UBC Theses and Dissertations

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UBC Theses and Dissertations

The annihilation of positrons in pure elements and chemical compounds Griffiths, George Motley 1950

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THE ANNIHILATION OF POSITRONS I N PURE ELEMENTS AND CHEMICAL COMPOUNDS by G e o r g e M o t l e y G r i f f i t h s us \hj A T h e s i s S u b m i t t e d i n P a r t i a l F u l f i l m e n t o f t h e R e q u i r e m e n t s f o r t h e D e g r e e o f MASTER OF ARTS i n t h e D e p a r t m e n t o f / PHYSICS THE UNIVERSITY OF B R I T I S H COLUMBIA O c t o b e r , 1950 T H E U N I V E R S I T Y O F BRITISH C O L U M B I A VANCOUVER, CANADA D E P A R T M E N T O F P H Y S I C S October 12, 1950. Dr. L. W. Dunlap, L i b r a r i a n , U n i v e r s i t y o f B r i t i s h Columbia. Dear Dr. Dunlap: T h i s l e t t e r w i l l c e r t i f y t h a t the t h e s i s of Mr. George M . G r i f f i t h s has been c a r e f u l l y s t u d i e d by the under-signed and t h a t the t h e s i s meets the r e q u i r e d standards, and an a b s t r a c t has been approved by t h e Department. Yours s i n c e r e l y , G. M. Shrum Head of t he Department GMS:1c j.* B. Warren A s s o c i a t e P r o f e s s o r of P h y s i c s THE:ANNIHILATION. OF POSITRONS IN PORE ELEMENTS AND CHEMICAL GQMPQDHBS by George M o t l e y G r i f f i t h s ABSTRACT The angular c o r r e l a t i o n between a n n i h i l a t i o n quanta due t o t h e decay o f p o s i t r o n s i n eleven d i f f e r e n t m a t e r i a l s has been measured w i t h anthracene s c i n t i l l a t i o n c o u n t e r s , ^.he m a t e r i a l s s t u d i e d were, the pure elements, Mg, S, Cu, Sn, P t , and Hg, and the chemical compounds L i C l , KC1, C s C l , KF, and EI. C a l c u l a t i o n s were performed to determine the e f f e c t o f the geometry on the shape o f the angular c o r r e l a t i o n c urves. The e f f e c t s o f s c a t t e r i n g were a l s o i n v e s t i g a t e d . 'J-'he appara-tus was t e s t e d by means o f measurements on the ^ - r a y s o f Co^® and Z n 6 5 . The c e n t r e o f mass momentum d i s t r i b u t i o n s of a n n i h i -l a t i n g p a i r s i n copper, p l a t i n u m and p o s s i b l y mercury were found to be e x p o n e n t i a l i n c h a r a c t e r and the mean centre o f mass momentum o b t a i n e d f o r copper was found to be i n reasonable agreement w i t h the r e s u l t s o b t a i n e d by DeBenedetti and co-workers and by P. E . A r g y l e . ^he momentum d i s t r i b u t i o n s f o r the o t h e r m a t e r i a l s were not found to be o f a simple exponen-t i a l form, 'i'he r e s u l t s suggest t h a t t h e r e i s a r e l a t i o n b e t -ween the shape o f the d i s t r i b u t i o n curve and the o u t e r e l e c t r o n i c s t r u c t u r e o f an atom. THE A N NIHILATION OF POSITRONS I N PURE ELEMENTS AND  CHEMICAL COMPOUNDS A b s t r a c t The a n g u l a r c o r r e l a t i o n b e t w e e n a n n i h i l a t i o n q u a n t a due t o t h e d e c a y o f p o s i t r o n s i n e l e v e n d i f f e r e n t m a t e r i a l s h a s b e e n m e a s u r e d w i t h a n t h r a c e n e s c i n t i l l a t i o n c o u n t e r s . The m a t e r i a l s s t u d i e d w e r e , t h e p u r e e l e m e n t s , Mg, S, Cu, S n , P t , a n d Hg, a n d t h e c h e m i c a l compounds L i C l , K C l , C s C l , KF, a n d K I . C a l c u l a t i o n s were p e r f o r m e d t o d e t e r m i n e t h e e f f e c t o f t h e g e o m e t r y o n t h e s h a p e o f t h e a n g u l a r c o r r e l a t i o n c u r v e s . The e f f e c t s o f s c a t t e r i n g w e r e a l s o i n v e s t i g a t e d . The a p p a r a t u s was t e s t e d by means, o f m e a s u r e m e n t s o n t h e Y - r a y s o f C o 6 0 a n d Z n 6 5 . The c e n t r e o f mass momentum d i s t r i b u t i o n s o f a n n i h i l a t i n g p a i r s i n c o p p e r , p l a t i n u m a n d p o s s i b l y m e r c u r y w e r e f o u n d t o be e x p o n e n t i a l i n c h a r a c t e r a n d t h e mean c e n t r e o f mass momentum o b t a i n e d f o r c o p p e r was f o u n d t o be I n r e a s o n a b l e a g r e e m e n t w i t h t h e r e s u l t s o b t a i n e d by D e B e n e d e t t i a n d c o - w o r k e r s a n d by P.E. A r g y l e . The momentum d i s t r i b u t i o n s f o r t h e o t h e r m a t e r i a l s w e r e n o t f o u n d t o be o f a s i m p l e e x p o n e n t i a l f o r m . The r e s u l t s s u g g e s t t h a t t h e r e i s a r e l a t i o n b e t w e e n t h e s h a p e o f t h e d i s t r i b u t i o n c u r v e a n d t h e o u t e r e l e c t r o n i c s t r u c t u r e o f a n a t o m . The m e a s u r e m e n t s o n t h e two a l k a l i h a l i d e s e r i e s c o n f i r m , a l t h o u g h w i t h p o o r s t a t i s t i c a l a c c u r a c y , t h e s u g g e s t i o n made by D e B e n e d e t t i a n d c o - w o r k e r s t h a t t h e p o s i t r o n s a n n i h i l a t e o n l y a g a i n s t t h e o u t e r s h e l l e l e c t r o n s o f t h e ' n e g a t i v e l y c h a r g e d h a l o g e n i o n s . The r e s u l t s i n d i c a t e t h a t t h e r e may be a m o n o t o n i c d e c r e a s e o f s l o p e o f t h e o u t e r p o r t i o n s o f t h e d i s t r i b u t i o n c u r v e s w i t h i n c r e a s i n g a t o m i c number. No e v i d e n c e was f o u n d f o r t h e p e r i o d i c c h a n g e w i t h a t o m i c number w h i c h m i g h t be e x p e c t e d . F u r t h e r w ork i s n e c e s s a r y t o c o n f i r m t h i s . ACKNOWLEDGEMENTS The e x p e r i m e n t t o be d e s c r i b e d was a c o n t i n u a t i o n o f w o r k c a r r i e d o u t i n t h i s l a b o r a t o r y on t h e d e c a y o f p o s i t r o n s i n c o p p e r by P.E. A r g y l e . The a u t h o r w i s h e s t o t h a n k Mr. A r g y l e f o r many h e l p f u l s u g g e s t i o n s . T h a n k s a r e e x t e n d e d t o D r . J . B . W a r r e n f o r s u g g e s t i n g t h i s r e s e a r c h a n d f o r h e l p a n d a d v i c e i n p e r f o r m i n g i t . The a u t h o r w i s h e s t o t h a n k t h e N a t i o n a l R e s e a r c h C o u n c i l f o r a summer s c h o l a r s h i p a n d t h e D e f e n c e R e s e a r c h B o a r d f o r t h e p r i v i l e g e o f w o r k i n g i n t h e N u c l e a r P h y s i c s T e c h n i q u e s L a b o r a t o r y a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . A c k n o w l e d g e m e n t i s made t o t h e f o l l o w i n g o f my c o -w o r k e r s who h e l p e d t a k e t h e f i n a l r e a d i n g s : D. A a r o n s o n , S. A r g y l e , A. Edmunds, K. Erdman, F. F l a c k , J . K i r k a l d y , B. M a c k a y , G. P h i l l i p s a n d L. S i l v e r . A s p e c i a l n o t e o f t h a n k s i s due t o my w i f e who h e l p e d w i t h t h e t e d i o u s c a l c u -l a t i o n s a n d w i t h many o t h e r a s p e c t s o f t h e e x p e r i m e n t . I a l s o w i s h t o t h a n k t h e A l u m i n u m Company o f C a n a d a f o r s u p p l y i n g v e r y p u r e a l u m i n u m i n w h i c h t o i r r a d i a t e C o ^ s a m p l e s i n t h e p i l e a t C h a l k R i v e r . INDEX I I n t r o d u c t i o n P a g e ( a ) A n n i h i l a t i o n o f P o s i t r o n s 1 (b) A n g u l a r C o r r e l a t i o n o f A n n i h i l a t i o n R a d i a t i o n 2 ( c ) M e a s u r e m e n t s o f t h e C e n t r e o f Mass Momentum o f A n n i h i l a t i n g P a i r s 4 (d) The P u r p o s e o f t h i s E x p e r i m e n t 9 I I S o u r c e s ( a ) P o s i t r o n S o u r c e 10 (b) A n n i h i l a t i o n R a d i a t i o n S o u r c e s - 14 I I I G e o m e t r y ( a ) G e n e r a l 18 ( b ) S o u r c e t o C o u n t e r D i s t a n c e 18 ( c ) A n g u l a r D i s t r i b u t i o n C u r v e s - 20 (d) E f f e c t o f G e o m e t r y on t h e , D i s t r i b u t i o n C u r v e s 23 I V S c i n t i l l a t i o n C o u n t e r s a n d A s s o c i a t e d C i r c u i t s ( a ) G e n e r a l 31 ( b ) S c i n t i l l a t i o n c o u n t e r s 34 ( c ) A m p l i f i e r s 38 (d) C o i n c i d e n c e M i x e r . 40 ( e ) C o u n t e r E f f i c i e n c i e s f o r 1 Mev. Y-Rays 46 ( f ) Zn ° 5 A n n i h i l a t i o n R a d i a t i o n 52 V A n g u l a r C o r r e l a t i o n E x p e r i m e n t s ( a ) C o u n t i n g P r o c e d u r e 55 ( b ) H e a l t h P r e c a u t i o n s 56 ( c ) S c a t t e r i n g C h e c k s 57 V I E x p e r i m e n t a l R e s u l t s ( a ) G e n e r a l 60 ( b ) P u r e E l e m e n t s 64 ( c ) A l k a l i M e t a l H a l o g e n s 6 5 . ( d ) C o n c l u s i o n s 67 ( e ) D i s c u s s i o n 69 A p p e n d i x I A b s o r p t i o n o f 0.51 Mev. Y-Rays 73 A p p e n d i x I I E v i d e n c e f o r t h e N u c l e a r Y-Ray f r o m C u 5 4 77 A p p e n d i x I I I T r i p l e P u l s e G e n e r a t o r 79 B i b l i o g r a p h y 83 1 THE ANNIHILATION OF POSITRONS I N PURE ELEMENTS , AND CHEMICAL COMPOUNDS I , INTRODUCTION a ) A n n i h i l a t i o n o f P o s i t r o n s Two w e l l known c o n s e q u e n c e s . o f t h e D i r a c h o l e t h e o r y o f t h e p o s i t r o n a r e p a i r p r o d u c t i o n a n d p a i r . a n n i h i l a t i o n . I n t h e f o r m e r p r o c e s s , a n e l e c t r o n a n d a p o s i t r o n s i m u l t a n e o u s l y a p p e a r when a t l e a s t 2 m c 2 o f e n e r g y i s a v a i l a b l e a n d c o n d i t i o n s a r e s a t i s f a c t o r y f o r e n e r g y a n d momentum c o n s e r v a t i o n . T h i s c a n h a p p e n i n s e v e r a l w a y s , t h e one w i t h t h e l a r g e s t c r o s s -s e c t i o n b e i n g p a i r p r o d u c t i o n by a Y - r a y i n t h e f i e l d o f a n u c l e u s . The p o s i t r o n i s s i m i l a r t o t h e e l e c t r o n e x c e p t f o r i t s p o s i t i v e c h a r g e a n d i t s . p r o p e r t y o f a n n i h i l a t i n g w i t h a n e l e c t r o n t o p r o d u c e two Y - r a y s . T h i s l a t t e r p r o p e r t y i s . b e s t v i s u a l i z e d i n t e r m s o f t h e D i r a c h o l e t h e o r y i n w h i c h t h e p o s i t r o n i s c o n s i d e r e d t o be a v a c a n c y o r h o l e i n a c o n t i n u u m o f u n o b s e r v a b l e e l e c t r o n s w h i c h a r e i n n e g a t i v e e n e r g y s t a t e s . P a i r a n n i h i l a t i o n o c c u r s when a n o r d i n a r y e l e c t r o n becomes " i n v i s i b l e " b y f a l l i n g . i n t o a h o l e ( p o s i t r o n ) i n t h e c o n t i n u u m . T h i s , o f c o u r s e , a l s o d e s t r o y s t h e e x i s t e n c e o f t h e h o l e o r p o s i t r o n . Dirac-'- h a s shown t h a t t h e t o t a l c r o s s - s e c t i o n f o r a n n i h i l a t i o n o f a p o s i t r o n o f e n e r g y E + w i t h a h e l e c t r o n a t r e s t i s g i v e n b y 1- P,A . M . D i r a c P r o c . Camb. P h i l . S o c , 26, 361 (1930). - 2 -0 = 7 t r 2 < Y 2 + 4T * 1 l o g [ Y + J Y 2 - 1 Y + 1 I Y2 - 1 L where r a n d Y = E + mc^ T h i s h a s a maximum f o r Y = 1; a t t h i s e n e r g y t h e h a l f l i f e o f p o s i t r o n s i n . m a t e r i a l , w i t h a t o m i c number Z i s g i v e n b y w h ere N = t h e number o f atoms p e r c . c . c = t h e v e l o c i t y o f l i g h t . p H e i t l e r h a s shown t h a t due t o t h e r a p i d s l o w i n g down o f p o s i t r o n s a l l b u t a f e w p e r c e n t o f t h e p o s i t r o n s r e a c h t h e e n d o f t h e i r p a t h o f i o n i z a t i o n b e f o r e a n n i h i l a t i o n . A f t e r b e i n g b r o u g h t t o r e s t , t h e p o s i t r o n s w i l l a n n i h i l a t e w i t h t h e r e l a t i v e l y l o w e n e r g y e l e c t r o n s , i n m a t t e r p r o d u c i n g two a n n i h i l a t i o n quanta.. To c o n s e r v e e n e r g y and., momentum i n t h i s p r o c e s s i t i s e a s i l y s e e n t h a t t h e two- q u a n t a . m u s t come o f f v e r y n e a r l y i n o p p o s i t e d i r e c t i o n s w i t h a n e n e r g y o f a b o u t m c 2 e a c h . T h i s i s d i s c u s s e d q u a n t i t a t i v e l y i n . t h e n e x t s e c t i o n . b) A n g u l a r C o r r e l a t i o n o f A n n i h i l a t i o n R a d i a t i o n L e t an. e l e c t r o n w i t h v e l o c i t y v a n d momentum p a n n i h i l a t e w i t h a p o s i t r o n a t r e s t . We assume t h a t t h e e l e c t r o n e n e r g y i s s m a l l , i n . w h i c h c a s e b o t h q u a n t a w i l l . h a v e a p p r o x i m a t e l y t h e same e n e r g y a n d w e " c a n w r i t e t h e momentum o f e a c h q u a n t a a s 2- W. H e i t l e r , The Quantum T h e o r y o f R a d i a t i o n , O x f o r d , 1 9 4 4 p . 2 3 1 . L l NZTtr-^c - 3 -h~0/c'i L e t t h e a n g l e b e t w e e n t h e d i r e c t i o n o f e a c h quantum a n d t h e / h u c p v e c t o r be 9; t h e s e , a n g l e s must be e q u a l i n o r d e r t o c o n s e r v e momentum i n t h e d i r e c t i o n p e r p e n d i c u l a r , t o p, • - e s i n c e we h a v e a s s u m e d t h a t b o t h q u a n t a h a v e t h e same energy.. L e t the. d e p a r t u r e f r o m . c o l l i n e a r i t y o f t h e two quanta, be X = 20 w h e r e 0 \ ^cT i s t h e complement o f ©. T h e n t h e c o n s e r v a t i o n o f e n e r g y g i v e s F i g u r e 1 2h"0= m c 2 (1 + 1 ) . i where . p =. v / c a n d c o n s e r v a t i o n . o f momentum g i v e s p = 2 I r p Cos© = 2 h\) sin0 2 c c E l i m i n a t i n g hO we g e t - a n e x p r e s s i o n f o r 0 sln0 - ^ 3 1 + _ i _ J 1 -I f p i s s m a l l ( t h a t i s p i s s m a l l ) we g e t t h e f o l l o w i n g e x p r e s s i o n f o r t h e n o n - c o l l i n e a r i t y X = 20 4 0 = p/mc 4 c ) M e a s u r e m e n t s o f t h e C e n t r e o f Mass Momentum o f A n n i h i l a t i n g  P a i r s . E q u a t i o n 4 a b o v e shows t h a t a m easurement o f t h e l a c k o f c o l l i n e a r i t y o f t h e a n n i h i l a t i o n q u a n t a g i v e s i n f o r m a t i o n a b o u t t h e c e n t r e o f mass momentum o f a n n i h i l a t i n g p a i r s . . F r o m t h e a n g u l a r c o r r e l a t i o n c u r v e i t i s - p o s s i b l e t o g e t t h e momentum d i s t r i b u t i o n o f t h e e l e c t r o n s w h i c h t a k e p a r t i n a n n i h i l a t i o n s . w i t h p o s i t r o n s , . E q u a t i o n , 1 i n d i c a t e s a n o t h e r m e t h o d o f g e t t i n g . , i n f o r m a t i o n a b o u t .the momentum.of a n a n n i h i l a t i n g p a i r . . N o t e t h a t i f . p = 0 t h e n hS5= mc 2, b u t i f p > 0 , t h e n fro > m c 2 . A more t h o r o u g h a n a l y s i s . w i t h o u t . t h e a s s u m p t i o n t h a t t h e two q u a n t a . h a d e q u a l e n e r g y g i v e s t h e r e s u l t t h a t one quantum t a k e s away c o n s i d e r a b l y more e n e r g y t h a n mc a n d t h e o t h e r one somewhat, l e s s t h a n mc'1. C o n s e q u e n t l y ,a m e a s u r e o f t h e e n e r g y s p e c t r u m , o f t h e a n n i h i l a t i o n , r a d i a t i o n g i v e s i n f o r m a t i o n a b o u t t h e c e n t r e o f mass momentum o f a n n i h i l a t i n g p a i r s . B o t h o f t h e s e m e t h o d s f o r f i n d i n g t h e momentum o f a n n i h i l a t i n g p a i r s h a v e b e e n s t u d i e d b y s e v e r a l a u t h o r s . Du Mond, L i n d a n d Watson-^ made a n a c c u r a t e s t u d y o f t h e w a v e l e n g t h s p e c t r u m o f a n n i h i l a t i o n r a d i a t i o n f r o m G u ^ 4 p o s i t r o n s a n n i h i l a t i n g i n c o p p e r u s i n g a c u r v e d c r y s t a l , f o c u s s i n g Y - r a y s p e c t r o m e t e r . The. m a i n .p u r p o s e ..of . t h e i r w o r k was t o g e t a n a c c u r a t e v a l u e o f t h e w a v e l e n g t h o f t h e a n n i h i l a t i o n r a d i a t i o n i n o r d e r t o g e t more a c c u r a t e v a l u e s o f f u n d a m e n t a l p h y s i c a l c o n s t a n t s . ; b u t t h e a u t h o r s w e re a l s o a b l e t o a n a l y s e t h e s h a p e o f t h e c u r v e a n d show t h a t t h e 3 - Du Mond, L i n d . a n d W a t s o n , P h y s . Rev., 7 5 , 1226 (1949) - 5 -w i d t h vras g r e a t e r t h a n c o u l d be a c c o u n t e d f o r b y g e o m e t r y . A s s u m i n g t h a t t h e e x t r a w i d t h o f t h e l i n e was d u e . t o a D o p p l e r e f f e c t o f t h e m o t i o n s o f c o m b i n i n g p a i r s . , a n d a s s u m i n g t h a t t h e p o s i t r o n s w e r e a t r e s t , t h e y c a l c u l a t e d t h e mean e n e r g y o f t h e a n n i h i l a t i n g e l e c t r o n s . i n c o p p e r t o be E c u = 16 e . v . o r p c u = 8 x 10"^ mc The c o n d u c t i o n e l e c t r o n s i n c o p p e r a r e t h e o n l y ones w i t h 4 w h i c h s u c h a l o w o r d e r o f s p e e d c a n .be a s s o c i a t e d . S e i t z has c a l c u l a t e d t h a t t h e f a s t e s t c o n d u c t i o n e l e c t r o n s i n c o p p e r s h o u l d have k i n e t i c e n e r g i e s o f a b o u t 7 e.v. S i n c e t h e l i n e b r e a d t h d e t e r m i n a t i o n i n v o l v e s r a t h e r l a r g e e r r o r s . , Du Mond c o n s i d e r s t h i s to- be a r e a s o n a b l e a g r e e m e n t . The f a c t t h a t t h e p o s i t r o n s o n l y a n n i h i l a t e w i t h t h e o u t e r o r c o n d u c t i o n e l e c t r o n s i n c o p p e r i s e x p l a i n e d b y two f a c t s : F i r s t , t h e p o s i t r o n s a r e b r o u g h t t o r e s t e x c e p t f o r t h e r m a l m o t i o n s . b e f o r e a n n i h i l a t i o n a n d s e c o n d t h e p r o b a b i l i t y o f a t h e r m a l i z e d p o s i t r o n p e n e t r a t -i n g f a r i n t o t h e e l e c t r o n s t r u c t u r e o f a n atom a g a i n s t t h e n u c l e a r r e p u l s i o n i s s m a l l , a s Du Mond has p o i n t e d o u t . Now we t u r n t o t h e a n g u l a r c o r r e l a t i o n m e t h o d . To f i n d t h e d i s t r i b u t i o n o f momenta o f t h e . . a n n i h i l a t i n g p a i r s b y t h e a n g u l a r c o r r e l a t i o n method., two c o u n t e r s , one f i x e d , t h e o t h e r movable;.-, a r e p l a c e d - o n o p p o s i t e s i d e s , o f a s o u r c e o f a n n i h i l a t i o n r a d i a t i o n a s shown i n F i g u r e 2., page. 6. The two c o u n t e r s a r e c o n n e c t e d t o a c o i n c i d e n c e s y s t e m a n d t h e 4- F. S e i t z , M o d e r n T h e o r y o f S o l i d s , McGraw, H i l l , 1940. - 6 -Movable F i g u r e 2 c o i n c i d e n c e c o u n t i n g r a t e i s t a k e n a s a . . f u n c t i o n o f t h e a n g u l a r p o s i t i o n o f t h e m o v a b l e s c o u n t e r . I f t h e s h a p e o f t h e a n g u l a r c o r r e l a t i o n c u r v e i s w i d e r t h a n t h a t w h i c h w o u l d be p r o d u c e d b y g e o m e t r y a l o n e a s s u m i n g 1 8 0 ° a n g u l a r c o r r e l a t i o n , t h e n t h i s e x t r a w i d t h c a n be a t t r i b u t e d t o l a c k o f c o l l i n e a r i t y o f t h e q u a n t a a n d t h e n c e ' b y e q u a t i o n 4 , page 3 , t o a n o n - z e r o momentum b e t w e e n a n n i h i l a t i n g p a i r s . T h u s , i f t h e " g e o m e t r y " , t h a t i s t h e r e g i o n o f o v e r l a p b e t w e e n t h e two c o u n t e r s a n d t h e s o u r c e , i s k e p t s m a l l a n d c o i n c i d e n c e c o u n t s a r e o b t a i n e d w i t h t h e m o v a b l e c o u n t e r o u t s i d e t h e g e o m e t r y , t h e s e c a n be a t t r i b u t e d t o t h e momentum b e t w e e n a n n i h i l a t i n g p a i r s . F r om t h e s h a p e o f t h e a n g u l a r d i s t r i b u t i o n c u r v e , t h e momentum d i s t r i b u t i o n c a n be o b t a i n e d . T h i s m e t h o d was f i r s t a t t e m p t e d by B e r i n g e r and. Montgomery-' u s i n g g e i g e r c o u n t e r s a n d a Cu s o u r c e o f p o s i t r o n s . They f o u n d no e v i d e n c e f o r a n y t h i n g b u t 1 8 0 ° c o r r e l a t i o n w i t h i n 5 - B e r i n g e r a n d Montgomery, P h y s . R e v . , 6 l , 2 2 2 ( 1 9 4 2 ) . -7-t h e a n g u l a r r e s o l u t i o n o f a b o u t 1° o f t h e i r a p p a r a t u s . I f we t a k e Du Mond's v a l u e o f .8 x 10"" ^ mc f o r t h e m e a n . c e n t r e o f mass momentum a n d f i n d t h e d e p a r t u r e f r o m c o l l i n e a r i t y o f t h e . q u a n t a , we g e t a b o u t 1/3° w h i c h i s t o o s m a l l t o h a v e b e e n . d e t e c t e d i n 19^2 by B e r i n g e r a n d Mo n t g o m e r y . The a n g u l a r . c o r r e l a t i o n e x p e r i m e n t h a s b e e n r e p e a t e d , w i t h s c i n t i l l a t i o n c o u n t e r s , w h i c h h a v e a h i g h e r Y - r a y e f f i c i e n c y a n d much b e t t e r a n g u l a r d e f i n i t i o n t h a n g e i g e r c o u n t e r s . D e B e n e d e t t i a n d c o - w o r k e r s ^ m e a s u r e d t h e a n g u l a r c o r r e l a t i o n o f a n n i h i l a t i o n r a d i a t i o n due t o p o s i t r o n s f r o m t h i n c o p p e r s h a v i n g s d y i n g i n g o l d . I t a p p e a r s f r o m c a l c u l a t i o n s p r e s e n t e d l a t e r t h a t t h e i r c o p p e r s h a v i n g s were o f s u c h a t h i c k n e s s ("a f e w m i l l s " ) t h a t a t l e a s t 25^ o f t h e p o s i t r o n s may h a v e a n n i h i l a t e d i n t h e c o p p e r . They o b t a i n e d a v a l u e o f t h e mean c e n t r e o f mass momentum o f g o l d : PAu = 8.8 x 10""^ mc. They a l s o p r e s e n t e d a t h e o r e t i c a l c a l c u l a t i o n o f t h e mean c e n t r e o f mass momentum.. F i r s t , t h e y showed t h a t t h e p o s i t r o n s a r e " t h e r m a l i z e d " i n a t i m e w h i c h . i s s h o r t c o m p a r e d t o t h e mean l i f e o f t h e p o s i t r o n s i n t h e g o l d ; t h a t i s , a f t e r r e a c h i n g t h e e n d o f t h e i r p a t h o f i o n i z a t i o n , t h e p o s i t r o n s , r a p i d l y l o s e e n e r g y b y i n e l a s t i c c o l l i s i o n s w i t h t h e t h e r m a l . l a t t i c e u n t i l t h e y a t t a i n t h e r m a l . e q u i l i b r i u m w i t h , t h e l a t t i c e . T h i s , t h e y do i n a t i m e v r h i c h . i s s h o r t c o m p a r e d t o t h e . h a l f l i f e f o r a n n i h i l a t i o n . A f t e r t h i s t h e p o s i t r o n s . d i f f u s e t h r o u g h , t h e 6- D e B e n e d e t t i , Cowan, K o n n e k e r a n d P r i m a k o f f , P h y s . Rev., 77, 205 (1950). - 8 -l a t t i c e u n t i l t h e y a r e a n n i h i l a t e d . T h e n t h e y r e p r e s e n t t h e t h e r m a l ! z e d p o s i t r o n s by a wave f u n c t i o n w h i c h i s d i f f e r e n t f r o m z e r o a n d r o u g h l y c o n s t a n t w i t h i n a n y a t o m i c p o l y h e d r o n , o n l y a t d i s t a n c e s f r o m t h e n u c l e u s g r e a t e r t h a n t h e p o s i t i v e i o n r a d i u s . Thus., o n l y e l e c t r o n s whose wave f u n c t i o n s e x t e n d b e y o n d t h e i o n i c v o l u m e s w i l l , .combine w i t h p o s i t r o n s ; i n t h e c a s e o f g o l d , t h e y show t h a t t o a f a i r d e g r e e o f a p p r o x i m a t i o n t h i s . i s o n l y t h e 6s e l e c t r o n s w h i c h c a n be r e p r e s e n t e d by p l a n e waves i n t h e r e g i o n where t h e p o s i t r o n wave f u n c t i o n i s n o t ' z e r o . T hey e v a l u a t e t h e i n t e g r a l , o f t h e m a t r i x e l e m e n t f o r a n n i h i l a t i o n o f the. p o s i t r o n a n d e l e c t r o n a n d a v e r a g e o v e r t h e e n e r g y d i s t r i b u t i o n o f t h e e l e c t r o n s a n d p o s i t r o n s t o o b t a i n t h e p r o b a b i l i t y f o r a n n i h i l a t i o n w i t h t o t a l momentum p o f t h e two p h o t o n s l y i n g i n t h e r a n g e d p . T h i s i s a l s o t h e p r o b a b i l i t y f o r a n n i h i l a t i o n w i t h a c e n t r e o f mass momentum o f e l e c t r o n a n d p o s i t r o n e q u a l t o p.. From t h i s t h e y e v a l u a t e an. a v e r a g e c e n t r e o f mass momentum, w h i c h , w i t h some a s s u m p t i o n s a b o u t t h e v o l u m e s -o f t h e p o s i t i v e g o l d i o n a n d t h e . g o l d a t o m i c p o l y h e d r o n , t h e y g i v e a s P A u = 0 . 8 mc/137 o r ^ 6 x 10~3 mc T h i s t h e y s t a t e i s a l o w e r l i m i t . a n d so c a n . b e c o n s i d e r e d t o be i n f a i r a g r e e m e n t w i t h , t h e i r e x p e r i m e n t a l . . r e s u l t . , e s p e c i a l l y s i n c e no c l a i m o f g r e a t a c c u r a c y i s made e i t h e r f o r t h e t h e o r y o r f o r t h e e x p e r i m e n t a l r e s u l t . A c c u r a t e m easurement o f t h e a n g u l a r . c o r r e l a t i o n o f a n n i h i l a t i o n r a d i a t i o n f r o m G u ^ 4 p o s i t r o n s . d y i n g i n c o p p e r -9-was o b t a i n e d by P.E. A r g y l e o f t h i s l a b o r a t o r y ' He o b t a i n e d » a v a l u e p c u = 0.984 + .01 mc/137 = (7.17 ± .07) x 10" 5 mc. B o t h .of t h e a b o v e w o r k e r s , f o u n d , t h a t .the t a i l . o f t h e i r a n g u l a r c o r r e l a t i o n curves., t h a t . i s . t h e p a r t o f t h e c u r v e o u t s i d e t h e g e o m e t r y h a d a n e x p o n e n t i a l s h a p e , o f , t h e . f o r m e~^^° a n d a s s u m i n g t h a t t h i s , d i s t r i b u t i o n , c o n t i n u e d b e y o n d t h e r e g i o n s i n w h i c h t h e y o b t a i n e d m e a s u r e m e n t s t h e y c a l c u l a t e d t h e mean c e n t r e o f mass momentum .by a method w h i c h w i l l be o u t l i n e d i n a l a t e r s e c t i o n . I t i s i n t e r e s t i n g t o n o t e t h a t t h i s e x p o n e n t i a l c h a r a c t e r J i s " ! i n q u a l i t a t i v e a g r e e m e n t w i t h t h e d i s t r i b u t i o n t o be e x p e c t e d o n t h e b a s i s o f t h e t h e o r y o f D e B e n e d e t t i a n d c o - w o r k e r s . d) The P u r p o s e o f t h i s E x p e r i m e n t I n v i e w o f t h e i n t e r e s t t h a t t h e s e e x p e r i m e n t s a r o u s e d a n d t h e v e r y s a t i s f a c t o r y r e s u l t s o b t a i n e d b y P.E. A r g y l e i n t h i s l a b o r a t o r y , we d e c i d e d t o m e a s u r e t h e a n g u l a r c o r r e l a t i o n o f t h e a n n i h i l a t i o n r a d i a t i o n f r o m p o s i t r o n s d y i n g : i n s e v e r a l d i f f e r e n t m a t e r i a l s . We c h o s e t h e m a t e r i a l s w i t h . a v i e w t o c h e c k i n g t h e c o n s e q u e n c e s o f t h e t h e o r y o f D e B e n e d e t t i a n d c o -w o r k e r s a n d . t o see i f t h e v a l u e s o f t h e momenta o b t a i n e d c o u l d be c o r r e l a t e d w i t h t h e p r o p e r t i e s o f t h e m a t e r i a l s . We h a v e o b t a i n e d r e s u l t s f o r e l e v e n d i f f e r e n t m a t e r i a l s : 7- P.E. A r g y l e , M.A. T h e s i s . , U n i v e r s i t y o f B r i t i s h C o l u m b i a , J u n e , 1950. # Now a t D o m i n i o n A s t r o p h y s i c a l O b s e r v a t o r y , V i c t o r i a , B.C. - 1 0 -Mg, S, Cu, Sn, P t , Hg - p u r e e l e m e n t s a n d L i C l , C s C l , KC1, KF, K I - i o n i c compounds. The s e r i e s o f p u r e e l e m e n t s w e re c h o s e n f o r a l a r g e r a n g e o f a t o m i c number. They a r e a l l m e t a l s e x c e p t s u l p h u r w h i c h i s w e l l known as. a g o o d i n s u l a t o r . One mig h t , e x p e c t t h a t t h e o u t e r e l e c t r o n s i n a n i n s u l a t o r w o u l d be m o r e . t i g h t l y b o u n d t h a n t h o s e i n . a m e t a l . w h i c h i s a. g o o d c o n d u c t o r . . The i o n i c compounds f a l l i n t o two g r o u p s . L i C l , .CsCl., KC1 w h i c h a r e . . t h r e e a l k a l i m e t a l c h l o r i d e s a n d .KC1, KF, K I w h i c h a r e p o t a s s i u m s a l t s o f t h r e e d i f f e r e n t h a l o g e n s . . The number o f m a t e r i a l s s t u d i e d was l i m i t e d b y t h e 12.8 h o u r h a l f l i f e o f t h e C u ^ 4 p o s i t r o n s o u r c e u s e d . D e t a i l s o f t h e e x p e r i m e n t a a n d j t h e r e s u l t s o b t a i n e d a r e g i v e n i n t h e f o l l o w i n g s e c t i o n s . I I . SOURCES a ) P o s i t r o n S o u r c e The s o u r c e s o f a n n i h i l a t i o n r a d i a t i o n . c o n s i s t e d o f two p a r t s , f i r s t , t h i n i f o i l s o f r a d i o a c t i v e c o p p e r w h i c h f o r m e d t h e s o u r c e o f p o s i t r o n s a n d second., l a y e r s o f t h e m a t e r i a l b e i n g s t u d i e d w h i c h w e r e p l a c e d on b o t h s i d e s o f t h e c o p p e r f o i l s a n d i n w h i c h t h e p o s i t r o n s d e c a y e d t o f o r m t h e a n n i h i l a t i o n r a d i a t i o n . 64 Cu was. the. o n l y r a d i o a c t i v e s o u r c e c o n s i d e r e d f o r t h i s w o r k f o r t h e r e a s o n s l i s t e d b e l o w : i ) Cu^c* c a n be made i n t h e C h a l k R i v e r , NRX p i l e . The 69% C u ^ o f n a t u r a l c o p p e r a b s o r b s n e u t r o n s ( ( T = 2.82 b a r n s ) -11-to become Cu which decays w i t h a h a l f l i f e of 12.88 hours. i i ) There are no i n t e r f e r i n g r a d i a t i o n s . There i s about.31% of C u ^ i n n a t u r a l copper and t h i s absorbs neutrons ( 6~ - 1.82 barns) to become Cu which i n t u r n decays by p~ emission f o l l o w e d by a Y - r a y . T h i s a c t i v i t y has a 5 minute p e r i o d so t h a t i n the time t h a t . t h e copper t r a v e l s from the p i l e to Vancouver (approximately 24 66 hours by a i r express) the Cu a c t i v i t y lb.eeomeso.-S n e g l i g i b l e . Cu 1^ 4 decays by p o s i t r o n e m i s s i o n (end p o i n t 0.66 mev., approximately 15%), by emission (end p o i n t 0.57 mev., approximately 30%) and by K capture (approximately 55%)• Experiments by Deutsch^ i n d i c a t e t h a t there i s a 1.35 Mev. Y-ray a s s o c i a t e d w i t h one of the above processes but i t s i n t e n s i t y i s o n l y 2.5% of the $ + i n t e n s i t y so t h a t i t does, not i n t e r f e r e w i t h the measurement of the a n n i h i l a t i o n r a d i a t i o n . i i i ) Copper can.be prepared i n f o i l s . w h i c h are t h i n enough to permit the escape of most.of the p o s i t r o n s . i v ) The energy of the p + r a d i a t i o n (end p o i n t 0.66 Mev.) i s great enough t h a t most of the p o s i t r o n s escape from a s u f f i c i e n t l y t h i n copper f o i l and yet not so l a r g e t h a t i t r e q u i r e s a great t h i c k n e s s of ab s o r b i n g m a t e r i a l t o stop the p o s i t r o n s . T h i s means t h a t sources f o r t h i s experiment can be made reasonably s m a l l . I f another source c o u l d be found s a t i s f y i n g the above 8- M i s s . L.M. S i l v e r 9 - M. Deutsch, Phys. -See a l s o .Appendix - p r i v a t e communication. Rev., 72, 729, ( 1 9 4 7 ) . II -12-requirements and having a c o n s i d e r a b l y longer h a l f l i f e , i t would be p r e f e r a b l e to Cu0"^. In t h i s experiment, measurements were taken c o n t i n u a l l y f o r one hundred hours a f t e r the, source a r r i v e d , d u r i n g which time the a c t i v i t y dropped from approximate-l y 100 mc. to l e s s than l / 2 mc., a f a c t o r of about 230. The t h i c k n e s s of the copper was chosen so t h a t a t , l e a s t 90^ of the p o s i t r o n s would be emitted from.the f o i l s . T h i s t h i c k n e s s was c a l c u l a t e d by assuming that the p o s i t r o n s have an o r d i n a r y Fermi d i s t r i b u t i o n w i t h end p o i n t 0.66 mev. The e f f e c t of coulomb r e p u l s i o n was n e g l e c t e d . I f taken i n t o account i t would g i v e a s l i g h t l y h igher average energy and so make the estimate of the per., cent emitted somewhat low. The c o r r e c t n e s s of t h i s assumption was cheeked by comparing the 64 experimental momentum d i s t r i b u t i o n f o r Cu p o s i t r o n s o b t a i n e d by T y l e r i n 1939"^ and Townsend i n 1941"''"*' w i t h the t h e o r e t i c a l Fermi d i s t r i b u t i o n . a s shown on page 13. P o s i t r o n ranges were assumed to be the same as the ranges of e l e c t r o n s of the same 12 energy and were computed from the Feather formulae. H e i t l e r has shown t h a t the d i f f e r e n c e i n p o s i t r o n and e l e c t r o n ranges due to the p o s s i b i l i t y of a n n i h i l a t i o n of the moving p o s i t r o n i s v e r y s m a l l f o r the energies t h a t we are c o n s i d e r i n g . The c a l c u l a t i o n s were done g r a p h i c a l l y where p o s s i b l e and the f i n a l r e s u l t s i n the form of a curve, showing the percentage of p o s i t r o n s 10- T y l e r , Phys. Rev., 56, 125 (1939). 11- Townsend, Proc. Roy. Soc.,A177, 357 (1941). 12- ¥. H e i t l e r , The Quantum Theory of R a d i a t i o n , Oxford, 1949, p224 and 230. -14-s t o p p e d v e r s u s t h e f o i l t h i c k n e s s , a r e p r e s e n t e d o n page 1 3 . T h i s shows t h a t f o r 90% o f t h e p o s i t r o n s t o e s c a p e f r o m t h e f o i l , t h e f o i l must be l e s s t h a n h a l f o f a t h o u s a n d t h o f a n i n c h t h i c k . S u c h f o i l s w e r e p r e p a r e d b y r e d u c i n g t h e t h i c k n e s s o f c o m m e r c i a l 2 t h o u c o p p e r f o i l i n a d i l u t e n i t r i c a c i d b a t h . The t h i c k n e s s e s m e a s u r e d by w e i g h i n g known a r e a s a n d ..by m i c r o m e t e r a g r e e d i n d i c a t i n g t h a t t h e f o i l s w e r e u n i f o r m . T h r e e c o p p e r f o i l s 3 x 2 x 0.0012 cm. o f t o t a l w e i g h t a p p r o x i m a t e l y 0.2 grams w e r e a c t i v a t e d . I n t h e p i l e a n d s e n t t o u s b y a i r e x p r e s s , t h e t o t a l d e l i v e r y t i m e b e i n g j u s t u n d e r 24 h o u r s ( a p p r o x i m a t e l y 2 h a l f l i v e s ) . On t h e b a s i s o f t h e c o u n t i n g r a t e s o b t a i n e d , we c a l c u l a t e d t h a t t h e . t o t a l s t r e n g t h o f t h e 3 f o i l s o n a r r i v a l was a b o u t 100 mc.. w h i c h means t h a t t h e a c t i v i t y a t t h e p i l e was a b o u t 400 mc. o r 2 '.•curies p e r g r am. T h i s i s i n a g r e e m e n t w i t h . t h e f i g u r e q u o t e d b y t h e I s o t o p e B r a n c h a t C h a l k R i v e r . b ) A n n i h i l a t i o n R a d i a t i o n S o u r c e s The m a t e r i a l s t o be s t u d i e d w e r e p l a c e d i n a l u m i n u m b o x e s , t h e c o p p e r f o i l s l y i n g b e t w e e n l a y e r s . o f t h e m a t e r i a l . The l a y e r t h i c k n e s s w a s . j u s t g r e a t e n o u g h t o . s t o p t h e p o s i t r o n s o f maximum r a n g e . W h i l e .the a c t i v i t y o f t h e f o i l s r e m a i n e d h i g h , o n l y one f o i l b e t w e e n two l a y e r s o f m a t e r i a l .was u s e d so t h a t t h e w i d t h o f t h e s o u r c e was k e p t a s s m a l l a s p o s s i b l e . L a t e r , two a n d e v e n t h r e e f o i l s h a d .to be u s e d i n o r d e r t o o b t a i n a r e a s o n a b l e c o u n t i n g r a t e . T h e . b o x e s were made o f 8 t h o u a l u m i n u m so t h a t l i t t l e s c a t t e r i n g o r a b s o r p t i o n c o u l d -15-o c c u r I n t h e box i t s e l f . S c a t t e r i n g i n t h e m a t e r i a l u n d e r s t u d y was. a s s u m e d t o be s m a l l o n t h e b a s i s o f c h e c k s done b y D e B e n n e d e t t i a n d c o - w o r k e r s . The w i d t h . o f t h e s o u r c e , i . e . t h e h o r i z o n t a l d i m e n s i o n t r a n s v e r s e t o t h e l i n e j o i n i n g t h e c o u n t e r s , was d e t e r m i n e d b y t h e number-'of l a y e r s a n d .the d e n s i t y o f t h e m a t e r i a l u n d e r s t u d y . The v e r t i c a l h e i g h t o f t h e . s o u r c e was 2 cm. f o r a l l m a t e r i a l s . . T h i s was, c h o s e n o n t h e b a s i s . o f g e o m e t r i c a l c o n -s i d e r a t i o n s d i s c u s s e d i n S e c t i o n I I I . The d i m e n s i o n , t , o f t h e s o u r c e i n l i n e w i t h t h e . c o u n t e r s was d e t e r m i n e d t o g i v e a maximum c o i n c i d e n c e c o u n t i n g r a t e by c o n s i d e r i n g , t h e amount o f a b s o r p t i o n o f t h e a n n i h i l a t i o n . r a d i a t i o n i n t h e s o u r c e . F o r a g i v e n s p e c i f i c a c t i v i t y , i f t i s t o o . s m a l l , t h e c o u n t i n g r a t e w i l l be t o o l o w ; b u t i f t i s t o o l a r g e , t h e c o i n c i d e n c e c o u n t i n g r a t e w i l l a g a i n . b e l o w , d u e . t o a b s o r p t i o n . . T h i s c a n be s e e n by c o n s i d e r i n g t h a t t h e sum o f t h e d i s t a n c e s t r a v e l l e d i n t h e s o u r c e by two c o i n c i d e n t a n n i h i l a t i o n q u a n t a i s e q u a l t o t h e s o u r c e l e n g t h , t . A l s o t must n o t be so l a r g e t h a t t h e s o l i d a n g l e s u b t e n d e d by t h e s o u r c e a t t h e c o u n t e r s .changes a p p r e c i a b l y a s t h e m o v a b l e c o u n t e r i s . s h i f t e d a few d e g r e e s t o t h e s i d e . From a s i m p l e . a n n a l y s i s .of t h i s p r o b l e m i t was c o n c l u d e d t h a t t h r e e s o u r c e s s i z e s w e r e s u i t a b l e f o r t h i s e x p e r i m e n t : i ) S o u r c e s w i t h t = 0.8 cm., w h e r e t h e d e n s i t y a n d t h e r e f o r e t h e Y - r a y a b s o r p t i o n o f t h e m a t e r i a l u n d e r s t u d y i s g r e a t - p l a t i n u m a n d m e r c u r y . - 1 6 -i i ) S o u r c e s w i t h t = 1.5 cm., f o r m a t e r i a l s . w i t h medium d e n s i t y - c o p p e r a n d t i n . i i i ) S o u r c e s w i t h t-"= 3 cm., f o r m a t e r i a l s w i t h l o w d e n s i t y - a l l o t h e r m a t e r i a l s u s e d . The m e r c u r y s o u r c e c o n s i s t e d o f one f o i l . o f c o p p e r d i s s o l v e d . i n m e r c u r y a n d p l a c e d i n a s m a l l . f l a t . g l a s s t u b e w i t h i n s i d e d i m e n s i o n s a p p r o x i m a t e l y 2.5 x 0.8 x 0.2 cm. I w i s h t o t h a n k .Mr.. K. E r d m a n who made t h i s , t u b e f o r me w h i l e h e l p i n g t o t a k e r e a d i n g s . A f t e r t h e b o x e s w e r e loaded., a n a l u m i n u m l i d was p r e s s e d i n a n d h e l d i n p o s i t i o n b y two a l l i g a t o r c l i p s , w h i c h w e r e r i g i d l y f a s t e n e d t o a s m a l l b r a s s b l o c k . T h i s a s s e m b l y c o u l d be r a p i d l y t r a n s f e r r e d t o a r i g i d s t a n d w h e r e i t was h e l d f i r m l y b y two b o l t s , a s shown a t t h e r i g h t i n t h e p h o t o g r a p h o n p a g e 1 7 . The s t a n d was. s c r e w e d t o t h e t a b l e h a l f way b e t w e e n t h e c o u n t e r s w i t h i t s h e i g h t a c c u r a t e l y a d j u s t e d s o t h a t hhe s o u r c e and. t h e two c o u n t e r s . l a y i n t h e same p l a n e . T h i s a r r a n g e m e n t s a t i s f i e d two r e q u i r e m e n t s : F i r s t , t h e s o u r c e s c o u l d be c h a n g e d r a p i d l y so t h a t t h e . o p e r a t o r was e x p o s e d t o a minimum o f r a d i a t i o n , a n d s e c o n d , i t p e r m i t t e d e a c h s o u r c e t o be p l a c e d i n a n a c c u r a t e l y p r e d e t e r m i n e d p o s i t i o n . Once t h e a p p a r a t u s was s e t u p , t h e o n l y a l i g n i n g t h a t was done a f t e r e a c h c h a n g e o f s o u r c e was t o c h e c k t h a t t h e o u t e r f a c e o f t h e s o u r c e box was p a r a l l e l t o t h e l i n e j o i n i n g t h e c o u n t e r s . T h i s a l i g n m e n t was f a c i l i t a t e d b y a f i n e t h r e a d s t r e t c h e d b e t w e e n t h e c o u n t e r s . -17-F i g u r e 5 S c i n t i l l a t i o n Counter and F a s t A m p l i f i e r . Source Stand on the R i g h t . -18-I I I . GEOMETRY a ) G e n e r a l T h e r e a r e two p r o b l e m s i n v o l v e d h e r e , f i r s t , t h e c h o i c e o f d e t e c t o r a n d s o u r c e s i z e a n d t h e d i s t a n c e s b e t w e e n them, a n d s e c o n d , once t h e s i z e s a n d d i s t a n c e s h a v e b e e n f i x e d what e f f e c t t h i s " g e o m e t r y " has o n t h e shape o f t h e a n g u l a r d i s t r i -b u t i o n c u r v e . P l a c i n g t h e c o u n t e r s a t e q u a l d i s t a n c e s f r o m t h e s o u r c e i s a n . o b v i o u s c h o i c e . The e f f e c t i v e c o u n t i n g v o l u m e i s t h e v o l u m e . o f t h e s c i n t i l l a t i o n c r y s t a l w h i c h i s p l a c e d o n t h e end o f t h e p h o t o m u l t i p l i e r t u b e a n d t h i s v o l u m e we c h o s e t o be l " x l " x 0.5". T h e r e w e r e s e v e r a l r e a s o n s f o r t h i s c h o i c e : i ) T h i s i s t h e s i z e o f t h e a n t h r a c e n e c r y s t a l s w h i c h we h a d . i i ) T h i s s i z e c a n be r e a d i l y f i t t e d o n t o t h e e n d o f t h e RCA 5819 p h o t o m u l t i p l i e r s t o make e f f i c i e n t u s e o f t h e p h o t o s e n s i t i v e a r e a . i i i ) R ough c a l c u l a t i o n s showed t h a t t h i s s i z e w o u l d g i v e a r e a s o n a b l e c o u n t i n g r a t e . i v ) I t w o u l d p r o v i d e s a t i s f a c t o r y a n g u l a r r e s o l u t i o n . b ) S o u r c e t o C o u n t e r D i s t a n c e C o n s i d e r t h e p r o b l e m o f f i n d i n g t h e optimum d i s t a n c e , D , b e t w e e n c o u n t e r s o f w i d t h Wc a n d s o u r c e o f w i d t h Ws a s shown i n F i g u r e 6, p a g e 19. F o r s i m p l i c i t y c o n s i d e r t h a t t h e . m o v a b l e c o u n t e r t r a v e l s a l o n g . a s t r a i g h t l i n e a n d d o t a l o n g t h e a r c - 1 9 -plane o-F counter * 1 0) (0 C o u n t e r A B 1 F i g u r e 6 o f a c i r c l e a s i t w o u l d i f t h e d i s t a n c e f r o m t h e s o u r c e were t o r e m a i n e x a c t l y t h e same f o r a l l c o u n t e r p o s i t i o n s . The c o r r e c t i o n f o r t h i s a p p r o x i m a t i o n i s n e g l i g i b l e due t o t h e s m a l l a n g l e s i n v o l v e d . C o u n t e r number 1 a t p o s i t i o n A i s d i r e c t l y i n l i n e w i t h t h e s o u r c e a n d c o u n t e r numtoer 2; a t B t h e r e i s j u s t no o v e r l a p b e t w e e n c o u n t e r s a n d s o u r c e , i . e . , no s t r a i g h t l i n e p a s s e s t h r o u g h b o t h c o u n t e r s a n d t h e s o u r c e . C o u n t e r number 1 must be moved t h e d i s t a n c e d f r o m A t o B B e f o r e s t a r t i n g t o t a k e r e a d i n g s s i n c e o n l y t h e p a r t o f t h e c u r v e n o t a f f e c t e d b y g e o m e t r y i s o f i n t e r e s t . A s i m p l e c a l c u l a t i o n shows t h a t d = Wc + ¥ s . F o r t h i s d i s c u s s i o n assume t h a t t h e - V x t a i l h a s a n e x p o n e n t i a l f o r m , e / A o , a s f o u n d by P.E. A r g y l e a n d by D e B e n e d e t t i a n d c o - w o r k e r s , where X i s t h e a n g u l a r d e p a r t u r e f r o m c o l l i n e a r i t y a n d X 0 i s a, c o n s t a n t . We want t o f i n d what v a l u e D s h o u l d h a v e i n o r d e r t o o b t a i n a maximum c o u n t i n g r a t e a t p o s i t i o n B, t h a t i s j u s t where we s t a r t m e a s u r -i n g t h e e x p o n e n t i a l t a i l . The a v e r a g e a n g l e b e t w e e n t h e c o u n t e r s a n d s o u r c e a t t h i s p o s i t i o n i s a p p r o x i m a t e l y d/D - 2 0 -r a d i a n s , s o t h a t t h e c o i n c i d e n c e c o u n t i n g r a t e i s g i v e n by w h e r e k i s a c o n s t a n t o f p r o p o r t i o n a l i t y C = IL. e - d / x „ D D 2 a n d l / D i s t h e s o l i d a n g l e f a c t o r . D i f f e r e n t i a t i n g t h i s w i t h r e s p e c t t o D, we g e t ,-d/D X< dC _ k e dD - " A _ _ 2 DAa T h i s i s z e r o when D =. d/ 2 \ o a n d p o s i t i v e when D &/2A.» A s a n u m e r i c a l e x a m p l e l e t u s assume t h a t X.= 4 x 10~^ r a d i a n s ( w h i c h i s c l o s e t o t h e v a l u e 3 . 6 -x 10"^ o b t a i n e d , b y P.E. A r g y l e ) a n d t h a t d = ¥ s + ¥ c = 0 .5 + 1.3 = 1.8 cm.; t h e n t h e o p t i m u m v a l u e o f D i s f o u n d t o be 225 cm. A s s u m i n g a f i x e d c o u n t e r w i d t h o f 1.3 cm. ( a p p r o x i m a t e l y 1/2 I n c h ) t h i s i s n o t v e r y s e n s i t i v e t o s o u r c e w i d t h ; f o r i n s t a n c e i f t h e s o u r c e w i d t h v a r i e s b e t w e e n 0 . 2 c m . a n d 1 cm. t h e optimum v a l u e o f D v a r i e s b e t w e e n 190 cm. a n d 290cm. T h e s e a r e a b o u t t h e l i m i t s o f s o u r c e w i d t h t h a t , w e r e u s e d i n t h e e x p e r i m e n t a n d t h e s o u r c e t o c o u n t e r d i s t a n c e was c h o s e n t o be 220 cm. ( 4 . 4 m e t e r s b e t w e e n c o u n t e r s ) . W i t h t h i s d i s t a n c e , t h e c o u n t e r s w e r e q u i t e c l o s e t o t h e w a l l s so t h a t some s c a t t e r i n g c o u l d o c c u r f r o m t h e w a l l s t o t h e c o u n t e r s . C o n s e q u e n t l y , a c h e c k was made o n t h e s c a t t e r i n g a n d a l t h o u g h m e a s u r a b l e i t was s m a l l e n o u g h t h a t i t d i d n o t i n t e r f e r e v / i t h t h e r e s u l t s . c ) A n g u l a r D i s t r i b u t i o n C u r v e s C o n s i d e r t h e p r o b l e m o f t h e e f f e c t o f g e o m e t r y o n t h e s h a p e o f t h e a n g u l a r d i s t r i b u t i o n f u n c t i o n when t h e r e i s a - 2 1 -c e n t r e o f mass momentum d i s t r i b u t i o n N ( p ) b e t w e e n a n n i h i l a t i n g p a i r s . We f i r s t c o n s i d e r t h e t r e a t m e n t g i v e n b y D e B e n e d e t t i a n d c o - w o r k e r s . C o n s i d e r t h e c a s e where t h e m o v a b l e c o u n t e r i s s h i f t e d i n a v e r t i c a l d i r e c t i o n a n d w h e r e t h e h o r i z o n t a l a n g u l a r a p e r t u r e i s s m a l l e n o u g h t o n e g l e c t i t s s q u a r e b u t l a r g e c o m p a r e d t o t h e a n g l e s b e t w e e n t h e a n n i h i l a t i o n q u a n t a . T h i s l a s t c o n d i t i o n was met b y t h e g e o m e t r y u s e d i n t h e p r e s e n t e x p e r i m e n t a n d b y t h a t u s e d b y D e B e n e d e t t i . As a r e s u l t , t h e e r r o r i n t r o d u c e d b y t r e a t i n g t h e v e r t i c a l p l a n e o n l y i s s m a l l . L e t N z ( p z ) be t h e d i s t r i b u t i o n o f a n n i h i l a t i o n s a c c o r d i n g t o z c o m p o n e n t s ( v e r t i c a l ) o f p . F r o m e q u a t i o n 4, o n p a g e 3, we h a v e p z/mc = a r a d i a n s , t h e v e r t i c a l a n g l e o f d e p a r t u r e f r o m 180°. The e x p e r i m e n t a l l y o b s e r v e d c o i n c i d e n c e r a t e a s a f u n c t i o n o f t h e a n g l e X i s g i v e n b y where K i s a c o n s t a n t a n d t h e l i m i t s a r e e x p l a i n e d b y f i g u r e 7. 1 \ \ F i g u r e 7 - 2 2 -When C ( X ) i s f o u n d e x p e r i m e n t a l l y , t h i s i n t e g r a l e q u a t i o n must be s o l v e d f o r N z ( X). A s o l u t i o n i s o n l y p o s s i b l e i n a f e w s p e c i a l cases., one o f w h i c h i s when C( X) h a s a n e x p o n e n t i a l f o r m . F o r t u a t e . l y , D e B e n e d e t t i a n d c o - w o r k e r s f o u n d a n e x p o n e n t i a l d i s t r i b u t i o n a n d c a l c u l a t e d t h e mean c e h r e o f mass momentum o f a n n i h i l a t i n g p a i r s a s o u t l i n e d b e l o w . From t h e f u n c t i o n N z ( p z ) o b t a i n e d a b o v e , t h e f u n c t i o n N ( p ) c a n be o b t a i n e d b y a s i m p l e c a l c u l a t i o n , t h e r e s u l t b e i n g „w \ „ dNz(r)) . • _ N ( p ) = 2p — . . . . . . . . 2 dp 1 F o r t h e c a s e o f a n e x p o n e n t i a l f o r m C(X)'= e ' ° N ( p ) = A p e ~ p / m c *° , w h e r e A i s a c o n s t a n t .... 3 The a v e r a g e p c a n be o b t a i n e d f r o m t h i s b y a s i m p l e i n t e g r a t i o n w h i c h g i v e s p N ( p ) dp p ~ ~Trf> = 2 m C ^ ° ( N(p) dp a n d t h u s p c a n be o b t a i n e d f r o m t h e s l o p e o f t h e e x p o n e n t i a l t a i l i f i t t u r n s o u t t o be a s t r a i g h t l i n e o n a l o g a r i t h m i c p l o t . . ' The t a i l s o f t h e a n g u l a r d i s t r i b u t i o n c u r v e s o b t a i n e d i n t h e p r e s e n t e x p e r i m e n t w e r e n o t a l l . o f a s i m p l e e x p o n e n t i a l f o r m ; b u t i n c a s e s w here t h e y w e r e e x p o n e n t i a l o r n e a r l y s o t h e a b o v e m e t h o d o f a n a l y s i s was u s e d . On some o f t h e c o r r e l a -t i o n c u r v e s o b t a i n e d i n t h i s e x p e r i m e n t , t h e r e a p p e a r s t o be -23-e v i d e n c e f r o m t h e s h a p e o f t h e p e a k s t h a t a l t h o u g h t h e t a i l o f t h e c u r v e a p p e a r s s t r a i g h t , t h e a s s u m p t i o n t h a t t h e same e x p o n e n t i a l t y p e d i s t r i b u t i o n c o n t i n u e s i n t o t h e " g e o m e t r y r e g i o n " i s f a l s e . I f t h i s i s s o , t h e a b o v e m e t h o d o f g e t t i n g p w h i c h assumes a n e x p o n e n t i a l f o r m f r o m z e r o t o i n f i n i t y i s n o t c o r r e c t . d ) The E f f e c t o f G e o m e t r y o n t h e D i s t r i b u t i o n C u r v e s The a b o v e t r e a t m e n t i s c e r t a i n l y v e r y n e a t b u t t h e d i f f i c u l t y o f s o l v i n g t h e i n t e g r a l e q u a t i o n when C ( X ) i s n o t a s i m p l e e x p o n e n t i a l i s f o r m i d a b l e a n d i t s s o l u t i o n was n o t a t t e m p t e d . A l s o , t h e t r e a t m e n t d o e s n o t g i v e much i n f o r m a t i o n a b o u t t h e e f f e c t o f t h e g e o m e t r y o n t h e s h a p e o f t h e a n g u l a r c o r r e l a t i o n c u r v e . T h e r e f o r e , a n a t t e m p t was made t o i n t e g r a t e t h e p r o b l e m a n a l y t i c a l l y . T h i s t u r n e d o u t t o be t o o d i f f i c u l t a n d so a n u m e r i c a l i n t e g r a t i o n f o r s e v e r a l t y p i c a l c a s e s was made. The method s u s e d a n d r e s u l t s o b t a i n e d a r e o u t l i n e d b e l o w . I w o u l d l i k e t o t h a n k Mr. Hugh D e m p s t e r f o r h i s h e l p i n s e t t i n g up t h e p r o b l e m a n d my w i f e f o r h e r a i d i n p e r f o r m i n g t h e c a l c u l a t i o n s . C o n s i d e r t h e c a s e where we h a v e a . s i m p l e e x p o n e n t i a l d i s t r i b u t i o n K e " 6 / ® 0 a n d where t h e s o u r c e a n d c o u n t e r s h a v e a f i n i t e a r e a a s shown i n x f i g u r e 8, page 2 4 . F i r s t . , we want t h e c o i n c i d e n c e c o u n t i n g r a t e , d C , d u e t o a n e l e m e n t o f s o u r c e , d S Q , a t p o s i t i o n r 0 f r o m t h e c e n t r e o f t h e s o u r c e , a n e l e m e n t o f c o u n t e r 1, dS]_> a t p o s i t i o n r ^ f r o m t h e c e n t r e o f c o u n t e r 1 a n d a n e l e m e n t o f c o u n t e r 2, dS2, a t p o s i t i o n r.2 f r o m t h e - 2 4 -1 F i g u r e 8 I f 2. c e n t r e o f c o u n t e r 2. The v e c t o r s , r 0 , r ^ a n d r 2 a r e i n t h e p l a n e s t h e s o u r c e a n d t h e c o u n t e r c r y s t a l s r e s p e c t i v e l y a n d a r e p e r p e n d i c u l a r t o t h e l i n e j o i n i n g t h e c r y s t a l s t o t h e s o u r c e . N o t e t h a t i f c o u n t e r 1 i s t h e m o v a b l e c o u n t e r , t h e v e c t o r rn_ must be m e a s u r e d f r o m t h e p o i n t where t h e c e n t r e o f c o u n t e r 1 i s when b o t h c o u n t e r s a n d s o u r c e a r e i n l i n e . The p a r t o f t h e c o i n c i d e n c e c o u n t due t o t h e s e e l e m e n t s o f a r e a , d S Q , d S ^ a n d d S 2 i s r e a d i l y s e e n t o be dC = n d S Q 1 4~* rf2 d s l K e""e/£o d S 2 A e-L e 2 i 2 i 2 p w h e r e n = - a n n i h i l a t i o n r a d i a t i o n a c t i v i t y o f t h e s o u r c e p e r cm . A = t h e a b s o r p t i o n f a c t o r i n t h e s o u r c e , e = e f f i c i e n c y o f d e t e c t o r . 9 = t h e a n g l e b e t w e e n t h e l i n e s j o i n i n g dS]_ a n d d S 2 t o d S Q , The t o t a l c o u n t i n g r a t e i s f o u n d b y i n t e g r a t i n g o v e r t h e a r e a s o f c o u n t e r s a n d s o u r c e w h i c h g i v e s = B (ff e " e / e o "& A ^2 wh e r e B = n A K en e dS dS. d S 0 . o 1 d. 1 e 2 4 * i « - 2 5 -By a g e o m e t r i c a l c a l c u l a t i o n , © c a n be f o u n d i n t e r m s o f r ( r - i , a n d r 2 . I f we assume t h a t 0 i s s m a l l , t h e r e s u l t i s _ J r2 + r l - 2 r o ) i s o t h a t C = B e r2 + r l - 2 r o j O ^ — d S Q d S x d S 2 I f r 0 , r i a n d r 2 a r e e x p r e s s e d i n r e c t a n g u l a r c o - o r d i n a t e s x o » 7o» x l > vl» x2» v2> w e n a v e j r 2 + r i - 2 r Q j = + l(x 2 + X l " 2 x o ) 2 + <T2 + Jl ~ 2?0) 2\ I / 2 No method was f o u n d f o r i n t e g r a t i n g t h i s e x p r e s s i o n a n a l y t i c a l l y ; t h e r e f o r e , a n a p p r o x i m a t e n u m e r i c a l s o l u t i o n t o t h e p r o b l e m was o b t a i n e d f o r t h e f o l l o w i n g c a s e s : i ) P o i n t s o u r c e a n d r e c t a n g u l a r c o u n t e r s . i i ) L i n e s o u r c e s o f t h r e e d i f f e r e n t l e n g t h s a n d r e c t a n g u l a r c o u n t e r s . i i i ) R e c t a n g u l a r s o u r c e a n d r e c t a n g u l a r c o u n t e r s . The i n t e g r a t i o n was done u s i n g t h e f o l l o w i n g n u m e r i c a l assump-t i o n s . : i ) The a n g u l a r c o r r e l a t i o n f u n c t i o n i s o f t h e f o r m - K e"®/® 0, where 6 Q = 4 x 10"*^  r a d i a n s , ( a v a l u e c l o s e t o t h a t o b t a i n e d by P.E.. A r g y l e ) i i ) The c o u n t e r a r e a i s 1 i n c h b y 1/2 i n c h o r 8 u n i t s b y 4 u n i t s - , w h e r e 1 u n i t = 0.3125 cm. T h e s e new u n i t s w e re c h o s e n t o s i m p l i f y t h e c a l c u l a t i o n s . i i i ) The d i s t a n c e , £ , i s 200 cm.,(= 640 u n i t s ) . - 2 6 -The s o u r c e a n d c o u n t e r a r e a s w e r e d i v i d e d i n t o s e c t i o n s a n d r e c t a n g u l a r , c o - o r d i n a t e s a s s i g n e d t o t h e c e n t r e o f e a c h s e c t i o n . The c o u n t i n g r a t e due t o e a c h s e c t i o n was as s u m e d t o be u n i f o r m -l y d i s t r i b u t e d o v e r t h a t s e c t i o n so t h a t t o g e t t h e t o t a l c o u n t i n g r a t e , we sum t h e c o n t r i b u t i o n s due t o a l l c o m b i n a t i o n s o f s e c t i o n s a s shown b y t h e f o l l o w i n g e x p r e s s i o n f o r t h e c a s e o f r e c t a n g u l a r c o u n t e r s a n d r e c t a n g u l a r s o u r c e : a n d w h e r e t h e s u m m a t i o n s a r e o v e r t h e number o f . s e c t i o n s i n t h e s o u r c e a n d c o u n t e r s a n d t h e i n t e g r a n d . i s t o be e v a l u a t e d u s i n g t h e c o - o r d i n a t e s o f t h e p o i n t a t t h e c e n t r e o f e a c h s e c t i o n . The s u m m a t i o n s h a d t o be done f o r e a c h o f s e v e r a l p o s i t i o n s o f t h e m o v a b l e c o u n t e r i n o r d e r t o o b t a i n a c u r v e . I t was f o u n d t h a t d i v i d i n g t h e c o u n t e r a r e a i n t o e i g h t s e c t i o n s gave s a r e a s o n a b l y a c c u r a t e a n s w e r . T h i s was c h e c k e d b y d o i n g one c a l c u l a t i o n t w i c e , once w i t h t h e c o u n t e r a r e a d i v i d e d i n t o e i g h t s e c t i o n s a n d o n c e w i t h i t d i v i d e d i n t o t h i r t y - t w o ; t h e two r e s u l t s d i f f e r e d by o n l y a b o u t 3/£. The c a l c u l a t i o n s w e r e g r e a t l y s i m p l i f i e d b y t h e s y m m e t r i e s w h i c h a p p e a r e d when t h e f a c t o r s R 2 = (X2+XT_-2X0 ) 2+ ( y 2 + y i - 2 y 0 ) 2 were :. l a i d o u t i n a s q u a r e a r r a y . The f o l l o w i n g e x a m p l e i s g i v e n f o r t h e p o i n t s o u r c e c a s e when t h e two c o u n t e r s a r e i n l i n e w i t h t h e s o u r c e . The c o - o r d i n a t e s o f t h e c e n t r e s o f t h e c o u n t e r s e c t i o n s a r e shown i n f i g u r e . 9, p a g e 2 7 . E a c h s e c t i o n 2 1 V 2 C = B d S 0 dS]_ d S 2 £ 2 2 e" 0 1 2 where d S 0 = ( 2 . 5 / 8 ) 2 dS-L = d S 2 = ( 2 . 5 / 4 ) 2 1 - 2 7 -8 - 1 , 3 a l 1, 3 f l - 1 , 1 ' b l 1, 1 S i -1,-1 c l 1,-1 h l - 1,-3 d l 1,-3 e 2 - 1 , 3 a 2 1, 3 f 2 - 1 , 1 1, 1 s 2 -1,-1 °2 1,-1 h 2 -1,-3 d 2 1,-3 F i g u r e 9 # 1 # 2 i s a l l o t t e d a l e t t e r f o r r e f e r e n c e . I n t h i s c a s e R h a s t h e s i m p l i f i e d f o r m R 2 = ( x 2 + X T _ ) 2 + ( y 2 + y x ) 2 a n d t h e p r o b l e m i s t o e v a l u a t e C = K Z 2 e - R / e ° * 1 2 w h e r e 9 0 = 4 x 1 0 ~ ^ r a d i a n s i = 200 cm = 640 u n i t s QQ£ = 2.56 = 4 x 1 0 ~ 5 x 640 K = a c o n s t a n t o f p r o p o r t i o n a l i t y . T h i s was done by l a y i n g o u t t h e f a c t o r s R 2 i n a s q u a r e a r r a y a s shown i n f i g u r e 1 0. F o r i n s t a n c e t h e f a c t o r R 2 f o r t h e a]_ P P P a n d a 2 s e c t i o n s i s g i v e n b y R = ( 1 +.1) * (3 + 3) = 4 0 . The i n t e g r a n d was e v a l u a t e d f o r e a c h v a l u e o f R 2 i n t h e t a b l e a n d m u l t i p l i e d by t h e number o f t i m e s , n, w h i c h t h a t v a l u e o f R a p p e a r e d a n d t h e s e r e s u l t s were a d d e d t o g i v e a number - 2 8 -a l b l c l d l e l f l S i h l n R 2 R/2.56 -R/2.56 nxe ' ^ a 2 40 20 | 8 4 36 16 4 0 4 40 2.46 0.342 b 2 20 8 4 8 16 4 0 4 4 36 2 . 3 4 0 .385 c 2 8 4 8' 20 4 0 4 16 8 20 1.74 1.404 d 2 4 8 20 40 0 4 16 36 8 16 1.56 1.681 e 2 36 16 4 0 40 20 8 * 8 1.10 4.000 *2 16 4 0 4 20 8 4 8 20 4 0.78 9.150 S2 4 0 4 16 8 4 8 20 8 0 0 8.000 h 2 0 4 16 36 4 8 20 40 74.886 = 3 x 24 .962 F i g u r e 10 p r o p o r t i o n a l to the c o i n c i d e n c e counting r a t e . The m u l t i p l i e r threecwas used t o make the r e s u l t s more convenient t o p l o t . The r e s u l t , 7 4 . 8 8 , i s the peak v a l u e f o r the. p o i n t source ease as shown on the graph on page 29. T h i s graph shows the r e s u l t s of the complete c a l c u l a t i o n s . The green l i n e s are drawn p a r a l l e l and w i t h a slope c o r r e s p o n d i n g t o the e x p o n e n t i a l e~^/&° where 80= 4 x 10~^ r a d i a n s . By comparing the slopes of the c a l c u -l a t e d l i n e s w i t h t h a t of the green l i n e s , we can f i n d the e f f e c t t h a t the f i n i t e s i z e of counters and source has on the assumed e x p o n e n t i a l d i s t r i b u t i o n . Two t h i n g s are immediately.apparent: F i r s t , the curves are not s t r a i g h t l i n e s , o u t s i d e t h e , o v e r l a p or geometry r e g i o n , and second, :the curves are f l a t t e n e d compared t o the o r i g i n a l d i s t r i b u t i o n , t h a t i s the slope i s decreased by the f i n i t e counter and source s i z e . The decrease i n slope gets g r e a t e r w i t h i n c r e a s e i n source s i z e . Actually., the l a c k of l i n e a r i t y i s h a r d l y great enough to be d e t e c t e d by the p a g e 29 F i g u r e 11 1 • -,. C a l c u l a t e d A n g u l a r C o r r e l a t i o n C u r v e s - 3 0 -p r e s e n t e x p e r i m e n t , P u t t h e c h a n g e i n s l o p e i s g r e a t e n o u g h t o be d e t e c t e d a n d r o u g h c o r r e c t i o n s b a s e d on t h e a b o v e r e s u l t s w e r e made. A l s o , a c o m p a r i s o n o f t h e g e n e r a l s h a p e s o f t h e e x p e r i m e n t a l c u r v e s w i t h t h e s e c a l c u l a t e d c u r v e s h e l p e d i n d e c i d i n g w h e t h e r t h e e x p e r i m e n t a l c u r v e was due t o a s i n g l e e x p o n e n t i a l t y p e d i s t r i b u t i o n o f e l e c t r o n momenta o r w h e t h e r t h e e l e c t r o n momentum d i s t r i b u t i o n was more c o m p l i c a t e d . The e f f e c t o f m a k i n g t h e s o u r c e l o n g e r i s n o t . g r e a t a n d f o r t h i s r e a s o n t h e s o u r c e s w e r e made 2 cm. h i g h , a l m o s t a s h i g h a s t h e c o u n t e r s ( 2 . 5 c m ) . I t c a n be q u i t e e a s i l y shown t h a t t h e r e i s no g a i n i n m a k i n g t h e s o u r c e l o n g e r t h a n t h e c o u n t e r s . The g e o m e t r i c a l a r r a n g e m e n t o f c o u n t e r s a n d s o u r c e u s e d i n t h i s e x p e r i m e n t i s shown i n f i g u r e 12 below.. The d i m e n s i o n s t a n d w o f t h e s o u r c e d e p e n d e d o n t h e m a t e r i a l u n d e r s t u d y a s e x p l a i n e d a b o v e . z V 71 ZZOcm 220 c « movable; c o u n t e r ' s o u r c e s t a t i o n a r y c o u n t e r F i g u r e 12 -31-I V . S C I N T I L L A T I O N COUNTERS AND ASSOCIATED CIRCUITS a ) G e n e r a l The y e a r 194-7 w i l l u n d o u b t e d l y be r e g a r d e d b y f u t u r e p h y s i c i s t s a s t h e b e g i n n i n g o f " t h e e r a o f s c i n t i l l a t i o n c o u n t e r s " . I n t h a t y e a r , K a l l m a n p u b l i s h e d t h e r e p o r t s o f h i s s t u d i e s o n t r a n s p a r e n t o r g a n i c p h o s p h o r s used, i n c o n j u n c -t i o n w i t h p h o t o m u l t i p l i e r s f o r d e t e c t i n g n u c l e a r r a d i a t i o n s . S i n c e t h a t t i m e t h e r e h a v e b e e n more t h a n one h u n d r e d a n d f i f t y a r t i c l e s p u b l i s h e d , i n E n g l i s h a l o n e , c o n c e r n i n g t h e c h a r a c t e r i s t i c s a n d u s e s o f s c i n t i l l a t i o n c o u n t e r s . F o r t h i s - . r e a s o n , no d e t a i l e d e x p l a n a t i o n w i l l be g i v e n h e r e . As v/as p o i n t e d o u t t h e g o o d a n g u l a r r e s o l u t i o n a n d r e l a t i v e l y h i g h e f f i c i e n c y make s c i n t i l l a t i o n c o u n t e r s v e r y u s e f u l i n Y - r a y s t u d i e s . A l s o , t h e v e r y f a s t r i s i n g s h o r t p u l s e s make them s u i t a b l e f o r c o i n c i d e n c e w o r k . As a r e s u l t o f t h e f a s t r i s e , s h o r t r e s o l v i n g t i m e s c a n be u s e d , t h u s m i n i m i z i n g a c c i d e n t a l c o i n c i d e n c e s . The f a c t t h a t t h e p u l s e s a r e s h o r t means t h a t h i g h c o u n t i n g r a t e s a r e p o s s i b l e w i t h o u t l a r g e d e a d t i m e c o r r e c t i o n s . I n o r d e r t o make t h e b e s t u s e o f t h e s e c h a r a c t e r i s t i c s , t h e a s s o c i a t e d e l e c t r o n i c c i r c u i t s must be a b l e t o h a n d l e t h e s h a r p p u l s e s , t h a t i s s t r a y c a p a c i t i e s must be k e p t t o a minimum a n d t h e b a n d p a s s must be w i d e . A p h o t o g r a p h o f t h e e l e c t r o n i c a p p a r a t u s i s shown o n page 32 a n d a b l o c k d i a g r a m i s g i v e n o n p a g e 33• T h e s e a r e - 3 2 -F i g u r e 13 E l e c t r o n i c A p p a r a t u s The s c i n t i l l a t i o n c o u n t e r and m i c r o s c o p e c a r r i a g e a r e on the t a b l e b e h i n d t h e r a c k s . -33-220 cm. C o u n t e r #1 ( m o v a b l e ) 220-cm. C o u n t e r #2 ( s t a t i o n a r y ) 2000V H T S e t F a s t A m p l i f i e r F a s t A m p l i f i e r C o i n c i d e n c e M i x e r S c a l e o f 100 S c a l e o f 1 0 0 r T S c a l e o f 1000 Sca^le of i o n S c a l e o f 100 BLOCK DIAGRAM OF ELECTRONIC APPARATUS F i g u r e 14 -34-s e l f e x p l a n a t o r y . Two s c a l e s o f 100 w e r e c o n n e c t e d i n s e r i e s t o r e c o r d e a c h o f t h e s i n g l e c h a n n e l c o u n t i n g r a t e s s i n c e t h e r a t e s e n c o u n t e r e d w e r e t o o h i g h f o r t h e m e c h a n i c a l r e g i s t e r o n a s i n g l e s c a l e o f 1 0 0 . The c o i n c i d e n c e c o u n t s were t a k e n o n a s c a l e o f 1000 d e s i g n e d by Mr. F.K. B o w e r s . The e l e c t r o n i c c i r c u i t s u s e d w e re d e s i g n e d o n t h e b a s i s o f e x p e r i e n c e g a i n e d by t h e a u t h o r w h i l e a t C h a l k R i v e r . To p e r f o r m t h e e x p e r i m e n t s d e s c r i b e d h e r e , t h e a p p a r a t u s was o n c o n t i n u a l l y f o r about. 5 d a y s and-4 n i g h t s ( 1 1 0 h o u r s ) d u r i n g w h i c h t i m e d e l a y s r e s u l t i n g f r o m f a i l u r e o f e l e c t r o n i c c o m p o n e n t s a m o u n t e d t o j u s t o v e r one h o u r . T h i s i s s a t i s f a c t o r y c o n s i d e r i n g t h a t a b o u t two h u n d r e d a n d f i f t y t u b e s , a n d a b o u t f o u r t h o u s a n d o t h e r e l e c t r o n i c c o mponents were d i r e c t l y i n v o l v e d . A l l - a p p a r a t u s e x c e p t t h e s c a l e r s w e r e r u n f r o m c o n s t a n t v o l t a g e S o l a t r a n s f o r m e r s a n d . e l e c t r o n i c v o l t a g e r e g u l a t i o n was e m p l o y e d where n e c e s s a r y . b) S c i n t i l l a t i o n C o u n t e r s The s c i n t i l l a t i o n c o u n t e r s c o n s i s t e d o f l " x 1" x 1/2" a n t h r a c e n e c r y s t a l s ( f r o m L i n d e A i r P r o d u c t s ) s e a l e d o n t o t h e e n d s o f RCA 5819 p h o t o m u l t i p l i e r t u b e s . The p h o t o m u l t i p l i e r s w e r e m o u n t e d o n t h e h e a d a m p l i f i e r b o x e s a n d made l i g h t t i g h t w i t h a w r a p p i n g o f f r i c t i o n t a p e a s shown i n t h e p h o t o g r a p h o n p a g e 1 7 . The p h o t o m u l t i p l i e r v o l t a g e was o b t a i n e d f r o m a b a t t e r y r e f e r e n c e d 2 000 v o l t h i g h t e n s i o n s e t w i t h , s e p a r a t e l y - 3 5 -f l i t e r e d o u t p u t s a n d s e p a r a t e v o l t a g e , c o n t r o l s f o r e a c h m u l t i -p l i e r . P h o t o m u l t i p l i e r s c a n be o p e r a t e d f r o m e i t h e r a p o s i t i v e o r n e g a t i v e h i g h v o l t a g e ; we c h o s e t h e p o s i t i v e s u p p l y , s i n c e t h i s a l l o w e d t h e p h o t o c a t h o d e c a p n e a r t h e end o f t h e t u b e t o be g r o u n d e d . C o o l i n g t h e p h o t o m u l t i p l i e r w i t h d r y i c e was t e s t e d b u t t h e i m p r o v e m e n t was n o t g r e a t e n o u g h t o w a r r a n t t h e t r o u b l e a n d so no s p e c i a l c o o l i n g was u s e d . Due t o t h e s h o r t r e s o l v i n g t i m e o f t h e c o i n c i d e n c e m i x e r , t h e n o i s e b a c k g r o u n d due t o t h e p h o t o m u l t i p l i e r s was i n s i g n i f i c a n t i n t h e c o i n c i d e n c e c h a n n e l . The s i n g l e c h a n n e l , n o i s e b a c k g r o u n d .count was a b o u t 5 t o 10 c o u n t s p e r s e c o n d a n d seemed t o v a r y by a s much a s 5 0 $ . f r o m d a y t o d a y . I t i s b e l i e v e d t h a t t h i s i s i n h e r e n t i n t h e p h o t o m u l t i p l i e r a n d n o t due- t o i n s t a b i l i t y i n t h e e l e c t r o n i c a p p a r a t u s , b e c a u s e c o i n c i d e n c e c o u n t i n g r a t e s w e r e r e p r o d u c i b l e f r o m day t o d a y t o w i t h i n t h e s t a t i s t i c a l . . e r r o r s . T h i s b a c k -g r o u n d r a t e i s f r o m f o u r t o f i v e t i m e s s m a l l e r t h a n t h a t o b t a i n e d by P.E. A r g y l e b e c a u s e t h e e f f e c t i v e d i s c r i m i n a t i o n l e v e l c o u l d be s e t h i g h e r i n t h e p r e s e n t e x p e r i m e n t , t h u s e x c l u d i n g more o f t h e n o i s e p u l s e s . The a n t h r a c e n e . c r y s t a l s u s e d i n t h i s e x p e r i m e n t a r e known t o p r o d u c e l a r g e r p u l s e s t h a n n a p h t h a l e n e w h i c h was u s e d by Mr. A r g y l e . * ^ I t a p p e a r s t h a t two t h i r d s o f t h e n o i s e f r o m t h e p h o t o -m u l t i p l i e r comes f r o m t h e p h o t o c a t h o d e , a n d t h e o t h e r t h i r d f r o m t h e d ynode s y s t e m . T h i s was c h e c k e d by m a k i n g n o i s e m e a s u r e m e n t s w i t h f o c u s s i n g v o l t a g e s b e t w e e n t h e p h o t o c a t h o d e . 13- P.R. B e l l , P h y s . Rev., 73, 1405 (1948). - 3 6 -a n d f i r s t d y node v a r y i n g f r o m z e r o t o two h u n d r e d . The n o i s e r a t e i n c r e a s e s by a f a c t o r 3 5 a p p r o x i m a t e l y , a s t h e v o l t a g e i s r a i s e d f r o m z e r o t o one h u n d r e d . T h e r e i s a s l i g h t d e c r e a s e i n r a t e f r o m 100 t o 200 v o l t s , u n d o u b t e d l y due t o d e f o c u s s i n g . T h i s r e s u l t i s n o t i n a g r e e m e n t w i t h t h e c o n c l u s i o n o f P. E . A r g y l e t h a t most o f t h e n o i s e p u l s e s a r e f r o m t h e f i r s t d y n o d e . The d i s c r e p a n c y m i g h t h a v e b e e n due t o t h e u s e o f d i f f e r e n t d i s c r i m i n a t i o n l e v e l s , b u t f u r t h e r c h e c k s a t s e v e r a l d i s c r i m i n -a t i o n l e v e l s g a v e t h e same r e s u l t s a s a b o v e . As h a s b e e n p o i n t e d o u t b y R.H. G i l l e t t e ^ c o n s i d e r a b l e c a r e s h o u l d be p a i d t o t h e m o u n t i n g o f t h e c r y s t a l o n t h e p h o t o m u l t i p l i e r i n o r d e r t o o b t a i n t h e b e s t o p t i c a l c o u p l i n g . The m e t h o d u s e d f o r t h i s e x p e r i m e n t i s d e s c r i b e d b e l o w . F i r s t , a one I n c h s q u a r e t h i n a l u m i n u m f r a m e 1/2" i n h e i g h t was g l u e d t o t h e end o f t h e p h o t o t u b e . The c r y s t a l was s e t i n t o t h i s a n d t h e s p a c e s w ere f i l l e d w i t h a c l e a r m i n e r a l o i l . T h e n a t h i n a l u m i n u m l i d was p u t o n t o p a n d t h e w h o l e t h i n g was made l i g h t t i g h t w i t h b l a c k p a i n t . The t o p a n d b o t t o m ( 1 i n c h s q u a r e ) s u r f a c e s o f t h e c r y s t a l w e r e p o l i s h e d by r u b b i n g w i t h a s o f t c l o t h dampened w i t h x y l e n e , b u t the' e d g e s were l e f t r o u g h s o a s t o s c a t t e r l i g h t b a c k i n t o t h e c r y s t a l (See r e f e r e n c e l 4 ) . The m i n e r a l o i l u s e d was P r i m o l D, k i n d l y s u p p l i e d t o u s b y I m p e r i a l O i l Co. L t d . The s p e c t r a l . t r a n s p a r e n c y o f t h i s o i l was c h e c k e d ont,a Beckman q u a r t z s p e c t r o p h o t o m e t e r a n d f o u n d t o 14- R.H. G i l l e t t e , P h o s p h o r s f o r S c i n t i l l a t i o n C o u n t e r s . - A R e p o r t f r o m t h e L a b o r a t o r y o f t h e L i n d e A i r P r o d u c t s Co., Tonawanda, N.Y. -37-be s a t i s f a c t o r y dovm to about 3000 A which i s past t h e . c u t -o f f of the s p e c t r a l response of the phototube. The best o p e r a t i n g c o n d i t i o n s , as regards H.T. v o l t a g e on the m u l t i p l i e r , g a i n of the a m p l i f i e r and pu l s e d i s c r i m i n a -t i o n l e v e l , were a d j u s t e d by methods s i m i l a r t o those o u t l i n e d by D e u t s c h ^ . The p u l s e d i s c r i m i n a t i o n l e v e l a t the input t o the c o i n c i d e n c e mixer was set a t 4 v o l t s . Values below t h i s would g i v e s l i g h t l y h i g h e r e f f i c i e n c i e s but they r e q u i r e d a s a c r i f i c e i n s t a b i l i t y . Curves of nois e versus H.T. v o l t a g e were taken f o r both p h o t o m u l t i p l i e r s ; these curves r i s e s lowly w i t h i n c r e a s i n g H.T. v o l t a g e u n t i l a c e r t a i n r a t h e r c r i t i c a l v o l t a g e i s reached (depending on the p a r t i c u l a r p h o t o m u l t i p l i e r ) a f t e r which the noise r i s e s r a p i d l y w i t h H.T. voltage... F o r tube number 1 t h i s v o l t a g e was about 950 v o l t s and f o r tube number 2 i t was 1150 v o l t s . I t i s d e s i r a b l e t o work the tubes: below these v o l t a g e s so small.changes i n H.T. v o l t a g e do not cause l a r g e changes i n the noise background. A c t u a l l y , f u r t h e r checks based on noise versus g a i n curves and e f f i c i e n c y versus g a i n curves showed t h a t very l i t t l e advantage would be gained by exceeding these v o l t a g e s . Consequently phototube number 1 was run a t 900 v o l t s and number 2 at 1050 v o l t s w i t h both a m p l i f i e r s a t f u l l g a i n throughout the experiment. 15- M. Deutsch, M.I.T. T e c h n i c a l Report No.3, 1 D e c , 1947. , -38-c ) A m p l i f i e r s The c i r c u i t d i a g r a m f o r t h e p h o t o m u l t i p l i e r , h e a d a m p l i f i e r a n d f a s t r i n g o f t h r e e a m p l i f i e r u s e d . a r e shown o n page 39. The a m p l i f y i n g s y s t e m f o r t h i s e x p e r i m e n t must meet two r e q u i r e m e n t s : F i r s t , i t must h a n d l e s h a r p p u l s e s w i t h ' a minimum o f d i s t o r t i o n , t h a t i s i t must h a v e a w i d e b a n d p a s s a n d s e c o n d , i t must be a b l e t o h a n d l e a l a r g e r a n g e o f p u l s e s i z e s w i t h o u t o v e r l o a d i n g a n d c o n s e q u e n t ) d o u b l i n g a n d l e n g t h -e n i n g o f p u l s e s . C o m m e r c i a l l y a v a i l a b l e . A t o m i c ..Instruments Company a m p l i f i e r s w e r e r e j e c t e d , f o r a l t h o u g h . t h e y h a d a g o o d b a n d p a s s , d i f f i c u l t i e s were e n c o u n t e r e d when t h e y w e r e o v e r l o a d e d w i t h v e r y l a r g e i n p u t p u l s e s . C o n s e q u e n t l y a m p l i -f i e r s w e r e b u i l t b a s e d o n t h e d e s i g n o f t h e s e c o n d r i n g o f t h r e e u s e d i n t h e 1444 f a s t a m p l i f i e r ^ d e s i g n e d a t C h a l k . R i v e r , b y N.F. Moody a n d c o - w o r k e r s . R e f e r e n c e c a n be made t o N a t i o n a l R e s e a r c h C o u n c i l p u b l i c a t i o n s f o r t h e p r i n c i p l e s o f o p e r a t i o n o f t h i s a m p l i f i e r . T h e . a m p l i f i e r s b u i l t by t h e a u t h o r c o n s i s t e d o f a s i n g l e r i n g o f t h r e e , w i t h f e e d b a c k f r o m t h e l a s t t u b e t o t h e f i r s t , p l u s a f i n a l t u b e w i t h c a t h o d e f o l l o w e r a n d anode f o l l o w e r o u t p u t c o n n e c t i o n s . The g a i n , o f t h e w h o l e a m p l i f i e r s y s t e m was a b o u t 1200 a t 1 Mc. The r e s p o n s e o f t h e s y s t e m was f r o m a b o u t 10 K c . t o 8 Mc. (1/2 g a i n p o i n t s ) w i t h - s o m e p e a k i n g a t a b o u t 7 Mc. The o u t p u t p u l s e s r o s e a t a b o u t 100 v o l t s p e r m i c r o s e c o n d w h i c h means t h a t t h e y r e a c h e d t h e d i s c r i m i n a t i o n # T h e s e a m p l i f i e r s a r e now a v a i l a b l e c o m m e r c i a l l y f r o m t h e N o r t h e r n E l e c t r i c Company, B e l l e v i l l e , O n t a r i o . 1 6 - N.F. Moody a n d W.D. H o w e l l , N.R.C. R e p o r t 1M-8 -- L i n e a r A m p l i f i e r Type AEP 1 4 4 4 . - 3 9 -6 A H 6 6AK5 6AH6 6ACT7 +300V O u t p u t s G a i n = 500 F a s t A m p l i f i e r F i g u r e 15 - 4 0 -l e v e l o f t h e c o i n c i d e n c e m i x e r (4 v o l t s ) i n l e s s t h a n . 0 . 0 5 m i c r o s e c o n d s a f t e r t h e s t a r t o f t h e p u l s e . The c o i n c i d e n c e m i x e r a c c e p t e d a l l p u l s e s w h i c h b e f o r e a m p l i f i c a t i o n r a n g e d f r o m 1 v o l t t o 4 m i l l i v o l t s . The a m p l i f i e r s y s t e m s a t i s f a c t -o r i l y c o p e d w i t h t h e s e p u l s e s w h i c h d i f f e r e d i n a m p l i t u d e by a f a c t o r o f 2 5 0 . 1N34 d i o d e c l i p p e r s w e r e u s e d t o p r e v e n t o v e r s h o o t i n g . The l a r g e s t p u l s e s w e r e l e n g t h e n e d t o 1 m i c r o -s e c o n d a n d h a d a maximum a m p l i t u d e o f 40 v o l t s a t t h e n e g a t i v e o u t p u t . d) C o i n c i d e n c e M i x e r - - C i r c u i t d i a g r a m o n page 4 1 . The c o i n c i d e n c e m i x e r was o f a w e l l known t y p e c o n s i s t i n g o f a. u n i v i b r a t o r a t t h e i n p u t o f e a c h c h a n n e l t o s t a n d a r d i z e t h e p u l s e s w h i c h a r e t h e n d i f f e r e n t i a t e d a n d f e d t o a R o s s i c i r c u i t . A s m a l l p o r t i o n o f t h e u n i v i b r a t o r p u l s e s was t a p p e d o f f , a m p l i f i e d a n d u s e d f o r m o n i t o r i n g t h e s i n g l e c h a n n e l s . The s i n g l e c h a n n e l r a t e s a r e n e c e s s a r y f o r m a k i n g d e a d t i m e a n d r e s o l v i n g t i m e c o r r e c t i o n s t o t h e c o i n c i d e n c e r a t e . The l a r g e s t d e a d t i m e i n e a c h c h a n n e l was s e t a t a b o u t 17 m i c r o -s e c o n d s b y t h e u n i v i b r a t o r a c t i o n t i m e . T h i s i s c o n s i d e r a b l y l o n g e r t h a n t h e l e n g t h . o f t h e l o n g e s t i n p u t . p u l s e s f r o m t h e a m p l i f i e r s ( l m i c r o s e c o n d ) b u t was c o n s i d e r e d n e c e s s a r y t o e n s u r e t h a t no e x t r a n o i s e p u l s e s " r o d e i n " o n t h e t a i l s o f l a r g e i n p u t p u l s e s . C o i n c i d e n c e o u t p u t p u l s e s w e r e s e l e c t e d b y a t h i r d u n i v i b r a t o r whose s e n s i t i v i t y c o u l d be c h a n g e d by a p o t e n t i o m e t e r a s shown i n t h e c i r c u i t d i a g r a m . T h i s c o n t r o l l e d t h e r e s o l v i n g t i m e o v e r a s m a l l r a n g e . The m a i n c o n t r o l o n t h e - 4 2 -r e s o l v i n g t i m e was v i a t h e d i f f e r e n t i a t i n g t i m e c o n s t a n t R6 i n e a c h c h a n n e l ; i n s t e a d o f t h e u s u a l f i x e d c o n d e n s e r s a t C, v a r i a b l e c e r a m i c t r i m m e r c o n d e n s e r s w ere e m p l o y e d i n o r d e r t o a d j u s t t h e m i x e r f o r minimum u s e f u l r e s o l v i n g t i m e . The r e s o l v i n g t i m e must be a s s m a l l a s p o s s i b l e t o k e e p t h e a c c i d e n t a l c o i n c i d e n c e r a t e (A = 2N]_N2l") l o w , b u t must n o t be so s m a l l t h a t t r u e c o i n c i d e n c e s a r e l o s t . The m e t h o d o f l i n i n g up t h e m i x e r was a s f o l l o w s . F i r s t , two 6 S J 7 R o s s i t u b e s w e re c h o s e n w i t h , a s n e a r l y a s p o s s i b l e t h e same m u t u a l t r a n s c o n d u c t a n c e . The d i s c r i m i n a t i o n l e v e l s w e r e s e t a t 4 v o l t s o n b o t h c h a n n e l s by t h e u n i v i b r a t o r b i a s c o n t r o l s . T h e n n e g a t i v e p u l s e s f r o m c h a n n e l s 2 a n d 3 o f t h e t r i p l e p o p p e r (See A p p e n d i x I I I ) w e r e f e d i n t o t h e two h e a d a m p l i f i e r s a n d t h e p u l s e s w e r e o b s e r v e d a t t h e R o s s i p l a t e s u s i n g t h e 1 m i c r o -s e c o n d sweep o f t h e ''.Tektronix o s c i l l o s c o p e w i t h t h e l o w c a p a c i t y p r o b e . C o n d e n s e r s C were a d j u s t e d t o g i v e p u l s e s a t t h e R o s s i p l a t e s w h i c h w e r e o f t h e same l e n g t h f r o m b o t h c h a n n e l s a n d a l i t t l e l o n g e r t h a n t h e d e s i r e d r e s o l v i n g t i m e . T h e n t h e o s c i l l o -s c o p e was u s e d t o o b s e r v e t h e m i x e d o u t p u t s o f c h a n n e l s 2 a n d 3 o n t h e t r i p l e p o p p e r . A s t h e d e l a y o f t h e p u l s e i n one c h a n n e l w i t h r e s p e c t t o t h a t i n t h e o t h e r c h a n n e l i s v a r i e d b y t h e p o p p e r no c o i n c i d e n c e s s h o u l d be o b s e r v e d e x c e p t when t h e two p u l s e s a s o b s e r v e d o n t h e o s c i l l o s c o p e a r e w i t h i n a p p r o x i m a t e l y h a l f t h e d e s i r e d r e s o l v i n g t i m e o f e a c h o t h e r , w i t h t h e c o n t r o l T s e t a t a m i d d l e v a l u e . A l s o t h e s y s t e m s h o u l d be p e r f e c t l y s y m m e t r i c a l t h a t i s c o i n c i d e n c e s s h o u l d c e a s e f o r e x a c t l y t h e same d e l a y b e t w e e n p u l s e s w h e t h e r t h e p u l s e i n c h a n n e l one i s b e f o r e o r a f t e r -43-t h a t i n c h a n n e l t w o . I f t h i s was n o t t h e c a s e , i t was made so b y a d j u s t i n g t h e v a l u e o f C i n one c h a n n e l o r t h e o t h e r ; i n c r e a s -i n g C i n one c h a n n e l , i n c r e a s e s t h e l e n g t h o f t h e p u l s e f r o m t h a t c h a n n e l o n t h e R o s s i s t a g e . When t h i s was c o m p l e t e d a l l d e l a y s i n t r o d u c e d i n t h e l e a d s o r a m p l i f i e r s y s t e m s w e r e comp-e n s a t e d f o r by t h e RC t i m e c o n s t a n t s b e f o r e t h e R o s s i s t a g e was r e a c h e d . F o r t h e a n g u l a r c o r r e l a t i o n m e a s u r e m e n t s as. s h o r t a r e s o l v i n g t i m e a s p o s s i b l e was r e q u i r e d w h i c h d i d n o t r e s u l t i n t h e l o s s o f t r u e c o i n c i d e n c e p u l s e s a n d d i d n o t s a c r i f i c e s t a b i l i t y . A f t e r m a k i n g t h e w h o l e s y s t e m s y m m e t r i c a l a s o u t l i n e d a b o v e a c u r v e was made o f r e s o l v i n g t i m e , T , v e r s u s d i a l r e a d i n g o f c o n t r o l T. (See page 44). The r e s o l v i n g t i m e was m e a s u r e d b y n o t i n g how f a r a p a r t t h e two i n p u t p u l s e s h a d t o be i n o r d e r t o j u s t s t o p t h e c o i n c i d e n c e c o u n t e r . Some o f t h e 7J* v a l u e s were c h e c k e d by m e a s u r i n g t h e a c c i d e n t a l - c o i n c i d e n c e r a t e , A , when u n c o r r e l a t e d random p u l s e s w e re f e d i n t o c h a n n e l s 1 a n d 2 a t r a t e s a n d N g r e s p e c t i v e l y . T h e n t h e w e l l known f o r m u l a f o r TJ" g i v e s , "T = A/2N, N j _ . The a g r e e m e n t was q u i t e s a t i s f a c t o r y a n d so t h e e a s i e r t r i p l e p u l s e r m e t h o d was u s e d t o o b t a i n t h e c u r v e s shown o n page 44. A c u r v e o f c o i n c i d e n c e c o u n t i n g r a t e v e r s u s d i a l s e t t i n g o f T.was t a k e n when some r a d i o a c t i v e s o u r c e w h i c h g i v e s o f f c o i n c i d e n t Y - r a y s , s u c h . a s C o ^ o r Z n ^ ( 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 ^ ' ' ' ) was p l a c e d b e t w e e n t h e c o u n t e r s . . A s shown o n t h e g r a p h o n page 44, t h i s c u r v e d r o p s r a p i d l y a f t e r a d i a l s e t t i n g o f 7 c o r r e s p o n d i n g t o a 7~ o f 0.10 m i c r o s e c o n d s . 17- K.C. Mann, D. R a n k i n a n d P . N . D a y k i n , P h y s . Rev., 76,1719 (1949), -44-F i g u r e 17 -45-T h i s i s the T v a l u e at which t r u e c o i n c i d e n c e s b e g i n to be l o s t and i t i s i n t e r e s t i n g t o note t h a t i t i s j u s t twice the time r e q u i r e d f o r the a m p l i f i e r p u l s e s to r i s e to the p o i n t where they t r i g g e r the u n i v i b r a t o r i n the c o i n c i d e n c e mixer. This i s the r e s u l t expected and i t a c t s as. a check on the apparatus. For the experiment, the d i a l was set a t about 5.5 g i v i n g a r e s o l v i n g time 0.15 microseconds at which no t r u e c o i n c i d e n c e s should be l o s t . C a r e f u l checks made at the b e g i n n i n g and end of the esperiment showed that the accurate r e s o l v i n g time was 0.145 microseconds. The procedure o u t l i n e d above may seem unduely complicated but as a r e s u l t of i t the r e s o l v i n g time was decreased by a f a c t o r of two over t h a t u s u a l l y o b t a i n e d w i t h t h i s type of c i r c u i t and i n the o p i n i o n of the author the r e l i a b i l i t y and s t a b i l i t y gained are worth the added e f f o r t . The t r i p l e popper was also, used to determine the dead times of the two s i n g l e channels ( "t» and 'Z* ) and of the c o i n c i d e n c e channel ( T l ) . To measure the dead time of a s i n g l e channel mixed p u l s e s from channels 2 and 3 of the t r i p l e , popper were f e d i n t o the h e a d . a m p l i f i e r and the delay time between the p u l s e s as observed on the T e k t r o n i x o s c i l l o s c o p e was decreased vjust u n t i l the two p u l ses were counted as one. T h i s delay time i s equal to the dead time of the channel. S i m i l a r measurements gave the c o i n c i d e n c e channel dead time. The measured dead times are l i s t e d below: = 18 microseconds ^ r = 16 microseconds "£l = 73 microseconds. -46-e) C o u n t e r E f f i c i e n c i e s f o r 1 Mev. Y Rays As a c h e c k o n t h e c o u n t e r s i t i s o f i n t e r e s t t o m e a s u r e t h e i r e f f i c i e n c i e s a n d compare t h e r e s u l t w i t h t h e t h e o r e t i c a l e f f i c i e n c y t o be e x p e c t e d o n t h e b a s i s o f t h e s t o p p i n g p o w e r o f t h e s c i n t i l l a t i o n c r y s t a l . T h e o r e t i c a l e f f i c i e n c i e s were c a l c u l a t e d o n t h e b a s i s o f t h e K l e i n N i s h i n a f o r m u l a : G^cm 2) p e r e l e c t r o n = 2TC r e 2 ( l + a J" 2(l+a) _ l l n ( l + 2a) 1 a 2 [ 1 + 2a a • + _1_ l n ( l + 2 a ) _ 1 + 3a 2a ( l + 2 a ) 2 w h e r e a = h "0/mc2 a n d r e = e 2 / m c 2 . F o r 0.51 Mev Y - r a y s , (7^  =--2.8 x 10~ 2 ^ c m 2 ( a n n i h i l a t i o n r a d i a t i o n ) F o r 1.2 Mev Y - r a y s , (Tc= 1.92 x 1 0 " 2 5 c m 2 ( A v e r a g e C o 6 0 Y r a y ) . The number o f e l e c t r o n s , n, p e r c u b i c c e n t i m e t e r i s f o u n d f o r a n t h r a c e n e (^-^H Q) o n t h e b a s i s o f t h e d e n s i t y (1.25 gm/c.c.) a n d t h e m o l e c u l a r w e i g h t ( 1 7 8 . 2 ) . T h e n t h e f r a c t i o n o f Y - r a y s w h i c h i n t e r a c t w i t h a t h i c k n e s s , x : , o f c r y s t a l i s g i v e n b y : E f f i c i e n c y = e = 1 - e " n ^ ~ c x F o r a 1 i n c h t h i c k n e s s , we g e t , f o r 0 . 5 1 Mev Y's e = 25% a n d f o r 1.2 Mev Y's e = 17-5% . E x p e r i m e n t a l e f f i c i e n c i e s s h o u l d be somewhat h i g h e r t h a n t h e s e due t o t h e c o n t r i b u t i o n o f t h e p h o t o e l e c t r i c e f f e c t , e s p e c i a l l y f o r s o f t e r Y r a y s . B u t due t o t h e f a c t t h a t some o f t h e - 4 7 - ' Compton e v e n t s i m p a r t s u c h a s m a l l amount o f e n e r g y t o t h e c r y s t a l t h a t no c o u n t i s o b t a i n e d , t h e e f f i c i e n c y may be somewhat l o w e r . T h i s - a l s o w i l l be e s p e c i a l l y t r u e f o r s o f t e r Y r a y s . ftf) F o r t h e c a s e o f Co Y - r a y s , t h e s e r e s u l t s c a n be e x p e r i m e n t a l l y c h e c k e d u s i n g c o i n c i d e n c e c o u n t i n g w i t h o u t 60 h a v i n g a s o u r c e o f . k n o w n s t r e n g t h . Co h a s t h i s v e r y u s e f u l p r o p e r t y b e c a u s e i t d e c a y s by B~ e m i s s i o n f o l l o w e d by two Y r a y s o f a l m o s t t h e same e n e r g y ( 1 . 1 7 a n d . 1 . 3 3 M e v . ) . I f we -i o assume t h a t t h e two Y r a y s a r e n o t a n g u l a r l y c o r r e l a t e d a n d t h a t t h e c o u n t e r s h a v e t h e same e f f i c i e n c y f o r b o t h 1.1 Mev. a n d 1 . 3 / q u a n t a , t h e n a s t h e r e s u l t o f a c o i n c i d e n c e c o u n t w i t h s o u r c e a n d c o u n t e r s a r r a n g e d a s i n F i g u r e 18, we g e t : N^ = c o u n t i n g r a t e i n c h a n n e l 1 = 2N 0J]_ 1 Ng = c o u n t i n g r a t e i n c h a n n e l 2 = .2Nu3 2 e 2 2 N Q = t r u e c o i n c i d e n c e c o u n t i n g r a t e = 2Nu>|kJ2 el e2 ••• 3 A = a c c i d e n t a l c o u n t i n g r a t e = 2 ^ ^ ? ^ = 8N c j - j t J 2 e l e 2 ... 4 c o u n t e r 1 s o u r c e c o u n t e r 2 F i g u r e 1 8 18- T h i s a s s u m p t i o n i s n o t s t r i c t l y t r u e - See B r o d y a n d D e u t s c h P h y s . Rev., 7 4 , 1 5 4 1 ( 1 9 4 8 ) . -48-N c ' = m e a s u r e d c o i n c i d e n c e c o u n t i n g r a t e .= N + A T h e n N Q = N c ' - A. where u>'s a r e t h e s o l i d a n g l e s s u b t e n d e d b y t h e c o u n t e r s a t t h e s o u r c e , e's a r e c o u n t e r e f f i c i e n c i e s , a n d N i s t h e s o u r c e s t r e n g t h i n d i s i n t e g r a t i o n s p e r s e c o n d . Then N _ N^Ng 5 2 N C ®1 = J k Nu^ 6 Nu^ 7 T h a t i s we g e t t h e s o u r c e s t r e n g t h a n d t h e e f f i c i e n c i e s o f t h e c o u n t e r s f r o m t h i s s i m p l e e x p e r i m e n t . The s i g n a l t o n o i s e r a t i o i s N c/A = 1/4N21. T h i s shows t h a t .we s h o u l d .use a s h o r t r e s o l v i n g t i m e a n d a weak s o u r c e . The. u s e o f a weak s o u r c e r e q u i r e s t h a t l a r g e s o l i d a n g l e s be u s e d s o t h a t s u f f i c i e n t l y h i g h c o u n t i n g r a t e s w i l l be o b t a i n e d . T h e r e a r e , h o w e v e r , some d i f f i c u l t i e s n o t t a k e n i n t o a c c o u n t i n t h e a b o v e s i m p l e t r e a t m e n t . As a c o n s e q u e n c e o f l a r g e . , s o l i d a n g l e s ( a c h i e v e d b y p u t t i n g t h e c o u n t e r s c l o s e t o t h e s o u r c e ) t h e s o l i d a n g l e s u b t e n d e d a t one c o u n t e r by t h e o t h e r , i s f a i r l y l a r g e a n d t h e p r o b a b i l i t y o f a quantum b e i n g b a c k s c a t t e r e d f r o m one c o u n t e r i n t o t h e o t h e r , a n d p r o d u c i n g a c o i n c i d e n c e c o u n t becomes r a t h e r h i g h . C a l c u l a t i o n s b a s e d o n t h e d i f f e r e n t i a l c r o s s s e c t i o n f o r s c a t t e r i n g ^ show t h a t t h e r a t i o o f t h e p r o b a b i l i t y o f a c o i n c i d e n c e c o u n t due t o b a c k 19- W. H e i t l e r , The Quantum T h e o r y o f R a d i a t i o n , O x f o r d , 1944,P 155. -49-s c a t t e r to the p r o b a b i l i t y of a t r u e c o i n c i d e n c e count can e a s i l y be as h i g h as 20% which would cause a s e r i o u s e r r o r i n any e f f i c i e n c y or source s t r e n g t h measurements based on the procedure o u t l i n e d above. Another d i f f i c u l t y i s t hat an a c c u r -ate v a l u e f o r the e f f e c t i s not e a s i l y c a l c u l a b l e s i n c e the b a c k - s c a t t e r e d . quantum i s of a d i f f e r e n t energy from the o r i g i n a l one, and the v a r i a t i o n of counter e f f i c i e n c y w i t h Y ray energy i s unknown. For example, the quantum which i s produced by s c a t t e r i n g a 1 Mev. Y-ray through an angle n has an energy of 0.2 Mev. counter 1 source l e a d absorber The e f f e c t of b a c k - s c a t t e r c o u l d be e l i m i n a t e d by u s i n g geometry l i k e t h a t shown i n f i g u r e 19 where s u f f i c i e n t l e a d absorber i s used to stop quanta s c a t t e r e d from one counter to the o t h e r . U n f o r t u n a t e l y , t h i s I n v o l -ves another d i f f i c u l t y . Quanta F i g u r e 19 s c a t t e r e d by the l e a d absorber may enter the counters and t h i s makes the e f f e c t i v e s o l i d angle l a r g e r than the g e o m e t r i c a l s o l i d angle by an.unknown amount. T h i s i n t r o d u c e s an e r r o r i n the e f f i c i e n c y f a c t o r s as g i v e n by equations 6 and 7, a l t h o u g h no e r r o r i s i n t r o d u c e d i n the source s t r e n g t h d e t e r m i n a t i o n as--g i v e n by e q u a t i o n 5 s i n c e i t does not depend onc.a knowledge of the s o l i d a n g l e . Consequently, the e f f i c i e n c y problem can be s o l v e d as f o l l o w s . F i r s t f i n d the source s t r e n g t h , N, u s i n g geometry as shown i n f i g u r e 19 and equation 5 and then use a - 5 0 -g e o m e t r y where no s c a t t e r i n g c a n o c c u r a n d u s e e q u a t i o n s 1 a n d 2 t o g e t t h e e f f i c i e n c i e s o f t h e c o u n t e r s . s o u r c e h o l d e r l e a d c o l l i m a t o r c o u n t e r #1 c o u n t e r #2 A s e c o n d way o f s o l v i n g t h e p r o b l e m i s t o u s e a l e a d c o l l i m a t o r a s shown i n f i g u r e 20 t o r e d u c e t h e s o l i d a n g l e f r o m one c o u n t e r t o t h e o t h e r w h i l e k e e p i n g t h e s o l i d a n g l e s f r o m t h e c o u n t e r s t o t h e s o u r c e a s l a r g e a s p o s s i b l e . T h i s t y p e o f g e o m e t r y s h o u l d p r o d u c e l e s s s c a t t e r i n g f r o m t h e l e a d i n t o t h e c o u n t e r s t h a n t h e g e o m e t r y o f f i g u r e . ; 1 9 . T h i s f a c t was v e r i f i e d by e x p e r i m e n t . Con-s e q u e n t l y e q u a t i o n s 6 a n d 7 s h o u l d F i g u r e 20 g i v e r e a s o n a b l e v a l u e s o f c o u n t e r e f f i c i e n c y . . A l e a d c o l l i m a t o r s u c h a s i s shown i n f i g u r e 20 was c o n s t r u c t e d a n d t h e f o l l o w i n g e f f i c i e n c i e s a n d s o u r c e s t r e n g t h w e r e o b t a i n e d : i ) e 1 = 2 0 % e 2 = 2 1 % N = 4 . 7 x 1 0 4 d i s i n t e g r a t i o n s p e r s e c A l s o m e a s u r e m e n t s w e r e made b y t h e f i r s t m e t h o d o u t l i n e d o n page 4 9 w i t h t h e f o l l o w i n g r e s u l t s : i i ) e i = 1 8 % e 2 = 1 9 % N = 4 . 2 x 1 0 ^ d i s i n t e g r a t i o n s p e r s e c . fad A f u r t h e r c h e c k was made w i t h a 1 r u t h e r f o r d Co s t a n d a r d s o u r c e . S i n c e no c a r e was t a k e n t o c o l l i m a t e t h e beam, t h e f o l l o w i n g r e s u l t s b a s e d o n s i n g l e c h a n n e l c o u n t i n g r a t e s a r e c e r t a i n l y h i g h due t o s c a t t e r i n g . - 5 1 -i i i ) e 1 - 25% e 2 = 27%. I n t h e o p i n i o n o f t h e a u t h o r , t h e r e s u l t s ( i ) a r e s l i g h t l y h i g h e r t h a n ( i i ) b e c a u s e o f some s c a t t e r i n g f r o m t h e l e a d , b u t n o t due t o b a c k - s c a t t e r . B a c k - s c a t t e r t h r o u g h t h e c e n t r a l h o l e was n e g l i g i b l e . . The amount o f t h e b a c k - s c a t t e r was c h e c k e d by t a k i n g a s e t o f m e a s u r e m e n t s w i t h t h e g e o m e t r y shown i n f i g u r e : 2 0 , a n d t h e n r e p e a t i n g t h e m e a s u r e m e n t s w i t h 'the s o u r c e a n d c o u n t e r s i n t h e same p o s i t i o n s ? ; b u t w i t h o u t t h e l e a d c o l l i m a t o r . The c o i n c i d e n c e r a t e was 3 0 % h i g h e r i n t h e l a t t e r c a s e due t o toack-scatter. T h i s i s h i g h e r t h a n t h e 2 0 % f i g u r e w h i c h was o b t a i n e d o n t h e b a s i s o f t h e o r e t i c a l c a l c u l a t i o n s . The r e a s o n s u g g e s t e d f o r t h i s d i s c r e p a n c y i s t h a t t h e e f f i c i e n c y f o r t h e b a c k - s c a t t e r e d q u a n t a (0.2 Mev.) may be h i g h e r t h a n f o r t h e i n c i d e n t (1 Mev.) q u a n t a . T h e s e e f f i c i e n c i e s were, a s s u m e d e q u a l f o r t h e t h e o r e t i c a l c a l c u l a t i o n . The Compton c r o s s - s e c t i o n i s g r e a t e r f o r t h e s o f t e r q u a n t a a n d a l s o t h e p h o t o e l e c t r i c e f f e c t c o n t r i b u t e s a t t h e s e l o w e n e r g i e s . I f t h i s i s s o , i t i s c e r t a i n l y s a f e t o assume t h a t t h e r e i s a l s o a f a i r l y h i g h e f f i c i e n c y f o r t h e 0.51 Mev. a n n i h i l a t i o n Y r a y s . The e f f i c i e n c i e s ( i i ) w h i c h a r e c o n s i d e r e d t o be r e a s o n a b l y a c c u r a t e a r e s t i l l s l i g h t l y h i g h e r t h a n t h e t h e o r e t i c a l v a l u e o f 17 . 5 % f o r Co^. 0 Y r a y s . The s m a l l d i f f e r e n c e may h a v e no s i g n i f i c a n c e due t o e x p e r i m e n t a l e r r o r s . The d i f f e r e n c e c a n n o t be a c c o u n t e d f o r b y t h e p h o t o e l e c t r i c e f f e c t s i n c e a r o u g h c h e c k b a s e d on t h e p h o t o e l e c t r i c c r o s s - s e c t i o n c a l c u l a t e d b y Hulme a n d o t h e r s 2 0 i n d i c a t e s t h a t t h i s e f f e c t c o u l d i n c r e a s e t h e e f f i c i e n c y b y o n l y l / 2 $ .  2 0 - Hulme, M c D o u g a l l , B u c k i n g h a m a n d F o w l e r , P r o c .Roy .Soc .A14-9 131 ( 1 9 3 5 ) . -52-f ) Zn D A n n i h i l a t i o n R a d i a t i o n 65 The r a d i a t i o n s f r o m Zn h a v e b e e n s t u d i e d , b y t h e p - r a y 17 g r o u p a t t h i s u n i v e r s i t y a n d a s a r e s u l t o f t h e s e i n v e s t i g a -t i o n s i t was e s t i m a t e d t h a t t h e p o s i t r o n a c t i v i t y was j u s t l e s s t h a n 1% o f t h e 1.14 Mev. Y r a y a c t i v i t y w h i c h p r e s u m a b l y f o l l o w s K c a p t u r e . As a f i n a l c h e c k o n t h e a p p a r a t u s , a n a n g u l a r c o r r e l a t i o n m easurement was done o n a s a m p l e o f Z n ^ , ( a b o u t 0.2 mc.) i n o r d e r t o s e e w h e t h e r t h e p r o f i l e h a d t h e same shape a s p r e d i c t e d by t h e c a l c u l a t i o n s a n d t o c h e c k , t h e a b o v e f i g u r e o f l e s s t h a n 1% p + e m i s s i o n . . The c o u n t e r s ' w e r e s e t 30 c e n t i m e t e r s f r o m t h e s o u r c e a n d a n a n g u l a r c o r r e l a t i o n c u r v e was t a k e n . T h e n t h e e x p e r i m e n t was r e p e a t e d w i t h t h e c o u n t e r s 100 c e n t i m e t e r s f r o m t h e s o u r c e . I n b o t h c a s e s a p e a k was o b t a i n e d c o r r e s p o n d i n g t o t h e 180° a n g u l a r c o r r e l a t i o n , o f t h e a n n i h i l a t i o n r a d i a t i o n a n d t h i s p e a k h a d a sh a p e i n s a t i s f a c t o r y a g r e e m e n t w i t h t h e s h a p e s o f t h e c a l c u l a t e d c u r v e s o n page 29* F o r t h e c a s e o f t h e 100 cm. s e p a r a t i o n b e t w e e n s o u r c e a n d c o u n t e r s d e f i n i t e e v i d e n c e f o r _ o t h e r t h a n 180° a n g u l a r c o r r e l a t i o n was o b t a i n e d i n t h e f o r m o f a s m a l l t a i l t o t h e c u r v e b u t t h e a c c u r a c y was not. g r e a t e n o u g h t o make a n e s t i m a t e o f t h e mean c e n t r e o f mass momentum o f a n n i h i l a t i n g p a i r s i n Z i n c I f we assume t h a t t h e Y r a y e f f i c i e n c i e s a r e t h e same a s t h e t h e o r e t i c a l l y c a l c u l a t e d v a l u e s o n page 4 6 , we c a n make a n e s t i m a t e o f t h e r a t i o o f p + a c t i v i t y t o t h e 1.14 Mev. Y r a y a c t i v i t y a s f o l l o w s : -53-S u p p o s e t h e s o u r c e g i v e s N a p o s i t r o n s p e r s e c o n d ( t h a t i s 2 N a a n n i h i l a t i o n q u a n t a ) a n d Ny 1.14 Mev. Y r a y s p e r s e c o n d . Then t h e c o u n t i n g r a t e s i n c o u n t e r s 1 a n d 2 w l l l . b e : N x = w ( N Y e Y 1 + 2 N a e & 1 ) 1 N 2 = w ( N Y e Y 2 + 2 N a e a 2 ) 2 where w = t h e s o l i d a n g l e s u b t e n d e d by t h e c o u n t e r s a t t h e s o u r c e e Y = t h e c o u n t e r e f f i c i e n c y f o r 1.14 Mev. Y r a y s e„= t h e c o u n t e r e f f i c i e n c y f o r 0.51 Mev. a n n i h i l a t i o n q u a n t a . I f t h e c o u n t e r s a r e e x a c t l y i n l i n e w i t h t h e s o u r c e a n d we assume 180° a n g u l a r c o r r e l a t i o n f o r t h e a n n i h i l a t i o n . q u a n t a ^ t h e n t h e c o i n c i d e n c e c o u n t i n g r a t e w i l l be g i v e n b y N c = 2 N aw e a l e a 2 • 3 F r o m 3 , we g e t N a = N c 4 2 w e a l e a 2 C o m b i n i n g 4 w i t h 1 a n d . w i t h .2 we g e t Ny = N l e a 2 ~ N c _ N 2 e a l - N c  e a 2 e Y l W e a l e Y 2 w From 4 a n d 5, we g e t t h e r a t i o = N 0 . e y 2 W Y 2 e a 2 ( N 2 e a l - N 0 ) A s s u m i n g e f f i c i e n c i e s o f 18% f o r t h e 1.14 Mev. Y r a y s a n d 25% f o r t h e 0.51 Mev. Y r a y s (See page 4 6 ) , t h i s r a t i o c a n be c a l c u l a t e d i n t e r m s o f t h e c o i n c i d e n c e c o u n t i n g r a t e ( N c ) a t t h e p e a k o f t h e p r o f i l e a n d t h e s i n g l e c h a n n e l c o u n t i n g r a t e ( N 2 ) , # T h i s a s s u m p t i o n i s o n l y j u s t i f i e d i f t h e a n g u l a r a p e r t u r e a t t h e c o u n t e r i s l a r g e r t h a n t h e a n g l e o f d e p a r t u r e f r o m c o l l i n e a r i t y o f t h e a n n i h i l a t i o n quanta.'.-F o r 30 cm. s o u r c e t o c o u n t e r d i s t a n c e , t h i s g a v e N a / N Y = 0.0078 o r 1/130 6 w h i c h i s l e s s t h a n 1%, i n r o u g h a g r e e m e n t w i t h t h e v a l u e p r e d i c t e d b y t h e p - r a y g r o u p . T h i s a g r e e m e n t c a n be c o n s i d e r e d t o be a c h e c k o n t h e Y - r a y e f f i c i e n c i e s a s s u m e d a b o v e . F o r 100 cm. s o u r c e t o c o u n t e r d i s t a n c e , t h i s g a v e . N a / N Y = 0.0052 o r 1/190 7 T h i s i s q u i t e a b i t l e s s t h a n t h e r e s u l t g i v e n by 6. The r e a s o n i s t h a t t h e a s s u m p t i o n s t a t e d i n t h e f o o t n o t e , o n p a g e 53 i s n o t c o r r e c t here;. The a n g u l a r a p e r t u r e o f t h e c o u n t e r , w h i c h i s a b o u t t h r e e t i m e s s m a l l e r t h a n f o r t h e c a s e . o f 30 cm. s e p a r a t i o n i s s m a l l e r t h a n t h e s p r e a d i n a n g u e s o f t h e a n n i h i l a t i o n q u a n t a . T h i s i s b o r n e o u t by t h e f a c t t h a t d e f i n i t e e v i d e n c e f o r a t a i l t o t h e p r o f i l e c u r v e was o b t a i n e d f o r t h i s c a s e . I n s p i t e o f t h e l o w s o u r c e s t r e n g t h (0.2 mc. o r a p p r o x i m -a t e l y 0.002 mc. p o s i t r o n a c t i v i t y ) t h e r e s u l t s o b t a i n e d a b o v e show t h a t t h e a p p a r a t u s i s a t l e a s t r o u g h l y a m e n a b l e t o c a l c u l a t i o n s . On t h e b a s i s o f t h i s , t h e a p p a r a t u s was c o n s i d e r e d r e a d y f o r t h e a n g u l a r c o r r e l a t i o n e x p e r i m e n t : w h i c h i s d e s c r i b e d n e x t . - 5 5 -V. ANGULAR CORRELATION EXPERIMENTS a ) C o u n t i n g P r o c e d u r e The a p p a r a t u s was s e t up a s d e s c r i b e d i n p r e v i o u s s e c t i o n s w i t h t h e g e o m e t r y shown on page 3 0 . The m o t i o n o f c o u n t e r 1 was c o n t r o l l e d by a m i c r o s c o p e c a r r i a g e o n w h i c h t h e c o u n t e r was m ounted as shown i n t h e p h o t o g r a p h s ( p a g e s 17 a n d 3 2 ) . A l l s o u r c e s w e r e p r e p a r e d i n t h e f o r m o f m e t a l p l a t e s (Cu, Mg, Sn, a n d P t ) , w e i g h e d s a m p l e s i n p o w d e r e d f o r ( S , L I C 1 , C s C l , KC1, KF, a n d K I ) o r l i q u i d (Hg) b e f o r e t h e e x p e r i m e n t b e g a n . The a p p a r a t u s was t u r n e d o n some h o u r s b e f o r e t h e e x p e c t e d a r r i v a l t i m e o f t h e s o u r c e so t h a t a s t e a d y o p e r a t i n g c o n d i t i o n was r e a c h e d b e f o r e r e a d i n g s were s t a r t e d . D u r i n g t h i s warm up p e r i o d , t h e t i m e c o n s t a n t s o f t h e a p p a r a t u s w e r e c h e c k e d a n d b a c k g r o u n d n o i s e r e a d i n g s w e re t a k e n . A f t e r t h e s o u r c e a r r i v e d , t h e f o l l o w i n g c o u n t i n g p r o c e d u r e was f o l l o w e d f o r e a c h s o u r c e u s e d : i ) The p e a k o f t h e a n g u l a r d i s t r i b u t i o n c u r v e was l o c a t e d by f i v e t o t e n p o i n t s . The p e a k o f t h e c u r v e was n o t a t t h e same m o v a b l e c o u n t e r p o s i t i o n f o r a l l s o u r c e s s i n c e t h e s o u r c e s v a r i e d i n w i d t h , i i ) The m o v a b l e c o u n t e r was s h i f t e d f r o m t h e p e a k p o s i t i o n by t h e w i d t h o f t h e c o u n t e r c r y s t a l p l u s t h e w i d t h o f t h e s o u r c e a n d r e a d i n g s o n t h e t a i l o f t h e c u r v e w e r e t a k e n e v e r y f e w m i l l i m e t e r s f r o m t h e r e o u t u n t i l t h e c o u n t i n g r a t e became t o o l o w . -56-i i i ) I n o r d e r t o d e t e r m i n e t h e s h a p e o f t h e a n g u l a r c o r r e l a t i o n c u r v e i n t h e l e a s t p o s s i b l e t i m e , i t was n e c e s s a r y w h i l e t a k i n g m e a s u r e m e n t s o n a s o u r c e t o d e c i d e a t what f u r t h e r p o i n t s r e a d i n g s w e re r e q u i r e d . T h e r e f o r e , a s f a r a s p o s s i b l e c a l c u l a -t i o n s were done d u r i n g t h e e x p e r i m e n t . C o r r e c t i o n s w e r e p e r -f o r m e d f o r a c c i d e n t a l c o i n c i d e n c e s , d e a d t i m e l o s s e s , a n d d e c a y o f t h e s o u r c e . The m e t h o d u s e d was s i m i l a r t o t h a t d e s c r i b e d by 7 P.E. A r g y l e . E x c e p t i n a f e w c a s e s , no l o n g e r t h a n one h o u r was s p e n t i n d e t e r m i n i n g a n y one p o i n t ; b u t s e p a r a t e r e a d i n g s w e r e t a k e n a t l e a s t e v e r y f i f t e e n m i n u t e s s o t h a t e l e c t r o n i c f a i l u r e s c o u l d be d e t e c t e d q u i c k l y . I n t h e c a s e s o f p l a t i n u m a n d l i t h i u m c h l o r i d e , c o m p l e t e p r o f i l e c u r v e s f o r r e g i o n s i n s i d e a n d o u t s i d e t h e g e o m e t r y w e r e t a k e n f o r c o m p a r i s o n w i t h t h e t h e o r e t i c a l c a l c u l a t i o n s o f s e c t i o n I I I . The t i m e t a k e n t o do t h e a n g u l a r c o r r e l a t i o n e x p e r i m e n t s o n t h e e l e v e n m a t e r i a l s l i s t e d a b o v e was 75 h o u r s . A f t e r t h i s , t h e s o u r c e was l e s s t h a n 2 mc, t o o weak t o g e t a c c u r a t e r e s u l t s , so t h e c o u n t e r s were moved c l o s e r t o g e t h e r i n o r d e r t o do t h e a b s o r p t i o n e x p e r i m e n t s d e s c r i b e d i n A p p e n d i c e s I a n d I I . b) H e a l t h P r e c a u t i o n s The s o u r c e o n a r r i v a l h a d a t o t a l s t r e n g t h o f 100 mc a n d , t h e r e f o r e , some p r e c a u t i o n s were t a k e n t o p r o t e c t t h e o p e r a t o r s . T h e s e a r e l i s t e d b e l o w : i ) A l a r g e 1/4" l e a d s h i e l d was p l a c e d b e t w e e n t h e o p e r a t o r s 64 a n d t h e s o u r c e h o l d e r . Cu f o i l s n o t i n u s e w e r e k e p t i n -57-a l e a d c a s t l e . i i ) The p r e p a r a t i o n o f s o u r c e s was p e r f o r m e d b e h i n d a l e a d s h i e l d a n d t h e o p e r a t o r wore g l a s s e s t o s t o p t h e p r a d i a t i o n f r o m e n t e r i n g h i s e y e s . i i i ) A d i r e c t r e a d i n g h e a l t h s u r v e y m e t e r was u s e d t o p l o t o u t s a f e r e g i o n s i n t h e room a n d t o m o n i t o r s o u r c e p r e p a r a t i o n s . i v ) A l l who w o r k e d o n t h e e x p e r i m e n t wore f i l m b a d g e s o b t a i n e d f r o m t h e N a t i o n a l R e s e a r c h C o u n c i l . A f t e r t h e e x p e r i m e n t t h e s e w e re d e v e l o p e d b y t h e N . R . C . R a d i a t i o n B r a n c h a n d no o v e r e x p o s u r e s w e r e f o u n d . c ) S c a t t e r i n g c h e c k s The e f f e c t s o f s c a t t e r i n g c a n c a u s e l a r g e e r r o r s i n a n y c o i n c i d e n c e e x p e r i m e n t a s h a s b e e n d e m o n s t r a t e d i n s e c t i o n I V - e ( p a g e s 48 - 51). C o n s e q u e n t l y , a n i n v e s t i g a t i o n o f t h e e f f e c t 64 o f s c a t t e r i n g o n t h i s e x p e r i m e n t was made w h i l e t h e Cu a c t i v i t y was f a i r l y h i g h . L e s s t h a n two h o u r s w ere s p e n t o n t h i s so t h e s t a t i s t i c a l a c c u r a c y i s n o t great;'; T h i s i n v e s t i g a -t i o n shows t h a t t h e l i m i t t o t h i s e x p e r i m e n t i s . n o t s e t b y t h e b a c k g r o u n d n o i s e o r a c c i d e n t a l c o i n c i d e n c e r a t e b u t by t h e s c a t t e r i n g f r o m w a l l s , t a b l e s , e t c . . F o r t h e f i r s t c h e c k , t h e p l a t i n u m s o u r c e was u s e d a n d c o u n t e r number 1 ( m o v a b l e ) was p l a c e d a b o u t 5 cm. f r o m t h e p e a k o f t h e c u r v e . R e a d i n g s were t a k e n w i t h a n d w i t h o u t t h e l e a d a b s o r b e r shown i n f i g u r e 21, page 58. The c o i n c i d e n c e r a t e d e c r e a s e d b y a b o u t 20$ a n d t h e number 2 s i n g l e c h a n n e l r a t e by 4 0 $ when t h e a b s o r b e r was ,put i n . T h i s means t h a t a c o n s i d e r a b l e p o s i t i o n f o r s e c o n d check--58-/ / / / / W / / / a l u m i n u m s c a t t e r e r s o u r c e c o u n t e r 2 . - - - - ' p o s i t i o n f o r V- f i r s t c h e c k l e a d s h i e l d y / / y y y y / y y / y y y y y F i g u r e . 21 p r o p o r t i o n o f t h e s i n g l e c h a n n e l c o u n t i n g r a t e was due t o s c a t t e r e d q u a n t a a n d t h e b a c k g r o u n d c o i n c i d e n c e c o u n t due t o s c a t t e r e d q u a n t a was a b o u t a s l a r g e a s t h e a c c i d e n t a l c o i n c i d e n c e r a t e . F o r t u n a t e l y , t h i s b a c k g r o u n d , l i k e t h e a c c i d e n t a l c o i n c i d e n c e s , was n o t s e n s i t i v e t o t h e p o s i t i o n o f c o u n t e r number 1 s i n c e f o r t h e s m a l l a n g l e s i n v o l v e d t h e s c a t t e r i n g f r o m t h e b a c k w a l l a n d t a b l e s r e m a i n e d r o u g h l y c o n s t a n t . A c h e c k d i d show t h a t s c a t t e r i n g i n c r e a s e d c o n s i d e r a b l y when c o u n t e r number 1 was moved f a r e n o u g h t h a t t h e "beam" o f q u a n t a , c o i n c i d e n t w i t h t h o s e p a s s i g g t h r o u g h i t . , s t r u c k t h e p r o j e c t i n g s e c t i o n o f w a l l a n d l o w a n g l e s c a t t e r i n g i n t o c o u n t e r 2 became p o s s i b l e . The d i f f e r e n t i a l c r o s s - s e c t i o n f o r s c a t t e r i n g o f 0.5 Mev. q u a n t a i n c r e a s e s r a p i d l y f o r s c a t t e r i n g a n g l e s b e l o w 21 60°. D u r i n g t h e a n g u l a r c o r r e l a t i o n e x p e r i m e n t s , c o u n t e r number 1 was n o t moved f a r e n o u g h f r o m t h e c e n t r e f o r t h i s e f f e c t t o i n t e r f e r e w i t h t h e r e s u l t s . S c a t t e r i n g may h a v e i n c r e a s e d t h e c o i n c i d e n c e r a t e s f o r p o i n t s a t t h e l a r g e s t a n g l e s u s e d b y 21- W. H e i t l e r , The Quantum Theory o f R a d i a t i o n , O x f o r d , 1944, p 156. - 5 9 -f i v e t o t e n p e r c e n t . T h i s i s n o t s e r i o u s s i n c e t h e s t a t i s t i c a l e r r o r s f o r most o f t h e s e e n d p o i n t s a r e o f t h e o r d e r o f 20%. A s e c o n d c h e c k c o n s i s t e d i n m o v i n g c o u n t e r 1 j u s t a l i t t l e "beyond t h e r e g i o n o f o v e r l a p b e t w e e n c o u n t e r s a n d s o u r c e a n d p l a c i n g a l u m i n u m s c a t t e r e r s i n t h e beam as .shown i n f i g u r e 2 1 , p age 5 8 . S u c h a s c a t t e r e r i n c r e a s e d t h e c o i n c i d e n c e r a t e by a s much as t e n p e r c e n t . From t h i s i t c a n be c o n c l u d e d t h a t t h e e f f e c t o f s c a t t e r i n g i n t h e a i r b e t w e e n c o u n t e r s was n e g l i g i b l e b u t t h a t t h e s c a t t e r i n g i n t h e s o u r c e c o u l d c a u s e a s m a l l amount o f b r o a d e n i n g o f t h e d i s t r i b u t i o n c u r v e s . No t h o r o u g h a n a l y s i s was made o f t h i s e f f e c t b u t r o u g h c a l c u l a t i o n s b a s e d o n t h e d i f f e r e n t i a l c r o s s - s e c t i o n f o r s c a t t e r i n g c o n f i r m t h a t i t i s s m a l l . T h e s e .show t h a t t o a f i r s t a p p r o x i m a t i o n t h e s c a t t e r e d i n t e n s i t y i s i n d e p e n d e n t o f a n g l e f o r s m a l l a n g l e s a n d t h e r e f o r e s h o u l d c o n t r i b u t e a c o n s t a n t b a c k g r o u n d f o r t h e a n g u l a r r e g i o n s t u d i e d . T h i s b a c k g r o u n d i s o f t h e o r d e r o f 1% o f t h e c o u n t i n g r a t e a t t h e f a r t h e s t o u t p o s i t i o n s w h i c h w e r e i n v e s t i g a t e d h e r e . T h i s i s s m a l l . c o m p a r e d w i t h t h e e x p e r i m e n t a l e r r o r s f o r t h e s e p o i n t s a n d w i l l h a v e . a v e r y s m a l l e f f e c t o n t h e d e t e r m i n a t i o n o f t h e s l o p e o f t h e t a i l o f t h e a n g u l a r c o r r e l a t i o n c u r v e . D e B e n e d e t t i a n d c o - w o r k e r s , r e a c h e d t h e same c o n c l u s i o n s a f t e r p e r f o r m i n g s c a t t e r i n g c h e c k s . - 6 0 -V I . EXPERIMENTAL RESULTS a) G e n e r a l When t h e e x p e r i m e n t a l r e a d i n g s w e re c o m p l e t e d , a l l . t h e c a l c u l a t i o n s w e r e r e p e a t e d t o o b t a i n g r e a t e r a c c u r a c y t h a n was p o s s i b l e d u r i n g t h e e x p e r i m e n t . The f i n a l , r e s u l t s a r e . shown i n t h e f o r m o f c u r v e s a s f o l l o w s : i ) F i g u r e 22 - A n g u l a r c o r r e l a t i o n o f a n n i h i l a t i o n r a d i a t i o n f r o m Mg, S, Cu, S n , P t , a n d Hg ( p u r e e l e m e n t s ) . i i ) F i g u r e 23 - A n g u l a r c o r r e l a t i o n o f a n n i h i l a t i o n r a d i a t i o n f r o m L i C l , KC1 a n d C s C l ( a l k a l i c h l o r i d e s ) . i i i ) F i g u r e 24 - A n g u l a r c o r r e l a t i o n o f a n n i h i l a t i o n r a d i a t i o n f r o m KF, KC1 a n d K I ( p o t a s s i u m h a l o g e n s ) . The s t a t i s t i c a l a c c u r a c y o f e a c h p o i n t b a s e d o n t h e number o f c o i n c i d e n c e s a n d t h e number o f a c c i d e n t a l c o i n c i d e n c e s i s shown by t h e s m a l l v e r t i c a l l i n e s t h r o u g h e a c h p o i n t . The edge o f t h e g e o m e t r y , i . e . t h e p o i n t a t w h i c h o v e r l a p b e t w e e n s o u r c e a n d c o u n t e r s e n d s , i s shown b y t h e v e r t i c a l c o l o u r e d l i n e f o r e a c h c u r v e . A c o n t i n u o u s c o l o u r e d l i n e i s d r a w n t h r o u g h e a c h c u r v e . A p p r o x i m a t i n g s t r a i g h t l i n e s a r e d r a w n i n b l a c k t h r o u g h t h e p a r t s o f t h e c u r v e s e x t e n d i n g b e y o n d t h e g e o m e t r y o r p e a k s e c t i o n s . The t a i l s o f some o f t h e a n g u l a r d i s t r i b u -t i o n c u r v e s a r e n o t s t r a i g h t . A n i n t e r p r e t a t i o n i n terms- o f mean c e n t r e o f mass momenta, i s g i v e n o n l y f o r t h o s e c a s e s w h ere t h e t a i l o f t h e c u r v e i s s t r a i g h t . Page 6 1 F i g u r e 22 A n g u l a r C o r r e l a t i o n o f A n n i h i l a t i o n R a d i a t i o n f r o m , S, Cu, S n , P t , a n d Hg. Page 62 F i g u r e 23 A n g u l a r C o r r e l a t i o n o f A n n i h i l a t R a d i a t i o n f r o m L i C l , KC1 a n d C s C l . Page F i g u r e 24 A n g u l a r C o r r e l a t i o n o f A n n i h i l a t i o n R a d i a t i o n f r o m E F , K C 1 , a n d K I . MADF IN U . S. K. -64-b) P u r e E l e m e n t s I n c a s e s w here t h e t a i l o f t h e c u r v e i s n o t s t r a i g h t a n d shows a d i s t i n c t b r e a k , (S a n d Sn) n o t one b u t two a p p r o x i m a t i n g s t r a i g h t l i n e s a r e d r a w n i n b l a c k , one f o r e a c h s e c t i o n . The c o p p e r , p l a t i n u m a n d m e r c u r y ( d o u b t f u l c a s e ) c u r v e s h a v e s t r a i g h t t a i l s , w i t h i n t h e s t a t i s t i c s , a n d t h e g e n e r a l s h a p e o f t h e c u r v e s i s . i n a g r e e m e n t w i t h t h e h y p o t h e s i s o f a s i m p l e e x p o n e n t i a l t y p e d i s t r i b u t i o n . T h i s c a n be s e e n - b y c o m p a r i n g t h e s h a p e s o f t h e s e c u r v e s w i t h t h e c a l c u l a t e d c u r v e s o n p age 2 9 * The'magnesium l i n e i s n o t s t r a i g h t a n d t h e r e . i s no d i s t i n c t b r e a k , so a r a t h e r a r b i t r a r y s t r a i g h t l i n e a p p r o x i m a t i n g t o t h e o u t e r p o r t i o n o f t h e t a i l h a s b e e n d r a w n . The s l o p e s o f t h e s e somewhat a r b i t r a r y b l a c k l i n e s e c t i o n s a r e shown i n T a b l e I , page 6 5 , i n t e r m s o f 0 O w h e r e t h e l i n e h a s t h e f o r m e~®/®°. The l a s t c o l u m n c o n t a i n s t h e v a l u e o f 0o c o r r e c t e d f o r w i d t h o f s o u r c e a n d c o u n t e r s b a s e d o n t h e t h e o r y o f S e c t i o n 1 1 1 ( d ) . T h i s c o r r e c t i o n v a r i e s f r o m a b o u t 5 t o 10%. E x c e p t f o r c o p p e r , t h e e r r o r s i n d i c a t e d a r e b a s e d o n i n s p e c t i o n o f t h e c u r v e s . The s l o p e f o r c o p p e r was o b t a i n e d by t h e m e t h o d o f l e a s t s q u a r e s a n d t h e e r r o r i s b a s e d on t h e r e s i d u a l s . The r a n g e o f measurement i s i n d i c a t e d by ©(min), t h e a n g l e a t w h i c h o v e r l a p b e t w e e n s o u r c e a n d c o u n t e r s e n d s , a n d ©(max), t h e maximum a n g l e t o w h i c h m e a s u r e m e n t s were, t a k e n . - 6 5 -TABLE I E l e m e n t Z 9 ( m i n ) 9(max) Shape o f 9 0 C o r r e c t e d 6p T a i l . Mg 12 9.8x10 - 3 2 2 . 5 x 1 0 - 3 c u r v e d 4 . 3 + 0 . 4 4.0 + 0 . 4 , •xlO - 3 x l 0 - 3 S 16 10.0 17.0 c u r v e d 4 . 0 5 ± 0.4 3 . 7 + 0 . 4 2.66 + 0.15 ..2.40 + 0.15 Cu 29 6 . 8 23.2 s t r a i g h t 3.81 + 0.02 3.62 + 0.02 Sn 50 7 . 5 15.2 c u r v e d 3 .63 ± 0.4 3 . 4 + 0.4 2 . 6 5 + 0.15 2.50 + 0.15 P t 78 6.8 2 0 . 9 s t r a i g h t 3 .35 + 0.2 3-2 + 0.2 Hg 80 7.3 13.0 s t r a i g h t 3.2 + 0 . 3 3.1 + 0 . 3 ( ? ) c ) A l k a l i M e t a l H a l o g e n s i ) L i C l , KC1, a n d C s C l . ' H e r e t h e l i n e s a r e n o t s t r a i g h t b u t t h e c u r v a t u r e i s n o t g r e a t s o b l a c k l i n e s were d r a w n r e p r e s e n t i n g t h e a v e r a g e s l o p e o f t h e t a i l . The r e s u l t s f o r t h i s g r o u p a r e r e c o r d e d i n T a b l e I I TABLE I I Compound 8 ( m l n ) 9(max) Shape o f A v e r a g e 9 n C o r r e c t e d 9o T a i l L i C l 8 . 9 x 1 0 - 3 1 7 . 7 x 1 0 - 3 c u r v e d 2.7 + 0.2 2.5 + 0.2 x l O - 3 x l 0 - 3 KC1 8 . 9 15 s t r a i g h t 2 . 7 + 0.4 2 . 5 + 0.4 ( ? ) C s C l 8.2 16.5 c u r v e d 2 . 7 + 0 . 2 2 . 5 + 0 . 2 B e c a u s e K C 1 was t h e l a s t m a t e r i a l s t u d i e d , t h e s o u r c e was weak a n d c o n s e q u e n t l y t h e a c c u r a c y f o r t h e KG1 r e s u l t i s l o w a n d t h e a n g u l a r r a n g e c o v e r e d , s m a l l . The L i C l a n d C s C l c u r v e s a n d t h e - 6 6 -K01 c u r v e a s f a r as i t was m e a s u r e d a r e s e e n t o n a v e t h e same s h a p e a n d t h e same s l o p e , w i t h i n t h e a c c u r a c y o f t h e s e r e s u l t s . i i ) KF, KC1 a n d K I . The c u r v e s f o r t h e s e compounds a r e n o t s t r a i g h t a n d b l a c k l i n e s w e r e d r a w n r e p r e s e n t i n g b o t h t h e a v e r a g e s l o p e o f t h e t a i l a n d t h e s l o p e s o f t h e two s e c t i o n s i n t o w h i c h t h e t a i l c o u l d be s e p a r a t e d . No s e p a r a t i o n was done f o r KC1 s i n c e t h e a c c u r a c y was n o t g r e a t e n o u g h t o w a r r a n t i t . The r e s u l t s a r e r e c o r d e d i n T a b l e I I I , w here 9 a i s t h e a v e r a g e s l o p e , 0 i , t h e s l o p e o f t h e i n n e r p a r t a n d 9-t, t h e s l o p e o f t h e o u t e r p a r t o f t h e t a i l . * TABLE I I I Shape o f C o r r e c t e d Compound 9 ( m i n ) 9 (max) T a i l S l o p e S l o p e KF 9-8x10-3 2 0 . 5 x 1 0 - 3 c u r v e d 9 a 3.4 + 0.2 3.1 + 0.2 x l O - 3 x l O - 3 9 i 3.0 + 0.1 2.7 + 0.1 9 t 4.5 + 0.4 4.1 + 0.4 KC1 8.9 15 s t r a i g h t 9 a 2.7 + 0.4 2.5 + 0.4 ( ? ) K I 8.5 16.5 c u r v e d 9 a 3-0 + 0 . 2 2 . 7 + 0 . 2 9 i 2.6 + 0.2 2.4 + 0.2 @t 3.5 ± 0.3. 3.2 + 0.3 The r a n g e s i n w h i c h m e a s u r e m e n t s were t a k e n f o r t h e s e compounds do n o t o v e r l a p v e r y w e l l . C o n s e q u e n t l y q u a n t i t a t i v e c o m p a r i s o n s a r e n o t j u s t i f i e d , b u t i t seems, s a f e t o s a y t h a t t h e s l o p e s o f t h e s e c u r v e s a r e n o t t h e same. - 6 7 -d) C o n c l u s i o n s No c o r r e c t i o n h a s b e e n made f o r t h e f a c t t h a t a b o u t 1 0 % o f t h e p o s i t r o n s d e c a y i n s i d e t h e c o p p e r f o i l s ; t h e a c c u r a c y o f t h e r e s u l t s do n o t w a r r a n t , s u c h a c o r r e c t i o n . A l s o . , t h e . e f f e c t s o f g e o m e t r y a n d s c a t t e r i n g h a v e o n l y b e e n i n v e s t i g a t e d a p p r o x -i m a t e l y . I n s p i t e o f t h e s e d e f e c t s , t h e a b o v e r e s u l t s j u s t i f y t h e f o l l o w i n g c o n c l u s i o n s : i ) The a n g u l a r c o r r e l a t i o n c u r v e s a r e n o t a l l e x p o n e n t i a l , t h a t i s n o t s t r a i g h t l i n e s o n a l o g a r i t h m i c p l o t ; c o n s e q u e n t l y , t h e momentum d i s t r i b u t i o n s o f e l e c t r o n s i s n o t o f a s i m p l e e x p o n e n t i a l f o r m . -For t h e c a s e s where t h e t a i l s ' a r e c u r v e d , t h e mean c e n t r e o f mass momentum o f a n n i h i l a t i n g p a i r s c a n n o t be o b t a i n e d b y means o f t h e s i m p l e t h e o r e t i c a l . r e s u l t , 4 o n ' pa g e 22. C o m p a r i s o n o f t h e s h a p e o f t h e p e a k s o f t h e c u r v e s w i t h t h e c a l c u l a t e d c u r v e s o n p a g e 29 a l s o l e a d s u s t o . t h e c o n -c l u s i o n t h a t t h e e l e c t r o n momentum d i s t r i b u t i o n s a r e n o t e x p o n e n t i a l . F o r i n s t a n c e , t h e p e a k s f o r s u l p h u r a n d magnesium a r e h i g h c o m p a r e d t o t h e & a i l a n d t h e p e a k f o r " p l a t i n u m seems t o be s l i g h t l y l o w . . i i ) Of t h e p u r e e l e m e n t s , t h e t a i l s o f t h e a n g u l a r c o r r e l a t i o n c u r v e s f o r c o p p e r , p l a t i n u m a n d m e r c u r y ( d o u b t f u l case.) a r e s t r a i g h t t o w i t h i n t h e s t a t i s t i c s . The s l i g h t . d r o p a t t h e t o p o f t h e t a i l i s due t o the. e f f e c t o f g e o m e t r y a s shown.by t h e c u r v e s o n page 29. A s s u m i n g t h a t t h e e x p o n e n t i a l t y p e d i s t r i -b u t i o n c o n t i n u e s i n t o t h e r e g i o n s w here m e a s u r e m e n t s w e r e n o t p o s s i b l e , t h e mean c e n t r e o f mass momentum o f a n n i h i l a t i n g p a i r s c a n be o b t a i n e d f r o m f o r m u l a 4 o n page 22: -68-p = 2 m c 9 0 Thus pou = ( 7 . 2 4 + 0.1) x 1 0 " 5 mc. ( 2 m c 0 o = ( 7 - 2 4 + 0 . 0 4 ) x l O - 3 m c ) p p t - (6.41 + 0.4) x 10~3 m c p h g = (6.2 + 0.6) x 10"- 5 mc. The e r r o r f o r c o p p e r h a s b e e n i n c r e a s e d f r o m a b o u t 0.6% a s o b t a i n e d - f r o m t h e l e a s t s q u a r e s a n a l y s i s o f t h e t a i l t o a b o u t 1.5% t o a l l o w f o r u n c e r t a i n s o u r c e s o f e r r o r s u c h a s s c a t t e r i n g a n d g e o m e t r y . i i i ) The a b o v e r e s u l t s may be c o m p a r e d w i t h t h e f o l l o w i n g v a l u e s o b t a i n e d by o t h e r a u t h o r s : Du Mond a n d c o - w o r k e r s p c u = 8 x 10 mc D e B e n e d e t t i a n d c o - w o r k e r s p a u = 8.8 x 10"3 mc ( e x p e r i m e n t a l ' ; ) p a u = 6 x 10 mc ( t h e o r e t i c a l l o w e r l i m i t ) . P.E. A r g y l e p c u = (7.20 + 0.08) x 10"3 mc.. The p r e s e n t v a l u e f o r c o p p e r a p p e a r s t o be i n e x c e l l e n t a g r e e m e n t w i t h t h a t o b t a i n e d b y P.E. A r g y l e b u t t h e a g r e e m e n t i s n o t a s g o o d a s i t a p p e a r s b e c a u s e a c o r r e c t i o n f o r g e o m e t r y o f a b o u t 5% h a s b e e n a p p l i e d t o t h e p r e s e n t v a l u e w h e r e a s no s u c h c o r r e c t i o n was a p p l i e d t o A r g y l e ' s r e s u l t . C o n s e q u e n t l y , t h e s e two r e s u l t s d i f f e r by a l i t t l e more t h a n t h e e r r o r s c l a i m e d f o r them. The a g r e e m e n t b e t w e e n t h e e x p e r i m e n t a l v a l u e o b t a i n e d by D e B e n e d e t t i f o r g o l d a n d t h e v a l u e s o b t a i n e d a b o v e f o r p l a t i n u m a n d m e r c u r y i s n o t g o o d a l t h o u g h t h e m a t e r i a l s a r e s i m i l a r . The p r e s e n t r e s u l t s f o r p l a t i n u m a n d m e r c u r y a r e i n a g r e e m e n t v / i t h D e B e n e d e t t i 1 s t h e o r e t i c a l v a l u e f o r g o l d . - 6 9 -i v ) D e B e n e d e t t i s u g g e s t e d t h a t t h e two a l k a l i h a l i d e s e r i e s i ) L i C l , KC1 a n d C s C l . • i i ) KF, KC1 a n d K I . s h o u l d be o f i n t e r e s t . S i n c e one e x p e c t s t h a t t o a f i r s t a p p r o x i m a t i o n t h e p o s i t r o n a n n i h i l a t e s " o n l y a g a i n s t t h e o u t e r s h e l l e l e c t r o n s o f t h e n e g a t i v e l y c h a r g e d h a l o g e n i o n s , one s h o u l d f i n d a b o u t t h e same v a l u e o f p f o r t h e ( i ) s e r i e s a n d a m o n o t o n i c v a r i a t i o n i n p f o r t h e ( i i ) s e r i e s . The p r e s e n t r e s u l t s seem t o c o n f i r m t h i s h y p o t h e s i s . U n f o r t u n a t e l y , t h e a c c u r a c y f o r KC1 i s t o o l o w t o t e l l w h e t h e r t h e r e i s d e f i n i t e l y a m o n o t o n i c v a r i a t i o n i n t h e ( i i ) s e r i e s . C e r t a i n l y t h e c u r v e s f o r t h e ( i ) s e r i e s a r e more a l i k e i n g e n e r a l s h a p e a n d s l o p e o f t h e t a i l t h a n t h o s e f o r t h e ( i i ) s e r i e s . e) D i s c u s s i o n - S p e c u l a t i o n s b a s e d on t h e r e s u l t s . A n a t t e m p t was made t o f i n d a r e l a t i o n b e t w e e n t h e s l o p e s shown i n T a b l e I , page 65, a n d t h e r a t i o s o r d i f f e r e n c e s o f .atomic a n d i o n i c v o l u m e s f o r t h e atoms a s s u g g e s t e d by t h e t h e o r e t i c a l c a l c u l a t i o n s o f D e B e n e d e t t i a n d c o - w o r k e r s . No r e l a t i o n was f o u n d . T h i s may h a v e b e e n due t o t h e l a c k o f a d e q u a t e i n f o r m a t i o n a b o u t t h e v o l u m e s . C o n s i d e r i n g t h e s l o p e s o f t h e o u t e r p o r t i o n s o f t h e t a i l s f o r t h e m a t e r i a l s i n T a b l e I , t h e r e d o e s a p p e a r t o be a m o n o t o n i c d e c r e a s e i n s l o p e w i t h i n c r e a s i n g z. T h i s i s shown i n t h e g r a p h o n p a g e 70 ( F i g u r e 2 5 ) . I f s u c h a n e f f e c t does e x i s t a n d t h e p o s i t r o n s i n a n a l k a l i h a l i d e l a t t i c e only a n n i h i l a t e w i t h t h e h a l o g e n o u t e r e l e c t r o n s a s i s i n d i c a t e d b y F i g u r e 25 - 7 1 -c o n c l u s i o n ( i v ) , t h e n t h e t a i l s f o r t h e ( i i ) s e r i e s o f a l k a l i h a l i d e s m i g h t be e x p e c t e d t o g i v e v a l u e s f o r F, C I a n d I w h i c h * a l s o f i t t h e c u r v e o f f i g u r e 2 5 . When t h e s l o p e s o b t a i n e d f r o m t h e l o w e r s e c t i o n s o f t h e c u r v e s a r e p u t o n t h e g r a p h , i t i s s e e n t h a t , e x c e p t f o r C I , t h e y do l i e w i t h i n t h e e r r o r s o n a c u r v e t h r o u g h t h e o t h e r p o i n t s . U n f o r t u n a t e l y , t h e KC1 c u r v e was n o t t a k e n o u t f a r e n o u g h t o show a n y l o w e r t a i l s e c t i o n a s i s shown by t h e KF a n d K I c u r v e s . B u t i f c o n c l u s i o n . (iv . ) i s c o r r e c t , , t h e c u r v e f o r a n y o t h e r a l k a l i c h l o r i d e s h o u l d p r o v i d e , a r e s u l t f o r c h l o r i n e . C o n s e q u e n t l y , a s l o p e was o b t a i n e d f r o m t h e o u t e r t a i l r e g i o n o f L i C l w h i c h was m e a s u r e d o u t t o a n a n g l e c o m p a r a b l e w i t h t h e o u t e r a n g l e s f o r KF a n d K I . T h i s -s l o p e i s g i v e n by Go = ( 3 . 6 0 + 0.5) x 1 0 " ^ . T h i s d o es l i e i n t h e c o r r e c t r e g i o n t o f i t a m o n o t o n i c d e c r e a s e i n . s l o p e w i t h i n c r e a s i n g z, as shown i n f i g u r e 25. To e s t a b l i s h t h a t s u c h a t r e n d r e a l l y d o e s e x i s t , f u r t h e r a n d more a c c u r a t e r e s u l t s a r e n e c e s s a r y . T h e r e i s no e v i d e n c e f o r a p e r i o d i c v a r i a t i o n o f t h e s l o p e w i t h z. S u c h a v a r i a t i o n m i g h t be e x p e c t e d o n t h e b a s i s o f p e r i o d i c i t i e s i n s i z e a n d e l e c t r o n i c s t r u c t u r e . A n o t h e r i n t e r e s t i n g r e s u l t i s s u g g e s t e d by t h e c u r v e s o f f i g u r e 22. C o n s i d e r i n g t h e r e l a t i o n b e t w e e n t h e s h a p e o f t h e c u r v e s a n d t h e e l e c t r o n i c s t r u c t u r e as shown i n T a b l e I V o n p age 72, i t i s n o t e d t h a t t h e s t r a i g h t l i n e c u r v e s c o r r e s p o n d t o e l e m e n t s w i t h one e l e c t r o n i n t h e o u t e r s h e l l , w h i l e t h e c u r v e d l i n e s c o r r e s p o n d t o e l e m e n t s w i t h more c o m p l i c a t e d d i s t r i b u t i o n s o f e l e c t r o n s i n t h e o u t e r s h e l l s . M e r c u r y i s a d o u b t f u l c a s e s i n c e t h e a n g u l a r r a n g e i n w h i c h - 7 2 -TABLS I V  E l e m e n t Z Shape E l e c t r o n s K L M N 0 P MS 12 c u r v e d 2 2 6 2 S 16 c u r v e d 2 .2C6 2 4 Cu 29 s t r a i g h t 2 2 6 2 6 10 1 S n 50 c u r v e d 2 2 6 2. 6 10 . 2 6 10 2 2 P t 78 s t r a i g h t 2 2 6 2 6 10 2 6 10 14 2 6 9 1 H g 80 s t r a i g h t 2 2 6 2 6 10 2 6 10 14 2 6 10 2 (?) m e a s u r e m e n t s were t a k e n i s v e r y s m a l l . Thus t h e r e a p p e a r s t o be a d e f i n i t e r e l a t i o n b e t w e e n t h e o u t e r e l e c t r o n i c s t r u c t u r e o f a n e l e m e n t a n d t h e s h a p e o f t h e c o r r e s p o n d i n g a n g u l a r c o r r e l a t i o n c u r v e . A g a i n f u r t h e r s t u d y i s n e c e s s a r y t o c o n f i r m t h i s h y p o t h e s i s a n d t o c o r r e l a t e more q u a n t i t a t i v e l y , i f p o s s i b l e , t h e s h a p e o f t h e c u r v e w i t h t h e e l e c t r o n i c s t r u c t u r e . - 7 3 -APPENDIX I  A b s o r p t i o n o f 0.51 Mev. X-rays I n t h e u s u a l m e t h o d s e m p l o y e d f o r a c c u r a t e m e a s u r e m e n t s o f Y - r a y a b s o r p t i o n c o e f f i c i e n t s , t h e m a i n d i f f i c u l t y i s t o p r e v e n t s c a t t e r e d r a d i a t i o n f r o m r e a c h i n g t h e d e t e c t o r . As was s u g g e s t e d by P.E. A r g y l e ^ t h e 180° a n g u l a r c o r r e l a t i o n o f a n n i h i l a t i o n q u a n t a p r o v i d e s a m e t h o d o f o v e r c o m i n g t h i s d i f f i c u l t y w i t h o u t s p e c i a l p r e c a u t i o n s s u c h a s e l i m i n a t i n g a l l 22 2"^  s c a t t e r i n g o r u s i n g c o m p l i c a t e d c o l l i m a t i o n J . I f two s c i n t i l l a t i o n c o u n t e r s a r e p l a c e d e x a c t l y o n o p p o s i t e s i d e s o f a s o u r c e o f a n n i h i l a t i o n q u a n t a , t h e one c o u n t e r a c t s a s a c o l l i m a t o r f o r t h e Y - r a y beam t o t h e o t h e r so t h a t a n a b s o r p t i o n measurement c a n be o b t a i n e d b y r e c o r d i n g t h e c o i n c i d e n c e c o u n t i n g r a t e a s a f u n c t i o n o f t h e t h i c k n e s s o f a b s o r b e r b e t w e e n one c o u n t e r a n d t h e s o u r c e . U s i n g t h i s m e t h o d a c c u r a t e v a l u e s f o r t h e a b s o r p t i o n c o e f f i c i e n t s o f 0 .51 Mev. 24 Y - r a y s i n l e a d , c o p p e r a n d a l u m i n u m w e r e o b t a i n e d . The same a p p a r a t u s a s was u s e d f o r t h e a n g u l a r c o r r e l a t i o n w o r k was u s e d f o r t h e s e e x p e r i m e n t s . S i n c e t h e s o u r c e was r a t h e r weak ( l e s s t h a n 2 mc) t h e c o u n t e r s were p u t 70 cm. f r o m t h e s o u r c e g i v i n g a maximum a n g u l a r a p e r t u r e o f O . 8 5 0 . The a b s o r b e r s were p l a c e d c l o s e t o t h e s o u r c e . T h i s makes t h e 2 2 - C.L. Cowan, P h y s . R e v . , 74, 1841, 1948. 2 3 - C M . D a v i s s o n a n d R.D. E v a n s , M.I.T. T e c h n i c a l R e p o r t No.37 F e b r u a r y 1, 1950. 2 4 - P.E. A r g y l e , G.M. G r i f f i t h s a n d J . B . W a r r e n - i n t h e p r e s s . - 7 4 -a n g l e s u b t e n d e d by t h e d e t e c t o r a t t h e a b s o r b e r s m a l l a n d m i n i m i z e s t h e number o f q u a n t a w h i c h s u f f e r l o w a n g l e s c a t t e r i n g i n t h e a b s o r b e r a n d e n t e r t h e d e t e c t o r . A f t e r c o r r e c t i o n s f o r a c c i d e n t a l s , d e a d t i m e a n d s o u r c e d e c a y , t h e a b s o r p t i o n c u r v e s o b t a i n e d w e r e v e r y s t r a i g h t when p l o t t e d l o g a r i t h m i c a l l y . T h i s i n d i c a t e s t h a t t h e s t a b i l i t y o f t h e a p p a r a t u s was s a t i s -f a c t o r y . A l s o a f t e r c o r r e c t i o n s t h e c o u n t i n g r a t e f o r t h e c o u n t e r w h i c h h a d no a b s o r b e r b e t w e e n i t a n d t h e s o u r c e was c o n s t a n t . The v a l u e o f t h e h a l f l i f e f o r Ou^ u s e d was 12.88 h o u r s 2 5 . The maximum a b s o r b e r t h i c k n e s s e s u s e d w e r e 4 cm. f o r l e a d , 4 . 7 cm. f o r c o p p e r , a n d 5 cm. f o r a l u m i n u m . The p u r i t y o f t h e l e a d was b e t t e r t h a n 9 9 . 9 $ ; t h e c o p p e r was e l e c t r o l y t i c a n d s o a t l e a s t 99.5$ p u r e ; a n d t h e a l u m i n u m was A l c a n 2s w h i c h t h e m a n u f a c t u r e r s s t a t e i s 99.5$ p u r e . The a b s o r p t i o n c o e f f i c r -i e n t s w e r e o b t a i n e d f r o m t h e a b s o r p t i o n c u r v e s by t h e m e t h o d o f l e a s t s q u a r e s , t h e e r r o r b e i n g o b t a i n e d f r o m t h e r e s i d u a l s . 26 T h e . p o i n t s were, w e i g h t e d a c c o r d i n g t o t h e f u n c t i o n rt - V s t a n d a r d d e v i a t i o n / T a b l e V shows a c o m p a r i s o n o f t h e e x p e r i m e n t a l r e s u l t s o b t a i n e d 22 2 by t h i s m e t h o d w i t h r e s u l t s o f o t h e r a u t h o r s a n d w i t h t h e o r y . ' The t h e o r e t i c a l a b s o r p t i o n c o e f f i c i e n t s w e r e c a l c u l a t e d f r o m the,. K l e i n N i s h i n a f o r m u l a ' ( f o r Compton a b s o r p t i o n ) a n d f r o m t h e r e s u l t s o f Hulme a n d o t h e r s ( f o r t h e p h o t o e l e c t r i c e f f e c t ) . 2 —1 A l l f i g u r e s a r e i n u n i t s o f (gm/cm ) 2 5 - M i s s . L.M. S i l v e r - p r i v a t e c o m m u n i c a t i o n . 2 6 - The a r g u m e n t f o r t h i s f o r m o f w e i g h t i n g p o i n t s o n a l o g a r i t h -m i c p l o t i s g i v e n by W i l s o n a n d B i s h o p , P r o c . R o y . S o c . 6 2 , 4 5 7 ( 1 9 4 ^ 2 7 - L.E. G l e n d e n i n , N u c l e o n i c s , M o l . 2 , N o . l , 1 2 ( 1 9 4 8 ) . 2 8 - Hulme, M c D o u g a l , B u c k i n g h a m a n d F o w l e r , P r o c . R o y . S o c . , A l 4 9 , 28 1 3 1 , ( 1 9 3 5 ) . - 7 5 -TABLE V P h o t o - T o t a l E l e c t r i c Corapton T h e o r e t i c a l P r e s e n t A b s o r b e r A b s o r p t i o n A b s o r p t i o n A b s o r p t i o n Re s u i t s G - l e n d e n i n Cowan P b 0.0802 0.0675 0.1477 0.1519 0.154 +0.0008 Cu . 0.0028 0.0778 0.0806 0.0819 0 . 0 7 9 +0.0005 A l 0.0002 0.0823 0.0825 0.0831 0.082 0 . 0 8 3 +0.0013 F i g u r e 26, page 76 shows t h e c o u n t i n g r a t e s i n t h e two c o u n t e r s a n d i n t h e c o i n c i d e n c e c h a n n e l a f t e r c o r r e c t i o n s , f o r t h e c a s e when l e a d a b s o r b e r s w e r e u s e d . T h e s e c u r v e s i n d i c a t e c l e a r l y how t h e e f f e c t o f s c a t t e r i n g f r o m w a l l s , t a b l e s a n d s u p p o r t s d i s t o r t s t h e c o u n t i n g r a t e f r o m c o u n t e r number 2 when t h e a b s o r b e r i s p u t b e t w e e n t h a t c o u n t e r a n d t h e s o u r c e w h i l e t h e c o i n c i d e n c e c u r v e i s u n a f f e c t e d . - 7 7 -APPENDIX I I E v i d e n c e f o r t h e N u c l e a r Y-Ray f r o m C u ^ 4 When t h e s o u r c e was t o o weak f o r f u r t h e r work o n t h e a b s o r p t i o n c o e f f i c i e n t s d e s c r i b e d i n A p p e n d i x I , a n a t t e m p t was made t o d e t e c t t h e C u ^ 4 n u c l e a r Y - r a y w h i c h has b e e n r e p o r t e d by s e v e r a l a u t h o r s 2 ^ ^ 0 , 3 1 T A s i n g l e f o i l o f c o p p e r ( l e s s t h a n 0 . 2 mc) was u s e d i n t h e g e o m e t r y shown i n f i g u r e 27. M o s t o f t h e p o s i t r o n s e s c a p e d f r o m t h e f o i l a n d d e c a y e d i n t h e l e a d . C o n s e q u e n t l y , f e w a n n i h i l a t i o n q u a n t a r e a c h e d c o u n t e r 2 . M o s t o f t h e r a d i a t i o n r e a c h i n g c o u n t e r 2 was due t o t h e C u ^ 4 n u c l e a r Y - r a y , a s i s shown by t h e l e a d a b s o r p t i o n c u r v e ( F i g u r e 2 8 , page^ 7 8 ) t a k e n w i t h t h e a b s o r b e r s p l a c e d as shown i n f i g u r e . 2 7 . The s t a t i s t i c s o n t h e c o i n c i d e n c e c u r v e a r e p o o r b e c a u s e t h e c o u n t was v e r y l o w s h o w i n g t h a t o n l y a s m a l l amount o f a n n i h i l a t i o n r a d i a t i o n r e a c h e d c o u n t e r 2 . The s c a l e s o n t h e g r a p h a r e a r b i t r a r y . P e a k c o u n t i n g r a t e s f o r e a c h c u r v e a r e shown a t t h e r i g h t . The # 2 a b s o r p t i o n c u r v e f a l l s r a p i d l y a t f i r s t c o r r e s p o n d -i n g t o t h e a b s o r p t i o n o f 0 . 5 1 Mev. a n n i h i l a t i o n r a d i a t i o n . T h e n t h e r a t e o f f a l l d e c r e a s e s t o a r a t e w h i c h i s f a i r l y c l o s e t o t h a t e x p e c t e d f o r 1 . 3 Mev. Y - r a y s . The a c c u r a c y i s ' v e r y p o o r due t o t h e p r e s e n c e o f s c a t t e r e d r a d i a t i o n as shown b y t h e f l a t t e n i n g a t t h e e n d o f t h e c u r v e , c o n s e q u e n t l y , no e s t i m a t e o f t h e Y - r a y i n t e n s i t y o r e n e r g y was made. a b s o r b e r s c o u n t e r 1 Y//////A "/ ' c o u n t e r 2 s h i e l d c o p p e r &/////, f o i l 29- B r a d t , G u g e l o t , H u b e r , M e d i c u s , P r e i s w e r k , S h e r r e r a n d S t e f f e n , H e l v . P h y s . A c t a , 1 9 , 2 1 9 ( 1 9 4 6 ) . 3 0 - M . D e u t s c h - P h y s . R e v . , 7 2 , 7 2 9 ( 1 9 4 7 ) . 3 1 - H.E. K u b i t s c h e k , P h y s . R e v . , 7 9 , 23 ( 1 9 5 0 ) . -79-APPENDIX I I I T r i p l e P u l s e G e n e r a t o r F o r t e s t i n g c o i n c i d e n c e m i x e r s a n d m e a s u r i n g d e a d t i m e s o f a p p a r a t u s s u c h as a m p l i f i e r s o r s c a l e r s , i t i s v e r y c o n -v e n i e n t t o h a v e a d e v i c e w h i c h p r o d u c e s two p u l s e s one o f w h i c h comes a t a v a r i a b l e d e l a y t i m e a f t e r t h e o t h e r . I t i s a l s o c o n v e n i e n t t o h a v e a t h i r d p u l s e w h i c h c a n be u s e d f o r t r i g g e r i n g a n o s c i l l o s c o p e o r t e s t i n g t r i p p l e c o i n c i d e n c e m i x e r s . S u c h d e v i c e s a r e f a i r l y common now a n d a r e g e n e r a l l y r e f e r r e d t o a s t r i p p l e p o p p e r s . The c i r c u i t d i a g r a m o f t h e t r i p l e p o p p e r b u i l t f o r t e s t i n g t h e e l e c t r o n i c s u s e d f o r t h e a n g u l a r c o r r e l a t i o n e x p e r i m e n t s i s shown o n p a g e s 80 a n d 8 1 . A n 884 t h y r a t r o n o s c i l l a t o r p r o d u c e s p u l s e s a t a r e p e t i t i o n r a t e c o n t r o l l a b l e f r o m a f e w p u l s e s p e r s e c o n d t o a f e w t h o u s a n d p e r s e c o n d . A s h a r p p o s i t i v e p u l s e f r o m t h e c a t h o d e i s a v a i l a b l e f o r t e s t i n g o r t r i g g e r i n g p u r p o s e s . The v e r y s h a r p n e g a t i v e p u l s e s f r o m t h e anode a r e u s e d t o t r i g g e r t h r e e s i m i l a r d e l a y s t a g e s s i m u l -t a n e o u s l y . E a c h o f t h e s e s t a g e s c o n s i s t s o f a 6SN7 u n i v i b r a t o r w h i c h p r o d u c e s a s q u a r e p u l s e when t r i g g e r e d b y t h e t h y r a t r o n . The l e n g t h o f t h e s q u a r e p u l s e i s f i x e d a t a b o u t 30 m i c r o s e c o n d s f o r c h a n n e l 1 b u t c a n be v a r i e d f r o m a b o u t 10 t o a b o u t 300 m i c r o -s e c o n d s b y t h e d e l a y c o n t r o l s o n c h a n n e l s 2 a n d 3« The s q u a r e p u l s e i s d i f f e r e n t i a t e d , a n d t h e p o s i t i y e p i p f o r m e d f r o m t h e b a c k edge t r i g g e r s a b l o c k i n g o s c i l l a t o r c o n s i s t i n g o f two 6AC7's a n d a U t a h p u l s e t r a n s f o r m e r . The b l o c k i n g o s c i l l a t o r T r i p l e P o p p e r F i g u r e 29 T r i p l e P o p p e r +320V +250V s e n s f o r m e r U t a h 9280 +250V •+300V Gnd. -150V +300V Gnd. +250V +300V U t a h 9280 C h a n n e l #3 -150V T r i p l e Popper - 8 1 -Power Sup p l y 110V —L • 5U4G -p//f4 ffi 6X5 7 -yrrv- -YvVW-IOOK% +320V +250V s t a b i l i z e d /5"o -150V P a n e l Layout Red numbers c o r r e s p o n d t o s i m i l a r l y numbered o u t p u t s on c i r c u i t d i a g r a m . B l u e numbers c o r r e s p o n d t o s i m i l a r l y numbered c o n t r o l s on c i r c u i t d i a g r a m . R e p e t i t i o n Rate 01 0k Course F i n e T h y r a t r o n Output 4 Channel 1 ^GalnsjZC 7 + o O, o Channel 2 Delay-5 Channel 3 Delaj Course F i n e Channel 2 P F i l o t l i g h t Si s w i t c h Course F i n e 2 f n d 3 Channel 3 M i x e d — • * 0 + C h a i n s 0 ^ O O O" o Note: C o n t r o l a m p l i t u d e of mixed p u l s e s by + g a i n c o n t r o l s of c h a n n e l s 2 and 3. - 8 2 -p r o d u c e s a v e r y f a s t r i s i n g s h o r t p u l s e a c r o s s a f a i r l y l o w i m p e d a n c e . P o s i t i v e a n d n e g a t i v e o u t p u t p u l s e s o f v a r i a b l e a m p l i t u d e a r e a v a i l a b l e f r o m e a c h o f t h e t h r e e s t a g e s ; t h e p o s i t i v e p u l s e s r i s e t o a p e a k a m p l i t u d e o f 55 v o l t s i n a b o u t 0.1 m i c r o s e c o n d , t h e t o t a l p u l s e l e n g t h b e i n g 0.3 m i c r o s e c o n d s . T h i s r e p r e s e n t s a p e a k c u r r e n t o f a b o u t 110 m i l l i a m p e r e s t h r o u g h t h e p u l s e f o r m i n g 6A.C7. The n e g a t i v e , o u t p u t p u l s e s h a v e a p e a k a m p l i t u d e o f 15 v o l t s a n d a r e n o t q u i t e a s f a s t a s t h e p o s i t i v e o u t p u t p u l s e s . . I t i s e a s y t o s e e t h a t t h i s d e v i c e makes i t p o s s i b l e t o p r o d u c e p u l s e s f r o m c h a n n e l s 2 a n d 3 t h a t come a n y t i m e f r o m 20 m i c r o s e c o n d s b e f o r e t o n e a r l y 300 m i c r o s e c o n d s a f t e r t h e p u l s e s f r o m c h a n n e l 1. I f t h e o u t p u t s o f two s t a g e s a r e c o n n e c t e d d i r e c t l y t o g e t h e r t o g e t two p u l s e s w i t h a v a r i a b l e d e l a y b e t w e e n them o n t h e same l e a d ( f o r d e a d t i m e m e a s u r e m e n t s ) d i f f i c u l t i e s a r i s e due t o i n t e r a c t i o n b e t w e e n t h e s t a g e s . . C o n s e q u e n t l y , a 6SN7 m i x e r s t a g e was a d d e d s o t h a t t h e p u l s e s f r o m c h a n n e l s 2 a n d 3 c o u l d be o b t a i n e d t o g e t h e r a t t h e same o u t p u t . The g e n e r a l f e a t u r e s o f t h i s c i r c u i t were c o p i e d f r o m a s i m i l a r p u l s e g e n e r a t o r u s e d a t t h e U n i v e r s i t y o f . C h i c a g o . The d e s i g n o f t h e b l o c k i n g o s c i l l a t o r o u t p u t s t a g e s was b a s e d 32 o n i n f o r m a t i o n g i v e n b y E l m o r e a n d S a n d s v . 3 2 - E l m o r e a n d S a n d s , E l e c t r o n i c s , McGraw H i l l , 194-9. -83-B I B L I 0 GRAPHY A r g y l e , P.E., M.A. T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , J u n e , 1950. B e l l , P.R., P h y s . R e v . , 73, 14-05, (194-8). B e r i n g e r a n d Montgomery, P h y s . Rev., 6 l , 222, (194-2). B r a d t , G u g e l o t , H u b e r , M e d i c u s , P r e i s w e r k , S h e r r e r a n d S t e f f e n , H e l v . P h y s . A c t a , 19, 219, (194-6). B r o d y a n d D e u t s c h , P h y s . Rev., 74-, 154-1, (194-8). Cowan, C.L., P h y s . Rev., 74-, 184-1, (1948). D a v i s s o n , C M . , a n d E v a n s , R.D., M.I.T. T e c h n i c a l R e p o r t , No.37, F e b r u a r y 1, (1950). D e B e n e d e t t i , Cowan, K o n n e k e r a n d P r i m a k o f f , P h y s . R ev., 77, 205, (1950). D e u t s c h , M., P h y s . Rev., 72, 729, (1947). D e u t s c h , M., M.I.T. T e c h n i c a l R e p o r t , No.3, December 1, (1947). D i r a c , P.A.M., P r o c . Camb. P h i l . S o c , 26, 3 6 I , (1930). Du Mond, L i n d a n d W a t s o n , P h y s . Rev., 75, 1226, (1949). E l m o r e a n d S a n d s , E l e c t r o n i c s , McGraw H i l l , (1949). G i l l e t t e , R.H.,, P h o s p h o r s f o r S c i n t i l l a t i o n C o u n t e r s - A R e p o r t f r o m t h e L a b o r a t o r y o f t h e L i n d e A i r P r o d u c t s Co., Tonawanda, N.Y. G l e n d e n i n , L.E., N u c l e o n i c s , V o l . 2 , N o . l , 12, (1948). H e i t l e r , ¥., The Quantum T h e o r y o f R a d i a t i o n , O x f o r d , (1944). Hulme, M c D o u g a l , B u c k i n g h a m a n d F o w l e r , P r o c Roy. S o c , A 149, 131, (1935). K u b l t s c h e k , H.E., P h y s . Rev., 79, 23, (1950).. -84-Mann, K . C . , R a n k i n , D., D a y k i n , P . N . , - P h y s . Rev., 76, 1719,(1949). Moody, N.F., H o w e l l , W.D., N . R . C . R e p o r t 1M-8 - L i n e a r A m p l i f i e r Type AEP 1444. S e i t z , F., M o d e r n T h e o r y o f S o l i d s , McGraw H i l l , (1940). Townsend, P r o c . R o y . S o c , A 177, 357, (1941). T y l e r , P h y s . Rev., 56, 125,(1939). W i l s o n a n d B i s h o p , P r o c R o y . S o c , 62, 457, (1949). 0 

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