Measurement of low energy beta-spectra

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MA SP8CTRA

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F U iFIU tfE H ? OF THE JUftVSUSfSNr; FOii m

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DKffUSK,

D o o m OF PHILGSOHflf, IK 1E S DEPARTMENT

of m u s i c s , Indiana w a r n c m A u gu st, 1% 9 ^ ou

p a rtia l

ProQuest Number: 10295199

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^

The w riter wishes to express hi® tippreaiatlon to

c-v

^ **r\

P rof. L« K. Langer tor the v&lmbl® assistan ce rendered m ,

w ell a® far th e o rig in a l suggestion of the problem. He i s also g ra te fu l to Prof. A«C*G. M itchell fo r th e frien d ly eneoiaragesient. and fo r t ho generous use of the laboratory •

tm m

or oomwrs

Chapter

1

XI

Introduction A.

Xntoroat in low EnergyMeaaureaianta

1

B.

Sxpoilacntal Problems

1

C*

Purpose o f Present gxparlsont

2

^Kperimontal Procedure A*

Prelimin&iy gaqparlmnt

B« Betermiiwition o f 8Effective* frintiow

111

4 7

0# Design o f S p e c tra * t e r

15

D. Keeoiution and f rssnsmis sion of Spec­ trometer

16

£« Kelmhoitss Coils for the Production o f Hie Magnetic Field

19

F. Deaigu of Counter

25

G» E le c tric a l & Vacuum Apparatus

27

B« ibcpurliaAntal ArrangoRniit

28

1. C alibration of Spectrometer

30

J*

Ur*© of Alcohol F ille d Countar

32

K.

Use of Thin Counter hindowa

36

L, Uaa of window!!eee Counter

37

M* Preparation of Sources

39

F ^crim ental Results

45

tmm of mmmn (conu)

I?

Disc usaion of R esults A* B«ta^p*otrum o f 3^5 &«

of Souro® Thicknasa on th® l'^X47 Spectrum Sliape

52 53

C* M fm t o f Counter Window Thiskrtosa on the Mpocfcrm Rhap®

55

'Wiiuhwlaaa*Counter U^mnrmmntn

56

&• V

Geneluaions

5@

VI

References

^0

VII

U a t o f Illu stra tio n ®

62

Introduction I n te re s t i n Low Knarigy U & m u m m n U H elatlvely l i t t l e exjmliaenfc&X d a ta is av ailab le in the extremely low energy region o f Beta sp e c tra .

As a r e s u lt,

the v a lid ity of the f e r a l Theory (PI) has not y e t been d e fi­ n ite ly e stab lish ed in th is region.

In f a c t, recen t experimental

in v estig atio n s ( H , L2) o f th© Beta sp ectra o f Cu*&, C u ^ , and £$$ have suggested deviations from Hie theory a t low energies. Further stu d ies are needed to help c la r ify H i a question, as w ell aa to determine the ex ten t to which ins trusssntal effect® in flu ­ ence the r e s u lts . Such studies would provide other In te re stin g Inform ation. An accurate d escrip tio n o f the ©haps of the sp ectra would reveal whether th ere are c e rta in forbidden tra n sitio n * whose shapes d if f e r

tn m th a t of an allowed shape (13# 14# Ml) in the low energy region any d ifferences would throw lig h t on th e p a rtic u la r in te ra c tio n between th e nucleon and © lootron-neutrino f ie ld which should bo assumed (2 a).

F urther, tr m H e shape of c u rta in low energy Beta

spectra such a® K?, I t is possible to evaluate the upper lim it o f the neutrino ren t mass (Cl, 12), Experimental Problems I t is no accident H a t l i t t l e information i s av ailab le a t low energies, since exporissantal d i f f ic u lt i e s are g re a te s t in th is region.

C ertain factor® , which wight rave l i t t l e o r no e ffe c t

on t o spectrum t o p e a t the higher energies, eon haw a pronounced e ffe c t a t th e lower energies.

These facto rs

bo sta te d as A llow s:

(a) Thickness of m w t m t o scores task in g (1 2 , M l, C2)

(b) Absorption of Counter Window (o)

Scattering of electron© from w alla, $ m ants, b a ffle s o f speotro&teier

(d) iieeoluiion of electrometer (FI) Along with these te e te rs , i t 1® important to not® th at there ere re la tiv e ly few counts a t t o low energies, and therefore i t 1® necessary In order to obtain good s t a ti s t i c a , th a t the spectrom­ e te r have m high a tonam ission as poasibl® ffer a glvaa resolu­ tio n . The irbhlau then, of ©fetatniaf re lia b le msiuiursmsnts o f t o low energy Beta sp e ctra , requires t o t adequate account be taken of t o e ffe c t of each of the above factor® and th a t m attempt be made to aditisd.ee or completely elim inate these e ffe c ts .

Purpose of present t e y t o i t l The object of the present experinent is to - f o ld s (a)

to design and build a ep ectom eter especially

adapted for low energy aeasuroments, (b)

to measure t o low energy Beta sp ectra of m

allowed tr a n s itio n 3?$, t o of a forbidden tra n s itio n , ggpmW, In p a rtic u la r, I t is intended 'to raduco the above awntioned eftpsrlasntftl e ffe c ts , and in t o m m of study the magnitude o f the o ffse ts of source thickness ana

~2-

§ to

window thickness on tee top® o f th e spectrum .

a p e t o l a tte n tio n

i s to be given to the problem of absorption in the counter window t o to a method designed to considerably minimise th is e f f e c t.

ftKpey&iMmfraX P r o c e d u r e

In ardor to o b tain any Bata Measurements a t a l l In th e low energy rang**, i t is f i r s t of a l l necessary to have a counter window tb ln enough to transm it such electrons*

Therefor®, the

question of how to make ’th in enou#* counter windows boeoitt&s the f i r s t problem to b® se ttle d * Ons p o ssib le approach to the so lu tio n of th ie problem Is to uso a d e te c to r which doe s not deperti on the io n is a tio n o f gases fo r i t s operation* and which can bo connected to tb s spec­ trom eter vacuum e lumber without the in ts re e p tio n o f a window* liuch a d e te c to r might bo found for example* in the si®©iron mul­ tip lie r * ' (A l), o r the eo ln tilX atio n counter (C3). On the o th er band* to a tt a i n th e Id e a l condition of no Window with & M l counter, i t i s lo g ic a l to in q u ire what o ffs e t i s produced by a c tu a lly removing the window from the counter and allowing tb s $a>a to d iffu se through the s l i t Into th* chamber of tb s spectrom eter.

vm m

Such a ste p would mean th a t fo r a

sm all enough s l i t opening* a p ressu re gradient would e x is t o u t^The w rite r i n i t i a l l y construe ted Mid ra$&stfjBmtecit w ith an e le ctro n m u ltip lie r tuba In the hops of vtaing i t for the detec­ tio n of beta ra y s. Tits r e s u lts of this* in v e stig a tio n revealed th a t the n a tu re o f the alec trod© surfaces was very c r i t i c a l f o r Beta ray d e te c tio n . Further* the preparation of such aurfaeee could not bo e a s ily c o n tro lle d or kept constant on exposure to a i r . Hough coaparieone between the counting m is s of the mul­ t i p l i e r tube and a G-M mmh&t in d icated th a t wMla the fbrmor could a e to c t tatavy p a rtic le s ouch a s alpha p a rtic le s w ith 100M officioncy* i t could only d e te c t & emeu f r a c tio n of in c id e n t Beta p a r tic le s . This agrees with Allen*a r e s u lts (AX) which re p o rt a decrease o f 301 in e ffic ie n c y f o r counting ele ctro n s abcrvc 6 le v . #

-4*"

side the counter s i l t * whtoh would present an 'e ffec tiv e * window having a c e rta in den sity md thickness to m y incoming p a rtic le s* Further* i t would

be

necessary to maintain a constant pressure

in the counter in

ord er

mb to ©hang© i t s D e ratin g c h a ra c te ris tic s *

as w all m to quickly r » w e toe gas glowing in to t o vacuus ehsator* I t i s a t onoe apparent th a t to maintain a constant pressure in the counter by t o use of a b a lla s t tank f i ll e d with th e usual counter Rilscfcure of 2 am alcohol and 7 m Argon* would be quite Im practical due to the large slue of t o tank that would be required*

This i* roughly demonstrated by th e following c al­

culations To sim plify m i t e r s , assume the s l i t opening 1® small compared to t o m m fre e path and th a t th ere i s only 7 oi! of Argon in the counter*

These condi­

tions would c e rta in ly ©all .tor a sm aller tank than t o a c tu a l case,

then*

(Eats o f effusion In e c /sc c /m ^ )s / —ft- ._\ ®

( a rrs)

to re

p « 7 x 1 3 * 6 x 9 8 0 tiy n m /m * * '

(pressure of Argon gee)

f z 1»53 x 10*^ gtas/cc (Density of Argon Ga® a t 20° C and 7 dm pressure) H en ce,

a # f £ » f f r ) ^ = *985 u tw ^

(1)

For a s l i t area »1

cm

Xojjg

akm!

#®5

wide,

fiat© of flow a «05 x * W » «®4$25 ttt* f* /e * e out of s i l t Hanae, during a run which la s ts aver a period of fiv e how s, the to ta l valuta® of jp s that w ill have occapod is i *04925 x 60 at 40 x 5 3 &S6 l i t e r s t h is means th&t i f w© allow a ms^Mom decrease in counter pressure o f X m& out of 7 cm during the run, i t would be necessary to have a b a lla s t tank w ith a volume of 3860 lite rs # [ t ? 38 (7 - *X)(V 4 086) —* V » $86® U tters

J

A Midi mors p ra c tic a l &rmngos®fst w uld he to f i l l the counter with the vapor of a aultable organic liquid such m eth y l alcohol*

Tlien* the m por pressure in the counter could be kept

constant by fixitsg tm t«ng»r&ture of the liquid in a constant temperature hath*

k prelim inary experiment was devised to t e s t tiw* feas­ i b i l i t y o f such a ' ’wlndowXaaa* apectreoe tor#

I t was f i r s t nee-

essary to det^s&im how sm all a oeun&er s i l t was needed in order to m aintain a reasonably good vaetnm in the speetR tueter, and to determine the affe ctiv e window by mm&miqg the pressure gradient a t the s i l t*

From these measurement *, i t could m learned whether

the s l i t width required 1b too narrow to be o^sipa tib ia with good spectrometer transm ission, and whether the e ffe c tiv e window th ic k ­ ness compares favorably with th a t of present th in windows*

The ea^ertaentel arrangement is shown In Pig# X* The vapor of ti* eth y l alcohol was allowed to l o a through the s l i t in to the evacuated c hasher*

The pressure mi d iffe re n t c&etafieaa

x from the a l i i was axe eu red bjr a sm all proha which eerved as the hosted filam ent of a F irani Gauge* The profee oonsisted o f p a rt o f a tungsten filament used in a 6 w&tt-XXO vs I t P ilo t bulb and was wound in fefee fora of a h e lic a l sol 1 having a length o f 5 » and a diam eter of apjproadmately #025

to #

The ends of tho c o il

ware fastened with solder to two humel contact#, and t he axis o f the c o il v&e Xiiiod up p a ra lle l to tha-length o f the s l i t*

The

distance of the probe from the s l i t could fee varied fros* loos than 1 m to 15 w fey a screw cm the outside of the diamber* The f im n l Gauge was calib re ted i&th a standard fIJi.G* type 501 *herfeocoupls Gauge Which was connected to the chamber* Tte rung© o f preeeuree extended from 10"^ to 10~^ m Mg# To caver the w g « , i t was f&und th a t the optimum operating condi­ tio n

ffer feha tun,,ston Hlament was with a current o f *003 amps

and &p o te n tia l drop of 9Z volts a t a proesum* of 10“^ wm Mg* The heated filam ent is connected

to

©ne am

of a

feheaietone bridge

using a heeds and iforthrup box type ^Ivanomi&ter laving a sensi­ t i v i t y of IflT® amp per division#

K ith the above operating condi­

tions* the galvanometer d efle ctio n la o ff scale* however, as the pressure i s inertmsed* the temperature md henee t o resistan ce of t o filament ie oacroased, giving gtdu&mmwter deflecttiona which a re on scale for t o above nange#

-r

Tit® re su ltin g c a lib ra tio n

3 E 3 CL

< Q.

/'w

curve is shown in

2* where the gslvanoiBster d e fle c tio n s f o r

the tungsten filam ent are plot ted against tfe© pressure# in wm llg o f ill® Thermocouple Gauge* o f the filam ent

Tm p o s s ib ility th a t the tem perature

would. v a r y a s

i t s distance

x

from tbs sd.it varied

r removing the vapor, anti which a t the &®m time, prevented contamination of the pumps* The a c tu a l v a ria tio n of pressure? wi to d is tance * from the s l i t is i&iom in Fig* 3* d iffe re n t s l i t s t

The re s u lts are given for two

on© was *5 ®m vide and X cm long, md th e

o th er was made up of 2 rows of .OX35*1 diam eter holes with, a to ta l width of *8 t o and a to ta l length of 1 cm*

I n te r e s t w ill

fo© centered on the *5 am wide s l i t since i t $ vm the la rg e r trssn ©mission. I f the counter hm a suudmua pleasure of 2 cm iig0, then i t i s aean that most of the ppeseure drop (from 2 cmHg to .01 cmHg) occurs within a &stares of .08 m iron tbs s lit .

Pirani

e E

Gauge

o> X

Calibration

o o

OJ

I

O

C \J

b> Ll_

O

o

o

o

uo;;o9|>ap ja+auuouDA|DO

o

o

OJ

o

fO

ro i O

o o a> I Fig, 3.

Pressure

Gr a d i e n t

at

Count er

Slit

th U region, th» pree®ur» tiro pa m m g rad u ally u n t i l i t reaches & f in a l value of *001 c©% a t-d ie tra c e s g re a te r than 2 m*

(The t&moctoupla gauge whtc h was lo ca te d a t a d istan c e o f

about 7 o®. from the e l l t recorded a pressure Xaao than «001 csiHg a t a l l t i m e .} The e ffe c tiv e window tfeieknsuis x

la given in 0k®/mft

bgr in te g ra tin g we r the t o t a l e le etso n path X t

r

j

* J f i t )

(3)

S t.

idler® p x preeaure of gm f « Teepm iturtt of §m in °K. For T0 s 273° K and p0 ® 76 cm Eg* JJ as #00126 g a ss /c o

Hence, fo r T s 293° £

X

= p To

j>

T

°

P

* 1.54 * 10“5P

^o

(4)

where p Is express sod in u nits of cm Hg.

Equation (2) then hcccmes

■£

-

1.54 X 10-5

j

£

12-

P (x)

(S)

Since no d ata i s a v a ila b le fo r x

< .OS m and x > 1*5 cm, an

exact c a lc u la tio n cannot be made® However, the o rd er of magci* tude of X

can be re a d ily eetiaated by the aifljplifying assump­

tio n s t h a t : (a) fo r x

< *08 m t the curve can fee ex tra*

isolated by the dotted s tr a ig h t lin e to th e % on p o in t on the p a x is , (b) fo r *08 cm £ x

^ 2 cm, the curve can b©

approximated by tbs d o tte d s tr a ig h t llm from p * #01 cmHg to p * *001 cmBg» (©) and fo r S e a i* x £■ JTA

(where A*

r 5 cm ®p@ etro»ter rad iu s) p i a constant and in equal 'to- #001 eaiHg* With then© assumption©, Equation (5) becomes

7T

~

where p^

(x) » *24*$75 x

+ 2

p2

(x) s **00469 x

+ *010375

p3

(x) ~ *001

1 .6

/ f

0

£

X

-r

2 ^ x £ 5 77

g c i/c * 2

This estim ated thickness e©{spare© favorably with the very th in n e st window® y e t developed (L5) which arc approxim ately

7.5 y^ga/cm2 and tran sm it electrons down to 2 Kev* A® w ill be described l a t e r , i t wan found d u r l ^ the course o f th e experiment

*13*

.08

I

t o t wiiwaowa qwM b® mad© having ibSoknesseo le a s than jt

fiance, these ptvXSmimry resxilta were encouraging enough to m erit the co n stru ctio n and fu rth e r in v e stig a tio n of aucfe a windowless ©peetomeber and such an alcohol m p o r-fi lie d counter. I t wouM be o f .interest; In designing the spectrom eter i© know what t o a sm fre e path i s for m to c b ro n Iw a rsm l in a gas having a pressure of *001 cm Bg, which i s th o m xlm w pressure fo r d ista n c e s x

2 m from. t o

o f tb s e le c tro n i s given by t o

s ilt,

Tbs moan tr m path

expression

A&

.J ^

(6)

w h ere

< T z: I

(Molecular diam eter o f e th y l alco h o l)

X 10

(no, of molecule a/ce) where fiemalty of gas a t pressure of *001 esd%See Iquation (4)

(m Jssol* wt* for l&hyX

M = Hi

N = i x

alcohol)

(Avogadro'e Humber)

/o '*

Hence# with the numerical su b stitu tio n s# >

'le

^

15*5 cm

I t is to be noted t o t th is Is the ^ p ro x im ate d ia tm c s tra v e lle d by an e le c tro n moving from source to co rn ier in a 180° typo spec**

•dwt**

2

.

trom ster having a 5 cm rad iu s. Design of Speotfgomotoi* Tte p a rtic u la r dssign o f t o apeo t o n s t e r was motivated by c e rta in requirem ents.

F irst# m on® of i t s novel fe a tu re s,

the im tm m n t l a to be used s&tfo a *wlmiowleaw* 0-44 counter In a manner described in t o pmvious m p a r t o n t,

fid® moan® t o t

to avoid excessive sc a tte rin g in a vacuum of 10"*^ mm % the t o ta l electron path should preferably bo no gran to r than tip ele ctro n

m m ir m p ath o f about 15 cm calcu lated previously,

(Equation ( 6 )) .

F urther, Um trninsdaalon of tb s speetjm nsisr ehouM bo largo be~ causa of the re la tiv e ly small in te n s itie s a t the low en erg ies. Also# a b a ffle armitgenent ie to b@ preferred where sc a tte rin g can be kept at a minimum, fo r t o s s reasons# i t was decided t o t the uniform f i e l d , sem icircular focussing type s p e c t n m te r mute ip mmt s u ita b le ,

then c e rta in ly , & sm all spec trass©ta r radius would give

a small electro n path and a large transadesioru p ra c tic a l lim it of tew sm all to make t o

However, t o

radius i s prescribed

by the re so lu tio n d e sire d , by sc a tte rin g e f f e c ts , and by- the max-

Usm magnetic fie ld required.

In th is ease, the moat favorable

arrangement wee obtained for a tra je c to ry radius of 5 e».

Then,

to focus electrons having a maximum energy of spproxieately 200

%m or 1500 HP , i t would require a maximum f ie ld of 300 Gauss*

-15«

?h© arrangement of the eertrce, detecto r s l i t , •••nd b a ffle s Is shown in Fig, 4® the source width unod m.M a ltiftr X

vm or 2 $m9 (fh& width of tbs detector s l i t was nuncio the

m m a s the source width for th e optimum condition of maximal in te n s ity for a given reso lu tio n ( l6 ) , except in tb s

cw js

of

the *wliidowleae* m unier where & source width o f 2 msa encl de­ te c to r s l i t width of ,5 mi was used*)

Because o f the increased

in te n s ity for a given source thickness, the source width o f 2 sm proved to he m w d« a ir ab le.

In a l l caeea', the height of the

©ource end the d etecto r s l i t win© fixed at 1 ci

■*■

wj ■ * » ■ * . ■ !.»

The spectrometer was calibrated by netiiuriTWr the F lin e of Thorium Uu This measurement was m&de with a source and s i l t width o f 2 asm and with » defining s l i t wMtb o f 1*03 am as bi®cussad in the section on Deaigi of Spectrometer*

T!*e resulting

lin e that was obtained is sfown in Fi&» 9# By extrapolating th® back edge of the line to i t s in te r cert ion with the background of the continuous Beta spectrum» i t i s seen that the detector s l i t accepts electrom having th© par­ tic u la r Hf

value of the Thorium B F

up to u value of th#

fie ld current equal to 243.9 me# This means th at such electrons w ill bo focussed with the sm allest rod!us of curvature permitted by the fin ite widths of the source and s l i t ,

fdnce in th is case,

the separation of the Inside edg^j» of the ucurae and detector s l i t s is 9,8 cm, the smallest radi.ua would bo 2j§

cm. Mow, the Ilf*

value of th® Thorium B F lin e m $iven by siegbalm ($1) is 1383*9 Oauae-cau

Therefore, in th is base, the currant

in tlie c o ils produces the magnetic fie ld B0,

-3 0 -

of 24B#9 ms

Current

(,m a)

Thori um

B

F Line

io

in

ID

ID

CM

ID CM

where

H0 2sM a

ajr

^

-

1303.9 Cause

however, In the moasuremoKt ©f continuous Beta spectra, the electio n s th at are detected for & given field have a spread in th e ir m i t e of curvature.

4s

I t is therejfo]* noccss&jy to use

an average radius (except very nc&r the end point) in computing the H $ value® fo r the continuous ttpeotnuu the average radius

f>

In the shove examplej

J |l caw Hence, to ce&puie the U J &v.

la

value corresponding to a given c o il currant* i t is only necessary to m ultiply the current by a certain constant K, since the H eld is lin e a r with the current.

In ihLs c&se* g

or

X .