 8 5 ] . Work i s by

of

into a

84].

mass

spectroscopic

of

investigation

separation

a mass

published

hydrofluoric

[Hie

where

skimmer-ion

investigations

and

[ Z e n 7 8 ] . Through r e c o i l

i n s i d e t h e r e a c t o r and a r e s e p a r a t e d by s e l e c t i v e has been a p p l i e d i n o n - l i n e

synthesis

because

In

case

ion of

a

s h o u l d be p o s s i b l e

temperatures

o f 6000 -

10000 Κ a r e r e a c h e d i n t h e p l a s m a . 6.

Outlook

Continuous

chemical

separations

have been p r o v e n

to

be p o w e r f u l

techniques

a l l o w i n g d e t a i l e d measurements o f t h e decay p r o p e r t i e s o f e x o t i c n u c l e i half-lives procedures

down

to

this

time

chemical

species

velocity

of

lived

nuclides of

nuclear

separations exchange choice

of

scale

will

in

thermalization

is

require

with

process.

close

the

periods the

range

processes introduce

of

limit

between

seem t o

of

time. set

two

explorations

development ways

chemically

may

to

layers

Further

Promising

the m i l l i s e c o n d

gases

long

boundary

and t h e r m a l i z a t i o n other

over

separations.

milliseconds. effects

second

through

phase

scale

a

by

of yet

helium.

It

by

unknown on of

the

time

specific mass

84] by c h a r g e

is conceivable t h a t

selectivity

of the

short­

On-line

have been p e r f o r m e d [ A r j

chemical

and

procedures

reactions.

with

chemical

diffusion

phases

be c o m b i n a t i o n s

selective

in

For

already

into

the the

73. KRATZ ET AL. Rapid, Continuous Chemical Separations

487

References

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch073

[Arm 85] [Aro 74] [Ärj 84]

P. Armbruster et al., Phys. Rev. Lett. 54, 406 (1985) P.O. Aronsson et al., Inorg. Nucl. Chem. Lett. 10, 499 (1974) J. Ärje et al., Department of Physics, University of Jyväskylä, Research Report No. 13 (1984) and J. Äystö et al., Phys. Lett. 138B, 369 (1984) [Bro 81] K. Brodén et al., J. Inorg. Nucl. Chem. 43, 765 (1981) [Brü 85] M. Brügger et al., Nucl. Instr. Meth. A234, 218 (1985) [Han 79] P.G. Hansen, Ann. Rev. Nucl. Part. Sci. 29, 69 (1979) [Her 82] G. Herrmann, N. Trautmann, Ann. Rev. Nucl. Part. Sci 32, 117 (1982) [Hic 80] U. Hickmann et al., Nucl. Instr. Meth. 174, 507 (1980) [Hic 84] U. Hickmann et al., GSI Scientific Report 1983, GSI 84-1, 230 (1984) and U. Hickmann, Doctoral thesis, Universität Mainz (1984) [Kar 85] T. Karlewski et al., Z. Physik, in press [Kla 84] H.V. Klapdor et al., Atomic Data Nucl. Data Tables 31, 81 (1984) [Maz 80] A.K. Mazumdar et al., Nucl. Instr. Meth. 174, 183 (1980) [Maz 81] A.K. Mazumdar et al., Nucl. Instr. Meth. 186, 131 (1981) [Moo 85] K.J. Moody et al., GSI Scientifie Report 1984, GSI 85-1, 93 (1985) [Rav 79] H. Ravn, Phys. Rep. 54, 203 (1979) [Rog 84] J. Rogowski et al., to be published [Ska 80] G. Skarnemark et al., Nucl. Instr. Meth. 171, 323 (1980) [Ska 83] G. Skarnemark et al., Radiochim. Acta 33, 97 (1983) [Sta 84] J. Stachel et al., Z. Physik A316, 105 (1984) [Ste 80] E. Stender et al., Radioanalyt. Lett. 42, 291 (1980) [Süm 84] K. Sümmerer et al., Preprint GSI-84-17 (1984) [Tak 73] K. Takahashi et al., Atomic Data Nucl. Data Tables 12, 101 (1973) [Tet 85] H. Tetzlaff et al., GSI Scientific Report 1984, GSI 85-1, 273 (1985) [Zen 78] M. Zendel et al., Nucl. Instr. Meth. 153, 149 (1978) [Zen 81] M. Zendel et al., Radiochim. Acta 29, 17 (1981) RECEIVED August 28, 1986

74 First Results at Système Accélérateur Rhône-Alpes (SARA) with a He-Jet Coupled to a High-Current Mass Separator Source 1

1

1

1

1

1

1

R. Beraud, A. Charvet, R. Duffait, A. Emsallem, M. Meyer, T. Ollivier, N. Redon, J. Genevey, A. Gizon, N. Idrissi, and J. Treherne 2

2

2

2

1

Institut de Physique Nucléaire (et IN2P3), Université Lyon 1, 43 boulevard du 11 Novembre 1918, F. 69622 Villeurbanne Cédex, France Institut des Sciences Nucléaires (IN2P3 et USMG), 53 avenue des Martyrs, F. 38026 Grenoble Cédex, France

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch074

2

We report on the performances of a He-jet connected to a Bernas-Nier ion source. After a brief description of the system we give the first spectroscopic results on very neutron deficient rare-earth isotopes. Among the techniques used to study the nuclear structure all over the mass surface, in-beam γ -spectroscopy and isotope separator on-line (ISOL) are the two most important ones. The first one gives access to high spin physics whereas the second one is mainly related with low-spin states at lower energy depending on available decay energy. The ISOL systems allow to investigate nuclear species produced with very small cross-sections since the products can be studied in a very low background environment. The use of intense beams and the development of fast and efficient ISOL systems are both necessary to study nuclei far off the valley of stability. In this paper I will explain our motivations concerning the technical choice of a He-jet coupled to a mass separator and then give our first results. 2- Experimental facility 2.1 SARA (Sy stème Accélérateur Rhône-Alpes) This facility is composed of two cyclotrons, a K=90 compact one and a K=160 separated sector one which is operating siiice 1982. An ECR ion source is now commonly used for the production of C,N,0 and Ne beams up to 40 MeV/u energy. The layout of the beam lines, as shown in fig. 1, allows to use also the first cyclotron alone when high intensity, moderate energy beams are needed. This is a common mode of operation to carry out spectroscopic studies by means of fusion-evapo­ ration reactions. Fig. 1 : General layout of the SARA machine arid experimental areas. 0097-6156/ 86/ 0324-0490506.00/ 0 © 1986 American Chemical Society

74.

BERAUD ET AL.

First Results with a He-Jet

491

2.2 L a y o u t of the on-line isotope separator A s c h e m a t i c plan view of the new on-line separator l o c a t e d on beam line C is given in f i g u r e 2. The beam f r o m the a c c e l e r a t o r enters the H e - j e t r e c o i l chamber through a t h i n N i w i n d o w ( 2 m g / c m ) , bombards tbe t a r g e t and is then stopped in a beam-stopper composed mainly of i r o n , lead and polystyrene in order to p r e v e n t f r o m both neutron and γ background. The ion-source of the separator is f e d by a capillary t r a n s p o r t i n g the r e c o i l s t h e r m a — lized in the H e - j e t c h a m b e r . The separator beam is e x t r a c t e d a t r i g h t angle to the axis of the beam line and then t r a v e l s in a 120° magnet of index n=1/2. F r o m the f o c a l plane the mass-separated beam is then t r a n s p o r t e d by means of a 6m long Einzel lens t o a w e l l - s h i e l d e d c o l l e c t i o n c h a m b e r . A p r o g r a m m a b l e t a p e - t r a n s p o r t device c a r r i e s the a c t i v i t y t o the c o u n t i n g s t a t i o n where X - r a y s , γ-rays and p a r t i c l e s are d e t e c t e d . The o v e r a l l p e r f o r m a n c e of the separator is mainly d e t e r m i n e d by the quality of the m a g n e t . The r e s o l u t i o n is nowadays 1000 F W H M a t mass 100 and the s e p a r a ­ t i o n 17 m m b e t w e e n A=100 and A = 1 0 1 . It is planned t o i m p r o v e the r e s o l u t i o n by changing mechanically the e n t r a n c e and e x i t magnet boundaries.

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch074

2

F i g . 2 : L a y o u t of isotope separator in beam line C. The numbers i n d i c a t e : (1) H e - j e t r e c o i l c h a m b e r , (2) beam-sto'pper, (3) ion-source, (4) analysing m a g n e t , (5) Einzel lens f o r t r a n s p o r t of mass-separated b e a m , (6) t a p e - t r a n s p o r t and c o u n t i n g s t a t i o n , (7) p o w e r / c o n t r o l rack of t a p e - t r a n s p o r t , (8) p o w e r / c o n t r o l of mass-separa~ tor.

492

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch074

2.3.

NUCLEI OFF THE LINE OF STABILITY He-jet

c o u p l e d to

ion-source

A s c h e m a t i c v i e w of the H e - j e t r e c o i l c h a m b e r and i n t e g r a t e d s k i m m e r i o n - s o u r c e is shown in f i g u r e 3. T h e r e c o i l c h a m b e r is e i t h e r of m u l t i c a p i l l a r y or sheet t y p e as d e s c r i b e d in [ P L A 81]. The collection volume ( 0 = 12mm, length=100 mm) is made of an Aluminium cylinder and connected to the main stainless c a p i l l a r y . It is placed in the m i d d l e of the H e p r e s s u r i ­ zed reaction chamber and He gas is fed through a temperature controled bubbler. D i f f u s i o n pump aerosols were mainly used in the experiments reported here. For monitoring of the beam, a Faraday cup f i x e d behind a 4 m g / c m Havar window was used. 2

F i g . 3 : S c h e m a t i c v i e w of H e - j e t integrated skimmer ion-source

The ion- source is of Bernas-Nier type and is described in more details in [CHA 67]. The extracted

r e c o i l c h a m b e r and

c u r r e n t may be Λ / 5 m A , a l l o w i n g thus o u t g a s i n g or t a r g e t e v a p o r a t i o n . A n i m p o r ­ t a n t a p p l i c a t i o n is the use of c a r r i e r gas a n d / o r c h e m i c a l p r o d u c t s w h i c h may g i v e v o l a t i l e c o m p o u n d s of r e f r a c t o r y e l e m e n t s . A high flow p u m p i n g s y s t e m c o m p o ­ sed of t w o r o o t s and a p r i m a r y p u m p (3000 m / h - 350 m / h - 120 m / n ) is used t o _ ^ k i m o f f the H e f r o m the s k i m m e r box w h e r e the p r e s s u r e is m a i n t a i n e d a r o u n d 10 t o r r . T h e s k i m m e r is a f l a t s t a i n l e s s s t e e l p l a t e w i t h a c i r c u l a r hole φ 1,2 m m in the m i d d l e . 3

3

3

3. Results 3.1

T h e decay

of 12s

1

4

3

T b [OLL

85]

112 T h e a c t i v i t y was p r o d u c e d by b o m b a r d i n g ^ a s e l f - s u p p o r t i n g 2 m g / c m Sn t a r g e t ( e n r i c h e d to 88 %) w i t h a 191 M e V C I b e a m . T h e r e c o i l s , s t o p p e d in 1 bar H e p r e s s u r e , w e r e t r a n s p o r t e d v i a a 6 m l o n g c a p i l l a r y to the t a p e - t r a n s p o r t s y s t e m . A t the c o u n t i n g p o s i t i o n , m e a s u r e m e n t s including γ -ray multianalysis d e c a y s ( t y p i c a l l y 8x2 s and 8x10 s), Ύ - Χ and Ύ-Ύ c o i n c i d e n c e s w e r e c a r r i e d out with intrinsic G e d e c t e c t o r s . P a r t i c l e spectra were simultaneously measured with a 500 μηη Si d e t e c t o r ; no s i g n i f i a n t p a r t i c l e a c t i v i t y was o b s e r v e d . T h e Ύ-ray s w e r e a s c r i b e d to T b decay on the basis of f o l l o w i n g e x p e r i m e n t a l e v i d e n c e : i) a l l t h e s e γ - r a y s a r e in c o i n c i d e n c e w i t h K X - r a y s of G d (see f i g u r e 4). ii) the a v e r a g e m e a s u r e d h a l f - l i f e of the m o s t intense γ - l i n e s is (12 ± 1) s. 2

a

74.

BERAUD ET A L .

First Results with a He-Jet

493 12s

( /2 ) 11

COUNTS

_

EC,/}*

1er

7) (9/,11/2").

Th 65 78

1 4 3

T b

CD CO 00 CM ID CM

2

CO

( /2, /2-)9

1250.7

11

c

5001

«

CD CO

cn 0+ transition in Sm has also been identified. These results are compared to IBM2 and cranking model predictions. 138

48

136

92

138

136

It

has l o n g been r e c o g n i z e d

deformed n u c l e i 82.

This

exists

away f r o m t h e l i n e o f

l y i n g beyond t h e p r o t o n d r i p

has made e x p e r i m e n t a l

a region o f permanently

i n t h e r e g i o n where Ζ and A a r e b o t h between 50 and

r e g i o n , however, i s l o c a t e d w e l l

with the centroid

terization

[SHE61] t h a t

line.

investigations d i f f i c u l t .

of these nuclei

has r e c e n t l y

development o f h e a v y - i o n a c c e l e r a t o r s

tion

of t h i s

arrays.

[LEA82].

model

a promontory o f s t r o n g deformation d i r e c t e d may e x i s t

systems

impetus f o r i n v e s t i g a ­ calcu­

back

around t h e samarium and promethium

The r e c e n t development o f an o n - l i n e t h e r m a l - i o n i z a t i o n i o n

s o u r c e [MLE86] a t UNISOR [SPE81] c a p a b l e o f e f f i c i e n t l y in this

nuclei

isotope separator

In a d d i t i o n , t h e o r e t i c a l

toward t h e l i n e of 3 - s t a b i l i t y nuclei

h o w e v e r , by t h e

capable o f producing these

r e g i o n has been p r o v i d e d by a r e c e n t deformed s h e l l

l a t i o n w h i c h shows t h a t

β-stability location

The c h a r a c ­

been f a c i l i t a t e d ,

c o u p l e d w i t h t h e c o n t i n u i n g development o f o n - l i n e and m u l t i - d e t e c t o r

The remote

region coupled w i t h t h e a v a i l a b i l i t y

40 t o 47 ( Z r t o Ag) as w e l l

as good beams o f

i o n i z i n g t h e elements

of f a v o r a b l e t a r g e t s w i t h Ζ from 3

2

S , * S , 5 C 1 , ** Ti 3

0097-6156/ 86/ 0324-0502$06.00/ 0 © 1986 American Chemical Society

3

8

and ^ T i

76.

available

from t h e Hoii f i e l d

Heavy-Ion F a c i l i t y

a program t o s t u d y t h e unknown o r l i t t l e specific

have l e d t o t h e i n i t i a t i o n

known n u c l e i

e x p e r i m e n t d e s c r i b e d here i s t h e p r o d u c t i o n

the f i r s t

o b s e r v a t i o n o f gamma r a y s f r o m t h e i r

in this of

1 3 6

region.

Eu

and

a very small

volume i o n s o u r c e h e a t e d w i t h a t u n g s t e n f i l a m e n t o f up t o 3000°K.

H e a t i n g by t h e i n c i d e n t

8

and

9 2

open t o t h e

a target/window of

a t an energy o f 225 MeV.

were s t o p p e d i n a l a y e r o f g r a p h i t e f e l t

9 2

Mo( * Ti ,p3n)

reactions

8

1 3 6

beam.

f r o m where t h e y were

and p r o j e c t i l e s

during

M o o f 1.85 mg/cm

9 2

eva­

8

Fig.

1.

con­

B

N

M

Β

\

m

/

UNISOR t h e r m a l

ionization

source.

target/window, felt

Ta M

catcher,

2) 3)

1) graphite

tungsten

filament,

4) Ta t a r g e t

retainer,

5) g r a p h i t e

felt

h e a t s h i e l d i n g , 6) Ta heat shield, graphite

7) Ta s u p p o r t

Eu

o f about t h e s e masses,

experiments.

Graphite •

1 3 8

f o r xn

were p r e d i c t e d by t h e e v a p o r a t i o n code OVERLAID ALICE [BLA76] and a l s o firmed in test

2

product

Μο(** Γί , p n )

E u were chosen because v e r y low c r o s s s e c t i o n s

r e l a t i v e t o pxn u s i n g t a r g e t s

is

internal

The r e c o i l i n g

i o n i z e d and e x t r a c t e d t o f o r m a beam. The r e a c t i o n s i

to

It

accelerator

beam i n c r e a s e s t h e t a r g e t / w i n d o w t e m p e r a t u r e

For t h e p r e s e n t e x p e r i m e n t ,

was used w i t h a beam o f * * T i nuclei

The t a r g e t / w i n d o w ,

reaches a maximum t e m p e r a t u r e o f 2200°K w i t h no i n c i d e n t

operation.

porated,

E u and

i s shown i n F i g . 1 .

temperatures beam l i n e ,

1 3 8

of

The

decay.

The i o n s o u r c e used i n t h e s e i n v e s t i g a t i o n s

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch076

503

Deformation in the Light Sm Region

MLEKODAJ ET AL.

for

felt. 3

0 Centimeters

504

NUCLEI OFF THE LINE OF STABILITY The m a s s - s e p a r a t e d beam o f a p p r o p r i a t e mass was d i r e c t e d down one o f

t h e UNISOR beam l i n e s

to a fast

tape c o l l e c t i o n

system.

After

a collection

t i m e o f 24 s , t h e t a p e moved i n 0 . 5 sec t o a c o u n t i n g s t a t i o n where m u l t i s p e c t r u m s c a l i n g and gamma-gamma c o i n c i d e n c e d a t a were acquired.

The

1 3 8

Eu

o n l y about 2 h r a t a t y p i c a l

** Ti

beam l e v e l

8

Two gamma r a y s a t t r i b u t e d

to

1 3 8

i n t e n s e enough t o p e r f o r m a h a l f - l i f e Fig.

2 ; t h e best value o f the *

the previously

simultaneously

decay was o b s e r v e d f o r about 20 h r and t h e

3 8

Eu

347 keV and 544 keV, were

analysis.

The r e s u l t s

i s 12±1 s .

are i n d i c a t e d

No i n d i c a t i o n

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch076

agrees w i t h a v a l u e o b t a i n e d i n an e a r l i e r

s i s o f X - r a y s and a t t r i b u t e d t o * The t o t a l The l e v e l

scheme d e r i v e d f o r

experiments

1 3 8

1 3 8

decay

1 3 8

Eu

( i . e . a 1+ l e v e l

1 J

in

1 3 8

Eu

F i g . 3.

The i d e n t i f i c a t i o n

1 3 8

o f t h e ground

recent

2

Sm indicates a

No i n d i c a t i o n

2

s p i n i s o m e r i s e x p e c t e d t o have a much s h o r t e r

may n o t be p o p u l a t e d t o a g r e a t e x t e n t

half-life

T h i s low

and may n o t escape

On t h e o t h e r h a n d , a low s p i n in this

heavy-ion

level

o f t h e low s p i n

as i n ^ ° E u and ^ E u ) c o u l d be i d e n t i f i e d .

t h e i o n s o u r c e i n t i m e t o be d e t e c t e d .

in-beam

and may be r e l a t e d t o t h e 7 -

* Eu [KEN75].

p l a c e m e n t o f a second 2+ l e v e l

analy-

S m based on a c o m p l e t e a n a l y s i s o f t h e c o i n -

The p o p u l a t i o n o f t h e 8+ s t a t e i n

i n t h e decay o f

times.

reported

decay i s shown i n

S m up t o a s p i n o f 8+ i s i n agreement w i t h

[LIS85].

of

[N0W82].

is given i n F i g . 4.

high spin f o r the decaying s t a t e identified

Eu

coincidence spectrum f o r

cidence r e l a t i o n s h i p s s t a t e band i n

3 8

in

o f 1.5 s and 35 s [B0G77] c o u l d be f o u n d

even t h o u g h d a t a were a l s o a c q u i r e d a t s h o r t e r and l o n g e r c o l l e c t i o n The 12 s h a l f - l i f e

for

o f 30 p a r t i c l e - n A .

Eu,

Eu half-life

reported h a l f - l i v e s

1 3 6

reaction.

isomer

The

f r o m i n - b e a m work [LUN85] a t 745 keV i s

s u b s t a n t i a t e d by o u r d a t a a l t h o u g h t h e s p i n c a n n o t be u n i q u e l y

also

deter-

mined. In a d d i t i o n , the

1 3 6

A l t h o u g h no gamma l i n e s (2+

0+ t r a n s i t i o n

in

E u decay was i n v e s t i g a t e d f o r a b r i e f

time.

c o u l d be d i s c e r n e d i n t h e s i n g l e s d a t a , t h e 256 keV 1 3 6

S m [LIS85])

l i n e was o b s e r v e d i n t h e t o t a l

coin-

cidence s p e c t r u m , F i g . 5. I n F i g . 6 , t h e 2+ e n e r g i e s energies

f o r e v e n - e v e n Sm i s o t o p e s

theoretical

predictions.

f r o m t h i s work a l o n g w i t h o t h e r known 2+ are p l o t t e d along w i t h the r e s u l t s

The IBM2 c a l c u l a t i o n s

were c a r r i e d o u t as d e s c r i b e d

by S c h o l t e n [SCH79] u s i n g p a r a m e t e r s f o r t h e l i g h t Puddu e t a l . [ P U D 8 0 ] .

The c r a n k i n g c a l c u l a t i o n s

o f some

Sm i s o t o p e s d e r i v e d

were made w i t h

from

76.

1

Ί

505

Deformation in the Light Sm Region

MLEKODAJ ET AL.

Γ t , » = 12 M S

104 ^£^347keV

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch076

f

442

J

J

L 12

Fig. for

2. 1 3 8

Half-life

;

571

6491

L

16

Time (sec)

;

20

determination

Eu.

Fig.

3.

Total

coincidence

s p e c t r u m f o r mass 138.

, J e

Eu

12S EC

+

β

Ί

1 ' Γ A= 136 7 — 7 COINCIDENCES

'

4_L II

Τ / , 8

Fig. for

4. 1 3 8

374 Pm

j 800

Sm

Derived level

Sm.

208 256 Eu

1600

2400

3200

Channel Number

scheme

Fig.

5.

Total

coincidence

s p e c t r u m f o r mass 136.

4000

506

NUCLEI OFF THE LINE OF STABILITY

Fig.

6.

Comparison

experimental

data

of

with

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch076

c r a n k i n g and IBM2 m o d e l s .

72

82 Ν

the modified o s c i l l a t o r

92

(Nilsson)

equilibrium deformations.

single-particle

model a t t h e

The a v e r a g e gap was o b t a i n e d by s c a l i n g t h e g l o b a l [JEN84].

The p r e s e n t c r a n k i n g c a l c u l a t i o n s

modifications

of c a l c u l a t i o n s

The e x p e r i m e n t a l the predictions

points

for

1 3 8

Sm

(N=76) and

o f t h e two c a l c u l a t i o n s .

et a l . [LIS85]

is

f o r m u l a o f Jensen e t

are s l i g h t

by Ragnarsson e t a l .

smooth r a p i d d e c r e a s e o u t t o N=74. Lister

extensions

and c o n t i n u e s t h e r a p i d d e c r e a s e .

between t h e s e n e u t r o n numbers

1 3 6

Sm

diction

is

and

(N=74) f a l l

between

The t r e n d o f t h e 2+ e n e r g i e s shows a

The 2+ e n e r g y a t N=72 as d e t e r m i n e d by calculations,

The t r e n d f r o m N=76 t o 72 appears more

predicted

[LEA82] l a r g e i n c r e a s e i n

deformation

( l o w e r branch o f t h e dashed c u r v e i n F i g .

t h a n w i t h t h e smooth e v o l u t i o n o f d e f o r m a t i o n o b t a i n e d e a r l i e r

the t h e o r e t i c a l

al.

[RAG74].

163 keV, a g a i n w i t h i n t h e range o f t h e

compatible with the recently

(upper branch)

Strutinsky

BCS p a i r i n g was t r e a t e d by t h e average gap m e t h o d .

and a l s o s u g g e s t e d by t h e IBM2 r e s u l t s . 2+ e n e r g i e s a r e h i g h e r f o r

N82 and t h i s

that

pre­

borne o u t by t h e d a t a .

Acknowledgment Support under c o n t r a c t

f o r t h i s work was p r o v i d e d by t h e U.S. Department o f numbers DE-AC05-760R00033, DE-AS05-76ER0-3346 and

DE-AC05-840R21400.

Energy

76.

MLEKODAJ ET AL.

Deformation in the Light Sm Region

507

References [BLA76] M. Blann, OVERLAID ALICE, U.S. Energy Research and Development Administration Report No. COO-3493-29, 1976 (unpublished). [BOG77] D.D. Bogdanov, A.V. Demyanov, V.A. Karnaukhov, L.A. Petrov, A. Plohocki, V.G. Subbotin and J. Voboril, Nucl. Phys. A275 229 (1977). [JEN84] A.S. Jensen, P.G. Hansen and B. Jonson, Nucl. Phys. A431 393 (1984). [KEN75] G.G. Kennedy, S.C. Gujrathi and S.K. Mark, Phys. Rev. C12 553 (1975).

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch076

[LEA82] G.A. Leander and P. Möller, Phys. Lett. 110B (1982) 17. [LIS85] C.J. Lister, B.J. Varley, R. Moscrop, W. Gelletly, P.J. Nolan, D.J.G. Lover, P.J. Bishop, A. Kirwan, D.J. Thornley, L. Ying, R. Wadsworth, M. O'Donnell, H.G. Price and A.H. Nelson, Phys. Rev. Lett. 55 810 (1985). [LUN85] S. Lunardi, F. Scarlassara, F. Soramel, S. Beghini, M. Morando, C. Signorini, W. Meczynski, W. Starzecki, G. Fortuna and A.M. Stefanini, Z. Phys. A321 177 (1985). [MLE86] R.L. Mlekodaj, to be submitted, Nucl. Instr. & Meth. [NOW82] M. Nowicki, D.D. Bogdanov, A.A. Demyanov and Z. Stachura, Act. Phys. Pol. B12 879 (1982). [PUD80] G. Puddu, O. Scholten and T. Otsuka, Nucl. Phys. A348 109 (1980). [RAG74] I. Ragnarsson, A. Sobiczewski, R.K. Sheline, S.E. Larsson and B. Nerlo-Pomorska, Nucl. Phys. A233 329 (1974). [SCH79] O. Scholten, in "Interacting Bosons in Nuclear Physics", ed. F. Iachello, Plenum Press, NY, 1979, p. 17. [SHE61] R.K. Sheline, T. Sikkeland and R.N. Chanda, Phys. Rev. Lett. 7 446 (1961). [SPE81] E.H. Spejewski, R.L. Mlekodaj and H.K. Carter, Nucl. Instr. & Meth. 186 71 (1981). RECEIVED September 10, 1986

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix001

Author Index Edmiston, M. D., 171 Ekstrom, Curt, 358 Emsallem, Α., 490 Estep, R. J., 190 F a l l e r , S., 517 Fazekas, B., 196 Feld, M. S., 516 Feng, Da Hsuan, 27 Fink, R. W., 245 Firestone, R. B., 516 Fowler, Kevin, 53 Funk, E. G., 239 Gabelmann, Η., 165 Gai, Moshe, 278 Gardner, D. G., 100 Gardner, Μ. Α., 100 Garg, U., 239 Gatenby, R. Α., 514 Genevey, J., 490

Abenante, V., 305,317 Adler, L. Α., 317 Ahmad, Irshad, 272 Ajzenberg-Selove, F., 513 Allardyce, B. W., 406 Alonso, C. E., 511 Aprahamian, A., 214 Arias, J . M., 511 Aysto, J., 448 Baktash, C , 305,317 Balantekin, Α. Β., 14 Barrett, B. R., 65 Becker, J. Α., 78 Behkami, A. N., 512 Belgya, T., 196 Bengtsson, Tord, 292 Berant, Z., 386 Beraud, R., 490 Bingham, C. R., 245,364 Bloom, S. D., 70,78,145 Bond, P. D., 335 Bounds, J. Α., 364 Braga, R. Α., 245,502 Brenner, Daeg S., 459 Browne, Ε., 516 Brussaard, P. J,, 115 Bunker, M. E., 426 Butler, G. W., 459 Carpenter, M., 245 Carter, Η. K., 364 Casten, R. F., 120,184 Ceo, Robert N«, 515 Cerny, Joseph, 448 Charvet, Α., 490 Chasman, R. R., 266 Chaudhury, Α., 239 Chen, C. Υ., 305 Chen, Y. S., 305,317 Chou, Wen-Tsae, 329 Chung, C , 517 Clark, David D., 177 Coenen, E., 258 D'Auria, John M., 432 Dasari, R. R., 516 Decman, D. J., 190 Dejbakhsh, H., 284,311 Deneffe, Κ., 258 Depta, K., 513 de Voigt, M. J. A., 252 Diamond, R. M., 341 Dietzsch, 0., 305,317 Dousse, J.-Cl., 464 Drigert, M. W., 239 Duffait, R., 490 Duong, H. T., 380

G i l l , R. L., 171,174,284,386,420 Gizon, Α., 490 Gnade, B., 502 Grawe, H., 399 Green, V. R., 227 Gregorich, Kenneth E., 518 Greiner, W., 513 G r i f f i n , H. C , 305,317,515 Haas, H., 399 Haenni, D. R., 311 Halbert, M. L., 317 Hamilton, J. H., 510 Hardy, J. C , 414 Harms, V., 165 Harwood, L. H., 454 Haustein, P. E., 126 Helppi, H., 239 Henry, Ε. Α., 190 Hensley, D. C , 317 Herrmann, G., 482 Herrmann, R., 513 Hesselink, W. Η. Α., 252 Heyde, K., 47, 184 Hichwa, R. D., 515 H i l l , John C , 208,386 Ho, J . K., 252 Hoffman, Darleane C , 517 Holzman, R., 239 Holzmann, R., 20 Honkanen, K., 305,317 Hoshi, M., 496 Hotchkis, M. A. C , 448 Howard, W. M., 134,149 Hubsch, T., 14 Hugel, Ε. Α., 515 520

INDEX

521 Ohm, H., 202 O l i v i e r , Wade, 329 O l l i v i e r , T., 490 Oshima, M., 305 Ionescu, V., 464 Otsuka, T., 47 I s h i i , M., 496 Otteson, M. S., 516 I s h i i , T., 496 Paar, V., 14 Ivascu, M., 513 Papanicolopoulos, C. D., 245 Janssens, R. V. F., 239 Passoja, Α., 221 Johnson, Noah R., 298,305,317 Penninga, J., 252 J u l i n , R., 221 Petry, R. F., 208,284 Kantele, J., 190,221 Piotrowski, Α., 171,177,284 Kelson, I., 511 Poenaru, D., 513 Kern, B. D., 502 Quivers, W. W., J r . , 516 Kern, J., 464 Rab, Shaheen, 153 Khoo, T. L., 239 Radford, D. C , 239 Kleppinger, E. W., 196,514 Ragnarsson, Ingemar, 292 Kluge, H.-J., 370 Raman, S., 512 Kohi, H. P., 202 Redon, Ν., 490 Kot, Wing, 518 Reeder, P. L., 171 Kozub, R. L., 514 Reich, C. W., 94 Kratz, J. V., 482 Rengan, Krishnaswamy, 517 Kratz, K.-L., 159,165 Riedinger, L. L., 245,305,317,323 Krumlinde, J., 159,165 Riezenbos, H. J., 252 Kumar, Krishna, 85 Rikovska, J., 227 Kupstas-Guido, Jane, 329 Robertson, J. D., 284,517 Lanier, Robert G., 476 Roeckl, Ernst, 439 Larabee, A. J., 245,305,317,323 Saladin, J. X., 305,317 Lawin, H., 202 Sambataro, M., 35 Leander, G. Α., 159,364,502 Sandulescu, Α., 513 Lee, D., 518 Sarantites, D. G., 305,317 Lee, I. Y., 305,317 Schmidt, Η. H., 512 Lhersonneau, G., 202 Schmitt, R. P., 311 Lieb, K. P., 233 Schneider, V., 513 L o i s e l e t , M., 20 Scholten, 0., 47 Love, D., 245 Schutz, Υ., 305,317 Lùhmann, L., 233 Seaborg, Glenn T., 518 Luontama, M., 221 Semkow, T. M., 305,317 Mach, H., 284 Seo, T., 202 Mahnke, H. E., 399 Sheline, R. K., 190 Maier, K. H., 392,399 Sher, Gerson S., 510 Makishima, Α., 496 S h e r r i l l , B., 454 Mann, L. G., 190 Shihab-Eldin, Adnan, 153 Maruhn, J. Α., 513 Shimkaveg, G., 516 Mathews, G. J., 70,134,145,149 Sistemich, K., 202,386 McElroy, Robert D., 177 Smith, D., 516 McHarris, William C., 329 Sorensen, Raymond Α., 53 Menzen, G., 202,386 Meyer, B. S., 149 Stenzel, Ch., 399 Meyer, M., 490 Stevenson, J., 454 Meyer, Richard A., 190,196,202 S t o f f l , W., 190 Mihelich, J . W., 239 Stolk, Α., 252 Mikolas, D., 454 Stone, C. Α., 70,517 Mlekodaj, R. L., 502 Stone, N. J., 227,350 Môller, P., 149,159,165 Takahashi, K., 134,145,149 Molnâr, G., 196 Talbert, W. L., J r . , 426 Moltz, D. M., 448 Tamura, Taro, 41 Moody, Kenton J., 518 Thomas, J. Ε., 516 Morrison, I., 65 Toth, K. S., 502,514 Moszkowski, Steven Α., 59 Trautmann, Ν., 482 N a v i l i a t , 0., 20 Treherne, J., 490 Nestor, C. W., Jr., 512 T u l i , Jagdish K., 512 Nolen, J. Α., J r . , 454 Ussery, L. E., 190

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix001

Huyse, M., 258 Iachello, F., 2 I d r i s s i , N., 490

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix001

522

NUCLEI OFF THE LINE OF STABILITY

Van den Berg, A. M., 239 Van Duppen, P., 258 Van Isacker, P., 47,184 van Klinken, J., 512 V a z i r i , Κ., 459 Verbaarschot, J. J . M., 115 Veres, A'., 196 Verheul, H., 252 Vervier, J., 20 V i e i r a , D. J., 459 von Egidy, T., 512 Waddington, J . C , 245 Walker, P. M., 227 Walters, W. B., 70,284,517 Warburton, Ε. K., 78 Ward, R. Α., 134 Warner, D. D., 386

Warner, R. Α., 171 Weiler, Η., 202 Welch, Robert B., 518 Wilmarth, P h i l l i p Α., 518 Wohn, F. K., 208,386,459 Wolf, Α., 386 Wollnik, H., 459 Wood, J. L., 184,239,245,258 Wormann, B., 233 Wouters, J. M., 459 Xie, Z. Q., 454 Yates, Steven W., 196,470,514 Zabolitzky, J . G., 65 Zemel, Α., 252 Zganjar, E. F., 245,284 Zhang, J.-Y., 323 Ziegert, W., 165

Subject Index A

α clustering, zirconium-96, 196-201 α decay, bismuth-190, -192, and -194, 26l,262f,263 (^scattering cross bands magnesium-24, 8 7 , 8 9 f silicon-28, 8 7 , 8 9 f spectrum obtained f o r A = 197, 260f Actinide h a l f - l i v e s , as standards for nuclear data measurements, 95-96 Actinide-nuclide decay data, coordinated research program, 95 Actinium-225 e l e c t r i c dipole transitions, 272-277 h a l f - l i f e , 273-274 time spectrum, 272f Actinium-227 band-head energies, 270f h a l f - l i f e , 275 parity doublets, 285f Aluminum-22, normalized angular correlation following 3 decay, 450f Angular d i s t r i b u t i o n of the 497-keV t r a n s i t i o n i n lead-196, 255,256f zirconium-96, 198f,199 Angular momentum lutetium-163, 321f praseodymium-135, 308,309f Antimony isotopes, magnetic dipole moments, 355t

Antimony-116, l e v e l scheme, 333f Antimony-133, energy l e v e l s , 72f,73t Astatine, odd mass, 259-261 Astatine n u c l e i , intruder states, 258-263 Astatine-197, decay scheme, 260f Atomic-beam spectroscopy, schematic view, 360f Atomic-beam technique, 358-363

Β

3-delayed f i s s i o n , calculations f o r the astrophysical r process, 149-152 3-delayed neutron emission properties, 153-158 3-delayed neutron emission p r o b a b i l i t i e s , 151f Band-head energies actinium-227, 270f protoactinium-227, -229, and -231, 270f Band-terminating configuration, schematic, 293f Barium, i n t e r a c t i n g boson model 2 parameter sets, 68t Barium-138, £ factors, 388t Barium-144 and -146, £ factors, 389t Barium-145, l e v e l scheme, 286,287f Barium-147, -148, and -149, h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Beryllium-12 and -14, 3-decay h a l f - l i v e s , 456f-457t

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

522

NUCLEI OFF THE LINE OF STABILITY

Van den Berg, A. M., 239 Van Duppen, P., 258 Van Isacker, P., 47,184 van Klinken, J., 512 V a z i r i , Κ., 459 Verbaarschot, J. J . M., 115 Veres, A'., 196 Verheul, H., 252 Vervier, J., 20 V i e i r a , D. J., 459 von Egidy, T., 512 Waddington, J . C , 245 Walker, P. M., 227 Walters, W. B., 70,284,517 Warburton, Ε. K., 78 Ward, R. Α., 134 Warner, D. D., 386

Warner, R. Α., 171 Weiler, Η., 202 Welch, Robert B., 518 Wilmarth, P h i l l i p Α., 518 Wohn, F. K., 208,386,459 Wolf, Α., 386 Wollnik, H., 459 Wood, J. L., 184,239,245,258 Wormann, B., 233 Wouters, J. M., 459 Xie, Z. Q., 454 Yates, Steven W., 196,470,514 Zabolitzky, J . G., 65 Zemel, Α., 252 Zganjar, E. F., 245,284 Zhang, J.-Y., 323 Ziegert, W., 165

Subject Index A

α clustering, zirconium-96, 196-201 α decay, bismuth-190, -192, and -194, 26l,262f,263 (^scattering cross bands magnesium-24, 8 7 , 8 9 f silicon-28, 8 7 , 8 9 f spectrum obtained f o r A = 197, 260f Actinide h a l f - l i v e s , as standards for nuclear data measurements, 95-96 Actinide-nuclide decay data, coordinated research program, 95 Actinium-225 e l e c t r i c dipole transitions, 272-277 h a l f - l i f e , 273-274 time spectrum, 272f Actinium-227 band-head energies, 270f h a l f - l i f e , 275 parity doublets, 285f Aluminum-22, normalized angular correlation following 3 decay, 450f Angular d i s t r i b u t i o n of the 497-keV t r a n s i t i o n i n lead-196, 255,256f zirconium-96, 198f,199 Angular momentum lutetium-163, 321f praseodymium-135, 308,309f Antimony isotopes, magnetic dipole moments, 355t

Antimony-116, l e v e l scheme, 333f Antimony-133, energy l e v e l s , 72f,73t Astatine, odd mass, 259-261 Astatine n u c l e i , intruder states, 258-263 Astatine-197, decay scheme, 260f Atomic-beam spectroscopy, schematic view, 360f Atomic-beam technique, 358-363

Β

3-delayed f i s s i o n , calculations f o r the astrophysical r process, 149-152 3-delayed neutron emission properties, 153-158 3-delayed neutron emission p r o b a b i l i t i e s , 151f Band-head energies actinium-227, 270f protoactinium-227, -229, and -231, 270f Band-terminating configuration, schematic, 293f Barium, i n t e r a c t i n g boson model 2 parameter sets, 68t Barium-138, £ factors, 388t Barium-144 and -146, £ factors, 389t Barium-145, l e v e l scheme, 286,287f Barium-147, -148, and -149, h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Beryllium-12 and -14, 3-decay h a l f - l i v e s , 456f-457t

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

INDEX

523

Cadmium-118—Continued β decay, cesium-145, 284-289 β decay h a l f - l i v e s , neutron-rich f i r s t observation of a U(5) n u c l e i , 443,444f nucleus, 214-220 Bismuth isotopes Cadmium-130 neutron-capture excitation β decay, 146-148,I47f functions, 105,106f calculated h a l f - l i f e , I47f neutron resonance spacing, 103,105t Calcium-35 Bismuth nuclei β-delayed two-proton intruder states, 258-263 spectrum, 451f systematics of e x c i t a t i o n p a r t i a l decay scheme, 451f energies, 259f Carbon-17, β-decay Bismuth-190, -192, and -194, α h a l f - l i v e s , 456f,457t Cerium, interacting boson model 2 decay, 26l,262f,263 parameter sets, 6 8 t Bismuth-209, e x c i t a t i o n Cerium-124 and -126, l e v e l scheme, 501f function, 101,102f Cerium-140, £ factors, 388t Boron-12, -14, and -15, β-decay Cesium-145, β decay, 284-289 h a l f - l i v e s , 456f,457t Cerium-146, perturbed angular Bose-Fermi symmetry, 5,7 correlation, 387f Boson expansion theory Cerium-146 and -147 Ginocchio model, 44f,45 r e a l i s t i c and model £ factors, 389t,424-425 applications, 41-46 Neff, 425f s i n g l e - ^ s h e l l model, 42-44 values of Neff, 390t Boson-fermion symmetry Cesium-147 and -148, h a l f - l i v e s and experimental tests, 20-26 delayed neutron emission for odd-odd nuclei, 14-19 p r o b a b i l i t i e s , 174t,175f Branching r a t i o comparison, Chart of nuclides, 418f zirconium-90 and -88, 79,80t,8l l i g h t proton-rich nuclei, 449f Bromine isotopes Clebsch-Gordon c o e f f i c i e n t , 301 onset of large quadrupole Cluster model prediction, radium deformation, 223-238 isotopes, 28l,282f quadrupole deformation Cluster model treatment, l i g h t parameters, 233,234t,235-236 actinides, 266-271 Bromine-72 and -73, mass spectral C o l l e c t i v e bands, peaks, 419f tellurium-124, 86,87f Bromine-73 and -75, yrast bands, 235f,236 C o l l e c t i v e magnetic multipole Bromine-87 strength, d i s t r i b u t i o n , 47-52 C o l l e c t i v e nuclear structures, calculated h a l f - l i v e s , 156,157f manifestations of fermion decay-energy values, 97t dynamical symmetry, 27-34 delayed neutron branching Collinear fast-beam laser r a t i o s , 156,157f spectroscopy, 361f Compton suppression spectrometer, 465-466 Continuous separations, 482-487 by chemical reactions i n the c a r r i e r gas, 485-486 on-line mass separation, 486 solvent extraction system, 483-485 Contour plot, tellurium-124, 86,87f Cadmium isotopes Copper-62, Sp(24) spectrum, l 8 f f i r s t observation of a U(5) Copper-75, h a l f - l i v e s and delayed nucleus, 214-220 neutron emission systematics of positive p a r i t y p r o b a b i l i t i e s , 174t,175f states, 228f Core p a r t i c l e weak coupling, 20 Cadmium systematics, 216f C o r i o l i s coupling, 329 Cadmium-106(S-32,xp,yn) Coulomb excitation, experimental reaction, 498f tests, 20-26 Cadmium-113(η, Y )cadmium-114 Coupled channel method, 87 reaction, populated l e v e l s , 465f Cranked s h e l l model frequency, Cadmium-118 platinum isotopes, 327f p a r t i a l l e v e l scheme, 2l8,219f Curved-crystal spectrometer, 466-469

524

NUCLEI OFF THE LINE OF STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

D

Decay europium-136 and -138, 502-506 polonium-198 and -200, 394,395f Decay curves lead-190 and -192, 402f total-projected coincidence spectra, 300f Decay scheme astatine-197, 260f europium-138, 4 9 3 , 4 9 4 f lutetium-163, 319,320f praseodymium-135, 307 protoactinium-231, 275f radium-225, 273f terbium-143, 4 9 2 , 4 9 3 f Deformation, europium-136 and -138, 502-506 Deformed n u c l e i , a mixed-symmetry interpretation of some low-lying bands, 47-52 Delayed neutron precursors, 171-176 Dipole c o l l e c t i v i t y , i n nuclei, 278-283 Dipole strength functions, l u t e t i u m - 1 7 6 , 110,111f Discrete l e v e l s i n analysis of primary γ-ray spectra, 111-112 i n deriving absolute dipole strength functions, 109-111 isomer r a t i o s , 106-109 level-density parameterization, 102-105 Droplet model of Myers and Swiatecky, 85 Dynamic deformation model, reviewed, 85-90 Dynamic symmetry with i - i coupling, 60-64 with k-k coupling, 60-64 Dynamical supersymmetry, f o r odd-odd nuclei, 14-19

Ε

E1 strength functions, y t t r i u m - 8 9 and zirconium-90, 110,111f E l e c t r i c dipole t r a n s i t i o n s , actinium-225 and -227 and radium-225, 272-277 Electromagnetic moments, polonium-198, -200, and -210, 392-398 Electromagnetic properties, lead isotopes, 399-404 Electromagnetic t r a n s i t i o n amplitudes, d i s t r i b u t i o n , 115-119

Elements, estimates of lower l i m i t h a l f - l i v e s , 353,354t Elements studied by low-temperature nuclear orientation, 351f Energy l e v e l s antimony-133, 72f,73t erbium-156, 344f,345 iodine-135, 75f,76 praseodymium-135, 306f tellurium-133, 74-75f tellurium-134, 7 3 , 7 4 f three-quasi-particle nuclides, 74,75f,76 tin-130, 73,74f tin-131, 72f,73t two-quasi-particle nuclides, 73,74f yttrium-88 and -90, 8 l , 8 2 f Erbium-145, l e v e l scheme, 344f Erbium-156 energy l e v e l s , 344f,345 sequence of states, 295,296f Erbium-158 decay curves, 300f i l l u s t r a t i o n of aligned 2 4 and 30 states, 295f p a r t i a l l e v e l scheme, 346f p o s i t i v e p a r i t y even spin configurations, 294f spectrum of t r a n s i t i o n s , 345,346f total-projected coincidence spectra, 300f t r a n s i t i o n quadrupole moments, 302f Erbium-258, band structure, 292,293f Estimator method, y t t r i u m - 8 9 , 103,104f Europium-136 decay and deformation, 502-506 t o t a l coincidence spectrum, 505f Europium-138 decay and deformation, 502-506 decay scheme, 493,494f h a l f - l i f e determination, 504,505f Excitation function bismuth-209, 101,102f lutetium-175, 109f strontium-88, 106,107f thulium-169, 100,101f yttrium-89, 100,101f Exotic l i g h t n u c l e i , d i r e c t mass measurements, 459-463 Exotic n u c l e i , techniques f o r study, 452-453 %

+

+

F

Fermion dynamical symmetry model, 27-34 Fermion pairs (L = 2), nuclear dynamic symmetry models, 59-64

INDEX

525

Fission lifetimes doubly magic n u c l e i , 8 8 , 8 9 f superheavy n u c l e i , 8 9 , 9 0 f Fluorescence spectrum, radon-207, 3 8 4 f Folded-Yukawa wave function, 1 6 2 - 1 6 4 Francium-209 measured wavenumbers, 3 8 3 t o p t i c a l resonances, 3 8 l - 3 8 2 f

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

G

γ anisotropy, iodine isotopes, 351,356f Y-ray e x c i t a t i o n curves, platinum-198, 472f,473 Ύ-ray spectrum following the mer cur y-198 ( α, 6, η ) 1 ead-196 reaction, 253f neodymium-143 and -144, 336,337f rhenium-182, 332f terbium-143, 493f t r a n s i t i o n energies i n lead-196, 253,254f £ factors barium-138, 3 8 8 t barium-144 and -146, 3 8 9 t cerium-140, 3 8 8 t cerium-146 and -148, 389t,424-425 lead isomers, 402,403f molybdenum-102 and -104, 389t polonium-198 and -200, 394-395f tellurium-134, 3 8 9 t xenon-136, 388t zirconium-100, 3 8 9 t Gadolinium-146, shell-model states, 3 3 5 , 3 3 6 f Gadolinium-14 8(ρ,t)gadolinium-146, spectrum, 479f Gadolinium-156, band-head energies, 48,49f Gallium-79, -80, -81, -82, and - 8 3 , h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Gamow-Teller 3 t r a n s i t i o n s , proton-rich n u c l e i , 440-441f Gamow-Teller properties allowed decay, 153-158 i n astrophysical r process, 149-152 i n astrophysical s and r processes, 145-148 3-strength functions, 159-164 Gilbert-Cameron level-density formalism, 102 Gold nuclei alignment processes, 323-328 band-head energies, 323,324f shape competition, 323,328

Gold-185 p a r t i a l l e v e l scheme, 326f shape coexistence, 245 Gold-185 and -187, electron and Ύ spectra, 249-250f Gold-185 and -195, shell-model states, 247f Gold-187, schematic of intruder states, 248t Gold-196 and -198, spectrum of low-lying states, 17f Gold-198, spectrum, 11f Gross β-decay properties rubidium-97, l 6 6 f rubidium-99, l 6 7 f rubidium-101, l 6 9 f strontium-99, I 6 8 f strontium-101, l 6 9 f Ground-state studies at ISOLDE, nuclei f a r from the s t a b i l i t y l i n e , 370-379 Ground-state wave function, molybdenum-100, 197f,199

H

Half-life actinium-225, 273-274 actinium-227, 275 radium-225, 274-275 silver-124, 176 H a l f - l i f e determination, europium-138, 504,505f Half-lifetimes neodymium-132, 500t samarium-136 and - I 3 8 , 500t H a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Hamiltonian, 3-5 boson, 35 interacting boson model 2, 2-19,38f,53-54,66-67,22 quadrupole-quadrupole, 3 8 f s h e l l model, 29 Hartree-bose angular momentum projection, 55t,56-58f approximation, 54,55f Hartree-Fock-Bogolyubov, 85 Hauser-Feshbach s t a t i s t i c a l model, 10C Heavy ion induced transfer reactions, 335-340 Heavy-element nucleosynthesis, 135-14* Heavy-ion produced n u c l e i , 439-445 Helium-jet a c t i v i t y transport studies, 427-428 Helium-jet coupled on-line mass separator, 426-427 Helium-jet coupled to ion source, 492

526

NUCLEI OFF THE LINE OF STABILITY

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

Hexadecapole deformation, thallium isotopes, 365f High energy resolution array, 341 High-spin states, interacting boson model, 53-58 High-temperature plasma ion source, schematic diagram, 421f High-spin structure, lutetium-163, 317-322 Hoiium-165 (α,3n,Ύ)thulium-166, spectrum, 468f Hydrogen burning processes, 140-142 Hyperfine structure measurements, 358-363 thallium-193, 366f

J

Janecke and Garvey-Kelson, nuclear mass model, 129,130f,131

Κ

K a l l i o - K o l l t v e i t two-body interaction, 71 Kronecker product, 8 Krypton-74, yrast bands, 235f,236

I L

In-beam spectroscopy, using the (t,p) reaction, 190-195 Indium isotopes, mean square charge r a d i i , 44l,442f Indium-127, -128, -129, -130, -131, and -132, h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Interacting boson model description, 27,47-52,65-66 Hamiltonian, 53-54,229f high-spin states, 53-58 mixing calculations, 230f microscopic theory, 35-40 paramet ers, 65-6 9 tellurium isotopes, 227-232 Intruder states astatine nuclei, 258-263 bismuth nuclei, 258-263 monopole f i e l d correction, 186 pairing f i e l d correction, 186-187 platinum-184, 239,244 polonium nuclei, 258-263 quadrupole proton-neutron energy correction, I 8 6 , l 8 7 f shell-model description, 184,l85f,186-189 Iodine isotopes γ anisotropy, 351,356f magnetic dipole moments, 355t Iodine-135, energy l e v e l s , 75f,76 ISOLDE overview, 406-413 summary of the elements available, 409f Isomer r a t i o s , discrete levels, 106-109 Isomers, polonium-210, 392,393f

LAMPF overview, 426,431 schematic, 428f Lanthanum-147, -148, and -149, h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Laser spectroscopy schematic, 381f short-lived isotopes, 380-385 Lead isomers £ factors, 402,403f magnetic moments, 402,403f quadrupole moments, 401f Lead isotopes electromagnetic properties, 399-404 0 states, 225f p a r t i a l l e v e l scheme, 399f,400 shape coexistence, i n neutrondeficient Pb isotopes, 252-257 Lead-190 and -192, decay curves, 402f Lead-190 and -200, systematics of the excitation energies, 258,259f Lead-194 and -196, shape coexistence, i n neutron deficient Pb isotopes, 252-257 Lead-196 angular d i s t r i b u t i o n , 255,256f p a r t i a l l e v e l scheme, 255f Lead-196 and -198 quadrupole modulation functions, 400f quadrupole moments, 400 Lead-202 and -204 energies of 0 states, 224f,225t E0 transitions and intruder states, 221-226 Level-density parameterization, discrete l e v e l s , 102-105 +

+

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

INDEX

Level-density parameters, near the neutron separation energy i n strontium-93 to - 9 7 , 177-182 Level scheme A r 100 n u c l e i , 208,209f antimony-116, 3 3 3 f barium-145, 286,287f cadmium-118, 2l8,219f cerium-124 and -126, 501 f erbium-145, 344f erbium-158, 346f gold-185, 326f lead isotopes, 399f,400 lead-196, 255f molybdenum-102, 1 9 1 Γ neodymium-132, 500f palladium-102 and -104, 222f palladium-112, 192f platinum-184, 242f samarium-134, -136, and -138, 500f samarium-138, 504,505f 40,142,144,146, 494f tantalum-182 ( α, 3n, Y )rhemium-182 reaction, 329,330f y t t r i u m - 9 7 , -98, and - 9 9 , 203,204f,205-206 zirconium-96 and -98, 194f,200f Level schemes ruthenium-102, 312f neodymium-142 and -144, 3 3 9 f Level structure nuclear reaction cross-section calculations, 100-114 radium-218 and -220, 279-280f Lifetimes palladium-106, 21,24,26t palladium-108, 21,24,26t polonium-198 and -200, 394,395f rhenium-103, 21,24,26t ruthenium-102, 21,24t,26t silver-107, 21,24,26t silver-109, 21,24,26t Lifetimes of states i n ground-state band, platinum-184, 240t Light i o n spectroscopy, 4 6 4 - 4 6 9 Light proton-rich nuclei chart of nuclides, 449f review, 448-453 Lithium-9 and -11, β-decay h a l f - l i v e s , 456f,457t Lutetium-163 angular momentum, 321f decay scheme, 319,320f 'energy i n the r o t a t i n g frame, 2 3 1 f high-spin structure, 317-322 signature s p l i t t i n g , 231f Lutetium-175 e x c i t a t i o n function, 109f primary Y-ray i n t e n s i t i e s , 109,110f Lutetium-175 and -176, primary dipole t r a n s i t i o n s , 111,112f

527

Lutetium-176, dipole strength functions, 1 1 0 , 1 1 1 f

M

Magnesium-24 α-scattering cross bands, 8 7 , 8 9 f potential functions, 8 7 , 8 8 f Magnetic dipole moments of isotopes, 355t Magnetic moments of excited states i n nuclei f a r from s t a b i l i t y , 386-391 lead isomers, 402,403f zirconium-90 and - 8 8 , 7 9 , 8 0 t , 8 l Magnetic resonances, potassium-44, 3 8 1 f Mainz c o l l i n e a r laser spectroscopy apparatus, schematic view, 3 8 3 f Majorana force, 47-51,49f Majorana interaction, 50,51t Mapping procedure, from fermion onto boson space, 35-40 Mass spectral peaks, bromine-72 and - 7 3 , 419f Mayer-Jensen method, 88 Mean square charge r a d i i , isotopes, 441-442f Mechanism of two-proton emission following β decay, 449-450 Mercury n u c l e i , band-head energies, 323,324f Mercury-182 and -198, energies of the spherical and deformed states, 246f Mercury-198(α,6n)lead-196 reaction, 252-253 Mixed-symmetry states, B(E2) values, 49,50t Molybdenum-96, t r a n s i t i o n schematics, 193f,194 Molybdenum-100, ground-state wave function, 1 9 7 f , 1 9 9 Molybdenum-100 and -102, E0(K) branching r a t i o s , 194t Molybdenum-102, l e v e l scheme, 1 9 1 f Molybdenum-102 and -104, £ factors, 389t Moment of i n e r t i a A = 100 n u c l e i , 209f radium-218, 279,280f

Ν

Ν -Ν p

systematics, i n nuclear phase t r a n s i t i o n regions, 120-125

528

NUCLEI OFF THE LINE OF STABILITY

Neodymium, interacting boson model 2 parameter sets, 68t Neodymium-132 h a l f - l i f e t i m e s , 500t l e v e l scheme, 500f Neodymium-142 and -144, l e v e l schemes, 339f Neodymium-143 and -144, Y-ray

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

spectrum, 336,337f Neodymium-144, -146, -148, and -150, values of Neff, 390t Neptunium-236 and - 2 3 7 d i s t r i b u t i o n of quantum numbers, 108f,109 isomer r a t i o , 108f l e v e l sets, 108t Neutron capture excitation functions, bismuth isotopes, 105,106f Neutron-induced reaction spectroscopy, 470-475 Neutron resonance spacing, bismuth isotopes, 103,105t Neutron-rich isotopes, 0-decay h a l f - l i v e s , 454-458 Neutron-rich nuclei 8-decay h a l f - l i v e s , 443,444f Neutron states, polonium-196 and -198, 396,397f Nilsson bands, yttrium-98, 211f Nilsson diagram, yttrium-99, -100, -101, and -102, 210f,212f Nilsson model, 323 Nilsson states, i n A = 100 nuclei, 165-170 Nilsson wave function, 161 Nuclear astrophysics, away from s t a b i l i t y , a review, 134-144 Nuclear decay data, 94-98 Nuclear mass model Janeeke and Garvey-Kelson, 129,130f,131 Seeger and Howard, 128f,129 Nuclear masses analysis methods, 127-128 analysis of selected i n d i v i d u a l models, 128-131 discussion, 126-131 global comparisons, 127-128 Nuclear reaction cross-section calculations, l e v e l structure, 100-114 Nuclear shapes at high spins, discussion, 298-304 Nuclei away from s t a b i l i t y , 134-144 3-strength functions, 149,150f chart, 372f neutron r i c h — S e e Neutron-rich nuclei proton r i c h — S e e Proton-rich nuclei schematic d i v i s i o n , l84f

Nuclei—Continued supersymmetry, 2-13 Nuclei at low e x c i t a t i o n energies, discrete-level descriptions, 100-102 Nucleosynthesis, heavy element, 135-144 Nucleosynthesis mechanisms ρ process, 140 r process, 137-138f,145-146 s process, 137-138f,145-146 Nuclide, chart, 460f,474f

0

Octupole correlation e f f e c t s , l i g h t actinides, 266-271 Octupole correlation energy, radium-226, 269f Odd-even staggering parameter of the isotopes around Ν = 1 2 6 , 378f Odd-odd n u c l e i boson fermion symmetry, 14-19 dynamical supersymmetry, 14-19 supersymmetry, 2-19 On-line isotope separators (ISOL), 433-434 On-line nuclear orientation method, 350-357 schematic, 352f One-quasi-particle nuclides, energy l e v e l s , 72f,73t Optical resonances francium-208, 38l-382f sodium-28, -29, -30, and -31, 380,38lf Optical spectroscopy at ISOLDE, on-line techniques, 3 7 6 , 3 7 7 t Oxygen-18, electromagnetic transitions, 278,279f

Ρ

ρ process, nucleosynthesis mechanisms, 140 Palladium isotopes, low-lying 0 and 2 states, 223f Palladium-102 and -104 E0 transitions and intruder states, 221-226 p a r t i a l l e v e l schemes, 222f Palladium-102 and -106, t r a n s i t i o n schematics, 193f,194 Palladium-106, l i f e t i m e s , 21,24t,26t Palladium-108(α,η)cadium-110 reaction, populated l e v e l s , 465f +

INDEX

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

Palladium-108(α,2n,Ύ)cadmium-110 Y-ray spectrum, 467f l i f e t i m e s , 21,26t,24t Palladiùm-110 and -112, EO(K) branching r a t i o s , 194t Palladium-112, l e v e l scheme, 192f Parity doublets actinium-227, 285f radium-225, 285f Parity states, yttrium-90 and - 8 8 , 8 3 f , 8 4 P a r t i a l radiation widths, yttrium-90, 101,102t Perturbed angular c o r r e l a t i o n , cerium-146, 3 8 7 f Platinum isotopes, cranked shell-model frequency, 327f Platinum n u c l e i , band-head energies, 323,324f Platinum region of the n u c l i d i c chart, 474f Platinum-184 B(E2) values, 243f intruder states, 239,244 l e v e l scheme, 242f Platinum-186, schematic of intruder states, 248f Platinum-194, i l l u s t r a t i o n , l 6 f , 1 7 Platinum-196, interacting boson model 2 parameter sets, 67f Platinum-198, Y-ray e x c i t a t i o n curves, 472f,473 Plutonium, r-process production r a t i o s , 151t Polonium isotopes B(E3), 3 9 6 , 3 9 7 f E2 properties, 3 9 6 , 3 9 7 f Polonium nuclei, intruder states, 258-263 Polonium-196 and -198, neutron states, 3 9 6 , 3 9 7 f Polonium-198 and -200 decay, 394,395f £ factors, 394-395f l i f e t i m e s , 394,395f Polonium-198, -200, and -210, electromagnetic moments, 392-398 Polonium-210 isomers, 3 9 2 , 3 9 3 f quadrupole coupling constants, 3 9 2 , 3 9 4 t quadrupole modulation patterns, 3 9 3 f quadrupole moments, 3 9 4 t Potassium-44, magnetic resonances, 3 8 1 f Potential functions magnesium-24, 87,88f silicon-28, 8 7 , 8 8 f Praseodymium-135 angular momentum, 308,309f decay scheme, 307 energy l e v e l s , 306f signature s p l i t t i n g , 305-310

529

Praseodymium-141, neodymium-142 reaction, spectrum,

338,339f

Primary Y-ray i n t e n s i t i e s , 109,110f Protoactinium-227, -229, and -231, band-head energies, 270f Protoactinium-231, decay scheme, 275f Proton-rich nuclei description, 439-443 Gamow-Teller β transitions, 440-44lf review, 448-453

Q

Quadrupole coupling constants, polonium-210, 392,394t Quadrupole deformation, thallium isotopes, 365f Quadrupole deformation parameters bromine isotopes, 233-236 rubidium isotopes, 223-236 Quadrupole modulation functions, lead-196 and -198, 400f Quadrupole modulation patterns, polonium-210, 393f Quadrupole moments, thallium-189, -191, and -193, 3 6 1 t Quadrupole moments erbium-158, 302f lead isomers, 401f lead-196 and -198, 400 polonium-210, 394t tungsten-172, 303f ytterbium-160 and - 1 6 1 , 301f zirconium-88 and -90, 79,80t,81

R

r process β-delayed f i s s i o n , 149-152 nucleosynthesis mechanisms, 137-138f,145-146 Radium isotopes B(E1)/B(E2) r a t i o s , 28l,282f c l u s t e r model prediction, 28l,282f Radium-218, moment of i n e r t i a , 279,280f Radium-218 and -220, l e v e l structure, 279,280f Radium-225 decay scheme, 273f e l e c t r i c dipole t r a n s i t i o n s , 272-277 h a l f - l i f e , 274-275 p a r i t y doublets, 285f

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

530

Radon-207, fluorescence spectrum, 384f Reaction product of mass separator, schematic, 454f Recoil-distance method, 21,24t,26t Reduced t r a n s i t i o n probability, for β decay, 154-155 Relative t r a n s i t i o n i n t e n s i t i e s , y t t r i u m - 9 8 , 211f R e l a t i v i s t i c fermi l i q u i d model, 85 Resonance i o n i z a t i o n spectroscopy, schematic, 375f RF mass spectrometer, schematic, 3 7 3 f Rhenium-103, l i f e t i m e s , 21,24t,26t Rhenium-182, Ύ-ray spectrum, 332f Rotational bands, i n deformed odd-odd nuclei, 329-334 Rotational structure, of yttrium nuclei, 208-213 Rubidium isotopes onset of large quadrupole deformation, 223-238 quadrupole deformation parameters, 233-236 Rubidium nuclei, β strength function, I6l-I62f Rubidium-77 and - 7 9 , yrast bands, 235f,236 Rubidium-92 and -102 calculated h a l f - l i v e s , 156,157f delayed neutron branching r a t i o s , 156,157f Rubidium-93, -94, -95, -96, and -97, precursors, 177-182,181t Rubidium-95, -97, -98, -99, and -100, h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Rubidium-97, gross β-decay properties, I66f Rubidium-99, gross β-decay properties, l 6 7 f Rubidium-101, gross β-decay properties, l 6 9 f Ruthenium-102 l i f e t i m e s , 21,24t,26t p a r t i a l l e v e l schemes, 312f p a r t i c l e alignment vs. r o t a t i o n a l frequency, 312f Routhian compared with crank s h e l l model, 3 1 3 f t r a n s i t i o n schematics, 193f,194 Ruthenium-103 negative p a r i t y band, 315f p a r t i c l e alignment vs. r o t a t i o n a l frequency, 314f positive parity band, 315f Ruthenium-106, E0(K) branching r a t i o s , 194t Radium-226, octupole c o r r e l a t i o n energy, 269f

NUCLEI OFF THE LINE OF STABILITY

S

s process, nucleosynthesis mechanisms, 137-138f,145-146 Samarium, interacting boson model 2 parameter sets, 68t Samarium-134, Y-rays, 499f Samarium-134, -136, and -138, l e v e l scheme, 500f Samarium-136 and -138, h a l f - l i f e t i m e s Samarium-138 l e v e l scheme, 504,505f Samarium-138, -140, -142, -144, and -146, p a r t i a l l e v e l scheme, 494f Samarium-148 and -149, single neutron transfer reaction, 335f Samarium-148, -150, -152, and -154, values of Neff, 390t Seeger and Howard, nuclear mass model, 128f,129 Selenium-72, yrast bands, 235f,236 Seniority truncated exact diagonalization scheme, 153-154 Shape changes at high angular momenta, spectroscopic consequences, 292-297 Shape coexistence gold-185, 245 yttrium-98, 203-206 Shell-model calculations β-decay rates for s- and r-process nucleosyntheses, 145-148 near tin-132, 70-77 yttrium-88 and -90, 78-84 zirconium-90,88, 78-84 Shell-model states gadolinium-146, 335,336f gold-185 and -195, 247f Short-lived fission-product decay data, 96-98 S i ( L i ) detector, 422 Signature s p l i t t i n g lutetium-163, 231f praseodymium-135, 305-310 S i l i c o n box in-beam Y-ray spectroscopy, 496-501 schematic, 496f Silicon-28 α-scattering cross bands, 87,89f potential functions, 87,88f Silver-107, l i f e t i m e s , 21,24t,26t Silver-109, l i f e t i m e s , 21,24t,26t Silver-124, h a l f - l i f e , 176 Sodium-28,29,30,31, o p t i c a l resonances, 380,381f Spectrometer, 221f

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

INDEX

531

Spectrum neodymium-143 and -144, 337f praseodymium-141, neodymium-142 reaction, 338,339f Spectrum of transitions, erbium-158, 345,346f S t e l l a r model calculations, 137-138f Strontium-88, e x c i t a t i o n function, 106,107f Strontium-93, -94, -95, -96, and -97, level-density parameters, 177-182 Strontium-97, -98, -99, -100, -101, and -102, h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Strontium-99, gross β-decay properties, I68f Strontium-101, gross β-decay properties, I69f Strontium isotopes, constant i n the mean square spin projection expression, 103t Structure t r a n s i t i o n , i n heavy yttrium isotopes, 202-207 Superconducting magnet, 422-423 Supersymmetry experimental tests, 20-26 i n nuclei, 2-13 odd-odd nuclei, 2-19 Surface 6 interaction, with i - i coupling, 60-64 Symmetric rotor, yttrium-99, 206 System accelerator, Rhone Alpes overview, 490-495 schematic, 491f Systematics of excitation energies bismuth nuclei, 259f lead-190 and -200, 258,259f thallium nuclei, 259f

Τ

Tandem accelerator superconducting cyclotron f a c i l i t y overview, 414-419 schematic, 414f Tantalum-182(α,3n ,Ύ )rhemium-182 reaction, l e v e l scheme, 329,330f Target material for nuclear reaction and spectroscopic studies, 476-480 Technetium, continuous separation flow sheet, 483f Technetium-99, β decay, 145-I46f

Tellurium isotopes interacting boson model, 227-232 systematics of positive parity states, 228f Tellurium-124 c o l l e c t i v e bands, 8 6 , 8 7 f contour plot, 86,87f Tellurium-133, energy l e v e l s , 75f,76 Tellurium-134 energy l e v e l s , 7 3 , 7 4 f £ factors, 388t Terbium-143 decay scheme, 492,493f Ύ-ray spectrum, 493f Thallium isotopes f i e l d s h i f t s , 361f hexadecapole deformation, 365f quadrupole deformation, 365f Thallium nuclei, systematics of excitation energies, 259f Thallium-189, -191, and -193, quadrupole moments, 361t Thallium-193, hyperfine structure data, 366f Thorium, r-process production r a t i o s , 151t Thorium isotopes, B(E1)/B(E2) r a t i o s , 28l,282f Thorium-232 B(E2) values, 33f yrast states, 31,32f Three-quasiparticle nuclides, energy l e v e l s , 74,75f,76 Thulium-169, excitation function, 100,101f Time-of-flight f a c i l i t y , schematic, 471f Time-of-flight isochronous spectrometer, 459-463 schematic, 461f Time-of-flight methods, 470 Time spectrum, actinium-225, 272f Tin isotopes, mean square charge r a d i i , 44l,442f Tin-130, energy l e v e l s , 73,74f Tin-131, energy levels, 72f,73t Tin-132, shell-model calculations, 70-77 Total coincidence spectrum, europium-136 and -138, 505f Transition energies i n lead-196, Ύ-ray spectrum, 253,254f Transition rates, i n odd-mass heavy nuclei, 276f Transitional A = 100 nuclei massive transfer reactions, 311-316 structure, 311-316 TRISTAN f a c i l i t y overview, 420-425 schematic, 421f

NUCLEI OFF THE LINE OF STABILITY

5 3 2

TRIUMF-ISOL f a c i l i t y , 432-438 postaccelerator, 435-436 target, 433f Tungsten-172, t r a n s i t i o n quadrupole moments, 303f Two-quasi-particle nuclides, energy levels, 73,74f

Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ix002

U

UNISOR c o l l i n e a r laser f a c i l i t y , r e s u l t s , 364-369 UNISOR c o l l i n e a r laser system, schematic, 365f UNISOR f a c i l i t y , 502 Uranium, r-process production r a t i o s , 151t

first

W

Wapstra, atomic mass evaluations, 127 Wavenumbers, francium-209, 383t Woods-Saxon potential, 325 Woods-Saxon wave function, 162-164

Ytterbium-168, energy spectrum, 57,57t Yttrium isotopes constant i n the mean square spin projection expression, 103t rotational structure, 208-213 structure t r a n s i t i o n , 202-207 Yttrium-89 E1 strength functions, 110,111f estimator method, 103,104f excitation function, 100,101f Yttrium-90, p a r t i a l radiation widths, 101,102t Yttrium-90 and -98 energy l e v e l s , 8l,82f parity states, 83f,84 she11-model calculations, 78-84,79t Yttrium-97, -98, and -99 l e v e l scheme, 203-206,204f structure t r a n s i t i o n , 202-207 h a l f - l i v e s and delayed neutron emission p r o b a b i l i t i e s , 174t,175f Yttrium-98 Nilsson bands, 21 I f relative transition i n t e n s i t i e s , 211 f shape coexistence, 203-206 Yttrium-99 symmetric rotor, 206 Yttrium-99, -100, -101, and -102 Nilsson diagram, 21 Of,212f rotational structure, 208-213 Yukawa form factor, 78

X

Xenon isotopes interacting boson model 2 parameter sets, 6 8 t magnetic dipole moments, 355t Xenon-136, g factors, 388t

Y

Yrast bands bromine-73 and -75, 235f,236 krypton-74, 235f,236 rubidium-77 and -79, 235f,236 selenium-72, 235f,236 Yrast states, thorium-232, 31,32f Ytterbium-160 and -161, t r a n s i t i o n quadrupole moments, 301f

Ζ

Zirconium-88 and -90 branching r a t i o comparison, 79,80t,8l magnetic moments, 79,80t,8l Zirconium-90 E1 strength functions, 110,111f shell-model calculations, 78-84 Zirconium-96 α clustering, 196-201 angular d i s t r i b u t i o n , 198f,199 p a r t i a l l e v e l scheme, 200f l e v e l scheme, 194f Zirconium-98, l e v e l scheme, 194f Zirconium-100, g factors, 389t