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The T([alpha,gamma]) Li⁷ reaction and a standard Geiger-Muller counter for gamma ray flux determinations Morrow, Richard Alexander 1959

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THE T(*X, tf)Lj/ REACTION AND A STANDARD GEIGER.-MULLER COUNTER FOR GAMMA RAY FLUX DETERMINATIONS by RICHARD ALEXANDER MORROW B . S c , Queen's U n i v e r s i t y , 1958 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e D e p a r t m e n t of. PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA September 1959 .ABSTRACT A s t u d y o f t h e T(0C , 3 f)Li/ r e a c t i o n has been made a t mean a l p h a p a r t i c l e e n e r g i e s o f 1320, 560 and 350 Kev i n a s o l i d t r i t i u m - z i r c o n i u m t a r g e t . A t t h e 1320 Kev e n e r g y t h e a b s o l u t e 90° 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 t r a n s i t i o n s t o t h e g r o u n d s t a t e has b e e n f o u n d t o be 1.89x10-31 cm2 p e r s t e r a d i a n f r o m a n a l y s e s o f s p e c t r a o b t a i n e d i n a 2§"XH4-u H a l c r y s t a l . A t t h i s e n e r g y t h e r a t i o o f 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 t r a n s i t i o n s t o t h e f i r s t e x c i t e d s t a t e t o t h a t f o r t r a n s i t i o n s t o t h e gro u n d s t a t e was f o u n d t o be 0.M+-6. T h i s r a t i o was o b s e r v e d t o r e m a i n t h e same a t a l l d e t e c t o r a n g l e s . The e x c i t a t i o n f u n c t i o n r o u g h l y d e t e r m i n e d b y a d d i t i o n a l r u n s a t 560 and 350 Kev mean e n e r g y f o l l o w e d t h e f o r m o b t a i n e d b y R i l e y o f t h i s l a b o r a t o r y i n 1958. .Angular d i s t r i b u t i o n measurements a t 1320 Kev gave t h e r e s u l t t h a t b o t h t h e above m e n t i o n e d gamma r a y s have t h e same a n g u l a r d e p e n d e n c e , t h i s b e i n g 1 -0 .11 c o s ^ Q + 0.39 c o s ^ © . A t 560 Kev mean e n e r g y t h e i r a n i s o t r o p y was measured t o be a b o u t % . A b a c k g r o u n d f r o m t h e t a r g e t has b e e n f o u n d t o have a n a n g u l a r d i s t r i b u t i o n a t 1320 Kev mean a l p h a p a r t i c l e e n e r g y o f 1+0.35 c o s © i n l a b o r a t o r y c o - o r d i n a t e s . B o t h i t s e x c i t a t i o n f u n c t i o n , d e t e r m i n e d r o u g h l y f r o m r u n s a t 560 and 350 Kev, and i t s a n i s o t r o p y f o l l o w e d a f o r m i n agreement w i t h n e u t r o n c o u n t e r measurements. I t i s s u g g e s t e d t h a t t h i s b a c k g r o u n d i s c a u s e d b y n e u t r o n s f r o m some s t i l l unknown r e a c t i o n i n t h e t a r g e t . A n i n v e s t i g a t i o n was a l s o made o f a s t a n d a r d t h i c k - w a l l e d b r a s s G e i g e r - M u l l e r c o u n t e r t o d e t e r m i n e i t s e f f i c i e n c y f o r p h o t o n e n e r g i e s f r o m 0 .5 t o 20 Mev. k smooth c u r v e was o b t a i n e d showing e f f i c i e n c y i n c r e a s i n g w i t h gamma r a y e n e r g y t h u s a g r e e i n g i n f o r m w i t h p r e v i o u s e x p e r i m e n t a l and t h e o r e t i  c a l r e s u l t s . In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia, Vancouver Canada. AG KHOWLEDGEMENTS The a u t h o r w i s h e s t o t h a n k D r . G . M . . G r i f f i t h s 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 i s h e l p a n d encouragement i n . c a r r y i n g i t o u t • . Thanks a r e a l s o e x t e n d e d t o Mr. P.P. S i n g h , whose a s s i s t a n c e i n much o f t h e e x p e r i m e n t a t i o n was i n v a l u a b l e . . A N a t i o n a l R e s e a r c h C o u n c i l o f Canada B u r a a r y w h i c h made t h i s work p o s s i b l e i s g r a t e f u l l y a c k n o w l e d g e d . TABLE OF CONTENTS CHAPTER PAGE Part I The-T(a,y)Li7 Reactions I Introduction: 1 II Experimental 6 1.. Apparatus: 6: (a) Van de Graaff Generator^ 6J (b) Sidearm Arrangement 7 (c) Scintillation. Counter 8 ( i ) Shielding '8 ( i i ) .Efficiency; 9 (d) Electronics . 12 2.. Tritium.Target 12 (a) Mounting 12 (b?) Tritium Content 13 ( i ) p-activity ... 13 ( i i ) ; T(p,?T/)He4 Yield 14 (c); Thickness for Alpha Particles . 17 3.. Angular Distribution.Measurements ............. 18 (a) Procedure..... • 18. (b:) Standard^Gamma Ray Spectrum 22. (c) ,T(a ty)U 7 Spectra 22 (d) Branching Ratios. •• • 24 (e) Angular Distribution....:."....."......; 25: (f_);:Doppler Shift 28 4.. Backgrounds;: = 29 (a) General 29 (b) Energy of-Neutrons. 30 (c) Yield and Anisotropy: of Neutrons:..... 31- (d) Background Yield from the S c i n t i l l a  tions Counter 32 (e) Angular Distribution 33 5. Absolute 90° Differential Cross-Section . 34 (a) Procedure..... 34 (b) , Cross-Section, at 1.6 Mev 35. (c) ; Excitation. Functions ... 36 (d) Target. Thickness, from: Gamma..Ray; Energy • 38 6~., Summary and Discussion, of Experimental. Results- 38 CH&PTER PAGE I I 7";. A p p l i c a t i o n o f . R e s u l t s t o A s t r o p h y s i c s : .. 40 P a r t . I I A. S t a n d a r d G e i g e r _ - M u l l e r C o u n t e r f o r Gamma Ra y F l u x D e t e r m i n a t i o n s . I I n t r o d u c t i o n : 44 I I D e t e r m i n a t i o n o f C h a r a c t e r i s t i c s . 48 1.. M e t h o d o f O p e r a t i o n 48 2.. C o n s t r u c t i o n a n d K i l l i n g 49 3.. P l a t e a u x a n d R e s o l v i n g Time ...... 51 4. G-M C o u n t e r E f f i c i e n c y . D e t e r m i n a t i o n ..... 52 . (a) D e f i n i t i o n o f E f f i c i e n c y 52 (b) E x p e r i m e n t a l P r o c e d u r e . 54 ( c ) . P r o c e d u r e a.t 0.£l Mev 55 (d) " " 1.25 Mev 56 (e) 1 11 6.16 Mev 57 (f.) '! M 12.1 Mev 58 (g) " " 16.3 Mev 60 (h) ; V " 20.3 Mev. 61 ( i ) ; Summary o f E f f i c i e n c y R e s u l t s 62 B i b l i o g r a p h y , 64 ILLUSTRATIONS FIGURE FACING NUMBER SUBJECT PAGE 1.. Low Energy Levels of IdT 1 2. Sldearm Arrangement. 7 3.. S c i n t i l l a t i o n Counter Efficiency 9 4. Block Diagram of Electronics 12 5. - 20 Mev T(p,T) He * Spectrum 14 6.. Gamma Ray Absorption Factor for Target Backing .. 15 7. Stopping Cross Sections i n Zirconium-tritium. Target 161 8. Target Thickness for Alpha Particles .... 18 9. T(a,T)Li 7 Spectra ............... 21. 10. Standard Gamma Ray Spectrum 22 11'.. Decomposition of T(a,Y)Li7 Spectrum 23 12.. T(a,Y)Li 7 Angular Distribution. 24 13. - Angular Distribution at 1;6 Mev 27 14. Neutron. Spectra. 31 15. Cross-section Factor, S 41 16. Standard G-M Counter 49 17. Counter F i l l i n g System 50 18. Circuit. Connections 54 19- Co 6 0 and Na 2 2 Spectra 55" 20.. Spectra of B-^CpjYjC.12 Gamma Rays 59 21., Spectra, of Li^(p,Y)Be 8 Gamma Rays 60 22... G-M Counter Efficiency 62 FIGURE I LOW ENERGY L E V E L S OF Li 2 . 4 6 5 + 3 / 7 E, 2 . 4 6 5 He4+ H 3 0 8 6 3 Be' 7.4 6 5-5 4 .61 0 . 4 7 7 5 / 2 " 11/2 , 3 / 2 + ) 1/2 3 / 2 " Li THE T (<*.Y) L i ' REACTION C h a p t e r I I n t r o d u c t i o n : I n r e c e n t y e a r s t h e r e has b e e n c o n s i d e r a b l e i n t e r e s t i n t h e mass 7 n u c l e i L i ' 7 and B e ? b o t h b e c a u s e o f t h e i r a s t r o - p h y s i c a l i m p o r t a n c e and b e c a u s e o f c o n s i d e r a b l e i n t e r e s t i n t h e n a t u r e o f t h e c o u p l i n g r e s p o n s i b l e f o r t h e e n e r g y l e v e l s . Much of t h i s i n t e r e s t has been c o n c e r n e d w i t h t h e gr o u n d s t a t e and f i r s t e x c i t e d s t a t e p r o p e r t i e s o f t h e s e n u c l e i and i n t h i s c o n  n e c t i o n a p u z z l i n g p o i n t i s t h e r e l a t i v e l y s m a l l e x c i t a t i o n e n e r g y o f a b o u t o n e - h a l f Mev o f t h e f i r s t e x c i t e d s t a t e s o f b o t h t h e s e n u c l e i a s compared w i t h a b o u t two Mev i n s u r r o u n d i n g o n e s . A c c o r d i n g t o s i m p l e s h e l l m o d e l t h e o r y t h e two n e u - 7 t r o n s i n t h e p - s h e l l o f L i ' c o u p l e t h e i r a n g u l a r momenta and s p i n s t o z e r o so t h a t t h e p r o p e r t i e s o f t h e two l o w e r s t a t e s a r e d e t e r m i n e d b y t h e odd p - s h e l l p r o t o n . T h i s s h o u l d r e s u l t i n t h e g r o u n d s t a t e b e i n g a 2P3/2 l e v e l and t h e f i r s t e x c i t e d s t a t e a 2 ^ l / 2 l e v e l . The s i t u a t i o n i n t h e mirror n u c l e u s B e ? i s s i m i l a r i n t h a t t h e r o l e s o f t h e n e u t r o n s and p r o t o n s a r e s i m p l y i n t e r c h a n g e d r e s u l t i n g i n t h e same l o w e r l e v e l d e s i g n a  t i o n s as i n L i ? . F r o m e x p e r i m e n t a l o b s e r v a t i o n s i t i s i n d e e d v e r i f i e d t h a t t h e g r o u n d s t a t e o f L i ? i s a J=3/2 l e v e l w i t h odd p a r i t y ( B r e i t and S t e h n , 1938). E x p e r i m e n t s on t h e a n g u l a r c o r r e l a  t i o n o f i f - r a y s and o C - p a r t i c l e s f r o m B 1 0 ( n , CK)L1^ (Rose a n d W i l s o n , 1950), J f-rays and oC - p a r t i c l e s f r o m B e ^ ( d , ( X ) L i ? , and - r a y s and p r o t o n s f r o m L i ^ ( d , p ) L i ? ( A j z e n b e r g and L a u r i t s e n 1955) show i s o t r o p y a s do measurements on t h e 0.1+78 Mev tf- r a y f r o m L i ^ t p j P 1 ) ! ^ * ( L i t t a u e r , 1950) t h u s p o i n t i n g t o t h e a s s i g n m e n t o f J = l / 2 t o t h e f i r s t e x c i t e d s t a t e . However, s u c h a c h o i c e i s i n c o n s i s t e n t w i t h t h e o b s e r v e d r a t i o s o f i n t e n s i  t i e s o f ^ r a y s f r o m B e ? and < * - p a r t i c l e s f r o m B 1 0 ( n , o O L i ? t o t h e f i r s t two l e v e l s o f A J=5/2 d e s i g n a t i o n would be n e  c e s s a r y t o e x p l a i n t h e s e l a t t e r o b s e r v a t i o n s (Hanna and I n g l i s , 19^9). S i n c e m a g n e t i c d i p o l e r a d i a t i o n w o u l d be e m i t t e d i n t h e d e - e x c i t a t i o n o f t h e f i r s t l e v e l w i t h e i t h e r a J=5/2 o r J = l / 2 a s s i g n m e n t no d i f f e r e n t i a t i o n c o u l d be made f r o m l i f e t i m e mea surements o f L i ? 3 * . The mean l i f e t i m e has b e e n measured, how e v e r , b y a number o f e x p e r i m e n t e r s ( A j z e n b e r g and L a u r i t s e n , -13 1955) t o be a b o u t 10 J s e c o n d w h i c h i s c o n s i s t e n t w i t h a mag n e t i c d i p o l e t r a n s i t i o n . I n t h e c a s e o f B e ? , u n s t a b l e b y K c a p t u r e t o L i ? b y O.863 Mev w i t h a h a l f - l i f e o f 53 d a y s , t h e n e g a t i v e r e s u l t s o f t h e r e a c t i o n He lf(c< ,n)Be' 7 s u p p o r t t h e a s s u m p t i o n t h a t t h i s n u  c l e u s has odd p a r i t y ( A j z e n b e r g and L a u r i t s e n , 1955). From s t r i p p i n g t h e o r y a p p l i e d t o L i ^ ( d , n ) B e ? t h e g r o u n d s t a t e o f B e ? i s again i n d i c a t e d t o have odd p a r i t y and t o have J £ 5/2. Ob-servations on the anisotropy of the neutrons with respect to the deuteron beam at Ed=0.60 Mev. and the gamma ray isotropy with respect to the neutrons definitely indicated that the 0.V3 Mev excited level of Be? has/: J=l /2 . The super allowed nature of the fi decay Be?(£ ) L i ? x limits the ground state of Be? to have J £ 3/2. A value of about lCT-^ second for the ha l f - l i f e of the J=l/2 level of Be? is in agreement with the supposition that this decay occurs by magnetic dipole emission. It would therefore appear that the single particle picture of these nuclei does give a qualitative picture of the two lowest levels but is not sufficient for a quantitative de scription of a l l features. Apart from the interest in the ground states of the mass 7 nuclei there is great interest in the formation of these nuclei in astrophysics from the standpoint of explaining quan ti t a t i v e l y the p-p chain in hydrogen-burning stars (Fowler, 1958). In this process four hydrogen atoms are converted to one helium atom accompanied by the release of 26.7 Mev of energy. The possible processes invoked to explain the reaction are: __.H,(p./8%)H,(p.!f)He3r (He*.2P)He* < « If The e n e r g i e s r e l e a s e d i n t h e t h r e e p o s s i b l e c h a i n s , e x c l u s i v e o f n e u t r i n o e n e r g y l o s s e s , a r e d i f f e r e n t , b e i n g 26.2 Mev, 2^.6 Mev and 19.1 Mev i n r e a c t i o n s ( 1) , (2) and (3) r e  s p e c t i v e l y . 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 i f t h e p r o c e s s p r o  c e e d s b y r e a c t i o n (3) c o n s i d e r a b l e e n e r g y e s c a p e s (29%) f r o m t h e s y s t e m v i a t h e v e r y e n e r g e t i c n e u t r i n o s accompa n y i n g t h e 15 Mev p+ d e c a y o f B 8 . k f a c t o r a f f e c t i n g t h e r e l a t i v e i m p o r t a n c e o f c h a i n s 7 (2) and (3) i s t h e r e l a t i v e p r o b a b i l i t y t h a t Be w i l l be d e  s t r o y e d b y e l e c t r o n o r b y p r o t o n c a p t u r e . The c a p t u r e c r o s s - s e c t i o n o f t h e l a t t e r r e a c t i o n , B e ? ( p , < f ) B 8 , has n o t b e e n r e  p o r t e d as y e t f o r p r o t o n s , however. The c h o i c e b e t w e e n c h a i n s (1) and (2) i s g r e a t l y a f  f e c t e d b y t h e s i z e o f t h e c a p t u r e c r o s s - s e c t i o n o f He3 f o r ot, - p a r t i c l e s i n t h e r e a c t i o n He3(<* , ) B e 7 . No c r o s s - s e c t i o n f o r t h i s r e a c t i o n was known u n t i l r e c e n t l y when H o l m g r e s s and J o h n s t o n (1959) measured i t u s i n g a He^ gas t a r g e t , k c h e c k on t h i s c r o s s - s e c t i o n may a l s o be made f r o m t h e c r o s s - s e c t i o n o f t h e m i r r o r r e a c t i o n T(<*.,S ) L i 7 . B o t h H o l m g r e n and J o h n s t o n (1959) and R i l e y (1958) have measured t h i s v a l u e f o r - p a r t i c l e e n e r g i e s f r o m 0.h7 t o 2 Mev and w h i l e t h e i r r e s u l t s a g r e e d w i t h  i n t h e combined u n c e r t a i n t i e s l a r g e e r r o r s were q u o t e d a m o u n t i n g t o a t l e a s t 30% i n e a c h c a s e . I t was t h e r e f o r e f e l t t h a t a more a c c u r a t e d e t e r m i n a t i o n o f t h e a b s o l u t e c r o s s - s e c t i o n w o u l d be o f some v a l u e . I n o r d e r t o g i v e a good e s t i m a t e o f t h e a b s o l u t e cross-section and also to aid in understanding the nature of the reaction angular distribution measurements on the direct radiative capture gamma rays have been made. This latter inves- + tigation was also prompted by the anisotropy of 0.39 - 0.37 observed by Riley at 1.6 Mev bombarding energy. 1 C h a p t e r I I E x p e r i m e n t a l : 1. A p p a r a t u s (a ) V an de G r a a f f G e n e r a t o r The s o u r c e o f t h e i o n beam f o r t h e e x p e r i m e n t t o be d e s c r i b e d was 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 ' s V a n de G r a a f f e l e c t r o s t a t i c g e n e r a t o r . Beams o f s i n g l y i o n i z e d a l p h a p a r t i c l e s o f e n e r g i e s up t o 2 Mev and o f i n t e n s i t y on t h e t a r g e t up t o 10 m i c r o a m p e r e s were a v a i l a b l e . The s t r a i g h t down beam f r o m t h e a c c e l e r a t i n g c o l u m n was b e n t t h r o u g h 90° b y a l a r g e e l e c  t r o m a g n e t i n t o a h o r i z o n t a l g l a s s s i d e a r m t u b e w i t h a t a r g e t a t t h e e n d . C a r e f u l a l i g n m e n t and f o c u s s i n g o f t h e beam e n t e r  i n g t h e t o p o f t h e magnet was n e c e s s a r y t o a v o i d h a v i n g i t s t r i k e t h e magnet box and c a u s e a l a r g e i n c r e a s e i n n e u t r o n i n  d u c e d b a c k g r o u n d f r o m r e a c t i o n s s u c h as C^(0( , n ) 0 ^ i t h e c a r b o n a r i s i n g b e c a u s e o f t h e p r e s e n c e o f d i f f u s i o n pump o i l v a p o r . The l o n g t e r m s t a b i l i t y o f t h e m a g n e t i c f i e l d has b e e n measured t o be o f t h e o r d e r o f 3 p a r t s i n 10,000 b y A a r o n - s o n (1950) and so was o f n e g l i g i b l e c o n c e r n i n t h i s e x p e r i m e n t . The e n e r g y o f t h e a c c e l e r a t e d p a r t i c l e s was r e a d on a g e n e r a t i n g v o l t m e t e r w h i c h l o o k e d a t t h e h i g h v o l t a g e dome. Any v a r i a t i o n i n a l p h a p a r t i c l e e n e r g y r e a c h i n g t h e t a r g e t as r e a d b y t h i s v o l t  meter was l e s s t h a n 3 Kev. C a l i b r a t i o n o f t h e e n e r g y s c a l e was c a r r i e d o u t b y o b s e r v i n g t h e r e s o n a n c e s o f u n d e r p r o t o n ' bombardment o f 0.3+0, 0.8735 and 1.372 Mev. e n e r g y . The c a l l -FIGURE 2 SIDEARM A R R A N G E M E N T V A N D E G R A A F F G E N E R A T O R 7 o r a t i o n r e m a i n e d c o n s t a n t t o - 1.5 Kev o v e r a p e r i o d o f 6 months. (h) S i d e a r m A r r a n g e m e n t The e x p e r i m e n t a l a r r a n g e m e n t o f t h e t a r g e t t u b e and t h e s i d e a r m i s shown i n F i g u r e 2. The t o t a l l e n g t h o f t h e h o r i z o n t a l s i d e a r m was a b o u t 6 f e e t and i t was l o c a t e d MJ>- i n c h e s o f f t h e f l o o r . P r o v i s i o n f o r l i n i n g t h e s i d e a r m up op t i c a l l y b e f o r e r u n n i n g a beam was made by h a v i n g a s m a l l (1/16") g l a s s window i n t h e 1/16" b r a s s t a r g e t p o t w a l l on t h e a x i s o f t h e s i d e a r m t u b e . A g o l d s t o p o f 1 cm. d i a m e t e r was u s e d p a r t way a l o n g t h e t u b e and two o t h e r s o f molybdenum ( 3/8 Hx 3/ l6") i n t h e t a r g e t p o t i t s e l f i n o r d e r t o d e f i n e t h e beam. T h e s e m a t e r i a l s o f h i g h a t o m i c number were u s e d i n o r d e r t o r e d u c e a n y C o u l o m b - e x c i t e d b a c k g r o u n d . A l i q u i d a i r c o o l e d t r a p was mounted i n f r o n t o f t h e t a r g e t chamber t o c o n d e n s e o u t d i f f u s i o n pump o i l v a p o r s p r e  s e n t i n t h e t u b e . O c c a s i o n a l l y , t h e magnet box was c l e a n e d w i t h s t e e l w o o l and h o t d i l u t e n i t r i c a c i d t o r e d u c e b a c k g r o u n d f r o m s t r a i g h t down beam components o t h e r t h a n t h o s e o f mass 4. The t a r g e t p o t and molybdenum s t o p s were c l e a n e d b e f o r e e a c h r u n . I n o r d e r t o measure t h e beam c u r r e n t t h e t a r g e t h o l d e r was i n s u l a t e d f r o m t h e t a r g e t p o t w i t h a l u c i t e s p a c e r and 9 0 Yvolt p o s i t i v e p o t e n t i a l was a p p l i e d t o i t t o r e d u c e s e c o n d a r y e l e c t r o n e m i s s i o n f r o m t h e t a r g e t . T h i s t a r g e t c u r r e n t was 8 measured on a c u r r e n t i n t e g r a t e r ( E d w a r d s , 1950) on t h e 1.0 jmf s c a l e where one i n t e g r a t o r c o u n t c o r r e s p o n d e d t o a b o u t 106 m i c r o c o u l o m b s w i t h t h e e x a c t v a l u e d e p e n d e n t u p o n t h e m a g n i t u d e o f t h e c u r r e n t b e i n g m e a s u r e d . T h i s d e v i c e was c a l i b r a t e d f r e  q u e n t l y and o b s e r v e d t o s t a y c o n s t a n t t o w i t h i n 1%. ( c ) S c i n t i l l a t i o n C o u n t e r ( i ) S h i e l d i n g Two s c i n t i l l a t i o n c o u n t e r s were t r i e d f o r t h i s e x  p e r i m e n t ; one, c o n s i s t i n g o f a 2%"xk2>" N a l ( T l ) c r y s t a l mounted on a Dumont K1213 p h o t o m u l t i p l i e r t u b e and t h e o t h e r a 2^-"x3^" NaI(T*+) c r y s t a l on a Dumont 6363 p h o t o m u l t i p l i e r a s u s e d by R i l e y . B o t h c o u n t e r s gave g o o d s p e c t r a f o r t r i a l r u n s o f a l p h a p a r t i c l e s on a t r i t i u m t a r g e t w i t h h e a v y l e a d s h i e l d i n g . The beam d e p e n d e n t b a c k g r o u n d c o u n t s , f o u n d b y r u n n i n g t h e beam on a p i e c e o f g i r c o n i u m , w e r e i n t h e r a t i o o f t h e v o l u m e s o f t h e two c r y s t a l s . F o r t h e l a r g e r c r y s t a l t h i s b a c k g r o u n d i n t h e 2 t o 3 Mev r e g i o n o f t h e s p e c t r a amounted t o 27 c o u n t s p e r m i n u t e p e r Mev a t t h e 1.6 Mev b o m b a r d i n g e n e r g y . B e c a u s e o f a l a r g e r volume and n o t i c e a b l y b e t t e r r e s o l u t i o n t h e l a r g e c r y s t a l was t h e one c h o s e n f o r use i n t h i s e x p e r i m e n t . F o r most o f t h e T(o^ ,tf ) L i ? r u n s t h e end o f t h e c o u n t e r was p l a c e d a b o u t 6 cm. f r o m t h e o u t s i d e o f t h e 2" d i a m e t e r t a r  g e t p o t . I n a l l r u n s t h e c o u n t e r and t a r g e t p o t were s u r r o u n d e d by a b o u t 5" o f l e a d on a l l s i d e s . I n a d d i t i o n a l e a d w a l l was r put up b e t w e e n t h e c o u n t e r and t h e magnet b o x w h i l e wax was i3or \ZO\- \\o\ \och FIGURE 3 SCINTILLATION COUNTER EFFICIENCY (23/4 " X41/2 " Nal Crystal ) 90h 6oY > o z UJ y 50h U- u. 6cr ^ ( l - e ^ S 50h J i_ J L J l_ J I 8 IO 12 14 G A M M A R A Y E N E R G Y ( M e v ) 16 18 20 p r e s e n t b e t w e e n t h i s w a l l and t h e magnet b o x . T h e s e m a t e r i a l s s h i e l d e d t h e c o u n t e r f r o m . a n y (<*,n) or (d , n ) r e a c t i o n s o f t h e beam w i t h pump o i l v a p o r s i n t h e magnet box. ( i i ) E f f i c i e n c y I n gamma r a y f l u x measurements where s c i n t i l l a t i o n c o u n t e r s a r e employed t h e c o u n t e r e f f i c i e n c y must be f o u n d f o r t h e p a r t i c u l a r gamma r a y e n e r g i e s i n v o l v e d . A commonly u s e d v a l u e i s t h a t d e d u c e d f r o m t h e t o t a l 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 , ju. , f o r t h e p a r t i c u l a r c r y s t a l and gamma r a y e n e r g y and d e f i n e d a s ( l - e ) where L i s t h e l e n g t h o f t h e s c i n  t i l l a t i n g c r y s t a l . When u s i n g t h i s e f f i c i e n c y , w h i c h i s p l o t t e d a s a f u n c t i o n o f e n e r g y f o r a p a r t i c u l a r N a l c r y s t a l i n F i g u r e 3, t h e t o t a l number o f c o u n t s r e c o r d e d b y t h e c o u n t e r a r e u s u a l l y f o u n d f r o m t h e gamma r a y s p e c t r u m b y e x t r a p o l a t i n g t h e s p e c t r u m t o z e r o e n e r g y w i t h a f l a t t a i l f r o m t h e minimum w h i c h o c c u r s a t a b o u t h a l f t h e f u l l gamma r a y e n e r g y . The c o r  r e c t n e s s o f t h i s method i s i n d o u b t , however, f o r t h e f o l l o w i n g 11 i p r e a s o n : i n t h e B ( p , f )CXe: s p e c t r u m , o b t a i n e d a t a l o w bom b a r d i n g e n e r g y w i t h a N a l c r y s t a l a t 9 0 ° . t o t h e beam d i r e c t i o n , t h e t o t a l number o f 12 Mev c o u n t s i s ' g r e a t e r , b y a b o u t 2 0 t o 25%, t h a n t h e t o t a l number o f h Mev c o u n t s a s d e t e r m i n e d b y t h e above method. T h i s c o n t r a d i c t s t h e f a c t t h a t t h e h Mev and t h e 12 Mev r a d i a t i o n s have t h e same i n t e n s i t y i n t h e 9 0 ° d i r e c t i o n ( A j z e n b e r g and L a u r i t s e n , 1 9 5 5 ) . A v a r i a t i o n i n t o t a l a b s o r p t i o n ^ c o e f f i c i e n t o f N a l c a n n o t a c c o u n t f o r t h i s s i n c e i t c a u s e s o n l y 1 0 a 3% d i f f e r e n c e i n t h e two e f f i c i e n c i e s a s d e f i n e d above and a s c a n be s e e n f r o m F i g u r e 3* I n a n a t t e m p t t o c l e a r up s u c h a s e r i o u s i n c o n s i s t e n c y i n f l u x measurements t h e e f f i c i e n c y has been d e f i n e d i n a s l i g h t l y d i f f e r e n t manner i n t h i s l a b o r a t o r y . The p r o c e e d u r e i s t o d e f i n e t h e e f f i c i e n c y t o t h e h a l f - e n e r g y b i a s a s t h e r a t i o o f t h e t o t a l c o u n t s above t h e h a l f - e n e r g y p o i n t on t h e gamma r a y s p e c t r u m t o t h e t o t a l number o f gamma r a y s i n c i d e n t on t h e c r y s t a l . E x p e r i m e n t a l l y , e f f i c i e n c i e s d e f i n e d i n t h i s way have been measured a t 0 . 5 1 Mev and 1 . 2 5 Mev u s i n g t h e r a d i a t i o n s 2 2 6>0 f r o m c a l i b r a t e d s o u r c e s o f Na and Co r e s p e c t i v e l y . A p o i n t a t 6 . 1 ^ Mev was a l s o o b t a i n e d f r o m F ^ C p , * , * ) 0 l D r a d i a t i o n , t h e a b s o l u t e y i e l d b e i n g d e t e r m i n e d f r o m a l p h a p a r t i c l e c o u n t i n g as d e s c r i b e d i n P a r t I I o f t h i s t h e s i s . U n f o r t u n a t e l y no e f  f i c i e n c y d e t e r m i n a t i o n c o u l d be made a t h i g h e r e n e r g i e s s i n c e t h e a b s o l u t e y i e l d o f gamma r a y s f r o m a n y p o s s i b l e r e a c t i o n was n o t known w i t h s u f f i c i e n t a c c u r a c y . However, a n e x t r a p o l a t i o n was p r e f o r m e d a s i n F i g u r e 3 t o h i g h e r e n e r g i e s k e e p i n g t h e e x  t r a p o l a t e d c u r v e between t h o s e f o r ( l - e " A l L ) and f o r * H ( l - e ~ A*"L). The f o r m e r i s t h e t o t a l t h e o r e t i c a l e f f i c i e n c y b a s e d on p r i m a r y a b s o r p t i o n p r o c e s s e s o n l y w h i l e t h e l a t t e r i s t h e t h e o r e t i c a l e f f i c i e n c y c o n s i d e r i n g p r i m a r y a b s o r p t i o n p r o c e s s e s w h i c h l e a v e more t h a n h a l f t h e gamma r a y e n e r g y i n t h e c r y s t a l , t h a t i s , t h e c o n t r i b u t i o n f r o m t h e p r i m a r y compton t a i l b e l o w h a l f e n e r g y 11 has b e e n d r o p p e d and t h e t r a n s f e r o f p u l s e s above and b e l o w t h e h a l f e n e r g y p o i n t due t o s e c o n d a r y p r o c e s s e s i n t h e c r y s t a l has n o t b e e n c o n s i d e r e d . T h i s e m p i r i c a l c u r v e f o r t h e e f f i c i e n c y a s a f u n c t i o n o f e n e r g y i s b e l i e v e d t o be a c c u r a t e t o w i t h i n 5%» up t o 12 Mev and t o w i t h i n 10% f r o m 12 t o 20 Mev. P a r t i a l j u s  t i f i c a t i o n f o r t h e shape drawn i s o b t a i n e d f r o m t h e r e s u l t s o f t h e s t a n d a r d G-M c o u n t e r e f f i c i e n c y d e t e r m i n a t i o n t o be d e s c r i b e d i n P a r t I I . The shape f o u n d f o r t h i s e f f i c i e n c y v e r s u s e n e r g y c u r v e was d e p e n d e n t u p o n t h e s c i n t i l l a t i o n c o u n t e r e f f i c i e n c y assumed and s i n c e a smooth c u r v e was f o u n d t h e v a l u e s u s e d f o r t h e s c i n t i l l a t i o n c o u n t e r a r e b e l i e v e d t o be c o r r e c t t o w i t h i n t h e s t a t e d e r r o r . A n o t h e r c h a r a c t e r i s t i c o f t h e s c i n t i l l a t i n g c r y s t a l u s e d was i t s e f f e c t i v e c e n t r e d i s t a n c e . T h i s d i s t a n c e f r o m t h e c r y s t a l f a c e t o i t s e f f e c t i v e c e n t r e may be f o u n d t h e o r e t i c a l l y as t = ->6rt [ 0 . 5 ( l + e " / U L ) 1. However t h i s i s f o u n d t o d i s a g r e e w i t h e x p e r i m e n t a l d e t e r m i n a t i o n s ( R i l e y , 1958). S i n c e t h e s e d i s t a n c e s as a f u n c t i o n o f gamma r a y e n e r g y have n o t b e e n mea s u r e d f o r t h e 2-|"x1+^ -M c r y s t a l used, v a l u e s were assumed on t h e b a s i s o f p r e v i o u s measurements on t h e 2^nx3^u c r y s t a l . The u n  c e r t a i n t y i n s u c h a n e s t i m a t e i s b e l i e v e d t o be l e s s t h a n - 0.5 cm. The e x p e r i m e n t a l v a l u e s o f e f f i c i e n c i e s d e s c r i b e d above a r e d e f i n e d f o r t h e N a l c r y s t a l i n a l e a d c a s t l e and t h e FIGURE 4 BLOCK DIAGRAM OF ELECTRONICS X - R A Y P H O T O C F . C R M U L T I P L I E R A M P L I F I E R P O W E R H I G H V O L T A G E S U P P L Y L O W V O L T G E S U P P L Y S C A L E R I O O - C H A N N E L K I C K S O R T E R 12 f a c t t h a t more l e a d was u s e d i n t h e e x p e r i m e n t t h a n i n t h e e f  f i c i e n c y measurements makes a s l i g h t d i f f e r e n c e w h i c h was n o t a l l o w e d f o r . T h i s , t h e r e f o r e , w i l l i n t r o d u c e a s m a l l unknown e r r o r i n t o a b s o l u t e f l u x measurements, (d) E l e c t r o n i c s H i g h v o l t a g e f o r t h e p h o t o m u l t i p l i e r s was u s u a l l y a b o u t 925 v o l t s s u p p l i e d b y a n I s o t o p e s D e v e l o p m e n t E.H.T. s u p p l y . N e g a t i v e o u t p u t p u l s e s f r o m a hO^B c a t h o d e f o l l o w e r were f e d i n t o a l o n g 100 ohm c a b l e t o a n o t h e r c a t h o d e f o l l o w e r u n i t u s e d t o d r i v e a D y n a t r o n R a d i o L i m i t e d a m p l i f i e r T y pe l V ^ O A . p o s i t i v e p u l s e s f r o m t h i s u n i t were f e d t o a D y n a t r o n R a d i o L i m i t e d s c a l a r Type 1009A i n p a r a l l e l w i t h a 100-channel Com p u t i n g D e v i c e s o f Canada k i c k s o r t e r . A b l o c k d i a g r a m i s shown i n F i g u r e k. The e l e c t r o n i c e quipment was c a l i b r a t e d f o r l i n  e a r i t y b y f e e d i n g p u l s e s f r o m a m e r c u r y r e l a y p u l s e g e n e r a t o r ( R o b e r s t o n , 1957) i n t o t h e +03B c a t h o d e f o l l o w e r u n i t on t h e s c i n t i l l a t i o n c o u n t e r . The p h o t o m u l t i p l i e r was c a l i b r a t e d s e  p a r a t e l y b y means o f a RdTh s o u r c e w h i c h a l s o s e t t h e e n e r g y s c a l e on t h e k i c k s o r t e r . 2. T r i t i u m T a r g e t ( a ) M o u n t i n g The t r i t i u m - z i r c o n i u m t a r g e t (#4) u s e d i n t h i s e x  p e r i m e n t c o n s i s t e d o f a s m a l l amount o f t r i t i u m a d s o r b e d i n a t h i n e v a p o r a t e d f i l m o f z i r c o n i u m on a p l a t i n u m b a c k i n g d i s c 13 o f t h i c k n e s s 0.25 Mn and d i a m e t e r 1". The amount o f z i r c o n i u m p r e s e n t as s p e c i f i e d b y t h e s u p p l i e r s , Oak R i d g e N a t i o n a l L a  b o r a t o r y , was 0.002705 gm on t h e 5.07 c m 2 d i s c a r e a . The t r i  t i u m c o n t e n t as measured b y t h e above l a b o r a t o r y was 731 m i l l i - c u r i e s on A p r i l 30, 1959. I n o r d e r t o p r e v e n t l o s s o f t r i t i u m c a u s e d b y t a r g e t h e a t i n g when a beam was b e i n g r u n p r e c a u t i o n s were t a k e n i n t h e m o u n t i n g a r r a n g e m e n t . The t h i n t a r g e t d i s c was h e l d r i g i d l y a g a i n s t a t h i c k (1/32") c o p p e r b a c k i n g p l a t e w h i c h was i n t u r n clamped t o a c o p p e r s u p p o r t i n g r o d . T h u s , good h e a t c o n d u c t i o n away f r o m t h e t a r g e t was o b t a i n e d . I n a d d i t i o n t h e l o w e r end o f t h e s u p p o r t i n g r o d was c o o l e d w i t h f o r c e d a i r . A p i e c e o f l u c i t e s w i t h a n g l e markings, on i t was p l a c e d o v e r t h e g l a s s w i n  dow on t h e t o p o f t h e t a r g e t p o t t o e n a b l e a n y t a r g e t a n g l e t o be s e t e a s i l y . ( b ) T r i t i u m C o n t e n t The amount o f t r i t i u m on t h e t a r g e t was e s t i m a t e d i n two ways: (1) ft'Activity A l l o w i n g f o r t h e d e c a y o f 1% o f t h e t r i t i u m w i t h a c h a r a c t e r i s t i c h a l f - l i f e o f 12.26 y e a r s f r o m t h e t i m e o f t h e Oak R i d g e N a t i o n a l L a b o r a t o r y ' s a c t i v i t y measurement t o t h e t i m e t h e e x p e r i m e n t was c a r r i e d o u t , t h e t r i t i u m c o n t e n t e s t i  mated f r o m t h e ^ - a c t i v i t y was 15.0x10^ atoms o f t r i t i u m , o r fe.95xl01^ t r i t i u m atoms p e r cm 2. S i n c e t h e amount o f z i r c o n i u m 2500 FIGURE 5 2 0 MEV T(p,r)He4 SPECTRUM IN 23/4x41/2" Nal CRSTAL 100 CHANNEL NUMBER 1 18 2 p r e s e n t was 3.53x10 atoms p e r cm o f t a r g e t a r e a t h e t r i t i u m t o z i r c o n i u m a t o m i c r a t i o may he f o u n d as O.S1*:!. ( i i ) T ( p . t f )He I f Y i e l d 7 Towards t h e end o f t h e T ( o C , t f ) L i work i t was d e c i d e d t o measure t h e t r i t i u m t a r g e t c o n t e n t b y means o f t h e T ( p , J J )He y i e l d u s i n g t h e 90° d i f f e r e n t i a l c r o s s - s e c t i o n d a t a o f P e r r y and Bame (1955). A c c o r d i n g l y , two T ( p , y )He l f r u n s were t a k e n s e p a r a t e d and p r o c e e d e d b y r u n s o f T ( o ( , Jf ) L i ^ w i t h t h e c o u n t e r a t 90° t o t h e beam. A l l o f t h e s e r u n s were done on t h e same s p o t on t h e t a r g e t , w i t h t h e same h e a v i l y s h i e l d e d s c i n t i l l a t i o n c o u n t e r and t h e same c o u n t e r - t o - t a r g e t d i s t a n c e . F o r t h e T ( p , Jf )He' + r e a c t i o n t h e 20 Mev s p e c t r u m i n F i g u r e 5 was o b s e r v e d w i t h t h e 100-channel k i c k s o r t e r a t b i a s 1. The s c i n t i l l a t i o n c o u n t e r e f f i c i e n c y u s e d f o r t h i s 20 Mev r a d i a t i o n was n o t t h a t d e f i n e d t o t h e h a l f e n e r g y b i a s - M l b u t t h e one d e f i n e d a s ( l - e ) t h e t o t a l number o f r e c o r d e d e v e n t s b e i n g f o u n d b y e x t r a p o l a t i n g t h e smooth t a i l o f t h e 20 Mev s p e c t r u m t o z e r o p u l s e h e i g h t a s shown i n t h e f i g u r e . T h i s d o u b t f u l method was a p p l i e d s i n c e i t was t h e same one u s e d b y P e r r y and Bame i n e s t a b l i s h i n g t h e i r c r o s s - s e c t i o n , so t h a t i f a n y e r r o r i s i n t r o d u c e d b y t h e method i t s h o u l d be c a n c e l l e d i n f i n d i n g t h e t a r g e t t r i t i u m c o n t e n t . T o r e c o r d t h e s p e c t r u m shown a beam o f a b o u t 7 m i c r o - Tamperes o f p r o t o n s a t 800 kev e n e r g y was u s e d . T h i s e n e r g y was c h o s e n f o r two r e a s o n s : f i r s t , t o be b e l o w t h e T ( p , n ) H e 3 t h r e s h o l d FIGURE 6 GAMMA RAY ABSORPTION FACTOR FOR TARGET BACKING Pt : 0 . 2 5 m m . Cu : 0 7 9 4 m m . Zr : 0 . 0 3 6 mm. 8 o _J z o I- Q. cc o (0 CQ < ( e ^ ' - l ) (e is i6 t? fa 2o 7 8 9 10 II 12 13 14 GAMMA RAY ENERGY ( M E V ) 15 19 a t 1.0 Mev a n d , s e c o n d , t o a v o i d t h e 0.873 Mev r e s o n a n c e o f F as much as p o s s i b l e s i n c e f l u o r i n e was known t o be on t h e t a r g e t . E v e n a t 800 k e v , however, some F ^ C p , * , ^ )0 1^ 6.1k Mev gamma r a y s were o b s e r v e d . The s p e c t r u m shown has b e e n c o r r e c t e d f o r beam d e p e n d e n t b a c k g r o u n d f o u n d b y r e v e r s i n g t h e t a r g e t and r u n n i n g t h e beam on a t h i n (.001^-") z i r c o n i u m s t r i p on t h e back f o r t h e same l e n g t h o f t i m e and number o f i n t e g r a t o r c o u n t s a s i n a T ( p , t f ) H e l f r u n . T h i s b a c k g r o u n d was so s m a l l t h a t i t wo u l d n o t show up i n t h e f i g u r e above a b o u t c h a n n e l 30. D u r i n g t h e r u n s t h e f r o n t - f a c e o f t h e s c i n t i l l a t i o n c o u n t e r was 5.96 cm away f r o m t h e o u t s i d e o f t h e b r a s s t a r g e t p o t and t h e t a r g e t was p o s i t i o n e d a t *+5° s o t h a t t h e r e a c t i o n gamma r a y s p a s s e d t h r o u g h t h e t a r g e t b a c k i n g . F o r a n e f f e c t i v e c e n t r e d i s t a n c e , f r o m t h e f r o n t f a c e o f t h e c r y s t a l , e s t i m a t e d t o be ^.0 cm. a s p a c i n g o f 1.03i+ cm betw e e n t h e c r y s t a l and t h e aluminum c a n c o v e r i n g t h e c r y s t a l , and a t a r g e t p o t r a d i u s o f 2.5k cm. 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 r y s t a l , f o r 20 Mev gamma r a y s , a t t h e t a r g e t was f o u n d t o be 0.198 s t e r a d i a n . The a b s o r p t i o n c o r r e c t i o n f o r l o s s o f gamma r a y i n  t e n s i t y i n t h e t a r g e t b a c k i n g o f p l a t i n u m - c o p p e r - z i r c o n i u m may be r e a d f r o m t h e c u r v e i n F i g u r e 6. A p p l y i n g a l s o a c o r r e c t i o n f o r gamma r a y a b s o r p t i o n i n t h e 1/16" t a r g e t p o t w a l l s r e s u l t s i n a f i n a l f a c t o r o f 1.137. T A L P H A ENERGY ( M E V ) 16 Hence, the number of tritium atoms on the target may be calculated from the following data: Nc = 62920 - 7$ - 6+120 i 7% after correcting for the effect of the counter solid angle on the sin angular distribution of 20 Mev gamma rays. I I = 0.198 - 6$ € = l-e " L = O.837 - 10$ Nn = (50 integrator counts)(103.8xl0 6) = ^ 2L, x 1 016 1.6x10-^ J.^H-XJ.U protons - 1$ . (3_£l) = 2.666xlO"3°cm2/steradian - 10$ for Ep = 753 kev. (du) ) 9 0 o The target thickness for 800 kev protons was found from the curve in Figure 7, drawn from Whaling1s (1958) data, as 95 kev - 5$ for the target at )+50. Hence the mean proton energy in the target was found to be Ep = 800-95 = 753 kev and the above 2 90 differential cross-section value was obtained for this energy from Perry and Bame (1955) M = lfA8xl0 1 8 atoms/cm2 - 18$ N p ( I fL) .JU (du>) 9 0o for the atomic surface density of tritium. This, then, leads to a tritium-zirconium ratio of / l . 3 : l which is in quite violent disagreement with the ft a c t i v i t y 17 measurements w h i c h gave 0.8^:1. T h i s m i g h t be e x p l a i n e d b y a v e r y n o n - u n i f o r m d i s t r i b u t i o n o f t h e t r i t i u m on t h e t a r g e t s u r  f a c e . 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 e s u p p l i e r , Oak R i d g e N a t i o n a l L a b o r a t o r y , c l a i m s t h a t t h e t r i t i u m - z i r c o n i u m r a t e s on t h e i r t a r g e t s i s a l w a y s a t l e a s t 1:1 and may be a s h i g h a s 1.8:1. S i n c e t h e i r a c t i v i t y measurements c o n t r a d i c t t h i s on a number o f t r i t i u m t a r g e t s r e c e i v e d f r o m them t h e i r a c t i v i t y measurements may be a t f a u l t ; p o s s i b l y a l l t h e low e n e r g y b e t a r a y s do n o t e s c a p e f r o m t h e t h i n z i r c o n i u m l a y e r s u s e d f o r t h e s e t a r g e t s . ( c ) T a r g e t T h i c k n e s s f o r A l p h a P a r t i c l e s S i n c e t h e s t o p p i n g c r o s s - s e c t i o n o f t r i t i u m atoms i s s m a l l compared t o t h a t f o r z i r c o n i u m atoms a 1:1 r a t i o o f t r i  t i u m t o z i r c o n i u m was assumed i n o r d e r t o make u s e o f t h e c u r v e s , shown i n F i g u r e 7, d e d u c e d f r o m W h a l i n g ' s r e p o r t , t o f i n d t h e s t o p p i n g c r o s s - s e c t i o n f o r a l p h a p a r t i c l e s . S uppose a p a r t i c l e o f e n e r g y E ^ i s i n c i d e n t on a t a r  g e t o f a t o m i c s u r f a c e d e n s i t y n (atoms p e r u n i t a r e a ) and em e r g e s w i t h a n e n e r g y E 0 . The l o s s i n e n e r g y o f t h e p a r t i c l e ( p ) . d n = / £ d (dx) N JQ where N i s t h e a t o m i c d e n s i t y o f t h e t a r g e t m a t e r i a l (atoms per u n i t v o l u m e ) and £ i s t h e s t o p p i n g c r o s s - s e c t i o n t h a t W h a l i n g t a b u l a t e s as a f u n c t i o n o f e n e r g y . From t h i s f o r m u l a , knowing t h e a t o m i c s u r f a c e d e n s i t y , t h e t a r g e t t h i c k n e s s i n e l e c - ^ t r o n - v o l t s may be f o u n d . However, t h e n u m e r i c a l i n t e g r a t i o n i s e>oo TARGET THICKNESS, AE , (KEV) 18 r a t h e r t e d i o u s and so a s i n g l e t r a n s f o r m a t i o n may be made t o a n o t h e r f o r m where jE± . I n t h i s f o r m n may be g i v e n n = dE e a s i l y i n t e r m s o f E 0 f o r a f i x e d Ej_, t h e p r o c e e d u r e b e i n g t o p l o t l/£ as a f u n c t i o n o f e n e r g y and d o i n g a s i n g l e n u m e r i c a l i n t e g r a t i o n . S u c h a p l o t f o r Ej_ e q u a l t o 1.6 Mev and 800 k e v i s g i v e n i n F i g u r e 8. F o r t h e t a r g e t u s e d i n t h i s e x p e r i m e n t t h e s u r f a c e d e n s i t y o f z i r c o n i u m - t r i t i u m p a i r s was t a k e n t o be TI^^ = 3.53xlO l8 Z r - T a toms/cm 2 b a s e d on t h e Oak R i d g e measurement o f t h e s u r f a c e d e n s i t y o f z i r c o n i u m on t h e t a r g e t . F o r t h e t a r g e t o p e r a t e d a t +5° t o t h e beam t h i s v a l u e was i n c r e a s e d t o 5.00x10-*- Z r - T a t o m s / c m 2 . U s i n g F i g u r e 8 t h e f o l l o w i n g may be c a l c u l a t e d : T a r g e t A n g l e n Z r - T A E E « = Eoc- 4 | (Kev) 800 ( d e g r e e s ) 90 Z r - T atoms /cm^ 3.53x1018 (Kev) 36+ (Kev) 618 +5 5.00 +80 560 1600 90 3.53 39+ 1+00 +5 5.oo 560 1320 3. A n g u l a r D i s t r i b u t i o n M easurements (a ) P r o c e d u r e - The m a i n e n e r g y c h o s e n f o r t h e a n g u l a r d i s t r i b u t i o n ^measurement was 1.6 Mev s i n c e a good y i e l d was o b t a i n e d and s i n c e 19 R i l e y ' s n o r m a l i z a t i o n o c c u r e d a t t h i s e n e r g y . I n t h e s e r u n s t h e 2-|-"x1+^ -" N a l (Harshaw) c r y s t a l was u s e d and t h e s c i n t i l l a t i o n c o u n t e r p o s i t i o n e d by means o f a l u c i t e s p a c e r s o t h a t i t s f r o n t f a c e was 5.96 cm f r o m t h e o u t s i d e o f t h e t a r g e t p o t . S i n c e i t was known f r o m R i l e y ' s r u n s and t h e low c r o s s - s e c t i o n o b t a i n e d t h a t b a c k g r o u n d c o u n t s c o u l d be t r o u b l e s o m e c a r e was t a k e n t o r e d u c e t h e s e t o a minimum a s d e s c r i b e d i n S e c t i o n 1 ( c ) ( i ) . A t t h e 1.6 Mev bombarding e n e r g y a t a r g e t c u r r e n t o f 3 t o k m i c r o a m p e r e s was m a i n t a i n e d f o r 50 i n t e g r a t o r c o u n t s i n a b o u t 25 m i n u t e s . T h i s t a r g e t c u r r e n t measurement was us e d a s t h e m o n i t o r and t a r g e t d e t e r i o r a t i o n c h e c k e d by r e p e a t r u n s a t t h e 90° c o u n t e r p o s i t i o n . No s i g n o f t a r g e t l o s s was n o t i c e d a t a n y t i m e . Runs were t a k e n w i t h t h e c o u n t e r a t 0°, ^5°» 90° and 13^° t o t h e beam d i r e c t i o n o n e a c h s i d e o f t h e beam. A t c e r t a i n c o u n t e r a n g l e s t h e t a r g e t was s e t a t 90° t o t h e beam and a t o t h e r a n g l e s i t was s e t a t ^5° t o t h e beam i n o r d e r t o a v o i d e x c e s s i v e a b s o r p t i o n o f gamma r a y s i n t h e t a r g e t b a c k i n g . A p r o c e e d u r e w h i c h e l i m i n a t e d a n y e f f e c t o f r i g h t - l e f t asymmetry was t o r u n a t c o u n t e r a n g l e s 0°and 90° ( b o t h s i d e s o f t h e beam) w i t h t h e t a r g e t a t ^-5°, t u r n t h e t a r g e t t h r o u g h 90° and r e p e a t t h e measurements a t t h e same c o u n t e r a n g l e s . F o r a l l r u n s t a k e n s p e c t r a were r e c o r d e d showing t r a n s  i t i o n s i n L i ? t o t h e g r o u n d s t a t e , ft, , t o t h e f i r s t e x c i t e d s t a t e 20 Jf^  and. from the f i r s t excited state to the ground state, ^3 . Measurements were also made at an 800 kev -particle bombarding energy. This energy was chosen because the yield was s t i l l quite high in order to see whether the angular d i s t r i  bution changed with bombarding energy. For this energy the counter was moved closer to the target pot, using a 2.12 cm. lucite spacer, since only the 0° and 90° angles were under i n  vestigation. A current of over 5 microamperes was run for 70 integrator counts taking about 25 minutes. Runs were taken with the target at *+5° (both angles) only. RdTh spectra were obtained frequently for energy c a l i  bration of the system. Occasionally, gain shifts of about 1 or 2 channels were observed probably due to a high counting rate in the s c i n t i l l a t i o n counter so that a l l runs had to be corrected for this before analyzing. In spite of the liquid air trap before the target pot carbon was deposited on the target changing it s color from a golden tan to a smudged brown appearance after a 1.6 Mev run and to light grey with blue edges after a run at 800 Kev. The target was moved as l i t t l e as possible in order to reduce the uncertainty in duplicating i t s angle and beam dependent background runs were then taken at the end of the work by reversing the target and running the beam on the piece J i i i i i i * — i — « _ i O 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 ' IOO CHANNEL NUMBER 21 o f z i r c o n i u m f o r t h e same number o f i n t e g r a t o r c o u n t s a s d u r i n g a r e g u l a r r u n . The t i m e d e p e n d e n t b a c k g r o u n d was a b o u t 7h c o u n t s p e r m i n u t e p e r Mev i n t h e r e g i o n o f gamma r a y e n e r g i e s 2 t o 3 Mev. The beam d e p e n d e n t b a c k g r o u n d however went f r o m 22 c o u n t s p e r mi n u t e p e r Mev a t 1.6 Mev bo m b a r d i n g e n e r g y t o 9 c o u n t s p e r mi n u t e p e r Mev a t 800 Kev i n t h e same r e g i o n , (b) S t a n d a r d Gamma R a y S p e c t r u m A f t e r c o r r e c t i n g f o r beam d e p e n d e n t b a c k g r o u n d t h e T( 0 C , } f ) L i ? gamma r a y s p e c t r a were p l o t t e d ; t y p i c a l s p e c t r a ob t a i n e d a t 1.6 and 0.8 Mev a r e shown i n F i g u r e 9. I n a d d i t i o n t o t h e !T( o*., tf" ) L i ? gamma r a y s i t was a p p a r e n t t h a t t h e r e was some b a c k g r o u n d p r e s e n t f r o m t h e t a r g e t i t s e l f s i m i l a r t o t h a t o b s e r v e d b y R i l e y . B e c a u s e o f t h i s unknown amount o f t a r g e t d e p e n d e n t b a c k g r o u n d two p r o c e e d u r e s were p o s s i b l e f o r t h e a n a l y s i s o f t h e d a t a . One was t o make a r o u g h e s t i m a t e o f t h i s b a c k g r o u n d b y a s s u m i n g t h a t i t d e c r e a s e d smoothly i n t h e r e g i o n of t h e 3 Mev gamma r a y peaks down t o t h e l e v e l o f t h e t a i l e x  t e n d i n g beyond t h e peaks.;- u p o n s u b t r a c t i o n t h e r e s u l t a n t s p e c  t r u m was t o be s e p a r a b l e i n t o two c u r v e s h a v i n g s t a n d a r d s h a p e s f o r gamma r a y s t o t h e g r o u n d s t a t e and f i r s t e x c i t e d s t a t e o f L i The a l t e r n a t i v e was t o make a d e c o m p o s i t i o n o f t h e T(oC , K ) L i ? gamma r a y s p e c t r u m i n t o i t s two gamma r a y components o f s t a n d a r d shape w h i c h c o u l d be s u b t r a c t e d l e a v i n g t h e t a r g e t d e p e n d e n t b a c k g r o u n d . B o t h methods were u s e d , however t h e s e c o n d one was c o n s i d e r e d more a c c u r a t e . FIGURE 10 STANDARD GAMMA RAY SPECTRUM 0 10 20 30 4 0 50 60 70 80 9 0 100 C H A N N E L N U M B E R 22 I n o r d e r t o make t h i s a n a l y s i s a 3 Mev s p e c t r u m o f s t a n d a r d shape was o b t a i n e d f r o m c o m p a r i s o n s o f gamma r a y s p e c t r a o f 3.09 Mev f r o m C 1 2(d,p,tf )C 1 3, 2.62 Mev f r o m RdTh, +.+3 Mev f r o m B " ( p , JT)C 1 2 and 6.1+ Mev f r o m F 1 9 ( p , ( * t* )o l 6. The 3.09 12 13 Mev gamma r a y f r o m C (d,p,K)C 3 w o u l d have b e e n s a t i s f a c t o r y a s a s t a n d a r d b y i t s e l f e x c e p t f o r t h e n e u t r o n s f r o m t h e C 1 3 ( d , n ) N 1 1 + r e a c t i o n w i t h t h e 1% o f C 1 3 i n t h e n a t u r a l c a r b o n (Aquadag) t a r g e t . The s t a n d a r d 3 Mev gamma r a y s p e c t r u m i s shown i n F i g u r e 10 a s i s t h e o b s e r v e d s p e c t r u m f r o m C 1 2 ( d , p )C 1 3* The d i f f e r e n c e o f t h e two g i v e s a t a r g e t d e p e n d e n t b a c k g r o u n d showing peaks a t 2.23 Mev f r o m t h e r e a c t i o n H ( f l , l f ) H 2 o f n e u - 1- t r o n s i n wax n e a r t h e c o u n t e r and a t l.*+3 Mev r e s u l t i n g f r o m a gamma r a y i n t h e d e c a y o f K i n t h e N a l c r y s t a l , ( c ) T(oC ,y ) L i 7 S p e c t r a A b o u t one h a l f o f t h e T ( * , l f ) L i gamma, s p e c t r a t a k e n were s u b j e c t e d t o a d e c o m p o s i t i o n i n t o two s t a n d a r d gamma r a y s and a smooth b a c k g r o u n d . The procedur-ec was t o f i t t h e p h o t o - peak o f t h e s t a n d a r d gamma r a y s p e c t r u m t o t h e u p p e r peak i n t h e n T ( o t , t f ) L i s p e c t r u m s u c h t h a t t h e d i f f e r e n c e , c o n s i d e r e d as b a c k g r o u n d , j o i n e d c o n t i n u o u s l y t o t h e t a i l above t h e u p p e r peak. The r e s t o f t h e s t a n d a r d gamma r a y s p e c t r u m was t h e n c o n - s t r u c t e d and s u b t r a c t e d f r o m t h e T(c< , j C ) L i r s p e c t r u m . A s i m i  l a r a n a l y s i s was p e r f o r m e d on t h e r e s u l t i n g c u r v e u s i n g , a s t h e s t a n d a r d gamma s p e c t r u m f o r ^ > a g°°3 RdTh s p e c t r u m . The r e  s u l t i n g b a c k g r o u n d , however, had o s c i l l a t i o n s i n i t — t h e peaks sooot- Soof FIGURE II DECOMPOSITION OF T(a/)Li7 SPECTRUM FOR E a = 1.6 MEV (1.3 M E V M E A N ) 3 M E V g 4 o o o r o I-< or e> UJ J- Booop Z o 0) i-z O o Zooof loooY E X P E R I M E N T A L 4 0 5 0 6 0 C H A N N E L N U M B E R 7 0 8 0 9 0 1 0 0 I 23 and v a l l e y s b e i n g o b s e r v e d t o change p o s i t i o n w i t h c h a n g i n g p a r t i c l e e n e r g y . The r e a s o n s f o r t h i s were two: f i r s t , b e c a u s e o f s t a t i s t i c a l e r r o r s i n t h e e x p e r i m e n t a l c u r v e a n d , s e c o n d , b e c a u s e t h e peaks o f t h e e x p e r i m e n t a l c u r v e were s u b s t a n t i a l l y b r o a d e r t h a n t h o s e due t o m o n o c h r o m a t i c gamma r a y s on a c c o u n t o f t h e t h i c k n e s s o f t h e t r i t i u m t a r g e t . No a l l o w a n c e f o r t h i s l a t t e r e f f e c t had been made i n c o n s t r u c t i n g t h e s t a n d a r d gamma r a y s p e c t r u m . S i n c e a snooth b a c k g r o u n d d i d n o t show up t h e two s t a n d a r d s p e c t r a c o r r e s p o n d i n g t o t h o s e f o r Jf, and & were a d  j u s t e d u n t i l t h e o s c i l l a t i o n s became a minimum and c o u l d be a v e r a g e d t o a smooth c u r v e . The d e c o m p o s i t i o n was t h e n r e g a r d e d as b e i n g a c c u r a t e t o a l m o s t w i t h i n s t a t i s t i c a l e r r o r s . S u c h a b r e a k - u p o f a T ( o»v, J M ? gamma r a y s p e c t r a f o r a b o m b a r d i n g e n e r g y o f 1.6 Mev i s shown i n F i g u r e 1 1 . A f t e r a number o f c u r v e s had b e e n a n a l y z e d i n t h e above manner t h e g e n e r a l shape o f t h e t a r g e t d e p e n d e n t b a c k  ground became known and t h e r e m a i n i n g c u r v e s were s u b j e c t e d t o a n a l y s i s b y t h e f i r s t method d e s c r i b e d above i n 3 ( b ) . T ( o ^ , J f ) L i ? gamma r a y s p e c t r a , c o r r e c t e d f o r a smooth b a c k g r o u n d , t a k e n a t a bo m b a r d i n g e n e r g y o f 1.6 Mev a r e shown i n F i g u r e 12 f o r t h e s c i n t i l l a t i o n c o u n t e r a t 0° and 9 0 ° . I t i s c l e a r l y s e e n t h a t t h e a n g u l a r d i s t r i b u t i o n o f tf\ and tf^is n o t i s o t r o p i c . A l s o n o t i c e a b l e i s t h e D o p p l e r s h i f t o f t h e t g r o u n d s t a t e t r a n s i t i o n gamma r a y , }f, . 250 FIGURE 1 2 T(a,y) Li7 SPECTRA = ANGULAR DISTRIBUTION AT Ea= 1.32 MEV 2+ (d) B r a n c h i n g R a t i o As a cons e q u e n e e o f t h e a n a l y s i s u s e d a b r a n c h i n g r a t i o 7x f o r t h e d e c a y o f L i t o t h e f i r s t e x c i t e d s t a t e and gr o u n d s t a t e c o u l d be made. The s c i n t i l l a t i o n c o u n t e r e f f i c i e n c y d e  f i n e d t o t h e h a l f - e n e r g y b i a s was t h e same f o r b o t h df> and tfj. . T h e r e f o r e t h e r a t i o o f i n t e n s i t i e s o f If, t o Jfuwas t h e same a s t h e r a t i o o f t h e number o f c o u n t s above t h e h a l f - e n e r g y b i a s i n t h e #a s p e c t r u m t o t h e c o r r e s p o n d i n g number i n ' t h e }f, s p e c t r u m e x c e p t f o r a n a b s o r p t i o n c o r r e c t i o n , w h i c h amounted t o l e s s t h a n 1% f o r t h e r a t i o . W i t h i n t h e e x p e r i m e n t a l a c c u r a c y t h e r a t i o was i n d e p e n d e n t o f a n g l e i n d i c a t i n g t h a t tfi and have t h e same a n g u l a r d i s t r i b u t i o n . D i s c r i m i n a t i o n f o r t h e r a t i o a t d i f f e r e n t e n e r g i e s c o u l d be made, however, w i t h t h e r e s u l t s . W o \ = 0.++6 ± 0.01+ a t E * = 1.6 Mev * = 0.361 - 0.001 a t E«. = 800 Kev = 0.52+ - 0.08 a t Eoc = 500 Kev T h i s l a s t f i g u r e was bas e d on a s i n g l e r u n t o be men t i o n e d l a t e r . From t h e above f i g u r e s t h e f r a c t i o n o f t h e t o t a l t r a n s i t i o n i n L i due t o g r o u n d s t a t e , ^, , d e c a y may be f o u n d w h i c h a r e n e c e s s a r y f o r d e t e r m i n i n g t h e c r o s s - s e c t i o n . 1 = 0 .69 - 0.007 a t E « = 1.6 Mev + N t f , + N K t = ° « 7 3 - 0.006 a t Eo< = 800 Kev + = 0.66 - 0.0+ a t E«t = 500 Kev. 25 ( e ) A n g u l a r D i s t r i b u t i o n s The s i m p l e s t t h e o r e t i c a l model f o r t h e T(oC , y ) L i r e a c t i o n i s one i n w h i c h i t i s assumed t h a t t h e c a p t u r e t a k e s p l a c e w i t h z e r o r e l a t i v e o r b i t a l a n g u l a r momentum (S wave A l p h a p a r t i c l e s ) f r o m t h e c o n t i n u u m d i r e c t l y t o t h e 3/2 g r o u n d s t a t e or t h e 1/2 f i r s t e x c i t e d s t a t e w i t h t h e e m i s s i o n o f e l e c  t r i c d i p o l e r a d i a t i o n . On t h e b a s i s o f t h i s model t h e a n g u l a r d i s t r i b u t i o n e x p e c t e d f o r t h e r a d i a t i o n c a n o n l y be i s o t r o p i c . However t h e p r e l i m i n a r y measurements o f P R i l e y (1958) a t a bombarding e n e r g y o f 1.6 Mev i n d i c a t e t h a t t h e r a t i o o f t h e y i e l d a t 0° t o t h a t a t 90° i s l A O t 0 .37 . I n v i e w o f t h e i n  t e r e s t i n t h e r e a c t i o n and t h e d i s c r e p a n c y o f t h i s r e s u l t f r o m t h e e x p e c t a t i o n s o f t h e s i m p l e model i t was f e l t t h a t t h e a c c u r a c y o f t h e a n g u l a r d i s t r i b u t i o n d a t a s h o u l d be i m p r o v e d and e x t e n d e d t o c o v e r a w i d e r r a n g e o f b o m b a r d i n g e n e r g i e s . S i n c e t h e b r a n c h i n g r a t i o f o r t h e two t r a n s i t i o n s & , and tf"j_was i n d e p e n d e n t o f a n g l e t o w i t h i n 3 p e r c e n t i n d i c a t i n g t h a t t h e t r a n s i t i o n s t o t h e f i r s t e x c i t e d s t a t e and t o t h e grou n d s t a t e had t h e same a n g u l a r d i s t r i b u t i o n , o n l y t h e a n g u l a r d i s t r i b u t i o n o f t h e gr o u n d s t a t e , Jf| was a n a l y z e d i n d e t a i l . The number o f c o u n t s t o t h e h a l f e n e r g y b i a s i n t h e Xt p o r t i o n o f t h e s p e c t r a a t 0° , ^5° , 90° and 135° on e a c h s i d e o f t h e t a r g e t were c o r r e c t e d f o r a b s o r p t i o n l o s s e s and t h e v a l u e s f r o m a t l e a s t 6 d i f f e r e n t r u n s a v e r a g e d f o r e a c h a n g l e t o g i v e t h e 26 f o l l o w i n g r e s u l t s : ( i ) 1.6 Mev - Mean a l p h a e n e r g y i n t h e t a r g e t = 1.32 Mev. WU = 1.30 ± . 0 ^ NU,5° = 1.08 ± .06 NI3U. 0 = l.oh t .06 N90° N90° N90° The e r r o r s g i v e n above a r e b a s e d on t h e c o u n t i n g s t a  t i s t i c s b u t a l s o a r e o f t h e same o r d e r a s t h e r o o t mean s q u a r e e r r o r s o f t h e i n d i v i d u a l r u n s f r o m t h e mean f o r e a c h a n g l e . The r e s u l t s show t h a t t h e d i s t r i b u t i o n i s s y m m e t r i c a l a b o u t 0°, i n  d i c a t i n g t h a t t h e l i n e o f t h e beam p a s s e d t h r o u g h t h e c e n t r e o f t h e c i r c l e on w h i c h t h e c o u n t e r r o t a t e d , and t h a t i t i s t o a good a p p r o x i m a t i o n s y m m e t r i c a l a b o u t 90° w h i c h s u g g e s t s t h a t t h e r e a r e no c o n t r i b u t i o n s f r o m o p p o s i t e p a r i t y i n c o m i n g waves. T h e r e f o r e t h e d i s t r i b u t i o n s s h o u l d be f i t t e d b y a n e x p a n s i o n i n e v e n powers o f c o s i n e © o n l y . I f o n l y d i p o l e t e r m s a r e i n c l u d e d t h e e x p a n s i o n i s t h e n o f t h e f o r m l+afcos© and t h e 0 t o 90 r a t i o r e q u i r e s a v a l u e o f " a " o f 0 .30. T h i s however g i v e s a poor f i t t o t h e U-5° and 135° v a l u e s . I n c l u d i n g , t h e n , t h e n e x t t e r m i n t h e e x p a n s i o n 1+acos 6 + bco s 0 a good f i t c a n be ob t a i n e d w i t h a = -0.06 and b = O . 3 6 . I t s h o u l d be n o t e d t h a t t h e number o f e x p e r i m e n t a l p o i n t s i s n o t g r e a t enough t o c o n s i d e r t h e i n c l u s i o n o f any h i g h t e r m s . T h e s e r e s u l t s were t h e n c o r  r e c t e d f o r t h e s o l i d a n g l e o f t h e c o u n t e r w h i c h i n c r e a s e d t h e 0° t o 90° r a t i o b y 1.6% w i t h o u t s i g n i f i c a n t e f f e c t on t h e o t h e r r a t i o s . Next t h e r a t i o s were t r a n s f e r r e d t o c e n t r e o f mass c o  o r d i n a t e s b y use o f t h e e q u a t i o n s FIGURE 13 ANGULAR DISTRIBUTIONS AT 1.6 MEV (1.32 MEV MEAN) (a) X T R A N S I T I O N . 5 - l - . l l COS20 + . 3 9 COS*0 0-5- L Centre ot mass angle _ i I -135° -90° -4-5* 4-5' go" 1 3 5 27 <Tcm. < © c m . ) = CTiao ( & l a b ) £ l - ? c o s 8 c m . ] and 0 c > n i ( = 8 l a b + £ s i n 8 c m . g i v e n b y Devons and H i n e (19+9). F o r a c o l l i s i o n o f a n a l p h a p a r t i c l e o f a v e r a g e e n e r g y E i n Mev w i t h a t r i t o n a t r e s t t h e v e l o c i t y o f t h e p a i r a f t e r c o l l i s i o n may be f o u n d as v = 3.91x10^ J/ECK i n m e t r e s p e r s e c o n d . On t h e b a s i s o f t h e s e f i g u r e s t h e c o r r e c t i o n s were c a l c u l a t e d and f o u n d t o change t h e above r a t i o s b y l e s s t h a n 3% and t h e a n g l e s b y l e s s t h a n 1 ° . The new v a l u e s f o u n d w e r e : N 0 o = 1.28*0.0+ N l f 5 0 = 1.06 ± 0.06 1*13^.6° = 1«02 £ 0.06 N 9 O . 8 0 N 9 0 . 8 ° N90.8 0 T h e s e c o r r e c t e d v a l u e s c a n t h e n be f i t t e d t o a n a n g u l a r d i s t r i  b u t i o n o f t h e f o r m M i L l = 1 + a c o s 2 e + b cos^ e w i t h t h e r e - N(90°) s u i t t h a t a = -0.11 and b = 0.39. T h i s d i s t r i b u t i o n i s shown i n F i g u r e 13 a l o n g w i t h t h e c o r r e c t e d e x p e r i m e n t a l r e s u l t s . F o r c o m p a r i s o n t h e f i g u r e a l s o shows t h e d i s t r i b u t i o n w h i c h i n  c l u d e s d i p o l e t e r m s o n l y f i t t e d t o t h e v a l u e s a t 0° and 90°. T h i s s i m p l e r t y p e o f d i s t r i b u t i o n c o u l d o n l y be f i t t e d w i t h i n t h e e r r o r s shown b y a s s u m i n g t h a t a l l +5°and 135° p o i n t s a r e low b y a n amount e q u a l t o or j u s t g r e a t e r t h a n t h e e r r o r s shown on t h e i n d i v i d u a l p o i n t s . I t s h o u l d be p o i n t e d o u t t h a t t h e t a r g e t d e p e n d e n t b a c k g r o u n d w h i c h was l e f t o v e r a f t e r s e p a r a t i n g out t h e s t a n d a r d gamma r a y s p e c t r a f o r tf, and |fv was n o t i t s e l f 28 i s o t r o p i c . T h i s p o i n t i s d i s c u s s e d i n more d e t a i l i n s e c t i o n k o f t h i s c h a p t e r . I t i s f e l t t h a t t h e d e c o m p o s i t i o n p r o c e e d u r e u s e d f o r t h e s p e c t r a has e f f e c t i v e l y removed a n y e f f e c t o f t h e b a c k g r o u n d a n i s o t r o p y f r o m t h e gamma r a y a n g u l a r d i s t r i b u t i o n s . ( i i ) 800 Kev - Mean a l p h a e n e r g y i n t h e t a r g e t = 560 Kev. A t t h i s e n e r g y measurements were made o n l y a t 0° and ^ 9 0 ° w h i c h , a f t e r t r a n s f e r r i n g t o c e n t r e o f mass c o - o r d i n a t e s , gave t h e a v e r a g e r e s u l t , f r o m a b o u t s i x r u n s , o f N0° = l 05 N 9 0 . 7 O - 0.06. S i n c e t h i s v a l u e i s much c l o s e r t o i s o t r o p i c t h a n t h a t o b t a i n e d a t t h e h i g h e r b o m b a r d i n g e n e r g y and s i n c e t h e y i e l d i s c o n s i d e r a b l y l o w e r a t t h i s e n e r g y i t was n o t c o n s i d e r e d w o r t h w h i l e t o make measurements a t any f u r t h e r a n g l e s , ( f ) D o p p l e r S h i f t The v e l o c i t y o f t h e a l p h a - t r i t o n p a i r a f t e r c o l l i s i o n has b e e n g i v e n p r e v i o u s l y a s a f u n c t i o n o f mean a l p h a p a r t i c l e e n e r g y i n t h e t a r g e t : v = 3.91x10^ i n m e t r e s p e r s e c . f o r Eot i n Mev. The v a l u e s o f E©< a p p r o p r i a t e have b e e n g i v e n i n s e c t i o n 2(b) o f t h i s c h a p t e r f o r t h e t a r g e t a t l+5° t o t h e beam. From t h e o r y t h e D o p p l e r s h i f t i n e n e r g y f o r t h e d e t e c t o r a t a n a n g l e 6 w i t h t h e beam i s E = E 0 — c o s Q . M e a s u r e - c ments were made on w i t h t h e r e s u l t s : & E EOQ E « E 0 9 T h e o r y E x p e r i m e n t ... (Mev) ... ( d e g r e e s ) (Kev) 1.6 1.32 3.03 0 M+.8 - 5 2 9 A E E ^ E * E 0 0 T h e o r y E x p e r i m e n t ( d e g r e e s ) 0 . 8 0 . 5 6 2 . 7 1 + 5 3 1 . 7 3 3 9 0 0 . 0 0 1 3 ^ - 3 2 . 2 - 3 0 0 3 1 A 2 8 9 0 0 . 0 0 t h e measurements a r e s e e n a g r e e w i t h t h e o r y s u p p o r t i n g t h e argument t h a t t h e l i f e t i m e o f t h e e x c i t e d L i 7 n u c l e u s t o gamma r a y e m i s s i o n i s s h o r t com p a r e d t o i t s s l o w i n g - d o w n t i m e i n t h e t a r g e t m a t e r i a l . B a c k g r o u n d ( a ) G e n e r a l A f t e r a n a l y z i n g t h e T(oC , ) L i ? gamma r a y s p e c t r a a smooth b a c k g r o u n d r e m a i n e d a s p o i n t e d o u t e a r l i e r . . T h i s t a r g e t d e p e n d e n t b a c k g r o u n d was f r o m some m a t e r i a l i n t h e t a r g e t i t  s e l f o t h e r t h a n a ny beam d e p o s i t e d c a r b o n s i n c e i t was p r e s e n t d u r i n g e a r l y r u n s a s w e l l as l a t e r r u n s w i t h a b o u t t h e same i n  t e n s i t y . A l s o , i t was n o t e d t h a t i t s g e n e r a l s p e c t r u m shape was s i m i l a r t o t h a t s e e n b y L a r s o n ( 1 9 5 7 ) when he l o o k e d a t t h e low e n e r g y n e u t r o n s f r o m t h e D ( d , n ) H e 3 r e a c t i o n w i t h t h e 2 t » x 3 | - " N a l c r y s t a l . R i l e y ( 1 9 5 8 ) had o b s e r v e d t h a t h i s t a r g e t d e p e n d e n t /background i n c r e a s e d a s t h e a l p h a p a r t i c l e b o m b a r d i n g e n e r g y 30 was d e c r e a s e d b e l o w 500 Kev and i n c r e a s e d above 1.6 Mev. The shape o f t h e T(oC ,t ) L i gamma r a y s p e c t r a t a k e n i n t h e p r e s e n t work showed t h a t t h e t a r g e t d e p e n d e n t b a c k g r o u n d d e c r e a s e d as e n e r g y d e c r e a s e d o v e r t h e whol e r a n g e s t u d i e d . T h i s b a c k g r o u n d c o u l d have b e e n due t o t h e Ih Mev n e u t r o n s f r o m t h e T ( d , n ) H e J r e a c t i o n c a u s e d b y a s m a l l amount o f m o l e c u l a r d e u t e r i u m i n t h e mass h beam, t o n e u t r o n s o f a few Mev e n e r g y f r o m c a r b o n b u i l d u p on t h e t a r g e t , o r f r o m s e c o n d a r y n e u t r o n s p r o d u c e d b y s c a t t e r e d t r i t i u m atoms i n t h e t a r g e t c o l l i d i n g w i t h f u r t h e r t a r g e t t r i  t i u m atoms. S i n c e i t was t h e r e f o r e p r o b a b l e t h a t n e u t r o n s were p r e s e n t i t was d e c i d e d t o measure t h e i r e n e r g y , y i e l d and a n i s o  t r o p y and t o c h e c k w h e t h e r t h e y c o u l d p o s s i b l y a c c o u n t f o r t h e a n i s o t r o p i c t a r g e t d e p e n d e n t b a c k g r o u n d f o u n d i n t h e a n g u l a r d i s t r i b u t i o n r u n s . ( b ) E n e r g y o f N e u t r o n s I n o r d e r t o r o u g h l y d e t e r m i n e t h e e n e r g y o f t h e s e n e u t r o n s f r o m t h e t a r g e t a beam o f a b o u t 3^ r m i c r o a m p e r e s o f a l p h a p a r t i c l e s a t 1.6 Mev was r u n on a t h i c k t r i t i u m t a r g e t (B-127-1) and t h e s p e c t r u m o b s e r v e d w i t h a f a s t n e u t r o n c o u n t e r o f t h e t y p e d e s c r i b e d b y S s u (1955). The p h o t o m u l t i p l i e r o f th e c o u n t e r was o p e r a t e d a t 1275 v o l t s o b t a i n e d f r o m a n I s o t o p e s D e v e l o p m e n t E.H.T. s u p p l y . P u l s e s were f e d f r o m a c a t h o d e f o l l o w e r i n t o a 100 ohm c a b l e t o a D y n a t r o n R a d i o L i m i t e d Am p l i f i e r and f r o m t h e r e t o t h e 100-channel Computing D e v i c e s o f /Canada k i c k s o r t e r . The k i c k s o r t e r was o p e r a t e d a t b i a s 1 t o F I G U R E 1 4 N E U T R O N S P E C T R A 1 11 i i i i i i i i i i O 10 20 30 40 50 60 70 8 0 90 IOO CHANNEL NUMBER o b s e r v e t h e many low v o l t a g e p u l s e s . A r u n o f 150 i n t e g r a t o r s ? l a s t i n g o v e r a n h o u r was t a k e n w i t h t h e c o u n t e r f a c e a s c l o s e a s p o s s i b l e t o t h e t a r g e t p o t . F o r c o m p a r i s o n p u r p o s e s a Ra Be n e u t r o n s p e c t r u m was o b t a i n e d w i t h t h e same c o u n t e r , t h e k i c k - s o r t e r b e i n g a t b i a s 2 t o a v o i d t h e numerous p u l s e s f r o m gamma r a y b u i l d up i n t h e c o u n t e r , w i t h t h e g a i n o t h e r w i s e t h e same. The two s p e c t r a a r e shown on a s e m i - l o g a r i t h m i c p l o t i n F i g u r e l * f . B y c o m p a r i n g t h e two c u r v e s w i t h t h o s e g i v e n by G r i f f i t h s e t a l (1959) t h e e n e r g y o f t h e n e u t r o n s f r o m t h e t a r g e t was s e e n t o be a b o u t 2 t o 3 Mev. T h i s , t h e r e f o r e , r u l e d o u t t h e p o s s i b i l i t y o f them b e i n g due t o t h e T ( d , n ) H e 3 r e a c t i o n f r o m m o l e c u l a r d e u t e r i u m i n t h e beam. ( c ) Y i e l d and A n i s t r o p y o f N e u t r o n s On two s e p a r a t e o c c a s i o n s t h e a n i s o t r o p y o f t h e n e u  t r o n s f r o m t h e t r i t i u m t a r g e t u s e d f o r t h e T(oC , ?f ) L i ? r u n s , when bombarded w i t h 1.6 Mev a l p h a p a r t i c l e s , was measured w i t h t h e n e u t r o n c o u n t e r m e n t i o n e d a b o v e . S i n c e t h e s e r u n s were n o t t a k e n f o r a l o n g enough t i m e t o a c c u m u l a t e many c o u n t s t h e p u l s e s were n o t f e d t o t h e k i c k s o r t e r b e i n g r e c o r d e d o n l y on a D y n a t r o n R a d i o L i m i t e d s c a l a r T y pe 1 0 0 9 A . U s i n g t h e r e s u l t s o f t h e s e r u n s t h e a n i s t r o p y o f t h e n e u t r o n s may be s t a t e d as N 0 o = 1.32 - 0 . 3 F r o m c u r v e s i n t h e p a p e r b y G r i f f i t h s e t a l . t h e d e  t e c t o r e f f i c i e n c y o f t h e n e u t r o n c o u n t e r f o r t h e n e u t r o n s 3 2 o b s e r v e d was b e l i e v e d t o be a b o u t 0,2%. A s s u m i n g t h e e f f e c t i v e c e n t r e o f t h e c o u n t e r t o be 1" b e h i n d t h e f r o n t o f t h e c o u n t e r f a c e and a l l o w i n g 1 - 1 / 8 " f o r t h e c o u n t e r f a c e - t o - t a r g e t d i s t a n c e t h e s o l i d a n g l e o f t h e c o u n t e r was c a l c u l a t e d t o be 0 . 7 s t e r a - d i a n u s i n g a c r o s s - s e c t i o n a l a r e a o f 2 0 c m 2 . T h e n f o r N c c o u n t s i n t h e c o u n t e r a t 0 ° p e r 5 ° i n t e g r a t o r c o u n t s t h e number o f n e u t r o n s e m i t t e d f r o m t h e t a r g e t p e r s t e r a d i a n a t 0 ° was N n = 7 0 8 N c . Fro m a number o f r u n s w i t h t h e c o u n t e r a t 0 ° t h e y i e l d a t 1 . 6 Mev and a t 8 0 0 Kev a l p h a p a r t i c l e e n e r g i e s was f o u n d : N c (Mev) 1 . 6 150-I5i 1.06xl0^i 20% 0 . 8 3 7 * 6 0 % 0 . 2 6 x 1 0 ^ - 6 5 % A y i e l d a t 8 0 0 Kev may t h e r e f o r e be g i v e n r e l a t i v e t o t h a t a t 1 . 6 Mev as = ^ ± 0 < l 6 . ( d ) B a c k g r o u n d Y i e l d f r o m t h e S c i n t i l l a t i o n C o u n t e r I n t h e gamma r a y e n e r g y r e g i o n f r o m 2 t o 3 Mev t h e t a r g e t d e p e n d e n t b a c k g r o u n d , r e s u l t i n g f r o m a n a l y s e s o f T(0C ) L i gamma r a y s p e c t r a , was f o u n d t o be a l w a y s l a r g e r t h a n t h e beam d e p e n d e n t one. When c o u n t s i n t h i s t a r g e t d e p e n d e n t b a c k g r o u n d were added f r o m t h e h a l f - e n e r g y b i a s o f if, t o a b o u t h Mev t h e f o l l o w i n g y i e l d r a t e s were o b t a i n e d f o r t h e c o u n t e r a t 9 0 ° t o t h e beam and f o r t h e b o m b a r d i n g e n e r g i e s shown i n b r a c k e t s : M = m & = °-37- "+ -017 33 I t i s t h e r e f o r e s e e n t h a t t h e r e l a t i v e b a c k g r o u n d y i e l d s a t 500 Kev and 1.6 Mev a s d e t e r m i n e d f r o m gamma r a y a n a l y s i s a g r e e s , w i t h i n t h e e x p e r i m e n t e d u n c e r t a i n t i e s , w i t h t h a t o b t a i n e d f r o m n e u t r o n c o u n t i n g t h u s l e n d i n g s u p p o r t t o t h e s u p p o s i t i o n t h a t t h e t a r g e t d e p e n d e n t b a c k g r o u n d i s n e u t r o n i n d u c e d . A t 1.6 Mev a l p h a p a r t i c l e b o m b a r d i n g e n e r g y t h e t o t a l t a r g e t d e p e n d e n t b a c k g r o u n d f o r t h e c o u n t e r a t 90° t o t h e beam amounted t o a b o u t 10,000 c o u n t s i n 50 i n t e g r a t o r c o u n t s . From t h e n e u t r o n c o u n t e r r e s u l t s , a s s u m i n g a s c i n t i l l a t i o n c o u n t e r s o l i d a n g l e o f 0.18 s t e r a d i a n and a n e u t r o n a n i s o t r o p y o f 32$, t h e number o f n e u t r o n s w h i c h e n t e r e d t h e s c i n t i l l a t i o n c o u n t e r were: N = 1»06x10^ x 0 . i 8 = 1 ,^500 n e u t r o n s . T h u s , i f n e u t r o n s i n t h e N a l c r y s t a l a r e t o be t h e e x p l a n a t i o n o f t h e t a r g e t d e  pendent b a c k g r o u n d t h e n two out o f e v e r y t h r e e n e u t r o n s e n t e r i n g t h e c r y s t a l must i n t e r a c t i n some way. T h i s p r o p o r t i o n may be r e d u c e d , however, by c o n s i d e r i n g t h e f l u x of gamma r a y s f r o m t h e r a d i a t i v e c a p t u r e o f n e u t r o n s i n t h e t a r g e t p o t and m a s s i v e s c i n t i l l a t i o n c o u n t e r s h i e l d i n g . ( e ) A n g u l a r D i s t r i b u t i o n C o u n t s i n t h e t a r g e t d e p e n d e n t b a c k g r o u n d s p e c t r a i n th e s c i n t i l l a t i o n c o u n t e r w h i c h were l e f t o v e r a f t e r s u b t r a c t i n g out & and ^ v w e r e added f r o m t h e h a l f - e n e r g y b i a s o f fli t o a b o u t h Mev f o r T(0< , > T ) L i 7 r u n s t a k e n a t d i f f e r e n t a n g l e s and a t two E n e r g i e s i n . o r d e r t o f i n d t h e a n g u l a r d i s t r i b u t i o n o f t h e b a c k -3^ g r o u n d . R e s u l t s may be s t a t e d i n t h e l a b o r a t o r y s y s t e m a s a t E * = 800 k e v : N n o . -2- = 1.17 - 0.18 N 9 0 ° a t E « = 1.6 Mev: N n o , . N k t ° . = 1.3.6 - 0.10 _ I 2 _ = 1.2U, - 0.09 N 9 0 °  N90° -±2Z- = o.75 - o.o5 N90° Applying.'.a l e a s t s q u a r e s f i t t o t h e d a t a a t Ee< = 1.6 Mev f o r a f u n c t i o n o f t h e f o r m N(6) = i + a c o s 0 y i e l d s N(90°) t h e r e s u l t t h a t a = 0.35 - 0 .9 . T h i s f u n c t i o n i s shown p l o t t e d i n F i g u r e 13. 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 e 0 ° t o 90° a n i s o - t r o p y o f t h i s t a r g e t d e p e n d e n t b a c k g r o u n d was t h e same as t h a t o f t h e n e u t r o n s p r e s e n t t h u s f u r t h e r i n d i c a t i n g t h a t t h e b a c k  ground m i g h t have been p r o d u c e d b y n e u t r o n s . o 5. A b s o l u t e 90 D i f f e r e n t i a l C r o s s - S e c t i o n ( a ) Procedures. The r u n s f o r t h e d e t e r m i n a t i o n o f t h e a b s o l u t 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 a t 90° t o t h e beam d i r e c t i o n were t a k e n a t t h e same t i m e as t h e T(oC )He r u n s w h i c h have b e e n u s e d t o d e t e r m i n e t h e t a r g e t t h i c k n e s s . To do t h e s e r u n s a r e l a t i v e l y new s p o t on t h e t a r g e t was s e l e c t e d and two T ( t f . , } f ) L i ? r u n s and •/two T ( p , o )He r u n s were i n t e r s p a c e d . No t a r g e t d e t e r i o r a t i o n was d e t e c t e d b y t h i s p r o c e e d u r e . F o r a l l o f t h e s e r u n s t h e 35 s c i n t i l l a t i o n c o u n t e r was a t 90° t o t h e beam and 5.96 cm. f r o m o t h e o u t s i d e o f t h e t a r g e t p o t . The t a r g e t was a t 4-5 t o t h e beam d i r e c t i o n and p o s i t i o n e d s o t h a t t h e ,gamma r a y s w o u l d p a s s t h r o u g h t h e t a r g e t b a c k i n g t o r e a c h t h e s c i n t i l l a t i o n c o u n t e r . n The T(©^ , If ) L i work was done a t a n e n e r g y o f 1.6 Mev as r e a d b y t h e g e n e r a t i n g v o l t m e t e r and w i t h a t a r g e t c u r r e n t o f k m i c r o a m p e r e s . The s p e c t r a were a n a l y z e d i n t o t h e i r two com p o n e n t s as d e s c r i b e d b e f o r e so t h a t t h e c r o s s - s e c t i o n c o u l d be g i v e n f o r ^ t r a n s i t i o n s . The t r i t i u m t a r g e t t h i c k n e s s u s e d was, a s f o u n d f r o m t h e T ( p , y ) H e ) + work, h-.k-QxlO^ a t o m s / c m 2 i 18$ f o r t h e t a r g e t a t +5°. ( b ) C r o s s - S e c t i o n a t 1.6 Mev The e f f i c i e n c y of t h e s c i n t i l l a t i o n c o u n t e r i n t h e l e a d c a s t l e f o r c o u n t s t o t h e h a l f e n e r g y b i a s o f t h e s p e c t r u m was r e a d f r o m F i g u r e 3 as € = 0.68 i 5$ and t h e e f f e c t i v e c e n t r e was u s e d as H-.8 cm f r o m t h e c r y s t a l f a c e . A f t e r c o r - 7 r e c t i n g f o r a b s o r p t i o n l o s s e s t h e a v e r a g e number of T ( ^ , i f ) L i c o u n t s above t h e h a l f - e n e r g y b i a s f o r tf| t r a n s i t i o n s , N c = 32H-0 - 5$. The r e s t o f t h e d a t a needed i s a s f o l l o w s . Ii = 0.179 - 6$ N«. = (50 i n t e g r a t o r c o u n t s ) IOO.H-XIO" 6 _ _ . . _ — fi = 3.137x10 o c - p a r t i c l e s - 1 9 1.6x10 y , -1$ n T = U,#l+8xl018 atoms o f t r i t i u m / c m 2 ± 15$ .'. = N c = 1.89x10-31 c m 2 / s t e r a d i a n - 20$, 36 f o r t h e a b s o l u t e 90° 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 €\ t r a n s i  t i o n s . U s i n g t h e r a t i o o f X] t r a n s i t i o n s t o t o t a l t r a n s i t i o n s as O.69 - 0.007 t h e n t h e a b s o l u t e 90° d i f f e r e n t i a l c r o s s - s e c t i o n 7 f o r f o r m a t i o n o f L i i s f o u n d as CdJL) s 1 . 8 9 X 1 0 " 3 1 = 2 . 7 t o 0 - 3 1 c m 2 / s t e r a d i a n 1 2 0 % < d u ) ) 9 0 ° 0.69 2 L. I n t e g r a t i n g t h e a n g u l a r d i s t r i b u t i o n , 1-0.11 c o s d+ .39 c o s Q, o v e r hV s t e r a d i a n s y i e l d s a t o t a l c r o s s - s e c t i o n f o r f o r m a t i o n 7 o f L i o f (T = 2.7^xl0" 3 1x(U,.l6 ) = 3.58xl0"3° c m 2 ± 20%. ( c ) E x c i t a t i o n F u n c t i o n B e s i d e s t h e 1.6 Mev bombarding e n e r g i e s two o t h e r s were a l s o u s e d : ( i ) 800 Kev U n f o r t u n a t e l y no 1.6 Mev r u n s were t a k e n on t h e same s p o t on t h e t a r g e t as 800 Kev r u n s . However, b y e x a m i n i n g t h e 800 Kev y i e l d f i g u r e s and t h o s e o f r u n s a t 1.6 Mev t a k e n w i t h i n a few d a y s o f t h e s e a r e a s o n a b l e c r o s s - s e c t i o n c a n be g i v e n a t 800 Kev r e l a t i v e t o t h a t a t 1.6 Mev. The 800 Kev r u n s a r e t h o s e t h a t were u s e d i n d e t e r m i n i n g t h e a n g u l a r d i s t r i b u t i o n and as m e n t i o n e d i n t h a t s e c t i o n t h e c o u n t e r was a p p r e c i a b l y c l o s e r t h a n f o r t h e 1.6 Mev r u n s . I n o r d e r t o d e t e r m i n e t h e r e l a t i v e c r o s s - s e c t i o n a t 800 Kev t h e f o l l o w i n g f i g u r e s a r e u s e d : } 37 (d < T ) _ % # , 800 Kev Noc ,1 .6 Mev ( d U > ) 9 0 ° * , 800 Kev Nr, , 1.6 Mev ^ 800 Kev 1.6 Mev ( d(T) -ft-800 Kev ( d u , ) 9 0 ° , , 1.6 Mev = . 99.0 0.179 (d<T) 3053 102.5 ' 0 3 2 ? • ( d u ) ) 9 0 o r 1.6 Mev (dU>)90°,<r, , 1.6 Mev - 11% or for the total cross-section <T= l.1+5xl0 3 ° cm2 - 23% assuming isotropy. (ii) 500 Kev An attempt was made to obtain a spectrum at 500 Kev incident alpha particle energy to note any change in target de pendent background. At the time of running however, only a small current (2/w.fl) was available and this necessitated a long running time of about an hour for 75 integrator counts of 96.5 microcoulombs apiece. Over most of the spectrum the beam de pendent background was more than half the number of counts re corded. However, a value was deduced for the cross-section relative to that at 1.6 Mev bombarding energy. Runs at 1.6 Mev on the same spot on the target had been taken just prior. Hence, ( d - ^ = Z52 99.0 0.179 (d<r) ( d »> >90°, * i , 500 Kev 3053 96T5 0 3 ? ( d u > ) 9 0 o ^ ^  1 > 6 M e v < 38 = O.IH-O (d£ri + _ (A,. \ - 15$» o r f o r t h e v a u ; 9 0 , Jf,, 1.6 Mev t o t a l c r o s s - s e c t i o n , <T" = 0 . 5 0 x l 0 ~ 3 0 c m 2 - 26$ a s s u m i n g i s o t r o p y . ( d ) T a r g e t T h i c k n e s s f r o m Gamma R a y E n e r g y ; The gamma r a y e n e r g i e s f r o m t h e r u n s t a k e n a t t h e t h r e e b o m b a r d i n g e n e r g i e s f o l l o w e d a f o r m Eg = Q + 2L > 7 w i t h i n t h e e x p e r i m e n t a l a c c u r a c y , i n d i c a t i n g t h a t t h e p r o p e r r e a c t i o n was b e i n g o b s e r v e d . From t h e RdTh e n e r g y c a l i b r a t i o n s t h e gamma r a y e n e r g i e s were f o u n d and mean a l p h a p a r t i c l e e n e r  g i e s c a l c u l a t e d f r o m them. T h e s e l a t t e r a r e compared w i t h e x  p e c t e d v a l u e s , b a s e d on t a r g e t t h i c k n e s s c o m p u t a t i o n s g i v e n i n s e c t i o n 2 ( c ) , i n t h e f o l l o w i n g t a b l e s : T a r g e t Ej* _ J X A n g l e E x p e r i m e n t F r o m t a r g e t - t h i c k n e s s (Mev) ( d e g r e e s ) (Mev) (Mev) 1.6 H-5 1.31^10$ 1.32 90 1.37 1+0 0.8 +5 0.567 0.560 0.5 +5 0.355 As c a n be s e e n t h e agreement i s w e l l w i t h i n t h e e x  p e r i m e n t a l e r r o r and so mean a l p h a e n e r g i e s may be c o n s i d e r e d a c c u r a t e t o 2$. 6. Summary and D i s c u s s i o n o f E x p e r i m e n t a l R e s u l t s The a b s o l u t e c r o s s - s e c t i o n f o r t h e T ( o t , J T ) L i r e - a c t i o n was measured a t 1.6 Mev a l p h a p a r t i c l e b o m b a r d i n g e n e r g y . 39 V a l u e s r e l a t i v e t o t h i s were f o u n d f o r e n e r g i e s o f 800 and 500 Kev. R e s u l t s a r e t a b u l a t e d below f o r mean e n e r g i e s i n t h e t a r g e t : Etc (Mev) (j-fj, ( c m 2 ) 1.32 3.58xlO"3° ± 20% 0.56 l.W-5 23% 0.35 0 .50 26% T h e s e v a l u e s a r e d e f i n i t e l y l o w e r t h a n t h o s e o f R i l e y b u t t h e r e l a t i v e v a l u e s a g r e e w e l l w i t h t h e t r e n d o f t h e c r o s s - s e c t i o n w i t h e n e r g y o b t a i n e d b y t h a t a u t h o r . On t h e o t h e r hand H o l m g r e n and J o h n s t o n ' s v a l u e s , o b t a i n e d w i t h a gas t a r g e t , a r e l o w e r b y a f a c t o r o f 2 a t 600 Kev and a f a c t o r o f 2 .5 a t 1.3 Mev and t h e i r e x c i t a t i o n f u n c t i o n f a l l s l e s s r a p i d l y w i t h e n e r g y . T h e r e i s no i m m e d i a t e l y a p p a r e n t e x p l a n a t i o n f o r t h i s r a t h e r l a r g e d i s c r e p a n c y b e t w e e n t h e r e s u l t s d e t e r m i n e d b y t h e two d i f f e r e n t methods a t t h e p r e s e n t t i m e . A n g u l a r d i s t r i b u t i o n measurements o f t h e r e a c t i o n 7 gamma r a y s f r o m T ( * , t ) L i i n d i c a t e d t h a t t h e gamma r a y s t o t h e g r o u n d s t a t e , tf| , and t o t h e f i r s t e x c i t e d s t a t e , , have t h e same a n g u l a r d i s t r i b u t i o n . T h e s e f o l l o w e d t h e f o r m 1-0.11 2 If c o s 0 + 0.39 c o s 6 a t 1.6 Mev bombarding e n e r g y w h i l e t h e r e was some i n d i c a t i o n o f a n i s o t r o p y (5% - 6%) a t 800 Kev. The p r e s e n c e o f t h e c o s i n e t e r m s a t t h e h i g h b o m b a r d i n g e n e r g y means t h a t t h e r e a c t i o n p r o c e e d s b y c a p t u r e o f a l p h a p a r t i c l e s o f a n g u l a r momentum g r e a t e r t h a n 1 = o t o some e x t e n t . I f t h e +0 7 g r o u n d s t a t e s o f LI' a r e pure 2P l e v e l s t h e n i t i s d i f f i c u l t t o see how t h e q u a d r u p o l e r a d i a t i o n , whose p r e s e n c e i s i n d i c a t e d b y t h e c o s & t e r r a , a r i s e s s i n c e s, p, o r d c a p t u r e o f a l p h a p a r t i c l e s w o u l d g i v e e l e c t r i c or m a g n e t i c d i p o l e r a d i a t i o n . The a n g u l a r d i s t r i b u t i o n o f t h e t a r g e t d e p e n d e n t b a c k g r o u n d was f o u n d t o be o f t h e f o r m 1 + 0 . 3 5 c o s 6 a t 1 . 6 Mev. T h i s a g r e e d w e l l w i t h a n i s o t r o p y measurements made w i t h a n e u  t r o n c o u n t e r . The e x c i t a t i o n f u n c t i o n o f t h i s b a c k g r o u n d a t 9 0 ° t o t h e beam was d e t e r m i n e d r o u g h l y b y measurements a t 1 . 6 0 . 8 and 0 . 5 Mev. T h i s a l s o a g r e e d v e r y w e l l w i t h t h e n e u t r o n c o u n  t e r r e s u l t s . T h e r e f o r e , i n d i c a t i o n s a r e t h a t t h e t a r g e t d e p e n  d e n t b a c k g r o u n d was due t o n e u t r o n s e m i t t e d f r o m t h e t a r g e t . One drawback t o t h i s however i s t h a t t h e y i e l d o f n e u t r o n s d i d n o t seem t o be l a r g e enough t o e x p l a i n t h e l a r g e b a c k g r o u n d i n t h e s c i n t i l l a t i o n c o u n t e r . F u r t h e r i n v e s t i g a t i o n s t o d e t e r m i n e t h e e x a c t s o u r c e o f t h e b a c k g r o u n d w o u l d , t h e r e f o r e , be worth w h i l e . 7 . A p p l i c a t i o n o f R e s u l t s t o A s t r o p h y s i c s B e c a u s e o f t h e a s t r o p h y s i c a l i n t e r e s t i n t h e a b s o l u t e 7 c r o s s - s e c t i o n o f t h e T ( o C , ^ f ) L i r e a c t i o n , a s f a r as i t d e t e r - 3 7 mines t h e c r o s s - s e c t i o n o f t h e m i r r o r r e a c t i o n He ( © C , o*)Be , t h e d a t a was p u t i n a f o r m c o n v e n i e n t f o r u s e . A c c o r d i n g t o B u r b i d g e e t a l ( 1 9 5 7 ) t h e c r o s s - s e c t i o n f a c t o r f o r a c h a r g e d p a r t i c l e r e a c t i o n i n a n e n e r g y r e g i o n w e l l b elow t h e coulomb FIGURE 15 CROSS-SECTION FACTOR,S o > 2 •IO •09 .OS' .07- .06- .OS- (/) 04- .03 - .02- • HOLMGREN AND JOHNSTON (1959) * P R E S E N T WORK o P.RILEY - normalized topresent work at 1.6Mev (1.32Mev Mean Energy) .01 -i 200 4-00 6 0 0 s o o 1000 1200 1400 MEAN ALPHA ENERGY,EQ- ( K E V ) 1 6 0 0 (Boo zooo hi b a r r i e r may be w r i t t e n a s S = O-CE-L) E1 _ A Q _ e x p ( 3 1 < 2 8 ZIZQAI^EI"^) K e v - b a r n s i n t h e A 0+A]_ c e n t r e - o f - m a s s s y s t e m , f o r E]_ t h e l a b o r a t o r y e n e r g y i n Kev o f t h e b o m b a r d i n g p a r t i c l e and C T ( E i ) . , t h e l a b o r a t o r y c r o s s - s e c t i o n i n b a r n s ( 1 0 ~ 2 l + c m 2 ) f o r t h e r e a c t i o n ; A 0 j r e f e r t o t h e mass o f t h e i n t e r a c t i n g p a r t i c l e s i n a t o m i c mass u n i t s and Z 0 , Z 1 ? t o t h e i r a t o m i c number. F o r t h e T ( o C , l f ) L i ? r e a c t i o n t h i s _ x becomes S = 3/7 (T (E« )exp ( 1 2 5.12E 2 ) . U s i n g R i l e y ' s e x c i t a t i o n f u n c t i o n , n o r m a l i z e d a t E ^ = 1320 Kev t o t h e a b s o l u t e c r o s s - s e c t i o n o b t a i n e d f r o m t h e p r e  s e n t work t h e dependence o f S o n E * was f o u n d . R i l e y ' s r e  s u l t s were c o r r e c t e d f o r t a r g e t t h i c k n e s s b y u s i n g t h e s t o p p i n g c r o s s - s e c t i o n v a l u e s f r o m F i g u r e 7 and t h e Oak R i d g e N a t i o n a l L a b o r a t o r y ' s f i g u r e o f 262 m i c r o g r a m s o f Z r / c m 2 f o r h i s t a r g e t . The r e s u l t s o f t h e p r e s e n t work and R i l e y ' s c o r r e c t e d r e s u l t s a r e shown p l o t t e d i n F i g u r e 1 5 . A l s o shown a r e v a l u e s o f the.same q u a n t i t y a s f o u n d b y H o l m g r e n and J o h n s t o n ( 1959) a f t e r c o n v e r t i n g t h e i r "S" t o t h e c e n t r e o f mass s y s t e m . W i t h i n t h e e x p e r i m e n t a l e r r o r t h e p r e s e n t r e s u l t s show t h a t S d o e s n o t change w i t h e n e r g y i n t h e r e g i o n i n v e s t i g a t e d . H o l m g r e n and J o h n s t o n ' s r e s u l t s show a s l o w v a r i a t i o n o f S t o w a r d s l o w e r e n e r g i e s . - T h i s may be due t o a s m a l l e r r o r i n mean b o m b a r d i n g e n e r g y a t t h e l o w e r e n e r g i e s , w h i c h w o u l d r e s u l t i n a l a r g e 4-2 change i n S b e c a u s e o f i t s e x p o n e n t i a l d e p e n d e n c e on Eoc . The s l o p e d l i n e s t h r o u g h t h e e x p e r i m e n t a l p o i n t s show t h e d i r e c t i o n i n w h i c h S w o u l d v a r y w i t h a s l i g h t change i n mean b o m b a r d i n g e n e r g y . Over most o f t h e e n e r g y r a n g e s t u d i e d t h e b e s t e x p e r i  m e n t a l e s t i m a t e f o r S i s 0.062 K e v - b a r n and i t r e m a i n s w i t h i n a b o u t 25$ o f t h i s v a l u e o v e r t h e r a n g e . I f t h e r e a c t i o n s T(<* , f ) L i 7 and He 3(oc , f ) B e 7 were e x a c t m i r r o r r e a c t i o n s t h e n t h e c r o s s - s e c t i o n f a c t o r s w o u l d be t h e same f o r b o t h . On t h e a s s u m p t i o n t h a t t h e y a r e e x a c t m i r r o r •3 7 r e a c t i o n s c r o s s - s e c t i o n s were f o u n d f o r t h e He (oC , € )Be r e - 7 a c t i o n f r o m t h o s e f o r t h e T(pv. , X ) L i r e a c t i o n b y m u l t i p l y i n g t h e l a t t e r v a l u e s b y t h e f a c t o r exp ( -125.12Eo( 2 ) w h i c h r e s u l t s f r o m t h e a s s u m p t i o n o f e q u a l l v a l u e s . R e s u l t s a r e t a b u l a t e d •x 7 below as w e l l as t h e c r o s s - s e c t i o n s f o r t h e He (o( ,jf ) B e ' r e  a c t i o n a s f o u n d b y H o l m g r e n and J o h n s t o n . Mean E n e r g y Q*~ „ T ( * , t f ) L i / exp ( - 1 2 5.12E* 2 ) H e J ( « ,)f)Be „ H o l m g r e n ' J o h n s t o n ' s He3 ( 0 t , j f)Be7 ( k e v ) ( l0-3O c m 2) (10"30 c m ^) ( 1 0-^cm 2) 350 O . 5 0 0.124-xlO" 2 0.00062 M mm mm mm H30 0.89 0.24-0 0.0021 0.021 560 l . H - 5 0.505 0.0070 O.O78 610 1.3 0.628 0.0082 0.12 860 1.9 1.4-0 0.027 0.35 1105 3.1 2.32 0.072 0.75 1320 3.58 3.20 0.11 1.25 1520 3.9 0.16 1830 +.5 5.4-0 0.24- I t i s r e a d i l y n o t i c e d t h a t t h e c r o s s -s e c t i o n s f o u n d f r o m t h e T ( < , * ) L i 7 r e a c t i o n a r e much l o w e r t h a n t h o s e o b t a i n e d by H o l m g r e n and J o h n s t o n a m o u n t i n g t o a b o u t a f a c t o r o f 10 o v e r t h e e n e r g y r a n g e s t u d i e d . T h i s i n d i c a t e s t h a t t h e r e a c t i o n s T ( , If ) L i 7 and He3(o< , JT )Be' ? a r e n o t e x a c t m i r r o r s o f e a c h o t h e r . The two v a l u e s o f t h e c r o s s - s e c t i o n w o u l d d i f f e r i n t h e same d i r e c t i o n i f t h e r e p u l s i v e f o r c e between t h e two p r o t o n s i n H e 3 e n l a r g e d i t s r a d i u s o v e r t h a t o f H 3 t h u s i n  c r e a s i n g t h e c r o s s - s e c t i o n o f t h e H e 3 ( oC , ) B e ^ r e a c t i o n . P a r t I I A S t a n d a r d G e i g e r - M u l l e r C o u n t e r f o r Gamma R a y F l u x D e t e r m i n a t i o n s C h a p t e r I I n t r o d u c t i o n ; The G e i g e r - M u l l e r c o u n t e r , a s a l l o t h e r n u c l e a r r a  d i a t i o n d e t e c t o r s , depends on t h e i o n i z i n g power o f t h e r a d i a  t i o n f o r i t s o p e r a t i o n . B y means o f gas a m p l i f i c a t i o n i t a m p l i f i e s t h e p r i m a r y i o n i z a t i o n , c a u s e d b y t h e r a d i a t i o n i n i t s i n t e r i o r , and t h e r e s u l t a n t f l o w o f c h a r g e , i s p r a c t i c a l l y i n d e p e n d e n t o f t h e number o f i o n s o r i g i n a l l y f o r m e d . The t e r m , G e i g e r c o u n t e r , a c t u a l l y r e f e r s t o a p o i n t c o u n t e r a s o r i g i n a l l y d e s i g n e d b y G e i g e r (1913). T h i s c o n  s i s t s cf a t h i n w i r e a t h i g h p o t e n t i a l s u r r o u n d e d b y a m e t a l l i c c a t h o d e ; t h e i n t e r i o r i s gas f i l l e d . Gas a m p l i f i c a t i o n t a k e s p l a c e a r o u n d t h e p o i n t o f t h e w i r e i n t h e g a s e o u s a t m o s p h e r e r e s u l t i n g i n a c o l l e c t e d c h a r g e i n d e p e n d e n t o f t h e amount of o r i g i n a l i o n i z a t i o n . A s l i g h t m o d i f i c a t i o n o f t h i s made b y G e i g e r and K l e m p e r e r (1928) was t o add a s m a l l m e t a l b a l l t o t h e end o f t h e w i r e . Over a s m a l l v o l t a g e r a n g e t h i s d e v i c e o p e r a t e s a s a p r o p o r t i o n a l c o u n t e r — t h e amount o f c h a r g e c o l  l e c t e d on t h e w i r e b e i n g p r o p o r t i o n a l t o t h e o r i g i n a l number o f i o n s f o r m e d . T h u s , c h a r g e d p a r t i c l e s g i v e a v o l t a g e p u l s e p r o - / p o r t i o n a l t o t h e i r e n e r g y . S i n c e t h e above c o u n t e r s o p e r a t e +5 o n l y a r o u n d t h e end o f t h e w i r e t h e a c t i v e volume i s s m a l l . I n o r d e r t o i n c r e a s e t h e s e n s i t i v e volume a new c o u n t e r was d e  v e l o p e d (Qeiger and M u l l e r , 1928) known as t h e G e i g e r - M u l l e r or G-M c o u n t e r . I n t h i s d e v i c e a m p l i f i c a t i o n o f i o n i z a t i o n o c c u r s a l o n g t h e c o m p l e t e l e n g t h o f t h e h i g h v o l t a g e w i r e t h u s g i v i n g g r e a t e r s e n s i t i v i t y . S i n c e gamma r a y s a r e d e t e c t e d b y t h e i o n i z a t i o n r e  s u l t i n g f r o m e l e c t r o n s l i b e r a t e d f r o m t h e m a t e r i a l s o f t h e c o u n t e r a good gamma r a y G-M c o u n t e r s h o u l d have a l a r g e s o l i d s u r f a c e a r e a s u r r o u n d i n g t h e g a s - f i l l e d i n t e r i o r . B e c a u s e t h e s e s e c o n d a r y e l e c t r o n s have a f i n i t e r a n g e i n t h e c a t h o d e m a t e r i a l t h e w a l l t h i c k n e s s s h o u l d be j u s t g r e a t e r t h a n t h i s r a n g e t o e n s u r e t h a t t h e maximum s e n s i t i v i t y i s o b t a i n e d . I f t h e w a l l s a r e t h i c k e r t h a n t h i s t h e n s e n s i t i v i t y i s l o s t as a r e s u l t o f gamma r a y a b s o r p t i o n i n t h e w a l l s w h i c h c a n n o t c o n  t r i b u t e e l e c t r o n s t o t h e i n t e r i o r . P r i m a r y i o n i z a t i o n i n t h e gas may be c o n s i d e r e d n e g l i g i b l e ( B l e u l e r and G o l d s m i t h , 1952). E v e n a w a l l t h i c k n e s s o f t h e o r d e r o f a m i l l i m e t r e s t o p s a l l b e t a and a l p h a p a r t i c l e s e n s u r i n g t h a t o n l y gamma r a y s and X- r a y s a r e d e t e c t e d . F o w l e r e t a l . (19+-8) as w e l l a s o t h e r a u t h o r s ( B l e u l e r and Z u n t i , 19+6) have made e l a b o r a t e t h e o r e t i c a l c a l c u l a t i o n s i n t h e e f f i c i e n c y o f a t h i c k w a l l e d G-M c o u n t e r . I n t h e i r p a p e r t h e y f i n d t h a t t h e gamma s e n s i t i v i t y v a r i e s e s s e n t i a l l y he l i n e a r l y w i t h p h o t o n e n e r g y f o r a n aluminum c a t h o d e b e t w e e n 1.5 and 25 Mev; a t t h e l o w e r e n e r g i e s t h e e f f i c i e n c y changes l e s s r a p i d l y w i t h e n e r g y . An a p p r o x i m a t e e x p r e s s i o n f o r t h e o v e r a l l e f f i c i e n c y was g i v e n b y v o n D r o s t e (1936) as € = C o n s t a n t ( fl"^ t ^ + 'c * c + 2 ^ ~ p *p) where ^ p h i s t h e c r o s s - s e c t i o n 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 , t p k i s t h e r a n g e o f t h e s e c o n d a r y e l e c t r o n s i n t h e w a l l m a t e r i a l and t h e o t h e r symbols have a n a l a g o u s mean i n g s . T h i s f o r m u l a p r e d i c t s t h a t t h e e f f i c i e n c y a t e n e r g i e s below a b o u t 3°0 Kev i n c r e a s e s s i g n i f i c a n t l y r a t h e r t h a n s m o o t h l y f a l l i n g t o z e r o w i t h d e c r e a s i n g p h o t o n e n e r g y . T h i s e f f e c t i s due t o t h e n a t u r e o f 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 a t t h e s e low e n e r g i e s and has b e e n b o r n - o u t i n t h e e x p e r i m e n t a l r e s u l t s o f B r a d t e t a l . (19k6) and Dunworth (19^0). h S i n c e t h e p h o t o e l e c t r i c e f f e c t d epends on Z , p a i r 2 p r o d u c t i o n on Z and t h e Compton e f f e c t on Z h i g h s e n s i t i v i t y t o gamma r a d i a t i o n i s g a i n e d b y e m p l o y i n g c a t h o d e m a t e r i a l s o f h i g h a t o m i c number, Z. A l t h o u g h G-M c o u n t e r s do n o t o c c u p y t h e same p o s i t i o n as t h e y d i d t e n y e a r s ago f o r gamma r a y f l u x measurements i t was f e l t t h a t a n e x p e r i m e n t a l d e t e r m i n a t i o n o f t h e i r e f f i c i e n c y o v e r a wide r a n g e o f p h o t o n e n e r g i e s w o u l d be w o r t h w h i l e n o t k7 o n l y t o make a v a i l a b l e a s t a n d a r d c o u n t e r f o r d e t e r m i n i n g ^amma r a y f l u x e s i n t h e l a b o r a t o r y b u t a l s p a s a n i n d e p e n d e n t c h e c k on t h e f l u x measurements made 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 . A c c o r d i n g l y e f f i c i e n c i e s have been f o u n d f o r a s t a n d a r d b r a s s (Z = 29) w a l l e d c o u n t e r o v e r t h e gamma r a y e n e r g y r a n g e f r o m 0.5 Mev t o 20 Mev. E f f i c i e n c y d e t e r m i n a t i o n a t 6.11+ Mev and 17.6 Mev gamma r a y s f o r a s i m i l a r c o u n t e r were made a few y e a r s a g o b y B a r n e s e t a l (1952); t h i s p r e s e n t work i s a n e x t e n s i o n o f t h e i r s . C h a p t e r I I D e t e r m i n a t i o n o f C h a r a c t e r i s t i c s t 1. Method o f O p e r a t i o n When a gamma r a y e n t e r s t h e c o u n t e r w a l l t h e r e i s a c e r t a i n p r o b a b i l i t y d e p e n d i n g on t h e gamma r a y e n e r g y and t h e c o u n t e r c o n s t r u c t i o n o f i t i n t e r a c t i n g a nd p r o d u c i n g e l e c t r o n s b y one o f t h e t h r e e e f f e c t s : Compton, p h o t o e l e c t r i c o r p a i r p r o d u c t i o n . T h e s e e l e c t r o n s , i f p r o d u c e d n e a r enough t o t h e i n n e r s u r f a c e o f t h e w a l l , w i l l r e a c h t h e g a s e o u s i n t e r i o r . Here t h e y w i l l be a c c e l e r a t e d b y t h e p o t e n t i a l g r a d i e n t b e t w e e n t h e t h i n w i r e anode and t h e c o u n t e r w a l l and w i l l i o n i z e t h e gas by c o l l i s i o n s p r o d u c i n g e l e c t r o n - i o n p a i r s . T h e s e e l e c t r o n s , i n t u r n , p r o d u c e more i o n i z a t i o n and s u c c e s s i v e c o l l i s i o n s i n t h e r e g i o n o f t h e c o u n t e r w i r e and i n i t i a t e a n e l e c t r o n a v a l a n c h e w h i c h s p r e a d s a l o n g t h e w i r e . The p r o d u c t i o n o f new a v a l a n c h e s c e a s e s when t h e p o s i t i v e i o n s h e a t h moving s l o w l y t o w a r d s t h e c a t h o d e r e d u c e s t h e f i e l d a t t h e anode t o s u c h a n e x t e n t t h a t no f u r t h e r m u l t i p l i c a t i o n c a n o c c u r . T h u s , a t t h i s t i m e , a f r a c t i o n o f a m i c r o s e c o n d a f t e r t h e p a s s a g e o f t h e p r i m a r y p a r t i c l e t h e p r i m a r y d i s c h a r g e i s t e r m i n a t e d . I f t h e i o n s h e a t h , w h i c h t a k e s f r o m 100 t o 500 m i c r o s e c o n d s t o c r o s s t h e c o u n t e r v o lume, i s a l l o w e d t o s t r i k e t h e c a t h o d e i t p r o d u c e s p h o t o n s w h i c h e j e c t e l e c t r o n s b y t h e p h o t o e f f e c t t h u s i n i t i a t i n g a new d i s c h a r g e . I n o r d e r t o p r e v e n t t h i s m u l t i p l e d i s c h a r g i n g w h i c h -y o c c u r s w i t h c o u n t e r s u s i n g p u r e g a s e s q u e n c h i n g c a n be accom-FIGURE 16 STANDARD G-M COUNTER Drawing to scale: AMPHENOL CONNECTOR 1/4 O.D. KOVAR TUBE HARD SOLDER a 0 0 6 TUNGSTEN / WIRE BRASS GLASS ^9 p U s h e d b y p r o p e r e l e c t r o n i c c i r c u i t r y ( B l e u l e r & G o l d s m i t h , 1952) w h i c h r e d u c e s t h e h i g h v o l t a g e a c r o s s t h e c o u n t e r f o r a s h o r t p e r i o d a f t e r e a c h d i s c h a r g e . A l t e r n a t i v e l y , i n s t e a d o f a pure c o u n t e r g a s , s u c h as a r g o n , a s m a l l amount o f p o l y a t o m i c v a p o r , s u c h a s a l c o h o l , may be added t o s e r v e as a q u e n c h g a s . T h i s gas m i x t u r e d o e s n o t a f f e c t t h e i n i t i a l p r o d u c t i o n , however a f t e r t h e d i s c h a r g e i n s t e a d o f t h e p o s i t i v e a r g o n i o n s h i t t i n g t h e c a t h o d e t h e y c o l l i d e w i t h a l c o h o l m o l e c u l e s , t h e r e b y t r a n s  f e r r i n g t h e i r c h a r g e t o t h e s e h e a v y m o l e c u l e s . The a l c o h o l m o l e c u l e s t h e n move t o w a r d s t h e c a t h o d e and d i s s o c i a t e u p o n h i t t i n g - i t r a t h e r t h a n e m i t t i n g a n e l e c t r o n . Due t o t h e d i s  s o c i a t i o n o f t h e quench gas t h e l i f e t i m e o f t h e c o u n t e r s i s Q -1 r\ l i m i t e d ; c o u n t e r l i f e i s u s u a l l y o f t h e o r d e r o f 10 t o 10 c o u n t s . 2. C o n s t r u c t i o n and F i l l i n g A s e c t i o n a l d i a g r a m showing t h e c o n s t r u c t i o n o f t h e G e i g e r - M u l l e r c o u n t e r u s e d f o r t h e e f f i c i e n c y d e t e r m i n a t i o n s i s shown i n F i g u r e 16. I t c o n s i s t e d of a p i e c e o f b r a s s t u b i n g o f cm. o u t s i d e d i a m e t e r o f 0.95 cm. w a l l t h i c k n e s s c l o s e d a t t h e e n d s . G l a s s - t o - m e t a l s e a l s a t b o t h ends k e e p t h e h i g h p o  t e n t i a l 0.006 i n c h d i a m e t e r t u n g s t e n w i r e i n s u l a t e d f r o m t h e c o u n t e r w a l l s . A g l a s s s l e e v e a t t h e e n t r a n c e end s e r v e s t o d e  f i n e t h e a c t i v e l e n g t h o f t h e w i r e more a c c u r a t e l y b y k e e p i n g t h e a c t i v e volume away f r o m t h e b r a s s end o f t h e c o u n t e r where t h e f i e l d i s n o n - u n i f o r m . T h i s p a r t i c u l a r c o u n t e r was d e s i g n a t e d FIGURE 17 COUNTER FILLING SYSTEM B A E PHILIPS GAUGE ft 7 D ~3L TO MERCURY DIFFUSION PUMP HEATER 50 as Mark I . A s l i g h t l y d i f f e r e n t c o n s t r u c t i o n was u s e d i n two l a t e r c o u n t e r s r e f e r r e d t o a s Mark I I Nos. 1 and 2. A c t i v e l e n g t h s , as d e f i n e d i n t h e f i g u r e were measured f o r t h e t h r e e c o u n t e r s : C o u n t e r L e n g t h (cm) Mark I 7.5 Mark I I No. 1 7.36 ± 0.08 Mark I I No. 2 7.58 - 0.08 The c o u n t e r s were f i l l e d b y t h e u s u a l method ( B l e u l e r and G o l d s m i t h ) ; t h e f i l l i n g s y s t e m i s shown i n F i g u r e 17. F i l l i n g p r o c e e d u r e was as f o l l o w s : t h e G-M c o u n t e r s A were s e a l e d t o t h e m a n i f o l d B and t h e s y s t e m pumped down w i t h t h e m e r c u r y d i f f u s i o n pump. The e v a c u a t i o n c o n t i n u e d w h i l e t h e c o u n t e r s were warmed i n h o t w a t e r t o o u t g a s them. Pumping c o n  t i n u e d t h i s way f o r a number o f h o u r s u n t i l l i t t l e i n c r e a s e above t h e n o r m a l 10 mm. Hg p r e s s u r e was n o t i c e d when t h e s y s  tem was s e a l e d o f f f r o m t h e pumps and t h e h o t w a t e r removed f r o m t h e c o u n t e r s . The t u b e was t h e n f l u s h e d w i t h a r g o n f r o m t h e f l a s k C. A f t e r c l o s i n g C t h e pumping l i n e was opened and t h e p r e s s u r e a l l o w e d t o f a l l t o n e a r l y i t s o r i g i n a l v a l u e where t h e e v a c u a t i o n was s t o p p e d . A l c o h o l f r o m t h e b o t t l e D was t h e n e v a p o r a t e d i n t o t h e s y s t e m u n t i l t h e p r e s s u r e r o s e 1 cm. a s r e a d b y t h e m e r c u r y manometer, E . The a l c o h o l was t h e n c l o s e d o f f and a r g o n i n t r o d u c e d , l e t t i n g t h e p r e s s u r e c l i m b t o 11 cm. A f t e r s i t t i n g a few h o u r s i n t h i s c o n d i t i o n s o t h a t u n i f o r m m i x i n g o f 51 g a s e s o c c u r r e d c o u n t e r p l a t e a u x were o b t a i n e d . F i n d i n g t h e s e s a t i s f a c t o r y t h e c o u n t e r s were removed f r o m t h e s y s t e m . 3» P l a t e a u and R e s o l v i n g Time I m m e d i a t e l y a f t e r t h e c o u n t e r s had b e e n removed f r o m t h e f i l l i n g s y s t e m a n o t h e r c h e c k on t h e i r c h a r a c t e r i s t i c s was 60 made u s i n g a B e r k e l y M o d e l 2105 D e c i m a l S c a l a r and a Co s o u r c e o f gamma r a y s . The G-M p u l s e s were v i e w e d c o n c u r r e n t l y w i t h a n o s c i l l o s c o p e ; b o t h s c a l a r and o s c i l l o s c o p e a g r e e d as t o where t h e G e i g e r t h r e s h o l d was. P l a t e a u c h a r a c t e r i s t i c s a r e g i v e n below f o r two o f t h e G-M c o u n t e r s i m m e d i a t e l y a f t e r f i l l i n g and a f t e r a b o u t n i n e months o f u s e : C o u n t e r A f t e r R e f i l l i n g A f t e r Use  L e n g t h S l o p e L e n g t h S l o p e Mark I •. 300 0.05/100 150 0.08/100 Mark I I , No. 1 200 0.06/100 200 0.08/100 A c o u n t e r i s c o n s i d e r e d s a t i s f a c t o r y i f t h e p l a t e a u i s 200 t o 300 v o l t s l o n g and has a s l o p e o f a b o u t 0.05/100 . The two s o u r c e method was employed t o f i n d t h e r e  s o l v i n g t i m e o f t h e Mark I c o u n t e r ( B l e u l e r and G o l d s m i t h ) . 60 F o r t h i s , two Co gamma r a y s o u r c e s were u s e d w i t h t h e r e s u l t s : m12 = o b s e r v e d c o u n t r a t e f o r two s o u r c e s = 20,956 - 6*+ per m i n m 1 = " " " " s o u r c e 1 o n l y = 9,100 - 1+2 » » m 2 = " " » " " 2 " = 12,672 * 50 " " m D = " » " *' no s o u r c e = 35.8 - 1.1+ » 1 1 52 T h e n t h e r e s o l v i n g t i m e i s d e t e r m i n e d f r o m T = T x [ l + |L (m 1 2-3m D)] a n d T, = m 1 +m 2-m 1 2-m b 2(m 1-m b) (mg-m^) g i v i n g f = 212 m i c r o s e c o n d s - % . T h i s i s a t y p i c a l v a l u e f o r a G-M c o u n t e r . h. G-M C o u n t e r E f f i c i e n c y ( a ) D e f i n i t i o n o f E f f i c i e n c y The o v e r a l l s e n s i t i v i t y or e f f i c i e n c y , 6 , o f a G e i g e r - M u l l e r c o u n t e r c a n be d e f i n e d b y t h e f o r m u l a Nri = A 6 „ m where = number o f c o u n t s i n t h e G-M c o u n t e r - c o r r e s p o n d i n g number o f gamma r a y s e m i t t e d f r o m t h e s o u r c e r = d i s t a n c e f r o m t h e s o u r c e t o t h e e f f e c t i v e c e n t r e o f t h e c o u n t e r A = e f f e c t i v e a r e a o f t h e c o u n t e r . The f a c t o r ^2 may be c o n s i d e r e d t o be t h e s o l i d a n g l e r o f t h e c o u n t e r and a n a n a l y t i c a l e x p r e s s i o n f o r i t i n t e r m s o f c o u n t e r d i m e n s i o n s i s g i v e n b y W o r l i n g ( 1 9 ^ 1 ) . However, i n t h i s p r e s e n t work A was t a k e n t o g e t h e r w i t h 6 and a n " e f f e c t i v e e f  f i c i e n c y " A€ d e f i n e d . S u c h a n e f f i c i e n c y i s , t h e r e f o r e , c h a r a c  t e r i s t i c o f t h e c o u n t e r u n d e r i n v e s t i g a t i o n . I f c o u n t s a r e r e c o r d e d a t a number o f d i s t a n c e s f r o m t h e s o u r c e t h e n a p l o t may be made o f A j y v e r s u s r , and a 53 s t r a i g h t l i n e o f s l o p e m = - | / Ng_ s h o u l d r e s u l t s o t h a t r V No. t h e e f f e c t i v e e f f i c i e n c y i s A € = + J T # A n e f f e c t i v e c e n t r e m d i s t a n c e f o r t h e c o u n t e r may a l s o be f o u n d b y n o t i n g t h e i n  t e r c e p t on t h e r a x i s . I n a n a l y z i n g t h e r e s u l t s a l e a s t s q u a r e s l i n e Y = mx+b was f i t t e d t o t h e i n v e r s e s q u a r e law p l o t and t h e s l o p e and i n t e r c e p t f o u n d as n £ x. y ± - < x . y ± ^ y . - m £"x. m = i 1 1 h i 1 1 and e - m = . n £ X l 2 - ( £ x ± ) : 2 nm i ~ i where n was t h e number o f i n d e p e n d e n t o b s e r v a t i o n s . A n e s t i m a t e o f t h e e r r o r i n v o l v e d f o r m and b was f o u n d b y a method d e s c r i b e d i n W h i t t a k e r and R o b i n s o n (192+) and o u t l i n e d h e r e : The c o n d i t i o n t h a t t h e l e a s t s q u a r e s l i n e must s a t i s  f y may be w r i t t e n i n two " n o r m a l " e q u a t i o n s : [ x x ] m + [ x l ] b = [ x y ] [ x l ] m + " l l ] b = [ly;]. where [ x y ] = ^ x± I f D i s t h e d e t e r m i n a n t o f t h e c o e f f i c i e n t s i n t h e s e e q u a t i o n s 2 and £ - [SS ] = [ y y ] - [ x y ] m - [ l y ] b t h e n t h e q u a d r a t i c mean e r r o r s a s s o c i a t e d w i t h m and b a r e 2 n-2 u D H^2 c2m = U U .JL!_ and £ 2 = Ixx].. S * D  b TTI FIGURE 18 CIRCUIT CONNECTIONS Beam Lead Shielding - i Tscintillation j C . F . i I j___c°. u _ r ! t _ e r  Low Voltage Supply C F Amplifier High Voltag e Supply Scaler G-M Counter 0 Target tOOChnnl Kicksorter S c a l e r Power 5h ( b ) E x p e r i m e n t a l P r o c e e d u r e The G-M c o u n t e r e f f i c i e n c y was d e t e r m i n e d by a p p l y i n g t h e t h e o r y o f t h e l a s t s e c t i o n t o d a t a t a k e n a t s i x d i f f e r e n t gamma r a y e n e r g i e s . The mean e n e r g i e s u s e d were 0.51, 1.25, 6.16, 12.1, 16.3, and 20.3 Mev f r o m t h e r e a c t i o n s Na (fi +)Ne , C 0 6 V > ) N i 6 0 , F 1 9(p , « ! f-)0 1 6, B 1 1 ( p , r ) 0 1 2 > L i 7 ( p , 0 B e 8 If T ( p , t f ) H e r e s p e c t i v e l y . and A b l o c k d i a g r a m o f t h e G-M c o u n t e r c i r c u i t c o n n e c t i o n s i s shown i n F i g u r e 18. G e i g e r p u l s e s were f e d t h r o u g h a n A t o m i c I n s t r u m e n t Co. L i n e a r A m p l i f i e r M o d e l *+03rB i n t o a 100 ohm c a b l e t o a D y n a t r o n R a d i o L t d s c a l a r T y p e 1009A. H i g h v o l  t a g e f o r t h e G-M c o u n t e r was 1175 v o l t s f r o m a n I s o t o p e s D e v e l o p  ment E.H.T. s u p p l y . T h i s r e s u l t e d i n a n o v e r v o l t a g e o f a b o u t 125 v o l t s p u t t i n g t h e o p e r a t i n g p o i n t a r o u n d t h e c e n t r e o f t h e p l a t e a u . F o r r u n s i n v o l v i n g a s c i n t i l l a t i o n c o u n t e r ( e i t h e r t h e 2^"x3^" c r y s t a l or t h e 2f"xIf-|-" c r y s t a l ) t h e c i r c u i t c o n n e c  t i o n s f o r t h i s c o u n t e r were a l s o as shown i n t h e f i g u r e . P u l s e s were f e d f r o m t h e o u t p u t c a t h o d e f o l l o w e r u n i t mounted on t h e s c i n t i l l a t i o n c o u n t e r t h r o u g h a 100 ohm c a b l e t o a c a t h o d e f o l  l o w e r and hence t o a D y n a t r o n R a d i o L t d A m p l i f i e r Type 1^30A. P o s i t i v e p u l s e s f r o m t h i s u n i t d r o v e a D y n a t r o n R a d i o L t d s c a l a r Type 1009A i n p a r a l l e l w i t h t h e 100 c h a n n e l Computing D e v i c e s o f Canada L t d . k i c k s o r t e r . C a l i b r a t i o n o f t h e s y s t e m was c a r r i e d o u t a s d e s c r i b e d i n P a r t I . 55 ( c ) P r o c e d u r e a t 0.51 Mev 22 I n t h e d e c a y o f Na a p o s i t r o n i s e m i t t e d i n 89$ o f t h e c a s e s ( K r e g e r , 195 )^ and a n e l e c t r o n i s c a p t u r e d i n t h e r e - op m a i n i n g ones r e s u l t i n g i n a n e x c i t e d s t a t e o f Ne o f 1.275 Mev ( A j z e n b e r g and L a u r i t s e n ) w h i c h d e c a y s w i t h a h a l f - l i f e o f -12 +.8x10 s e c o n d ( A l k h a z o v , D.K. e t a l . , 1959). The r a d i a t i o n f r o m t h e a n n i h i l a t i o n o f t h e p o s i t i o n was u s e d t o d e t e r m i n e t h e G-M c o u n t e r e f f i c i e n c y a t . t h i s 0.51 Mev p h o t o n e n e r g y . The num b e r o f 0.51 Mev gamma r a y s was I.78 t i m e s t h e number o f 1.28 Mev gamma r a y s . 22 I n o r d e r t o d e t e r m i n e t h e a b s o l u t e s t r e n g t h o f Na a c t i v i t y t h e s p e c t r u m o f t h e 1.275 Mev gamma r a y shown i n F i g u r e 19 was r e c o r d e d w i t h t h e 2-2~"x3 "^ N a l c r y s t a l m e n t i o n e d i n P a r t I and t h e number o f c o u n t s above t h e h a l f - e n e r g y b i a s compared w i t h t h e a n a l a g o u s number i n t h e s p e c t r u m a l s o shown i n t h e f i g u r e o f 1.17 and 1.33 Mev gamma r a y s f r o m a n a c c u r a t e l y known C o ^ ° s o u r c e . F o r t u n a t e l y t h e mean C o ^ ° gamma r a y e n e r g y i s a l - 22 most e x a c t l y t h e same as t h e Ne 1.28 Mev gamma r a y so t h a t t h e s c i n t i l l a t i o n c o u n t e r e f f i c i e n c y i s t h e same i n b o t h c a s e s t h e 22 60 + r a t i o o f Na c o u n t s t o Co c o u n t s was f o u n d t o b e , R=0.110 - 1.2$ on December 31, 1958. T h i s r a t i o has b e e n c o r r e c t e d f o r t h e l o s s o f c o u n t s due t o t h e k i c k s o r t e r r e s o l v i n g t i m e o f (30 + c h a n n e l number) m i c r o s e c o n d s . The s o u r c e s u s e d were N a 2 2 60 #2 and Co #1. T h i s l a t t e r s o u r c e had been c a l i b r a t e d b y 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 o f Canada on A p r i l 11, 1956 as h a v i n g 56 a s t r e n g t h o f 0.031 m i l l i c u r i e s w i t h i n % . P.P. S i n g h o f t h i s l a b o r a t o r y u s i n g c o i n c i d e n c e t e c h n i q u e s on t h e two c a s c a d e gamma r a y s had f o u n d t h e a c t i v i t y t o be 0.0237 m i l l i c u r i e s w i t h i n 3$ on A p r i l 22, 1958, i n agreement w i t h t h e p r e v i o u s measurement a s s u m i n g a Co h a l f - l i f e o f 5.2 y e a r s . T a k i n g a c  c o u n t o f t h e f a c t t h a t one d i s i n t e g r a t i o n o f a C o ^ ° n u c l e u s rer- 22 s u i t s i n two gamma r a y s , t h e s t r e n g t h o f t h e Na #2 s o u r c e , on December,.31, 1958 was O.OOU-32 m i l l i c u r i e s ± % f o r t h e 1.27 Mev gamma r a y s . T o do t h e e f f i c i e n c y measurements t h e G-M c o u n t e r was h e l d a b o u t t h r e e f e e t o f f t h e f l o o r w i t h i t s a x i s v e r t i c a l and 22 c o u n t s were t a k e n f o r Na s o u r c e - t o - c o u n t e r d i s t a n c e s , r , f r o m 15 cm. t o hO cm. The p r o c e e d u r e was t h e n r e p e a t e d w i t h t h e C o ^ s o u r c e f o r t h e same c o u n t i n g t i m e and d i s t a n c e s . I f N 2 2 i s t h e 22 number c o u n t s due t o t h e Na s o u r c e and N ^ Q i s t h e a n a l a g o u s number f r o m t h e C o ^ ° s o u r c e t h e n t h e c o u n t s due t o t h e 0.51 Mev gamma r a y a r e (N 2 2~k N^Q) and t h e e f f e c t i v e e f f i c i e n c y a t 0.51 Mev i s f o u n d f r o m A € = TT r 2 . ( N 9 9 - k N z n ) w h e r e N 0.89k N 6 0 J i s t h e number of d i s i n t e g r a t i o n s o f Co n u c l e i i n t h e c o u n t i n g t i m e . E f f i c i e n c i e s and e f f e c t i v e c e n t r e s f o r b o t h Mark I and Mark I I , No. 1 c o u n t e r s were measured i n t h i s way. (d) Procedure..,, a t 1.25 Mev. 60 When a Co n u c l e u s d e c a y s two gamma r a y s o f e n e r g y 1.17 and 1.33 Mev a r e e m i t t e d i n c a s c a d e . The G-M c o u n t e r e f  f i c i e n c y was assumed t o v a r y l i n e a r l y b e t w e e n t h e s e two e n e r g i e s 57 so that a mean energy could he defined as 1.25 Mev. The data obtained with the Co^O source.in the previous section was used for the determination of the ef f e c t i v e e f f i c i e n c y and e f f e c t i v e centre at this energy.. For , ..the number of disintegrations, of C o ^ nuclei i n the counting time, the e f f i c i e n c y i s given by A . € = . - 2 i r r 2 M 6 Q . (e) Procedure at 6.16 Mev A GaF 2 target mounted i n the target chamber described by Larson (1957),was bombarded with 365 Kev protons. The pro tons were captured i n the 34-0 Kev resonance and a.; highly excited state of Ne 2^ was formed. This decayed mainly to the 6.14 Mev l e v e l of O1^ by the emission of an alpha - p a r t i c l e . Other states at 6.91 and 7.12 Mev.v/ere formed i n 2.3% ± 0.2% of the decays (Dosso, 1957). The mean gamma ray energy for the G-M counter e f f i c i e n c y determination was therefore 6.T6 Mev.,. The isotropicallyyemitted alpha-particles (Devons and Hine: 1949) to the 6.14 Mev state vrere counted by a propor t i o n a l counter i n an accurately known geometry:. U 3 = (2.357" + 0.005)xl0~^ of a sphere. From the alpha counts the number of gamma rays: emitted isotropically> could be found as Ng, — oC counts (1.023. ± 0.002). , The G-M counter was held with i t s axis v e r t i c a l and positioned so that the gamma rays from the target would pass 58 p e r p e n d i c u l a r l y t h r o u g h t h e t h i n c o p p e r t a r g e t b a c k i n g and t h e one m i l l i m e t r e t h i c k aluminum window t o r e a c h i t . The c o u n t e r - t o - t a r g e t d i s t a n c e was v a r i e d f r o m a b o u t 20 cm. t o 60 cm. P u l s e s f r o m t h e p r o p o r t i o n a l c o u n t e r were a m p l i f i e d b y a Dy n a  t r o n R a d i o L i m i t e d . A m p l i f i e r Type 1^ 30A and r e c o r d e d on t h e 100 c h a n n e l k i c k s o r t e r i n p a r a l l e l w i t h a D y n a t r o n R a d i o L t d s c a l a r Type 1009A. F o r a c o u n t NQ. i n t h e G-M c o u n t e r c o r r e s p o n d i n g t o Ny gamma r a y s e m i t t e d t h e e f f e c t i v e e f f i c i e n c y was f o u n d s i m p l y as A€ = h TT r 2 . % Ny A g a i n , e f f i c i e n c i e s and e f f e c t i v e c e n t r e s were c a l  c u l a t e d f o r Mark I and Mark I I , No. 1 G-M c o u n t e r s , ( f ) Procedmasc a t 12.1 Mev B y bombarding a B 1 1 t a r g e t w i t h 275 Kev p r o t o n s gamma r a y s o f e n e r g i e s ^.^3? 11.67 and 16.10 Mev were e m i t t e d ( A j z e n b e r g and L a u r i t s e n , 1955). A t t h i s p r o t o n e n e r g y t h e 16.0 Mev c o n t r i b u t i o n was s m a l l b u t n o t n e g l i g i b l e . . A B ^ t a r g e t was mounted i n a 3.65 cm o u t s i d e d i a m e t e r 1/16" b r a s s w a l l e d t a r g e t p o t . The Mark I G-M c o u n t e r and t h e s c i n t i l l a t i o n c o u n t e r w i t h t h e 2^f,xh^" N a l c r y s t a l were p o s i t i o n e d a t 90° t o t h e p r o t o n beam. The f r o n t f a c e o f t h e s c i n t i l l a t i o n c o u n t e r was l o c a t e d 15 cm f r o m t h e o u t s i d e o f t h e t a r g e t p o t i w h i l e t h e G-M c o u n t e r - t o - t a r g e t d i s t a n c e was v a r i e d f r o m a b o u t 5 cm t o hO cm. C H A N N E L NUMBER 59 A t y p i c a l s p e c t r u m o b t a i n e d i n t h e s c i n t i l l a t i o n c o u n t e r I s shown i n F i g u r e 20. The number o f gamma r a y s o f e a c h e n e r g y e m i t t e d i n t h e 90° d i r e c t i o n was f o u n d b y d e t e r m i n i n g t h e number o f c o u n t s above t h e h a l f - e n e r g y b i a s i n t h e s c i n t i l  l a t i o n c o u n t e r s p e c t r a and u s i n g a s c i n t i l l a t i o n c o u n t e r e f  f i c i e n c y as r e a d f r o m F i g u r e 3. The e f f i c i e n c i e s and e f f e c t i v e c e n t r e d i s t a n c e s u s e d were 0.705, 0.790, O.798 and h-,6 cm., H-.l cm., K.l cm. f o r gamma r a y e n e r g i e s o f 4-.H-3, 11.67 and 16.10 Mev r e s p e c t i v e l y . F r om p r e v i o u s r e s u l t s a n e f f i c i e n c y f o r t h e h.+3 Mev gamma r a y i n t h e G-M c o u n t e r was f o u n d f r o m i n t e r p o l a t i o n ; t h e v a l u e t a k e n was ( A € )\+ = 0.59. U s i n g t h i s e f f i c i e n c y and t h e i n t e n s i t y o f 4-.U-3 Mev gamma r a y s i n c i d e n t i n t h e d i r e c t i o n of t h e G-M c o u n t e r as d e t e r m i n e d f r o m s c i n t i l l a t i o n c o u n t e r s p e c t r a t h e +.H-3 Mev gamma r a y c o n t r i b u t i o n t o t h e c o u n t s i n t h e G-M c o u n t e r was d e t e r m i n e d . The r e m a i n i n g c o u n t s were t h e n due t o t h e 11.67 and 16.10 Mev gamma r a y s . From t h e i r r e l a t i v e i n t e n s i t i e s i n t h e s c i n t i l l a t i o n c o u n t e r a mean e n e r g y f o r use w i t h t h e G-M c o u n t e r was c a l c u l a t e d t o be 12.1 Mev. Hence t h e e f f e c t i v e e f f i c i e n c y f o r 12.1 Mev p h o t o n e n e r g y was i n f e r r e d f r o m : where N E was t h e number o f gamma r a y s o f e n e r g y " E " Mev b e i n g e m i t t e d f r o m t h e t a r g e t a s f o u n d f r o m t h e s c i n t i l l a t i o n c o u n t e r s p e c t r a and a s s u m i n g i s o t r o p i c d i s t r i b u t i o n . loo«y- FIGURE 21 SPECTRA OF Li(p/)Be GAMMA RAYS , (in23/4 n X 41/2" Nal Crystal) 800H 6O0\- V- Z 2ooh 14.4 M e v 17.2 M e v 10 2 0 3 0 4 0 5 0 6 0 C H A N N E L N U M B E R 7 0 8 0 9 0 I O O . 60 (g) PToceducat. a t 16.3 Mev A t h i n L i 7 t a r g e t e v a p o r a t e d o n t o a c o p p e r b a c k i n g b y t h e method d e s c r i b e d b y S i n g h (1959) was bombarded w i t h *+50 Kev p r o t o n s . The p r o t o n s were c a p t u r e d i n t h e h.hl Kev r e s o n - o ance o f Be . I n t h e s u b s e q u e n t d e c a y a Ih.h o r a 17.2 Mev gamma r a y was e m i t t e d ( A j z e n b e r g and L a u r i t s e n , 1955) b o t h b e i n g s e p a r a t e l y i s o t r o p i c (Devons and L i n d s e y , 1950). S i n c e t h e i r r e l a t i v e i n t e n s i t i e s were 2:1 ( W a l k e r and M c D a n i e l , 19+8), t h e 17.2 Mev gamma r a y b e i n g t h e more i n t e n s e , a mean p h o t o n e n e r g y was f o u n d a s 16.3 Mev. The l a r g e s c i n t i l l a t i o n c o u n t e r , u s e d f o r t h e m e a s u r e  ments a t 12.1 Mev, was p o s i t i o n e d a t 90° t o t h e p r o t o n beam, i t s f r o n t f a c e b e i n g 29 .65 cm. f r o m t h e o u t s i d e o f t h e 2" d i a m  e t e r b r a s s w a l l e d t a r g e t p o t m e n t i o n e d i n P a r t I . The Mark I G-M c o u n t e r was l o c a t e d o p p o s i t e t h e s c i n t i l l a t i o n c o u n t e r a l s o a t 90° t o t h e beam. I t s d i s t a n c e f r o m t h e t a r g e t was v a r i e d f r o m a b o u t 5 cm t o hO cm. A t y p i c a l s p e c t r u m o b t a i n e d i n t h e s c i n t i l l a t i o n c o u n t e r i s shown i n F i g u r e 21. The t o t a l number o f gamma r a y s e m i t t e d Ny was f o u n d b y a d d i n g c o u n t s i n t h e s p e c t r a f r o m a w e i g h t e d h a l f - e n e r g y b i a s and u s i n g a mean s c i n  t i l l a t i o n c o u n t e r e f f i c i e n c y o f 0.797 f r o m F i g u r e 3 . The e f f e c  t i v e c e n t r e d i s t a n c e u s e d was +.1 cm. T h u s , a G-M c o u n t e r e f  f i c i e n c y a t 16.3 Mev was f o u n d s i m p l y f r o m NQ = Afe N i+TT r 2 61 (h) P r o c e d u r e s a t 20.3 Mev A 20.3 Mev gamma r a y was o b t a i n e d b y b o m b a r d i n g a t h i c k t r i t i u m t a r g e t (B-127-1) w i t h 800 Kev p r o t o n s . S i n c e t h e s e gamma r a y s a r e e m i t t e d i n a s i n d i s t r i b u t i o n ( P e r r y and Bame, 1955) b o t h t h e s c i n t i l l a t i o n c o u n t e r w i t h t h e 2-2-"x3 -^" N a l c r y s t a l and t h e Mark I G-M c o u n t e r were p o s i t i o n e d a t 90° t o t h e p r o t o n beam. The s c i n t i l l a t i o n c o u n t e r f a c e was 29.65 cm f r o m t h e o u t s i d e o f t h e 2X} d i a m e t e r b r a s s t a r g e t p o t w h i l e t h e G-M c o u n t e r - t o - t a r g e t d i s t a n c e was v a r i e d f r o m 5 cm. t o 50 cm. The s p e c t r a o b t a i n e d i n t h e s c i n t i l l a t i o n c o u n t e r were s i m i l a r t o t h a t i n F i g u r e 5. C o u n t s were added i n t h e s p e c t r a above t h e h a l f - e n e r g y b i a s and a n e f f i c i e n c y o f 0.72 was assumed f o r t h i s s c i n t i l l a t i o n c o u n t e r f r o m a c o m p a r i s o n o f t h e ( l - e " ^ 4 " 1 1 ) e f f i c i e n c i e s o f t h e two s c i n t i l l a t i o n c o u n t e r s u s e d t h r o u g h o u t t h e work and t h e e f f i c i e n c y o f t h e l a r g e c r y s t a l t o t h e h a l f e n e r g y b i a s t a k e n f r o m F i g u r e 3. An e f f e c t i v e c e n t r e d i s t a n c e o f 3.6 cm. was a l s o c h o s e n on t h e same b a s i s . The G-M c o u n t e r e f f i c i e n c y was t h e n o b t a i n e d s i m p l y f r o m N Q = A £ V7Tr 2 r ~ Ac€ iLiL. N s where N s was t h e number o f c o u n t s t o t h e h a l f - e n e r g y b i a s i n t h e 20 Mev s p e c t r u m and St^ , 6 G a r e t h e s o l i d a n g l e and e f f i c i e n c y r e s p e c t i v e l y o f t h e s c i n t i l l a t i o n c o u n t e r . 62 ( i ) Summary o f E f f i c i e n c y R e s u l t s The e f f i c i e n c i e s a r e t a b u l a t e d b e l o w . The s t a t i s t i c a l e r r o r shown i n t h e f o u r t h c o l u m n does n o t i n c l u d e a n e r r o r f o r t h e s c i n t i l l a t i o n c o u n t e r e f f i c i e n c y . S i n c e a s c i n t i l l a t i o n c o u n t e r was u s e d t o d e t e r m i n e t h e l a s t t h r e e e n t r i e s a n u n c e r  t a i n t y , c o n s i d e r e d t o be 10$ a t t h e p r e s e n t t i m e i n t h e e f  f i c i e n c y a t e n e r g i e s o v e r 12 Mev, s h o u l d be added t o t h e s t a  t i s t i c a l e r r o r t o g i v e a t o t a l e r r o r e s t i m a t e f o r t h e s e e n t r i e s : . , F o r t h e f i r s t t h r e e e n t r i e s t h e s t a t i s t i c a l e r r o r i s t o be t a k e n as t h e t o t a l e r r o r . Afe ( c m 2 ) S t a t i s t i c a l * Mark I Mark I I , N o . l E r r o r (Mev) 0.51 0.04-4-4- 0.04-36 12$ 1.25 0.138 q.li+6 0.8 % 6.16 0.84-5 0.787 2 % 12.1 1.97 3 % 16.3 2.77 . 2 % 20.3 3.68 3 % To w i t h i n t h e e x p e r i m e n t a l e r r o r t h e e f f e c t i v e c e n t r e o c c u r s a t t h e g e o m e t r i c a l c e n t r e o f t h e c o u n t e r f o r a l l p h o t o n e n e r g i e s up t o 20 Mev. T h e s e e f f i c i e n c y r e s u l t s a r e shown p l o t t e d i n F i g u r e 22. The smooth v a r i a t i o n a g r e e s w i t h t h e r e  s u l t s o f F o w l e r e t a l . (194-8). The two o t h e r p o i n t s p l o t t e d a r e t h o s e o f B a r n e s e t a l . (1952), t h e v a l u e s b e i n g 0.73 - 3% a t 6.13 Mev and 2.50 - 5% a t 16.8 Mev. A r o u g h c u r v e d r a w n t h r o u g h t h e o r i g i n and t h e s e two p o i n t s w o u l d have t h e same shape as t h e one f o u n d i n t h i s r e p o r t t h u s l e n d i n g c o n f i d e n c e t o t h e s c i n t i l l a t i o n c o u n t e r e f f i c i e n c y v a l u e s i n P'igure 3. Bibliography Aaronson, D.A., 1950, M.A. Thesis, University of B r i t i s h Columbia. Alkhazov, D.K., Grinberg, A.D., Lemburg, I. Kh., and Rozhdestvenskii, V.V., 1959, Soviet Physics, JETP, 36, 222 Ajzenberg, F., and Lauritsen, T., 1955, Rev. Mod. Phys. 22 77. Barnes, C.A., Carver, J.H., Stafford, G.H., and Wilkinson, D.H. 1952, Phys. Rev. 86, 359. Bleuler, E., and Goldsmith, G.J., 1952, "Experimental Nucleonic Bradt, H., Gugelot, P.C, Huben, 0., Medicus, H., Preiswerk, P. and Scherren, P., 19^6, Helv. Phys. Acta. 1£, 77. Breit, G., and Stehn, J.R.,' 1938, Phys. Rev. j>3, +59. Burbidge, E.M., Burbidge, G.R., Fowler, W.A., and Hoyle, F., 1957, Rev. Mod. Phys. 2£, 559. Devons, S., and Hine, M.G.N., 19+9, Proc. Roy. Soc. (London) A199. 56. Devons, S., and Lindsey, G.R., 1950, Proc. Phys. Soc. (London) 63A, 1202. Dosso, H.W., 1957, M.A. Thesis, University of British Columbia. v Droste, G., 1936", Zeits. fur Physik 100, 529. Dunworth, J.V., 19"+0, Rev. Sci. Instr. 11, 167 Edwards, M., 1950, M.A. Thesis, University of British Columbia. Fowler, W.A., 1958, Astrophys. J. 12Z, 551. Fowler, W.A., Lauritsen, C.C., and Lauritsen, T., 19^8, Rev. Mod. Phys. 20, 236. Geiger, H., 1913, Verh. d. D. Phys. Ges., 1^, 53+, Phys. Zeits ik, 1129. Geiger, H., and Klemperer, 0., 1928, Zeits. fur Physik 2^, 753. Geiger, H., and Muller, V / . , 1928, Phys. Zeits, 29_, 839. G r i f f i t h s , G.M., Singh, P.P., Ssu, Y.I., and Warren, J.E., 1959, Can. Jour. Phys. 17_, 1959. Hanna, S.S., and Inglis, D.R., 19^9, Phys. Rev. 25, 1767. Holmgren, H.D., and Johnston, R.L., 1959, Phys. Rev. 113? 1556. Kreger, W.E., 195*+, Phys. Rev. 96, 155^. Larson, E.A.G., 1957, M.A. Thesis, University of British Columbia. Littauer, L.M., 1950, Proc. Phys. Soc. A63., 29^. Norling,F., 19^1, Arkiv. Mat. Astron. Pysik 22A, 27. Perry, Jr., J.E., and Bame, Jr., S.J., 1955, Phys. Rev. 99 1368. Riley, P.J., 1958, M.A.Sc. Thesis, University of B r i t i s h Columbia. Robertson, L.P., 1957, M.A. Thesis, University of B r i t i s h Columbia. Rose, B., and Wilson, A.R.W., 1950, Phys. Rev. £8, 68. Singh, P.P., 1959, Phd. Thesis, University of B r i t i s h Columbia. Ssu, W., 1955, M.Sc. Thesis, University of British Columbia. Walker, R.L., and McDaniel, B.D., 19^8, Phys. Rev. 315. Whaling, W., 1958, Handbuch der Physik, Vol. 31)-, 193- Y/hittaker, E.J., and Robinson, G., 192l+, "The Calculus of Ob servations" . 

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