The Spectroscopy of Nuclear Gamma-Rays

Citation preview

THE

SPECTROSCOPY

OP

NUCLEAR

GAMMA-RAYS.

hy

E„ R. Rae, Department o f N a tu r a l P h ilo so p h y , U n iv e r s it y

of

Glasgow

P re s e n te d as a t h e s i s f o r th e d egree o f Ph.D. in t h e U n iv e r s it y o f Glasgow. A p r i l , 1950.

ProQuest N um ber: 13870197

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P RE F ACE .

In t h i s t h e s i s I have t r i e d to show how th e method o f G-amma-Ray S p ectro sco p y i s used as a t o o l i n o b ta in in g in f o rm a tio n about t h e s t a t i o n a r y s t a t e s o f n u c l e i .

P art I,

i n which I have drawn f r e e l y from Devons (E x c ite d S t a t e s o f N u c le i) , d e a ls w ith t h e g e n e r a l argument and w ith t h e te c h n iq u e s a v a i l a b l e in th e a p p l i c a t i o n of t h e method. P a r t I I c o n t a in s an a n a l y s i s o f t h e r e l a t i v e m e r it s o f t h e v a r i o u s ty p e s o f sp e o tro m e te r employing m agnetic r e s o l u t i o n , and l e a d s t o th e c h o ic e and d esig n of t h e i n s t ­ r u m e n t s b u i l t h e re and used i n t h e e x p e rim en ts d e s c r ib e d la te r.

The a n a l y s i s and d e s ig n s a r e i n g e n e r a l o r i g i n a l ;

t h e p r i n c i p l e s in v o lv e d a r e n o t .

I m ight mention h e re

Appendix I , which c o n t a in s a d esig n f o r a new ty p e o f b e t a r a y s p e c tr o m e te r o f v e r y h ig h i n t e n s i t y f a c t o r .

T h is work

has been p la c e d i n an appendix s o l e l y b ec au se t h e i n s t r u ­ m e n t i s n o t s u i t a b l e f o r u se as a gamma-ray s p e c tr o m e te r , b u t th e d e s ig n , which i s a development o f an i d e a su g g e ste d by Dr. S.C. C urran, may prove to be im p o rta n t in th e s e p a r a tio n o f complex b e t a - r a y s p e c t r a by t h e method o f beta-gamma c o in c id e n c e s . P a r t s I I I and IV d e s c r ib e t h e e x p e rim e n ta l work and th e s i g n i f i c a n c e o f th e r e s u l t s o b ta in e d ;

t h e m a tte r h e re i s

o r i g i n a l , a l l th e work having been c a r r i e d out s o l e l y by m yself w ith t h e e x c e p tio n o f t h e experim ent on T h is/

P> ( i l l , 2).

T h is ex p e rim en t, which in v o lv e d t h e use of t h e p ro to n a c c e l e r a t o r , was su g g e ste d by Mr. J.G-. R u th e rg le n , and was c a r r i e d out in c o l l a b o r a t i o n w ith him and w ith Mr. R.D. Smith, t h e s e w orkers b e in g r e s p o n s i b l e f o r th e p r e p a r a t i o n of t h e t a r g e t s , and f o r t h e s a t i s f a c t o r y perform ance o f t h e a c c e l e r a t o r and i t s a u x i l i a r y equipm ent. I must th a n k P r o f e s s o r P . I . Dee and Dr. S.C, Curran f o r t h e i r s u s t a i n e d i n t e r e s t and encouragement th ro u g h o u t th e work, a ls o Dr. B.E.X. Touschek and Mr. D.L. P u rsey f o r h e l p f u l d i s c u s s io n on s e v e r a l p o i n t s o f t h e o r y , and f i n a l l y Mr. H.Vif. Wilson f o r p e rm is s io n to re p ro d u c e t h e spectrum o f t h e gamma-rays from Hg 203^ which he observed w ith one o f t h e s p e c tr o m e te r s m entioned above.

E.R.R*

A p r i l, 1950.

THE

SPECTROSCOPY

OP

NUCLEAR

GAMMA-RAYS

CONTENTS Pages PART I ,

-

GENERAL

INTRODUCTION.

1-21

1 .1

The Purpose o f Garoma-Ray S p ectro sco p y ; c a p a b i l i t i e s and l i m i t a t i o n s .

1

1 .2

T echniques i n Gamma-Ray S p ectro sco p y . (a) D i f f r a c t i o n ; (b) Simple A b so rp tio n ; (o) N u clear P h o to - E f f e c t: (d) Coin­ c i d e n c e A b so rp tio n ; (e) Magnetic A n a ly s is .

4 - 1 0

1*3

Survey o f Work Done. (a) C l a s s i f i c a t i o n ; (b) N a tu ra l R adio: a c t i v e E lem ents; (c) A r t i f i c i a l R a d io a c tiv e E lem ents; (d) N uclear R e a c tio n s

10 - 18

1.4-

O p p o r tu n itie s f o r U seful R esearch. (a) The G eneral P i e ld ; (b) The P r e s e n t R e sea rc h .

18 - 21

PART I I . -

INSTRUMENTATION.

-

4

22

-

58

-

35

1 1 .1

Comparison o f D i f f e r e n t Types o f M agnetic A n a ly s e rs. (a) S e m i-C irc u la r R e s o lv e rs ; (b ; Magnetic L enses; (c) The Double P o cu ssin g S p e c tro m e te r.

22

1 1 .2

The S e m i-C irc u la r R e s o lv e r. (a) The E lec tro m ag n e t; (b) The S p ectro m e ter; (o ; The C ou nters; (d) C a l i b r a t i o n o f t h e S p ectro m e ter.

36 - 45

II.5

T h e -P a ir S p e c tro m e te r. (a ) An E a r ly Id e a ; (b) The Double S e m i-C irc u la r R e so lv e r; (c) The M u lti-C han nel P a i r S p ectro m eter; (d) C o n s id e r a tio n s i n th e Design o f a M ulti-C hannel In s tru m e n t; (e) The Glasgow P a i r S p ectro m e ter.

45 - 58

PART I I I . /

Pages PART I I I . - ENERGY DETERMINATION AND THE CONSTRUCTION OF ENERGY LEVEL DIAGRAMS.

PART IV.

59 - 75

111.1

Praseodymium-142. (a) P re v io u s Work; (b) The Beta-Ray Spectrum; (c) The Gamma-Ray Spectrum; (d) The Decay Scheme.

60 - 69

1 1 1 .2

F lu o rin e -1 9 « (a) P re v io u s Work; (b) The Gamma-Ray Spectrum; (c) D is c u s s io n .

69 - 75

- DETERMINATION OF ENERGY AND MULTIPOLE ORDER. THE COMPLETE SOLUTION.

76 - 98

IV .1

T h e o r e t i c a l Background. (a) G en e ra l; (b) I n t e r n a l Conversion; (c) I n t e r n a l P a i r C r e a tio n .

76

-

86

I V .2

Sodium-24»

86

-

93

(a) E xperim ent; I V .3

APPENDIX I SOLID

F u tu re Work and P o s s i b l e E x te n s io n s o f The te c h n iq u e .

A MAGNETIC ANGLE

APPENDIX I I - CIRCUITS SPECTROMETER.

REFERENCES

(b) D is c u s s io n .

SPECTROMETER

OP

LARGE

OP THE GLASGOW PAIR

93 - 98

i

xvi

PART 1 ,1 .

I.

-

GENERAL

INTRODUCTION.

The purpose o f Gamma-Ray S p ectro sc o p y ; and l i m i t a t i o n s .

i t s c a p a b ilitie s

I t might be s t a t e d t h a t gamma-rays a re t h e l i g h t of th e atom ic n u c le u s s in c e th e y a re t h e e le c tr o - m a g n e tic r a d i a t i o n e m itte d by t h e n u c le u s d u rin g a change from one s t a t e t o a n o th e r in th e absence o f p a r t i c l e e m issio n .

Now i t i s w ell

known t h a t t h e i n t e n s i v e stu d y o f o p t i c a l s p e c t r a which too k p la c e tow ard s t h e end of th e n i n e t e e n t h c e n tu r y , and t h e g e n e r a l e m p ir ic a l laws which were found to govern t h e s p e c t r a e m itte d by hydrogen and a few o th e r elem e n ts, l a i d t h e b a s i s f o r t h e t h e o r i e s which were l a t e r t o e x p la in n o t o n ly t h e em ission of o p t i c a l s p e c t r a , b u t th e whole e l e c t r o n i c s t r u c t u r e o f th e atom.

C onsequently i t might seem n o t u n re a s o n a b le t o

suppose t h a t t h e stu d y of t h e n u c l e a r gamma-rays would le a d t o a s i m i l a r c o l l e c t i o n of d a t a co n c ern in g n u c l e a r s p e c t r a , which must le a d i n th e end t o t h e f o r m u la tio n of e m p ir ic a l r u l e s and so t o a b e t t e r u n d e rs ta n d in g of t h e s t r u c t u r e o f t h e atomic n u clei . While i t i s arguments of t h i s k in d which p ro v id e t h e main j u s t i f i c a t i o n f o r t h e stu d y of gamma-ray s p e c tro sc o p y , i t must be c l e a r l y u n d e rsto o d t h a t t h e analogy b e t ween o p t i c a l and gamma-ray s p e c tro sc o p y i s on ly a v e ry lo o s e one, f o r t h e f o llo w in g r e a s o n s .

F i r s t l y , i n th e atomic ca se i t i s com-

: p a r a t i v e l y easy t o e x c i t e t h e whole spectrum , and measurements

o f t h e energy ( o r w avelength) of each l i n e can be made w ith a v e r y hig h degree o f p r e c i s i o n , w h ile in th e n u c le a r case e x c i t a t i o n i s on ly p o s s i b l e th ro u g h s p e c i f i c n u c l e a r r e a c t i o n s o r th ro u g h r a d i o a c t i v e d e c a y ,+ and a p a r t from th e low energy r e g io n (up t o about 1 M.E.V.) where o p t i c a l d i f f r a c t i o n te c h n iq u e s can be u sed , t h e p r e c i s i o n a v a i l a b l e i n gamma-ray energy measurement i s n o rm ally only about 1%.

In th e second

p la c e th e o b s e rv a tio n of atom ic s p e c t r a r e p r e s e n t s , i f n o t th e only way, c e r t a i n l y t h e most a c c u r a te way i n which in fo rm a tio n can be o b ta in e d about th e energy l e v e l s i n t h e e l e c t r o n i c s t r u c t u r e of t h e atom:

in th e n u c l e a r case however, th e

measurement of gamma-ray e n e r g ie s i s on ly one of s e v e r a l t e c h :n ia u e s f o r o b ta in in g in fo rm a tio n about n u c le a r l e v e l s , and w h ile i t i s t h e most g e n e r a l method a v a i l a b l e , t h e r e a re c e r t a i n l y o t h e r s w ith l i m i t e d a p p l i c a t i o n s which p ro v id e a much h ig h e r degree o f p r e c i s i o n . I t i s however t h i s f e a t u r e o f g e n e r a l i t y which makes th e method o f gamma-ray sp e c tro sc o p y so a t t r a c t i v e and p o t e n t i a l l y so im p o rta n t i n th e stu d y o f n u c l e a r s t r u c t u r e , f o r alth o u g h i t i s p o s s i b l e by t h e stu d y o f e x c i t a t i o n cu rv es due t o bombard­ m e n t by p r o to n s and n e u tro n s , t o o b ta in v e r y a c c u r a te and d e ta ile d /

4* E x c i t a t i o n by c o l l i s i o n i s o f co u rse p o s s i b l e u s in g beams o f f a s t p a r t i c l e s , b u t i s v e r y d i f f i c u l t compared w ith t h e methods a p p l i c a b l e t o t h e e x c i t a t i o n of atom ic s p e c t r a .

3. d e t a i l e d in f o rm a tio n concerning a sm all p a r t of th e energyl e v e l diagram o f th e compound n u c le u s formed, and alth o u g h i t i s p o s s i b l e i n p a r t i c l e - p a r t i c l e r e a c t i o n s , by o b se rv in g th e energy o f th e outcoming p a r t i c l e , to o b ta in in f o rm a tio n about th e a b s o lu te p o s i t i o n of th e l e v e l s in th e r e s i d u a l n u c le u s , each of th e s e methods i s l i m i t e d in p r i n c i p l e , and b o th can be made t o y i e l d s t i l l more in fo rm a tio n by combining w ith t h e i r r e s u l t s , measurements of th e e n e r g ie s of t h e gamma-rays p ro­ d u c e d in th e r e a c t i o n s con cern ed.

A l i m i t a t i o n t o th e form er

of t h e te c h n iq u e s m entioned above i s t h a t th e c a p tu r e of a nucleon by t h e n u c le u s o f a l i g h t element always p rod uces a compound n u c le u s which i s in a h ig h ly e x c ite d s t a t e , and so t h i s method cannot be used to e x p lo re th e r e g io n n e a r t h e ground s t a t e ;

f o r i n s t a n c e i t could no t be used to f i n d th e

f i r s t e x c ite d s t a t e of such a n u c le u s .

A l i m i t a t i o n which

a p p l i e s t o b o th o f t h e above te c h n iq u e s i s t h a t i t may n o t be p o s s i b l e t o i s o l a t e th e d e s ir e d r e a c t i o n because th e t a r g e t n u c le u s may be r a d i o a c t i v e w ith a s h o r t h a l f - l i f e .

The

im p o rta n t p o in t i s t h a t t h e s e l i m i t a t i o n s i n t h e a p p l i c a b i l i t y o f two of th e b e s t te c h n iq u e s f o r t h e stu d y o f n u c l e a r l e v e l s a re l i m i t a t i o n s which depend on t h e n a t u r e o f m a tte r .

The

l i m i t a t i o n s i n th e u se of gamma-ray sp e c tro sc o p y however, th e d i f f i c u l t y in e x c i t i n g th e n u c l e i and in a c h ie v in g a h igh d egree o f p r e c i s i o n , a r e r a t h e r l i m i t a t i o n s in te c h n iq u e , which su g g est t h a t th e stu d y of t h i s method may be v e r y much w o rth /

w orth w h ile . One f u r t h e r g e n e r a l f e a t u r e of gamma-ray sp e c tro sc o p y must be m entioned b e f o r e we proceed to d is c u s s in r a t h e r more d e t a i l t h e k in d of work t h a t has been done i n t h i s f i e l d up t o t h e p r e s e n t , and t h a t i s t h a t i n th e exam ination of gamma-ray s p e c t r a w ith m agnetic s p e c tr o m e te r s , i t i s p o s s i b l e to o b ta in in f o rm a tio n , n o t on ly about th e energy of th e gamma-ray l i n e s observed , but a ls o about th e m u ltip o le o r d e r of th e t r a n s i t i o n s g iv in g r i s e t o th o s e l i n e s .

The re a s o n f o r t h i s i s t h a t th e

em ission o f a photon by a n u c le u s always t a k e s p la c e in c o m p e titio n w ith th e em ission o f an e l e c t r o n ( i n t e r n a l C onversion) o r of a p o s i t r o n - e l e c t r o n p a i r ( I n t e r n a l P a i r - C r e a t io n ) th e ex c ess energy ap p e a rin g as k i n e t i c energy o f th e ele c tro n or p a ir .

Now th e p r o b a b i l i t y of o cc u rre n c e of t h e s e

phenomena i s a f u n c t i o n o f t h e m u ltip o le o r d e r o f t h e n u c le a r t r a n s i t i o n concerned, and so a d e te r m in a tio n of t h i s p r o b a b i l i t y ( I n t e r n a l Conversion C o e f f i c i e n t , o r I n t e r n a l P a ir - C r e a ti o n C o e f f i c i e n t ) y i e l d s in fo rm a tio n about th e m u ltip o le o r d e r o f th e t r a n s i t i o n , and so about th e s p in s o f t h e n u c l e a r l e v e l s in v o lv e d .

1 .2 . (a)

T echniques i n G-amma-Hav b p ec tro sco p y .

D iffra c tio n . I f we now c o n s id e r i n more d e t a i l th e problem of t h e

measurement/

5. measurement o f gamma-ray e n e r g ie s , i t i s c l e a r t h a t s in c e gamma-rays r e a c t w ith m a tte r in a number of d i f f e r e n t ways, t h e r e a r e c o rre s p o n d in g ly many ways i n which t h e i r e n e rg ie s may be deduced.

C e r t a i n l y th e most fun d am ental and p r e c i s e

method o f measurement i s t h a t a f f o rd e d by d i f f r a c t i o n a t a g la n c in g an g le i n a c r y s t a l .

T h is method, which i s r e a l l y an

e x te n s io n of t h e o p t i c a l te c h n iq u e , i s o f co u rse c a p a b le of g r e a t accu rac y s in c e i t m easures w avelength i n te rm s o f th e c r y s t a l l a t t i c e sp a c in g ;

i t has a ls o been improved l a t e l y by

th e use of curved c r y s t a l s to produce a f o c u s s in g e f f e c t and in t h i s form has been u se d , among o th e r t h i n g s , t o determ ine th e w avelength o f th e two-quantum p o s i t r o n a n n i h i l a t i o n r a d i a t i o n (Du Mond, l i n d and Watson, 1949)*

The l i m i t a t i o n s

o f t h i s method a r e t h a t i t demands a v e ry s tr o n g sou rce and a ls o t h a t t h e r e i s an u pp er l i m i t to th e energy a t which i t can be used on account o f t h e v e r y sm all a n g le s in v o lv e d , which d im in ish w ith i n c r e a s i n g energy.

Du Mond e t a l . used so u rce s

o f t h e o r d e r of 1 C urie t o o b ta in t h e i r ac cu racy o f 1 p a r t in 1 0,000, and th e h ig h e s t energy l i n e th e y have i n v e s t i g a t e d ap p e ars to be t h e 1 .3 M.E.V. l i n e from r a d i o - c o b a l t ( l i n d , Du Mond and Brown, 1949)*

Thus f o r e n e r g ie s much i n ex cess of 1

M.E.Y., and f o r a l l c a s e s where o nly sm all so u rc e s a r e a v a i l ­ a b l e , i n d i r e c t methods must be used, such as th e measurement of t h e a b s o rp tio n c o e f f i c i e n t of t h e r a y s in d i f f e r e n t m a t e r i a l s , and measurements on secondary p a r t i c l e s produced by th e /

6

t h e gamma-rays.

(b)

Simple A b so rp tio n . The f i r s t o f th e s e methods, t h a t of d e te rm in in g t h e

a b s o rp tio n c o e f f i c i e n t o f t h e gamma-rays in v a r i o u s m a t e r i a l s , i s u s e f u l in t h e d e te r m in a tio n o f t h e energy o f s o f t gamma-ra d ia tio n .

The measurements must however be c a r r i e d out w ith

g r e a t c a re i f e r r o r s due to s c a t t e r i n g a r e to be av oided , and t h e method sh ou ld p r e f e r a b l y be used only e m p ir i c a l ly , t h a t i s where gamma-rays o f known energy a r e a v a i l a b l e f o r c a l i b r a t i o n p u rp o se s,

where more th a n one gamma-ray i s p r e s e n t i n th e same

energy r e g io n , th e method b re a k s down co m p letely , and i t i s a ls o made d i f f i c u l t a t e n e rg ie s much in excess o f 1 .5 M.E.V. by t h e f a c t t h a t a t h ig h e n e r g ie s t h e a b s o rp tio n c o e f f i c i e n t s change to o slow ly w ith energy t o p ro v id e much in f o r m a tio n . There i s a ls o th e d i f f i c u l t y t h a t s in c e t h e a b s o rp tio n c o e f f i c i e n t s have a minimum v a l u e , i t i s n e c e s s a r y t o determ ine t h e c o e f f i c i e n t i n more th a n one m a t e r i a l to avoid am b ig u ity. An example o f t h e e r r o r s in v o lv e d i n t h i s method i s g iv en in t h e p u b lis h e d r e s u l t s on t h e r a d i a t i o n s o f P r ^ ^ quoted in III.l. In comparison w ith t h e l i m i t e d a p p l i c a b i l i t y of t h e method of sim ple a b s o r p tio n , measurements on t h e secondary p a r t i c l e s produced by gamma-rays have p ro v id ed u s e f u l in fo rm a tio n th ro u g h ­ o u t th e e n t i r e observ ed gamma-ray spectrum .

The secondary

p a r t i c l e s may be f u r t h e r su b d iv id ed i n t o l i g h t and heavy p a rtic le s/ s

7. p a r t i c l e s , t h e fo rm e r, e l e c t r o n s and p o s i t r o n s , o r i g i n a t i n g i n th e p h o t o - e l e c t r i c e f f e c t , t h e Compton e f f e c t and p a i r p r o d u c tio n , and t h e l a t t e r , p r o to n s and n e u tro n s m ainly, i n th e n u clear p h o to -e ffe c t.

(c)

H uclear P h o to - E f f e c t. While a l l t h e s e e f f e c t s have been u t i l i s e d in t h e d e t e r ­

m i n a t i o n o f gamma-ray e n e r g i e s , th e use of t h e n u c l e a r photo­ e f f e c t has of n e c e s s i t y been r a t h e r l i m i t e d .

I t i s l i m i t e d on

th e low energy s id e by th e f a c t t h a t th e n u c le u s most commonly used (Deuterium) r e q u i r e s t h e t h r e s h o l d energy o f 2 .2 M.E.V. b e fo re t h e e f f e c t can be ob serv ed, w hile on t h e h ig h energy s id e th e u se o f t h e te c h n iq u e i s made d i f f i c u l t by th e f a c t t h a t th e c r o s s - s e c t i o n f o r t h e e f f e c t f a l l s o f f , and a ls o a t h ig h e n e rg ie s (above 10 M.E.V.) o th e r n u c l e i s t a r t to d i s ­ i n t e g r a t e which co n fu se s th e i n t e r p r e t a t i o n o f t h e observed d ata.

The method used by Gibson, Green and L ivesey (1947) was

t o im pregnate an I l f o r d D uclear P l a t e w ith heavy w a te r, expose i t t o th e gamma-rays, th e n develop i t and examine th e p ro to n tra c k s.

In t h i s way th e y were a b le to measure th e energy of

th e 6 M.E.V. gamma-rays from th e F (p ,« 0 r e a c t i o n .

Here th e

use o f t h e method i s c e r t a i n l y r e s t r i c t e d a t h ig h e n e rg ie s by th e p h o t o - d i s i n t e g r a t i o n o f o th e r m a t e r i a l s i n th e p h o to g ra p h ic p la te . Another u s e f u l a p p l i c a t i o n o f t h e n u c l e a r p h o t o - e f f e c t t o th e measurement o f gamma-ray e n e rg ie s was t h a t o f Baldwin and Koch/

Koch (1945)*

These a u th o rs made up a l i s t of elem ents in which

t h e (2f,n) r e a c t i o n l e f t a r a d i o a c t i v e n u c le u s w ith a h a l f - l i f e of a t l e a s t s e v e r a l m inutes and t h e i r t h r e s h o l d s ran g e from 9-3 M.E.V. f o r Ag"^^ t o 19 M.E.V. f o r C ^ .

With t h i s l i s t i t i s

t h e o r e t i c a l l y p o s s i b l e t o determ ine th e end p o in t o f a gamma- r a y spectrum by a ’’B r a c k e tin g 1’ p r o c e s s , and t h i s method was used r e c e n t l y by Devons and Hereward (1948) t o dem o n strate th e e x is te n c e o f p ro to n c a p tu r e gamma-rays from F l u o r i n e , u s in g Cu J as d e t e c t o r .

The method i s of c o u rse r a t h e r cru d e , b ut

has th e g r e a t advantage t h a t i t makes i t p o s s i b l e to d e t e c t a v e r y weak h ig h energy r a d i a t i o n i n t h e p re se n c e o f i n t e n s e r a d i a t i o n o f a low er energy, as i n t h e example quoted where th e h ig h energy r a d i a t i o n had n o t p r e v io u s l y been o bserved by any o th e r method.

I t i s however c l e a r from th e above, t h a t th e

u se of t h e n u c l e a r p h o t o - e f f e c t does n o t p ro v id e a method o f gamma-ray sp e c tro sc o p y c a p ab le o f v e r y g e n e r a l a p p l i c a t i o n s in c e i t can o n ly be used a t r a t h e r hig h e n e r g i e s , and even th e n t h e most co n v en ien t method of u s in g i t , th e deuterium lo a d ed p l a t e , b re a k s down a t much h ig h e r e n e r g ie s because of th e d i s i n t e g r a t i o n of o t h e r m a t e r i a l s i n t h e p l a t e .

(d)

C oincidence A b so rp tio n . I t rem ain s th e n t o d is c u s s t h e u se o f t h e l i g h t secondary

p a r t i c l e s in te c h n iq u e s f o r t h e measurement o f gamma-ray en e rg ies.

The s im p le s t method h e re i s t o measure t h e ran g e of

t h e s e c o n d a rie s by th e c o in c id e n c e a b s o rp tio n method. m ethod/

In t h i s

method t h e secondary p a r t i c l e s produced in a ’’C o n v e rto r11 a r e caused t o p a s s r i g h t th ro u g h one t h i n w a lle d G.M. c o u n te r and e n t e r a second c o u n te r .

The ran g e o f t h e p a r t i c l e s i s th e n

found by p la c in g s h e e ts of a b s o rb e r between th e c o u n te rs and p l o t t i n g th e c o in c id e n c e c o u n tin g r a t e a g a in s t th e a b s o rb e r th ic k n e ss.

When th e a b s o rb e r th ic k n e s s i s g r e a t e r th a n th e

ra n g e of t h e secondary p a r t i c l e s , no f u r t h e r drop i n t h e c o in c id e n c e c o u n tin g r a t e can ta k e p l a c e .

T h is method, i n th e

hands o f e x p e rie n c e d w orkers, i s ca p ab le o f d ete rm in in g th e energy of a s i n g l e gamma-ray l i n e t o a few p e r c e n t, over a v e r y wide ran g e o f e n e r g ie s (C urran, Dee and P e t r i z i l k a , 1938); but i t b re a k s down when i t i s n e c e s s a r y t o d is c r i m in a te between two l i n e s of com parable energy because i t has v e r y bad re so lu tio n .

I t may a ls o g iv e t r o u b l e i f two gamma-rays a re

p r e s e n t i n c o in c id e n c e , ( in cascad e) o r i f t h e energy o f t h e gamma-ray i s v e r y h ig h so t h a t p a i r p ro d u c tio n and brem sstrahluqg become im p o r ta n t.

C onsequently t h i s method i s o n ly used now f o r

rough survey work, o r w ith v e r y weak s o u rc e s , where i t s extreme s i m p l i c i t y and i t s h ig h s e n s i t i v i t y outw eigh i t s d is a d v a n ta g e s .

(e)

M agnetic A n a ly s is . In a l l a c c u r a te work however, (ex ce p t a t v e ry low e n e r g ie s

where t h e p r o p o r t i o n a l c o u n te r te c h n iq u e developed r e c e n t l y by Curran and h i s co-w orkers (C urran, Angus and C o c k ro ft, 1949), has proved a v e r y pow erful t o o l ) , t h e te c h n iq u e used has been t o analyse, i n a m agnetic r e s o l v e r of some k in d , t h e l i g h t se c o n d a ry /

secondary p a r t i c l e s produced by th e gamma-rays.

A c ritic a l

d is c u s s io n o f t h e v a r i o u s methods o f r e s o l u t i o n and t h e i r use t o determ in e gamma-ray e n e r g ie s w i l l be g iv en in th e next c h a p te r ;

i t i s s u f f i c i e n t t o n o te h e re t h a t w ith good modern

te c h n iq u e s i t i s p o s s i b l e to measure gamma-ray e n e r g ie s in th e ran g e 50 K.E.V. t o 20 M.E.V. and p ro b ab ly h ig h e r , w ith an ac cu racy of 1^, and t o r e s o l v e l i n e s s e p a r a te d by 10/6 o f t h e i r energy (Siegbahn, 1946;

Walker and McDaniel, 1948).

T h is

l a t t e r f i g u r e can be g r e a t l y improved upon where s tr o n g i n t e r sn al c o n v e rsio n o c c u rs in th e so u rce ( E l l i s and S k in n er, 1924)> o r where v e r y s tr o n g so u rc e s a r e a v a i l a b l e , so t h a t v e r y t h i n c o n v e rto rs can be used and b e t a - r a y s from th e so u rce su p p ressed m a g n e tic a lly (L aty sh ev, 1947).

1.5* (a)

Survey o f Work Done.

C la ssific a tio n . As was rem arked in an e a r l i e r p a ra g ra p h , one o f t h e main

l i m i t a t i o n s to th e u se of gamma-ray sp e c tro sc o p y i s t h e d i f f i c u l t y of e x c i t i n g th e n u c l e a r s p e c t r a .

T h is d i f f i c u l t y

a t once p ro v id e s a way of c l a s s i f y i n g th e work done by th e v a r io u s w orkers i n t h e f i e l d , s in c e a l l must have used one of two methods o f e x c i t a t i o n , e i t h e r e x c i t a t i o n by r a d i o a c t i v e decay, o r e l s e by c o l l i s i o n o r th ro u g h a n u c l e a r r e a c t i o n , each of which p r o c e s s e s r e q u i r e th e use of a so u rce o f bombard:in g p a r t i c l e s . s u b d iv id e d /

The f i r s t o f th e s e groups may be f u r t h e r

11.

su b d iv id ed i n t o work done on t h e " N a tu r a l” r a d i o a c t i v e elem e n ts, and t h a t done on t h e more r e c e n t l y a v a i l a b l e " A r t i f i c i a l " elem e n ts.

Since t h e work done on t h e n a t u r a l

r a d i o a c t i v e elem ents in c lu d e s some o f t h e e a r l i e s t measure­ m e n t s made on th e n u c l e a r gamma-rays, (and a l s o some of t h e b e s t ) , we s h a l l c o n s id e r t h i s group f i r s t o f a l l .

0>)

IMatural R a d io a c tiv e E lem ents. The e a r l y i n v e s t i g a t i o n s of th e gamma-ray s p e c t r a o f th e

n a t u r a l r a d i o a c t i v e b o d ie s were r e a l l y i n v e s t i g a t i o n s of t h e i r b eta-ra y sp e c tra ;

in d e ed t h e work o f Von Baeyer, Hahn and

M eitn er (1911) was c a r r i e d out i n o r d e r to d eterm in e w hether o r n o t th e b e t a - r a y spectrum o f a r a d i o a c t i v e element was co n tin u o u s,

w ith t h e i n t r o d u c t i o n of s e m i - c i r c u l a r f o c u s s in g

by Banysz in 1913, t h e modern te c h n iq u e o f d e r iv in g gamma-ray s p e c t r a from ph o to g rap h s of th e i n t e r n a l c o n v e rsio n s p e c t r a o f th e heavy r a d i o a c t i v e elem ents was v i r t u a l l y com plete, and in t h e i n t e r v e n i n g y e a r s th e s p e c t r a o f most o f t h e n a t u r a l r a d i o : a c t i v e b o d ie s have been th o ro u g h ly i n v e s t i g a t e d , many by E l l i s whose r e s u l t s have s in c e been used as s ta n d a r d s f o r t h e c a l i b r a t i o n o f m agnetic r e s o l v e r s .

The accu racy of E l l i s ’ s

b e s t work ( E l l i s and S k in n er, 1924) i s quoted as 1 p a r t in 500, which i s rem ark ab le s in c e i t was c a r r i e d out as lo n g ago as 1924.

One re a s o n f o r th e h ig h accuracy o b ta in e d i s t h a t th e

so u rc e s used were c h e m ic a lly s e p a r a te d and o f v e ry h ig h s p e c i f i c a c t i v i t y so t h a t th e y were v e ry th in ^ and s t r a g g l i n g o f/

o f th e i n t e r n a l co n v e rsio n e l e c t r o n s was n e g l i g i b l e ;

a ls o t h e

i n t e r n a l c o n v e rsio n c o e f f i c i e n t s were h ig h on account o f th e h ig h n u c l e a r charge o f th e elem ents i n v e s t i g a t e d .

Hence i t was

p o s s i b l e and p r o f i t a b l e t o work w ith a s p e c tr o m e te r o f hig h r e s o l v i n g power.

Even so th e ac cu racy o b ta in e d was rem ark ab le,

s in c e i t was n o t m erely t h e r e l a t i v e p o s i t i o n o f t h e l i n e s which was determ in ed ( t h i s was quoted t o 1 p a r t i n 1 ,0 0 0 ) b u t th e a b s o lu te v a l u e , which in v o lv e d a measurement of a m agnetic f i e l d t o 1 p a r t in 1 ,0 0 0 .

(T his in tr o d u c e d a ls o th e q u e s tio n o f t h e

u n if o rm ity o f t h e f i e l d . )

More r e c e n t work on t h e n a t u r a l

r a d i o a c t i v e elem en ts has been concerned m ainly w ith q u e s tio n s o f 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 l i n e s , w ith th e d e te r m in a tio n o f t h e m u ltip o le o r d e r o f th e t r a n s i t i o n s , and w ith t h e s o r t i n g out o f complex b e t a - r a y s p e c t r a by t h e method o f beta-gamma c o in c id e n c e m easurem ents. gamma-ray s p e c t r o s c o p y .)

( I f t h i s can p r o p e r ly be re g a rd e d as In o t h e r words, most o f t h e e x p e r i­

m e n ts in gamma-ray sp e c tro sc o p y t h a t can be done on th e n a t u r a l r a d i o a c t i v e elem en ts w ith th e te c h n iq u e s a v a i l a b l e a t t h e moment^have a lr e a d y been done;

and w h ile , on account o f

t h e i r co m p lex ity , th e l e v e l schemes o f t h e s e n u c l e i a re by no means com plete, t h e r e does n o t seem a t t h e moment to be much o p p o r tu n ity f o r t h e a p p l i c a t i o n o f o u r method o f i n v e s t i g a t i o n . The r e s u l t s o f r e c e n t work on th e n a t u r a l r a d i o a c t i v e elem en ts have been w e ll summarised in rev iew a r t i c l e s by Latyshev (1947) and F e a th e r (1949)*

ic l/

13 (c)

A r t i f i c i a l R a d io a c tiv e E lem ents. The p o s i t i o n w ith r e g a r d t o th e stu d y o f th e gamma-rays

from th e a r t i f i c i a l r a d i o a c t i v e elem en ts i s v e r y d i f f e r e n t . Here i t i s n o t p o s s i b l e , in g e n e r a l, t o o b ta in s tr o n g so u rce s o f h ig h s p e c i f i c a c t i v i t y and so th e u se o f th e p h o to g ra p h ic te c h n iq u e i s made d i f f i c u l t .

I t has however been u sed , n o ta b ly

by H elm holtz (194-1) and Cork (1949), th e l a t t e r a u th o r employrin g A lnico permanent magnets and making exp osures o f sometimes s e v e r a l weeks.

Even so t h i s te c h n iq u e , w hile v e ry pow erful in

d eterm in in g th e energy o f s o f t r a d i a t i o n from t h e h e a v ie r e lem e n ts, h as been v e ry l i t t l e used on elem ents w ith an atom ic weight o f l e s s th a n 50, and i s of co u rse u s e l e s s f o r d e te rm in rin g th e energy o f th e h a r d e r gamma-rays (say ov er 1 M.E.V.) on account o f t h e r a p i d drop in t h e i n t e r n a l co n v ersio n c o e f f i c i e n t w ith i n c r e a s i n g en erg y .

F or t h e measurement o f th e

energy o f t h e h a r d e r gamma-rays, i t has been n e c e s s a r y to f i n d a d e t e c t o r o f much g r e a t e r s e n s i t i v i t y th a n t h e p h o to g ra p h ic p la te .

T h is has been p ro v id e d by th e G-.M. c o u n te r , which n ot

only p r o v id e s t h e in c r e a s e d s e n s i t i v i t y , b u t a l s o makes p o s s i b l e t h e c o u n tin g o f t h e i n d i v i d u a l secondary e l e c t r o n s , th u s g r e a t l y s im p lif y in g th e problem of d e te rm in in g r e l a t i v e in te n sitie s.

The d isa d v a n ta g e o f t h e G-.M. c o u n te r i s t h a t i t

can only r e c o r d th e i n t e g r a l o f a sm all p a r t of t h e spectrum a t one tim e , and so to o b ta in th e com plete spectrum th e m agnetic f i e l d must be v a r i e d and a l a r g e number of such o b se rv a tio n s/

14. o b s e r v a tio n s made.

I t may be t h a t th e r e c e n t development o f a

p h o to g ra p h ic p l a t e which can d e t e c t s i n g l e e l e c t r o n s (Berrim an, 1948) w i l l p ro v id e t h e adv antages o f b o th methods, b u t t h i s i s by no means c e r t a i n as such a p l a t e would have t o be s u b je c te d t o lo n g and te d i o u s m ic ro sc o p ic exam ination a f t e r ex po sure. In any c a se t h e problem of o b ta in in g a s e n s i t i v e d e t e c t o r i s only one p a r t o f t h e d i f f i c u l t y i n making o b s e r v a tio n s on th e a r t i f i c i a l r a d i o a c t i v e elem en ts;

t h e r e rem ains th e d i f f i c u l t y

t h a t in th e ca se of t h e l i g h t elem e n ts, and f o r e n e r g e t i c r a d i a t i o n from th e h e a v ie r n u c l e i , t h e i n t e r n a l co n v e rsio n c o e f f i c i e n t s a re so sm all t h a t w ith th e r e s o l u t i o n a t t a i n a b l e i t becomes im p o s s ib le to d e t e c t th e i n t e r n a l co n v ersio n l i n e s a g a in s t th e background of t h e co n tin u o u s b e t a - r a y s p e c tru m .. In t h i s case i t i s n e c e s s a r y to u se a c o n v e r to r and make o b s e r v a tio n s on th e secondary e l e c t r o n s from t h i s .

In t h i s

c o n n e ctio n th e te c h n iq u e o r i g i n a t e d by Siegbahn (1946 o^ has become s ta n d a r d p r a c t i c e .

T h is c o n s i s t s in p la c in g t h e so u rce

i n s i d e a hollow copper c o n t a i n e r w ith w a lls t h i c k enough to absorb a l l th e b e t a - r a y s from t h e s o u rc e .

(Copper i s chosen

as i t i s dense and t h e r e f o r e can be made re a s o n a b ly t h i n , and y e t has a low enough n u c l e a r charge t o make th e p h o t o - e l e c t r i c e f f e c t in i t sm all f o r most r a d i a t i o n s . )

Round t h e copper

c o n t a in e r i s p la c e d a v e r y t h i n le a d f o i l (T his may be o f g o ld o r p latin u m l e a f i f n e c e s s a r y ) i n which p h o to - e l e c t r o n s of n e a r l y homogeneous energy a r e p roduced.

When t h e secon dary

e l e c t r o n s from t h i s c o n v e rto r a r e examined in a m agnetic s p e c tr o m e te r /

15. s p e c tro m e te r, t h e p h o t o - e l e c t r o n s from th e l e a d f o i l can he c l e a r l y seen a g a in s t th e background o f Compton e l e c t r o n s from th e cop per.

At e n e r g ie s of a few hundred K i l o v o l t s , peaks can

be observed due to co n v e rsio n of t h e gamma-rays i n t h e K, 1, and M s h e l l s of th e l e a d w hile even a t e n e r g i e s as h ig h as 2.76 M.E.V. ( th e h ig h energy l i n e from E a ^ ) t h e K co n v ersio n peak s t i l l shows q u i t e p l a i n l y .

With t h e use of t h i s te c h n iq u e ,

Siegbahn was a b le to make measurements o f e n e r g ie s up to th e o rd e r o f 3 M.E.V. t o b e t t e r th a n l c/^ w i t h so u rc e s o f t h e o r d e r o f a few m ic ro C u rie s, th e g r e a t improvement b ein g due t o t h e su p p re ss io n of th e i n t e n s e b e t a - r a y spectrum which n o rm ally accompanies th e gamma-ray s e c o n d a r ie s .

The use o f t h i s t e c h -

:n iq u e by many d i f f e r e n t i n v e s t i g a t o r s has s u p p lie d a l a r g e body o f e x p e rim e n ta l r e s u l t s on t h e energy and r e l a t i v e i n t e n ­ s i t y of t h e gamma-rays from many o f t h e a r t i f i c i a l r a d i o a c t i v e elem e n ts.

Since th e s e a r e so numerous however, t h e r e i s s t i l l

a g r e a t d e a l o f work of t h i s k in d t o be done, t o p ro v id e a c c u r a te d a t a where a t p r e s e n t t h e only in fo rm a tio n a v a i l a b l e i s d e riv e d from v e r y rough a b s o r p tio n ex p e rim e n ts.

On th e

q u e s tio n o f t h e d e te rm in a tio n of m u ltip o le o r d e r , v e r y l i t t l e work h as been done, bu t t h i s q u e s tio n w i l l be d is c u s s e d more fu lly la te r .

(d)

E u o lea r R e a c tio n s . With r e g a r d to t h e stu d y o f t h e gamma-rays e m itte d by

n u c le i/

n u c l e i e x c ite d by n u c l e a r r e a c t i o n s , l i t t l e work o f a p r e c i s e n a t u r e has been p u b lis h e d .

T h is i s l a r g e l y a t t r i b u t a b l e to

th e t e c h n i c a l d i f f i c u l t i e s in v o lv e d in s e t t i n g up and u s in g a m agnetic sp e c tro m e te r i n th e v i c i n i t y o f t h e so u rce o f t h e bombarding p a r t i c l e s , e s p e c i a l l y s in c e in t h i s case th e r a d i a t i o n i s l i k e l y t o be much more e n e r g e t i c th a n in th e case o f r a d i o a c t i v e decay.

T h is f a c t makes n e c e s s a r y t h e use of

l a r g e and expensive r e s o lv i n g equipment, and a ls o new techniques depending on p a i r - p r o d u c t i o n , s in c e measurements b ased on th e o b s e rv a tio n of p h o to - e le c tr o n peaks beg in t o f a i l above about 3 M.E.V.

Most o f th e work done on t h e r a d i a t i o n s from th e l i g h t

elem ents u nder p ro to n and d eu tero n bombardment has t h e r e f o r e been accom plished by th e u se of a b s o r p tio n te c h n iq u e s (C urran, Dee and P e t r i z i l k a , 1938;

F ow ler, L a u r its e n and L a u r its e n ,

1948) which may be, as d is c u s s e d e a r l i e r , s u b je c t t o s e r io u s e r r o r s a t hig h e n e r g i e s , and which have p oo r r e s o l u t i o n . The achievement of good r e s o l u t i o n and ac cu racy in measurements on h ig h energy r a d i a t i o n s was only made p o s s i b le when th e p a i r p ro d u c tio n mechanism was u t i l i s e d by t h e o b s e rv a tio n of t h e t r a c k s of p a i r s produced in a t h i n le a d f o i l in th e g as o f a 'Wilson chamber p la c e d i n a s tr o n g m agnetic fie ld ;

h e re th e momentum, and hence energy o f each component

o f t h e p a i r co u ld be measured, and so t h e energy o f t h e gamma-ra y in fe rre d .

Using t h i s method, l e l s a s s o , Fow ler and

l a u r i t s e n (1937) were a b le f o r t h e f i r s t tim e t o show t h a t th e •7

hard gam m a-radiation r e s u l t i n g from th e bombardment o f l i p ro to n s/

w ith

p ro to n s c o n s is te d o f a s tr o n g l i n e a t 17 M.E.V. t o g e t h e r w ith a weaker b road component i n th e r e g io n o f 14 M.E.V.

T h is

method has been used t o i n v e s t i g a t e t h e r a d i a t i o n s from a few n u c le a r r e a c t i o n s , b ut i t s u f f e r s from th e d is a d v a n ta g e t h a t a g r e a t d e a l o f tim e and e f f o r t has t o be expended i n o b ta in in g and a n a ly s in g a l a r g e number of p h o to grap hs i f good s t a t i s t i c s a r e to be o b ta in e d .

F urth erm ore g r e a t c a re must be ta k e n to

av o id sp u rio u s r e s u l t s owing t o a c c i d e n t a l s u p e r p o s i tio n of tra c k s.

These d i f f i c u l t i e s were p a r t l y overcome by t h e u se o f

two s e m i - c i r c u l a r m agnetic r e s o l v e r s f i t t e d w ith G.M. c o u n te r s , t o a n a ly se t h e p a i r s produced i n a f o i l , th e em ission of a p a i r o f t h e a p p r o p r ia te energy ca u sin g a c o in c id e n c e between t h e two c o u n te rs (McDaniel, von D ardel and Walker, 1947);

i t was how-

:e v e r t h e m u lt i - c o u n t e r ty p e o f p a i r sp e c tro m e te r used by Walker and McDaniel i n 1948 which f i n a l l y overcame t h i s d i f ­ f i c u l t y and made p o s s i b l e t h e o b ta in in g of good s t a t i s t i c s on t h e h ig h energy gamma-rays i n ho urs i n s t e a d o f weeks.

The

Walker and McDaniel in s tru m e n t c o n s i s t s e s s e n t i a l l y o f a number of s e m i - c i r c u l a r r e s o l v e r s s e t on e i t h e r s id e o f th e f o i l being i r r a d i a t e d , t h e o u tp u ts from a l l of th e s e u n i t s b ein g combined in a l a r g e m u l t i p l e c o in c id e n c e c i r c u i t which o b ta in s t h e maximum amount o f in fo rm a tio n from th e s i g n a l s from t h e c o u n te rs and d is p l a y s t h i s in f o rm a tio n on a row o f m echanical r e g i s t e r s from which a number o f p o i n t s i n t h e energy d i s ­ t r i b u t i o n o f th e p a i r s can im m ediately be p l o t t e d .

(A d e t a i l e d

d e s c r i p t i o n o f th e d esig n and o p e r a tio n o f an in s tru m e n t o f t h i s ty p e /

ty p e w i l l be g iv en in t h e n e x t c h a p t e r . )

With t h e a i d o f t h i s

in s tru m e n t Walker and McDaniel were a b le to produce cu rv es showing t h e high energy gamma-ray s p e c t r a o f F lu o r in e and Lithium when s u b je c te d t o p ro to n bombardment.

They were a ls o

a b le to show th e v a r i a t i o n in t h e energy of t h e Lithium r a d i a t i o n w ith change i n bombarding energy.

Apart however from

t h e s e measurements and from some u n p u b lish e d o b s e r v a tio n s on n eu tro n c a p tu r e r a d i a t i o n by K insey, th e p r e c i s i o n stu d y of h ig h energy n u c l e a r gamma-rays has h a r d ly y e t been begun. D eterm in atio n of t h e m u ltip o le o r d e r o f t h e s e r a d i a t i o n s has s c a r c e ly been a tte m p te d a t a l l .

1 .4 . (a)

O p p o r tu n itie s

fo r

U sefu l

R esearch

The G eneral F i e l d . Summing up th e v a r i o u s p o i n t s d is c u s s e d i n t h e c o u rse o f

t h i s c h a p te r , i t would seem t h a t w hile a g r e a t d e a l o f work i s s t i l l b eing c a r r i e d out on th e r a d i a t i o n s from t h e n a t u r a l l y r a d i o a c t i v e elem en ts (L atyshev, 1947;

F e a t h e r , 1949) 9 t h i s

work can no lo n g e r be d e s c r ib e d as sim ple gamma-ray s p e c tr o :scopy, and in d e e d t h e r e does n o t seem to be much o p p o r tu n ity o f adding s i g n i f i c a n t l y to th e in fo rm a tio n a lre a d y a v a i l a b l e concerning t h e l e v e l schemes o f th e s e elem e n ts, by th e a p p l i c a t i o n o f our method. In th e stu d y o f th e r a d i a t i o n s from th e a r t i f i c i a l r a d i o : a c t i v e elem e n ts, however, a g r e a t d e a l o f u s e f u l work rem ains to be done in d ete rm in in g a c c u r a te ly t h e energy and i n t e n s i t y o f/

o f t h e gamma-rays e m itte d by th e s e e le m e n ts.

In a d d i tio n to

th e d e te r m in a tio n o f t h e energy o f t h e v a r i o u s l e v e l s in t h e s e n u c l e i , a n o th e r f e a t u r e which i s o f g r e a t t h e o r e t i c a l i n t e r e s t i s t h e d e te r m in a tio n of t h e s p in s o f t h e s e l e v e l s .

T h is i s a

s u b je c t on which v e r y l i t t l e e x p e rim e n ta l work has been done (Latyshev, 1947;

H elm holtz, 1941)> h u t one on which th e study

o f gamma-ray s p e c t r a i n c o n ju n c tio n w ith measurements of th e p r o b a b i l i t y o f i n t e r n a l co n v e rsio n and i n t e r n a l p a i r c r e a t i o n , can throw much l i g h t . I f we go back f o r a moment and c o n s id e r t h e lo o s e analogy between gamma-ray and atom ic s p e c t r a , i t w i l l be remembered t h a t th e f i r s t advances i n t h e u n d e rs ta n d in g of atom ic s tr u c t u r e came th ro u g h th e stu d y o f t h e spectrum o f Hydrogen.

Hence i t

seems r e a s o n a b le to suppose t h a t a f r u i t f u l f i e l d o f stu d y i n n u c l e a r sp e c tro sc o p y w i l l l i e i n t h e exam ination o f th e s p e c t r a o f th e l i g h t elem e n ts.

Of co u rse t h e r e a r e c e r t a i n s t a t i s t i c a l

p r o p e r t i e s o f n u c l e i , such as l e v e l d e n s i t i e s , which can be b e t t e r s tu d i e d i n th e h e a v ie r elem e n ts, b u t t o th e u se o f th e method o f gamma-ray sp e c tro s c o p y , which i s ca p ab le of g iv in g d e t a i l e d in f o rm a tio n about th e energy and sp in o f i n d i v i d u a l l e v e l s , t h e l i g h t elem ents u nd oubtedly p ro v id e a s tro n g c h a l­ le n g e .

I t w i l l of co u rse be a p p r e c ia te d t h a t v e r y few of t h e

l i g h t n u c l e i can be e x c i t e d by r a d i o a c t i v e decay, becau se most o f t h e decay p r o c e s s e s t a k e p la c e w ith v e r y s h o r t h a l f - l i v e s . Hence t h e main method o f e x c i t a t i o n must be by n u c l e a r r e a c t i o n s , and h e r e , f o r t u n a t e l y , th e gamma-ray s p e c t r a of many/

many o f t h e l i g h t elem ents can be e a s i l y e x c ite d by p ro to n o r n eu tro n c a p tu r e , o r by t h e e q u iv a le n t d eu tero n r e a c t i o n s , or (d ,p ).

( d ,n )

These s p e c t r a demand t h e b e s t modern te c h n iq u e s f o r

t h e i r i n v e s t i g a t i o n , s in c e th e y extend t o h ig h e n e r g i e s , and th e y a ls o demand new te c h n iq u e s f o r t h e d e te r m in a tio n o f t h e m u ltip o le o r d e r o f t h e t r a n s i t i o n s ob serv ed .

The P r e s e n t R esearch . I t i s c l e a r from th e above summary t h a t th e f i e l d o f op­ p o r t u n i t y p r e s e n te d in t h e s tu d y o f gamma-ray s p e c tro sc o p y i s v e ry wide, e s p e c i a l l y when i t i s c o n s id e re d 40 y e a r s o f i n v e s t i g a t i o n ,

th a t a f te r n ea rly

th e stu d y o f t h e r a d i a t i o n s from th e

n a t u r a l r a d i o a c t i v e elem ents i s n o t y e t com plete. s in c e we, i n G-lasgow, were in t h e f o r t u n a t e

N e v e rth e le s s ,

p o s s e s s io n o f a

sou rce o f h ig h energy p r o to n s and d e u te r o n s , and s in c e t h e r e was a ls o a v a i l a b l e an ele c tro m a g n e t o f dim ensions s u i t a b l e f o r th e r e s o l u t i o n o f e l e c t r o n s up t o 30 M.E.V. i n energy , i t was d ecided t h a t te c h n iq u e s should be developed f o r t h e in v e s tig a tio n o f gamma-rays from t h e a r t i f i c i a l r a d i o a c t i v e elem en ts, and from e x c ite d s t a t e s o f th e l i g h t elem en ts caused by p a r t i c l e bombard:ment.

These te c h n iq u e s were th e n t o be u sed to c o l l e c t d a t a in

t h i s f i e l d , le a d in g t o th e c o n s tr u c tio n o f energy l e v e l diagrams, and i f p o s s i b l e to th e d e te r m in a tio n o f t h e s p in s of some o f th e s e l e v e l s .

The rem a in d er o f t h i s t h e s i s i s concerned w ith

t h e e x e c u tio n o f t h i s programme, P a r t I I d e a lin g w ith th e te c h n iq u e s developed, and P a r t s I I I and IV w ith s e v e r a l in v e stig a tio n s/

i n v e s t i g a t i o n s i n which th e s e te c h n iq u e s have been employed in th e stu d y of t h e gamma-ray s p e c t r a o f p a r t i c u l a r n u c l e i , and th e r e s u l t s o b ta in e d used to c o n s tr u c t an energy l e v e l diagram , o r e l s e to v e r i f y o r augment an e x i s t i n g diagram .

In P a r t IV

t h e u se f o r t h e f i r s t tim e of t h e i n t e r n a l p a i r c r e a t i o n e f f e c t to d eterm ine th e m u ltip o le o r d e r o f a gamma-ray l i n e from a l i g h t element i s d e s c r ib e d , and t e n t a t i v e sp in v a lu e s a re a s s ig n e d t o two l e v e l s i n t h e Mg24-^ n u c le u s .

PART I I . 1.

II.

-

INSTRUMENTATION.

Comparison of D i f f e r e n t Types of M agnetic A n a ly s e rs.

In o r d e r t o c a r r y out t h e d e s ir e d programme o f experim ents, i t was n e c e s s a r y t o p ro v id e an in s tru m e n t o r in s tr u m e n ts capable o f a n a ly s in g th e secondary e l e c t r o n s and p o s i t r o n s from gamma- r a y s i n t h e energy ran g e say 100 K.E.V. t o 20 M.E.V.

With

t h i s req u ire m e n t i n mind l e t us c o n s id e r b r i e f l y t h e ad van tag es and l i m i t a t i o n s o f t h e v a r i o u s ty p e s of a n a ly s e r t h a t have been d e s c r ib e d i n t h e l i t e r a t u r e .

These in s tr u m e n ts can be b ro u g h t

ro u g h ly u nd er t h r e e heads; (a)

S e m i- c i r c u la r r e s o l v e r s ,

(b)

M agnetic l e n s e s ,

(c)

Double f o c u s s in g s p e c tr o m e te r s u t i l i s i n g c irc u la r tr a je c to rie s .

V ario u s o th e r ty p e s o f in s tru m e n t have been proposed from tim e to tim e (Korunsky, 1945;

R ich ard so n , 1947), b ut f o r p r a c t i c a l

r e a s o n s a l l t h e in s tr u m e n ts to d a te w ith which s e r i o u s work has been done have belonged t o one o r o th e r o f th e s e c l a s s e s , and t h e i r development has ta k e n p la c e i n th e o r d e r i n which th e y have been l i s t e d .

(a)

S e m i- c i r c u la r R e s o lv e rs . The s e m i - c i r c u l a r a n a ly s e r i s o f co u rse t h e d ev ice

in tr o d u c e d by Danysz (1913) and depends on t h e f a c t t h a t i f a p la n e p e n c i l o f charged p a r t i c l e s of homogeneous energy and d iv e rg in g w ith an ang le 2Q a re s u b je c te d t o t h e a c tio n of a u n ifo rm /

uniform m agnetic f i e l d a c tin g p e r p e n d i c u la r ly t o t h e p la n e o f t h e p e n c i l , th e n th e y a r e b rought back t o a fo c u s a f t e r th e y have d e s c r ib e d ap p ro x im a tely a s e m i - c i r c l e .

F ig u re 1

i l l u s t r a t e s t h e geom etry o f t h i s p r o c e s s , th e m agnetic f i e l d

F ig u re 1 .

S e m i-C irc u la r F o c u ssin g .

a c tin g along OZ, and th e p a r t i c l e s b ein g e m itte d from 0 in th e X-Y p la n e i n t o a p e n c i l o f h a l f - a n g l e Q su rro u n d in g OY.

S ince

t h e t r a j e c t o r y of each p a r t i c l e i s a c i r c l e , i t i s c l e a r t h a t p a r t i c l e s e m itte d along OY i n t e r s e c t OX ag a in i n th e p o in t (2 R ,0 ,0 ) where R

i s t h e r a d i u s of c u r v a t u r e . Those e m itte d a t

an an g le A, say ,

to OY, i n t e r s e c t OX ag ain in th e p o in t

(2R jcos A , 0 , 0 ) .

Hence i t f o llo w s t h a t a l l th e p a r t i c l e s i n th e

p en c il in te r s e c t

OX ag a in between th e p o i n t s P ( 2 R ,0 ,0 ) , and

Q (2R .cosO ,0 , 0 ) ; i . e . ,

t h e p o in t 0 form s an

image PQ o f le n g t h

2 R (l-c o sO ). I f we now c o n s id e r t h e case o f a p a r t i c l e e m itte d i n t h e p la n e /

24. p la n e OYz, so t h a t i t s d i r e c t i o n o f em ission makes an an g le B w ith OY, i t s momentum, p, can be r e s o lv e d i n t o a component p .s in B along 02, which i s u n a f f e c t e d by t h e m agnetic f i e l d , and a component p.cosB i n t h e X-Y p la n e , which i s r o t a t e d by th e fie ld .

The p a r t i c l e t h e r e f o r e moves in a h e l i x on th e s u r f a c e

o f a r i g h t c i r c u l a r c y l i n d e r o f r a d i u s 2R.cosB w ith i t s a x is p a r a l l e l t o OZ, and i n t e r s e c t s t h e X-Z p la n e ag ain i n th e p o in t S, (2R.cosB,0,TiR.sinB).

Hence i f B i s allow ed t o v a ry so t h a t

- 0 / 2 ^B ^ 0 / 2 , S w i l l t r a c e out a p o r tio n of t h e e l l i p s e x

2 / £ R ) 2 * X 2/ ( 1 f E ) 2 = 1 ,

y = o ly in g between th e p o i n t s (2 R .co s0 /2 ,0 /fT R .sin 0 /2 ) and ( 2 R .c o s 0 /2 ,0 ,-4 ? R .s in 0 /2 ) .

Thus where, f o r r a y s l y i n g in t h e

X-Y p la n e , th e image o f t h e p o in t 0 was a sequence o f p o i n t s on th e X -axis between t h e p o i n t s P and Q, t h e c o rre sp o n d in g image f o r r a y s which a r e allow ed t o emerge in a r e c t a n g u l a r p e n c i l of h a l f - a n g l e Q in th e X-Y p la n e , and 0£ in th e Y-Z p la n e , s u r : rounding OY, i s g iven i f each of t h e p o i n t s i n th e l i n e image i s expanded i n t o a p o r tio n o f an e l l i p s e in t h e X-Z p la n e , as shown above.

The image o f a p o in t so urce i s th u s a s e c tio n o f

th e above e l l i p s e , of l e n g t h ap p ro x im a tely 2 ^ . s i n 0 / 2 , and t h i c k n e s s 2 R .(l-c o s Q ), as shown i n F ig u re 2 ( a ) . The image o f a broad l i n e so urce can be i n f e r r e d from t h e above a n a l y s i s , f o r i f 0 and 0 a r e b o th made v e ry sm a ll, every p o in t ( x , z ) in th e so u rce w i l l produce an image p o in t (x+2R ,z), th u s p rod ucin g an ex a ct image o f t h e source d isp la c e d /

d is p la c e d a d i s t a n c e 2R in th e d i r e c t i o n o f OX,

The e f f e c t

o f allo w in g f i n i t e b u t sm all v a l u e s o f Q amd 0, i s t o t u r n each p o in t image i n t o a p o r tio n o f th e c h a r a c t e r i s t i c e l l i p s e . Hence i f we l e t t h e so u rce have l e n g t h 1?R/ and th ic k n e s s t , and i f we r e s t r i c t t h e image l e n g th t o i\R0, we produce a f i g u r e o f th e g e n e r a l shape shown i n F ig u re 2 ( b ) , th e o v e r a l l

't

2 R (i-c « e )

" ,

(a)

z

T ^ 0

1

11

OC W

-

*

. A . .

F ig u re 2.

Images o f p o in t and l i n e s o u rc e s .

w idth, w, of th e image, b ein g g iv en by; w =

t + 2R(l - cosQ.cos0)

= T h is q u a n t i t y ,

t + R (e 2

•* 0 2 )

w, i s c a l l e d th e " F u ll l i n e Width11 o f th e

s p e c tro m e te r, and

i f t h e mean i n t e n s i t y o f t h e image

i s p lo tte d

as a f u n c tio n o f x, t h e !,Line Shape11 o b ta in e d i s ro u g h ly t r i a n g u l a r (Cork, 1949) w ith th e maximum n e a r th e h ig h energy sid e .

Hence th e "H alf Width1’, o r w idth o f t h e l i n e a t h a l f

maximum i n t e n s i t y , i s g iv en ap p ro x im a tely by w/2. How/

Now we have d is c u s s e d above t h e image formed by a l i n e so urce of homogeneous e l e c t r o n s , in a uniform m agnetic f i e l d , and have deduced i t s h a l f w idth.

I t i s , of c o u rse , formed a t

a d i s t a n c e from th e so urce which i s p r o p o r t i o n a l to th e momentum p, o f th e e l e c t r o n s from t h e so u rc e .

Hence, i f t h e

so u rce i s e m ittin g s e v e r a l groups o f e l e c t r o n s o f d i f f e r e n t momenta, each group w i l l produce i t s own image, a t a d is t a n c e from th e sou rce p r o p o r t i o n a l to i t s momentum, and so i f t h e r e a re tv/o groups o f n e a r l y equal momentum, t h e i r images w i l l j u s t be r e s o lv e d when t h e i r d is t a n c e a p a r t i s equal to t h e i r h a l f w id th .

I f t h e momentum d i f f e r e n c e i n t h i s case i s £p,

and i f th e mean momentum of t h e two l i n e s i s p, th e n we can d e f in e th e ’’R eso lv in g Power” o f t h e sp e c tro m e te r a s; P

=

p /£ p

=

2R/(w/2)

— 4R/w.

T h is th e n g iv e s a measure of t h e r e s o lv i n g power o f t h e semi: c i r c u l a r sp e c tro m e te r as used t o form images o f th e so u rc e , say on a p h o to g ra p h ic p l a t e .

I f now we c o n s id e r i t s u se w ith

a G-.M. c o u n te r as d e t e c t o r , th e n we must p la c e a s l i t of U \, tfeu X - Z jhJtAAVflu Uh J L

s u i t a b l e dimensionsKat r i g h t a n g le s t o th e X -a x is, and a t a s u i t a b l e d is t a n c e from th e so u rc e , and th e n cause each l i n e o f th e spectrum t o be f o c u s s e d , in t u r n , on t o th e s l i t , by a d j u s t i n g th e v a lu e o f th e m agnetic f i e l d .

In t h i s c a se ,

o b v io u sly an i n f i n i t e l y narrow s l i t would g iv e th e same r e ­ v o l v i n g power as t h e p h o to g ra p h ic p l a t e , b u t a s l i t o f f i n i t e w id th would i n t e g r a t e t h e p h o to g ra p h ic spectrum over a momentum range/

rang e c o rresp o n d in g to i t s own w id th .

Hence t h e l i n e w idth

f o r a s l i t of f i n i t e w idth wQ i s given by: w =

( t 4* wQ + R(©2 4- 0 2 ))

and th e r e s o l v i n g power i s a l t e r e d a c c o r d in g ly . I f now we c o n s id e r a sp e c tro m e te r

in which th e v a r io u s

so u rc e s of l i n e w idth a r e made to c o n t r i b u t e e q u a lly to t h i s w id th , i . e . : _ t

= wo

w =

=

R©2

=

R02, th e n ,

4R£^

and th e r e s o l v i n g power i s g iven by: P Also th e

= 4-R/w =

O- 2

s o l i d an g le i n t o which t h e p a r t i c l e s a r e p r o j e c t e d i s

g iven ap p ro x im a tely by 200, o r

20 , and th e so u rce a r e a

is

'ttRe.Re2, o r/uR2e 3. How t h e d e s i r a b l e q u a l i t i e s in a m agnetic r e s o l v e r which has t o be used f o r gamma-ray s p e c tro sc o p y a r e , in th e f i r s t i n s t a n c e , l a r g e c o l l e c t i n g a n g le , l a r g e so urce a r e a , and good re so lu tio n .

The f i r s t two c r i t e r i a a r e p a r t i c u l a r l y im p o rta n t

when weak so u rc e s have to be s t u d i e d .

I f th e so u rc e s have a

low s p e c i f i c a c t i v i t y , th e n t h e i r s t r e n g t h s a r e l i m i t e d , f o r i n t e r n a l co n v e rsio n measurements, by t h e s u r f a c e a r e a t h a t can be exposed, and f o r e x t e r n a l c o n v e rsio n , by t h e volume t h a t can be c o n ta in e d w ith in a copper v e s s e l o f a p p r o p r ia te dim ensions t o s u i t t h e s p e c tro m e te r so u rce h o ld e r .

In t h e case

o f t a r g e t s b ein g bombarded by a beam o f p a r t i c l e s , s in c e t h i s beam i s n orm ally of f i n i t e c r o s s - s e c t i o n , i t i s ag a in c l e a r th a t/

t h a t th e s t r e n g t h o f sou rce a v a i l a b l e w i l l depend on i t s a r e a . Hence i n every ca se th e i n t e n s i t y o f th e secondary r a d i a t i o n to be s tu d ie d depends on t h e sou rce a r e a .

The i n t e n s i t y o bserved

a t th e d e t e c t o r i s a ls o p r o p o r t i o n a l t o th e c o l l e c t i n g s o l i d a n g le , and so, as su g g e sted by P e r s ic o (1949), a con ven ien t measure of th e i n t e n s i t y observed a t th e d e t e c t o r o f a m agnetic r e s o l v e r i s a f f o rd e d by t h e p ro d u c t o f t h e so u rce a r e a and th e c o l l e c t i n g a n g le .

T his f i g u r e , which we s h a l l c a l l t h e

i n t e n s i t y f a c t o r , P, t o g e t h e r w ith th e c o rre sp o n d in g r e s o l v i n g power, P, d e te rm in e s t h e perform ance of t h e s p e c tr o m e te r . To r e t u r n t o th e case of th e s e m i - c i r c u l a r r e s o l v e r , i t was shown t h a t f o r t h e case o f equal c o n t r i b u t i o n s t o t h e l i n e w idth o f each of t h e independent v a r i a b l e s , th e r e s o l v i n g power, s o l i d an g le o f c o l le c tio n ^ a n d sou rce a r e a ; cou ld a l l be ex p re sse d as sim ple f u n c t i o n s o f th e a p e r t u r e a n g le , Q*

Hence we can

w rite : P

=

Q~2

F

=

(so u rc e a r e a ) ( s o l i d a n g le )

= 1?R2e 3 .2 e 2 =

2 fm2« 5

and we th u s have th e r e l a t i o n : p

=

2 f e 2P~5//2

Thus w ith t h e two v a r i a b l e s R and 0 a t our d is p o s a l , i t i s c l e a r t h a t f o r good d esig n we must make R as l a r g e as p o s s i b l e , and choose Q i n such a way as to g iv e a good compromise between h ig h /

29.

h ig h r e s o l v i n g power and h ig h i n t e n s i t y .

In p r a c t i c e , th e

v a lu e o f Q i s l i m i t e d by t h e geom etry of t h e ele c tro m a g n e t u se d , s in c e a l a r g e v a lu e o f Q in v o lv e s t h e u se o f a wide gap between t h e p o le s , which i n t e r f e r e s w ith th e u n if o r m ity o f t h e m agnetic fie ld , ( I t i s t o be n o ted t h a t t h e above c a l c u l a t i o n s , c a r r i e d out by th e a u th o r, a r e n o t r i g o r o u s .

An ex a ct th e o r y of th e

s e m i - c i r c u l a r s p e c tro m e te r has been c a r r i e d out v e ry r e c e n t l y by G e o ffrio n (Septem ber, 1949) who d e r iv e s optimum c o n d i tio n s o f o p e r a tio n , which a r e s l i g h t l y d i f f e r e n t from th o s e chosen above (e q u a l c o n t r i b u t i o n s t o th e l i n e w id th .)

'With th e

optimum c o n d i tio n s , however, th e same fundam ental r e l a t i o n s h i p between I‘ and P i s d e r iv e d , th e only change b ein g i n t h e v a l u e of th e n u m erical c o n s t a n t . )

(b)

Magnetic L enses. The term, m agnetic l e n s

i s n o rm ally u sed to d e s c r ib e any

m agnetic f o c u s s in g arrangem ent where t h e f i e l d p o s s e s s e s a x i a l symmetry.

The s im p le s t ca se of t h i s i s , o f c o u rse , t h a t o f a

uniform a x i a l f i e l d , such as i s c o n v e n ie n tly o b ta in e d by th e use o f a lo n g s o le n o id .

In t h i s c a s e , p a r t i c l e s of t h e same

energy and e m itte d from a p o in t so u rce a t t h e same an g le to th e m agnetic f i e l d , d e s c r ib e h e l i c e s of t h e same dim ensions and a r e brought back t o a fo c u s in a p o in t a t t h e same d i s t a n c e from th e a x is as was th e p o in t o f em issio n . p la c e /

The method o f u se i s to

30. p la c e th e so u rce and th e d e t e c t o r a t p o i n t s on t h e a x i s o f t h e s o le n o id , and to i n t e r p o s e between them a b a f f l e which t r a n s m i t s on ly th o s e p a r t i c l e s which p a ss th ro u g h an a n n u la r a p e r t u r e whose dim ensions and p o s i t i o n c o n t r o l th e c o l l e c t i n g s o l i d a n g le , and r e s o l u t i o n o f th e in s tr u m e n t.

T h is method was f i r s t

su g g e ste d by K a p itz a and i n v e s t i g a t e d by T r i c k e r (1924) u sin g th e p h o to g ra p h ic p l a t e method of d e t e c t i o n which was no t v e r y s u i t a b l e f o r u se w ith t h i s te c h n iq u e .

The f i r s t sp e c tro m e te r

u sin g t h i s method w ith a G-.M. c o u n te r was c o n s tr u c te d by W itcher (1941) and ac h iev ed a s o l i d a n g le of 0.126 s t e r a d i a n s and a so u rce a r e a o f 3.14 cm2 w ith a r e s o l v i n g power of 1 6 .7 . T h is perform ance can t h e o r e t i c a l l y be e q u a lle d by a sem i- c i r c u l a r r e s o l v e r o f 12 cm r a d i u s , w ith an a p e r t u r e an g le Q o f 0.245 r a d i a n s .

The s o le n o id used by W itcher, which c o n ta in e d

about 360 l b s of cop p er, was 60 in c h e s lo n g , had an i n t e r n a l d ia m e te r of 1 0 .5 in c h e s and was w a te r-c o o le d so t h a t i t cou ld d i s s i p a t e a power o f 18 kW.

The maximum energy of e l e c t r o n

t h a t could be f o c u s s e d was 4*4 M.E.V.

I t w i l l be observed t h a t

from t h i s p o in t o f view th e s o le n o id i s a v e r y i n e f f i c i e n t in stru m e n t when compared w ith a s e m i - c i r c u l a r r e s o l v e r , which, w ith t h e same amount o f copper on a 1 2 ” magnet would fo c u s e l e c t r o n s o f 30 M.js.V. w ith th e e x p e n d itu re o f o nly one t h i r d o f th e power. R e c e n tly , however, a g r e a t d e a l o f a t t e n t i o n h as been p a id t o th e d esig n of th e s o le n o id sp e c tro m e te r, and an e x c e l l e n t p ap er/

31. p ap e r by P e r s ic o (1949) c o n s id e r s t h i s d esig n problem n o t on ly from th e p o in t o f view o f optimum g e o m e tr ic a l perform ance, bu t a ls o b e a rin g in mind t h e q u e s tio n o f economy o f copper and power P e r s ic o c la im s t h a t w ith a s o le n o id o f t h e s i z e used by W itcher, optimum d esig n co uld g iv e f o u r tim es th e i n t e n s i t y f a c t o r f o r t h e same r e s o l v i n g power, o r tw ice th e r e s o l v i n g power f o r th e same v a lu e of P.

A b e t t e r comparison between t h e b e s t d esig n

o f s o le n o id and o f s e m i - c i r c u l a r ty p e r e s o l v e r s i s , however, a v a i l a b l e s in c e P e r s ic o g iv e s th e r e l a t i o n s h i p between t h e i n t e n s i t y f a c t o r and r e s o l v i n g power f o r th e s o le n o id a s : F

=

5.4B2 .P_5/ 2

where D = 2p/eH, e b ein g t h e e l e c t r o n i c charge in e .m .u .

T h is

l e n g t h d ete rm in e s ro u g h ly th e dim ensions o f t h e s o le n o id , b ein g o f t h e o r d e r o f i t s d ia m e te r. I t w i l l be observed t h a t t h e r e l a t i o n s h i p i s s i m i l a r t o t h a t go verning th e perform ance o f th e s e m i - c i r c u l a r r e s o l v e r , ^ 2 . I t i s th u s c le a r th e a r e a 5*4D 2 b ein g s u b s t i t u t e d f o r 2liR t h a t t h e r e i s no e s s e n t i a l d i f f e r e n c e between th e perform ances o f t h e two in s tr u m e n ts , s in c e e i t h e r ty p e can be made to g iv e any d e s ir e d perform ance by s u i t a b l e ch o ice o f d im en sion s.

It

i s c l e a r , however, t h a t in p r a c t i c e th e s o le n o id ty p e i s s u p e r i o r where a l a r g e s o l i d an g le i s e s s e n t i a l , as where a so u rce i s l i m i t e d in t o t a l s t r e n g t h b u t can be c o n c e n tr a te d i n t o a sm all a r e a .

Here a l a r g e so u rce a r e a i s p o i n t l e s s ,

w h ile th e l a r g e s t p o s s i b l e s o l i d an g le i s d e s i r a b l e , and i n t h i s case/

32. c a se th e s e m i - c i r c u l a r ty p e i s n o t s u i t a b l e , s in c e l a r g e s o l i d a n g le s mean wide g ap s, and hence d i f f i c u l t y i n m a in ta in in g th e u n if o r m ity of t h e f i e l d .

T h is ad van tage o f t h e s o le n o id f o r

weak so u rc e s o f sm all s i z e , i s however q u i t e outw eighed by i t s l i m i t a t i o n in t h e energy ran g e t h a t can be fo c u s s e d by a s o le n o id o f r e a s o n a b le d im ensions;

and where a sp e c tro m e te r

i s d e s ir e d which w i l l p ro v id e good i n t e n s i t y and r e s o l v i n g power f o r work on so u rc e s o f low s p e c i f i c a c t i v i t y and v e r y h ig h energy, as in t h e p r e s e n t c a s e , t h e r e i s l i t t l e doubt t h a t t h e s e m i - c i r c u l a r r e s o l v e r p r o v id e s a b e t t e r in s tr u m e n t. The above c r i t i c i s m s o f s o le n o id ty p e le n s e s ap ply e q u a lly t o l e n s e s o f o th e r ty p e s .

Of th e s e th e s h o r t c o i l ty p e (Deutsch,

E l l i o t t and Evans, 1944) i s more econom ical th a n t h e s o le n o id , b ut p r o v id e s an i n f e r i o r p erform an ce.

Recent d e s ig n s o f l e n s e s

having sm all s p h e r i c a l a b e r r a t i o n (R ich ard so n, 1949;

S l& tis

and Siegbahn, 1949) prom ise t o p ro v id e ex trem ely l a r g e s o l i d a n g le s f o r t h e stu d y o f weak s o u r c e s , b u t a r e r a t h e r s p e c ia lis e d in s tr u m e n ts u s in g p o in t so u rc e s and would not be a p p l i c a b l e t o our problem .

(c)

The Double F o cu ssin g S p ectro m e ter. In 1946, i n a l e t t e r to N atu re, Svartholm and Siegbahn

d e s c r ib e d a new ty p e of a n a ly s e r i n which th e p a r t i c l e s move ap p ro x im a tely in c i r c l e s , b ut undergo second o r d e r f o c u s s i n g b o th in th e median p la n e o f t h e in s tr u m e n t, and in t h e i r motion a t/

33. a t r i g h t a n g le s t o t h i s p la n e .

T h is ty p e o f in s tr u m e n t, which

has s in c e come t o be known as th e Double F o cu ssin g S p e c tro :m e te r, depends on th e p r i n c i p l e t h a t had a l r e a d y been used in b e t a t r o n d e s ig n , t h a t a m agnetic f i e l d w ith a x i a l symmetry, which d im in ish e s w ith i n c r e a s i n g r a d i u s , te n d s t o produce f o c u s s in g in a beam of p a r t i c l e s moving i n ap p ro x im a tely c i r c u l a r o r b i t s round th e c e n t r a l a x i s .

A f u l l th e o r y o f t h e

e f f e c t has s in c e been p u b lis h e d by S h u ll and Dennison (1947)> and th e y t r e a t th e motion o f th e p a r t i c l e s as due to sm all p e r t u r b a t i o n s of th e c e n t r a l c i r c u l a r e q u ilib r iu m o r b i t ,

and

show t h a t f o r a c e r t a i n law of v a r i a t i o n o f t h e f i e l d , which _-L co rresp o n d s v e r y c l o s e l y t o HoCR 2 , th e ’’Y /avelengths” of th e p e r t u r b a t i o n s , i n t h e median p la n e and normal to i t , a r e

eq u al

and co rresp o n d t o an a n g u la r d i s t a n c e o f From th e e q u a tio n s o f S h u ll and Dennison, i t i s p o s s i b l e t o a r r i v e a t a r e l a t i o n s h i p between F and P f o r t h i s ty p e o f r e s o l v e r as w ell as f o r th e o t h e r two which we have c o n s id e r e d . In t h i s c a s e , i f Q o r 0 a r e l i n e a r l y r e l a t e d , we once ag ain o b ta in F = ( c o n s t )

o n ly t h i s tim e t h e c o n s ta n t may be

made s e v e r a l tim e s as l a r g e as f o r t h e s e m i - c i r c u l a r in s tru m e n t, s in c e by a s u i t a b l e c h o ic e of th e second o r d e r c o e f f i c i e n t in th e r a d i a l v a r i a t i o n of th e f i e l d , i t i s t h e o r e t i c a l l y p o s s i b l e t o ac h iev e t h i r d o r d e r f o c u s s in g in t h e median p la n e and so a c h iev e c o m p a ra tiv e ly l a r g e c o l l e c t i n g a n g le s in t h i s p la n e . (Q = k0, say, where k i s a d esig n p a r a m e te r) . is /

T h is advantage

34.

i s only r e a l i z a b l e in p r a c t i c e , however, i f t h e a n g le s concerned a re sm a ll, s in c e t h e p e r t u r b a t i o n th e o ry b re a k s down f o r l a r g e d is p la c e m e n ts .

F o r t h i s r e a s o n , th e use o f t h i s ty p e o f s p e c tr o -

:m eter has been r e s t r i c t e d to th e c a se o f h ig h r e s o l u t i o n (K u rie, Osoba and S lack , 1948;

S h u ll, 1948) (R esolving power of s e v e r a l

h u n d re d s), f o r which case i t can p ro v id e a h ig h e r i n t e n s i t y th a n e i t h e r of t h e o th e r ty p e s o f comparable s i z e . Summing up t h i s s h o r t d is c u s s io n of t h e r e l a t i v e m e r it s of th e t h r e e main ty p e s of m agnetic a n a ly s e r s , then, we must o b serv e t h a t th e i n t e n s i t y f a c t o r , which we d e fin e d e a r l i e r , i s in each case p r o p o r t i o n a l t o th e 5/2 power of th e i n v e r s e o f t h e r e s o l v i n g power, and t o th e sq u are o f t h e l i n e a r dim ensions of th e a p p a r a tu s .

Hence, f o r t h e purpose o f gamma-ray s p e c t r o -

:scopy, t h e r e i s no fundam ental v i r t u e i n one ty p e r a t h e r th a n a n o th e r , s in c e any one can be made to equal th e perform ance o f a n o th e r by making i t l a r g e enough.

In p r a c t i c e , however, th o s e

in s tr u m e n ts u s in g i r o n magnets a r e more economical f o r u se a t h ig h e n e r g i e s , w hile th e l e n s e s a r e ca p a b le o f p ro v id in g l a r g e r s o l i d a n g le s th a n th e o th e r ty p e s , though u s u a l l y a t th e expense o f sou rce s i z e .

They a r e most u s e f u l th e n , a t low

e n e r g i e s , and w ith weak so u rc e s o f high s p e c i f i c a c t i v i t y . Where h ig h r e s o l u t i o n i s e s s e n t i a l , th e double f o c u s s in g ty p e o f in s tru m e n t i s c a p a b le o f p ro v id in g th e l a r g e s t i n t e n s i t y o f th e t h r e e t y p e s .

I t s h a re s w ith th e s e m i - c i r c u l a r ty p e th e

advantage of u s in g an i r o n magnet which e n a b le s i t t o be used a t/

35.

a t r e l a t i v e l y h ig h e n e r g ie s , b u t s u f f e r s from t h e p r a c t i c a l d i f f i c u l t y t h a t i t r e q u i r e s a shaped f i e l d . In view o f arguments o f t h e above ty p e , and a ls o of t h e im p o rta n t f a c t t h a t an e lectro m a g n et o f s u i t a b l e dim ensions was a v a i l a b l e in t h e D epartm ent, i t was d ec id ed ( e a r l y i n 1948), t o c o n c e n tr a te on t h e u se o f s p e c tro m e te rs employing an e l e c t r o : magnet to p ro v id e th e f i e l d .

F u rth erm o re, s in c e i t v/as

r e a l i z e d t h a t i n t h e stu d y o f t h e e n e r g ie s o f v e r y hard gamma r a d i a t i o n s th e o n ly way t o ac h iev e good r e s o l u t i o n was t o o bserve s im u lta n e o u s ly th e e n e r g ie s o f th e p o s i t r o n s and e l e c t r o n s produced as p a i r s by th e gamma-rays, (se e I , 3 > ( d ) ) i t was decided t o c o n c e n tr a te i n i t i a l l y on th e s im p le s t p o s s i b l e ty p e of r e s o l v e r , namely th e s e m i - c i r c u l a r ty p e .

The id e a ,

th e n , was t o c o n s tr u c t a sim ple sp e c tro m e te r o f t h i s ty p e f o r t h e i n v e s t i g a t i o n of Compton and p h o t o - e l e c t r o n s produced by gamma-rays in th e energy ran g e 100 K.E.V. t o 3 M.E.V. u s in g th e w e ll e s t a b l i s h e d te c h n iq u e of Siegbahn, and f u r t h e r , t o c o n s tru c t a double s e m i - c i r c u l a r r e s o l v e r f o r t h e sim u lta n eo u s a n a l y s i s of t h e p o s i t r o n s and e l e c t r o n s e j e c t e d from a t h i n f o i l by hard gamma-rays in t h e energy ran ge 3 M.E.V. t o 20 M.E.V.

The

fo rm e r of t h e s e p r o j e c t s was c a r r i e d th ro u g h as o r i g i n a l l y p la n n ed , b u t th e l a t t e r was a l t e r e d a f t e r t h e p u b l i c a t i o n of Y/alker and McDaniel’ s p ap e r i n August, 1948, and t h e p a i r s p e c tro m e te r f i n a l l y b u i l t was a m u l t i p l e r e s o l v i n g chamber of t h e ty p e d e s c r ib e d by th e s e a u th o r s .

I I . 2 ./

36.

I I . 2. (a)

The S e m i - C i r c u l a r R e s o l v e r .

The E l e c t r o m a g n e t . The d e s i g n o f t h i s i n s t r u m e n t was n a t u r a l l y ,

a f f e c t e d by t h e e l e c t r o m a g n e t w h ic h was a v a i l a b l e ,

t o some e x t e n t and so i t

would p e r h a p s be w i s e t o b e g i n w i t h a s h o r t d e s c r i p t i o n o f t h i s apparatus.

The e l e c t r o m a g n e t o f w h ic h a p h o t o g r a p h i s shown i n

f i g u r e 3> has c i r c u l a r p o le p ie c e s of tw elve in c h e s in diam eter,

f i g u r e 5*

The e l e c t r o m a g n e t .

and a gap which i s a d j u s t a b l e i n q u a r t e r i n c h s t e p s , from one q u a rte r in ch to e ig h t in ches.

V.ith a gap o f two i n c h e s , t h e

f i f t e e n hundredw eights of copper in th e w indings enable a f i e l d o f t e n t h o u s a n d g a u s s t o be o b t a i n e d w i t h a c u r r e n t o f t h i r t y - f i v e a m p e r e s , which r e p r e s e n t s a d i s s i p a t i o n o f t h e o r d e r o f tw e lv e hundred w a t ts . four tons.

I t w i l l be o b s e r v e d from t h e p h o t o g r a p h t h a t i n i t s

present p o sitio n , it/

The g r o s s w e i g h t o f t h e magnet i s a b o u t

i n t h e beam room o f t h e p a r t i c l e a c c e l e r a t o r ,

i t i s mounted on a b o g ie which e n a b le s i t to be moved out of th e way along t h e r a i l s p ro v id e d , when n o t in u s e .

(b)

The S p e c tro m e te r. To r e t u r n th e n t o th e d esig n of th e s e m i - c i r c u l a r

r e s o l v e r , t h i s i s e s s e n t i a l l y s i m i l a r t o th e numerous examples o f t h e ty p e d e s c r ib e d in t h e l i t e r a t u r e , excep t p o s s i b l y t h a t more c a r e th a n u s u a l was ta k e n in i t s d esig n in o r d e r t o ac h iev e h ig h i n t e n s i t y .

Most e a r l i e r d e s ig n s were e s s e n t i a l l y

f o r two dim ension al in s t r u m e n ts , and n o t u n t i l th e p u b l i c a t i o n o f G-eoffrion*s p ap e r in September 1949 was t h e ex a ct c a l c u l a t i o n o f t h e optimum r e l a t i o n between th e v a r i o u s d esig n p a ra m e te rs c a r r i e d o u t.

The p r e s e n t a u th o r, however, w ith th e a id o f t h e

c a l c u l a t i o n s d e s c r ib e d in 1 1 , 1 , (a) had a lr e a d y c o n s tr u c te d an in s tru m e n t o f good d e s ig n , and a diagram o f th e i n t e r n a l s t r u c t u r e o f t h e s p e c tro m e te r i s shown i n f i g u r e 4.

I t w i l l be

observed from t h e diagram t h a t th e vacuum ta n k , which i s th e s t r u c t u r a l b a s i s o f th e a p p a r a tu s , c o n s i s t s o f two h a l f - i n c h s t e e l p l a t e s f o u r te e n in c h e s i n d ia m e te r, s e p a r a te d by a hollow copper c y l i n d e r o f q u a r t e r - i n c h w all t h i c k n e s s , to g iv e a space two in c h e s deep.

One s t e e l p l a t e i s s o ld e re d t o th e copper

c y l i n d e r , w hile th e o th e r i s a t ta c h e d w ith a number o f s t e e l screw s, and s e a le d w ith a r u b b e r g a s k e t.

The s t e e l p l a t e s

were d e l i b e r a t e l y made l a r g e r i n d ia m e te r th an th e magnet p o le s , in o r d e r to red u ce th e f r i n g i n g f i e l d e f f e c t i n s i d e th e /

th e ta n k ,

‘T hree o f th e s e ta n k s were c o n s tr u c te d , one b ein g

used f o r each of t h e r e s o l v e r s d is c u s s e d above, and t h e t h i r d b eing k e p t as a s p a re . To r e t u r n t o t h e diagram of th e s e m i - c i r c u l a r r e s o l v e r ,

To pum p

F i g u r e 4»

The S e m i - C i r c u l a r S p e c t r o m e t e r ,

S i s t h e p o s i t i o n of th e so u rce which i s mounted thro u g h a h o le i n th e l i d of t h e vacuum ta n k .

C i s th e p o s i t i o n of t h e c o u n te r

which a ls o mounts th ro u g h a h o le in th e l i d , and D i s an aluminium p l a t e in which i s m ille d th e a p e r t u r e th e v a l u e s of Q and 0 u t i l i s e d .

which d e f in e s

S e v e ra l o f t h e s e p l a t e s a re

a v a i l a b l e , p ro v id in g a v a r i e t y of s o l i d a n g le s , and a c o r r e s p o n d in g /

co rre sp o n d in g s e t o f p l a t e s E i s a v a i l a b l e , w ith s l i t s m ille d in them t o s u i t th e v a l u e s o f s o l i d a n g le a v a i l a b l e w ith D. The b a f f l e s B a r e f i x e d and have no p a r t in d e f in in g th e beam o f p a r t i c l e s , b u t th e y h e lp t o su p p re ss unwanted p a r t i c l e s which might o th e rw is e e n t e r th e c o u n te r a f t e r s c a t t e r i n g a t th e w a lls of th e a p p a r a tu s .

A ll exposed s u r f a c e s in th e s p e c tr o -

: m eter a r e covered w ith aluminium s h e e tin g t o re d u c e such s c a t t e r i n g to a minimum.

Of th e rem aining f e a t u r e s o f th e

a p p a ra tu s , F i s a f l i p c o i l which i s used , in c o n ju n c tio n w ith a Cambridge F lu x m eter, t o determ in e th e v a lu e of th e m agnetic f i e l d , and P^ and

a re p o r t s which r e s p e c t i v e l y en able a

beam of p r o to n s o r d e u te ro n s to be d i r e c t e d on t o a t a r g e t s i t u a t e d a t th e sou rce p o s i t i o n , and a p r o p o r t i o n a l c o u n te r to be f i t t e d t o th e a p p a ra tu s in o r d e r to d e t e c t heavy p a r t i c l e s emanating from th e t a r g e t .

H i s a sm all s h u t t e r which can be

o p e ra te d from o u ts i d e th e vacuum, and to which can be a t ta c h e d a c o n v e r to r which can th u s be p la c e d i n f r o n t o f th e source d u rin g an exp erim ent, i f d e s i r e d .

A ll o f th e s e f e a t u r e s have

e i t h e r been used a lr e a d y i n ex p erim en ts w ith t h i s sp e c tro m e te r o f e l s e t h e i r u se i s plann ed i n f u t u r e ex p e rim en ts.

(c)

The C o u n ters. One of th e sm all double G-.M. c o u n te r s used w ith th e

in s tru m e n t i s shown i n F ig u re 5*

These c o u n te r s a r e made as

sm all as p o s s i b l e in o r d e r to red u ce t h e i r background, bu t th e /

t h e s m a l l e s t b a c k g r o u n d o b t a i n e d i n t h i s way w i t h a s i n g l e c o u n t e r was a b o u t t e n c o u n t s p e r m i n u t e .

W ith t h e u s e o f two

I__________i -------------101 cm3

0

1‘igure 5»

^he Double Counter.

s m a l l c o u n t e r s i n c o i n c i d e n c e h o w e v er , t h e b a c k g r o u n d was f i n a l l y reduced to 1 .5 co u n ts p e r m inute, t h i s r e d u c tio n b eing h i g h l y i m p o r t a n t i n t h e s t u d y o f weak e f f e c t s l i k e i n t e r n a l p a i r c r e a t i o n , w h i c h , w i t h t h e i n t e n s i t y f a c t o r a v a i l a b l e , may y i e l d a c o u n t i n g r a t e o f o n l y a few t i m e s t h i s f i g u r e , l e s s than te n p e r m inute. i s o f alu m in iu m l e a f , of a i r ,

and c e r t a i n l y

The window b e tw e e n t h e two c o u n t e r s

and i s e q u i v a l e n t t o o n l y one o r two mm.

w h i l e t h e o u t e r window, w h ic h h a s t o w i t h s t a n d

a t m o s p h e r i c p r e s s u r e when t h e s p e c t r o m e t e r i s o p en ed t o t h e a t m o s p h e r e , i s n o r m a l l y o f m ic a and o f t h i c k n e s s e q u i v a l e n t t o one o r two cm. o f a i r .

(d)

j

C a li b r a t i o n of th e S p e c tro m e te r. In o r d e r t o t e s t th e working o f th e i n s t r u m e n t ,

and a l s o

i

t o o b t a i n a c a l i b r a t i o n of t h e f lu x - m e a s u r in g system, a s h o r t s t u d y was made o f t h e r a d i a t i o n s o f T h l and i t s p r o d u c t s .

The

s o u r c e u s e d was a p i e c e o f f i n e t i n n e d c o p p e r w i r e on w h ic h a v e r y t h i n l a y e r o f T h i had been d e p o s i t e d from t h e e m a n a t i o n o f RaTh by t h e a c t i o n o f an e l e c t r i c f i e l d .

T his p ro v id ed a source

o f n e g l i g i b l e w i d t h , w h ic h e m i t s a w e l l known s e r i e s o f i n t e r n a l c o n v e r s i o n l i n e s w h ic h e x t e n d o v e r t h e e n t i r e r a n g e o f e n e r g i e s f o r which t h e s p e c t r o m e t e r was d e s i g n e d , and t h e r e s u l t s o f t h e r u n s t a k e n on t h i s s o u r c e a r e shown i n f i g u r e s 6 and 7.

F igure 6

V, - 241 KEV (TkB)

o

a.

c o U tj >

o hC+CM)

shows t h e low e n e r g y r e g i o n o f t h e b e t a - r a y s p e c t r u m when ex am in ed w i t h a n o m i n a l r e s o l v i n g power o f 200.

The l a r g e s t

p e a k i s t h e w e l l known "F—l i n e " whose momentum v a l u e h a s b e en m easured/

42. m e a s u r e d v e r y a c c u r a t e l y ( t o a t l e a s t 1 / 5 0 0 ) by E l l i s and o t h e r s ( R u t h e r f o r d , Chadwick and E l l i s ,

1 950, p p . 3 6 9 - 5 7 0 ) ,

and

t h e d e t e r m i n a t i o n o f t h e f l u x m e t e r r e a d i n g f o r t h i s p e ak a l o n e i s t h e o r e t i c a l l y s u f f i c i e n t to c a l ib r a t e the instrum ent f o r a l l energies.

I t was d e c i d e d , how ev er, t h a t a c h e c k on t h e

c a l i b r a t i o n a t h i g h e n e r g i e s would b e a d v i s a b l e , i n o r d e r t o be c e r t a i n o f t h e l i n e a r i t y o f t h e f l u x m e t e r , and so a r e c o r d was ta k e n o f t h e b e t a - r a y spectrum of t h e so u rc e , n e a r i t s e n d - p o i n t , w i t h a r e s o l v i n g powe r o f 50, w i t h a v i e w t o o b s e r v i n g t h e internal-conversion ThCM.

T his l i n e ,

(K) l i n e o f t h e 2 . 6 2 M.E.V. gamma-ray from

though f e e b l e ,

was o b s e r v e d , and f o u n d t o

"300

-200 Li.

-IOO

Xio

20

E i g u r e 7»

30 40 50 Fluxmeter Divisions

60

70

High E n e r g y B e t a - r a . y Spectrum o f Th(E+C+C")

y i e l d a c a l i b r a t i o n o f t h e i n s t r u m e n t i n good a g r e e m e n t w i t h th at/

t h a t o b t a i n e d fro m t h e F - l i n e o f ThB.

The s p e c t r u m o b t a i n e d i s

shown i n F i g u r e 7, and t h e c a l i b r a t i o n c u r v e o f t h e s p e c t r o : m e t e r , b a s e d on t h e F - l i n e i s shown i n F i g u r e 8, w i t h t h e p o i n t due t o t h e 2 . 6 2 M.E.V. gamma-ray a l s o shown.

2-5 ThC* 2 62 MeV.) »

■20

r C7>

fcio 0-5 ThB KF - line

O

20

40 F lu x m e t e r

F ig u re 8.

60

80

D ivisions.

C a l i b r a t i o n Curve o f S p e c t r o m e t e r .

( i t may be n o t i c e d i n F i g u r e 6 t h a t t h e F - l i n e a c t u a l l y h a s a h a l f - w i d t h o f a b o u t 1 . 5 # d e s p i t e t h e h i g h r e s o l v i n g power used.

T h i s i s due t o t h e s o u r c e m o u n t i n g ,

sin ce th e use of

l o w e r r e s o l v i n g p o w ers d i d n o t i n c r e a s e g r e a t l y t h e w i d t h o f t h e lin e,

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

t h e m o u n t i n g , and a l s o by s e l f a b s o r p t i o n o f t h o s e e l e c t r o n s w h ic h come fro m t h e s i d e s o f t h e w i r e and so emerge n e a r l y tan g en tially /

to i t s

surface.

The p r o b l e m o f s o u r c e m o u n ti n g i s one o f t h e

main d i f f i c u l t i e s i n t h e u s e o f m a g n e t i c a n a l y s e r s f o r t h e s t u d y o f lo w e n e r g y b e t a - r a y s p e c t r a . ) W hile f i g u r e 6 shows v e r y c l e a r l y t h e o r d e r o f r e s o l u t i o n p r o v i d e d by t h e s p e c t r o m e t e r i n t h e a n a l y s i s o f t h e i n t e r n a l c o n v e r s i o n e l e c t r o n s from a s o f t gamma-ray (241 X . E . V . ) and a heavy n u c le u s , i t i s i n t e r e s t i n g t o observe th e o r d e r of r e s o l u t i o n p o s s ib l e w ith th e use of Siegbahnfs tec h n iq u e .

Here

ThE and i t s p r o d u c t s do n o t p r o v i d e a v e r y s u i t a b l e s o u r c e s i n c e t h e y e m i t a l a r g e number o f g a m m a-ra y s, and w i t h t h e d i m i n i s h e d r e s o l u t i o n o b t a i n a b l e by e x t e r n a l c o n v e r s i o n , i t becomes d i f f i c u l t to i n t e r p r e t the r e s u l t s obtained.

A v e r y good

K - 190 KcV -4 278 KeV.

c o

’> Q v w

E LL

c

2 3oc

U

F lu x m e te r

f i g u r e 9.

D ivisions

__ 203 S e c o n d a r y E l e c t r o n s from Gamma-Rays o f hg

exam ple o f t h e r e s o l u t i o n o b t a i n a b l e w i t h t h e i n s t r u m e n t i s h ow ever shown i n f i g u r e 9. ele ctro n s/

T h i s i s t h e s p e c t r u m o f t h e se c o n d a iy :

e l e c t r o n s e j e c t e d from a g l a s s tu b e covered w ith s e v e r a l t h i c k n e s s e s o f p la tin u m l e a f , by th e 270 K.E.V. gamma-rays from 203 Hg ^ and was o b ta in e d by Mr. H.vv. Wilson d u rin g t h e co u rse o f h i s ?/ork on t h i s s o u rc e .

I t w i l l be observed t h a t a t t h i s

energy t h e Compton e f f e c t in th e ( t h i c k ) g l a s s p roduces comi p a r a t i v e l y few e l e c t r o n s , w hile th e p h o t o - e l e c t r i c e f f e c t in th e v e r y t h i n p la tin u m i s so s tr o n g t h a t th e peaks due to con­ v e r s i o n i n th e K and 1 s h e l l s o f t h e p la tin u m a r e c l e a r l y seen, and t r a c e s of t h e M -conversion e l e c t r o n s a r e a ls o v i s i b l e . Since t h e mercury so u rce was weak (^so^ciC), i t i s c l e a r t h a t t h e sp e c tro m e te r p r o v id e s a good method o f i n v e s t i g a t i n g t h e e n e r g ie s o f gamma-rays in t h i s energy r e g io n .

II.3 « (a)

The P a i r S p e c tro m e te r.

An E a r ly I d e a . In 1947, th e a u th o r was working w ith Dr. S.C. Curran on

t h e p r o p e r t i e s o f G-.M. c o u n te r s w ith beads of con d u ctin g o r i n s u l a t i n g m a t e r i a l s on th e w ire . (Curran and Rae, 1947)

Out

o f t h i s work a r o s e an i d e a o f Dr. C u rra n ’ s to u t i l i s e t h i s e f f e c t i n th e d esig n of a s p e c tr o m e te r , i n p a r t i c u l a r a p a i r s p e c tr o m e te r , and a model was c o n s tr u c te d , of which a schem atic diagram i s shown i n F ig u re 10.

The p la n was to su rro u n d th e

so u rce of p a r t i c l e s w ith a r i n g shaped G.M. c o u n te r having i t s a x i s l y i n g along th e d i r e c t i o n o f th e m agnetic f i e l d , and to d iv id e /

d iv id e t h i s c o u n te r i n t o a l a r g e number of ind ep en d en t s e c t i o n s , by means of b ea d s, o r t h e i r e q u i v a l e n t s , p la c e d a t r e g u l a r i n t e r v a l s on t h e w ire .

F ig u re 10.

Then a p a r t i c l e e m itte d by th e sou rce in

The 360° S p e c tro m e te r.

t h e p la n e o f th e p ap e r w i l l , i n g e n e r a l , i n t e r s e c t only one o r two s e c t i o n s of th e c o u n te r , and w i l l produce a p u ls e o f c o rre sp o n d in g s i z e in t h e o u tp u t.

I f , however, th e p a r t i c l e i s

e m itte d w ith a momentum such t h a t i t s r a d i u s o f c u r v a tu r e w i l l cause i t t o d e s c r ib e a p a th t a n g e n t i a l t o th e o u te r w all o f th e c o u n te r, th e n t h i s p a r t i c l e w i l l t r i g g e r some f i v e o r s i x s e c t i o n s of t h e c o u n te r and produce a c o rre s p o n d in g ly l a r g e r p u lse .

Hence i f t h e so u rce c o n s i s t s o f a q u a n t i t y o f some

m a t e r i a l e m ittin g h ard gamma-rays (energy much g r e a t e r th a n 1 M .E .V .), surrounded by t h i n le a d f o i l , i t i s c l e a r t h a t p o s itro n e l e c t r o n p a i r s e j e c t e d from t h e f o i l by t h e gamma-rays, f o r t h e c o rre c t/

c o r r e c t v a lu e o f t h e m agnetic f i e l d , and f o r t h e ca se o f e q u ip a r t i t i o n o f energy between th e two components o f th e p a i r , could produce p u ls e s c o rre sp o n d in g to t h e t r i g g e r i n g of t e n o r tw elv e s e c t i o n s of th e c o u n te r . T h is was, i n e s se n c e , th e i d e a beh in d th e f i r s t p a i r s p e c tr o m e te r c o n s tr u c te d i n t h e l a b o r a t o r y , and a c o n s id e r a b le amount o f e f f o r t , on th e p a r t o f t h e a u th o r, was a p p lie d to i t s developm ent.

U n f o r tu n a te ly , f o r a number o f t e c h n i c a l r e a s o n s ,

t h e in s tru m e n t i n i t s o r i g i n a l form d id n o t prove s u i t a b l e f o r u se as a p a i r s p e c tr o m e te r .

The b a s i c id e a , o f a 360° semi­

c i r c u l a r f o c u s s in g s p e c tr o m e te r , has however been developed by t h e a u th o r, by th e a n a l y s i s o f t h e g e n e r a l c a se where t h e p a r t i c l e s a r e n o t c o n fin e d to th e neighbourhood o f t h e median p la n e , and an in s tru m e n t o f t h i s ty p e would seem t o b e p a rtic u la rs ly s u i t e d to c e r t a i n b ra n c h e s o f b e t a - r a y sp e c tro s c o p y .

In

p a r t i c u l a r , th e v e r y l a r g e s o l i d an g le of c o l l e c t i o n , which may approach 50% o f

would make such an in s tru m e n t i d e a l f o r th e

stu d y o f complex b e t a - r a y s p e c t r a by th e method o f beta-gamma c o in c id e n c e s .

(See P a r t I l l . l . ( d ) . )

D e s p ite t h e im p o rtan ce o f t h i s development o f t h e i d e a o f th e 360° s p e c tr o m e te r , i t was f e l t t h a t a d e t a i l e d d is c u s s io n o f th e s u b je c t a t t h i s p o in t might i n t e r f e r e w ith th e l o g i c a l development o f t h e main theme o f t h i s t h e s i s .

C onsequently

such a d is c u s s io n h as been o m itte d from th e main body of t h e t e x t , b u t a f u l l accou nt has been p re p a re d and a c c e p te d f o r p u b lic a tio n /

48 . p u b l i c a t i o n (Rae, 1 9 5 0 ,c) and t h i s i s g iv en i n Appendix I .

(b)

The Double S e m i-C irc u la r R e s o lv e r. In November 1947 McDaniel, von D ardel and Walker p u b lis h e d

a l e t t e r i n t h e P h y s ic a l Review g iv in g th e r e s u l t s o f an experim ent i n which t h e p a i r s produced by t h e 17 M.E.V. gammar a y s from t h e p ro to n bombardment o f l it h iu m were an a ly se d by means o f two G.M. c o u n te r s p la c e d on e i t h e r s id e o f a l e a d f o i l which was b ein g i r r a d i a t e d by th e gamma-rays.

By t h i s means

th e y o b ta in e d a curve which r e s o lv e d t h e 17 M.E.V. component o f t h e r a d i a t i o n q u i t e c l e a r l y , and su g g e ste d t h e p re se n c e o f low er energy r a d i a t i o n .

T h is dem o nstrated t h e f e a s i b i l i t y o f stu d y in g

h ig h energy gamma-ray s p e c t r a by a n a ly s in g th e p a i r s produced, i n a double s e m i - c i r c u l a r r e s o l v e r , a t l e a s t i n t h e 17 M.E.V. energy r e g i o n .

S ince however t h e c r o s s - s e c t i o n f o r p a i r

p r o d u c tio n f a l l s o f f w ith d e c re a s in g energy, and s in c e t h i n n e r c o n v e r to r s must a ls o be used on account o f in c r e a s e d s c a t t e r i n g and r e l a t i v e l o s s o f energy in t h e c o n v e r to r , i t was by no means c e r t a i n , from th e d a t a o f McDaniel and h i s co -w o rk e rs, t h a t t h i s method would be p r a c t i c a b l e a t e n e r g ie s much below 17 M.E.V. F or t h i s re a s o n a v e r y cru de model was c o n s tr u c te d u s in g two b e l l ty p e G.M. c o u n te r s sunk i n a le a d b lo c k as shown i n F ig u r e 11.

T h is l e a d b lo c k was f i x e d between th e p o le s o f th e

e le c tr o - m a g n e t, and th e whole surrounded by a t h i n b r a s s s t r i p , s e a le d v/ith Q-compound and e v a cu a ted . 10 mC/

Gamm a-radiation from

10 mC o f RaTh was th e n caused t o f a l l on t h e t h i n le a d f o i l ,

To Pump

Al. lining

to Pb. foil.

RaTh. S o u rce.

G.M. 2. Counter.

F ig u re 11*

E x p erim en tal P a i r Spectrom eter*

as i s shown i n th e diagram, and th e c o in c id e n c e r a t e between th e two c o u n te r s p l o t t e d a g a i n s t t h e magnet c u r r e n t .

T h is gave t h e

curve shown in F ig u re 12, i n d i c a t i n g t h a t even a t 2.6 M.E.V,,

E» - 2-7 MeV. 2 f 11 1 } ~T 0

1

2

3

Magnet

F ig u re 12.

1

4

5

1

6

7

C u r r e n t Jn A mperes.

Gamma-Ray Spectrum o f ThC”

th e p a i r - p r o d u c t i o n c r o s s - s e c t i o n was s t i l l h ig h enough t o make th e /

50. t h e method u s a b le .

(c)

The M ulti-C hannel P a i r S p e c tro m e te r. When t h i s f a c t had been e s t a b l i s h e d , draw ings were made

f o r t h e c o n s t r u c t i o n o f a p r o p e r ly d esig n ed double r e s o l v e r , bu t b e f o r e work had a c t u a l l y s t a r t e d on t h i s sp e c tro m e te r, McDaniel and Walker (194-8) p u b lis h e d t h e i r l a t e r p ap e r d e s c r ib in g t h e i r m u lti- c h a n n e l in s tr u m e n t, and as t h i s r e p r e s e n te d such an o bvious advance on th e s in g l e - c h a n n e l ty p e , i t was a t once d e c id e d t o b u i l d such an in s tru m e n t h e r e .

A schem atic diagram

Foil.

Source

Coincidence Array.

F ig u re 13*

Recorders.

The M ulti-C han nel P a i r S p e c tro m e te r.

o f th e a p p a ra tu s i s shown i n F ig u re 13, and i t w i l l be ob served t h a t th e f o i l i r r a d i a t e d by th e gamma-rays i s v e r y w ide. a b ility /

The

51. a b i l i t y t o use a wide f o i l and so p la c e a l a r g e q u a n t i t y o f c o n v e rtin g m a tte r in th e p a t h o f th e gamma-rays, w ith o u t u sin g a t h i c k c o n v e rto r, was one of th e g r e a t adv an tag es o f t h i s ty p e o f sp e c tro m e te r p o in te d out by McDaniel e t a l .

T h is can be

t o l e r a t e d b ecau se a t r e l a t i v i s t i c v e l o c i t i e s t h e energy o f a p a r t i c l e i s p r o p o r t i o n a l t o i t s momentum, and so t h e sum of th e e n e r g ie s o f th e p o s i t r o n and th e e l e c t r o n in a p a i r , which i s a measure of t h e energy o f th e gamma-ray p rod ucing t h e p a i r , i s alsc p r o p o r t i o n a l t o th e sum o f t h e i r momenta, and so t o t h e sum o f t h e i r r a d i i o f c u r v a tu r e i n a uniform m agnetic f i e l d .

Now, i f

a p a r t i c l e i s e j e c t e d in a d i r e c t i o n n e a r l y normal t o th e p la n e o f t h e c o u n te r s and t h e f o i l , i t i s bro ug ht back to th e c o u n te r p la n e a t a d i s t a n c e from i t s p o in t o f em ission eq ual t o tw ic e i t s r a d i u s o f c u r v a tu r e in t h e f i e l d . p r o p e r t i e s of s e m i - c i r c u l a r f o c u s s i n g ) .

(T h is fo llo w s from th e Hence i f a p o s i t r o n

and e l e c t r o n i n a p a i r a r e e j e c t e d n e a r l y normal t o th e c o u n te r p la n e , th e y a r e b ro u g h t back t o th e p la n e a t a d i s t a n c e a p a r t eq ual to tw ic e th e sum o f t h e i r r a d i i of c u r v a t u r e .

I f now

each o f t h e s e p a r t i c l e s e n t e r s and t r i g g e r s a c o u n te r , th e n t h e d i s t a n c e a p a r t o f t h e two c o u n te r s i s a measure o f t h e energy o f th e gamma-ray concerned, and t h i s i s in d e p en d en t of t h e p o i n t o f em ission of t h e p a i r , and of t h e a b s o lu te p o s i t i o n o f t h e c o u n te r s .

Hence i f a l a r g e number of c o u n te r s i s used , as in

t h e diagram , a c o in c id e n c e between th e t r i g g e r i n g o f any c o u n te r on one s id e o f t h e f o i l and one on th e o t h e r , g iv e s a measure o f t h e energy o f th e gamma-ray which produced th e p a i r . th e /

I f fu rth e r

t h e o u tp u ts o f a l l th e c o u n te r s a r e conn ected as shown t o a m u l t i p l e c o in c id e n c e c i r c u i t which r e g i s t e r s a l l such p o s s i b l e co m b in atio n s of c o u n te r s , and adds t o g e t h e r a l l th e co m binations c o rre sp o n d in g to th e same c o u n te r s e p a r a t i o n , th e n th e o u tp u ts from th e c o in c id e n c e c i r c u i t g iv e a number o f p o i n t s on t h e spectrum o f t h e gamma-rays which a r e under o b s e r v a tio n .

It is

c l e a r t h a t w ith th e a i d of such a c i r c u i t , th e in f o rm a tio n t h a t can be o b ta in e d i n a giv en tim e from any source, i s p r o p o r t i o n a l t o t h e number o f p a i r s o f c o u n te r s in u se ;

but i f th e re are n

c o u n te r s on each s id e o f t h e f o i l , th e n th e number o f such p a i r s 2

is n .

Hence, though th e u se of f o u r o r f i v e c o u n te r s on each

s id e o f th e f o i l makes th e n e c e s s a r y c o in c id e n c e c i r c u i t v e r y la rg e ,

( th e s i z e o f th e c i r c u i t i s a ls o p r o p o r t i o n a l t o n ) th e

i n c r e a s e i n speed i n ta k in g s p e c t r a w ith t h e in s tr u m e n t, which i s th e g r e a t advantage i t en jo y s ov er t h e cloud-cham ber, makes t h i s e x p e n d itu r e w orth w h ile .

(d)

C o n s id e r a tio n s i n t h e Design of a M u lti-C han nel I n s tr u m e n t. In th e above d e s c r i p t i o n of t h e a c tio n o f t h e p a i r s p e c t r o -

:m e te r, no account has been ta k e n o f t h e v a r i o u s f a c t o r s which o p e r a te to re d u c e i t s e f f i c i e n c y and r e s o l u t i o n .

These have

been d is c u s s e d a t le n g t h by Walker and McDaniel, and i t w i l l s u f f i c e h e re t o m ention t h e main d i f f i c u l t i e s , and th e l i m i t a t i o n s th e y impose on th e u se o f t h e in s tr u m e n t.

I t was

assumed i n th e above d is c u s s io n t h a t th e p a i r p a r t i c l e s were p ro je c te d /

53. p r o j e c t e d forw ard a t r i g h t a n g le s to th e p la n e o f t h e f o i l and co u n ters.

In

p a r t i c l e s are

p r a c t i c e t h i s i s n o t so because t h e p a i r i n f a c t p r o j e c t e d i n such a wayt h a t t h e m a jo r i ty

o f them a r e c o n ta in e d w ith in a cone o f s o l i d a n g le mQc^ /k v su rro u n d in g th e d i r e c t i o n o f th e gamma-rays, where mQ i s th e r e s t —mass o f an e l e c t r o n .

( H e itle r , 1936; p . 198)

At an energy

o f 3 M.E.V. t h i s s o l i d an g le i s o f t h e o r d e r o f l / 6 and t h e co rre sp o n d in g

s e m i - c i r c u l a r l i n e - w i d t h i s 17$. There i s

a ls o

th e f a c t th a t

t h e gamma-ray beam i s d iv e rg in g and so t h e axes

o f t h e cones of p a r t i c l e s a r e i n c l i n e d t o th e normal t o t h e c o u n te r p la n e .

T h is i s only a sm all e f f e c t p ro v id e d t h e so u rce

o f t h e gamma-rays i s s u f f i c i e n t l y f a r from th e f o i l .

Even

i f , however, t h e p a r t i c l e s commence t h e i r motion n e a r l y p e r p e n d i c u l a r l y to t h e c o u n te r p la n e , i t i s e s s e n t i a l t h a t th e y should n o t be s c a t t e r e d th ro u g h ’ l a r g e a n g le s in emerging from t h e c o n v e r tin g f o i l .

I t might be th o u g h t t h a t t h i s

c r i t e r i o n would make th e s e l e c t i o n o f a f o i l m a t e r i a l easy , s in c e one d e s i r e s t h e h ig h e s t p a i r p ro d u c tio n c r o s s - s e c t i o n f o r a g iven amount o f n u c l e a r s c a t t e r i n g .

T h is i s n o t, however,

t h e c a s e , s in c e b o th phenomena i n c r e a s e i n t h e same way, ( p r o p o r t i o n a l t o z^) w ith Z, ( H e i t l e r , 1936, p . 200;

R u th e r fo r d ,

Chadwick and E l l i s , 1930, p . 225) and so i t i s e q u a lly p o s s i b l e t o u se aluminium o r le a d c o n v e r to r s , and in d e ed Walker and McDaniel d id u se b o th .

Hence th e s c a t t e r i n g e f f e c t s e t s a

l i m i t on th e e f f e c t i v e th i c k n e s s of c o n v e rto r t h a t can be used , b u t/

b u t n o t on t h e m a t e r i a l .

I t m i g h t be n o t e d h e r e t h a t t h e l o s s

of energy o f a p a r t i c l e in t r a v e r s i n g th e f o i l i s norm ally t r i v i a l co m p ared w i t h i t s a p p a r e n t l o s s o f e n e r g y due t o s c a t ­ terin g ,

w h ic h c a u s e s i m p e r f e c t f o c u s s i n g and a l w a y s h a s t h e

e f f e c t o f m aking t h e p a r t i c l e i n t e r s e c t t h e c o u n t e r p l a n e a t a s h o r t e r d i s t a n c e from t h e p o i n t o f e m iss io n t h a n tw ic e i t s ra d iu s of cu rv atu re in th e f i e l d . I t i s c l e a r t h e n t h a t t h e two main f a c t o r s w hic h c o n t r o l t h e r e s o l v i n g po wer o f a p a i r s p e c t r o m e t e r a r e t h e w i d t h o f t h e c o u n t e r s and t h e t h i c k n e s s o f t h e f o i l s u s e d .

The f o r m e r can

t h e o r e t i c a l l y b e i m p r o v e d by t h e u s e o f s l i t s ,

w ith a correspond-

:in g lo s s in in te n s ity ;

b ut in p r a c t i c e i t i s extrem ely

d i f f i c u l t t o c o n s t r u c t a s l i t t o l i m i t a beam o f e l e c t r o n s w i t h an e n e r g y o f 10 t o 20 M . E . V . , on a c c o u n t o f t h e i r v e r y h i g h p e n e t r a t i n g p ow e r, and so a n y s u c h i n c r e a s e i n r e s o l u t i o n would be more l i k e l y t o come t h r o u g h t h e c o n s t r u c t i o n o f s m a l l e r counters.

The l i m i t a t i o n i n f o i l t h i c k n e s s seems t o be o f an

a b s o l u t e n a t u r e , b u t owing t o t h e p r o p e r t i e s o f s e m i - c i r c u l a r focussing,

a t h i c k f o i l p r o d u c e s a b r o a d e n i n g o f t h e gamma-ray

l i n e o n l y on t h e low e n e r g y s i d e , r e s o lu tio n of th e in stru m en t, i t

so t h a t a l t h o u g h i t l o w e r s t h e s t i l l e n ab les th e energy o f a

l i n e t o b e a c c u r a t e l y d e t e r m i n e d fro m t h e s h a r p h i g h e n e r g y e d g e , and s o , f o r a s i n g l e - l i n e s p e c t r u m , g i v e s good i n t e n s i t y w i t h o u t much l o s s i n a c c u r a c y . Only one more d e s i g n l i m i t a t i o n e x i s t s f o r t h i s t y p e o f j

instrum ent/

I

55. in s tr u m e n t, and t h i s i s i n th e c i r c u i t d e s ig n .

I t i s w ell known

t h a t i f two t r a i n s o f random im p u lses o f mean r e c u r r e n c e r a t e s p and q, and o f d u r a tio n s and t , a r e compared, th e n t h e number o f o v e r la p s t h a t occu r in u n i t tim e between members o f th e two s e r i e s i s g iv e n by p . q ( s + t ) .

Hence i f p and q r e p r e s e n t th e

background r a t e s i n two o f t h e c o u n te r s of t h e p a i r s p e c tr o m e te r 3 one b e lo n g in g to each s e t , and i f s and t r e p r e s e n t th e d u r a tio n o f t h e p u ls e s produced by th e c o u n te r s and t h e i r a s s o c i a t e d c i r c u i t s , th e n th e e x p re s s io n p . q ( s

t ) g iv e s th e number o f

random c o in c id e n c e s o c c u rr in g p e r u n i t of tim e .

Hence th e

c o u n te r backgrounds must be made as sm all a s p o s s i b l e , by making t h e i r p h y s ic a l s i z e sm a ll, and by p la c in g as much a b s o rb e r ( le a d ) as p o s s i b l e between th e so u rce and th e c o u n te r s ;

a l s o th e

c i r c u i t s must produce as s h o r t p u l s e s as p o s s i b l e , i f th e number o f random c o in c id e n c e s i s t o rem ain sm all i n com parison w ith th e number o f r e a l c o in c id e n c e s caused by th e p a i r s .

(e )

The Glasgow P a i r S p e c tro m e te r. A p h o to g rap h of th e p a i r s p e c tr o m e te r b u i l t a t Glasgow

t o g e t h e r w ith i t s a s s o c i a t e d c i r c u i t s i s shown in F ig u r e 14The in s tru m e n t i s f i t t e d w ith te n s e p a r a te m in ia tu r e G.M. coun: t e r s , A, which a re d e s c r ib e d elsew here (Rae, 195Qb), and a re f i l l e d t o a p r e s s u r e s l i g h t l y i n excess of one atm osphere in o r d e r to p ro v id e a h ig h e f f i c i e n c y , t o g e t h e r w ith a s t a b l e t h i n window (20 cm. of a i r e q u i v a l e n t ) . a/

The c o n v e rto r i s mounted on

a t h i n w i r e f r a m e w h ic h i s p i v o t e d so t h a t t h e f o i l may be p i a x ed i n ,

o r rem oved f r o m , t h e beam o f gamm a-rays w i t h o u t d i s ­

t u r b i n g t h e vacuum.

Each c o u n t e r i s c o n n e c t e d by a s h o r t p i e c e

o f l o w - c a p a c i t y s c r e e n e d c a b l e t o a c a t h o d e f o l l o w e r B, which i n tu rn r e l a y s th e c o u n te r im pulses through a long c a b le to a p u lse s h a p i n g c i r c u i t C.

T his c i r c u i t produces a p u lse of d u ra tio n

fro m 0 . 3 t o 3 m i c r o s e c o n d s whose l e a d i n g edge i s c o i n c i d e n t w i t h

F ig u r e 14.

Tpe Glasgow P a i r S p e c t r o m e t e r .

th e sharp r i s e of the c o u n te r p u ls e ,

and f e e d s t h i s s h o r t p u l s e

i n t o a row o f c o i n c i d e n c e c i r c u i t s i n t h e c o i n c i d e n c e c i r c u i t array.

The c o i n c i d e n c e c i r c u i t o u t p u t s a r e c o n n e c t e d up

d i a g o n a l l y , i n s u c h a way t h a t e a c h o f t h e n i n e f i n a l o u t p u t s corresponds to a d e f i n i t e counter se p a ra tio n . feed/

The n i n e o u t p u t s

feed in to nine p u lse -le n g th e n in g c i r c u i t s ,

w h ic h p r o d u c e p u l s e s

l o n g en ough t o o p e r a t e a p o s t o f f i c e t e l e p h o n e r e g i s t e r ,

and t h e

t o t a l number o f p a i r s i n e a c h c h a n n e l i s r e c o r d e d on t h e s e i n s t r u m e n t s D.

The e l e c t r i c a l c i r c u i t s u s e d , w h ic h were

d e s i g n e d by t h e a u t h o r w i t h a v i e w t o o b t a i n i n g t h e s h o r t e s t r e s o l v i n g tim e p o s s i b l e w ith v a lv e s of th e E .F .50 ty p e , a re d e s c r i b e d i n more d e t a i l i n A p p e n d ix I I .

3c 5 -2

*4

Na

2 7 6 MeV.

c c

O O .c

in

uc yV u c o O 3 3 4 4 5 5 Hq of mean e l e c t r o n in K i l o - G a u s s . c m .

F i g u r e 13*

G-amma-Ray S p e c t r a o f T h ( B f r C + C f ! ) and N a ^ T hick C onvertors*

Y/hen t h e s p e c t r o m e t e r was f i r s t

com pleted, th e e l e c t r o ­

m agnet was h o u s e d i n a s e p a r a t e room fro m t h e p a r t i c l e a c c e l e r a ­ to r,

and so t h e o n l y s o u r c e s o f e n e r g e t i c gamm Cv 1* ^ av a r 1 ab 1 e

t o t e s t and c a l i b r a t e i t were r a d i o a c t i v e o n e s . in strum ent/

Hence t h e

in s tru m e n t was t e s t e d u s in g so u rc e s o f Th(Bt.C+C") and Ha2^, and t h i c k c o n v e r to r s i n o r d e r t o o b ta in good s e n s i t i v i t y a t th e r e l a t i v e l y low e n e r g ie s o f t h e r a d i a t i o n s p ro v id e d by th e s e sources.

The s p e c t r a o b ta in e d a r e shown in F ig u re 15, and i t

w i l l be observed t h a t th e l i n e s a r e v e r y b ro ad , as ex p e cte d . however, a p o i n t h a lf-w a y up th e h ig h energy edge o f t h e l i n e s i s ta k e n as s i g n i f i c a n t , th e n t h e i r e n e r g ie s can be d eterm ined w ith a r e l a t i v e a c c u ra c y of th e o r d e r of -

Also th e

d e te r m in a tio n of th e s e two w ell known s p e c t r a e n a b le s a c a l i b : r a t i o n t o be made o f t h e f l u x m easuring arrangem ent of th e s p e c tr o m e te r , though i t w i l l be a p p r e c ia t e d t h a t on acco un t of t h e r e l a t i v e l y low energy o f t h e r a d i a t i o n from th e s e s o u r c e s , t h i s d e te r m in a tio n i s n o t as a c c u r a te as would be d e s i r e d .

If

Hote on th e Korroalisation o f R e su lts obtained w ith the M u ltiChannel P air Spectrom eter. H e i t l e r has shown t h e o r e t i c a l l y ( H e i t l e r : Quantum th e o ry o f R a d ia tio n p . 199) t h a t f o r gamma-rays i n t h e energy r e g io n co vered by t h e p a i r sp e c tro m e te r, say 3 to 20 M.E.V., t h e energy spectrum o f p o s i t r o n s o r e l e c t r o n s produced as p a i r s i s ro u g h ly r e c t a n g u l a r , p ro v id e d we ig n o r e t h e d i s t o r t i o n caused by th e Coulomb f i e l d o f t h e n u c l e i o f t h e m a t e r i a l i n which th e p a i r s a r e form ed.

The e f f e c t o f t h e Coulomb f i e l d i s t o r a i s e

t h e h ig h energy end and d e p re s s t h e low energy end o f t h e p o s i t r o n spectrum , w ith a complementary e f f e c t on t h e e l e c t r o n spectrum .

T h is e f f e c t i s however q u i t e n e g l i g i b l e , even in

l e a d , ex cep t a t t h e low end o f t h e ran g e o f gamma-ray e n e r g ie s i n which we a r e i n t e r e s t e d . by ex p e rim en t.

These r e s u l t s have been confirm ed

(D e lsa sso , Fowler and L a u r its e n , 1937;

A lichanov, A lic h a n ia n and Kosodaev, 1936)

Elwfr&As

Pcsit to rvs

Counters of Widtk U>

D istr ib u tio n o f p a ir s among cou n ters. Hence i f we c o n s id e r th e c a se o f p a i r s produced by h ig h energy p h o to n s f a l l i n g no rm ally on t o a narrow elem ent of a t h i n f o i l p la c e d between two s e t s of c o u n te r s i n a m agnetic fie ld /

f i e l d , as shown i n t h e diagram , th e n th e number o f p o s i t r o n s f o c u s s e d by th e magejntic f i e l d i n t o R l, w i l l be t h e same as t h e number f o c u s s e d i n t o B2, R3 o r R4, s in c e each c o u n te r of w id th w r e p r e s e n t s t h e same f i x e d momentum i n t e r v a l Hw, and so f o r r e l a : t i v i s t i c p a r t i c l e s , th e same energy i n t e r v a l .

(P rov id ed always

t h a t t h e v a lu e o f t h e m agnetic f i e l d has been s u i t a b l y c h o se n ). S i m i l a r l y t h e number o f e l e c t r o n s f o c u s s e d i n t o each o f t h e e l e c t r o n c o u n te r s w i l l be c o n s t a n t .

Hence i f we ta k e c o i n c i ­

d e n c e s between H and R l, and so measure t h e number o f p a i r s o f 4.

t o t a l momentum Hd^ - Hw e n t e r i n g th e s e two c o u n te r s , we s h a l l f i n d t h a t t h i s i s t h e same number as e n t e r 12 and R2, 13 and R3, o r 14 and R4*

S im il a r ly c o in c id e n c e s between 11 and R2, 12 and

R3, o r 13 and R4 w i l l r e c o r d t h e number of p a i r s o f t o t a l momen:tum Hdg - Hw, and so on.

In t h e M ulti-C hannel P a i r S p e c tro -

:m e te r, t h e o u tp u t o f each p a i r o f c o u n te r s a p p e a rs on a r e g i s : t e r c o rre s p o n d in g to t h e t o t a l momentum concerned, a s shown i n F ig u re 13> and a l l t h a t i s n e c e s s a r y t o n o rm a lise t h e r e s u l t s f o r a s i n g l e s e t t i n g o f t h e m agnetic f i e l d i s t o d iv id e t h e r e a d in g of each r e g i s t e r by th e number o f c h a n n e ls re c o rd e d on i t , and so o b ta in t h e number o f c o in c id e n c e s p e r ch ann el p e r momentum i n t e r v a l Hw.

S ince t h e above argument i s t r u e f o r any narrow

elem ent o f f o i l p la c e d between t h e s e t s o f c o u n te r s , i t i s c l e a r l y a l s o t r u e f o r t h e c a se of a wide f o i l . When t h e m agnetic f i e l d i s changed to a n o th e r v a lu e , say H-^, th e n t h e momentum i n t e r v a l i s changed t o H^w, and i f th e r e s u l t s o b ta in e d have t o be compared w ith th o s e f o r th e sta n d ard /

58c.

f i e l d H, th e n a l l th e r e g i s t e r r e a d in g s must be reduced t o a momentum i n t e r v a l Hw by m u ltip ly in g by th e f a c t o r H/H^. The a p p l i c a t i o n o f t h i s sim ple g e o m e tric a l n o r m a lis a tio n p ro ced u re has been found t o g iv e s a t i s f a c t o r y r e s u l t s , ex c ep t i n th o s e c a s e s where r e l a t i v e l y low energy r a d i a t i o n s have been i n v e s t i g a t e d w ith t h e use o f t h i c k le a d f o i l s (See pp. 57 and 5 8).

In t h e s e c a s e s th e p a i r s a r e n o t p r o j e c t e d n o rm ally t o

th e f o i l , and s e v e re s c a t t e r i n g i n c r e a s e s t h i s e f f e c t (See p . 53) so t h a t a number o f p a r t i c l e s a r e d e f l e c t e d so f a r from t h e p la n e o f t h e s p e c tro m e te r t h a t th e y a r e not re c o r d e d .

In ad -

r d i t i o n , th e use o f a le a d f o i l a t low e n e r g ie s c a u se s c o n s id e r ­ a b l e Coulomb d i s t o r t i o n , and so i t i s c l e a r t h a t f o r such s p e c t r a no a c c u r a te measurement o f r e l a t i v e i n t e n s i t i e s would be p o s s i b l e .

In th e two c a s e s c i t e d , however, no q u e s tio n o f

r e l a t i v e i n t e n s i t i e s was r a i s e d , t h e i n t e r e s t b e in g e n t i r e l y i n th e energy measurement.

Even so, an attem p t was made to c o r r e c t

e m p i r i c a l l y f o r th e e f f e c t of t h e d e f l e c t i o n o f t h e p a r t i c l e s , by m u lt ip ly in g th e r e s u l t s by a f a c t o r o f t h e form ( by J a e g e r and Hulme. 5 These a u th o rs p u b lis h e d curved showing th e v a l u e s o f t h e I n t e r n a l P a i r C re a tio n C o e f f i c i e n t ( i . P . C . C . ) f o r Z=0 and Z=84> and f o r e l e c t r i c d ip o le and quadrupole t r a n s i t i o n s , i n th e energy ran g e 1 t o 3 M.E.Y.

The c u rv es a r e shown in P ig u re 26,

and i t w i l l be observed t h a t u n lik e th o s e f o r t h e I . C . C . , th e y

O -15

E.D. Z- O^ 3 II N

O

o

z

o

k -IO

/

X-= o

/

XX >S x

Cl

-5

84 ThC * (Latyshev)

15

I 20

Gamma-Ray

F ig u re 26.

I 25

1 30

Ene rgy, MeV.

T h e o r e t i c a l Y alues o f t h e I .P .C .C .

show a r i s e w ith i n c r e a s i n g gamma-ray energy, and a l s o e x h i b i t v e r y l i t t l e dependence on th e atom ic number.

At th e tim e when

t h e s e t h e o r e t i c a l p r e d i c t i o n s were made, A lichanov, A lic h a n ia n and/

83.

and Kosodaev were i n t e r e s t e d i n t h i s e f f e c t , and in 1936 th e y p u b lis h e d th e r e s u l t s o f t h e i r s tu d y o f t h e i n t e r n a l p a i r c r e a t i o n i n ThB and Radon i n e q u ilib r iu m w ith t h e i r decay p r o d u c ts .

They c a r r i e d out t h i s stu d y by o b se rv in g th e

p o s i t r o n s e m itte d by each o f th e two s o u rc e s m entioned, in a s e m i - c i r c u l a r f o c u s s in g sp e c tro m e te r o f 10 cm r a d i u s , and th e y found th e shape o f t h e spectrum o f th e p o s i t r o n s to a g re e w e ll w ith t h a t p r e d i c t e d by J a e g e r and Hulme.

The main d i f f i c u l t y

i n th e experim ent was t h e d e t e c t i o n o f t h e sm all numbers o f p o s i t r o n s a g a i n s t th e s tr o n g background caused i n th e c o u n te r by t h e gamma-rays from t h e so u rc e .

The a u th o rs overcame t h i s

d i f f i c u l t y by th e use o f two c o u n te r s i n c o in c id e n c e , and were th u s a b le t o red u ce th e background t o a workable l e v e l .

Using

s o u rc e s having a s t r e n g t h o f th e o r d e r o f 1 mC, t h e a u th o r s observed th e p o s i t r o n spectrum o f t h e so u rc e ;

th e y th e n

r e v e r s e d th e p o l a r i t y o f t h e e le c tro - m a g n e t, c u t down t h e s o l i d an g le o f th e s p e c tr o m e te r by a known f a c t o r , and o b se rv e d th e b e t a - r a y spectrum .

In t h i s way th e y were a b le t o d eterm in e

th e number o f p o s i t r o n s e m itte d , and t h e r e f o r e th e number o f p a i r s c r e a t e d , p e r b e t a - r a y e m itte d by th e s o u rc e .

T h is

q u a n t i t y th e y found t o have a v a lu e o f ap p ro x im a te ly 2 xlCT^ f o r b o th t h e ThB and Radon s o u r c e s .

T h is work was r e p e a te d

i n 1946 by B ra d t, H a l t e r , Heine and S c h e r r e r , and was c a r r i e d to a v e r y h ig h degree o f p r e c i s i o n i n l a t e r R u ssian work review ed by L atyshev (1947).

In k i s rev iew p a p e r, L atyshev

e x h i b i t s c u rv e s showing th e p o s i t r o n s p e c t r a o f t h e two so u rc e s m e n tio n e d /

84. m entioned above, which show n o t on ly th e main spectrum due to t h e s tr o n g e n e r g e t i c gamma-ray in each c a s e , b u t a ls o s u b s i d ia r y s t e p s in th e s p e c t r a l d i s t r i b u t i o n s , c o rre s p o n d in g to t h e i n t e r n a l p a i r c o n v e rs io n o f o th e r minor gamma-rays.

By

m easuring th e a r e a s under b o th th e main and component c u rv e s , t h e a u th o r s were a b le to d e te rm in e th e r e l a t i v e v a l u e s o f th e I .P .C .C . f o r th o s e gamma-rays whose r e l a t i v e i n t e n s i t i e s were known from o th e r e x p e rim e n ts . produced by th o s e gam m a-rays.)

(On t h e Compton e l e c t r o n s On th e assum ption t h a t one

p a r t i c u l a r gamma-ray l i n e from each so u rce was o f e l e c t r i c d ip o le o r q uadrupole o r i g i n , a s t h e c a s e may b e , t h e a u th o r s were a b le to show t h a t th e p o i n t s c o rre s p o n d in g to th e o t h e r minor l i n e s a l l l a y c l o s e t o one o r o th e r o f t h e c u rv e s o f J a e g e r and Hulme.

L atyshev a l s o quoted an experim ent i n which

t h e a b s o lu te m agnitude o f t h e I .P .C .C . was measured f o r th e 2.62 M.E.V. l i n e o f ThC", and once ag a in t h e v a lu e o b ta in e d a g ree d w ell w ith t h a t g iv e n by J a e g e r and Hulme f o r an e l e c t r i c quadrupole t r a n s i t i o n . I t i s c l e a r th e n , t h a t th e above work, m ainly c a r r i e d o ut by t h e R u s s ia n s , e s t a b l i s h e d t h a t th e c u rv e s o f J a e g e r and Hulme gave t h e c o r r e c t v a l u e s f o r t h e I .P .C .C . f o r e l e c t r i c d i p o l e and q u adru po le t r a n s i t i o n s i n a heavy elem en t.

More r e c e n t work has

been c o n f in e d to th e i n v e s t i g a t i o n o f t h e 100$ tr a n s itio n in

p a i r p ro d u cin g

(Hornyak and L a u r i t s e n , 1 9 4 ^ and th e i n t e r n a l

p a ir/ * T h is i s a v e r y s p e c i a l ca se where t h e emission o f gammar a d i a t i o n i s co m p letely fo rb id d e n , and need n o t concern us h e r e .

85. p a i r c r e a t i o n due t o t h e 3*1 M.E.V. gamma—r a y s from th e r e a c t i o n 12 1*5 C (d,p)C . (Dougherty, Hornyak, L a u r its e n and Rasmussen, 1948), These l a t t e r a u th o rs measured th e I .P .C .C . v e r y ro u g h ly f o r th e t r a n s i t i o n i n v e s t i g a t e d , and found i t to be o f t h e o r d e r o f 10“ ^ p a i r s p e r quantum, th u s showing t h a t th e p r e d i c t i o n o f J a e g e r and Hulme, t h a t th e I .P .C .C . i s n e a r l y in d e p en d en t o f Z, i s c e rta in ly tru e q u a lita tiv e ly .

I t i s t h i s somewhat s u r p r i s i n g

r e s u l t ( s u r p r i s i n g b ecau se th e e x t e r n a l p a i r - c r e a t i o n e f f e c t i s p r o p o r t i o n a l to Z ) which makes t h e I .P .C .C . so im p o rta n t i n th e d e te r m in a tio n o f t h e m u ltip o le o r d e r o f t r a n s i t i o n s i n t h e lig h t n u c le i.

The im p o rtan ce o f t h e p r o c e s s i s enhanced s t i l l

f u r t h e r by th e f a c t t h a t i t i n c r e a s e s w ith t h e energy o f th e t r a n s i t i o n , so t h a t i t p r o v id e s a method which i s complementary to t h a t o f o b se rv in g i n t e r n a l c o n v e rs io n , s in c e t h e new e f f e c t i s s tr o n g i n t h e v e ry c a s e s where t h e o t h e r i s weak. In view o f th e above argum ent, i t seems s u r p r i s i n g t h a t th e p o s s i b i l i t y o f t h e use o f t h e i n t e r n a l p a i r - c r e a t i o n e f f e c t t o d eterm in e m u ltip o le o r d e r was c o m p le te ly o v erlo o k ed u n t i l 1949 when i t was p o in te d o u t in d e p e n d e n tly by Devons (1949, p . 1 0 0 ), and t h e p r e s e n t a u th o r (Rae, 1949) who used th e e f f e c t t o d e te rm in e t h e m u ltip o le o r d e r o f t h e 2#76 M.E.V. gamma-ray from t h e r a d i o a c t i v e decay o f Sodium-24.

In 1949 a l s o , th e

th e o r y o f th e e f f e c t was s u b je c te d to f u r t h e r i n v e s t i g a t i o n by Rose, who p u b lis h e d a com prehensive s e t o f c u rv e s , g iv in g th e I .P . C .C . f o r b o th e l e c t r i c and m agnetic t r a n s i t i o n s up t o 25 - p o le , f o r a l i g h t elem en t. T h e/

The rem ain in g s e c t i o n s o f t h i s c h a p te r w i l l d e s c r ib e th e a u t h o r ’ s ex p erim en ts on Sodium-24, and p o s s i b l e e x te n s io n s o f t h e te c h n iq u e employed, t o d eterm in e t h e m u ltip o le o r d e r o f t r a n s i t i o n s n o t f o llo w in g b e ta - d e c a y , o r where t h e l i f e t i m e o f t h i s decay i s v e r y s h o r t .

1 7 .2 . (a)

Sodium-24.

E xperim ent. Sodium-24 was chosen as th e s u b je c t o f t h i s experim ent

b ecau se i t i s t h e o n ly l i g h t elem ent whose r a d i o a c t i v e decay combines t h e d e s i r a b l e q u a l i t i e s o f a re a s o n a b ly lo n g h a l f - l i f e (15 h o u rs) w ith t h e em issio n o f an e n e r g e t i c gamma-ray (2.7 6 M .E .Y .).

I t was p a r t i c u l a r l y s u i t a b l e f o r th e ex p e rim en t, in %

t h a t , i n a d d i t i o n t o t h e above two p r o p e r t i e s , i t was a l s o known t o s u f f e r a sim p le b e ta - d e c a y f o llo w e d by t h e em issio n o f two gamma-rays i n c a sc a d e , o f e n e r g ie s 1 .3 8 and 2.76 M.E.Y. (Wiedenbeck, 1947, and see a l s o r e f e r e n c e s q u o te d .)

T h is meant

t h a t a measurement o f th e t o t a l number o f p o s i t r o n s c r e a t e d by th e gamma-ray co n cern ed , i n a g iv e n tim e , combined w ith a s i m i l a r measurement o f t h e number o f decay e l e c t r o n s e m itte d , would p ro v id e a d i r e c t d e te r m in a tio n o f t h e I .P .C .C . o f t h e lin e .

The main so u rce o f e r r o r i n such a d e te r m in a tio n would be

l i k e l y t o a r i s e b ecau se o f th e p o s s i b l e change i n t h e o v e r a l l e f f i c i e n c y o f t h e s p e c tr o m e te r u s e d , w ith e n e rg y .

Here ag a in

t h e c h o ic e o f Na2^ was a p a r t i c u l a r l y happy one, i n t h a t th e maximum energy o f t h e p o s i t r o n s produced i s 1 . 8 M.E.Y. which

87. i s q u i t e c l o s e t o t h e maximum energy o f th e d i s i n t e g r a t i o n e l e c t r o n s ( 1 . 4 M .E .V .).

Thus t h e e r r o r a r i s i n g i n t h i s way i s

c e r t a i n l y t r i v i a l , s in c e o n ly a n e g l i g i b l e p a r t o f each s p e c t :rum l i e s i n th e low energy re g io n where l o s s e s i n e f f i c i e n c y become a p p r e c i a b l e . The H a ^ , which was o b ta in e d from A .E .R .E ., was in th e form o f sodium c a rb o n a te , and 100 mg of t h e a c t i v e m a t e r i a l was d is s o lv e d i n a few d rop s o f w a te r and th e n ev a p o ra te d t o d ry n e ss on a sm all t r a y o f t h i n aluminium f o i l (0.002* t h i c k ) m easuring 3 .5 cm by 8 mm.

The so u rc e t h u s formed was o f s u i t a b l e

dim ensions f o r u se i n t h e s e m i - c i r c u l a r s p e c tr o m e te r , and had an i n i t i a l a c t i v i t y o f t h e o r d e r o f 10 mC.

The s p e c tr o m e te r

was u sed w ith a r e s o l v i n g power o f 50, and w ith double c o u n t e r s t o keep t h e background low.

The te c h n iq u e used was t o r e c o r d

t h e p o s i t r o n spectrum w h ile t h e so u rce was as a c t i v e as p o s s i b l e , and th e n t o compare t h e a r e a u n d er t h i s cu rv e w ith t h e a r e a u n d er t h e cu rv e o b ta in e d by r e c o r d in g th e b e t a - r a y spectrum , th e l a t t e r b e in g d eterm in ed a f t e r t h e so u rce had been allow ed t o age f o r a few d ay s, i n o r d e r t o b r i n g th e b e t a - r a y i n t e n s i t y down t o a w orkable l e v e l .

The c u rv e s o b ta in e d a r e

shown i n F ig u r e 27, and th e v a l u e o f t h e I .P .C .C . d eterm in ed from t h i s d a t a i s (1.16 - 0 .1 0 )x l0 ~ ?

The t h e o r e t i c a l v a l u e s

o f t h e c o e f f i c i e n t , as c a l c u l a t e d by J a e g e r and Hulme, a r e shown i n F ig u re 26, and i t w i l l be n o t i c e d t h a t t h e above v a l u e v e r y n e a r l y c o i n c id e s w ith th e Z=0 cu rve f o r e l e c t r i c d ip o le tra n sitio n s* A/

A f u r t h e r check on t h i s measurement i s a v a i l a b l e i f t h e number o f p o s i t r o n s from t h e N a ^ so u rce i s compared w ith th e number from a so u rce of ThCw, p ro v id e d t h e r a t i o o f t h e gammar a y i n t e n s i t i e s i s known.

In o r d e r t o a s c e r t a i n t h i s r a t i o ,

t h e s h u t t e r on t h e s p e c tr o m e te r was u sed t o p la c e a t h i c k le a d f o i l im m ediately i n f r o n t o f t h e so u rc e .

The p o s i t r o n s p e c t r a

ENERGY M.E.V. 0-5

10

20

ENERGY M.E.V.

0

0-5

1-0

1-5

Spectra of Nh24. (a) Positrons from bare source. (6) Positrons from thick lead foil. (c) Electrons.

F igu re 27»

Spectra o f Sodium-24»

o f U a ^ w ith and w ithout th e le a d f o i l in p la c e are shown in F igu re 27> and a s im ila r p a ir o f curves was ob tain ed f o r a source o f ThC".

By comparing th e areas under th e fo u r curves

and making a sm all c o r r e c tio n fo r th e d iffe r e n c e in energy between th e two gamma-rays, a v a lu e o f 2 .3 8 - 0 . 3 0 was obtained fo r /

89.

f o r t h e r a t i o I .P .C .C .( N a ) / l.P .C .C .( T h C " ) .

Assuming t h a t th e ThC11

l i n e i s o f e l e c t r i c q u ad rup ole o r i g i n (L atyshev, 1947), we can obs t a i n from F ig u re 26 t h e o r e t i c a l v a l u e s o f t h i s r a t i o f o r th e c a s e s of t h e Ha l i n e b e in g e i t h e r o f e l e c t r i c d ip o le o r quadrupole o rig in .

These v a l u e s a r e 2.32 and 1 .3 5 r e s p e c t i v e l y .

Hence t h i s

e x t r a p o l a t i o n from t h e known c a s e of t h e ThC” l i n e a ls o p la c e s th e c o e f f i c i e n t f o r t h e Ha l i n e on th e e l e c t r i c d ip o le c u rv e .

A lte r­

n a t i v e l y t h i s measurement may be re g a r d e d as c o n firm a tio n o f th e r e s u l t quoted by L aty sh ev, t h a t th e I .P .C .C . of t h e ThC" l i n e l i e s on t h e e l e c t r i c quadrupole cu rv e , t h i s method o f measurement b e in g s im p le r th a n t h a t used by t h e R u s sia n s who had t o make assu m p tio n s about th e v e r y complex decay o f Th(BvC-vC") i n o r d e r t o a r r i v e a t an a b s o lu te v a lu e f o r t h e c o e f f i c i e n t .

(b)

D is c u s s io n .

I

The experim ent c e r t a i n l y shows t h a t t h e th e o r y p r e d i c t s th e

j

c o r r e c t o r d e r o f m agnitude f o r t h e I .P .C .C . o f t h e gamma-ray i n ­ v e s tig a te d .

Since* however th e th e o r y i s known t o be i n a c c u r a te

agreem ent w ith experim ent i n t h e c a se o f th e heavy r a d i o a c t i v e e le m e n ts, i t seems r e a s o n a b le to go f u r t h e r and assume t h a t i t p re: d i e t s t h e c o r r e c t r e s u l t s f o r t h e sim p le r ca se o f t h e l i g h t e l e - j :m ents.

I f t h i s i s so, th e n th e gamma-ray i n v e s t i g a t e d i s o f

|

e l e c t r i c d ip o le o r i g i n . T h is in f o rm a tio n e n a b le s us t o e s t a b l i s h a 24-

sim ple energy l e v e l scheme f o r t h e Mg

n u c le u s , f o r i t has been

shown by Wie&enbeck 0-947) t h a t t h e l e v e l scheme i s g iven by e i t h e r (a)/

!

90. (a) o r (b) i n F ig u re 28.

How P o l l a r d and A lb urg er (194-8), from

ex p e rim en ts on t h e l a r g e an g le s c a t t e r i n g o f t h e gamma-rays from Ha

by t a r g e t s o f Mg and Al, s t a t e t h a t t h e ^ t r a n s i t i o n s

t o th e ground s t a t e o f t h e M n u c l e u s from t h e l e v e l s a t o>* oj w W t ^

ftx tt OfUOtbJ

1 .3 8 and 2.76 M .E .v .,

"thoy- Qxlofr) a r e c e r t a i n l y of quadru-

:p o le o r h ig h e r o r d e r .

I f th e n we a c c e p t t h a t t h e 2.76 M.E.V.

l i n e i s o f e l e c t r i c d ip o le o r i g i n , we must r e j e c t scheme (b) and assume t h a t scheme (a) i s c o r r e c t .

M.E.V. 24

-6

-4

Energy Level Diagram of Mg24 Nucleus.

F ig u re 28.

Energy L evel Diagram o f M g ^ N ucleus.

We can a l s o go f u r t h e r and a s s ig n t e n t a t i v e s e t s o f sp in and p a r i t y v a l u e s to t h e l e v e l s i n t h e decay scheme.

I f we

make t h e s im p le s t assu m p tio n , namely t h a t th e 1 .3 8 M.E.V. l i n e i s o f e l e c t r i c qu ad ru p o le o r m agnetic d ip o le o r i g i n , th e n s in c e th e /

91

th e ground s t a t e h as ze ro s p in and even p a r i t y , i t fo llo w s from t h e t a b l e quoted i n I V . l . ( b ) t h a t th e 1 .3 8 M.E.V. l e v e l i s o f even p a r i t y and has sp in 1 o r 2.

The e l e c t r i c d ip o le n a t u r e o f

t h e 2.76 M.E.V. r a d i a t i o n makes th e p a r i t y o f t h e 4 .1 4 M.E.V. l e v e l odd, and i t s s p in 0 ,1 , 2 o r 3 •

To choose between th e

v a r i o u s p o s s i b l e s e t s o f v a l u e s , i t i s n e c e s s a r y t o c o n s id e r th e n a t u r e o f t h e b e ta - d e c a y , which i s f i r s t f o r b id d e n . (Siegbahn, 1 9 4 6 ,b ) .

T h is l e a d s to t h e s e l e c t i o n r u l e s

= 0 , 1 , 2 w ith a change i n p a r i t y .

IJ1 - IJ*I

The s p in change ze ro i s n o t

p e r m is s ib le i n t h i s c a s e , however, s in c e t h i s would always p e rm it an allow ed b e t a decay t o t h e l e v e l a t 1 .3 8 M.E.V. which i s n o t o b se rv e d .

(Spin change 0 ,1 w ith no change i n p a r i t y ) .

Also i t i s known from th e o b serv ed shape o f th e spectrum , which i s s i m i l a r to t h a t o f an allow ed t r a n s i t i o n , t h a t t h e change i n s p in cannot have t h e v a lu e 2.

(Konopinski and U hlenbeck, 1941)*

Hence t h e s p in change must have th e v a lu e 1, and so i t i s p o s s i b l e t o make a diagram o f a l l t h e p o s s i b l e s e t s o f sp in v a l u e s , as shown i n F ig u re 29* and t h e s e a r e seen s t i l l t o be e le v e n i n number,

l e t u s c o n s id e r t h e s e s e t s in t u r n .

( 0 , 1 , 0 , 1 ) i s u n te n a b le b ecause i t p e r m its an allow ed b e t a - r a y t r a n s i t i o n t o t h e s t a t e a t 1 .3 8 M.E.V., and in t h e same way we can r u l e o ut th e s e t s (0 ,2 ,1 ,2 ),

(0 ,2 ,2 ,1 ),

(0 ,1 ,1 ,0 ),

(0 ,1 ,1 ,2 ),

( 0 , 2 , 2 , 3 ) and ( 0 ,2 ,3 * 2 ) .

th e t h r e e s e t s ( 0 ,1 ,2 ,3 ) >

(0 ,1 ,2 ,1 ), T h is l e a v e s

( 0 , 2 , 1 , 0 ) and (0 ,2 ,3 * 4 ) o f which

t h e m iddle s e t i s a l s o u n te n a b le b ecause i t would p erm it a d ip o le /

92. d ip o le t r a n s i t i o n from t h e l e v e l a t 4 .1 4 M.E.V. to t h e ground s t a t e , which i s n o t o b se rv e d .

Hence from t h e ap p a re n t maze o f

p o s s i b l e s e t s o f s p in v a l u e s f o r t h e t h r e e unknown l e v e l s i n t h e decay scheme, a knowledge o f t h e m u ltip o le o r d e r o f one o f t h e gamma-rays and t h e assum ption o f th e o r d e r o f t h e o th e r ,

STATE

PARITY

SPIN

even

odd

even

even

F ig u re 29*

P o s s i b l e S e ts o f Spin V a lu e s.

e n a b le s u s to red u ce th e number o f p e r m is s ib le s e t s t o two. I f th e l a t t e r assum ption i s n o t made, and t h e 1 .3 8 M.E.V. l i n e i s allow ed to be o f e l e c t r i c o c tu p o le o r m agnetic quadru po le o r d e r , th e n a l l t h e p o s s i b l e c a s e s a r e c o n s id e r e d , s in c e h ig h e r m u lt ip o le s a r e r u l e d out by c o n s i d e r a t i o n s o f t h e l i f e ­ rtim e o f t h e s t a t e . o n ly /

T h is a d d i t i o n a l p o s s i b i l i t y , however,

only in tr o d u c e s one new s e t o f s p in v a l u e s , s in c e an a n a l y s i s o f t h e above ty p e shows t h a t in t h i s c a se t h e p a r i t i e s a re (even, odd, even, odd), and t h e allow ed s e t s o f sp in v a lu e s

SPIN SPIN maq. electric PARITY mag. electric dipole quad. quad. octupole

STATE

F ig u re 30*

even

odd

odd

even

even

odd

even

even

Allowed S e ts o f Spin and P a r i t y V alu e s.

a r e (0 ,2 ,3 > 4 ) and (0 ,3 > 4 j5 )*

The f o u r p o s s i b l e com plete

s p e c i f i c a t i o n s o f th e decay scheme a r e shown i n F ig u re 30.

IV.3»

F u tu re Yifork and p o s s i b l e E x te n s io n s o f t h e T echnique.

I t w i l l be c l e a r from th e above d is c u s s i o n , t h a t th e sim ple measurement o f t h e I .P .C .C . f o r one gamma-ray l i n e , when combined w ith t h e r e s u l t s o f o th e r e x p e rim en ts on th e same n u cleu s/

94 n u c le u s , can le a d to th e d ed u c tio n o f a s u r p r i s i n g l y l a r g e amount o f in f o rm a tio n c o n c ern in g th e s t a t i o n a r y s t a t e s o f t h a t n u c le u s .

I t i s u n f o r t u n a t e , t h e r e f o r e , t h a t th e c a se o f H a ^

i s unique i n t h a t i t I s b e t a r a d i o a c t i v e w ith a re a s o n a b ly lo n g h a l f - l i f e , has a sim ple spectrum , and e m its a h a rd gamma-ray. There a r e s e v e r a l more b e t a - e m i t t e r s among th e l i g h t elem ents which a l s o em it h ard gamma-rays, such as F

20

and A1

28

, but a l l

have v e r y s h o r t h a l f - l i v e s , and co u ld no t be i n v e s t i g a t e d away from t h e i r p la c e o f o r i g i n .

The method o f i n v e s t i g a t i o n would

th e n have t o be t o produce th e s e is o t o p e s by means o f a n u c l e a r r e a c t i o n u s in g th e p a r t i c l e a c c e l e r a t o r , and th e n t o i n t e r r u p t th e beam p e r i o d i c a l l y , and c o l l e c t d a t a on th e p o s i t r o n s and d i s i n t e g r a t i o n e le c tr o n s , d u rin g t h e s e b r e a k s i n t h e bombardment. A part from th e s e b e t a - e m i t t e r s , t h e r e a r e a ls o t h e r e a c t i o n s i n which a heavy p a r t i c l e i s e m itte d , such as F 1c (p,oO 0 , where t h e a l p h a - p a r t i c l e s co u ld be u t i l i s e d t o

iq

p ro v id e a measure o f t h e number o f t r a n s i t i o n s ta k in g p l a c e , and t h i s f i g u r e c o u ld th e n be compared w ith th e number o f p o s i t r o n s p roduced, t o d eterm in e th e I .P .C .C .

Here t h e

d i f f i c u l t y l i e s i n t h e v e r y s h o r t l i f e t i m e s o f t h e compound n u c l e i , which make i t n e c e s s a r y t o count t h e a l p h a - p a r t i c l e s a g a i n s t an i n t e n s e background o f s c a t t e r e d p r o to n s , b u t such ex p e rim en ts a r e p o s s i b l e and c o u ld be b e s t perform ed w ith a s p e c tr o m e te r c a p a b le o f f o c u s s in g th e a l p h a - p a r t i c l e s as w e ll a s th e p o s i t r o n s . cases/

I t i s c l e a r , however, t h a t t h e r e a r e many

95

c a s e s o f th e em ission o f e n e r g e t i c gamma-rays from l i g h t n u c l e i , where t h e r e i s no p a r t i c l e em ission a t a l l , such as th e v a r i o u s p ro to n and n e u tro n c a p tu r e r a d i a t i o n s *

F o r th e s e c a s e s

t h e o n ly means o f c o u n tin g th e number o f t r a n s i t i o n s o c c u rr in g i s to count th e gamma-rays e m itte d by t h e t a r g e t , u s in g a G.M. c o u n te r , and to compare t h i s f i g u r e w ith t h e number o f p o s i t r o n s observed i n t h e s p e c tr o m e te r .

T h is method i s by no means as

u n r e l i a b l e as might be im agined, because t h e v a r i a t i o n i n t h e e f f i c i e n c y o f G.M. c o u n te r s o f known c o n s t r u c t i o n w ith e n e rg y , has been s tu d i e d a t g r e a t le n g t h (Fow ler, L a u r its e n and la u ritse n , c o n f id e n c e .

1 9 4 8 ),

and co u ld be a p p lie d - w ith c o n s id e r a b le

The main so u rce o f d i f f i c u l t y would be th e

c a l c u l a t i o n o f t h e o v e r a l l e f f i c i e n c y o f t h e s p e c tr o m e te r . T h is , however, need no t be a tte m p te d , s in c e i t can be compared

accurately with that o f th e c o u n te r by means o f a c a l i b r a t i o n ex p e rim en t, u s in g a known b e t a - e m i t t e r such as Ha

O A



The

r e l a t i v e e f f i c i e n c i e s o f t h e s p e c tr o m e te r and t h e c o u n te r co u ld be measured a t low er e n e r g i e s , u s in g some o th e r r a d i o a c t i v e 0 s o u rc e , such as Co , and o n ly i n t h e e x t r a p o l a t i o n t o much h ig h e r e n e r g ie s would t h e p o s s i b i l i t y o f e r r o r a r i s e .

T h is ,

however, i s t h e re g io n where t h e t h e o r e t i c a l b e h a v io u r o f t h e c o u n te r i s b e s t known, and where a ls o th e e f f i c i e n c y o f th e s p e c tr o m e te r co uld be ex p e cte d t o rem ain c o n s t a n t , s in c e t h e two main s o u rc e s o f i n e f f i c i e n c y , window and so u rce t h i c k n e s s , would be n e g l i g i b l e ; w ith some c o n f id e n c e . It/

hence th e e x t r a p o l a t i o n co uld be made

I t i s proposed to i n v e s t i g a t e a l l t h e s e methods o f d e t e r ­ m in i n g th e I .P .C .C . of h ig h energy t r a n s i t i o n s i n t h e l i g h t e l e ­ m e n t s , and in d e e d th e sp e c tro m e te r has been p re p a re d f o r th e s e ex perim en ts and would have been used f o r t h i s purp ose some tim e ago had i t n o t been f o r t h e r e c e n t c o n c e n tr a t io n o f e f f o r t on energy d e te r m in a tio n s c a r r i e d out w ith t h e p a i r s p e c tr o m e te r . There i s however one fund am en tal d i f f i c u l t y which w i l l c e r t a i n l y l i m i t th e scope o f such ex p erim en ts as c a r r i e d ou t w ith th e p r e : s e n t s e m i - c i r c u l a r r e s o l v e r , and t h a t i s t h e weakness o f th e so u rc e s o f r a d i a t i o n a v a i l a b l e .

The so u rce s t r e n g t h used i n th e

sodium experim ent was 10 mC, w h ile even w ith t h e P " ^ ( p ,^ ) 0 " ^ r e : a c t i o n , which i s ex tre m ely v ig o r o u s , t h e y i e l d o f gamma-rays t h a t cou ld be ex p ected from th e a v a i l a b l e p ro to n beam would be o f th e o r d e r o f 1 mC a t t h e 660 K.E.V. re so n a n c e , and 340 K.E.Y. re so n a n c e ; le ss.

3

mC a t th e

f o r most r e a c t i o n s t h e y i e l d would be much

T h is i s a s e r i o u s d i f f i c u l t y when i t i s r e a l i s e d t h a t even

w ith th e s tr o n g sodium s o u rc e , th e c o u n tin g r a t e i n t h e p o s i t r o n spectrum was o n ly o f t h e o r d e r o f

50

c o u n ts p e r m inute, compared

w ith t h e u l t i m a t e c o u n te r background o f

1 .5

co u n ts p e r m in u te.

(The a c t u a l c o u n te r background was 19 c o u n ts p e r m inute, on a c :c o u n t o f th e le a k a g e o f gamma-rays th ro u g h t h e le a d s h i e l d i n g . ) I t i s c l e a r th e n , t h a t w h ile th e s tr o n g f l u o r i n e r a d i a t i o n s can p ro b ab ly be a n a ly se d s u c c e s s f u l l y w ith th e p r e s e n t s p e c tr o m e te r , any atte m p t t o s tu d y t h e r a d i a t i o n s from much weaker r e a c t i o n s would in v o lv e t h e u se o f a sp e c tro m e te r o f much g r e a t e r i n t e n s i t y f a c t o r . a lso /

S ince t h e in s tru m e n t would

97.

a l s o be r e q u i r e d t o f o c u s h ig h energy p a r t i c l e s , i t would seem t h a t t h e b e s t ty p e o f r e s o l v e r to u se would be some m o d if ic a tio n o f th e d o u b le -f o c u s s in g in s tr u m e n t, d esig n e d t o g iv e a l a r g e s o l i d a n g le w ith c o m p a ra tiv e ly low r e s o l u t i o n .

( i t w i l l be

remembered h e re t h a t th e d o u b le -f o c u s s in g in s tr u m e n ts con­ s t r u c t e d so f a r , have a l l been d esig n ed w ith h ig h r e s o l u t i o n as t h e i r f i r s t r e q u ir e m e n t.)

T h is problem has been d is c u s s e d

proton beam

target

!! ,.\ If ■

...

vacuum tank.

F ig u r e 31*

peto-pi«c«s to f v t M k tocaaniny.

S e m i-C irc u la r D oub le-F ocu ssin g Wedge S p e c tro m e te r.

a t l e n g t h by t h e a u th o r and Mr. J.G-. R u th e rg le n , who i s a ls o i n t e r e s t e d i n t h e c o n s t r u c t i o n o f such an in s tru m e n t as an alphap a r t i o l e s p e c tr o m e te r , and t h e d esig n most s u i t e d t o t h e problem and t o t h e e le c tro - m a g n e t a v a i l a b l e seems t o be a s e m i - c i r c u l a r d o u b le -f o c u s s in g "wedge” .

Such an in s tru m e n t which i s shown

s c h e m a tic a lly i n F ig u re 31, would have a s o l i d a n g le o n l y /

o n ly s l i g h t l y s m a lle r th a n a f u l l double f o c u s s in g r e s o l v e r , and would have t h e advantage t h a t w ith t h e g r e a t e r r a d i u s o f c u r v a tu r e a v a i l a b l e , p a r t i c l e s o f h ig h e r momentum co u ld be fo c u s s e d .

O ther p o i n t s in f a v o u r o f t h e "wedge” d esig n a r e

t h a t more space i s a v a i l a b l e f o r le a d s h i e l d i n g , and a ls o t h a t th e so u rc e and d e t e c t o r a r e o u ts i d e t h e m agnetic f i e l d which makes th e bombardment o f th e t a r g e t much e a s i e r , and which would a l s o p e rm it t h e u se o f an e l e c t r o n m u l t i p l i e r as d etecto r.

I t i s proposed t o p ro ceed w ith t h e d esig n and

c o n s t r u c t i o n o f such an in s tru m e n t o r in s tr u m e n ts which w i l l be used i n t h e stu d y o f problem s such as th o s e d is c u s s e d above. To sum up t h i s l a s t c h a p te r , we m ight say t h a t th e experim ent on U a ^ i l l u s t r a t e s t h e s i m p l i c i t y and power o f t h e method o f d e te rm in in g th e s p in s of n u c l e a r l e v e l s th r o u g h measurements made on t h e i n t e r n a l p a i r e f f e c t .

With t h i s

method a v a i l a b l e , and p o s s i b ly r e i n f o r c e d i n t h e f u t u r e by t h e c o n s t r u c t i o n o f a s p e c tr o m e te r o f much h ig h e r i n t e n s i t y f a c t o r , and w ith th e p a i r s p e c tro m e te r a v a i l a b l e f o r r a p i d su rv ey measurements o f whole gamma-ray s p e c t r a , i t seems p o s s i b l e to c l o s e th e c h a p te r and in d e ed t h i s t h e s i s in f u l l c o n fid e n c e t h a t i f th e work d e s c r ib e d i n th e s e pages i s c a r r i e d fo rw ard d i l i g e n t l y , th e n some r e a l p r o g r e s s w i l l have been made i n t h e stu d y o f t h e s t a t i o n a r y s t a t e s o f t h e l i g h t n u c l e i , and one more s te p w i l l have been ta k e n tow ards our f i n a l u n d e r s ta n d in g o f t h e s t r u c t u r e o f t h e atom ic n u c le u s .

i. A P P E N D I X

A MAGNETIC

SPECTROMETER

OF

I.

LARGE

SOLID

ANGLE.

by E. R. Rae, Department of N a tu ra l P h ilo so p h y , The

U n iv e r s it y

of

Glasgow.

(A p a p e r a c c e p te d f o r p u b l i c a t i o n by th e ^P h ilo so p h ical M agazine1) SUMMARY. An account i s g iv e n o f a m agnetic sp e c tro m e te r o f l a r g e s o l i d an g le and good r e s o l u t i o n which should f i n d a p p l i c a t i o n s i n th e s tu d y o f complex b e t a - r a y s p e c t r a by th e method o f beta-gamma c o in c id e n c e s . The o r i g i n a l a p p a r a tu s , c o n s i s t i n g o f a segmented a n n u la r G-.M. c o u n te r s e t round a r a d i o a c t i v e so u rce i n a m agnetic f i e l d i s d e s c r ib e d , t h e method of use b ein g to s e l e c t from th e o u tp u t of t h e c o u n te r , l a r g e p u ls e s which co rresp o n d to t h e sim u lta n e o u s t r i g g e r i n g o f s e v e r a l s e c t i o n s by th e p assag e o f an e l e c t r o n t a n g e n t i a l l y t o t h e a n n u la r c o u n te r .

The perform ance o f t h e

in s tru m e n t i s d is c u s s e d and m o d if ic a ti o n s a r e d e s c r ib e d which r e c t i f y th e d e f e c t s in th e e a r l i e r d esig n and g iv e a s o l i d an g le of 2.5% of

4 I?

w ith a r e s o l u t i o n o f 5%.

The geom etry o f t h i s ty p e o f s p e c tr o m e te r i s c o n s id e r e d and t h e p erform ance which might be o b ta in e d w ith good d e sig n i s d isc u sse d /

d is c u s s e d .

I t i s concluded t h a t c o l l e c t i n g a n g le s up t o th e

o r d e r o f 50?o o f 4" a r e p o s s i b l e w ith good r e s o l u t i o n .

1.

I INTRODUCTION. An account has r e c e n t l y been p u b lis h e d by Siegbahn and

S l a t i s (1949) o f an in s tru m e n t f o r th e d e te r m in a tio n of t h e e n e r g ie s o f b e t a and gamma r a d i a t i o n s .

The d e v ic e c o n s i s t s of

an arrangem ent f o r p la c in g th e so u rce of th e r a d i a t i o n s a t t h e c e n t r e o f an a n n u la r G.M. c o u n te r whose p la n e i s a t r i g h t a n g le s t o th e d i r e c t i o n o f t h e m agnetic f i e l d .

C o n sid e ra b le work has

been done h e re on an a p p a ra tu s which i s s u p e r f i c i a l l y v e r y s i m i l a r t o t h a t of th e above a u th o r s , b ut which i n f a c t has s e v e r a l ad­ v a n t a g e s over i t .

F or t h i s r e a s o n i t has been d ec id ed t o p la c e

on r e c o r d t h i s s h o r t account of our method which co n firm s some of th e r e s u l t s o f Siegbahn and S l a t i s and which a ls o l e a d s to th e d esig n o f a m agnetic sp e c tro m e te r of v e r y l a r g e s o l i d a n g le which sh ould prove a v a l u a b le t o o l i n t h e exam ination o f complex b e t a r a y s p e c t r a by th e method o f beta-gamma c o in c id e n c e s .

2.

DESCRIPTION

OF

ORIGINAL

APPARATUS.

The d ev ice as o r i g i n a l l y d esig n ed by Dr. S.C. Curran c o n s i s t e d o f an a n n u la r c o u n te r w ith t h e w ire su p p o rte d on a l a r g e number (about 40) o f sm all i n s u l a t i n g p i l l a r s which had t h e e f f e c t o f s p l i t t i n g t h e main c o u n te r i n t o a l a r g e number o f sm all c o u n te r s a c tin g in p a r a l l e l (Stever, 1942; 1947)

./

Curran and Rae,

iii.

1 947).

A s k e tc h o f th e a p p a ra tu s i s given i n F ig u re 1 and i t

w i l l be seen t h a t th e c o u n te r had no window, th e whole a p p a ra tu s being f i l l e d w ith th e c o u n tin g m ix tu re .

The i n t e n t i o n was to use

th e d ev ice t o measure t h e energy of hard gamma-rays by d e t e c t i n g th e p o s i t r o n - e l e c t r o n p a i r s e j e c t e d from a t h i n le a d f o i l p la c e d round t h e so u rc e , f o r in th e ca se o f e c u y p a r t i t i o n o f energy, and

23616065332662138240^^^00^53

f I I

taodC:

/

aourcc

1

0

2

F ig u re 1.

4



8

to cm.

To Filling System.

Schem atic Diagram of O r i g in a l A pp aratus.

and f o r t h e c o r r e c t v a lu e o f t h e m agnetic f i e l d , b o th p o s i t r o n and e l e c t r o n cou ld t r i g g e r f o u r o r f i v e s e c t i o n s of t h e co u rlter, t h u s g iv in g a p u ls e e ig h t t o t e n tim e s as l a r g e as th e background s i n g l e s e c t i o n p u ls e s . U n f o r tu n a te ly /

U n fo r tu n a te ly t h i s sim ple and e le g a n t arrangem ent d id not y i e l d th e ex p ected r e s u l t s , f o r two main r e a s o n s :

firs tly

b ecause th e background was found i n f a c t to c o n ta in a l a r g e number o f double and m u lt ip le p u ls e s owing to bad geom etry which made i t h ig h ly p ro b a b le t h a t a p a r t i c l e e n t e r i n g one s e c t i o n o f th e c o u n te r would be s c a t t e r e d i n t o a t l e a s t one more.

T h is meant

t h a t t h e r e was a c o n s id e r a b le number o f f o u r and f i v e - f o l d p u ls e s when a s tr o n g gamma-ray so urce was b eing u se d , and so t h e number o f a c c i d e n t a l c o in c id e n c e s between t h e s e , g iv in g e i g h t to t e n ­ f o l d p u ls e s was n o t n e g l i g i b l e .

The second d i f f i c u l t y was t h a t

because t h e c o u n te r s e c t i o n s were so s h o r t r e l a t i v e to t h e i r le n g th

th e y had v e r y s e r i o u s end e f f e c t s which caused them t o

have o n ly a v e r y s h o r t p l a t e a u .

!

T h is meant t h a t even on t h e

p l a t e a u th e p u ls e s i z e was a s te e p f u n c tio n o f t h e h ig h t e n s io n v o l t a g e , and so i t was d i f f i c u l t to g e t s t a b l e working and r e p r o d u c ib le r e s u l t s , s in c e th e method depended on s e l e c t i n g p u l s e s o f p a r t i c u l a r s i z e w ith a d i s c r i m i n a t o r .

These same two

\

d i f f i c u l t i e s a ls o p re v e n te d t h e d e v ice from b ein g used s a t i s f a c t o r i l y i n a s i m i l a r manner to d eterm in e o r d in a r y b e t a r a y and secondary e l e c t r o n s p e c t r a .

I t was a t t h i s p o in t t h a t

| I

th e method o f removing t h e d i s c r i m i n a t o r and c o u n tin g a l l t h e

j

p u ls e s o f a l l s i z e s was t r i e d , s in c e though i t does n o t g iv e t h e

I |

spectrum o f t h e so urce d i r e c t l y , i t does overcome t h e d i f f i c u l t i e s

j

m entioned above.

T h is i s o f c o u rse t h e same method as t h a t used

!j

1

by Siegbahn and S l a t i s , and though i t was n o t s tu d i e d h e re in d e ta il/

i

d e ta il,

th e r e s u l t s o b ta in e d were v e ry s i m i l a r t o th o s e

p u b lis h e d by them.

F o r comparison t h e c u rv es o b ta in e d from th e

secondary e l e c t r o n s e j e c t e d from a t h i c k le a d f o i l by th e gammaa r e shown i n F ig u re 2.

From th e s e r e s u l t s and a number o f o t h e r s , an

e m p iric a l c a l i b r a t i o n curve was c o n s tr u c te d f o r t h e d ev ice as used, i n t h i s way.

2 4 6 8 IO Magnet Current in Amperes.

F ig u re 2. I n t e g r a l Momentum S p e c tra o f Secondary E l e c t r o n s from t h e G-amma-Ra.ys of Co^O and th e A n n ih ila tio n R a d ia tio n from Cu^4-7 T h is method i s however s u b je c t to s e v e r a l s e r i o u s d i s ­ a d v a n ta g e s.

F i r s t l y , even when one has o b ta in e d th e e x p e rim en ta l

i n t e g r a l spectrum t h e r e i s no e x p l i c i t way o f o b ta in in g th e t r u e sp e c tru m /

spectrum o f t h e so u rce because o f t h e f a c t t h a t f o r any s e t t i n g o f t h e m agnetic f i e l d th e s o l i d an g le o f t h e d ev ice i s a f u n c tio n of t h e energy of th e p a r t i c l e s d e t e c t e d .

Thus when

used in t h i s way, th e d ev ice i s on ly s u i t a b l e f o r d e te rm in in g end­ p o i n t s , u n le s s one i s p re p a re d to c a r r y out lo n g and te d io u s s u c c e s s iv e a p p ro x im a tio n s.

Secondly, because of t h e h ig h back­

ground i n th e c o u n te r , p h o to - e le c tr o n l i n e s and any o th e r k in d of f i n e s t r u c t u r e a r e q u i t e i n v i s i b l e , and t h i c k c o n v e r to r s must be used f o r t h e d e te r m in a tio n of gamma-ray e n e r g ie s which makes th e r e s o l u t i o n o f th e d e v ice p o o r. t h a t in th e c u rv e s f o r Co

F o r i n s t a n c e i t w i l l be n o ted

g iv en by Siegbahn and Sl§Ltis and

th e p r e s e n t a u th o r, i n n e i t h e r c a se was i t p o s s i b l e to r e s o l v e th e low er energy l i n e a t 1 .1 M.E.Y. from t h a t a t 1 .3 M.E.V. T h ir d ly , as s t r e s s e d by Siegbahn and S l& tis , th e e f f e c t of s c a t t e r i n g i n th e gas i s such as to produce cou nts a t v a l u e s o f t h e m agnetic f i e l d much h ig h e r th a n t h a t c o rre sp o n d in g to th e t r u e e n d -p o in t of th e spectrum b e in g examined, and t h i s ca u ses d i f f i c u l t i e s i n th e i n t e r p r e t a t i o n o f t h e c u rv e s .

In a d d i tio n

t o th e s e c r i t i c i s m s i t should be m entioned t h a t s in c e one of t h e obvious u s e s f o r a l a r g e s o l i d a n g le sp e c tro m e te r o f t h i s s o r t would be th e s e p a r a tio n o f complex b e t a - r a y s p e c t r a by th e method o f beta-gamma c o in c id e n c e s , i t would be a g r e a t advantage i f t h e d e v ic e co uld be made to g iv e t h e t r u e spectrum i n s t e a d of

an i n t e g r a l one, s in c e th e form er would re d u c e th e background o f |j a c c i d e n t a l c o in c id e n c e s by a v e ry l a r g e f a c t o r n e a r th e endp o in t/

!

v ii.

e n d - p o in t, t h a t i s in th e r e g io n o f th e g r e a t e s t i n t e r e s t .

F or

t h e s e re a s o n s i t was d ecid ed t h a t i t was w orth w hile to a tte m p t to overcome th e d i f f i c u l t i e s in th e o r i g i n a l d esig n in a d i f f e r e n t wav.

3.

THE

IMPROVED

APPARATUS.

A s k e tc h of t h e improved a p p a ra tu s i s shown in F ig u re 3 and i t w i l l be seen t h a t th e number of s e c t i o n s i n t o which th e c o u n te r was d iv id e d has been red u ced , th u s g iv in g lo n g e r

counter anode

• source

baffles.

F ig u re 3.

polythene. partitions.

S ketch of Improved A p paratu s.

s e c t i o n s and v e ry much improved e l e c t r i c a l perform ance.

I t w ill

a l s o be n o ted t h a t th e s e c t i o n s a r e s e p a r a te d by p o ly th e n e p a r t i t i o n s i n s t e a d o f t h e p i l l a r s o f th e o r i g i n a l d e s ig n , and th a t/

v iii.

t h a t t h e s e p a r t i t i o n s have openings in them j u s t l a r g e enough t o p erm it th e p assag e o f e l e c t r o n s w ith in th e d e s ir e d momentum ra n g e .

T h is has th e e f f e c t o f c u t t i n g down t o a v e ry l a r g e

e x te n t th e number of p a r t i c l e s which a r e a c c i d e n t a l l y s c a t t e r e d i n t o more th an one s e c t i o n .

F i n a l l y th e d e v ic e has been f i t t e d

w ith a s e t o f b a f f l e s which p erm it only p a r t i c l e s o f th e c o r r e c t s ig n of charge and th e c o r r e c t momentum ran g e t o e n t e r t h e c o u n tin g system , and which t o g e t h e r w ith t h e p a r t i t i o n s e n s u re s t h a t on ly th o s e p a r t i c l e s a r e d e t e c t e d which have n o t been s e r i o u s l y s c a t t e r e d in th e g a s . With t h e s e improvements i t was found p o s s i b l e to t a k e s p e c t r a w ith th e d i s c r i m i n a t o r s e t to count s i n g l e , d o ub le, o r t r i p l e s e c t i o n p u ls e s w ith good r e p r o d u c i b i l i t y .

The s i n g l e

s e c t i o n s p e c t r a c o n ta in e d a l a r g e number o f s p u r io u s c o u n ts a t low e n e r g ie s b ecau se o f s c a t t e r i n g , b u t th e s p e c t r a o b ta in e d from th e double and t r i p l e s e c t i o n p u ls e s were v e r y s i m i l a r . The spectrum of RaE as o b ta in e d from an o ld t h i n w a lle d Radon seed w i t h . t r i p l e s e c t i o n p u ls e s i s shown i n F ig u re 4 and i t w i l l be o bserved t h a t th e shape i s good a p a r t from a d isp la c e m e n t o f th e number maximum tow/ards h ig h e r e n e r g ie s b ecau se o f th e s c a t t e r i n g of th e s o f t e r b e t a - r a y s i n th e gas f i l l i n g .

The

f i l l i n g f o r t h i s run v/as 3 cm. Argon f 1 cm, A lcohol, t h e working v o l t a g e about 1100 V. and th e e s tim a te d r e s o l u t i o n ( f o r t r i p l e s ) o f th e o r d e r o f 5$. These m o d if ic a ti o n s t o C u rra n ’ s o r i g i n a l a p p a ra tu s th u s p ro d u c e d /

p r o d u c e d a 3 6 0 ° s p e c t r o m e t e r w i t h a r e s o l u t i o n o f a b o u t 5% and a s o l i d a n g l e o f 2 . 5°/° o f 4-Tl a s compared w i t h 1 $ o f 4-ii" f o r a corresponding s e m i-c irc u la r fo cu ssin g sp ectro m eter.

I t can

howre v e r e a s i l y be shown t h a t by a l t e r i n g t h e t y p e o f c o u n t i n g s y s te m and so o b t a i n i n g a much w i d e r s l i t ,

an i n s t r u m e n t can

be b u i l t w h ic h w i l l g i v e a s o l i d a n g l e o f 20 / geom etrical r e s o lu tio n ,

0

1

2

and f u r t h e r ,

3

4

o f 4 M w i t h a 5/

th a t i f th e a p e rtu re s in

5

6

7

in Kilo-Gauss.centimetres.

Figure 4 .

The B e t a - R a y Spe c trum o f an o l d Radon S eed .

t h e p a r t i t i o n s b e tw e e n t h e c o u n t e r s and t h e c o r r e s p o n d i n g b a f f l e s y s t e m s a r e s p e c i a l l y s h a p e d , t h e n s o l i d a n g l e s up t o t h e o r d e r o f 50 / o f 4-ff m i g h t be o b t a i n e d w i t h 5 / r e s o l u t i o n . The d e s i g n c o n s i d e r a t i o n s f o r s u c h an i n s t r u m e n t b o t h i n t h e restric te d /

r e s t r i c t e d and g e n e r a l form a r e d i s c u s s e d i n t h e n e x t section.

4- DESIGN CONSIDERATIONS FOR VERY LARGE SOLID ANGLE SPECTROMETER I f we c o n s i d e r t h e d i a g r a m i n F i g u r e 5 ( a ) w h ic h shows a s e c t i o n o f t h e s p e c t r o m e t e r by t h e m edian p l a n e ,

then th e c i r c l e

Y

M

(a)

(b)

F i g u r e 5» Geom etry o f 560° S p e c t r o m e t e r . ( a ) S e c t i o n by Median P l a n e . ( b ) S e c t i o n by P l a n e C o n t a i n i n g t h e Axis o f Sym m etry~ AB r e p r e s e n t s t h e i n n e r edge o f t h e c o u n t i n g a r e a w h ic h h a s r a d i u s 2R.

OLM r e p r e s e n t s t h e p a t h o f a p a r t i c l e ,

r a d i u s r , wher

r i s j u s t g r e a t enough t o e n s u r e t h a t i t i n t e r s e c t s n c o u n t e r sectio n s./

x i.

se c tio n s,

Now i t

can e a s i l y be shown t h a t i f

i s th e angle

subtended a t 0 by a s i n g l e s e c t i o n , t h e n : r /R

=

sec(n-l«