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The Li ⁷ (α, γ) B¹¹ reaction and some other topics Singh, Prithe Paul 1959

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THE L l  7  ( a , y) B  1 1  REACTION  and SOME OTHER TOPICS by PRITHE PAUL SINGH B.Sc,  Agra U n i v e r s i t y  (India),  1949  M . S c , Agra U n i v e r s i t y  (India),  1951  A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS POR THE DEGREE OF DOCTOR OP PHILOSOPHY  i n the Department 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 the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA November, 1959  In presenting the  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  r e q u i r e m e n t s f o r an advanced degree at the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t freely  a v a i l a b l e f o r r e f e r e n c e and  agree t h a t p e r m i s s i o n f o r e x t e n s i v e for  s c h o l a r l y purposes may  study.  I further  copying of t h i s  be g r a n t e d by the Head o f  Department o r by h i s r e p r e s e n t a t i v e .  Department o f  be a l l o w e d w i t h o u t my w r i t t e n  ,  The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver S, Canada. Date  my  I t i s understood  that copying or p u b l i c a t i o n of t h i s t h e s i s f o r g a i n s h a l l not  thesis  financial  permission.  GRADUATE Field  of S t u d y :  STUDIES  'Stye Ptttuergtig of Jfeitsij (EalimtHa  Physics  Elementary Quantum Mechanics, Electromagnetic Theory Theory of Measurements N u c l e a r Physics Physics of N u c l e a r Reactions  G . M . Volkoff J . R . H . Dempster A . M . Crooker K . C . Mann J . B . Warren  Faculty of Graduate Studies  'A,  OtherStudies: Theory and Applications of D i f f e r e n t i a l Equations. , N u m e r i c a l Analysis Servomechanisms Analogue Computers  F.M.C. ,  T . Hull Goodspeed E . V . Bohn E , V . Bohn  PROGRAMME  O FT H E  FINAL ORAL E X A M I N A T I O N FOR T H E D E G R E E OF  D O C T O R OF PHILOSOPHY of  PUBLI C A T I O N S A  PRITHE  Simple G a m m a - R a y Insensitive Fast-Neutron Counter. G . M . Griffiths, P . P . Singh, Y . I . S s u a n d J . B . Warren. C a n . J . P h y s . , 37, 858, 1959.  2 2  SINGH  B . S c , Agra University, India, 1951 M . S c , Agra University, India, 1953  T h e Neutron Y i e l d from H e a v y Ice Targets Bombarded with Protons Below the D (p, n) 2p Threshold. P . P . Singh, G . M . Griffiths, Y . I . S s u a n d J . B . Warren. C a n . J . P h y s . , 37, 866, 1959.  T h e Energies and R e l a t i v e Pair Production Cross Section for Z n Na G a m m a Rays. P . P . Singh, H . W . Dosso and G . M . Griffiths. C a n . J . Phys., 37, 1055, 1959.  PAUL  Q 0  and  IN R O O M 301, PHYSICS B U I L D I N G T U E S D A Y , N O V E M B E R 10th, 1959 A T 2:00 P . M .  COMMITTEE  IN CHARGE  D E A N F . H . S O W A R D : Chairman G. M . G R I F F I T H S K. C. M A N N  C. A . M c D O W E L L E . V. BOHN  J. B. W A R R E N  C. A . SWANSON  J. ft. P R E S C O T T  J. B. BROWN  External Examiner:  C. A . B A R N E S  California Institute of Technology  T H E LI  (a. ,lr ) B  remaining k i n e t i c energy of the pair electrons with moderate a c c u r a c y gives the energy of the g a m m a - r a y s with considerably greater p e r c e n t age accuracy. T h e present results are,  R E A C T I O N A N D S O M E O T H E R TOPICS ABSTRACT  Z n ^ , g a m m a - r a y Energy N a " g a m m a - r a y Energy 5  T h e University of British C o l u m b i a V a n - D e - G r a a f f generator was used to study the resonant capture of oC-particles by Li? to form in .the three e x c i t e d states at 8. 92 M e v , 9, 19 M e v and 9, 28 Mev.. B , being in the m i d d l e of the p shell, has been rather extensively studied in the past decade, with considerable disagreement between results o b tained from the L i (a,Y) B and B (d, p) B * l reactions. With seven particles outside the closed shell theoretical calculations are difficult and the calculations of Kurath have been l i m i t e d to the negative parity states only. 1  7  u  1  1 0  T h e energies, intensities and angular distributions of the g a m m a rays which d e - e x c i t e the three states of B have been studied. It was found that the 9. 28 and 9. 19 M e v states cascade through the 6. 76 M e v and 4. 46 M e v states and n e g l i g i b l y , if at a l l , through the 6. 81 M e v state. T h e g a m m a - r a y widths for many of the g a m m a - r a y transitions have been obtained and compared with the average radiative widths reported by W i l k i n s o n . O n the basis of the angular distribution results spins and parities have been assigned to some of the levels up to an. excitation of 9. 28 M e v , T h e results are i n good agreement with recent work on the B^O (d, p) reaction. Tentative speculations concerning the nature, of some of the transitions have been made, a l though no detailed comparison with theory seem possible at the m o m ent. 1  T h e assignments based upon the present work are B l e v e l  Spin and Parity  9. 28 M e v 9. 19 M e v 8 . 9 2 Mev 6. 76 M e v 4. 46 M e v  5/2+  7/2+  5 / 2  +  ,  5 / 2 "  7/25 / 2 "  T h e 4. 46 M e v l e v e l assignment of 5 / 2 " was previously w e l l known. For the 8. 92 M e v l e v e l the present work favours the assignment of 5 / 2 which is supported by the recent stripping work on the B^O (d, p) B ^ - r e a c t i o n ; however, the present results do not rule out the possibility of this l e v e l being 5 / 2 . +  _  A three crystal pair spectrometer was used to determine accurately the energies of the gamma-rays from Z n ^ and Na22, T h e e n ergies of these gamma-rays are above 1.022 M e v and since the accurately known rest mass of the pair electrons is subtracted from each incident photon by pair production, a measurement of the s m a l l  1, 1124 + 0. 0019 M e v 1. 2736 + 0, 0018 M e v  T h e pulse height spectrum and absolute e f f i c i e n c y of a ZnS -lucite fast neutron counter, consisting of a number of thin sheets of l u c i t e coated with zinc sulphide and sandwiched together to form a rectangular block, was investigated using neutrons with energies from 280 K e v . to 16 M e v and g a m m a - r a y s with energies of 1 M e v and 6 M e v . A t a bias setting where the. absolute neutron detection e f f i c i e n c y v a r i e d f r o m 0. 15% for 2 M e v neutrons to O, 3% for 4 M e v neutrons, the 6 M e v g a m m a ray sensitivity was less by a factor of 109. Using this counter the y i e l d and angular distribution of neutrons was measured from thick and thin heavy ice targets bombarded with p r o tons below the D (p, n) 2p threshold. T h e y i e l d and the angula,r d i s t r i bution data fit very w e l l with theoretical results c a l c u l a t e d by Y . I . Ssu on the hypothesis that neutrons are produced by deuterons, scattered i n the target by incident protons, which, then, c o l l i d e d with other target deuterons producing D (d, n) H e ^ neutrons. A s e m i - e m p i r i c a l method has been developed to c a l c u l a t e the gamma-ra.y detection e f f i c i e n c y of N a l ( T i l ) crystals for g a m m a - r a y s from 0. 5 M e v to 12 M e v . T h e results were c o m p a r e d with the e x p e r i mental e f f i c i e n c i e s at . 5 M e v , 1. 25 M e v , 4 M e v , 6 M e v and 12 M e v , independently determined by absolute methods at . 5 M e v , 1. 25 M e v and 6 M e v and by relative comparison at 4 M e v and 12 M e v . The agreement is within 5% up to 6 M e v . T h e effects of scattered g a m m a rays by l e a d shielding was also investigated.  iii ABSTRACT The 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 Van De G r a a f f g e n e r a t o r was used t o s t u d y t h e r e s o n a n t c a p t u r e o f a - p a r t i c l e s  11  7  by L l '  t o form B  i n t h e t h r e e e x c i t e d s t a t e s a t 8.92 Mev,  9.19 Mev and 9.28 Mev.  B  1 1  , being i n the middle of the p s h e l l ,  has been r a t h e r e x t e n s i v e l y s t u d i e d i n t h e p a s t decade w i t h c o n s i d e r a b l e disagreement Li^  (a, 7 ) B  1 1  and B  1 0  between r e s u l t s o b t a i n e d from t h e  ( d , p) B  1 1  reactions.  p a r t i c l e s outside the closed s h e l l t h e o r e t i c a l  With  seven  calculations  are d i f f i c u l t and t h e c a l c u l a t i o n s o f K u r a t h have been l i m i t e d to t h e n e g a t i v e p a r i t y s t a t e s o n l y . The e n e r g i e s , i n t e n s i t i e s and a n g u l a r d i s t r i b u t i o n s o f t h e 7 - r a y s which d e - e x c i t e t h e t h r e e s t a t e s o f B been s t u d i e d . cascade  1 1  have  I t was found t h a t t h e 9.28 and 9.19 Mev s t a t e s  t h r o u g h t h e 6.76 Mev and 4.46 Mev s t a t e s and n e g l i g i b l y ,  i f at a l l ,  t h r o u g h t h e 6.8l Mev s t a t e .  The 7 - r a y w i d t h s f o r  many o f t h e 7 - r a y t r a n s i t i o n s have been o b t a i n e d and compared w i t h t h e average r a d i a t i v e w i d t h s r e p o r t e d by W i l k i n s o n .  On  t h e b a s i s o f t h e a n g u l a r d i s t r i b u t i o n r e s u l t s s p i n s and p a r i t i e s have been a s s i g n e d t o some o f t h e B"^ l e v e l s up t o an e x c i t a t i o n o f 9.28 Mev.  The r e s u l t s a r e i n good agreement  w i t h r e c e n t work on t h e B  ( d , p) B  1 0  1 1  reaction.  Tentative  s p e c u l a t i o n s c o n c e r n i n g t h e n a t u r e o f some o f t h e t r a n s i t i o n s have been made, a l t h o u g h no d e t a i l e d comparison seemspossible  a t t h e moment.  with theory  iv The assignments based upon the present work are B  level  1 1  Spin and P a r i t y  9.28 Mev  5/2*  9.19 Mev  '  7/2+  8.92 Mev  5/2+, 5/2"  6.76 Mev  7/2-  4.46 Mev  5/2"  The assignment previously.  of 5/2" to the 4.46 Mev state was well known  Por the 8.92 Mev state the present work favours  5/2"** and i n t h i s i s supported by recent r e s u l t s from the s t r i p p i n g reaction B  1 0  p a r i t y f o r the l e v e l ;  (d, p) B  1 1  which suggests p o s i t i v e  however, the present r e s u l t s do not  rule out the p o s s i b i l i t y of 5/2* and formation of the state by d-wave a - p a r t i c l e s . A three c r y s t a l p a i r spectrometer was used to determine accurately the energies of the 7-rays from and N a . 22  Zrfi^  The energies of these 7-rays are above 1.022 Mev  and since the accurately known rest mass of the p a i r electrons i s subtracted from each incident photon by p a i r production, a measurement of the small remaining k i n e t i c energy of the p a i r electrons with moderate accuracy gives the energy of the 7-rays with considerably greater percentage accuracy.  The present  r e s u l t s are, Zn 5 7-ray Energy 6  Na  2 2  7-ray Energy  1.1124 + 0.0019 Mev 1.2736: + 0.0018 Mev  V  The p u l s e h e i g h t spectrum  and a b s o l u t e e f f i c i e n c y  o f a Z n S - l u c i t e f a s t n e u t r o n c o u n t e r , c o n s i s t i n g o f a number o f t h i n s h e e t s o f l u c i t e c o a t e d w i t h z i n c s u l p h i d e and sandwiched t o g e t h e r t o form a r e c t a n g u l a r b l o c k , was i n v e s t i g a t e d u s i n g n e u t r o n s w i t h e n e r g i e s from 280 Kev. t o 16 Mev and 7 - r a y s w i t h e n e r g i e s o f 1 Mev and 6 Mev.  At a b i a s  s e t t i n g where t h e a b s o l u t e n e u t r o n d e t e c t i o n e f f i c i e n c y v a r i e d from 0.15$  f o r 2 Mev n e u t r o n s t o 0.3$ f o r 4 Mev n e u t r o n s , t h e  6 Mev 7 - r a y s e n s i t i v i t y was l e s s by a f a c t o r o f 10^. U s i n g t h i s c o u n t e r t h e y i e l d and a n g u l a r d i s t r i b u t i o n o f n e u t r o n s was measured from t h i c k and t h i n heavy i c e t a r g e t s bombarded w i t h p r o t o n s below the D (p, n) 2p t h r e s h o l d .  The  y i e l d and 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 f i t v e r y w e l l w i t h t h e o r e t i c a l r e s u l t s c a l c u l a t e d by Y . I . Ssu on t h e h y p o t h e s i s t h a t n e u t r o n s a r e produced by deuterons, s c a t t e r e d i n t h e t a r g e t by i n c i d e n t p r o t o n s , which, t h e n , c o l l i d e d w i t h o t h e r t a r g e t d e u t e r o n s p r o d u c i n g D ( d , j i ) He3  neutrons.  A s e m i - e m p i r i c a l method has been d e v e l o p e d t o c a l c u l a t e the 7 - r a y d e t e c t i o n e f f i c i e n c y of N a l ( T i l ) c r y s t a l s f o r 7 - r a y s f r o m 0.5 Mev t o 12 Mev.  The r e s u l t s were compared  w i t h t h e e x p e r i m e n t a l e f f i c i e n c i e s a t .5 Mev, 1.25 Mev, 4 Mev, 6 Mev and 12 Mev, i n d e p e n d e n t l y d e t e r m i n e d  by a b s o l u t e methods  a t .5 Mev, 1.25 Mev and 6 Mev and by r e l a t i v e comparison 4 Mev and 12 Mev.  at  The agreement i s w i t h i n 5$ up t o 6 Mev.  The e f f e c t s o f s c a t t e r e d 7 - r a y s by l e a d s h i e l d i n g was a l s o investigated.  ii ACKNOWLEDGEMENTS  Words f a i l t o e x p r e s s my deep g r a t i t u d e t o my s u p e r v i s o r , D r . George M. G r i f f i t h s , f o r h i s u n t i r i n g a s s i s t a n c e , e n l i g h t e n i n g d i s c u s s i o n s ( t e c h n i c a l and p h i l o s o p h i c a l ) and l e a r n e d guidance t h r o u g h o u t t h e c o u r s e o f my work u n d e r him a t U.B.C. l e g e and a p l e a s u r e I am i n d e b t e d  I t was a p r i v i -  t o work w i t h him. t o Dean G.M. Shrum, who  provided  e v e r y f a c i l i t y t o make my J o i n i n g t h e department p o s s i b l e . I w i s h t o thank a l l t h e members o f t h e Van De G r a a f f group, e s p e c i a l l y M e s s r s . D. L i n d q u i s t , P. R i l e y , R. Morrow and G. Jones, f o r t h e i r h e l p i n maintenance and o p e r a t i o n o f t h e Van De G r a a f f g e n e r a t o r and f o r t h e u s e f u l d i s c u s s i o n s on many p o i n t s from time t o time. T e c h n i c a l a s s i s t a n c e o f t h e members o f t h e workshop i s also highly  appreciated.  L a s t , b u t n o t l e a s t , I am g r a t e f u l t o 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 f o r t h e s c h o l a r s h i p which e n a b l e d me t o c a r r y out these s t u d i e s .  TABLE OF CONTENTS CHAPTER  TITLE  PAGE  PART A I  INTRODUCTION 1.  Aims and A s p i r a t i o n s  2.  P r e v i o u s work on B (1) L i (ii) B  II  7  ( a , y) B  1 1  ( d , pr) B  1  1 1  Reaction  2  Stripping Reaction  5  ( i i i ) Theoretical Investigations  8  1 0  1 1  APPARATUS 1.  VanDe Graaff  Generator  ( i ) H e l i u m F i l l i n g System ( i i ) Beam E x t r a c t i o n ( i i i ) B e n d i n g o f t h e Beam ( i v ) L i t h i u m Target P r e p a r a t i o n 2.  11 12 13 15  Gamma Ray D e t e c t i o n  16  ( i ) S c i n t i l l a t i o n Counter  16  ( i i ) Background and S h i e l d i n g ( i i i ) C o u n t e r Energy C a l i b r a t i o n ( i v ) S c i n t i l l a t i o n Counter E f f i c i e n c y  III  11  18 21 22  EXPERIMENTAL 1.  Decay Scheme  24  2.  Angular D i s t r i b u t i o n  21  s  CHAPTER  TITLE  III  PAGE  ( i ) General ( i i ) 9 . 2 8 Mev B ( i i i ) 9 . 1 9 Mev B ( i v ) 8 . 9 2 Mev B 3.  27 1 1  State  29  1 1  State  33  1 1  State  34  Gamma-Ray Y i e l d s  34  ( i ) R e l a t i v e Y i e l d and B r a n c h i n g Ratios  34 36  ( i i ) Absolute Y i e l d 4.  IV 1.  2.  C a l c u l a t i o n s o f Widths  44  ( i ) P a r t i a l R a d i a t i o n Widths  45  DISCUSSION  47  Assignments  47  ( i ) 9 6 0 Kev. Resonance  49  ( i i ) 8 2 0 Kev. Resonance  54  ( i i i ) 400 Kev. Resonance  57 59  Conclusions  PART B 1.  The E n e r g i e s o f Zn^5 and N a  2.  The Performance o f a S i m p l e 7-Ray  2 2  7-Rays  I n s e n s i t i v e P a s t Neutron Counter  60  62  CHAPTER  TITLE  3.  PAGE  The N e u t r o n Y i e l d Prom HeavyIce T a r g e t s Bombarded W i t h P r o t o n s Below The D (p, n) 2p  APPENDIX  I. II. III.  IV.  BIBLIOGRAPHY  Threshold  64  Thermal Leak  66  Angular D i s t r i b u t i o n C o e f f i c i e n t s  69  Rate o f Energy L o s s o f a - P a r t i c l e s i n Lithium.  77  E f f i c i e n c y of N a l C r y s t a l s  8l  97  LIST OP ILLUSTRATIONS  F i g u r e No.  Title  F a c i n g Page  1.  Energy l e v e l diagram o f B^*  3  2.  He gas f i l l i n g  3.  D i s c h a r g e tube  4.  S i d e Arm  5.  C i r c u i t d i a g r a m of the cathode f o l l o w e r  17  6.  B l o c k diagram o f the c o u n t i n g system  18  7.  7-Ray s p e c t r a ; N a , C o  and RdTh  19  8.  7-Ray s p e c t r a ; 4 . 4 3 , 6.14  and 9 . 1 8 Mev  20  9.  7-Ray e f f i c i e n c y c u r v e s  21  10.  7-Ray spectrum from 9 . 2 8 Mev l e v e l  22  11.  7-Ray spectrum f r o m 9 - 1 9 Mev l e v e l  23  12.  7-Ray spectrum from 8 . 9 2 Mev l e v e l  24  13.  1 Mev t o 3 . 5 Mev spectrum ( 9 . 2 8 l e v e l )  25  14.  Decay Scheme  26  15.  a.  Y i e l d v s . time c u r v e s  b.  6 . 7 6 Mev and 9 . 2 8 Mev 7-ray spectrum  11  system  12 13  '  2 2  5 0  30  16.  4 Mev spectrum ( 9 . 2 8 Mev l e v e l )  32  17.  Thermal l e a k  66  18.  S t o p p i n g power v s . a - p a r t i c l e energy  79  19.  a.  Some S e c t i o n s o f t h e C r y s t a l s  b.  Cornpton E l e c t r o n Energy D i s t r i b u t i o n  84  20.  C o i n c i d e n c e Curve  91  21.  E f f i c i e n c y Curves f o r the Three C r y s t a l s  95  Chapter  I  INTRODUCTION  Alms and  Aspirations. " N u c l e a r s p e c t r o s c o p y aims on the one hand t o h e l p  to d e v e l o p , on the o t h e r hand t o get a l o n g w i t h o u t , a det a i l e d knowledge o f the n a t u r e o f n u c l e a r ' f o r c e s ' .  This  seeming c o n t r a d i c t i o n a r i s e s from the g r e a t d i f f i c u l t y of u n c o v e r i n g the p r o f o u n d laws of n a t u r e , and the hope of d o i n g so i n a s t e p w i s e f a s h i o n .  I t i s too much t o hope i n the near  f u t u r e t o c a l c u l a t e the energy l e v e l s of B ^ ,  say, on the  b a s i s of a c o m p l e t e l y s a t i s f a c t o r y meson t h e o r y of n u c l e a r structure.  I n s t e a d one hopes t o d i v i d e the problem up  a phenomenological  into  one i n which the i n t e r a c t i o n s between the  n u c l e o n s are assumed t o have one of the s e v e r a l p o s s i b l e s i m p l e forms, i t b e i n g determined  by t r i a l which form seems  to have the g r e a t e s t e m p i r i c a l v a l i d i t y , and a second i n which the phenomenological  i n t e r a c t i o n thus s e l e c t e d  i s t o be u n d e r s t o o d on the b a s i s of a t h e o r y of the of  the n u c l e o n s t h e m s e l v e s ,  step  structure  a k i n t o the p r e s e n t meson  t h e o r i e s which as y e t are not e n t i r e l y f r e e from d i v e r g e n c e s . " Dr. D.R.  I n g l i s ( 1 9 5 3 ) i n h i s r e v i e w a r t i c l e on the  energy  l e v e l s and the s t r u c t u r e of l i g h t n u c l e i t h u s summed up the m o t i v a t i o n b e h i n d low energy e x p e r i m e n t a l n u c l e a r p h y s i c s , t o p r o v i d e c o n s i s t e n t d a t a about the  energy  -  2 -  of l e v e l s , t h e i r spins and p a r i t i e s and t h e i r modes of decay, checked and rechecked by entering a given nuclear l e v e l through as many channels as possible so that t h i s information can be used to test the p r e d i c t i o n s of empirical models. Already there i s enough information available i n the case of l i g h t n u c l e i (Ajzenberg and Lauritsen, 1955) many serious attempts have been made to understand  that  the nature  of the i n t e r a c t i o n between nucleons, such as those of Peenberg  et a l (1937), I n g l i s (1953) and Kurath (1952, 1956).  Though  the p r e d i c t i o n s of the intermediate coupling model (Kurath, 1956)  f o r the n u c l e i at the beginning and at the end of the  1 p - s h e l l are quite s a t i s f a c t o r y i n some respects, i t i s not so f o r the n u c l e i i n the middle of the s h e l l such as B H and Cil.  Unfortunately, experimental information available about  the n u c l e i i n the middle of the s h e l l i s i n many respeets i n s u f f i c i e n t and also Inconsistent.  Therefore f u r t h e r exper-  imental i n v e s t i g a t i o n i s required f o r n u c l e i such as B , 1 1  which i s the subject of the present  2.  study.  Previous Work on (i)  Li7(q, 7 I B , ; reaction. 1  1  H i s t o r i c a l l y Bennettet a l (1950) were the f i r s t to observe the resonant capture of o p a r t i c l e s by L i 7 forming i n three excited states at 8.92, 9.19 and 9.28 Mev, corresponding to the resonant cr-particle energies of 400, 820 and  B  xx  Jones . 9 6 0 9-28 820 9-19 8-67 4 0 0 I 8-92 Li + a 8-57  Meyer-S  5/2*5/2 3/2,5K2  5/2~7/2  Phillips Stripping 5/2*  3 / 2 , 5 / 2 " 3/2~5/2~  Qtt£  r s  3/2,5/2  3/2*  KURATH 3/2"  7/2-5/2~-  3/2^  6-81  5/2" 7/2"  6-76  5-03  1/2 +  4-46  5/2*"  2-14  3/2*5/2"  5/2", 3/2" 5/2"  1/2*  I/2--  3/2-  B  3/2"  II  FIG.I  E N E R G Y L E V E L DIAGRAM  - 3960 kev respectively.  The gamma rays were observed by a  p a i r of coincident beta-counters.  Due to the l i m i t a t i o n s of  t h i s device they could not i d e n t i f y the i n d i v i d u a l radiations and therefore l i t t l e could be said about the decay scheme of the excited B  1 1  states.  They, however, d i d estimate the width  of each resonance from the slope of the e x c i t a t i o n functions obtained with thick targets.  An upper l i m i t of 1 kev was  placed on the width of the lower and the middle resonances while the width of the upper resonance was measured to be 6 kev.  They also made rough estimates of the t o t a l radiative  width of each resonance by comparing the y i e l d of the Li7(p,7)Be8 reaction to the L i 7 ( a , ? ) B H y i e l d .  (fr)f7) f o r  Values of  the lower, middle and upper resonances were  . 0 4 ,  0.6 and 4.7 ev respectively, where (*> i s the s t a t i s t i c a l f a c t o r and H i s the gamma ray width. Using Nal ( T i l ) c r y s t a l s Jones and Wilkinson (1952) observed the 7-rays emitted as the three excited states of B  ll decayed to the ground state, d i r e c t l y or through some of  intermediate l e v e l s .  On the basis of t h e i r angular d i s t r i -  bution data and some "reasonable assumptions" they assigned the spins and p a r i t i e s to the B l l l e v e l s up to 9 Mev, shown i n P i g . 1, on the assumption that these l e v e l s were those of the ofid proton i n Heydenberg et a l (1954) also observed the gamma rays from LJ7(a, r j B  1 1  and reported that the widths of the .82  - 4 and O . 9 6 Mev r e s o n a n c e s were 6 and 11 kev r e s p e c t i v e l y . Next M e y e r - S c h u t z m e i s t e r and Hanha ( 1 9 5 7 ) the  studied  a n g u l a r d i s t r i b u t i o n o f most o f t h e gamma r a y s f r o m t h e  t h r e e r e s o n a n c e s and suggested t h e s p i n s and p a r i t i e s which are of  a l s o shown i n P i g . 1 .  I n t h e same y e a r P h i l l i p s  (1957)  t h i s laboratory studied the r e a c t i o n i n d e t a i l using  2 . 5 " d i a m e t e r by 3 . 5 " l o n g N a l c r y s t a l .  Prom h i s a n g u l a r  d i s t r i b u t i o n d a t a he a s s i g n e d 5/2+ t o t h e 9 . 2 8 Mev l e v e l and made t e n t a t i v e a s s i g n m e n t s t o some o f t h e o t h e r l e v e l s a s shown i n P i g . 1 . F e r g u s o n e t a l . ( 1 9 5 7 ) r e p o r t e d t h e gamma r a y decay schemes f o r t h e f i r s t n i n e s t a t e s o f B Be^ (He^, P 7 ) B  1  1  1 1  e x c i t e d by t h e  r e a c t i o n and by o b s e r v i n g t h e 7 - r a y s f r o m  each s t a t e I n c o i n c i d e n c e w i t h p r o t o n groups. 6 . 7 6 and 6 . 8 1 Mev s t a t e s were n o t r e s o l v e d .  However, t h e They o b s e r v e d  ground s t a t e t r a n s i t i o n s f o r a l l l e v e l s i n a d d i t i o n t o t h e cascade t h r o u g h t h e f i r s t e x c i t e d s t a t e f r o m t h e 5 . 0 3 , 7 . 3 0 , 7 . 9 9 , 8 . 5 7 Mev s t a t e s and t h e u n r e s o l v e d d o u b l e t around 6 . 8 Mev w i t h an i n t e n s i t y comparable w i t h t h a t o f t h e c o r r e s p o n d i n g ground s t a t e t r a n s i t i o n .  From t h e p a r t i c l e spectrum c o i n c i d e n t  w i t h 7 - r a y s o f energy g r e a t e r t h a n 7 . 5 Mev, i t was I n f e r r e d t h a t t h e gamma r a y w i d t h o f t h e 8 . 9 2 Mev l e v e l i s comparable to  i t s a-particle width.  - 5 (ii)  B (d,p7)B 10  i:L  s t r i p p i n g reaction.  Perhaps the only other way by which the B  1 1  system  has been investigated i s the s t r i p p i n g reaction Bl°(d,p7)BH. As a matter of f a c t the l e v e l s of B  1 1  were f i r s t determined _  accurately by Van Patter et a l (1951) and E l k i n d (1953) by i d e n t i f y i n g proton groups.  Because of the competing  process B H ( d , n 7 ) c H and the complex contribution i n the pulse height spectrum by neutrons from the B H ( d , n ) c H r e action, the study of gamma rays associated with Bl°(d,p7)BH (Bent et a l , 1955) 18 d i f f i c u l t .  The study of proton  angular d i s t r i b u t i o n s from t h i s reaction has l e d to valuable information about  A l l the l e v e l s below 7 Mev seem to  be formed (Ajzenberg and Lauritsen, 1955) by p-wave neutrons, thus r e s t r i c t i n g these states to odd p a r i t y and t h e i r t o t a l angular momentum to values between 3/2 and 9/2. The ground state (3/2"") proton group shows a well defined p-wave s t r i p p i n g pattern f o r a l l deutron energies greater than 2 Mev, though s t r i p p i n g seems to predominate even below t h i s energy.  Also the r e l a t i v e l y large neutron  capture p r o b a b i l i t y would suggest a single p a r t i c l e character f o r the ground state.  The single p a r t i c l e s h e l l model  (Mayer and Jensen, 1955) suggests 3/2" (lp3/2) f o r the ground Btate  of E H which i s consistent with the nuclear magnetic  moment and with the s t r i p p i n g data. The angular d i s t r i b u t i o n of protons corresponding to the B l l 2.14 Mev state produced i n the Bl°(d,p)BH  reaction  -  6  -  I n d i c a t e s t h a t t h i s s t a t e i s formed by p wave n e u t r o n s  which  would i m p l y t h a t t h e t o t a l a n g u l a r momentum J f o r t h i s  state  i s between 3/2"" and 9/2".  T h i s i s i n c o n t r a d i c t i o n t o the  s h e l l model e x p e c t a t i o n o f 1/2"  for this level.  c u l t y can be r e s o l v e d i f one assumes f i r s t , B  1 0  (d,p)B  This d i f f i -  t h a t i n the  r e a c t i o n the o u t g o i n g p r o t o n r e v e r s e s i t s s p i n and  1 1  t r a n s m i t s the e x t r a u n i t o f a n g u l a r momentum t o t h e r e m a i n i n g n u c l e u s as suggested by F r e n c h (Evans, 1954)  o r second, t h a t  t h e o u t g o i n g p r o t o n comes f r o m the t a r g e t n u c l e u s and  not  1958).  f r o m t h e d e u t r o n as o r d i n a r i l y b e l i e v e d (Evans,  H e n s e l e t a l ( 1 9 5 8 ) o b s e r v e d t h a t t h e p o l a r i z a t i o n o f the protons i n the B 0 ( d , p ) B ^ 1  r e a c t i o n going t o the f i r s t  excited  s t a t e i s o p p o s i t e t o t h a t o f the p r o t o n group g o i n g t o the ground s t a t e and p o i n t out t h a t t h i s i s c o n s i s t e n t w i t h b o t h of  the above hypotheses  which i n c r e a s e t h e p o s s i b l e range o f  a n g u l a r momentum v a l u e s f o r t h i s s t a t e f r o m 1/2" The i s o t r o p i c  p - 7 c o r r e l a t i o n i n the B ^ ( d , p 7 ) B 1  t h r o u g h t h e 2.14 Mev  )  1 1  reaction  s t a t e (Cox and W i l l i a m s o n , 1957)  i s o t r o p i c d i s t r i b u t i o n o f the 7 - r a y s i n t h e B r e a c t i o n ( B l a i r e t a l , 1955) assignment -1/2"  t o 11/2".  1 1  and  (p,p7)B  can o n l y be e x p l a i n e d by  the  1 1  an  l e a d i n g t o M l r a d i a t i o n o r 3/2" l e a d i n g t o  p u r e E2 r a d i a t i o n .  I n o r d e r t o d i s t i n g u i s h between t h e s e  two  p o s s i b i l i t i e s W i l k i n s o n ( 1 9 5 7 ) measured an u p p e r l i m i t o f 4xl0*" *sec f o r t h e l i f e t i m e o f the 2.14 Mev li  s t a t e and more  r e c e n t l y H e n s e l e t a l ( 1 9 5 8 ) measured t h e mean l i f e t i m e o f 4 . 6 x l O " ^ e c f o r t h i s s t a t e , which i s much t o o f a s t f o r an 1  S  -  E2 t r a n s i t i o n .  7  -  Thus i t appears that a l l the experimental  information i s consistent with 1/2"" f o r the 2.14 Mev l e v e l as predicted by the s h e l l model.  In f a c t Kurath  (1957)  on the  intermediate coupling model calculated a mean l i f e time of ( 2 . 5 to 5 ) x 10-15 sec f o r t h i s state. The 4.46 Mev state has also been studied by the B (d,p)B 1 0  1 1  reaction.  The proton angular d i s t r i b u t i o n  indicates that t h i s state i s formed by p wave neutrons. Also the p-7 angular c o r r e l a t i o n i s i s o t r o p i c to within 5# (Cox et a l ,  1957).  with the assignment Phillips  (1957)  This favours  3/2"  or 5/2" consistent  of Meyer -Schutzmeister and Hanna  r u l e s out  3/2"  (1957).  on the basis of angular d i s t r i -  bution measurement made with the L i ( a , 7)B - reaction. 7  mean l i f e time measured by Rasmussen e t a l reaction f o r the 4.46 Mev B  B {y,7)B  11  11  The  13  1 1  (1957)*  Btate,  using the  Is  Tm « 1 . 1 7 x 1 0 ~ 5 sec, assuming J * 5 / 2 f o r t h i s state. 1  i s i n good agreement with c a l c u l a t i o n s done by Kurath  This  (1957)  on  the Intermediate coupling model which also p r e d i c t s 5/2" f o r t h i s state. Prom the proton angular d i s t r i b u t i o n obtained from the B ( d , p 7 ) B 1 0  et  al  (1957)  1 1  reaction forming the 6 . 7 6 Mev B  1 1  state Cox  concluded that t h i s state i s also formed by p-wave  neutrons, r e s t r i c t i n g i t s p a r i t y to an odd value and i t s spin to a value between 3 / 2 and 9/2.  Prom t h e i r p-7 angular  c o r r e l a t i o n they ruled out 3/2" and suggested that 9/2" i s unlikely.  - 8 Prom t h i s r e v i e w o f the e x p e r i m e n t a l d a t a the f o l l o w i n g c o n c l u s i o n s seem t o be (a)  Justified.  P o r the ground s t a t e and the f i r s t and the second e x c i t e d s t a t e s we know the s p i n and p a r i t i e s w i t h some c o n f i d e n c e .  (b)  The d a t a a v a i l a b l e f o r the o t h e r l e v e l s i s n e i t h e r complete n o r c o n s i s t e n t enough t o p e r m i t d r a w i n g any c o n c l u s i o n s about the s p i n s and p a r i t i e s of these  (ill)  firm  levels.  Theoretical Investigations. On the t h e o r e t i c a l s i d e many a t t e m p t s t o  understand  the energy l e v e l schemes o f the l i g h t n u c l e i have been made and i t soon became apparent  t h a t one cannot o b t a i n a s a t i s -  f a c t o r y p i c t u r e , c o n s i s t e n t w i t h the e x p e r i m e n t a l  facts,  w i t h e i t h e r the L-S model (Peenberg  o r w i t h the  J-J  model ( K u r a t h , 1952).  e t a l . , 1937)  T h i s l e f t the hope t h a t perhaps  the t r u e p i c t u r e l i e s between these two extremes, t h a t i s t o say i n the r e g i o n o f i n t e r m e d i a t e c o u p l i n g .  Inglis i n  1953  p r e s e n t e d an i n t e r p o l a t e d e s t i m a t e o f l e v e l schemes f o r the p - s h e l l n u c l e i on t h i s p i c t u r e .  Recently Kurath  (1956)  u s i n g the i n t e r m e d i a t e c o u p l i n g model has computed the energy l e v e l schemes o f a l l the n u c l e i i n the 1 p - s h e l l as a f u n c t i o n o f the t h r e e parameters,  a/K,  L/K,  and K, where a/K  measures  the r e l a t i v e s p i n - o r b i t and c e n t r a l energy c o n t r i b u t i o n , depends on p,  L/K  the r a t i o o f n u c l e a r s i z e t o range o f n u c l e a r  f o r c e s and K i s the parameter chosen t o match the l e v e l scheme w i t h the e x p e r i m e n t a l energy s c a l e .  Por B , 1 1  the  theoretical  - 9 spin assignments f o r the negative p a r i t y states are 1/2,  5/2  and 7/2,  and 3/2 f o r one of the states at 6.8  These are shown i n P i g . 1. a 5/2"  3/2,  In addition the model predicts  state somewhere around 11 Mev.  c u l t i e s (Kurath, 1957)  Mev.  There are many d i f f i -  i n Identifying t h i s 5/2"  any of the states around 9 Mev i n B . 1 1  state with  Tikis no doubt that  by considering the various possible combinations of a/K,  L/K  and K values one may be able to obtain a scheme which compares reasonably well with the experimental information f o r low l y i n g l e v e l s of  i t i s already apparent that there i s not  much hope of t h i s r e l a t i v e l y simple model explaining a l l the f a c t s , e s p e c i a l l y those pertaining to the region of higher excitation.  This may be because these c a l c u l a t i o n s do not  take into consideration (a)  e x c i t a t i o n of two nucleons from the 1 p into the 2 s and 1 d shells.  (b)  p o s s i b i l i t i e s of c o l l e c t i v e motion of the nucleus.  (c)  that coupling parameters may vary with e x c i t a t i o n energy. I t may be i n s t r u c t i v e to conclude t h i s section with  two quotations from Kurath (1956 and 1957).  "The o v e r - a l l  picture f o r the 1 p - s h e l l shows that the intermediate coupl i n g model gives considerable improvement over the models of extremely weak or strong spin-orbit coupling.  One can even  begin to make quantitative comparison with experiment using what Is conceptually a very simple model.  While the agree-  - 10 raent with the complicated B  1 0  nucleus i s very encouraging,  one w i l l have to wait f o r more experimental i d e n t i f i c a t i o n s i n the neighbouring Be9 and B  1 1  n u c l e i to t e s t the model  further." "The predictions of t h i s intermediate-coupling model do not give a s a t i s f a c t o r y picture of the experimental evidence concerning gamma t r a n s i t i o n s i n the 1 p - s h a l l .  There are  some cases of good agreement, a few unexplained contradictions and a number of cases which suggest that Introduction of some c o l l e c t i v e motion might bring them into agreement with observation.  In addition there are t r a n s i t i o n s observed f o r  which there are not enough data to draw any conclusions. This i s p a r t i c u l a r l y true of the low l y i n g states i n  This thesis deals with the problem of the spins and p a r i t i e s of the states of B ray t r a n s i t i o n p r o b a b i l i t i e s .  1 1  as well as with the gamma-  TO PIRANI  t  REGULATING VALVE  CHARCOAL AND LIQUID NITROGEN TRAP  X | LIQUID NITROGEN T TRAP  SOLENOID VALVE  HELIUM BOTTLE  THERMAL VALVE  TO PUMP  TO MANIFOLD  HELIUM CYLINDER  FIG. 2  HELIUM  GAS  FILLING  SYSTEM  CHAPTER I I APPARATUS  1.  Van-De-Graaff Generator. A beam of singly ionized helium atoms, hereafter referred to as a - p a r t i c l e s , was obtained by i o n i z i n g the helium gas i n a conventional radio-frequency ion source and accelerated by means of the Van de graaff generator at the University of B r i t i s h Columbia.  (i)  Helium P i l l i n g System. Since, a small contamination of hydrogen or of deu-  terium i n the helium gas w i l l be p r e f e r e n t i a l l y ionized due to t h e i r lower Ionization potentials, (H - 13.6 ev; He 24.6 ev; He+ - 54.4 ev; Kayeand Laby, 1956), the 99.99# pure helium gas, from the Matheson Corporation, was cleaned of such contaminations by slowly passing i t through a l i q u i d nitrogen cooled charcoal trap.  The block diagram of the  f i l l i n g system i s shown i n P i g . 2.  The charcoal adsorbs  the hydrogen gas e s p e c i a l l y at lower temperatures.  TS  s t a r t with,the s t a i n l e s s - s t e e l charcoal trap was outgassed by heating i t under vacuum u n t i l f u r t h e r heating of any section d i d not raise the pressure as seen by the p i r a n l gauge.  I t was then cooled and kept immersed i n a dewar - 11 -  DISCHARGE  DARK  1  ALUMINUM CANAL GLASS  SKIRT  QUARTZ  •DISCHARGE TUBE P^WZ'  2  PLATE  1 TO  FIG. 3  LENS  SPACE  ASSEMBLY  DISCHARGE  TUBE  0' KING  - 12 of l i q u i d nitrogen.  On cooling the pressure dropped further.  I f i t d i d not r i s e i n f i v e minutes, when i s o l a t e d from the pump, the system was considered to be vacuum t i g h t .  The  vapours from the pump were kept away from the charcoal trap by an intermediate l i q u i d nitrogen trap.  The helium gas  then was allowed to pass through the charcoal trap and into the storage b o t t l e very slowly.  I t took about one hour to  f i l l the helium bottle to 60 l b s . gauge.  Due to the l i m i t e d  quantity of charcoal i n the trap, 60 l b s . of helium was about the  maximum amount that could r e l i a b l y be cleaned  without  outgassing the trap again. The helium gas from the bottle leaks into the manif o l d , which i s also connected to hydrogen and deuterium b o t t l e outlets, through a thermal leak (see Appendix I) enclosed i n the helium b o t t l e and a solenoid shut-off valve. Prom the manifold the gas passes to the radio-frequency i o n source.  (ii)  Beam Extraction. P i g . 3 shows the base of the discharge tube, the  aluminum extractor canal, the quartz sleeve and the glass skirt.  P o s i t i v e charge c o l l e c t e d on the Insulating quartz  sleeve as a r e s u l t of probe voltage applied at the top of the discharge space r e s u l t s i n the formation of a dark space between the plasma region and the extractor canal.  Most of  FIG, 4  SIDE  ARM |  V.D.GGENERATOR  - 13 the probe voltage appears across t h i s space and r e s u l t s i n a focusing of the ions from the plasma into the c e n t r a l hole of the extractor.  Therefore i t i s e s s e n t i a l that the  quartz sleeve be accurately aligned a x i a l l y with respect to the extractor canal.  Also i t i s important  that the top of  the quartz be smooth and accurately p a r a l l e l to the top of the extractor.  Whenever these conditions were not met  extraction was a matter of luck (mostly bad l u c k l ) .  the  The  top of the aluminum canal was tapered to reduce the amount of aluminum sputtered onto the quartz due to the beam bombardment.  Aluminum sputtered onto the quartz destroyed i t s  i n s u l a t i n g properties, thus reducing the amount of beam that could be extracted.  Poor alignment had the same e f f e c t .  The best height of the quartz above the aluminum canal 3 mm.  was  Slight v a r i a t i o n s i n t h i s height could be o f f s e t by  adjusting the height of the tank c o i l f o r optimum performance.  (iii)  Bending of the Beam. A well focused beam of 40-50 microamperes i n a  c i r c u l a r spot of 3 mm.  diameter, was allowed to enter the  magnet box where i t was bent through 90 degrees by a large electromagnet so that itemerged h o r i z o n t a l l y into the side arm tube, shown i n P i g . 4,  The v e r t i c a l spread of the beam  was l i m i t e d by molybdenum beam s t a b i l i z i n g probes. be  I t could  sharply focused i n the h o r i z o n t a l d i r e c t i o n by means of  the magnet shims.  A gold stop with 1 cm. diameter hole,  - 14 l o c a t e d before  t h e s o l e n o i d o p e r a t e d beam s h u t t e r , and two  o t h e r s o f molybdenum (3/8 in.„-x.!.3/l6 i n . ) p l a c e d i n t h e s i d e t:  arm o f t h e t a r g e t chamber d e f i n e d t h e beam.  The l a s t two  s t o p s were g e o m e t r i c a l l y so p l a c e d t h a t t h e beam p a s s i n g t h e f r o n t stop d i d n o t h i t anywhere e x c e p t t h e t a r g e t , w h i l e t h e second stop t r a p p e d target.  secondary e l e c t r o n s f r o m g o i n g t o t h e  By v i e w i n g t h r o u g h a s m a l l (1/16 i n . ) g l a s s window  i n t h e t a r g e t p o t , t h e t h r e e s t o p s , molybdenum s n i f f e r s and the e x i t h o l e o f t h e magnet box were a l i g n e d o p t i c a l l y .  The  beam was f o c u s e d  on t h e beam chopper b e f o r e l e t t i n g i t t h r o u g h  to the target.  When t h e beam l a n d e d on t h e t a r g e t i t was  /  s u f f i c i e n t l y defocused that i t f i l l e d the hole through the s t o p s , t h u s a v o i d i n g any s e r i o u s l o c a l h e a t i n g o f t h e t a r g e t . The t a r g e t , i n s u l a t e d f r o m t h e r e s t o f t h e chamber, was k e p t a t 90 v o l t s p o s i t i v e t o r e c o v e r t h e secondary e l e c t r o n s knocked o u t o f t h e t a r g e t by t h e beam.  The beam  was measured by means o f a c u r r e n t i n t e g r a t o r (Edwards, 1950) which was c a l i b r a t e d o c c a s i o n a l l y d u r i n g t h e p e r i o d o f t h e e x periments u s i n g a standard volt battery.  voltmeter,  1# r e s i s t o r s and a 90  Over a p e r i o d o f a few months t h i s c a l i b r a t i o n  remained c o n s t a n t  t o w i t h i n 1#.  Por the 1 microfarad  scale,  w h i c h was used t h r o u g h o u t t h i s work, t h e average c a l i b r a t i o n gave l l O ^ m l c r o coulombs p e r I n t e g r a t o r c o u n t .  - 15 (iv)  L i t h i u m Target P r e p a r a t i o n . The t a r g e t chamber b u i l t by P h i l l i p s (1957) was  p r o v i d e d w i t h an upper s i d e arm, shown i n P i g . 4, which cont a i n e d an e x t e r n a l l y h e a t e d s t a i n l e s s - s t e e l f u r n a c e which m e t a l l i c l i t h i u m c o u l d be p l a c e d .  into  Two s m a l l p i e c e s  of l i t h i u m m e t a l (.4 cm. cube) were c u t under b e n z o l and q u i c k l y t r a n s f e r r e d to the l i t h i u m furnace.  The t a r g e t  chamber was t h e n evacuated, f i r s t by a b a c k i n g pump t h r o u g h one o f t h e f l a t v a l v e s i n t h e s i d e arm and t h e n by t h e magnet box d i f f u s i o n pump.  The f u r n a c e was h e a t e d a t l o w  heat (30 w a t t s ) f o r about h a l f an h o u r t o o u t g a s t h e f u r n a c e and t h e l i t h i u m o f a l l adsorbed vapours i n c l u d i n g b e n z o l . The power was t h e n g r a d u a l l y i n c r e a s e d o v e r a p e r i o d o f f i v e m i n u t e s t o 100 w a t t s .  Soon a b l a c k d e p o s i t , presumably o f  l i t h i u m o x i d e , appeared on t h e w a l l o f t h e t a r g e t chamber f a c i n g t h e f u r n a c e tube e x i t which l a t e r t u r n e d i n t o p a l e white.  A t t h i s stage t h e c o p p e r rod, c a r r y i n g t h e t a r g e t  b a c k i n g was r a i s e d t o f a c e t h e f u r n a c e e x i t .  A black uni-  f o r m d e p o s i t o f l i t h i u m appeared which t u r n e d t o grey and t h e n w h i t e as t h e t h i c k n e s s i n c r e a s e d .  The t h i c k n e s s o f a  t a r g e t was d e t e r m i n e d by r u n n i n g an e x c i t a t i o n f u n c t i o n o v e r the d e s i r e d resonance.  More l i t h i u m c o u l d be e a s i l y  laid  on i n a few m i n u t e s i f r e q u i r e d . The y i e l d from t h e t a r g e t d e c r e a s e d s t e a d i l y w i t h t i m e , perhaps due t o o x i d a t i o n o r n i t r i d e f o r m a t i o n o f  - 16 l i t h i u m p a r t l y under beam bombardment and p a r t l y due air  leak.  T h i s change was  to  finite  r a t h e r e r r a t i c i n the f i r s t h a l f  h o u r of the bombardment,because o f f l u c t u a t i o n s i n the beam p o s i t i o n d i f f e r e n t p o r t i o n s o f the l i t h i u m t a r g e t s were underg o i n g above mentioned changes.  These f l u c t u a t i o n s i n the  y i e l d were l e s s t r o u b l e s o m e i n the case o f t h i c k e r t a r g e t s and bombarding e n e r g i e s  about 20-40 kev h i g h e r t h a n t h e  resonance energy so t h a t the r e s o n a n t r e a c t i o n was  taking  p l a c e a l i t t l e i n s i d e the t a r g e t and not on i t s s u r f a c e . T h i s would i n d i c a t e t h a t the r e d u c t i o n i n y i e l d i s not due  solely  t o beam.bombardment. B e s i d e s the l i t h i u m t a r g e t s v a r i o u s o t h e r  were u s e d .  B ,  .002  t h i c k gold f o i l  1 1  inch<  i s o t o p i c a l l y separated  targets  and d e p o s i t e d on  ( k i n d l y s u p p l i e d by the e l e c t r o -  magnetic s e p a r a t o r group a t H a r w e l l ) , was u s e d t o o b t a i n Mev  7 - r a y s p e c t r a f r o m the r e a c t i o n B  energy c a l i b r a t i o n o f the c o u n t e r .  1 1  (p, 7) C  1  (p, ay)  Harwell)  O  was  reaction. A C ^  16  1  1 2  4.43  f o r the  Calcium fl^pride targets,  l o c a l l y p r e p a r e d , were used t o o b t a i n 6 Mev P ^  a  7 - r a y s f r o m the  target (also supplied  by  u s e d t o o b t a i n c a l i b r a t i o n s p e c t r a a t 8 and  9  Mev.  2.  Gamma Ray (i)  Detection.  S c i n t i l l a t i o n Counters. Two  experiments.  s c i n t i l l a t i o n c o u n t e r s were u s e d d u r i n g t h e s e One  c o n s i s t e d o f a N a l ( T i l ) c r y s t a l 2.5  inches  FIG. 5  CIRCUIT  DIAGRAM  OF  CATHODE  FOLLOWER 3-9 K  H.T. 295 V  P.T.  - ive, IOO  4-7 K  27  Ki  D.L.  Output  8K  500  -1  5-  403B  IM IN459N 100' K  2-2 K J  P. T. = P u l s e T r a n s f o r m e r VALOR RT.530D  100  K D . L . = I H- S e c . Delay Line Type H.H 2 5 0 0  01  220  IOK  i  *0I  220  -01  680  -  17  -  i n diameter and 3.5 i n c h e s l o n g (Harshaw) mounted on a Dumont 6363 p h o t o m u l t i p l i e r .  The second N a l c r y s t a l ,  2.75 i n c h e s i n diameter and 4.5 i n c h e s l o n g , was mounted on a Dumont  KL213  photomultiplier.  I n both cases the  c r y s t a l , p h o t o m u l t i p l i e r , r e s i s t a n c e c h a i n and cathode f o l l o w e r , were mounted i n b r a s s c y l i n d e r s 3 . 5 i n c h e s i n diameter, 15 i n c h e s l o n g and 4 i n c h e s i n diameter by 1 6 . 5 inches long r e s p e c t i v e l y . o f the cathode f o l l o w e r .  P i g . 5 shows the c i r c u i t An a d j u s t a b l e diode  cathode f o l l o w e r c i r c u i t prevented  diagram  l i m i t e r i n the  severe o v e r l o a d i n g of the  p u l s e a m p l i f i e r by cosmic r a y p u l s e s . High v o l t a g e f o r both p h o t o m u l t i p l i e r s was s u p p l i e d by an Isotopes Development L i m i t e d type 532 E.H.T. u n i t and a potentiometer  with a separate  Both m u l t i p l i e r s were operated  adjustment f o r each at  +900 V o l t s .  counter.  At h i g h e r  o p e r a t i n g v o l t a g e s they showed s i g n s of g a i n s h i f t with counting r a t e s .  No a p p r e c i a b l e changes i n the h i g h  power supply were n o t i c e d over the.course  high  tension  of a few days.  A  Lambda model 28 r e g u l a t e d power supply f e d both cathode followers. The 4.5 i n c h  n e g a t i v e p u l s e s from the cathode f o l l o w e r o f the  counter were c a r r i e d by means o f a l o n g 100 ohm  c a b l e t o a p r e - a m p l i f i e r which drove a Dynatron Radio L i m i t e d a m p l i f i e r type 1430 A.  P o s i t i v e output  p u l s e s t f r o m the  a m p l i f i e r were f e d i n t o a 100 channel t r a n s i s t o r i s e d k i c k -  CO  o  > (-  p  m  3D  AMPLIFIER  oo r~ o o  o > o  > •2-D  >  •n rn m 1  CO  CO  O  in  c  O o o  ~o  o  o  m m  si > 3)  EL  m  H z m z  o o c z H m  1  o o <z  3)  H O  CO -< CO H  m  AMPLIFIER  > JO  COUNTER  o  rn H  CO  o > rm  30  i  CD  m  3>  - 18 s o r t e r (Computing D e v i c e s o f Canada) f o r p u l s e h e i g h t analysis.  The o u t p u t o f t h e a m p l i f i e r was a l s o f e d I n t o a  s c a l e o f 100 D y n a t r o n t y p e 1009 A s c a l e r i n p a r a l l e l w i t h the k i c k s o r t e r . arrangement. monitor.  The b l o c k diagram o f F i g . 6 shows t h i s  The 3^5 i n c h  c o u n t e r was o n l y used a s a  The n e g a t i v e o u t p u t p u l s e s from I t s cathode f o l l o w e r  were f e d d i r e c t l y i n t o a 'Dynatron' a m p l i f i e r and t h e n i n t o a •Dynatron' s c a l e r , w i t h t h e b i a s s e t j u s t above t h e 2.62 Mev gamma r a y l e v e l .  (ii)  Background and S h i e l d i n g .  (a)  Background. There a r e two s o u r c e s o f c o u n t e r background. The  f i r s t i s t h e room background due t o cosmic r a y s , c o n t a m i n a t i o n o f r a d i o a c t i v e m a t e r i a l i n t h e w a l l s , f l o o r and s h i e l d i n g l e a d . T h i s i s c o m p l e t e l y t i m e dependent and f o r a g i v e n c o u n t e r geometry c a n be a c c u r a t e l y d e t e r m i n e d . dependent background.  The second i s t h e beam  T h i s i s p a r t l y due t o X - r a y s produced  by e l e c t r o n s f r o m t h e r e v e r s e e l e c t r o n gun s t a b i l i s i n g h i t t i n g t h e t o p o f t h e Van de G r a a f f g e n e r a t o r .  system,  T h i s source  i s n o t v e r y s e r i o u s below 1 Mev. bombarding energy s i n c e t h e X - r a y s a r e s o f t and a r e r e a d i l y absorbed i n t h e l e a d  shield.  The o t h e r source o f beam dependent background i s t h e n u c l e a r r e a c t i o n s produced by a l p h a p a r t i c l e s , p r o t o n s and d e u t r o n s i n t h e u n r e s o l v e d beam t h r o u g h r e a c t i o n s such as C ^ ( a , n) O ^, 1  C  1 2  ( d , n7) N ^ o r C 1  1 2  ( p , 7) N ^, 1  The c a r b o n c o n t a m i n a t i o n  1  - 19 i n s i d e t h e magnet box, and on t h e s t o p s and w a l l s o f t h e g l a s s tube and sometimes on t h e t a r g e t came m o s t l y f r o m the d i f f u s i o n pump o i l v a p o u r s and t h e g r e a s e u3ed i n t h e s e a l i n g g a s k e t s and o ' r i n g s . N e u t r o n s a r e t h e most s e r i o u s source o f background due t o t h e complex shape o f t h e p u l s e h e i g h t spectrum produced by them i n t h e c o u n t e r .  (b)  Shielding. Most o f t h e room background c o u l d be e a s i l y removed  by s h i e l d i n g t h e c o u n t e r ( a l l around) w i t h 4 t o 5 i n c h e s o f lead;  t h i s a l s o e l i m i n a t e s most o f t h e s o f t X - r a y s produced  by t h e machine.  To keep t h e background produced by n u c l e a r  r e a c t i o n s t o a minimum, I t was e s s e n t i a l , f i r s t t o have a l i q u i d n i t V o g e n t r a p on t h e magnet box pumping system, second t o use t h e minimum amount o f vacuum g r e a s e on t h e s e a l i n g g a s k e t s and o' r i n g s and t h i r d t o c l e a n t h e magnet box w i t h h o t d i l u t e n i t r i c a c i d and s t e e l wool a t l e a s t once e v e r y two weeks.  Use o f a second l i q u i d n i t r o g e n t r a p I n t h e beam tube  ( P i g . 4) k e p t t h e vapour p r e s s u r e down i n t h e neighbourhood of the t a r g e t .  The beam s t a b i l i s i n g s n i f f e r s g e n e r a l l y r a n  h o t enough under beam bombardment t o p r e v e n t a p p r e c i a b l e c a r b o n f r o m d e p o s i t i n g on them.  The Hydrogen and D e u t e r i u m b o t t l e s  i n t h e V.D.G. g e n e r a t o r were d i s c o n n e c t e d f r o m t h e m a n i f o l d t o reduce t o a minimum t h e d e u t e r o n and p r o t o n c o n t e n t s o f t h e a beam, t h e r e f o r e m i n i m i s i n g t h e background produced by p r o t o n and d e u t e r o n i n d u c e d r e a c t i o n s .  C H A N N E L  NUMBER  - 20 -  The c o u n t e r and s h i e l d i n g were mounted on a s t e e l 'dexion' t r o l l e y on t o p o f which were mounted two s t e e l p l a t e s s e p a r a t e d by q u a r t e r i n c h b a l l b e a r i n g s so t h a t t h e upper p l a t e c o u l d be moved f r e e l y on t h e l o w e r one. j u s t i n g screws were p r o v i d e d  Ad-  to f a c i l i t a t e the r e l a t i v e  p o s i t i o n i n g between t h e p l a t e s .  The f r o n t end o f t h e t r o l l e y  c o u l d be j a c k e d up l e a v i n g l t f r e e t o r o t a t e about a u n i v e r s a l b e a r i n g mounted on, a degree c i r c l e p l a c e d on t h e f l o o r .  The  c e n t r e o f t h e t a r g e t was p l a c e d v e r t i c a l l y above t h e c e n t r e of the u n i v e r s a l bearing.  As t h e f l o o r was n o t e x a c t l y  level  s m a l l a d j u s t m e n t s o f t h e upper s t e e l p l a t e were r e q u i r e d t o b r i n g the counter a x i s i n t o l i n e with the centre and  of the t a r g e t  t o keep t h e c o u n t e r t a r g e t d i s t a n c e c o n s t a n t as t h e a n g l e  was changed.  The c o u n t e r c o u l d be r o t a t e d up t o 135* on  e i t h e r s i d e o f t h e i n c i d e n t beam d i r e c t i o n .  The c o u n t e r was  mounted I n a c y l i n d r i c a l h o l e t h r o u g h f o u r i n t e r l o c k i n g l e a d b r i c k s (6  n  x 6" x 6") w h i c h were l i n e d w i t h q u a r t e r i n c h t h i c k  i r o n tubing to provide obtained  f r o m a l i g h t mu-metal s h i e l d p l a c e d o v e r t h e p h o t o -  multiplier. placed  a d d i t i o n a l magnetic s h i e l d i n g o v e r t h a t  Three I n c h e s o f a d d i t i o n a l l e a d s h i e l d i n g was  around t h i s whole assembly.  To s h i e l d t h e c o u n t e r f r o m  the n e u t r o n and 7-ray background, produced i n t h e magnet box, a l e a d and p a r a f f i n w a l l was c o n s t r u c t e d  i n f r o n t o f t h e magnet  box so t h a t t h e c o u n t e r d i d n o t see any p o r t i o n o f t h e box.  GAMMA  8  RAY  E N E R G Y - MEV 1 2  - 21 (Hi)  C o u n t e r Energy C a l i b r a t i o n . Since the p u l s e h e i g h t response o f the N a l ( T i l )  c r y s t a l s i s l i n e a r l y p r o p o r t i o n a l t o t h e energy o f t h e i n c i d e n t 7 - r a y s , t h e energy c a l i b r a t i o n o f t h e c o u n t e r c o u l d e a s i l y be e f f e c t e d by means o f 7 - r a y s o f known e n e r g i e s and a standard pulse generator.  The s t a n d a r d p u l s e g e n e r a t o r  ( R o b e r t s o n 1 9 5 7 ) u s e d d u r i n g t h e s e e x p e r i m e n t s had a l i n e a r i t y b e t t e r than 0 . 1 $ .  The p u l s e s f r o m t h i s d e v i c e h a d t h e  same r i s e t i m e a s a t y p i c a l N a l p u l s e ( 0 . 2 5 m i c r o s e c o n d ) and were o f s u f f i c i e n t l y l o w l e v e l t o be f e d d i r e c t l y i n t o t h e p h o t o m u l t i p l i e r cathode f o l l o w e r .  T h i s p r o v i d e d an independent  check on t h e l i n e a r i t y o f t h e e l e c t r o n i c equipment used a f t e r t h e cathode f o l l o w e r .  The gamma r a y s e m i t t e d by r a d i o a c t i v e  s o u r c e s o f N a , C o 6 ° and Rd Th were used f o r c a l i b r a t i o n a t 2 2  e n e r g i e s o f 0 . 5 1 , 1 . 3 3 and 2 . 6 2 Mev r e s p e c t i v e l y and f o r obn 1? t a i n i n g r e p r e s e n t a t i v e 7-ray s p e c t r a .  The B  ( p , 7) C  r e a c t i o n was used t o o b t a i n 4 . 4 3 Mev and 1 2 Mev 7 - r a y s , t h e P 1  (p, ar) O ^ r e a c t i o n p r o v i d e d 6 . 1 4 Mev 7 - r a y s and t h e . 1  C"^ ( p , r) O ^ r e a c t i o n was u s e d t o o b t a i n 9.18 Mev 7 - r a y s . 1  T h i s c o v e r e d t h e whole range o f 7 - r a y s e n c o u n t e r e d i n t h e p r e s e n t s t u d y o f t h e L i 7 ( a , 7) B  1 1  reaction.  A detailed  knowledge o f t h e shape o f gamma r a y s p e c t r a a s a f u n c t i o n o f energy i s r e q u i r e d f o r s e p a r a t i n g t h e i n d i v i d u a l components f r o m a complex spectrum.  Typical spectra obtained f o r t h i s  purpose a r e shown i n P i g . 1 ( 0 . 5 , 1 . 3 3 and 2 . 6 2 Mev) and P i g . 8 (4.43,  6.14  and  9.18  Mev).  - 22 (iv)  Scintillation  Counter  Efficiency.  I n o r d e r t o o b t a i n a b s o l u t e ?-ray i n t e n s i t i e s f r o m the complex k i c k s o r t e r s p e c t r a i t was n e c e s s a r y t o have a knowledge n o t o n l y o f t h e spectrum  shape b u t a l s o o f t h e  absolute e f f i c i e n c y of the s c i n t i l l a t i o n counter f o r d e t e c t i n g gamma r a y s a s a f u n c t i o n o f energy. t a i n e d f r o m an independent  T h i s i n f o r m a t i o n was ob-  t h e o r e t i c a l and e x p e r i m e n t a l s t u d y  of t h e e f f i c i e n c y o f s e v e r a l s c i n t i l l a t i o n c o u n t e r s , I n c l u d i n g t h o s e used i n t h e p r e s e n t s t u d y , a s o u t l i n e d i n appendix I V . T h i s s t u d y c o v e r e d t h e gamma r a y energy range from 0.5 Mev t o 20 Mev and i n c l u d e d a b s o l u t e measurements a t e n e r g i e s o f 0.5* 1.25  and 6.14 Mev a s w e l l a s t h e comparison  o f the s c i n t i l l a t i o n  counter e f f i c i e n c y curve w i t h the e f f i c i e n c y curve f o r a standard G e i g e r c o u n t e r o f t h e type used b y B a r n e s e t a l . (1952). e f f e c t s o f s c a t t e r i n g due t o t h e presence o f t h e c o u n t e r and mounting were a l s o i n v e s t i g a t e d .  The shield  I n t h i s study, t h e  e f f i c i e n c y h a s been d e f i n e d as t h e r a t i o o f t h e number o f c o u n t s i n t h e gamma r a y spectrum above a b i a s e q u i v a l e n t t o h a l f t h e 7-ray energy t o t h e number o f gamma r a y s i n c i d e n t on an a r e a equal t o the area o f the face of the X - t a l .  I t was assumed  t h a t t h i s a r e a was p l a c e d a t t h e e f f e c t i v e c e n t r e o f t h e c r y s t a l . The e f f e c t i v e c e n t r e b e i n g t a k e n a s t h a t p o i n t i n t h e c r y s t a l f r o m which measurements o f source t o c r y s t a l d i s t a n c e were made i n o r d e r t o g i v e an i n v e r s e square r e l a t i o n between c o u n t i n g r a t e and d i s t a n c e .  The r e a s o n s f o r t h i s c h o i c e o f e f f i c i e n c y  d e f i n i t i o n are g i v e n i n appendix I V i  P i g . 9 shows t h e c u r v e  FIG. II  4-73  9-19  MEV  LEVEL  o o o  I to 5  oo©  5 to 9-5 Mev  Mev  6-76  Mev  SPECTRUM  Spectrum Spectrum  - 23 o f e f f i c i e n c y t o h a l f energy b i a s o b t a i n e d f r o m the above mentioned s t u d y f o r t h e 2 . 7 5 i n c h by 4 . 5 i n c h c r y s t a l used i n the p r e s e n t work when t h a t c r y s t a l i s i n i t s 4 i n c h t h i c k lead  shield. The e f f i c i e n c y , £ , a t any o t h e r b i a s c o u l d be b  e m p i r i c a l l y d e t e r m i n e d i n terms o f t h e e f f i c i e n c y a t t h e h a l f energy b i a s , £  8111(1  e x p e r i m e n t a l 7 - r a y spectrum shape  u s i n g the r e l a t i o n ,  L  C  V b = ^1/2  v x  No. o f c o u n t s above b i a s b No. o f c o u n t s above h a l f e n e r g y b i a s  I n t h i s work due t o t h e complex n a t u r e o f t h e 7 - r a y s p e c t r a o b t a i n e d , i t was n o t always p o s s i b l e t o o b s e r v e t h e complete spectrum o f a p a r t i c u l a r gamma r a y down t o i t s h a l f energy p o i n t because o f t h e p r e s e n c e o f o t h e r gamma r a y s . C o n s e q u e n t l y f o r h i g h e r energy gamma r a y s an e f f i c i e n c y t o a b i a s 2 Mev below t h e peak gamma r a y energy h a s been u s e d . T h i s e f f i c i e n c y a s o b t a i n e d by t h e above mentioned method i s a l s o shown a s a f u n c t i o n o f gamma*ray energy i n P i g . 9.  CHAPTER I I I EXPERIMENTAL  1.  Decay Scheme. Three e x c i t e d s t a t e s o f B ^ have been produced 1  by t h e r e s o n a n t c a p t u r e o f a p a r t i c l e s i n L I . 7  9.28  Mev produced by 96O k e v a p a r t i c l e s , 9.19  by 820  k e v a p a r t i c l e s and 8.92  particles.  These a r e Mev produced  Mev formed by 400 k e v a  The gamma r a y s p e c t r a o b t a i n e d f r o m each o f t h e s e  r e s o n a n c e s a r e shown i n F i g s . 10, 11, and 12 w h i c h c o v e r an energy range o f about 1.5  Mev t o 9.5  i t i s a p p a r e n t t h a t t h e 8.92  Mev. From t h e s p e c t r a  Mev l e v e l decays c h i e f l y t o t h e  ground s t a t e and a s m a l l f r a c t i o n o f t h e 9.28  Mev l e v e l decays  t o t h e ground s t a t e b u t t h e r e i s no e v i d e n c e f o r any s i g n i f i c a n t f r a c t i o n o f t h e 9.19  l e v e l d e c a y i n g t o t h e ground s t a t e .  These  s p e c t r a a l s o show t h a t t h e upper two l e v e l s decay t o one o f t h e two l e v e l s o f t h e d o u b l e t around 6.8 Mev w h i c h i n t u r n p r i m a r i l y decays t o t h e ground s t a t e g i v i n g a 7 - r a y o f about 6.8 Mev. For  t h e 9.28  and 9.19  the  cascade t h r o u g h t h e 4.46 l e v e l g i v i n g two gamma r a y s o f  about e q u a l energy.  l e v e l s t h e most p r o m i n e n t t r a n s i t i o n i s  The s e p a r a t i o n o f t h i s p a r t o f t h e spectrum  i n t o i t s ,two components i s d i s c u s s e d i n s e c t i o n 2 o f t h i s chapter.  F o r t h e 8.92  l e v e l , t h e r e i s an i n d i c a t i o n  that a  s m a l l f r a c t i o n o f t h e decay goes .via t h e 4.46 Mev s t a t e .  - 24 -  FIG. 13  2 MEV  SPECTRUM—9-28  40 C H A N N E L  MEV  60 NUMBER  LEVEL  SO  -25  -  I n o r d e r t o d e t e r m i n e t h e energy o f t h e 2.5 t r a n s i t i o n f r o m t h e 9.28 the  Mev  Mev l e v e l t o one o f t h e l e v e l s  d o u b l e t around 6.8 Mev,  of  7-ray s p e c t r a c o v e r i n g t h e  range 1 Mev t o 3 Mev were o b t a i n e d as shown i n P i g . 13. The w i d t h o f a k i c k s o r t e r . c h a n n e l was 20 kev f o r t h e s e r u n s . U s i n g t h e l i n e a r p u l s e g e n e r a t o r and t h e 2.62 Mev Rd Th the  line,  energy o f t h e prominent peak was d e t e r m i n e d t o be 2.52  0.015  Mev.  +  T h i s gamma r a y must t h e r e f o r e be a s s i g n e d t o t h e  transition  f r o m the 9.28  Mev l e v e l t o t h e 6.76  level. A  transition  t o t h e 6.8l l e v e l would l e a d t o a 7 - r a y o f energy  2.47 Mev which i s o u t s i d e t h e e x p e r i m e n t a l e r r o r f o r t h e obs e r v e d energy.  There a r e no o t h e r p o s s i b l e t r a n s i t i o n s  known l e v e l s of B  1 1  between  t o which t h i s 7 - r a y c o u l d be a s s i g n e d .  A s i m i l a r a n a l y s i s f o r t h e 9.19 energy o f 2.43 + 0.015 Mev,  l e v e l l e d t o an  a g a i n c o n s i s t e n t w i t h the decay  o f t h e 9.19 Mev l e v e l t o t h e 6.76  Mev  level.  The second peak t o t h e l e f t o f t h e 2.52 Mev peak was d e t e r m i n e d t o have an energy o f 2.30 + 0.02 Mev and  was  t h e r e f o r e i d e n t i f i e d w i t h t h e p a r t i a l decay of t h e 6.76  Mev  s t a t e t o t h e 4.46 Mev l e v e l and n o t t o t h e decay o f t h e  4.46  l e v e l t o t h e 2.14 Mev l e v e l because t h e r e was no e v i d e n c e o f the  subsequent 2.14 Mev t r a n s i t i o n  i n t h e 7 - r a y spectrum.  T h i s was c o n f i r m e d by a b s o l u t e i n t e n s i t y the  2.52 Mev,  2.3 Mev and 6.76  Mev  t o l a t e r , i n which t h e i n t e n s i t y  determinations of  7 - r a y s ; which a r e r e f e r r e d  o f t h e 2.52 Mev  7-ray was  5  /: 2  7/£  5/2\(5/2)  ±  ±  90-5I  8  ±  7/2"  73  _±_  5/2'  1/2'  100  85  85  18  3/2"  B  II  FIG. 14 D E C A Y S C H E M E  -  -  26  f o u n d t o be a p p r o x i m a t e l y e q u a l t o the sum o f the of the 2 . 3 Mev  and 6 . 7 6  Mev  intensities  gamma ray3.  The d e t e r m i n a t i o n o f t h e energy o f the 6 . 7 6  Mev  7 - r a y s f r o m s p e c t r a c o v e r i n g an energy range o f 5 Mev  to 7 ^ev  f o r b o t h t h e 9 . 2 8 and 9 . 1 9  7-ray  l e v e l s , u s i n g the 6.14  (p, cey) O ^  obtained from the  1  Mev  r e a c t i o n and the l i n e a r p u l s e  g e n e r a t o r , f u r t h e r c o n f i r m e d the above c o n c l u s i o n t h a t b o t h t h e s e s t a t e s decay t o t h e 6 . 7 6  Mev  l e v e l and n o t t o the 6 . 8 1  T a b l e I l i s t s t h e 7-rays I d e n t i f i e d  a t each  Mev  level.  resonance.  TABLE I 400  kev Resonance  ( 8 . 9 2 Mev B  1 1  state)  820 kev Resonance  960 kev Resonance  (9.19  ( 9 . 2 8 Mev B  Mev B  1 1  state)  1 1  8.92  Mev  6.76  Mev  9.28  Mev  6.76  Mev  4.73  Mev  6.76  Mev  4.46 Mev  4.46  Mev  4.82  Mev  2.14  2.46  Mev  4.46  Mev  2.3  Mev  2.53  Mev  2.3  Mev  Mev  state)  The decay scheme as suggested by t h e s e r e s u l t s i s shown i n P i g . 1 4 , are  w h i c h a l s o shows the b r a n c h i n g r a t i o s  obtained i n a l a t e r s e c t i o n of t h i s chapter.  which  - 27 2.  Angular D i s t r i b u t i o n . (l)  General. T h i n t a r g e t s r a n g i n g I n t h i c k n e s s f r o m 100 kev t o  200 k e v were u s e 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 measurements. The maximum p e r m i s s i b l e t h i c k n e s s , w i t h t h e c o n d i t i o n t h a t o n l y one resonance was e x c i t e d a t a t i m e , was used f o r each of the three resonances.  The bombarding a - p a r t l c l e e n e r g i e s  were chosen somewhat above t h e resonance energy so t h a t t h e y i e l d was r e l a t i v e l y independent o f s m a l l changes i n t h e bomb a r d i n g energy.  The y i e l d a t t h e b e g i n n i n g o f t h e r u n s on a  f r e s h t a r g e t showed some f l u c t u a t i o n and a d e c r e a s e i n t h e y i e l d a s a f u n c t i o n o f t h e t a r g e t bombardment.  Therefore  t h e measurements t a k e n i n t h e f i r s t h a l f hour o f t h e bombardment were n o t used i n t h e a n a l y s i s .  T h i s was n e c e s s a r y because  d u r 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 measurements a t t h e 9.19 Mev and 8.92 Mev r e s o n a n c e s no s e p a r a t e m o n i t o r c o u n t e r was used due t o t h e r e l a t i v e l y l o w y i e l d f r o m t h e r e s o n a n c e . The t r o l l e y c a r r y i n g t h e c o u n t e r mounted i n t h e 1  s h i e l d was p l a c e d n e a r t o t h e t a r g e t so t h a t i t c o u l d be r o t a t e d around a s d e s c r i b e d i n s e c t i o n 2 o f t h e l a s t c h a p t e r . I n o r d e r t o ensure t h a t t h e beam h i t t h e c e n t r e o f t h e t a r g e t , measurements were made w i t h t h e c o u n t e r a t 0°, 45°, 90° and 135° and w i t h t h e normal t o t h e t a r g e t p l a n e a t 45° t o t h e l e f t and t h e n t o t h e r i g h t o f t h e i n c i d e n t beam.  The a n g u l a r  d i s t r i b u t i o n measurements were t a k e n on b o t h s i d e s o f t h e beam  - 28 as a f u r t h e r check on the t a r g e t c o u n t e r symmetry.  Several  measurements were made a t each a n g l e and an e s t i m a t e o f t h e change i n t a r g e t y i e l d was made by p l o t t i n g y i e l d bombardment time c u r v e s f o r each a n g l e .  versus  T y p i c a l curves are  g i v e n i n Pig.15a w h i c h show the change of y i e l d w i t h bombardment t i m e .  U s i n g t h e s e c u r v e s a l l the measurements c o u l d  be n o r m a l i s e d t o t h e same bombardment t i m e . s l o p e o f the c u r v e s f o r d i f f e r e n t a particular rejected.  a n g l e s i s . t h e same and i f ;  p o i n t l a y f a r o f f the a p p r o p r i a t e c u r v e , i t was  F o r t h e 9 . 2 8 Mev  h i g h , a 3.5  I n g e n e r a l , the  l e v e l where the y i e l d i s r e l a t i v e l y  i n c h e s l o n g N a l c r y s t a l , h a n g i n g v e r t i c a l l y above  t h e t a r g e t , was used as a m o n i t o r .  T h i s p r o v i d e d an a d d i t i o n a l  r e f e r e n c e f o r n o r m a l i s i n g the measurements.  The  experimental  d a t a were a n a l y s e d , d e t a i l s o f the a n a l y s i s are g i v e n below f o r each resonance,, and the e x p e r i m e n t a l a n g u l a r f u n c t i o n f o r each 7-ray l i n e was F The  (9) « A (1 + A  e x p r e s s e d i n the g e n e r a l f o r m ,  Cos 0 + A 2  2  distribution  Cos ©) 4  4  (l)  r a t i o o f t h e number o f c o u n t s a t v a r i o u s a n g l e s f o r each  7-ray was used t o d e t e r m i n e perimental  A  2  and A^.  ratios  No. = ® 9 o  1 + A  45 « %0  1 + 0.5 A  Np  1 + A  N  N45  =  2  2  +  A^  + 0.25  2  A  4  + A4  i + 0.5 A  2  + 0.25  A4  F o r example, the  ex-  -  29 -  gave s u f f i c i e n t i n f o r m a t i o n t o d e t e r m i n e A  and A4.  2  Only  i n a few c a s e s was A4 f o u n d t o be a s b i g a s 5 $ o f A and 2  s i n c e t h i s i 3 about t h e o r d e r o f e r r o r i n A , A^ h a s been 2  neglected I n the a n a l y s i s of the r e s u l t s .  The measurements  a t 1 3 5 ° were t a k e n t o d e t e c t any f o r w a r d backward about 9 0 ° .  asymmetry  W i t h i n the s t a t i s t i c a l e r r o r s no s i g n i f i c a n t  d i f f e r e n c e between t h e 4 5 ° and 1 3 5 ° measurement was d e t e c t e d . To p u t t h e c o u n t e r a t 1 3 5 ° q u i t e a b i t o f l e a d s h i e l d i n g had t o be removed which r e s u l t e d i n a d d i t i o n a l background butions.  contri-  T h e r e f o r e t h e s e measurements were n o t used i n t h e  a n a l y s i s of angular d i s t r i b u t i o n s .  The a n g u l a r d i s t r i b u t i o n  c o e f f i c i e n t s were c o r r e c t e d f o r f i n i t e s o l i d a n g l e o f t h e counter.  The c o r r e c t i o n s were i n no case g r e a t e r t h a n 1 0 $ .  (ii)  9 . 2 8 Mev B  (a)  Angular D i s t r i b u t i o n  1 1  State. o f 9 . 2 8 Mev and 6 . 7 6 Mev y-Raya.  The a n g u l a r d i s t r i b u t i o n o f 9.28 Mev ground  state  gamma r a y s and 6 . 7 6 Mev ground s t a t e gamma r a y s were d e t e r m i n e d f r o m t h e s p e c t r a t a k e n c o v e r i n g an energy range f r o m 5 Mev t o 9 . 5 Mev. 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 9 . 2 8 Mev 7-ray was e a s i l y d e t e r m i n e d f r o m t h e t o t a l number o f c o u n t s , a f t e r c o r r e c t i n g f o r t h e background, i n t h e energy range f r o m 7 . 2 8 Mev t o 9 . 5 Mev a s t h e r e was no c o n t r i b u t i o n f r o m any o t h e r 7-rays i n t h i s range.  P i g . 15  A.  Y i e l d v s . time c u r v e s  B.  6 . 7 6 Mev  013IA  and 9 . 2 8 Mev  7 - r a y spectrum  SiNOOO  - 30 To d e t e r m i n e t h e a n g u l a r d i s t r i b u t i o n o f 6.76 Mev r - r a y t h e s p e c t r a f r o m each measurement were p l o t t e d and f r o m an e m p i r i c a l knowledge o f t h e shape o f t h e 9 Mev s p e c t r a o b t a i n e d a t t h e I.76 Mev resonance o f t h e C ^ x  (p, 7) N^**  r e a c t i o n , t h e t a i l o f t h e 9.28 Mev 7-ray spectrum was e x t r a p o l a t e d under t h e 6.76 Mev 7-ray spectrum ( P i g . 15 b ) .  The  r a t i o o f t h e 9.28 Mev c o n t r i b u t i o n under t h e 6.76 Mev peaks t o t h e 9.28 Mev c o n t r i b u t i o n above t h e 6.76 Mev peaks was obt a i n e d f o r each o f t h e c u r v e s . f o r a l l angles.  T h i s r a t i o s h o u l d be c o n s t a n t  Due t o s t a t i s t i c a l f l u c t u a t i o n s and t h e  u n c e r t a i n t y i n shape o f t h e s p e c t r a t h e r a t i o was n o t e x a c t l y c o n s t a n t and t h e r e f o r e a mean v a l u e was o b t a i n e d .  On t h e b a s i s  of t h i s mean v a l u e and t h e number o f c o u n t s i n t h e 9.28 Mev peak i n each spectrum, t h e 9.28 Mev t a i l under t h e 6.76 Mev spectrum was s u b t r a c t e d .  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  r e m a i n i n g j p a r t , a t t r i b u t e d t o 6.76 Mev 7-rays,was A second method was employed of t h e above method.  then obtained.  t o check t h e c o n s i s t e n c y  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 o t a l  number o f c o u n t s i n t h e 6 Mev r e g i o n , t h a t i s ;5 Mev t o 7.28 Mev, was o b t a i n e d .  This i s , of course, a combination of the angular  d i s t r i b u t i o n s o f the.6.76 Mev 7 - r a y s and t h e 9.28 Mev 7 - r a y s and c a n be e x p r e s s e d as A  T  (1 + A? C O S 0 ) = (A^ + A ) + (h k% + A A^) C o s e 2  6  9  where t h e a n g u l a r d i s t r i b u t i o n s o f t h e t o t a l ,  6  2  (3)  t h e 9.28 Mev 7 - r a y s  - 31 and t h e 6.76 Mev 7 - r a y s a r e a l l e x p r e s s e d i n t h e form, NQ = A  1  (1 + A* Cos e) 2  and t h e s u p e r s c r i p t I t a k e s on v a l u e s T, 9 and 6 r e f e r r i n g to  t h e t o t a l c o u n t s i n t h e spectrum range f r o m 5 Mev t o  7.28 Mev o r t h e 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 same range f r o m 9.28 and 6.76 Mev 7 - r a y s . Prom t h i s r e l a t i o n i t f o l l o w s t h a t N|_  _  4)  '  _ (K +  FLT  2  where K » A^/A^ the  N  1) + K A | , +  (4)  4  K +1  and d e t e r m i n e s t h e r e l a t i v e c o n t r i b u t i o n o f  two 7 - r a y s , i n a g i v e n energy r e g i o n , a t 90°.  This last  r e l a t i o n leads t o the r e s u l t A  T  m  KAJ +  K +  4  (5)  1  Thus, knowing Ag and A|, i f K does n o t c o r r e s p o n d t o t h e c o r r e c t t a i l o f t h e 9.28 Mev 7 - r a y s under t h e 6.76 Mev peaks,, t h e n A | d e t e r m i n e d f r o m r e l a t i o n (5) w i l l n o t agree w i t h t h e v a l u e o f A^ c a l c u l a t e d by t h e f i r s t method.  By r e q u i r i n g t h a t t h e two  methods g i v e a c o n s i s t e n t v a l u e f o r A  g  i t was p o s s i b l e t o g e t  a more a c c u r a t e e s t i m a t e o f t h e c o n t r i b u t i o n f r o m t h e 9.28 Mev t a i l under t h e 6.76 Mev r e g i o n t h a n would have been p o s s i b l e f r o m a p r i o r i knowledge o f t h e spectrum shape a l o n e .  - 32 (b)  A n g u l a r D i s t r i b u t i o n o f 4.82  Mev and 4.46  Mev 7 - r a y s .  The a n g u l a r d i s t r i b u t i o n of t h e 4.82  and 4.46  Mev  7 - r a y s was d e t e r m i n e d f r o m t h e a n a l y s i s o f e x p e r i m e n t a l s p e c t r a t a k e n c o v e r i n g t h e energy range f r o m 2.5 Mev such spectrum i s shown i n P i g . 16 a. shapes o f t h e 4.82  Mev and 4.46  same as t h a t o f the 4.43 B  1 1  (p, 7) C  1 2  Mev  Mev  7-ray s p e c t r a were the  s p e c t r a o b t a i n e d from the ,  reaction.  and t h e background under the 4 Mev Mev  and 9.28  7-rays  Mev  s p e c t r a were s u b t r a c t e d .  spectrum, n o r m a l i s e d t o t h e number o f c o u n t s i n the  upper p a r t o f t h e photopeak o f t h e 4.82  Mev  t r a c t e d f r o m the complex e x p e r i m e n t a l 4 Mev shape o f t h e r e s i d u a l 4.46 o f 4.82  One  I t was assumed t h a t t h e  The c o n t r i b u t i o n s f r o m the 6.76  A 4.43  t o 5 Mev.  Mev  spectrum.  Mev  7 - r a y s , was spectrum.  subThe  spectrum was matched w i t h t h a t  I f t h e two decomposed 4 Mev  s p e c t r a were  n o t a p p r o x i m a t e l y o f the same shape, t h e n s l i g h t a d j u s t m e n t s were made t o t h e shape o f t h e 4.43  Mev  s t a n d a r d spectrum so  t h a t the d e c o m p o s i t i o n d i d r e s u l t i n two s p e c t r a o f the same shape.  These a d j u s t m e n t s were r e q u i r e d i n t h e low energy end  o f t h e s t a n d a r d spectrum, l a r g e l y because the a p r i o r i knowledge  11 o f t h i s shape o b t a i n e d f r o m t h e B  12 (p, 7) C  v e r y a c c u r a t e s i n c e a f a i r l y l a r g e 12 Mev  r e a c t i o n was  t a i l had t o be removed  f r o m t h e e x p e r i m e n t a l spectrum t o o b t a i n the 4.43 P i g . 16 4.46  Mev  shows a t y p i c a l spectrum decomposed i n t o 4.82  Mev components .  not  spectrum. and  - 33 A f t e r the separation of a l l the experimental spectra i n t o two components, t h e a n g u l a r d i s t r i b u t i o n s o f t h e two 4 Mev 7 - r a y s were d e t e r m i n e d by u s i n g b o t h t h e methods o u t l i n e d i n s u b s e c t i o n (a) o f t h i s  (c)  section.  Angular D i s t r i b u t i o n  o f t h e 2.52 Mev 7-Rays.  A t y p i c a l spectrum c o v e r i n g t h e range f r o m 0.7  Mev  t o 3.5 Mev, a s used i n t h 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 2.52 Mev 7 - r a y s , I s shown i n P i g . 1 3 the  The t a i l o f  4 Mev 7 - r a y s under t h e 2.52 Mev spectrum was s u b t r a c t e d  f o r a l l t h e s p e c t r a and t h e a n g u l a r d i s t r i b u t i o n f o r 2.52 Mev was d e t e r m i n e d f r o m t h e c o u n t s i n i t s photopeak c o n t r i b u t i o n due t o 2.3 Mev 7 - r a y s .  t o a v o i d any  I n t h i s case a l s o b o t h  methods were u s e d t o check t h e c o n s i s t e n c y o f t h e l e v e l o f t h e 4 Mev t a i l  s u b t r a c t e d f r o m t h e complex  spectra.  The r e s u l t s o f t h e s e measurements a r e t a b u l a t e d i n table I I .  (iii)  9.19 Mev B  1 1  State.  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 6.76 Mev, 4.73 4.46 B  1 1  Mev and 2.43 Mev 7 - r a y s e m i t t e d by decay o f t h e 9.19  Mev, Mev  s t a t e were d e t e r m i n e d e s s e n t i a l l y i n t h e same way, as f o r  the  9.28 Mev l e v e l d e s c r i b e d above.  are  also l i s t e d i n table I I .  The r e s u l t s f o r t h i s l e v e l  - 34 (iv)  8.92 Mev B  State.  1 1  Due t o v e r y l o w y i e l d o f t h i s r e s o n a n c e , 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 8.92 Mev 7 - r a y s c o u l d be d e t e r m i n e d w i t h any a c c u r a c y .  The v a l u e o f Ag i n t h i s case i s a l s o shown  i n table I I .  TABLE I I 9.28 Mev s t a t e  9.19 Mev s t a t e  8.92 Mev s t a t e  A  A  A  E7  9  Mev  2  2  -0.41+0.04  -0.25+0.1;  6.76 Mev  +0.7  + 0.1  +0.37 + 0.04  4.8  +0.56 + 0.1  -0.26 + 0.04  4.46 Mev  -0.07+0.03  -0.08+0.03  2.5  -0.38 + 0.04  +0.60 + 0.10  Mev  Mev  g  Qamma-Ray Y i e l d s . (i)  R e l a t i v e Y i e l d s and B r a n c h i n g R a t i o s . The measurements o f t h e r e l a t i v e y i e l d s o f t h e gamma  r a y s were made w i t h t h i n t a r g e t s o f t h e same s p e c i f i c a t i o n s a s described  i n s e c t i o n one o f t h i s c h a p t e r .  of counts observed, N  I n general  t h e number  (e), f o r a g i v e n 7 - r a y and t a r g e t geometry  Q  i s g i v e n by N  0  ( ) 0  53  %  x  G  J  x  *b  x  A  (  x +  A  2  C o s 2 e  )  ( ) 6  -  where  35  -  i s t h e t o t a l number o f gamma r a y s e m i t t e d b y t h e  t a r g e t p e r count o f t h e c u r r e n t i n t e g r a t o r c o r r e s p o n d i n g t o a f i x e d number o f a - p a r t i c l e s i n c i d e n t on t h e t a r g e t , U> I s the s o l i d a n g l e subtended  by t h e c o u n t e r a t t h e target,£  b  I s t h e gamma-ray d e t e c t i o n e f f i c i e n c y o f t h e N a l c r y s t a l f o r a b i a s b, ( 1 + A  Cos ©) i s t h e a n g u l a r d i s t r i b u t i o n f u n c t i o n 2  G  f o r t h e 7 - r a y under i n v e s t i g a t i o n and A n o r m a l i z e s t h i s f u n c t i o n t o u n i t y o v e r t h e t o t a l s o l i d a n g l e such t h a t •4l  JA^CI  o  + A  Cos e) d w « 2  2  1  (7)  E q u a t i o n (7) on i n t e g r a t i o n g i v e s A -  yiir  (1  A g / 3 ) .  +  On s u b s t i t u t i n g f o r A and C J and r e a r r a n g i n g t h e E q u a t i o n (6) we g e t N  - Np ( 0 ) l 6 i r r 0  t  3 R £ 2  b  2  ( 3+ k)  (  9  8)  (1 +A ) 2  where N Q ( 0 ° ) i s t h e number o f c o u n t s o b s e r v e d above t h e b i a s b w i t h t h e c o u n t e r a t z e r o degrees p l a c e d a t an e f f e c t i v e d i s t a n c e r f r o m t h e c e n t r e o f t h e t a r g e t and R i s t h e r a d i u s o f t h e c y l i n d r i c a l Nal crystal. Using Equation ( 8 ) , e x p e r i m e n t a l l y determined distribution coefficients A  2  angular  and t h e number o f c o u n t s N Q ( 0 ° )  p e r count o f t h e c u r r e n t i n t e g r a t o r , t h e y i e l d o f I n d i v i d u a l gamma r a y s f o r each resonance  was d e t e r m i n e d .  Except f o r t h e  - 36 2.5 Mev  7 - r a y s , f o r which a h a l f energy b i a s was used, the  b i a s b chosen was two Mev below the 7 - r a y energy. o f c o u n t s N Q (0°)  The number  f o r a l l the 7-rays, from the three resonances,  were I n d i v i d u a l l y d e t e r m i n e d by s e p a r a t i n g t h e c o n t r i b u t i o n o f each 7 - r a y f r o m t h e complex 7 - r a y s p e c t r a , f o r each resonance t a k e n a t 0 d e g r e e s , i n t h e manner d e s c r i b e d I n s e c t i o n two o f t h i s chapter.  These o b s e r v e d c o u n t s were c o r r e c t e d f o r ab-  s o r p t i o n i n t h e 1/16  i n c h t h i c k b r a s s w a l l of the t a r g e t pot  and 1 / 6 4 I n c h t h i c k t a r g e t b a c k i n g o f c o p p e r .  The  calculated  r e s u l t s f o r r e l a t i v e 7-ray i n t e n s i t i e s i n p e r c e n t a r e g i v e n I n t a b l e I I I ' and shown i n F i g . 1 4 .  TABLE I I I 7-ray T r a n s i t i o n 9 Mev  9.28  t o ground s t a t e  Mev L e v e l 18$  9.19  Mev L e v e l  ^0.5$  8.92 Mev 85$  9 Mev t o 6.76 Mev "  8$  9$  «~5$  9 Mev t o 4 . 4 6 Mev "  73$  90.5$  5$  "  15$  15$  6.76 Mev t o 6.76  4.46  Mev  Mev  t o ground  "  85$  85$  4 . 4 6 Mev  t o ground  "  100$  100$  (ii)  Level  Absolute Y i e l d . The a b s o l u t e y i e l d s were d e t e r m i n e d by u s i n g f r e s h l y  l a i d t a r g e t s o f about 500 kev t h i c k n e s s and o b t a i n i n g 7 - r a y s p e c t r a a t z e r o degrees c o v e r i n g an energy range f r o m 1 t o 9.5  Mev  - 37 f o r a c c u r a t e l y known c o u n t e r geometry. D u r i n g t h e measurements o f t h e t h i c k t a r g e t y i e l d f o r t h e 9.28 Mev l e v e l b o t h t h e resonances,  a t 960 kev and  820 kev, were e x c i t e d and t h e r e f o r e t h e t o t a l 7 - r a y s p e c t r a contained c o n t r i b u t i o n s from both the l e v e l s . 9.19  Since the  l e v e l does n o t decay t o t h e ground s t a t e d i r e c t l y ,  was no c o n t r i b u t i o n f r o m t h e 9.19  l e v e l under t h e 9.28  7 - r a y spectrum f r o m t h e upper l e v e l .  there Mev  Thus by d e t e r m i n i n g t h e  a b s o l u t e t h i c k t a r g e t y i e l d o f t h e 9.28 Mev 7-ray, t h e a b s o l u t e t h i c k t a r g e t y i e l d f o r t h e other 7-rays f r o m t h e 9.28 Mev were determined  r e l a t i v e l y by u s i n g t h e p e r c e n t a g e  level  y i e l d s of  t a b l e I I I . The r e s u l t s a r e g i v e n i n t a b l e IV and a r e e x p r e s s e d as t h i c k t a r g e t y i e l d s o f 7 - r a y s p e r i n c i d e n t o c - p a r t l c l e .  Por  t h e 9.19 Mev l e v e l , t h e a b s o l u t e y i e l d o f 6.76 Mev 7 - r a y s was determined  and t h e a b s o l u t e t h i c k t a r g e t y i e l d s o f o t h e r 7 - r a y s  vrere o b t a i n e d u s i n g t h e r e l a t i v e y i e l d r e s u l t s .  Similarly f o r  t h e 8.92 Mev l e v e l t h e a b s o l u t e t h i c k t a r g e t y i e l d o f t h e 8.92 Mev 7 - r a y s was o b t a i n e d and u s e d t o e v a l u a t e t h e a b s o l u t e target y i e l d s of other t r a n s i t i o n s .  thick  I n a l l t h e s e measurements  t h e h a l f angle subtended by t h e c o u n t e r a t t h e c e n t r e o f t h e t a r g e t was 9  degrees.  As a check, t h e s p e c t r a o b t a i n e d w i t h t h i c k t a r g e t s were a n a l y s e d i n d e p e n d e n t l y ,  as d e s c r i b e d i n t h e s e c t i o n on  r e l a t i v e y i e l d s f o r t h e 9.28  and 9.19  levels.  Since the t a r g e t s  were v e r y t h i c k t h e 7 - r a y spectrum o b t a i n e d f o r t h e 9.28 c o n t a i n e d c o n t r i b u t i o n f r o m t h e 9.19  level.  level  After subtracting  - 38 t h i s c o n t r i b u t i o n t h e s e r e s u l t s agreed w e l l w i t h t h o s e described  above.  TABLE IV T h i c k T a r g e t A b s o l u t e 7-Ray Y i e l d s , ( t o t a l 7-rays p e r i n c i d e n t 7-Ray T r a n s i t i o n  9 . 2 8 Mev L e v e l  9  t o ground  7 . 2 + .2 x I O "  9  to 6.76  2.8 + . 1 x 1 0 "  9  t o 4.46  29.2 + 1 x 1 0 '  6 . 7 6 t o 4.46  0.2 x IO"  6 . 7 6 t o ground  2.6 + . l x 1 0 "  4.46 Total  t o ground  8.92 Mev  <0.04 x 1 0 "  0.5  1 1  0.6 + . 0 ' 5 x l O "  1 1  7.0 + .2 x IO" 0.09 x I O "  1 1  l x 10'  9 . 1 9 Mev L e v e l  1 1  1 1  2 9 . 2 +. l x I O " 39.3 +  1 1  a-particle)  1 1  1 1  0.5+  U  11  Level  x 10"  1 1  0.03 x 1 0 "  1 1  0.03 x 1 0 "  1 1  1 1  .05 x 10"  7.0 + .2 x I O  1 1  - 1 1  7.67 + . 5 x 1 0 " 0 . 6 1 1  x IO"  1 1  - 39 a and 7 - r a y W i d t h s . I n g e n e r a l an e x c i t e d s t a t e o f a n u c l e a r system may decay by t h e e m i s s i o n o f e i t h e r 7 - r a y s o r p a r t i c l e s o r both.  The l i f e time o f t h e system i s g e n e r a l l y d e s c r i b e d  i n terms o f t h e l e v e l w i d t h w h i c h i s p r o p o r t i o n a l t o t h e decay p r o b a b i l i t y , t h a t i s , t h e r e c i p r o c a l o f t h e l i f e This i s convenient expressed  because t h e t o t a l l e v e l w i d t h , P , c a n be  as t h e sum o f t h e p a r t i a l w i d t h s f o r decay t h r o u g h  v a r i o u s e n e r g e t i c a l l y p o s s i b l e channels.  (~7 + 21  P  Por the three capture  time.  i nLi?  Thus  rparticle 3tates  of B  1 1  formed by a - p a r t i c l e  t h e o n l y e n e r g e t i c a l l y p o s s i b l e modes o f  decay a r e r e - e m i s s i o n o f t h e a - p a r t i c l e and 7 - r a y decay t o v a r i o u s lower s t a t e s o f B  1 1  .  So f o r t h e s e  s t a t e s we c a n w r i t e  P . la +21  (9)  Knowledge o f t h e 7 - r a y p a r t i a l w i d t h s when compared w i t h t h e o r e t i c a l v a l u e s g i v e s some i n f o r m a t i o n c o n c e r n i n g t h e character of the decaying  (i)  states.  P a r t i a l R a d i a t i o n Width,  [7.  I n most c a s e s , where e n e r g e t i c a l l y p o s s i b l e , i t has been f o u n d t h a t t h e p a r t i c l e w i d t h s a r e c o n s i d e r a b l y greater than the r a d i a t i o n widths, although,  t h i s i s not  - 4o -  always t r u e ,  where t h i s i s t r u e , t h e p a r t i a l r a d i a t i o n  w i d t h o f a l e v e l f o r decay t o a n o t h e r l e v e l c a n be d e t e r m i n e d d i r e c t l y from the absolute t h i c k t a r g e t y i e l d of the appropriate 7 - r a y as f o l l o w s .  Consider the d i f f e r e n t i a l 7 - r a y y i e l d from a  t h i n l a y e r o f t h i c k n e s s dx i n s i d e a t h i c k l i t h i u m t a r g e t . y i e l d c a n be e x p r e s s e d dN  7  This  as  =CT(E) N d x x  or as dN  7  =<5"(E) N  x  (10)  dx dE  dE where <5"(E) i s t h e c r o s s s e c t i o n p e r e n - p a r t i c l e o f energy E p e r target nucleus,  i s t h e number o f l i t h i u m atoms p e r c u b i c  c e n t i m e t e r and dx i s t h e r e c i p r o c a l o f t h e s t o p p i n g power f o r  HE  a - p a r t i c l e s i n l i t h i u m w h i c h c a n be c o n s i d e r e d t o be c o n s t a n t o v e r t h e narrow r e s o n a n c e s e n c o u n t e r e d i n t h i s work. In order to o b t a i n the t o t a l t h i c k t a r g e t y i e l d the d i f f e r e n t i a l y i e l d must be i n t e g r a t e d o v e r t h e p a t h o f t h e a - p a r t i c l e i n t h e t h i c k t a r g e t o r by i n t r o d u c i n g t h e s t o p p i n g power, a s done above, t h e i n t e g r a t i o n c a n be p e r f o r m e d  over  the energy o f t h e a - p a r t i c l e as i t slows down i n t h e t h i c k target.  T h i s i s convenient  because f o r n a r r o w  resonances,  the e n e r g i e s which g i v e a p p r e c i a b l e c o n t r i b u t i o n t o t h e t o t a l y i e l d l i e i n a narrow r e g i o n about t h e resonance energy .  - 41  -  Thus i n t e g r a t i n g (10) we g e t , N  7  = NI dx  f  as J  oie  L  (11)  0  where E i i s t h e i n c i d e n t p a r t i c l e energy.  Substituting f o r  «"(E) t h e B r e l t - W i g n e r , s i n g l e l e v e l , resonance c r o s s  section  and i n t e g r a t i n g between t h e l i m i t s z e r o and i n f i n i t y , E q u a t i o n ( 1 1 ) , becomes,  where  i s t h e De B r o g l i e w a v e l e n g t h o f t h e a - p a r t i c l e s o f  energy E,  i s the s t a t i s t i c a l w e i g h t i n g f a c t o r ,  s, j-^ and J  are the  spins of the i n c i d e n t a - p a r t i c l e s i n i t i a l state of l i t h i u m and compound s t a t e o f B  1 1  respectively.  S i n c e t h e i n c i d e n t a - p a r t i c l e energy, E ^ , used i n t h i s work, was h i g h e r t h a n resonance energy by a t l e a s t t e n t i m e s t h e t o t a l w i d t h o f t h e resonance, f o r a l l r e s o n a n c e s , the upper l i m i t o f E± i n t h e i n t e g r a l c a n be r e p l a c e d by I n f i n i t y because t h e c o n t r i b u t i o n f r o m t h e B r i e t - W i g n e r f o r m u l a f o r e n e r g i e s above E t h a n 2$ o f t h e t o t a l  yield.  i  i s i n t h e w o r s t case n o t more  - 42 we c a n p u t l a n I  I n c a s e s where  i n (12)  which t h e n r e l a t e s t h e 7 - r a y w i d t h d i r e c t l y t o t h e t h i c k target  7 - r a y y i e l d as f o l l o w s : N  '  = N, x  4£  dE  2  TT^^OCyPy  (13)  The number o f l i t h i u m atoms p e r c u b i c  c e n t i m e t e r , N-L, c a n be  d e t e r m i n e d i n terms o f Avogadro's number, n, t h e d e n s i t y o f l i t h i u m , d (0.534 grams p e r c u b i c  centimeter),  and t h e atomic  w e i g h t o f l i t h i u m , M (6.94), by t h e r e l a t i o n N-i = ^ M  = 4.64 x 1 0  2 2  atoms p e r c u b i c  centimeter.  The s t o p p i n g power f o r a - p a r t i c l e s i n l i t h i u m ,  f o r the dx  t h r e e a - p a r t i c l e resonance e n e r g i e s was o b t a i n e d by e x t r a p o l a t i n g from t h e c o m p i l a t i o n  o f W h a l i n g (1958) and from  c a l c u l a t i o n s suggested by Bethe (1937) as d e s c r i b e d i n appendix I I I . U s i n g the a b s o l u t e t h i c k t a r g e t y i e l d o f each gamma r a y g i v e n i n t a b l e IV, and t h e s t a t i s t i c a l w e i g h t i n g f a c t o r , t a k i n g f o r the  compound s t a t e s p i n s J t h e v a l u e s o b t a i n e d  f r o m 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 (see t h e c h a p t e r on d i s cussion), to  t h e v a l u e s o f l"V were c a l c u l a t e d f o r t h e t r a n s i t i o n s  t h e ground s t a t e , 4 . 4 6 Mev s t a t e and 6.76 Mev s t a t e , f o r  each r e s o n a n c e .  The r e s u l t s a r e g i v e n i n t a b l e V.  W e i s s k o p f , on t h e b a s i s o f t h e s i n g l e p a r t i c l e model, has  c a l c u l a t e d the l i f e times of e x c i t e d  by gamma r a d i a t i o n f o r v a r i o u s m u l t i p o l e  s t a t e s , a g a i n s t decay radiations.  The  - 43 p a r t i a l r a d i a t i o n widths f o r dipole Weisskopf  (Weis3kopf, 1955,  r a d i a t i o n o b t a i n e d by  and Moszkowski, 1955)  are g i v e n  by ( E l ) = 0.11 E3 A  P  7  (Ml) = 0.019  2 / 3  ev.  E^ ev.  (14)  W i l k i n s o n (1955), h a v i n g surveyed o v e r 100  transitions i n  l i g h t n u c l e i , c h i e f l y d i p o l e , concluded that E l t r a n s i t i o n s have a most p r o b a b l e speed o f about 0.032 t i m e s the  Weisskopf  v a l u e s w i t h a spread i n speed of about a f a c t o r o f seven e i t h e r way  and t h a t the c o r r e s p o n d i n g q u a n t i t i e s f o r Ml  have v a l u e s 0.15  t i m e s the Weisskopf  f a c t o r o f 20 e i t h e r way.  transitions  v a l u e s w i t h a spread  The d i f f e r e n c e  between the  Weisskopf  s i n g l e p a r t i c l e v a l u e s and the e x p e r i m e n t a l v a l u e s have been q u a l i t a t i v e l y d i s c u s s e d by W i l k i n s o n (1955) i n terms o f v a r i o u s s h e l l model assumptions. Weisskopf  The v a l u e s c a l c u l a t e d  from  r e l a t i o n ( 1 4 ) , the average v a l u e s suggested  the by  W i l k i n s o n ' s s u r v e y and the p r e s e n t e x p e r i m e n t a l v a l u e s are shown i n the columns a, b and c r e s p e c t i v e l y  of t a b l e  V.  _ 44  -  TABLE  V  P a r t i a l R a d i a t i o n Widths ( i n ev.) 9.28  Transition  a  9.19  Level b  to ground  El  322  state  Ml  15.2  2.3  t o 4.46  El  45.1  1.44  Mev s t a t e  Ml  2.1 0 . 3 2  to 6 . 7 6  El  6.5  Mev s t a t e  Ml  10.3  0.21  c_  a  O.96  312  b_ 9.98  14.7 3-9  £ <0.005  2.2  42.1  1.36  0.84  O.38  5.8  0.19  Level  a  b_ 9.5  13.5  2.0  35.7  1.1  4 . 3 0.14  0.08  resonance w i d t h s a r e g r e a t e r t h a n t h e t o t a l r a d i a t i o n w i d t h s .  the 8 . 9 2 l e v e l , t h e e x p e r i m e n t a l that  i s Justified.  e v i d e n c e by i t s e l f  Pa may be o f t h e same o r d e r as (7.  But f o r suggests  So t h e r a d i a t i o n  w i d t h s l i s t e d f o r t h i s l e v e l on t h e assumption t h a t Pa i s greater than P  7  must be c o n s i d e r e d t o be minimum v a l u e s .  p o i n t i s discussed f u r t h e r i n the next  .01  .02  .18  0.92  t h e assumption t h a t fa -c P  .15  0.20 0.03  F o r t h e 9 . 2 8 Mev and 9 . 1 9 Mev l e v e l s t h e e x p e r i m e n t a l  Therefore  £  1.7 0 . 2 6  0 . 2 7 0.04 5.24  8.92  296  2.0 0 . 3  0.31 0.05  Total fj.  Level  chapter.  This  - 45 (ii)  Reduced a-Particle Width. The reduced a-particle width  which i s a measure  of the"emission p r o b a b i l i t y f o r a - p a r t i c l e s from the nucleus i n the absence of the coulomb and centrifugal barriers,  was  calculated from the relationship r| =  _C_  (15)  2k v i R  where k i s the wave number of the incident p a r t i c l e s . Vi - 1/A  2  =  + G|), where F  x  and  are coulomb functions  depending upon the height of the coulomb b a r r i e r and the angular 2 momentum of the incident a - p a r t i c l e s .  Values of  were calcu-  lated from the tables of Block et a l . (1951) and from the graphs of Sharp et a l . (1953). given by R = r  0  R Is the i n t e r a c t i o n radius and i s  ( A j ^ + A * ^ ) , where r  = 1.45 x l O " ^ centimeter. 1  Q  Prom a series of experiments with a - p a r t i c l e s bombarding  a large  range of d i f f e r e n t target nuclei i t has been found that i n t e r action radius can be expressed as R = r r  A ' + b, where J  0  = 1.414 x l O " ^ centimeter and b = 2.2 x 1 0 ^ centimeter. 1  Q  - 1  (Annual Progress Report of Cyclotron Research Group, 1957, U. of Washington.)  The two formulae give R = 5.07 x 1 0 3 c e n t i _ 1  meter and R = 4.89 x l O " ^ centimeter respectively. 1  value of R = 4.98 x l O " ^ centimeter was used. 1  t o t a l width of the resonance.  P  An average i s the  Por the 960 kev. resonance an  upper l i m i t of 8 kev. i s assigned by P h i l l i p s (1957) which i s i n agreement with the measurements of Bennet et a l . (1951). Recently Meyer-Schutzmeister and Hanna (1958) from t h e i r study  - 46 of r e s o n a n t a b s o r p t i o n o f gamma r a y s r e p o r t t h a t t o t a l w i d t h Cf  t h e 9 . 1 9 Mev l e v e l i s 100 ev.  The p r e s e n t l y a v a i l a b l e  e x p e r i m e n t a l d a t a o f Bennet e t a l . ( 1 9 5 1 ) and P h i l l i p s ( 1 9 5 7 ) i n d i c a t e t h a t t h e t o t a l w i d t h o f t h i s resonance  i s l e s 3 than  t h e i r e x p e r i m e n t a l r e s o l u t i o n o f about 1 k e v . The v a l u e s o f t h e reduced a - p a r t i c l e w i d t h s f o r t h e 9 . 2 8 l e v e l and t h e 9 . 1 9 l e v e l , c o n s i d e r i n g t h a t t h e s e two s t a t e s a r e formed by p and f waves r e s p e c t i v e l y , as i n d i c a t e d by the a n g u l a r  distribution  data discussed i n the next chapter, are 9.28  Mev l e v e l  9 . 1 9 Mev l e v e l  7% = 260 kev. y\ < 1 . 1  Mev  P o r t h e 8 . 9 2 Mev l e v e l t h e reduced a - p a r t i c l e w i d t h cannot be c a l c u l a t e d s i n c e the l a b o r a t o r y w i d t h i s much s m a l l e r t h a n experimental r e s o l u t i o n .  However, t h e reduced w i d t h i s g i v e n  below i n terms o f t h e unknown l a b o r a t o r y w i d t h f wave i n g o i n g a - p a r t i c l e s . 2  - 2 x 10  4  n  x I ev.  p  wave  7  d  wave  7^ = 3 . 5 x 10^ x P ev.  f  wave  7  a  a  = 8 x 10^ x P  ev.  f o r p, d and  CHAPTER TV DISCUSSION  1.  Assignments. By comparing t h e e x p e r i m e n t a l a n g u l a r d i s t r i b u t i o n coefficient A  2  f o r each 7-ray w i t h t h e t h e o r e t i c a l l y c a l c u l a t e d  v a l u e s (see appendix I V ) one c a n g e t i n f o r m a t i o n and p a r i t i e s o f t h e l e v e l s I n v o l v e d example, i n a g e n e r a l  about t h e s p i n s  i n the t r a n s i t i o n . P o r  case t h e s y s t e m a t i c s  o f the r e a c t i o n can  be r e p r e s e n t e d a s f o l l o w s : Li  .+  7  spin  Angular momentum  3/2where:  a  l 3/2"  B  1 1  spin  spin  spin  0  J  1  a  a-particles. is J  Angular momentum  1 1  spin J  7  2  ground s t a t e  1959).  The i n t r i n s i c  spin of the a - p a r t i c l e s  zero.  i s t h e t o t a l a n g u l a r momentum o f t h e e x c i t e d of B 7  1 1  2  state  .  i s t h e o r b i t a l a n g u l a r momentum c a r r i e d away by the p h o t o n which has i n t r i n s i c  J  B  i s t h e o r b i t a l a n g u l a r momentum c a r r i e d i n by t h e  a  1  +  1  I s t h e s p i n and p a r i t y o f t h e Ll? ( A j z e n b e r g and L a u r i t s e n ,  l  7-ray  —>•  s p i n o f 1.  i s t h e t o t a l o r b i t a l a n g u l a r momentum o f t h e f i n a l state of B  1 1  .  - 47 -  - 48 I n g e n e r a l t h e case where an a - p a r t i c l e i s c a p t u r e d and a r a d i a t i v e t r a n s i t i o n goes d i r e c t l y f r o m the compound s t a t e formed t o any o t h e r l o w e r s t a t e , w i l l be r e f e r r e d t o as a two stage p r o c e s s , f o r which t h e sequence o f a n g u l a r momenta can be w r i t t e n as f o l l o w s : ( l ) J (1 )  3/2  a  7  J  2  I n p a r t i c u l a r i f t h e t r a n s i t i o n goes d i r e c t l y t o t h e ground state then J  2  = 3/2"  (Mayer and Jensen, 1955,  and L a u r i t s e n , 1959).  and  AJzenberg  P o r t h e c a s e s where t h e decay  cascades  t h r o u g h an i n t e r m e d i a t e s t a t e the sequence f o r the c o r r e s p o n d i n g t h r e e stage p r o c e s s can be w r i t t e n 3/2 whe*re l  7 l  (l )J (l i) J  and 1  a  7 2  7  i  n  t  as  (1 ) 7 2  J  2  are the a n g u l a r momenta c a r r i e d away by the  two 7 - r a y s and J i n t  i s  the t o t a l a n g u l a r momentum o f t h e  inter-  mediate s t a t e . I f i t i s assumed t h a t we are d e a l i n g w i t h i s o l a t e d t h e n the a n g u l a r d i s t r i b u t i o n s f o r t h e 7 - r a y s  resonances  c o r r e s p o n d i n g t o the above sequences can be e x p r e s s e d i n the form f  (©)  » 1 + A  Cos © + A^ Cos © + 2  g  4  F o r v a r i o u s p o s s i b l e v a l u e s o f t h e p a r a m e t e r s i n the above sequences, t h e a n g u l a r d i s t r i b u t i o n c o e f f i c i e n t s A  2  were c a l c u l a t e d u s i n g W i l k i n s o n ' s Method (1954) and  and the  A^  - 49 t a b l e s of Biedenharn  and Rose (1953).  The r e s u l t s are g i v e n  i n appendix I I f o r 1« = 0, 1, 2 and 3 and f o r \ and 2, i n a d d i t i o n  are mixed.  i n the L i ? ( a , r ) B  x±  S i n c e f o r the t h r e e reaction,  d i s t r i b u t i o n s were n o t i s o t r o p i c , l i t necessarily  equal to 1  a number o f c a s e s are i n c l u d e d where  E 2 and M l r a d i a t i o n s observed  y  a  resonances,  the gamma r a y a n g u l a r  • 0 i s r u l e d out because  leads to i s o t r o p i c d i s t r i b u t i o n s only.  Comparison o f the e x p e r i m e n t a l a n g u l a r d i s t r i b u t i o n c o e f f i c i e n t s w i t h the t h e o r e t i c a l v a l u e s s e v e r e l y r e s t r i c t s the p o s s i b l e  v a l u e s o f the p a r a m e t e r s ,  l , 1, a  J,  7  and  J  2  as d i s c u s s e d below, (see a l s o appendix IV B)  F u r t h e r because  t h e p a r i t i e s o f the ground s t a t e s o f L i ? and B  1 1  Mev B  xx  and the  4.46  s t a t e are w e l l known (see c h a p t e r I ) and the p a r i t y  a s s o c i a t e d w i t h l a i s (-1)^°, one can i n many c a s e s d e c i d e  on  the magnetic o r e l e c t r i c c h a r a c t e r o f a p a r t i c u l a r r - r a y f r o m the knowledge o f the e l e c t r o m a g n e t i c s e l e c t i o n r u l e s .  I n some  c a s e s , however, t h e r e I s not s u f f i c i e n t I n f o r m a t i o n c o n c e r n i n g the p a r i t i e s o f the l e v e l s i n v o l v e d . possible  t o determine  I n these c a s e s i t may  be  t h e p a r i t y by f i r s t d e t e r m i n i n g the  c h a r a c t e r o f the r a d i a t i o n by comparing the a b s o l u t e  radiative  t r a n s i t i o n p r o b a b i l i t y w i t h t h e o r e t i c a l v a l u e s o b t a i n e d on the a s s u m p t i o n o f the s i n g l e p a r t i c l e s h e l l model (Weisskopf, and W i l k i n s o n , 1955)  and second by u s i n g the s e l e c t i o n  1951,  rules  t o r e l a t e the c h a r a c t e r o f the r a d i a t i o n t o the p a r i t y change. (i)  96O  Kev.  Resonance.  (a)  9.28 Mev B  1 1  Level.  Comparison o f the e x p e r i m e n t a l c o e f f i c i e n t A  2  for  - 50 the 9.28  Mev l  a  7-ray w i t h the t h e o r e t i c a l p o s s i b i l i t i e s t o 1 o r 3i  J t o 3/2* o r 5/2+  A s i m i l a r comparison f o r t h e 4.82 by t h e decay o f the 9.28 l  a  t o 1;  J t o 5/2+  and 1  (9 Mev) t o 1.  and 1  7  7 - r a y s , produced  Mev  Mev l e v e l t o t h e 4.46  limits  Mev l e v e l ,  limits  (4.8 Mev) t o 1.  7  I n t h i s comparison i t was assumed t h a t t h e ground s t a t e o f i s 3/2"  and t h e 4.46  Mev  s t a t e i s 5/2"  (see c h a p t e r I ) .  B  1 1  Prom  t h e s e two c o m p a r i s o n s one i s l e d t o t h e c o n c l u s i o n t h a t t h e 9.28  Mev  o f 5/2  s t a t e i s formed by p-wave a - p a r t i c l e s and has a s p i n  and even p a r i t y and decays t o the ground s t a t e and t o  t h e 4.46  Mev  s t a t e by e l e c t r i c d i p o l e r a d i a t i o n s .  This conclusion  i s s u p p o r t e d by a c o m p a r i s o n of the e x p e r i m e n t a l p a r t i a l  radiation  w i d t h (3.9 ev.) w i t h t h e t h e o r e t i c a l W i l k i n s o n v a l u e (1.44 f o r t h e 4.82  Mev t r a n s i t i o n t o t h e 4.46  Mev  s t a t e , which s u g g e s t s  that t h i s t r a n s i t i o n i s a favoured e l e c t r i c dipole. c l u s i o n a l s o r e q u i r e s t h e p a r i t y o f t h e 9.28 positive.  ev.)  Mev  T h i s con-  s t a t e t o be  The r e d u c e d p-wave a - p a r t i c l e w i d t h (260 kev.) f o r  t h i s resonance i s an a p p r e c i a b l e f r a c t i o n o f the Wigner (about 2 Mev)  limit  s u g g e s t i n g t h a t t h e l e v e l has some s i n g l e a - p a r t i c l e  character. The p r e s e n t s p i n assignment i s i n agreement w i t h t h e assignment o f P h i l l i p s (1957).  The r e c e n t s t r i p p i n g work o f  B i l a n i u k and H e n s e l (1958), who measured t h e p r o t o n a n g u l a r d i s t r i b u t i o n s from the r e a c t i o n B  1 0  ( d , p) B , 1 1  indicates that  - 51 the 9-28  Mev  s t a t e i s formed w i t h S-wave i n g o i n g n e u t r o n s ,  t h u s l i m i t i n g i t s p a r i t y t o p o s i t i v e and i t s s p i n t o 5/2 7/2.  A s i m i l a r c o n c l u s i o n was drawn f o r t h e 9.19  Mev l e v e l .  C o n s i d e r i n g t h e s e two l e v e l s as a s p i n d o u b l e t t h e i n t e n s i t y r a t i o f o r the two l e v e l s f a v o u r s 5/2 Mev l e v e l and 7/2+  f o r t h e 9.19  +  or  stripping  f o r the  9.28  Mev l e v e l which i s i n agreement  w i t h o u r assignment f o r the 9.28  Mev l e v e l .  neutron capture p r o b a b i l i t y i n the  F u r t h e r , the h i g h  ( d , p) B  reaction  1 1  would suggest t h a t t h i s 3tate i s a s i n g l e p a r t i c l e n e u t r o n s t a t e formed by d i r e c t n e u t r o n c a p t u r e i n t o I d — 2s s h e l l . Recent work of F e r g u s o n e t a l . (1958) w i t h t h e L i  7  ( a , y)  B  1 1  'i  r e a c t i o n a l s o s u p p o r t s the assignment 5/2+  f o r t h e 9.28  Mev  state.  (b)  6.76  Mev  Level.  A comparison o f t h e e x p e r i m e n t a l a n g u l a r d i s t r i b u t i o n coefficient A  2  o f t h e 2.52  Mev  7-rays w i t h the  theoretical  p o s s i b i l i t i e s , i n t h e l i g h t o f the known f a c t s about t h e system and the c o n c l u s i o n drawn above ( t h e 9.28 5/2+), l i m i t s t h e 6.76 c o m p a r i s o n f o r t h e 6.76 6.76 3/2  Mev  Mev Mev  s t a t e t o 3/2 o r 7/2.  Mev  B^  state i s  But a s i m i l a r  7 - r a y , produced by t h e decay o f t h e  s t a t e t o t h e ground s t a t e , i s n o t c o n s i s t e n t w i t h t h e  assignment b u t i s i n agreement w i t h t h e o t h e r p o s s i b l e  assignment o f 7/2 f o r the 2.52  f o r t h i s state.  The p a r t i a l r a d i a t i o n w i d t h  Mev t r a n s i t i o n i s f o u n d t o be O.38  ev. w h i c h i s  s l i g h t l y b i g g e r t h a n W i l k i n s o n ' s a d j u s t e d v a l u e o f 0.21  ev.  -  52 -  This s t r o n g l y suggests that the t r a n s i t i o n i s e l e c t r i c  dipole  i n c h a r a c t e r and t h e r e f o r e l e a d s t o the c o n c l u s i o n t h a t t h e 6.76 Mev s t a t e i s o f odd p a r i t y .  Hence, t h i s s t a t e i s 7/2".  R e c e n t l y B i l a n i u k and H e n s e l (1958) r e p o r t e d  that  the a n g u l a r d i s t r i b u t i o n o f p r o t o n s r e s u l t i n g f r o m the n e u t r o n capture  t o t h e 6.76 Mev s t a t e i n the r e a c t i o n B  1 0  ( d , p) B**  ( r e s o l v e d f o r the f i r s t t i m e f r o m t h o s e c o r r e s p o n d i n g 6.81 Mev s t a t e ) c o r r e s p o n d s t o a p-wave ( l capture p a t t e r n .  n  to the  = 1) n e u t r o n  Thus s u g g e s t i n g n e g a t i v e p a r i t y f o r t h i s  s t a t e which i s i n agreement w i t h o u r c o n c l u s i o n s and a l s o I n agreement w i t h Cox e t a l . (1957) (see I n t r o d u c t i o n ) .  This,  however, l i m i t s i t s s p i n t o a v a l u e between 3/2 and 9/2. t h e i r p - 7 c o r r e l a t i o n s t u d y Cox e t a l . (1957) r u l e d out and  suggested t h a t 9/2 i s v e r y u n l i k e l y .  o r 7/2.  Prom 3/2  Thus f a v o u r i n g 5/2  Now l f t h i s s t a t e was 5/2", t h e n the a n g u l a r  dis-  t r i b u t i o n o f t h e 2.52 Mev 7 - r a y s , f r o m the 9.28 Mev s t a t e t o the 6.76 Mev s t a t e , s h o u l d be t h e same a s t h a t o f t h e 4,82 Mev 7 - r a y s , f r o m the 9.28 Mev s t a t e t o t h e 4.46 Mev s t a t e . I s not i n agreement w i t h the p r e s e n t  experimental  This  r e s u l t s , which  r u l e s o u t 5/2" and t h e r e f o r e s t r o n g l y f a v o u r s 7/2" f o r t h e 6.76 Mev s t a t e .  The o n l y o b j e c t i o n t o t h i s assignment i 3 t h e  weak magnetic d i p o l e t r a n s i t i o n t o t h e 4.46 Mev s t a t e as compared to t h e r e l a t i v e l y strong e l e c t r i c quadrupole t r a n s i t i o n t o t h e ground s t a t e .  T h i s d i f f i c u l t y i s r e s o l v e d i f one a c c e p t s t h e  t h e o r e t i c a l p r e d i c t i o n o f K u r a t h based on the i n t e r m e d i a t e model.  coupling  These c a l c u l a t i o n s show t h a t i n t h i s case the M l m a t r i x  element f o r the 7/2" t o 5/2" t r a n s i t i o n v a n i s h e s ( K u r a t h , 1957, and F e r g u s o n e t a l . , 1958).  - 53 (c)  4.46  Mev  Level.  The a n g u l a r d i s t r i b u t i o n o f 4.82 by t h e decay o f t h e 9.28  Mev  l e v e l t o t h e 4.46  c o n s i s t e n t w i t h t h e f a v o u r e d assignment f o r t h e 4.46  Mev  state.  The  Mev  o f 5/2"  7-rays, Mev  level, i s  (see c h a p t e r I)  a n g u l a r d i s t r i b u t i o n o f 4.46  7 - r a y s show a s i g n i f i c a n t m i x i n g o f E2 w i t h M l . g i v e an E2/M1  produced  a m p l i t u d e r a t i o o f 0.15.  Mev  Present r e s u l t s  This i s i n excellent  agreement w i t h the work r e p o r t e d by F e r g u s o n e t a l . (1958), 0.14,  and w i t h the p r e d i c t i o n o f K u r a t h (1957), 0.21,  s u p p o r t i n g t h e assignment  o f 5/2"  f o r t h i s s t a t e and t h e p r e -  d i c t i o n s o f K u r a t h c o n c e r n i n g t h e c h a r a c t e r o f the  (d)  2.14  Mev  thus  state.  Level.  No t r a n s i t i o n t o the 2.14 Mev  s t a t e was  observed.  T h e r e f o r e n o t h i n g i n . p a r t i c u l a r c a n be s a i d about t h i s  state.  I n g e n e r a l , t h e absence o f any t r a n s i t i o n t o t h i s l e v e l frOm the 9.28 t h a n 1/2, have |M|2  Mev  5/2+  s t a t e w i l l r u l e out s p i n a s s i g n m e n t s  greater  because o t h e r w i s e "the m i s s i n g E l t r a n s i t i o n would 2 x 10"*^, which i s much l e s s t h a n one u s u a l l y c a r e s  t o e n v i s a g e i n t h e l i g h t n u c l e i i f t h e r e i s no I n h i b i t i o n by t h e i s o t o p i c s p i n s e l e c t i o n r u l e " , ( W i l k i n s o n , 1957). s u p p o r t s the now  a c c e p t e d assignment  o f 1/2"" f o r t h i s  This state.  Prom the p r e s e n t work and t h a t o f B i l a n i u k and (1958) i t would appear t h a t the 9.28  Mev  s t a t e has b o t h a s i n g l e  a - p a r t i c l e and a s i n g l e n e u t r o n c h a r a c t e r . t r a n s i t i o n s t o the 6.76  Mev  and 4.46  Mev  Hensel  S i n c e the  7-ray  s t a t e s show p o s s i b l e  - 54  -  s i n g l e p a r t i c l e t r a n s i t i o n p r o b a b i l i t i e s I n comparison w i t h the W i l k i n s o n a d j u s t e d v a l u e s , I t i s i n t e r e s t i n g t o as t o whether i t i s the the  odd  speculate  p r o t o n o r a n e u t r o n which makes  single p a r t i c l e transition.  The  r e s u l t s of B i l a n i u k  would  suggest t h a t i t i s the n e u t r o n w h i c h makes the  transition.  Thus i t may  radiative  be p o s s i b l e  to e x p l a i n  t r a n s i t i o n p o s s i b i l i t y f r o m the 9.28 state  i n terms of the  the Mev  smaller state  t o the  f a c t t h a t b o t h the p r o t o n and  must change t h e i r s t a t e  i n making t h i s t r a n s i t i o n .  t r a n s i t i o n s t o the  Mev  6.76  r e q u i r e a change I n the I n the  and  t o the  4.46  Mev  2s-ld s h e l l i n B ,  Whereas  o r b i t a l m o t i o n of the n e u t r o n o n l y .  Mev  s t a t e of the a - p a r t i c l e  s t a t e must r e s u l t i n one  d u r i n g the  These " q u a l i t a t i v e s p e c u l a t i o n s may,  Kev.  (a)  9.19  Mev  the  parity  however, be lp  the  decay.  too c r u d e t o shell.  Level.  Mev  l e v e l t o the  of  Resonance.  Comparison o f the 4.73  the  subsequent r a d i a t i v e  d e s c r i b e the m o t i o n of seven p a r t i c l e s i n the  820  may  whereas t h e r e i s no f u r t h e r change i n  1 1  (ii)  neutron  states  l p - n e u t r o n s o f L i T b e i n g promoted, t o the p o s i t i v e  of the  the  case of a - c a p t u r e i t would appear, t h e n , t h a t  f o r m a t i o n o f the 9.28  ground  experimental angular d i s t r i b u t i o n  7 - r a y s , produced by the decay of the 9.19  4.46  Mev  l e v e l (5/2"), w i t h the  Mev  theoretical  possibilities limits l  a  to 3  and  J to  7/2.  T h i s i s f u r t h e r c o n f i r m e d by a s i m i l a r c o m p a r i s o n  - 55 - , f o r the 2.43  7-ray, produced by the decay o f the 9.19  Mev  l e v e l t o the 6.76  Mev  Mev  as c o n c l u d e d above.  l e v e l i s 7/2"  w i d t h o f O.85  l e v e l , on the assumption  t h a t the  The p a r t i a l  ev. f o r the t r a n s i t i o n t o the 4.46  electric dipole radiation. 0.08  6.76  radiation  Mev  compares v e r y w e l l w i t h the W i l k i n s o n v a l u e o f 1.3  Mev  state  ev. f o r  The p a r t i a l r a d i a t i o n w i d t h of  ev. f o r the t r a n s i t i o n t o the 6.76  Mev  s t a t e a l s o compares  f a v o u r a b l y w i t h the c o r r e s p o n d i n g W i l k i n s o n v a l u e o f 0.19 f o r an E l r a d i a t i o n . the 9.19  Mev  ev.  These f a c t s and t h e above r e s u l t t h a t  s t a t e i s formed by f-wave ( l  a  = 3)  Ingoing  a - p a r t l c l e s show t h a t t h i s s t a t e has p o s i t i v e p a r i t y and s p i n 7/2.  The reduced a - p a r t i c l e w i d t h , f o r f-waves, i s l e s s  o r e q u a l t o 1.1 limit.  Mev  than  which i s a l a r g e f r a c t i o n o f the Wigner  T h i s s u g g e s t s t h a t t h e 9.19  Mev  s t a t e a l s o has  a  single a-partlcle character. These c o n c l u s i o n s are i n agreement w i t h the r e s u l t s from the s t r i p p i n g work of B i l a n i u k and H e n s e l f a v o u r s a 7/2+  (1958) which  \  assignment f o r t h i 3 l e v e l , as d i s c u s s e d i n  s e c t i o n ( i ) of t h i s chapter.  The  l a r g e neutron  capture  p r o b a b i l i t y observed f o r t h i s l e v e l a l s o p o i n t s t o I t s s i n g l e neutron character.  (b)  6.76  Mev L e v e l . As s t a t e d above the a n g u l a r d i s t r i b u t i o n  ( A 2 = +0.6  + 0.1)  f o r the 2.43  Mev  coefficient  7 - r a y s , produced by  the  - 56 decay of the 9.19 Mev l e v e l to the 6.76 Mev l e v e l , l a explained by the t h e o r e t i c a l value of the sequence 3/2 (3) 7/2 (1) 7/2, which i s Ag = +0.57. sequence, consistent with the assignment  The only other  7/2 f o r the 9.19 Mev  l e v e l , which gives a value of Ag, (Ag = +0.77), close to the experimental value, although outside i t s error, i s 3/2 (2) 7/2 (1) 7/2.  However, on comparing the experimental  angular d i s t r i b u t i o n of the 6.76 Mev 7-ray, produced by the decay of the 6.76 Mev state to the ground state, with;the t h e o r e t i c a l values, the sequence corresponding to l  a  = 2 is  ruled out while the sequence 3/2 (3) 7/2 (1) 7/2 (2) 3/2 agrees with.the experimental r e s u l t s .  This further confirms the above  findings that the 9.19 Mev state i s formed by f-wave ( l  a  « .3)  a - p a r t i c l e s and also that the 6.76 Mev state i s 7/2".  (c)  4.46 Mev Level. Here also the experimental d i s t r i b u t i o n of the 4.46  Mev r-rays showsthat the e l e c t r i c quadrupole radiation (E2) i s mixed with magnetic dipole (Ml) i n the same amplitude (0.15) as i n the decay of the 9.28 Mev l e v e l . consistency of the assignment  This checks the  to t h i s l e v e l and also the con-  sistency of the method used i n the analysis.  (d)  ratio  2.14 Mev Level. No t r a n s i t i o n to t h i s l e v e l was observed.  - 57 (e)  Qround State Transition. No s i g n i f i c a n t amount of the ground state  was observed.  transition  This i s not surprising i n the l i g h t of the  assignment 7/2+  f o r the 9 . 1 9 l e v e l , because i t would require  a magnetic quadrupole radiation which would compete very unfavourably with the strong e l e c t r i c dipole t r a n s i t i o n s to other l e v e l s .  (iii)  400 Kev. Resonance.  (a)  8.92  Mev Level.  This resonance has a very low y i e l d (a f a c t o r of 1 0 0 l e s s than the 9 6 0 kev. resonance) and the 8.92 Mev predominantly decays to the ground state. angular d i s t r i b u t i o n of the 8 . 9 2 Mev with any accuracy.  Hence only the  7-rays could be determined  A comparison of the experimental angular  distribution coefficients, A  g  = -0.25  +0.1,  with the t h e o r e t i c a l  values l i m i t s J to 5/2 but cannot distinguish 2 or 3 .  level  between l  a  = 1,  Unfortunately there i s no other experimental angular  d i s t r i b u t i o n available  to eliminate further values of  Thus t h i s state i s either 5/2+  or 5/2".  The reduced  l . a  a-particle  width of t h i s l e v e l cannot be determined due to the lack of any knowledge about i t s t o t a l width, except that i t i s c e r t a i n l y l e s s than 1 kev.  I f the width of the 8 . 9 2 Mev l e v e l i s about  10 ev. or more, then a comparison of the reduced  a-particle  width with t h e o r e t i c a l widths favours the formation of t h i s  - 58  -  l e v e l by p-wave a - p a r t i e l e s o v e r d-wave a - p a r t i c l e s , because the l a t t e r c o r r e s p o n d s t o an a - p a r t i c l e reduced w i d t h o f Mev  o r more.  3.5  T h i s i s much b i g g e r t h a n the Wigner l i m i t .  However, i f t h e t o t a l resonance w i d t h o f the 8.92  Mev  level  i s about 1 ev. o r l e s s , t h e n the above argument i s weakened and d-wave f o r m a t i o n i s as a c c e p t a b l e as p-wave f o r m a t i o n . The r e c e n t s t u d y o f the B B i l a n i u k and H e n s e l by d-wave ( l (l  n  n  1 0  ( d , p) B  1 1  r e a c t i o n by  (1958) shows t h a t t h i s s t a t e i s formed  = 2) n e u t r o n s w i t h a s m a l l admixture  ~ 0) n e u t r o n s .  o f s-wave  T h i s would i m p l y t h a t the s t a t e has even  p a r i t y and a s p i n o f 5/2  o r 7/2.  S i n c e i n the p r e s e n t work  t h i s s t a t e i s found t o decay m o s t l y t o ground s t a t e (85$), an assignment of 7/2 magnetic quadrupole t o e i t h e r the 4.46 seems u n l i k e l y .  t o t h i s l e v e l would i m p l y a f a v o u r e d  +  t r a n s i t i o n over p o s s i b l e e l e c t r i c d i p o l e s Mev  s t a t e o r the 6.76  Thus combining  Mev  s t a t e , which  the r e s u l t s o f the p r e s e n t  i n v e s t i g a t i o n and t h o s e o f B i l a n i u k and H e n s e l one f a v o u r the assignment 5/2"*" f o r the 8.92  Mev  level.  would However,  t h i s assignment would i m p l y t h a t the ground s t a t e r a d i a t i o n i s electric dipole.  The  r e l a t i v e l y s m a l l v a l u e o f the r a d i a t i o n  w i d t h , as compared t o the c o r r e s p o n d i n g W i l k i n s o n v a l u e , does n o t g i v e a c o n f i r m a t i o n o f t h e assignment w i t h any h i g h degree of c e r t a i n t y . S i n c e the r a t i o (8.92/4.46)3  (85/5), t h e r a t i o o f  t h e i n t e n s i t i e s o f the 7 - r a y s from the 8.92  Mev  l e v e l t o the  -  59  -  ground s t a t e and t o t h e 4; 46 Mev s t a t e , i t would appear  that  the two t r a n s i t i o n s a r e about e q u a l l y f a v o u r e d d i p o l e t r a n sitions.  Conclusions. Prom t h e p r e s e n t I n v e s t i g a t i o n i t i s c o n c l u d e d t h a t t h e 9 . 2 8 Mev s t a t e l a 5 / 2 " , t h e 9 - 1 9 Mev s t a t e i s 7/2+,  the 6.76  Mev s t a t e i s 7 / 2 " and t h e 8 . 9 2 Mev s t a t e I s e i t h e r 5/2+ o r 5/2".  However, t h e assignment o f 5/2+ f o r t h e 8 . 9 2 Mev  i s favoured.  state  T h i s i n v e s t i g a t i o n a l s o c o n f i r m s t h e assignment  5/2*" f o r t h e 4.46  Mev s t a t e and i n d i r e c t l y s u p p o r t s t h e  assignment 1/2" f o r t h e 2.14 Mev s t a t e . The g e n e r a l s i m i l a r i t y I n t h e decay p a t t e r n s o f t h e 9 . 2 8 Mev and t h e 9 . 1 9 Mev s t a t e s may i n d i c a t e t h a t t h e s e two s t a t e s form a s p i n d o u b l e t .  A l s o s i n c e t h e 8 . 9 2 Mev  state  decays p r e d o m i n a n t l y t o t h e ground s t a t e , u n l i k e t h e 9 . 2 8 Mev and 9 . 1 9 Mev s t a t e s which decay p r e d o m i n a n t l y t o t h e 4.46  Mev  s t a t e , p r o b a b l y t h e 8 . 9 2 Mev s t a t e i s formed by a s i n g l e p a r t i c l e ( l i k e l y n e u t r o n ) t r a n s i t i o n f r o m t h e ground configuration.  S i m i l a r l y t h e 9 . 2 8 Mev and 9 . 1 9 Mev  state states  may be formed by s i n g l e p a r t i c l e ( l i k e l y n e u t r o n ) t r a n s i t i o n s from* t h e 4.46  Mev s t a t e which h a s a d i f f e r e n t p - s h e l l con-  f i g u r a t i o n t h a n t h e ground s t a t e .  PART B  1.  The E n e r g i e s o f Zn^5 and N a  2 2  y-Rays.  The t h r e e c r y s t a l p a i r s p e c t r o m e t e r by H.W.  built  Dosso (1957) was used t o determine the e n e r g i e s  o f the y-rays e m i t t e d by Zn^5 and N a . 2 2  The r e s u l t s o f  t h i s work have been p u b l i s h e d i n the Canadian J o u r n a l o f P h y s i c s , V o l . 37, 1055, 1959, and a r e p r i n t i s a t t a c h e d t o the f o l l o w i n g page.  - 60 -  T H E ENERGIES A N D R E L A T I V E PAIR P R O D U C T I O N CROSS F O R Zn«s A N D N a " G A M M A R A Y S  SECTIONS  P. P. SINGH, H . W . DOSSO, AND G . M . GRIFFITHS  For gamma rays just above 1.02 Mev a three-crystal pair spectrometer of even moderate resolution can be used to determine the gamma-ray energies very accurately. Since exactly the rest mass of the pair electrons is subtracted from each incident photon by pair production, a measurement of the small remaining kinetic energy of the pair electrons establishes the energy of the gamma rays with considerably greater accuracy than that of the kinetic energy measurement. This method has been used to determine the energies of the gamma rays from Zn and Na sources. The spectrometer consists of three sodium iodide (ThI) crystals as shown in Fig. 1. The annihilation of the 66  22  G A M M A RAYS •-  H 1  Single Channel Analyzer  1  hi H  Delay  h  Amplifier  Amplifier  Single Channel Anoly2er  Gate Generator Triple Coincidence Circuit  f  KICK SORTER  Biased Amplifier  etor GeGna et ra t  s  •  F I G . 1. Block diagram of the three-crystal spectrometer.  positron after the pair event in the center crystal (1.75 cm X 4 cm X*4 cm) gives two .51-Mev quanta which leave the center crystal in opposite directions. The colinear .51-Mev annihilation quanta are detected in coincidence in the Can. J. Phys. Vol. 3 7 (1959)  1055  1056  C A N A D I A N J O U R N A L O F P H Y S I C S . V O L . 37, 1959  side crystals (2 in. long and I f in. diameter). The pulses produced in the side channels enter single-channel differential discriminators which select only those pulses which correspond to .51-Mev absorption in the side crystals. The output from the side-channel analyzers and the pulses from the center channel pass into a triple coincidence circuit. T h e triple coincidence output pulses open a gate which allows coincident center channel pulses to enter the 30channel kicksorter. The differential discrimination in the side channels greatly reduces the background due to coincidences from multiple scattering, double Compton events, and cascade gamma rays and so increases the resolution of the apparatus. The three N a l (ThI) crystals were mounted on R C A 6342 photomultipliers and had a resolution of about 8.3% for 1.3-Mev gamma rays. A 0.2-in. diameter collimated beam of radiation, obtained with a 31-cm long lead collimator, was incident along the center crystal axis. T h e collimation improved the resolution significantly. Photomultiplier gain changes were kept to a minimum by using stabilized power supplies and relatively low counting rates. N o significant gainshifts were recorded over a period of 1 day. T h e kicksorter spectrum was recorded after every 2 to 3 hours and thus a regular check was kept on the gainshifts. Linearity of the center crystal was established to better than 0.1% for the energy range from 40 kev to 500 kev by the use of a standard pulse generator and gamma-ray sources of known energies from C s , E u , and N a . T y p i c a l spectra produced by C o alone, and by C o with N a , and by C o with Z n are shown in F i g . 2. Since the C o 7-rays have been established to better than 1 kev ( 1 . 3 3 2 5 ± . 0 0 0 3 and 1 . 1 7 2 8 ± . 0 0 0 5 M e v ) , using a doublefocusing spectrometer (Lindstrom 1953) to compare the C o lines with the accurately known R a C 1 . 4 1 5 8 ± . 0 0 0 2 M e v transition, the energies of the N a and Z n 7-rays can be obtained from the present experiment to better than 2 kev. The individual peaks for each of the gamma rays were isolated graphically by subtracting the typical C o spectrum and the background from the composite spectra as shown in F i g . 2. Assuming a Gaussian shape for the peaks, the mean energy and the variance of each peak was computed with the help of the University of British Columbia Alwac I I I E Computer. The statistical uncertainty in the mean energy for each peak was also calculated from the variance and total number of counts in the peak; in all cases this uncertainty was not greater than 1 kev. A more realistic estimate of the uncertainty in the mean gamma-ray energies was obtained by calculating the standard deviation in the measured means from seven runs for the N a and Z n sources. Since the N a and Z n gamma-ray energies were determined by simultaneous measurement with respect to the C o gamma rays, gainshifts and other systematic errors were effectively cancelled out. The final results of the present experiment are 137  165  22  60  65  60  22  60  60  60  22  65  60  22  22  66  66  60  Zn  66  gamma-ray energy  1.1124±.0019 M e v ,  Na  22  gamma-ray energy  1.2736db.0018 M e v .  NOTES I  t  '  1057  l  l  KILOVOLTS  F I G . 2. Typical spectra obtained with three-crystal pair spectrometer. Curve (c) is for Co , curve (b) for C o and Zn , and curve (a) for C o and N a gamma rays. 60  60  65  so  22  The present results for Z n gamma rays agree, to within the errors, with those reported by Johanson (1956), 1 . 1 1 2 ± . 0 0 3 M e v , and Waggoner (1950), 1 . 1 1 2 ± . 0 0 7 M e v ; and they are significantly different from those of Hedgran (1950), 1.125 M e v , and Good (1951), 1 . 1 2 7 ± . 0 0 9 . The N a gamma-ray energy agrees with that of P. M a r m i e r as reported by Ajzenberg (1955), 1 . 2 7 5 ± . 0 0 5 . In both cases our estimated errors are less than those reported earlier. 65  22  Relative Pair Production Cross Sections We have also measured the relative pair production cross sections for 7-rays of Z n , N a , C o , and R d T h , using the pair spectrometer. For a source of cascade gamma rays such as C o the relative pair production cross section is simply obtained from the ratio of the number of counts in the two pair peaks since the number of gamma rays of each energy is the same. T h i s method has been used b y Griffiths and Warren (1952) for C o and N a ' g a m m a rays. West (1956), with much-improved apparatus and a detailed study of the overall efficiency of the three-crystal spectrometer, was able to obtain absolute pair cross sections for the same gamma-ray cascades in both sodium iodide and anthracene. In the present work we have extended the energy range of the measurements of the relative pair production cross sections in sodium iodide by using Z n , N a , C o , and R d T h sources of known strength in exactly the same geometry. Since some of these sources emit only single gamma rays above 66  22  60  60  60  65  22  60  24  - 61 -  1058  C A N A D I A N J O U R N A L O F P H Y S I C S . V O L . 37. 1959  1.02 M e v it was necessary to know the relative strengths of the sources in order to obtain relative pair production cross sections. T h e strength of the sources was independently measured to better than 5 % with a sodium iodide scintillation counter employing a crystal 2 | i n . i n diameter b y 3§ in. long whose efficiency as a function of gamma-ray energy had been studied in some detail in this energy range. (Details of this work will be published.) T h e ratio of pair production cross sections obtained for the gamma-ray energies given i n brackets are: *(2.62) a(1.33) ~  r(1.33) , «r(1.17) "  <r(1.17) <r(l.ll) "  1  b  If we take the absolute cross section for the 1.33-Mev gamma rays of C o from the work of West (1956) as (6.81 ± . 1 7 ) X 1 0 ~ c m then these ratios lead to the following absolute pair production cross sections in sodium iodide: 60  26  2  (1.11) = ( 0 . 3 2 ± . 0 3 ) X 1 0 -  26  cm  2  (1.17) = ( 1 . 3 4 ± . 1 2 ) X 1 0 -  26  cm  2  (2.62) = ( 1 1 6 ± 1 0 ) X 1 0 -  26  cm  2  The errors of about 10% include that quoted b y West for the 1.33-Mev gamma ray (about 2.5%) plus statistical and estimated systematic errors introduced by our ratios. T h e ratios obtained here for pair production b y C o , N a , and R d T h gamma rays are in good agreement with the results collected by West (1956) and the Z n result combined with the absolute values given b y West for C o gamma rays provides a measurement of the pair production cross section in sodium iodide at an energy about 90 kev above the pair production threshold. 60  22  65  60  We are pleased to acknowledge the help of M r . G . Jones of this laboratory for his assistance with the computer programing. One of us (P.P.S.) gratefully acknowledges the receipt of a National Research Council Studentship. A J Z E N B E R G , F . and L A U R I T S E N , T . 1955. Revs. Modern Phys. 27, 77. G O O D , M . L . 1951. Phys. Rev. 81, 891. G R I F F I T H S , G . M . and W A R R E N , J . B. 1952. Proc. Phys. Soc. A , 65, 1050. H E D G R A N , A . , S I E G B A H N , K . , and S V A R T H O L M , N . 1950. Proc. Phys. Soc. A , 63, 960. JOHANSON, K. E. 1956. A r k i v Fysik, 10, 247. L I N D S T R O M , G . , H E D G R A N , A . , and A L B U R G E R , D . E . 1953. Phys. Rev. 89, 1303. W A G G O N E R , M . A . , M O O N , M . L . , and R O B E R T S , A . 1950. Phys. Rev. 80, 420. W E S T , H . I. 1956. Phys. Rev. 101, 915. R E C E I V E D M A Y 19, 1959. D E P A R T M E N T O F PHYSICS, UNIVERSITY OF BRITISH COLUMBIA, VANCOUVER, B . C .  - 62 -  The Performance o f a Simple y-Ray I n s e n s i t i v e F a s t Neutron C o u n t e r . The performance of a z i n c c o u n t e r assembled by Y . I . Ssu ( 1 9 5 5 ) ,  sulphide-lucite was  investigated  by u s i n g n e u t r o n s and gamma r a y s o f v a r i o u s e n e r g i e s . The d e t a i l s a r e g i v e n i n the a t t a c h e d r e p r i n t p u b l i s h e d i n the Canadian J o u r n a l o f P h y s i c s , V o l . 3 7 , 8 5 8 , 1 9 5 9 .  A  SIMPLE  G A M M A - R A Y  INSENSITIVE  FAST-NEUTRON  COUNTER G.  M .  G R I F F I T H S ,  P.  P.  S I N G H ,  Y.  I.  Ssu,  A N D J.  B.  W A R R E N  A SIMPLE GAMMA-RAY INSENSITIVE FAST-NEUTRON COUNTER 1  G .  M .  GRIFFITHS,  P.  P.  S I N G H ,  Y .  I.  Ssu,  A N D  J.  B.  W A R R E N  ABSTRACT A g a m m a - r a y insensitive fast-neutron counter is described which consists of a number of t h i n rectangular sheets of lucite coated w i t h zinc sulphide and sandwiched together to form a rectangular block which is mounted on a photom u l t i p l i e r . Pulse height spectra and absolute efficiency curves are presented for neutrons from 300 kev to 15 M e v . INTRODUCTION  Chadwick in 1932 first identified fast neutrons by observation of the knockon protons ejected from hydrogenous materials. Since that time many neutron counters have used the same neutron-proton interaction in either hydrogenfilled proportional counters (Coon and Nobles 1947), ionization chambers (Stafford 1948), or solid hydrogenous materials. Bell (1948) and Segel et al. (1954) employed organic phosphors successfully; however, these suffer from the fact that they are gamma-ray sensitive if the volume used is sufficiently large to give good neutron-detection efficiency. A thin layer of zinc sulphide powder placed on the face of a photomultiplier has been used to detect proton recoils from a layer of plastic resulting in a neutron counter with a very low gamma-ray sensitivity; however, the neutron efficiency is also small. Hornyak (1952) made a great improvement in detection efficiency while maintaining low gamma-ray sensitivity by using a molded button of lucite with zinc sulphide powder dispersed in it. As zinc sulphide is opaque to its own radiation the useful size of this device is limited. Since then several attempts have been made to improve the neutron-detection efficiency without increasing the gamma-ray sensitivity (Emmerich 1954; Brown and Hooper 1958). Recently a method, based on the fact that the ratio of the intensity of the slow light decay component to that of the fast component is different for protons and electrons in organic scintillators, has been used to discriminate between gamma rays and neutrons (Litherland et al. 1959; Owen 1958). Below we describe the properties of a counter used in our laboratory for several years, which has an efficiency comparable to others we have seen reported, along with an excellent gamma-ray rejection ratio and simplicity of construction. COUNTER CONSTRUCTION  The counter consists of a number of thin rectangular lucite sheets coated with zinc sulphide over their large faces and then sandwiched together to form a rectangular block which is mounted on an RCA 6342 photomultiplier. Pro' M a n u s c r i p t received F e b r u a r y 24, 1959. C o n t r i b u t i o n from the D e p a r t m e n t of Physics, U n i v e r s i t y of B r i t i s h C o l u m b i a , Vancouver, B.C. Can. J. Phys. Vol. 37 (1959)  858  GRIFFITHS  E T A L . : G A M M A - R A Y INSENSITIVE  COUNTER  859  tons knocked out of the lucite produce light in the thin zinc sulphide layers and the lucite plates conduct the light to the photomultiplier. T o make the block, the lucite sheets were dipped in ethyl formate and while still wet a weighed quantity of zinc sulphide powder was sprinkled on evenly through a fine mesh nylon cloth. Then the plates were stuck together under pressure until dry. The block was then polished on a face perpendicular to the plane of the sheets and this face was mounted on the photomultiplier with D o w Corning silicone oil. The other faces of the block were smoked with burning magnesium ribbon. The construction of a typical phosphor block is shown in Fig. 1.  F I G . 1.  The Incite - zinc sulphide sandwich block.  Both Patterson D and R C A 33-Z-20A zinc sulphide phosphors were tested. W i t h a radium-beryllium neutron source the R C A phosphor gave about 30% more counts above a selected bias than the Patterson D phosphor and so was used for all further work. Tests to determine the optimum thickness of the zinc sulphide powder indicated that for thicknesses greater than 12 m g / c m the gamma-ray sensitivity becomes appreciable and thicknesses less than 10 m g / c m gave a satisfactory neutron response. Several lucite sheet thicknesses were tried and it was found that for radium-beryllium neutrons the efficiency decreased for thicknesses greater than 0.125 inch. The plate thickness determines a limit to the height of the block that can be usefully employed, since for a given height the light from the top of the block will not reach the photomultiplier as efficiently with thin plates as it would with thicker ones due to absorption in the zinc sulphide. Thus with increasing height a decreasing proportion of the light will get into the photomultiplier and after a certain height, which depends on the plate thickness, any additional height contributes very little light. However, greater plate thickness, although it means that the detector may be made longer, does not necessarily mean greater efficiency since for thicker plates more of the protons lose all their energy in the lucite. Protons stopped in lucite alone produce very small 2  2  860  C A N A D I A N J O U R N A L O F PHYSICS. V O L . 37, 1959  pulses which are lost in the noise. A check on the transmission of light down the block was made by preparing a plastic sandwich with 0.125 inch thick plates 5 inches long mounted on a photomultiplier. A radium-beryllium source was placed 25 cm away to one side and the counting rate was observed, as a function of the length, which was altered by cutting sections from the end of the sandwich block. Little change in counting rate was observed until the length was reduced to 3 inches and the counting rate became roughly proportional to length for lengths less than 1.5 inches. A rectangular block- consisting of 1/8 inch square lucite rods packed together with zinc sulphide powder on all internal faces was made and tested. Its efficiency per unit volume for neutron detection was little if any better than that of the flat sheet assemblies and as it was more difficult to construct no further ones of this type have been made. Tests were performed to find out whether the neutron-detection efficiency of the counter (using radium-beryllium neutrons) depended on the direction of neutron entrance (i.e. parallel or perpendicular to the lucite sheets). One might expect such an effect since the protons are scattered forward in the laboratory system, but within the errors of about 10% no effect was found either in the shape of the spectrum or in the number of counts obtained above a given bias. T w o blocks with the following characteristics were tested in some detail: Block I  Block II  Lucite thickness 1/32 inch Length 1 cm Cross section 4.2X4.2 cm No. of plates 50 ZnS thickness 7 mg/cm  1/16 inch 2 cm 4.4X4.4 cm 28 7 mg/cm  2  2  The efficiency per unit volume for block I was 1.75 times that for block II. However, since its volume was less than half of that of block II it gave fewer counts for a given neutron flux. T h e results described below were obtained with block II. COUNTER PERFORMANCE  (a) Pulse Height Spectra The pulse height spectra and absolute efficiencies for the neutron counter were measured for neutrons of energies from 225 kev to 4.4 M e v using neutrons from the T(p, n)He and D(d, « ) H e reactions and for 17-Mev neutrons from the T(d, w)He reaction. T h e differential pulse height spectra are shown in Figs. 2 and 3 along with spectra for photomultiplier noise and 7-rays of 1 M e v from C o and 6.14 M e v from the F (p, a, y)0 reaction. T h e pulse height scale is the same for all curves but the vertical scale is arbitrary and the curves are not normalized to each other. 3  3  4  60  n  1&  (b) Absolute Efficiency The absolute efficiencies were determined from knowledge of the neutron fluxes from the targets used. T h e tritium content of the tritium-zirconium  GRIFFITHS ET A L . : G A M M A - R A Y INSENSITIVE COUNTER  8 6 1  3  PULSE  HEIGHT  F I G . 2. Pulse height spectra for low-energy neutrons and for gamma rays. The curves are not normalized with respect to each other. F I G . 3. Pulse height spectra for high-energy neutrons. The curves are not normalized with respect to each other.  862  CANADIAN  JOURNAL  O F P H Y S I C S . V O L . 37, 1959  target, k i n d l y supplied b y the O a k R i d g e N a t i o n a l L a b o r a t o r y , was measured in  t e r m s of t h e a b s o l u t e g a m m a - r a y y i e l d f r o m t h e T(p,  800  k e v , using absolute differential cross-section  7)He  4  reaction at  d a t a of P e r r y a n d B a m e  (1955) for t h i s r e a c t i o n a n d t h e o r e t i c a l e s t i m a t e s of t h e s c i n t i l l a t i o n c o u n t e r efficiency. L o w - e n e r g y n e u t r o n s f r o m 280 k e v t o 940 k e v were p r o d u c e d b y t h e T(p, « ) H e w)He  4  3  reaction  reaction  a n d h i g h - e n e r g y n e u t r o n s were  using the same  target.  1.9 M e v to 4.2 M e v were p r o d u c e d b y t a r g e t of k n o w n t h i c k n e s s . T h e D  2  Intermediate  D(d, n)He  3  produced b y the energy  T(d,  neutrons f r o m  r e a c t i o n s u s i n g a h e a v y ice  0 t a r g e t s were m a d e b y c o n d e n s i n g h e a v y  water v a p o r from a constant v o l u m e dispenser onto a liquid air cooled gold plate. T h e dispenser-target system was calibrated b y observing the shift i n the 3 4 0 - k e v r e s o n a n c e of t h e F (p, a', y)0 l9  v a p o r was deposited o n a t h i n F  1 9  16  r e a c t i o n a f t e r a g i v e n pressure of  t a r g e t . F r o m t h e m e a s u r e d e n e r g y loss of  p r o t o n s i n p a s s i n g t h r o u g h t h e ice l a y e r a n d f r o m t h e s t o p p i n g p o w e r d a t a g i v e n b y W h a l i n g (1958) t h e n u m b e r of t a r g e t d e u t e r o n s p e r s q u a r e c e n t i m e t e r w a s c a l c u l a t e d . N e u t r o n y i e l d s were o b t a i n e d f r o m c r o s s - s e c t i o n  data  g i v e n b y t h e r e v i e w a r t i c l e of F o w l e r a n d B r o l l e y (1956). The energy  n e u t r o n - d e t e c t i o n efficiency for t h e c o u n t e r is d e p e n d e n t o n the n e u t r o n as s h o w n i n F i g . 4.  D(d, « ) H e  3  1  0  3 0  1 4-14  Curve  (a)  s h o w s t h e a n g u l a r d i s t r i b u t i o n of  n e u t r o n s for 1 . 0 - M e v i n c i d e n t d e u t e r o n s as o b t a i n e d b y H u n t e r  1 4  1  6 0 9 0 L A B O R A T O R Y I 3 - 5  120 A N G L E  1 3 N E U T R O N  150  I  I  2 5  2  180 I 1-76  E N E R G Y - M E V  F I G . 4. The angular distribution of D(d, » ) H e neutrons at 1.0 Mev. Curve (a): The distribution of Hunter and Richards (1949) obtained with a long counter. Curve (6): The distribution as seen by the l u c i t e - z i n c sulphide sandwich counter. Curve (c): The ratio of the curves (b) and (a), which are normalized to each other at zero degrees. 3  863  GRIFFITHS E T A L . : G A M M A - R A Y INSENSITIVE COUNTER  O  400  600  1200  DISCRIMINATION  1600  LEVEL  2000  2400  280O  F I G . 5. Absolute efficiency vs. discrimination level for the low-energy neutrons. The ordinate for the gamma-ray curves should be multiplied by 10 . F I G . 6. Absolute efficiency vs. discrimination level for the high-energy neutrons. -2  864  C A N A D I A N J O U R N A L O F PHYSICS. V O L . 37.  1959  and Richards (1949) using a long counter and making small corrections for the change in efficiency with neutron energy as given by Hanson and M c K i b b e n (1947). Curve (b) shows the curve obtained with the present counter normalized to curve (a) at zero degrees. The ratio between the curves is shown by the upper line and indicates the decrease in efficiency for decreasing neutron energies. The absolute intrinsic efficiencies defined as the number of counts observed divided by the number of neutrons incident on the front face of the counter for various neutron energies as a function of discriminator bias level (integral bias curves) are shown in Figs. 5 and 6. The efficiency falls off rapidly for neutrons with energies less than 300 kev and is very small for thermal neutrons. It should be noted that the efficiency figures given here are smaller by a factor A, equal to the area of the front face of the counter, than those quoted by some authors who give the number of counts per unit neutron flux at the position of the counter. Figure 5 also shows on an expanded vertical scale the absolute efficiencies for C o and 6-Mev gamma rays. Note that for the gamma-ray curves the ordinates should be multiplied by 10~ . The curves indicate that a bias may be chosen without serious loss of neutron counts to give gamma-ray efficiencies of 10~ to 10~ of the neutron efficiency at that bias. 60  2  6  10  As a crude first approximation one would expect the neutron-detection efficiency to be proportional to the neutron-proton scattering cross section, a, and the mean range, R, of the scattered protons in the lucite, since for  7  ENERGY  M E V  F I G . 7. Absolute efficiency vs. neutron energy for various biases. The thick curve shows a rough theoretical estimate of efficiency with energy on an arbitrary vertical scale.  - 63 -  GRIFFITHS  E T A L . : G A M M A - R A Y INSENSITIVE COUNTER  865  all energies studied here the proton ranges are smaller than the thickness of the lucite plates. The validity of this assumption is indicated in Fig. 7, which shows experimental absolute efficiencies as a function of neutron energy for several discriminator levels and also shows a curve of the product <r-R as a function of neutron energy with arbitrary vertical normalization. The agreement in shape of the curves is quite good; the theoretical curve is rather flatter than the experimental ones suggesting that for lower-energy neutrons a larger proportion of the pulses are lost in the noise. This counter has been used to detect the small yield of secondary neutrons produced by proton bombardment of heavy ice targets below the D(/>, n) threshold in the presence of a much larger yield of 6-Mev y-rays, and as a general monitor for fast neutrons. ACKNOWLEDGMENT  One of us (P.P.S.) gratefully acknowledges the receipt of a National Research Council Studentship. REFERENCES  B E L L , P. R. 1948. Phys. Rev. 73, 1405. B R O W N , B . and H O O P E R , E . B., J R . 1958. Nucleonics, 16, 96. C H A D W I C K , J . 1932. Proc. Roy. Soc. A , 136, 692. C O O N , J . H . and N O B L E S , R. A . 1947. Rev. Sci. Instr. 18, 44. E M M E R I C H , W . S. 1954. Rev. Sci. Instr. 25, 69. F O W L E R , J . L . and B R O L L E Y , J . E . 1956. Revs. Modern Phys. 28, 103. H A N S O N , A . O . and M C K I B B E N , J . L . 1947. Phys. Rev. 72, 673. HORNYAK, W . F. 1952. Rev. Sci. Instr. 23, 264. H U N T E R , G . T . and R I C H A R D S , H . T . 1949. Phys. Rev. 76, 1445. L I T H E R L A N D , A . E . , A L M Q U I S T , E . , B A T C H E L O R , R., and G O V E , H . E . 1959.  Letters, 2, 104.  O W E N , R. B. 1958. Nucleonics, 16 (6), 54. P E R R Y , J . E . , J R . and B A M E , S. J . , J R . 1955. Phys. Rev. 99, 1368. S E G E L , R. E . , S W A R T Z , C D . , and O W E N , G . E . 1954. Rev. Sci. Instr. 25,  S T A F F O R D , G . H . 1948. Nature (London), 162, 771. W H A L I N G , W . 1958. Handbuch der Physik, Vol. 34 (Springer-Verlag,  Phys. Rev.  689.  Berlin), p. 193.  - 64 -  The N e u t r o n Y i e l d From Heavy I c e T a r g e t s Bombarded W i t h P r o t o n s Below t h e D (p. n) 2p T h r e s h o l d . Using the f a s t neutron counter d e s c r i b e d e a r l i e r the y i e l d and a n g u l a r d i s t r i b u t i o n s o f n e u t r o n s produced, when b o t h t h i n and t h i c k heavy i c e t a r g e t s were bombarded w i t h p r o t o n s , were s t u d i e d .  The p r o t o n e n e r g i e s used were  below t h e D (p, n) 2p t h r e s h o l d .  The r e s u l t s were compared  w i t h t h e t h e o r e t i c a l c o m p u t a t i o n s c a r r i e d o u t by Y . I . Ssu (1955).  T h i s work has a l s o been p u b l i s h e d i n t h e Canadian  J o u r n a l o f P h y s i c s , V o l . 37, 866, a t t a c h e d t o t h e n e x t page.  1959,  and a r e p r i n t i s  THE NEUTRON YIELD FROM HEAVY ICE TARGETS BOMBARDED WITH PROTONS BELOW T H E D(p, n)2p THRESHOLD P.  P.  S I N G H ,  G .  M .  G R I F F I T H S ,  Y .  I.  Ssu,  A N D  J.  B .  W A R R E N  THE NEUTRON YIELD FROM HEAVY ICE TARGETS BOMBARDED WITH PROTONS BELOW THE D(p, n)2p THRESHOLD 1  P.  P.  S I N G H ,  G .  M.  G R I F F I T H S ,  Y .  I.  Ssu,  A N D  J.  B .  W A R R E N  .ABSTRACT In connection with some experiments on the gamma-ray yield from the D(p, 7 ) He reaction using heavy ice targets a considerable yield of neutrons was found even for proton bombarding energies well below the D(p,n)2p threshold of 3.3 Mev. The yield, excitation function, and angular distribution of this neutron yield have been investigated both experimentally and by means of theoretical calculations. These studies confirm the suggestion that the neutrons are produced by a secondary reaction in which deuterons, scattered in the target by incident protons, collide with further target deuterons to produce D(S, w)He reactions. 3  3  INTRODUCTION  The production of neutrons when heavy ice targets are bombarded with protons below the T)(p, n)2p threshold has been reported by Jennings et al. (1950), who suggested that the neutrons arise from deuterons, scattered by incident protons, colliding with other target deuterium atoms and producing D(d, w)He reactions. In connection with some measurements on the gammaray yield from the D(p, 7 ) H e reaction this effect was found to contribute a considerable background (Griffiths and Warren 1955). Consequently we have made a detailed experimental and theoretical study of the effect. 3  3  EXPERIMENTAL  The gamma-ray insensitive neutron counter used in these experiments has been described previously (Griffiths et al. 1959). It consists of a block of lucite sheets with thin layers of zinc sulphide powder sandwiched between them, mounted on an R C A 6342 photomultiplier. A bias setting which made the 6-Mev gamma-ray sensitivity less than 10~ of the neutron sensitivity was used. The absolute efficiency for neutron detection varied with neutron energy from 0.15% for 2 - M e v neutrons to 0.3% for 4 - M e v neutrons at this bias. The pulse height spectrum was analyzed with a 100-channel Computing Devices of Canada kicksorter. The target chamber used is shown in F i g . 1. A gold-plated liquid air cooled copper plate formed the target backing. This could be turned to face an inlet hole through which heavy water vapor from the dispenser was admitted to the target chamber. For thin targets, the constant volume dispenser was evacuated, taps T and T were closed, and tap T was opened to admit the required pressure of water vapor as measured by the oil manometer. Then tap T was closed and T i was opened to admit the vapor slowly v i a the 9  t  2  3  3  'Manuscript received March 12, 1959. Contribution from the Physics Department, University of British Columbia, Vancouver B.C. Can. J. Phys. Vol. 37 (1959)  866  SINGH E T A L . : N E U T R O N - Y I E L D  867  F I G . 1. Target chamber and heavy water vapor dispenser. The graph on the right shows the dispenser calibration in terms of target thickness versus dispenser pressure.  glass-wool diffuser to the target chamber. The target thickness as a function of dispenser pressure was calibrated by freezing the vapor on top of thin fluorine targets for various initial pressures in the dispenser and measuring the shift in the F (p, a, 7)0 340-kev resonance due to the energy loss of the protons in passing through the ice layers. From a knowledge of the stopping power of the protons in ice (Whaling 1958) the number of deuterium atoms per square centimeter on the target could then be calculated as a function of the manometer pressure (Fig. 1). When a thick target was required so that the incident protons would be stopped completely in the ice layer, taps T i and T were opened for 2 minutes and then a measurement of the yield was made. The taps were opened for a further 2 minutes and a second yield measurement was made. When no increase in yield occurred for additional ice on the target, the target was judged to be "thick". 19  16  3  RESULTS  1. Thick Target Yield and Excitation Function  A thick heavy ice target was bombarded with protons of energies from 350 kev to 1.5 Mev and the neutron yield at zero degrees to the proton beam per millicoulomb of beam per steradian was obtained. Since the detection efficiency is a function of the neutron energy and since at any angle the neutron energies incident on the counter varied from approximately 2 Mev to 4 Mev, the mean neutron energy at 0° was estimated for each bombarding energy by assuming that on the average the deuterons were scattered at 45° to the proton beam direction and then by calculating the neutron energy in  C A N A D I A N J O U R N A L O F PHYSICS. V O L . 37,  868  1959  the direction of the counter from the mechanics of the D(d, w)He reaction. The experimental excitation function, shown in Fig. 2, has been corrected for the change in efficiency due to the change in mean neutron energy. The theoretical neutron yield as a function of proton energy calculated on the basis of the secondary process is also shown in Fig. 2. 3  P R O T O N  F I G . 2.  E N E R G Y -  M E V  The theoretical and experimental thick target excitation functions.  2. Thick Target Angular Distribution  With the counter subtending a solid angle of 0.15 steradian at the target the thick target neutron yield was measured for a proton energy of 1.5 Mev  F I G . 3. The thick target angular distribution for 1.5-Mev incident protons. Curve (a), experimental results—uncorrected; curve (b), theoretical result; curve (c), experimental results—corrected for change in neutron-detection efficiency with mean neutron energy.  SINGH  869  E T AL.: N E U T R O N YIELD  at seven different angles. The neutron yield observed at each is shown by the lower curve in Fig. 3. Since, for each counter position, neutrons from deuterons, scattered with various energies and travelling in various directions in the target, may reach the counter a rough estimate of the mean neutron energy and thence the mean detection efficiency for each counter position was made. The correction for efficiency change results in the upper curve of Fig. 3. The theoretical curve is also shown in the figure. The increase in neutron yield towards backward angles after a minimum at 90° results from the corresponding increase in the D(d, «)He neutron yield at backward angles. In this case the effect is less pronounced than for a D(d, «)He experiment since it is averaged over the scattered deuteron directions and energies in the target. 3  3  8. Pulse Height Spectrum  The pulse height spectrum from the fast-neutron counter produced by bombarding a thick heavy ice target with 1.5-Mev protons is shown in Fig. 4.  P U L S E  H E I G H T  F I G . 4. The differential pulse height spectra from the neutron detector for 4-Mev and 2-Mev monoenergetic neutrons and for the neutrons from a heavy ice target bombarded with protons of 1.5-Mev energy.  For comparison the spectra produced by monoenergetic neutrons of 2-Mev and 4-Mev energy from the D(d, w)He reaction are also shown. It is apparent that the neutrons from the ice target are comparable in energy to those from the D(rf, n)He reaction. 3  3  4-. Thin Target Yield and A ngular Distribution  A thin target containing 24X10 deuterium atoms per square centimeter, approximately 70 kev thick for 1.5-Mev protons, was bombarded by 1.5-Mev protons and the neutron yield was measured as a function of angle. The 18  870  C A N A D I A N J O U R N A L O F PHYSICS. V O L . 37,  1959  results are shown in Fig. 5. Since, a large number of scattered deuterons escape from the back of the ice, it is not easy to make an estimate of the mean neutron-detection efficiency because it is difficult to estimate the neutron energy spectrum as a function of counter angle. Therefore no correction for  the change of efficiency with neutron energy was applied to the curve. The theoretical curve is also shown. The two curves show good agreement in shape and the factor of about two between the absolute values may be partly accounted for by the fact that in the theory for the thin target it was assumed, for the sake of simplicity, that all the deuterons scattered in the ice layer started out at the front face of the layer which gives an overestimate of the neutron yield. 5. Effect of D2O Concentration  If the neutron production from heavy ice targets is due to primary processes one would expect the neutron yield to depend linearly on the deuterium concentration in the target, whereas if the yield is due to secondary processes, as suggested here, one would expect the neutron yield to depend on the square of the deuterium concentration. This was checked by measuring the zero-degree neutron yield for 1.5-Mev protons using thick targets with various concentrations of heavy water in ordinary water. The results are shown in Fig. 6. The 6-Mev gamma-ray yield from the D(p, 7)He reaction is directly proportional to the deuterium concentration as expected since it arises from a direct interaction of the incident protons with the target nuclei. However, it is clear that the neutron yield increases as the square of the 3  SINGH  ET A L . : NEUTRON  YIELD  871  D0 CONCENTRATION — PERCENT 2  F I G . 0. The effect of D 2 O concentration on the gamma-ray and neutron yields. The gammaray yield is plotted on a linear scale and the neutron yield is on a square-root scale.  concentration. This leaves no doubt about the secondary nature of the neutron production. THEORETICAL  ANALYSIS  Calculations have been made of the yield, excitation function, and angular distribution of neutrons from thick and thin targets of heavy ice bombarded with protons on the assumption that they are produced by scattered deuterons colliding with other deuterons in the target and producing D(rf, »)He' reactions. In the case of a thick target the calculations involved the following steps. The target was divided into six layers perpendicular to the proton beam direction as shown in Fig. 7(a), so that each layer has approximately one sixth of the incident proton energy of 1.5 Mev dissipated in it and in each layer the protons were considered to have a constant energy equal to the mean proton energy in the layer. The data of Sherr et al'. (1947) and Taschek (1942) on proton-deuteron scattering were used to calculate the energy and the angular distribution of the deuterons from each layer. The scattered deuterons from each layer were divided into overlapping cones, Fig. 7(b), symmetrical about the proton beam direction, with angular limits for each cone such that the difference in the deuteron energies at the outside and the inside of the cone was equal for all cones. It was assumed that all deuterons entering a cone have an energy equal to the mean energy of the deuterons entering the cone. Further, assuming Rutherford scattering and using the analytical expression for the energy and angular dependence of the protondeuteron scattering cross section the number of deuterons scattered into each cone was obtained by analytical integration between the angular limits of the cone. To allow for the fact that the scattering does not follow the Rutherford formula for all energies and angles due to some nuclear interaction, the results from the Rutherford formula were multiplied by the ratio of the measured cross section to the Rutherford cross section. This ratio was interpolated for  872  C A N A D I A N J O U R N A L O F PHYSICS. V O L . 37,  1959  the required energies from the results of Sherr et al. (1947) and Taschek (1942). Each cone was subdivided into 12 "tubes", Fig. 7(b), each tube containing 1/12 of the deuterons in the cone. All deuterons in each tube were assumed to travel down the center of the tube. For each tube the angle between this direction and the line joining the target to the detector was obtained geometrically. These angles were computed for the counter at 0°, 45°, 90°, and 135° with respect to the incident beam direction. Finally each tube was divided into "sections" along its length such that the energy loss of the deuterons in traversing each section was approximately equal to the difference between the deuteron energies at the outside and the inside of the particular cone. In all there were 672 sections. The stopping power data for heavy ice of Wenzel and Whaling (1952) was used to compute the thickness and hence the number of target deuterons in each section of the target. The yield and angular distribution of D(d, «)He neutrons has been expressed by Hunter and Richards (1949) in terms of Legendre polynomials which were used to provide the relevant neutron yields from each section in the direction of the counter for four counter positions at 0°, 45°, 90°, and 135°. The total neutron yield from the thick target in the counter direction can be obtained by summing over all sections of each tube, over all tubes of each cone, over all cones of each layer, and over all layers. 3  - 65 -  ' SINGH E T AL.:  NEUTRON YIELD  873  Table I gives typical neutron yield data at 0° for each of the six layers with the energy of the protons in each layer. TABLE I  Layer A B C D E F  Proton energy, kev 1500 1322 900 563 338 113  0° neutron yield per steradian per millicoulomb  to 1322 to 900 to 563 to 338 to 113 to 0  3.25X10 7.02X10 1.55X10 1.08X10 1.08X10 Neglected 6  6  6  4  4  From this table the thick target yield of neutrons as a function of energy can easily be obtained by adding the zero-degree contribution from the bottom of the table to the layer which has an incident proton energy equal to the particular energy at which the total yield is required. The theoretical results are plotted in Figs. 2, 3, and 5 along with the experimental results. In principle the calculations for the thin target yield and angular distribution function were the same as for the thick target calculations except that only one target layer was considered; however, since a large fraction of the higherenergy scattered deuterons escape from the thin target layer the yield from the low-energy scattered deuterons was considered in greater detail than for the thick target calculation. The over-all agreement between theory and experiment leaves no doubt as to the secondary process responsible for the neutron production. ACKNOWLEDGMENT  One of us (P.P.S.) wishes to thank the National Research Council of Canada for an award of a Studentship. REFERENCES G R I F F I T H S , G . M . and W A R R E N , J. B . 1955. Proc. Phys. Soc. A , 68, 781. G R I F F I T H S , G . M . , S I N G H , P. P., Ssu, Y . I., and W A R R E N , J . B. 1959. Can. J . Phys. 37, 858. H U N T E R , G . T . and R I C H A R D S , H . T . 1959. Phys. Rev. 7 6 , 1445. J E N N I N G S , B., S U N , K . H . , and L E I T E R , H . A . 1950. Phys. Rev. 80, 109. S H E R R , R., B L A I R , J., K R A T Z , H . , B A I L E Y , C , and T A S C H E K , R. 1947. Phys. Rev. 72, 662. T A S C H E K , R. F . 1942. Phys. Rev. 6 1 , 13. W E N Z E L , W . and W H A L I N G , W . 1952. Phys. Rev. 8 7 , 499.  WHALING, W .  1958.  Handbuch der Physik, Vol. 34 (Springer-Verlag, Berlin), p. 193.  HELIUM  OUT  - BRASS SCREW  COPPER  ASBESTOS  TUBE  MILD S T E E L Jfe  STEEL  HELIUM BALL  BRASS  FIG.  17  THERMAL  LEAK  IN  SEAT  BODY  ROD BALL  APPENDIX I Thermal Leak.  A t h e r m a l v a l v e o f the type shown i n P i g . 17 was i n s t a l l e d I n t h e h e l i u m gas b o t t l e .  The f u n c t i o n i n g o f the  v a l v e depends on the d i f f e r e n t i a l t h e r m a l e x p a n s i o n o f d i s s i m i l a r metals.  The b r a s s body o f the l e a k expands more  t h a n t h e m i l d s t e e l r o d when heat i s a p p l i e d , t h u s d e c r e a s i n g t h e p r e s s u r e on t h e b a l l which i n t u r n l e t s h e l i u m gas t h r o u g h the body and out t h r o u g h the copper tube t o t h e m a n i f o l d . The b a l l seat and t h e copper tube were h a r d s o l d e r e d i n p l a c e i n t h e main b r a s s body o f t h e l e a k and the body was then c l e a n e d w i t h warm d i l u t e n i t r i c a c i d .  The b a l l and s t e e l  r o d were p l a c e d i n p o s i t i o n and t h e b r a s s screw was screwed i n as f a r as i t would go.  The l e a k was t h e n clamped I n a v i s e  so t h a t t h e end w i t h t h e screw was t i l t i n g downwards i n o r d e r t o a v o i d s o l d e r r u n n i n g i n t o the main body o f the l e a k v i a the screw t h r e a d s .  A l i t t l e t e n a c i t y f l u x was a p p l i e d t o t h e  screw and the end was t h e n s l o w l y t i g h t e n e d u n t i l i t j u s t touched the s t e e l r o d and t h e l e a k was a l l o w e d t o c o o l .  Two  c o i l s , made o f 9 i n c h e s o f nichrome w i r e (2.67 ohms p e r f o o t ) , o f 8 t u r n s each were t h e n wound o v e r a t h i n l a y e r o f a s b e s t o s p l a c e d around the b r a s s body (see P i g . 17).  One end o f b o t h  c o i l s was a t t a c h e d t o t h e body o f t h e l e a k .  Power t o b o t h t h e  c o i l s was o b t a i n e d from two 6.3 v o l t , 400 c y c l e h e a t e r t r a n s -  - 66 -  - 67 formers.  The p r i m a r y o f one t r a n s f o r m e r was connected t o  the mains t h r o u g h a 100 ohm r e s i s t o r w h i l e t h e o t h e r  coil  was c o n n e c t e d t o t h e mains v i a a v a r i a c which c o u l d be m a n u a l l y operated  from t h e c o n t r o l b o a r d by means o f s e l s y n  motors and a n y l o n c o r d r u n n i n g from t h e bottom o f t h e machine t o t h e t o p .  About 15 w a t t s were d i s s i p a t e d i n t h e  f i r s t c o i l w h i l e a n o t h e r 15 w a t t s were a v a i l a b l e f o r t h e 2nd c o i l f r o m t h e v a r i a c . The  .'•••* •;.  main advantages o f t h i s l e a k l i e i n i t s  s i m p l i c i t y o f d e s i g n , i t s s m a l l s i z e and f a s t r e s p o n s e . The h e l i u m l e a k was mounted i n s i d e t h e h e l i u m  storage b o t t l e  to a v o i d any a i r l e a k s and t o p r o v i d e t h e l e a k w i t h an environment h a v i n g a r e a s o n a b l y T h i s was n e c e s s a r y  l o n g t h e r m a l time  constant.  s i n c e these l e a k s were q u i t e s e n s i t i v e  t o ambient temperature f l u c t u a t i o n s . The  g e n e r a l performance o f t h i s l e a k was q u i t e  s a t i s f a c t o r y o v e r a p e r i o d o f s e v e r a l months r u n n i n g on helium.  There was v e r y l i t t l e i f any h e l i u m l e a k t h r o u g h  the v a l v e when shut o f f .  I t i s i n t e r e s t i n g t o note t h a t  the v a l v e r e q u i r e d l e s s power and was r a t h e r more s e n s i t i v e to  temperature f l u c t u a t i o n s and s u p p l y v o l t a g e f l u c t u a t i o n s  than s i m i l a r valves operated  w i t h hydrogen g a s .  This  d i f f e r e n c e may be e x p l a i n e d by t h e d i f f e r e n t h e a t cond u c t i v i t i e s o f t h e gases. was s a t i s f a c t o r i l y s h o r t ;  The response time o f t h e v a l v e changes i n o s c i l l a t o r l o a d i n g  - 68 -  corresponding to changes i n leak rate were noted a few seconds a f t e r adjustment of the heater power.  I t took  about 1 minute to open the leak at f u l l power when s t a r t i n g cold.  APPENDIX I I Angular D i s t r i b u t i o n Functions.  A.  The a n g u l a r d i s t r i b u t i o n f u n c t i o n s , e x p r e s s e d i n  the form W (e) = 1 + A  C 0 s 9 + A4 Cos^O  (1)  2  2  were c a l c u l a t e d u s i n g the method o u t l i n e d by W i l k i n s o n (1954) and t a b l e s of c o e f f i c i e n t s by B i e d e n h a m and Rose (1953) and t h o s e o f Sharp e t a l . (1953).  A n u c l e u s of s p i n J , may  absorb  an a - p a r t l c l e c a r r y i n g i n an a n g u l a r momentum 1^, t o form a s t a t e of s p i n J which t h e n goes t o the f i n a l s t a t e o f s p i n J by the e m i s s i o n o f a 2^" -pole r a d i a t i o n .  T h i s two  2  2  stage  sequence can be e x p r e s s e d as J  1  ( l ) J (1 ) J 2  x  (2)  2  F o r a "pure" t r a n s i t i o n , i n v o l v i n g a r a d i a t i o n o f s i n g l e m u l t i p o l a r l t y and p a r i t y , the a n g u l a r d i s t r i b u t i o n i s of the form W (9) - Z ^ F ^ ( 1  1  J , J) EU. ( 1  2  J  2  J)  (3)  /At  where,  = 2  1 1  (1]. + l j / 2  1 1  U i + 1)  1) i s t h e  " p a r t i c l e f a c t o r " , P^, i s the Legendre p o l y n o m i a l of orderyUs and the v a l u e s o f P^u. are l i s t e d by B i e d e n h a m and Rose (1953). F o r a "Mixed" t r a n s i t i o n , c o n t a i n i n g 1 p a r t o f pole r a d i a t i o n to a  2  p a r t s o f 2 - p o l e the sequence can be l 2  - 69 -  2 l2  - 70 -  e x p r e s s e d as J  l d l )  (ll)  J  J  Only c a s e s where l g = 1  2  2 + 1 were c o n s i d e r e d , f o r these t h e  angular d i s t r i b u t i o n f u n c t i o n i s W (6) = Z  J l J)  a  (lg J  2  (21  J) +  2  S  U  (- )  2 a  1  + 1) (21^ + 1)J  1 / 2  2  2  J  J _  Z z  J 2  >  +  " [ ( 1  O^tlg 4  J  2  J  + !)  2 )} J  W  E q u a t i o n 4 s i m p l y c o n t a i n s t h e c o r r e l a t i o n s o b t a i n e d f o r pure l'  1  2 - p o l e and pure 2 2-pole r a d i a t i o n s , weighted 2  according to  t h e i r r e l a t i v e i n t e n s i t i e s , and an i n t e r f e r e n c e term c h a r a c t e r i z e d by G .  The G's a r e g i v e n i n t h e B i e d e n h a r n  and Rose (1953)  compilation. I f the s p i n o f t h e compound s t a t e , o f s p i n J , p r o c e e d s t o the f i n a l s t a t e , o f s p i n J ^ , through an i n t e r m e d i a t e s t a t e , o f s p i n J , w i t h t h e e m i s s i o n o f two gamma r a y s o f m u l t i p o l a r i t y 2  2^2 and 2^3 then t h e sequence o f t h i s t h r e e stage p r o c e s s c a n be w r i t t e n as J  x  (l ) J (1 ) J x  2  2  (1 ) 3  J3  The a n g u l a r d i s t r i b u t i o n f u n c t i o n f o r t h e second 7-ray ( 1 ^ ) can be w r i t t e n as  (5)  - 71 W (0) = ( - ) 1 ~ - 2 [ ( J + 1) ( 2 J + 1 ) J L  J  J  2  x£P ^(l J J)  1 / 2  2  A  1  1  A*-  F*, ( 1 J J ) W ( J J J J > ^ 1 ) 2  3  2  2  2  (6)  2  The v a l u e s f o r W's a r e g i v e n i n t a b l e s o f Sharp e t a l . An e x p r e s s i o n s i m i l a r t o (4) can be w r i t t e n f o r t h e "mixed" t h r e e stage t r a n s i t i o n . P o r t h e p r e s e n t work the c o e f f i c i e n t s A  and A^  g  were c a l c u l a t e d , f o r two stage and t h r e e stage p r o c e s s e s , f o r t h o s e c a s e s where a compound s t a t e of B  1 1  i s formed by  p-wave, d-wave o r f-wave a - p a r t l c l e s and f o r t h e c a s e s where d i p o l e o r quadrupole emitted.  ( E l e c t r i c o r Magnetic) 7 - r a d i a t i o n i s  Since a l l the e x p e r i m e n t a l l y observed 7-rays are  a n i s o t r o p i c i n d i s t r i b u t i o n , t h e f o r m a t i o n o f B"^  compound  s t a t e s by s-wave p a r t i c l e s i s r u l e d out because i t l e a d s t o Isotropic distributions.  The v a l u e s o f A  and A^ c a l c u l a t e d  2  f o r t h e v a r i o u s c a s e s o f i n t e r e s t i n t h i s work a r e l i s t e d i n the t a b l e below. 3/2 and so (a)  The s p i n o f t h e ground  = 3/2 f o r a l l c a s e s .  Two stage p r o c e s s e s  h 1  s t a t e of l i t h i u m i s  J  X  1/2  3/2  2  1  1  —  (l-^) J ( 1 ) J 2  J  2  A  2  2  A  3/2  0  1/2  0  5/2  +.125  3/2  -.42  1/2  0  4  72 -  J  J  2  A  2  A  4  3/2  2  7/2  + .18  5/2  1  7/2  -.33  5/2  + .56  3/2  -.37  7/2  + .77  5/2  -.38  7/2  + .52  -.75  5/2  + .92  +1.3  3/2  + 2.3  -1.3  7/2  -.07  5/2  + .27  3/2  -.22  5/2  0  3/2  0  7/2  1  2  5/2  3/2  9/2  1  1  1  2  7/2  1  2  5/2  1  11/2  -.23  9/2  + .85  7/2  -.39  7/2  -1.35  +1.83  5/2  +2.02  -1.28  7/2  + .57  5/2  -.29  7/2  -.5  + .25  5/2  + .29  -.31  3/2  + .42  + .20  7/2  -.115  - 73 -  1  3/2  2  (b)  Three stage p r o c e s s e s  -  5/2  +.42  3/2  -.30  5/2  -.115  3/2  -.56  1/2  -.5  7/2  +.18  J  1  A  Sequence  -.27  (2) 3/2  + .6  3/2 (1) 5/2 (1) 3/2 (1) 3/2 3/2 (1) 5/2 (1) 5/2  ib  + .39 -.116  f o r a = .15  -.06  (2) 7/2 (1) 5/2 (1) 3/2  -.40  3/2 (2) 7/2 (1) 7/2  (2) 3/2  +1.0  3/2 (2> 7/2 (1) 5/2  <l>  3/2  A  4  .  3/2  f o r a - .1  3/2  2  x  2  3/2 (1) 5/2 (1) 5/2 (1) 3/2 3/2 (1) 5/2 (1) 7/2  ( l ) J (1 ) J  3/2  f o r a = .15  -.09  (3) 3/2 (1) 3/2 (1) 3/2  + .1  3/2 (3) 5/2 (1) 3/2 (1) 3/2  + .29  3/2 (3) 7/2 (2) 3/2 (1) 3/2  + .31  3/2 (3) 7/2 (1) 5/2 (1) 3/2  -.30  -.4  2  (1 ) J 3  3  -  74  A  Sequence 3/2  (3)  7/2  -  (1)  5/2  (\)  3/2  f o r a = .15 3/2  (3)  7/2  B.  (1)  7/2  2  (2)  3/2  -.07  '  +.07  +.4  P o r the t h r e e r e s o n a n c e s , v a r i o u s t h e o r e t i c a l  sequences which have v a l u e s of a n g u l a r d i s t r i b u t i o n comparable w i t h t h e e x p e r i m e n t a l v a l u e s of A  2  coefficients  , f o r each o f t h e  7 - r a y s , are t a b u l a t e d below.  (i)  960 Kev.  Resonance.  (a)  9 . 2 8 Mev  state.  (1)  9 . 2 8 Mev  7-ray  (2)  3/2"  (1)  5/2+  (1)  3/2"  A  2  3/2"  (1)  3/2+  (1)  3/2"  A  2  =  -.37  =  -.41  Experlmental A  7-ray  4 . 8 2 Mev 3/2"  (1)  5/2+  (1)  5/2"  A n  =  3/2"  (1)  3/2  (1)  3/2"  A  =  This evidently assignment (b)  Experimental A  5/2  6 . 7 6 Mev  +  2  f o r t h e 9 . 2 8 Mev  state.  level.  = -0.41 +  .04  2  = +O.56 +  .08  +.56  -.42  r u l e s out t h e second sequence. +  2  Hence the  - 75 (1)  (2)  2.52  Mev  7-ray  Experimental A  3/2- (1) 5/2+  (1) 3/2  A  2  =  -0.37  3/2  (1) 7/2  A  2  =  -0.33  6.76  (1) 5/2+ Mev  7-ray  Experimental A  3/2- (1) 5/2+  (1) 3/2 (1)3/2-  A  2  =  +0.4  -3/2- (1) 5/2+  (1) 7/2 (2) yz"  A  2  =  +0.6  Here a l s o the assignment 7/2  f o r 6.76  Mev  2  = -O.38  2  = +0.7  +  +  .04  .1  state i s quite  conclusive.  (c)  4.46  Mev  state.  4.46  Mev  7-ray  Experimental A  3/2 (1) 5/2 (1) 5/2 (1) 3/2 3/2 (1) 5/2 (1) 5/2 (\)  820  Kev.  (a)  9.19  Mev  level.  4.73  Mev  7-ray  +  .03  E x p e r i m e n t a l Ag = -0.26  +  .04  A  2  =  -0.27  A  2  =  -0.07  3/2  f o r a = 0.14  (ii)  = -0.07  2  Resonance.  3/2 (3) 7/2 (1) 5/2  A  2  »  3/2 (3) 3/2 (1) 5/2  A  2  = -0.115  3/2 (2) 7/2 (1) 5/2  A  2  =  The l a s t two  -0.29  -0.38  sequences g i v e v a l u e s of A  the e x p e r i m e n t a l e r r o r and so are r u l e d o u t . assignment 7/2  +  f o r the 9.19  Mev  level.  2  f a r outside  Hence the  -  (b)  6 . 7 6 Mev l e v e l .  (1)  2 . 4 3 Mev 7-ray  (2)  76 -  Experimental A  3/2  ( 3 ) 7/2 (1) 7/2  A  2  = +0.57  3/2  ( 2 ) 7/2 (1) 7/2  A  2  = +0.77  6 . 7 6 Mev 7-ray  Experimental A  3/2  ( 3 ) 7/2 (1) 7/2  3/2  ( 2 ) 7/2  (2)  g  = +0.6 + .1  g  = +0.37 + .04  3/2  A  2  = +0.4  A  4  = +.07  (1) 7/2 ( 2 ) 3 / 2  A  2  = +1.0  A  4  » -.4  The assignment f o r t h e 6 . 7 6 Mev l e v e l , o f 7/2, i s q u i t e " e v i d e n t from t h e s e c o m p a r i s o n s .  (c)  4.46 Mev s t a t e . 4.46 Mev 7 - r a y  Experimental A  3/2 (3) 7/2 (1) 5/2 (1) 3/2  A  2  = -0.3  A  2  = 0.07  0  = -.07 + .02  3/2 (3) 7/2 (1) 5/2 (|) 3/2 for a  2  = .14  ( i i i ) 400 Kev. Resonance, (a)  8.92 Mev s t a t e .  (1)  8.92 Mev 7-ray  E x p e r i m e n t a l A« = -0.25 + .1  3/2 (1) 5/2 (1) 3/2  A  2  = -0.37  3/2 (2) 5/2 (1) 3/2  A  2  = -0.22  3/2 (3) 5/2 (1) 3/2  A  2  = -0.3  APPENDIX I I I Energy L o s s o f a - P a r t l c l e s I n L i t h i u m .  The energy l o s s o f a charged p a r t i c l e o f mass M, charge Ze, v e l o c i t y v and energy E i s g i v e n by dE dx  =  e Z m v^  4TT  2  (1)  2  where m i s t h e e l e c t r o n mass, N i s t h e number o f s t o p p i n g atoms p e r c u b i c c e n t i m e t e r and B i s c a l l e d t h e " S t o p p i n g Number".  B l o c h (1933) h a s shown t h a t f o r an i o n v e l o c i t y v,  l a r g e compared t o t h e v e l o c i t y o f t h e atomic e l e c t r o n s i n the s t o p p i n g m a t e r i a l , B approaches t h e f o r m B = Z l n (2m v / I Z )  (2)  2  0  where I  0  i s an e m p i r i c a l c o n s t a n t , a measure o f t h e average  e x c i t a t i o n p o t e n t i a l o f t h e a b s o r b i n g atoms, and Z i s t h e atomic number o f t h e s t o p p i n g m a t e r i a l .  One c o u l d c a l c u l a t e  the energy l o s s f o r l o w energy a - p a r t i c l e s l n l i t h i u m by u s i n g t h e above e x p r e s s i o n .  However, t h e r e s u l t s so o b t a i n e d  are n o t v e r y a c c u r a t e a t low e n e r g i e s u n l e s s due account i s t a k e n o f t h e changes i n t h e e f f e c t i v e Z and I  Q  which r e s u l t  f r o m t h e e l e c t r o n c a p t u r e and l o s s by t h e a - p a r t i c l e s . Unfortunately, there i s not s u f f i c i e n t experimental data t o make these c o r r e c t i o n s a c c u r a t e l y .  However, i f one knows t h e  s t o p p i n g power as a f u n c t i o n o f energy f o r one m a t e r i a l , say a i r , one c a n f i n d i t f o r a n o t h e r m a t e r i a l by o b t a i n i n g f r o m experiments  t h e r a t i o o f t h e s t o p p i n g number f o r t h e two  - 77 *  - 78 m a t e r i a l s a t some energy.  Bethe (1937) h a s shown t h a t  t h i s r a t i o s h o u l d be independent o f energy.  Thus we c a n  write 8  %<i / A i r " constant  53  B  where s i s t h e " s t o p p i n g p o w e r target material. M dx N  r e l a t i v e t o a i r f o r the  0  Thus  (Lithium) .  I ix s x M NAir dx  (  A i r  (3)  )  A i r * 5 . 2 8 x 10-*-9 atoms p e r c u b i c c e n t i m e t e r .  NJ s  J1  = 4.64 x 1 0  2 2  atoms p e r c u b i c c e n t i m e t e r .  «• 0 . 5 2 f o r l i t h i u m - Average o f ( J e i g e r ' s and Mano's v a l u e s a s quoted by Bethe ( 1 9 3 7 , P« 7 2 ) . 2  The v a l u e s o f dE ( A i r ) were t a k e n f r o m Bethe ( 1 9 5 0 ) . dx The v a l u e s c a l c u l a t e d by e q u a t i o n ( 3 ) o f dB i n dx l i t h i u m f o r a - p a r t i c l e s are: dE ax  E,a 0.400  Mev  1.04  x  ev./om.  0.820  Mev  1.09  x 10-  ev./em.  0.960  Mev  1.11  x 109  ev./cm.  109  As a check on these v a l u e s t h e p r o c e d u r e by Whaling (1958) t o determine where £ - - 1 N  the stopping cross  outlined section^  dE/dx i n u n i t s o f ev.-cm , i n any m a t e r i a l was 2  P i g . 18  S t o p p i n g power v s . a - p a r t i c l e energy  - 79 He computed the r a t i o £ /6p, f o r a - p a r t l c l e s  a l s o used.  a  and p r o t o n s o f the same v e l o c i t y , f r o m a l l the known experimental values.  Assuming t h a t t h e r a t i o £ /£p i s a a  f u n c t i o n o f i o n v e l o c i t y a l o n e , the e x p e r i m e n t a l r a t i o s f o r a l l s t o p p i n g m a t e r i a l s were averaged t o o b t a i n the average U s i n g these r a t i o s , t h e s t o p p i n g c r o s s sections £  a  i n l i t h i u m , h e l i u m and hydrogen were e s t i m a t e d  f r o m the known v a l u e o f £  p  i n these m a t e r i a l s and are p l o t t e d  i n P i g . 18 as a f u n c t i o n o f a - p a r t i c l e energy. v a l u e s (Weyl, 1953)  Experimental  o f s t o p p i n g c r o s s s e c t i o n f o r low energy  a - p a r t i c l e s i n He and H i n the energy range from 150 kev. t o 400 kev. a r e a l s o p l o t t e d .  On the b a s i s o f the d i f f e r e n c e a t  low e n e r g i e s i n the e x p e r i m e n t a l c u r v e and the c u r v e  obtained  f r o m the p r o t o n d a t a , t h e shape o f the l i t h i u m c u r v e was m o d i f i e d f r o m the shape o b t a i n e d u s i n g the p r o t o n d a t a so t h a t i t corresponded  more c l o s e l y t o the shape o f the e x -  p e r i m e n t a l c u r v e s a t l o w e n e r g i e s f o r H and He. The e r r o r I n the v a l u e s t a k e n f r o m the c o r r e c t e d l i t h i u m c u r v e were e s t i m a t e d t o be + 10$.  The p r o b a b l e e r r o r i n Weyl's r e s u l t s i s quoted  t o be + 5#. U s i n g the s t o p p i n g c r o s s s e c t i o n o f a - p a r t i c l e s  E  dE die  a  0.400 Mev  0.93  x 10^ ev./cm.  0.820 Mev  1.02  x 10^ ev./cm.  0.960 Mev  1.00  x l O ^ ev./cm.  - 80 The two methods gave v a l u e s o f t h e s t o p p i n g power w i t h i n b e t t e r t h a n 10$ o f each o t h e r .  The v a l u e s o b t a i n e d f r o m  the second method were used t o f i n d the a b s o l u t e t h i c k target y i e l d described i n chapter I I I .  APPENDIX I V E f f i c i e n c y of Nal Crystals. S i n c e s c i n t i l l a t i o n c o u n t e r s are now so e x t e n s i v e l y used f o r 7-ray s t u d i e s ,  a c c u r a t e knowledge c o n c e r n i n g t h e i r  7-ray d e t e c t i o n e f f i c i e n c i e s i s v e r y d e s i r a b l e .  Many a t t e m p t s  t o c a l c u l a t e the e f f i c i e n c i e s o f N a l c r y s t a l s by m o n t e - c a r l o methods have been made ( B e r g e r e t a l . , 1956 1957).  and M i l l e r e t a l . ,  T h i s method i n v o l v e s e x t e n s i v e c o m p u t a t i o n s  t h e u s e o f e l e c t r o n i c computers.  requiring  I t was d e c i d e d t o develop  a s e m i - e m p i r i c a l method f o r c a l c u l a t i n g the e f f i c i e n c y o f N a l c r y s t a l s o f any s i z e o r shape f o r 7-rays i n the range 0.5 t o 12 Mev and t o check the method e x p e r i m e n t a l l y by det e r m i n i n g the a b s o l u t e e f f i c i e n c i e s w i t h known f l u x e s o f 7-rays o f s e v e r a l e n e r g i e s .  I n any e x p e r i m e n t a l arrangement  t h e d i s t o r t i o n o f t h e spectrum by s c a t t e r i n g and g e o m e t r i c a l d e t a i l s can cause e f f e c t s o f the o r d e r o f 10$ o r more, c o n s e q u e n t l y i t i s i m p o r t a n t t o have some a c c u r a t e e x p e r i m e n t a l c h e c k s on the d e t e c t i o n e f f i c i e n c y .  F u r t h e r , i f these a b s o l u t e  e f f i c i e n c i e s are a v a i l a b l e somewhat l e s s 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 are v e r y u s e f u l f o r making i n t e r p o l a t i o n s between the e x p e r i m e n t a l  (i)  points.  Gamma Ray A b s o r p t i o n and P u l s e H e i g h t D i s t r i b u t i o n . Gamma r a y s i n t e r a c t w i t h m a t t e r by t h r e e p r o c e s s e s ,  cornpton s c a t t e r i n g , p h o t o e l e c t r i c g r e a t e r t h a n 1.02 Mev,  a b s o r p t i o n and, when E  by the p a i r p r o d u c t i o n p r o c e s s .  - 81 -  7  is  Below  - 82  -  0.3 Mev t h e p h o t o e l e c t r i c p r o c e s s p r e d o m i n a t e s i n N a l , above t h i s t o about 7 Mev  the compton s c a t t e r i n g a c c o u n t s f o r t h e  majior p a r t o f t h e a b s o r p t i o n and above t h i s p a i r  becomes predominant.  production  Each of t h e s e p r o c e s s e s I m p a r t s , a  c e r t a i n amount of t h e 7 - r a y energy t o t h e e l e c t r o n s , f r o m t h e phosphor w i t h an energy d i s t r i b u t i o n of the process i n v o l v e d .  released  characteristic  The e l e c t r o n energy d i s t r i b u t i o n i s  r e p r o d u c e d i n t h e p u l s e h e i g h t spectrum from t h e p h o t o m u l t i p l i e r . C o n s i d e r i n g o n l y the primary i n t e r a c t i o n s , p h o t o e l e c t r i c results i n a  line  energy, E ^ j  effect  spectrum c o r r e s p o n d i n g t o the f u l l 7-ray,  t h e p a i r p r o d u c t i o n p r o c e s s g i v e s a second l i n e  c o r r e s p o n d i n g t o an energy r e l e a s e o f E -2mc 7  2  i n t h e phosphor;  t h e compton s c a t t e r e d e l e c t r o n s have a b r o a d d i s t r i b u t i o n , w i t h a c u t - o f f a t about E -0.25 Mev, y  I f . Hi. dT mc2  1 [ ;g <?f l ( T - T m a x ) B T  +  2 a  2  2  +  which i s g i v e n by: a^lw-  2T )1 a-Tmax J m f l y  ( 1 )  where, dS" •^r = t h e number o f compton e l e c t r o n s p e r t a r g e t e l e c t r o n p e r Mev w i t h e n e r g i e s between T and T + 2Q! T  max ~ l+'^o*  t h e  Maximum energy of t h e compton e l e c t r o n  i n u n i t s of mc mc  r  0  2  dT.  2  2  » 0.5108  = 2.818  Mev  x Iff  1 3  cm.  mc . 2  '  - 83 The  primary  spectrum i s broadened a s a r e s u l t o f  s t a t i s t i c a l f l u c t u a t i o n s i n the number o f p h o t o e l e c t r o n s produced i n the p h o t o m u l t i p l i e r and by the n o n - u n i f o r m i t i e s i n t h e l i g h t p r o d u c t i o n and c o l l e c t i o n .  Further;, t h e spectrum  shape i s c o n s i d e r a b l y m o d i f i e d by secondary a b s o r p t i o n  processes  i n the c r y s t a l and escape o f e l e c t r o n s and secondary q u a n t a f r o m the w a l l s o f the c r y s t a l ( G r i f f i t h s , 1955).  To compute  •the p u l s e h e i g h t d i s t r i b u t i o n produced by y - r a y s i n N a l a f t e r t a k i n g a l l the above f a c t o r s i n t o account, tedious process.  crystals,  would be a  However, one can do t h i s e f f e c t i v e l y by a  m o n t e - c a r l o method.  I n p r a c t i c e , however, one i s more I n t e r e s t e d  i n o b t a i n i n g the 7-ray d e t e c t i o n e f f i c i e n c y l n terms o f t h e number o f c o u n t s above a g i v e n b i a s r a t h e r t h a n i n v e r y knowledge o f the spectrum shape.  detailed  The p r o b l e m o f d e t e r m i n i n g  the e f f i c i e n c y above a g i v e n b i a s i s d i s c u s s e d below.  (ii)  Gamma Ray E f f i c i e n c y - T h e o r e t i c a l . Let N  be the number o f gamma r a y s o f energy Hy which  Q  are i n c i d e n t on the f a c e o f a N a l c r y s t a l o f l e n g t h L . n  w  The  t o t a l number o f 7 - r a y s w h i c h i n t e r a c t i n the c r y s t a l i s g i v e n by tyt =  N  0  (1  -  e"^ ) L  - N T + I ^  +  NO-,  where^c,T , ST and ir are the t o t a l , p h o t o e l e c t r i c , cornpton and p a i r p r o d u c t i o n a b s o r p t i o n c o e f f i c i e n t s i n N a l r e s p e c t i v e l y and N^,  Ny* and N$- are the c o u n t s produced by the t h r e e  processes  separately.  interaction  I n p r a c t i c e we count o n l y the  above a d e f i n i t e b i a s , say 1/2 E . 7  pulses  Obviously not a l l i n t e r -  FIG,  19  (a)  Sections  Of The  Crystal  - 84 a c t i o n s w i l l l e a d t o s u f f i c i e n t energy r e l e a s e i n t h e c r y s t a l t o produce p u l s e s g r e a t e r t h a n t h e b i a s chosen. C o n s i d e r t h e t h e o r e t i c a l compton e l e c t r o n energy spectrum (Eq. 1, P i g . 19b) and d e s i g n a t e i n t h e spectrum above t h e b i a s as %  t h e number o f c o u n t s  i and t h a t below l t as  N^g, t h e n t h e t o t a l number o f c o u n t s i n t h e compton d i s t r i b u t i o n i s N(jp =  + Ng-g'  Du  g  t o  t n e  absorption  o f t h e secondary  compton photons, some o f the c o u n t s , below t h e s e l e c t e d b i a s , i n t h e p r i m a r y t h e o r e t i c a l d i s t r i b u t i o n w i l l be s h i f t e d L e t a f r a c t i o n "K" o f Ngg be s h i f t e d up.  above.  A l s o due t o t h e  escape o f e l e c t r o n s f r o m t h e s i d e s and t h e f r o n t end o f the c r y s t a l and due t o t h e l o s s o f b r e m s s t r a h l u n g produced by t h e e l e c t r o n s o f h i g h energy, some c o u n t s from t h e upper end w i l l be s h i f t e d down. below be "m".  L e t t h e f r a c t i o n o f H i which i s s h i f t e d  The t o t a l number o f c o u n t s e x p e c t e d above t h e  b i a s due t o t h e compton e v e n t s o n l y i s Nffi = since f o r a given  + KNg-g -  mN^  bias  constant, c a l l y , and  N6"  we c a n w r i t e  which c a n be c a l c u l a t e d t h e o r e t i -  - 85 N«i = dN<r + K (1 - d) % = N^. d T l + K (  1  - mdN^-  -, ) - ml d  a  u  = Ng.xb  J  (2)  where b = d T l + K (  " ) - ml d  1  d  u  J  S i m i l a r l y a c e r t a i n f r a c t i o n 'a' o f t h e t o t a l photoe l e c t r i c e v e n t s , N , and a f r a c t i o n 'c' o f t h e p a i r e v e n t s , N , T  T  w i l l produce p u l s e s above t h e c o u n t i n g b i a s .  Therefore, the  t o t a l number o f c o u n t s , N^, e x p e c t e d above t h e b i a s i s , N^. = Ny» + N^- + N^ aNy» + bN^- + GN^ ^ • [ ^ a r + bS-+ oir] = N  0  (  1  -  e  -  ej '  )jaT + b«r +  cirj  (3)  /*• The 7 - r a y d e t e c t i o n e f f i c i e n c y above a c e r t a i n b i a s , b, i s d e f i n e d as £, h  Prom e q u a t i o n  _ N/>.(1 - e^  ) CaT + b g +  ~ No"  A  L  fori  (4) i t I s e v i d e n t t h a t by e s t i m a t i n g a, b and c  one cart c a l c u l a t e the e f f i c i e n c y above a c e r t a i n b i a s f o r a g i v e n c r y s t a l s i z e u s i n g t h e t h e o r e t i c a l v a l u e s o f T , 6 ™ and i r . The e f f i c i e n c i e s have been c a l c u l a t e d equal t o h a l f the 7 - r a y energy.  f o r a bias  T h i s b i a s was chosen because  - 86 t h e 7 - r a y s p e c t r a a r e g e n e r a l l y l o w and f l a t i n t h i s r e g i o n and. t h e r e i s r e l a t i v e l y l i t t l e due  c o n t r i b u t i o n above t h i s b i a s  t o photons s c a t t e r e d i n t o t h e c r y s t a l f r o m t h e s h i e l d i  and  surroundings.  A l s o f o r those c a s e s where t h e p a i r  p r o d u c t i o n c r o s s s e c t i o n i s s i g n i f i c a n t compared t o t h e comptqn c r o s s s e c t i o n (above 2 Mev),  t h i s b i a s i s below  E -2mc , so t h a t one does n o t have t o c o n s i d e r t h e t r a n s f e r y  o f p u l s e s among t h e t h r e e p a i r peaks due t o t h e a b s o r p t i o n of a n n i h i l a t i o n quanta.  The e f f i c i e n c y f o r any o t h e r b i a s  can be c a l c u l a t e d e m p i r i c a l l y f r o m t h e e x p e r i m e n t a l  7-ray  spectra with the f o l l o w i n g r e l a t i o n  (D (iii)  _ r 1  . /  x  2  c o u n t s above b i a s b c o u n t s above 1/2E b i a s  (5)  7  P r o c e d u r e F o r C a l c u l a t i n g 'a', 'b' and ' c . f  The  f o l l o w i n g s i m p l i f y i n g a s s u m p t i o n s were made i n  the e s t i m a t i o n o f t h e f r a c t i o n s a, b and c.  First,  only  p r i m a r y and secondary a b s o r p t i o n p r o c e s s e s were c o n s i d e r e d so t h a t i f a compton photon i n t e r a c t e d i n t h e c r y s t a l i t was assumed t o be absorbed c o m p l e t e l y .  Second, t h e energy l o s s  r e s u l t i n g f r o m t h e escape o f t h e b r e m s s t r a h l u n g  radiations  produced by t h e h i g h energy e l e c t r o n s was n e g l e c t e d . s h o u l d be a r e a s o n a b l e  approximation  This  because 12 Mev e l e c t r o n s  i n N a l l o s e o n l y about 25$ o f t h e i r energy i n t h e f o r m o f bremsstrahlung absorbed.  quanta and most o f t h e s e a r e s o f t and r e a d i l y  - 87  (1)  -  Correction to the P h o t o e l e c t r i c Absorption C o e f f i c i e n t . At e n e r g i e s  absorption  g r e a t e r t h a n about 1 Mev t h e p h o t o e l e c t r i c  c o e f f i c i e n t , T , i s so s m a l l compared t o t h e t o t a l  absorption c o e f f i c i e n t , ^ , that f o r higher energies assumed t o be u n i t y . due  Por energies  t o the l o s s of photoelectrons  'a' was  below 1 Mev, c o r r e c t i o n s f r o m t h e w a l l s and t h e f r o n t  f a c e o f t h e c r y s t a l were made i n t h e same manner a s d e s c r i b e d below f o r t h e p a i r e l e c t r o n s .  (2)  C o r r e c t i o n t o the P a i r Production  Absorption C o e f f i c i e n t .  A c o r r e c t i o n f o r t h e escape o f p a i r e l e c t r o n s f r o m t h e end and w a l l s o f t h e c r y s t a l was a p p l i e d by r e j e c t i n g a l l t h o s e e v e n t s which o c c u r r e d  s u f f i c i e n t l y close to the  s u r f a c e s t h a t t h e p a i r e l e c t r o n s escaped l e a v i n g an energy l e s s t h a n E^/2 i n t h e c r y s t a l .  T h i s c o r r e c t i o n amounted t o  5$ o f t h e t o t a l p a i r a b s o r p t i o n  f o r 6 Mev 7 - r a y s i n t h e  3.5 i n c h l o n g by 2.5 i n c h d i a m e t e r c r y s t a l .  The  stopping  power f o r e l e c t r o n s i n N a l , r e q u i r e d f o r t h e s e c a l c u l a t i o n s , was o b t a i n e d  (3)  f r o m t h e f o r m u l a e g i v e n by H e i t l e r (1954).  C o r r e c t i o n t o the Cornpton A b s o r p t i o n C o e f f i c i e n t . The  l o s s o f cornpton e l e c t r o n s f r o m t h e w a l l s and  the-end was c o n s i d e r e d electrons.  i n t h e same f a s h i o n a s f o r t h e p a i r  This c o r r e c t i o n r e f e r s t o the f r a c t i o n m i n  e q u a t i o n (2) and was about 5# f o r 6 Mev  7-rays.  - 88 The c o r r e c t i o n due t o t h e a b s o r p t i o n o f secondary photons was c a l c u l a t e d as f o l l o w s .  The c r y s t a l was d i v i d e d  i n t o t h r e e c o n c e n t r i c c y l i n d r i c a l r i n g s , A, B and C, o f e q u a l c r o s s s e c t i o n a l a r e a and i n t o 4 l e n g t h w i s e III  and I V , o f e q u a l l e n g t h .  s e c t i o n s , I,  II,  P i g . 19a shows t h e s e d i v i s i o n s  i n a plane s e c t i o n of the c r y s t a l .  The p a r t o f the compton  e l e c t r o n energy d i s t r i b u t i o n f u n c t i o n , P i g . 19b>  'Which i s  below t h e h a l f energy b i a s was d i v i d e d i n t o f o u r p a r t s , D, E , P and G, such t h a t t h e a r e a i n each p a r t i s t h e same. A l l t h e e l e c t r o n s i n each p a r t were c o n s i d e r e d  t o have an  energy (T^, T E , Tp, T Q ) e q u a l t o t h e average energy f o r t h e group.  A l l t h e compton photons c o r r e s p o n d i n g  e l e c t r o n s i n a p a r t were c o n s i d e r e d  t o t h e compton  t o have an energy  ( E , Eg, Ep, E Q ) e q u a l t o t h e d i f f e r e n c e between t h e i n c i d e n t n  photon energy and the average energy of t h e compton e l e c t r o n s In that part.  The a n g l e s a t which t h e s e compton photons a r e  s c a t t e r e d a r e g i v e n by cos 9 = where,  1  +  q  a  - A Hz. f o r p a r t D o f t h e spectrum, a Ejj  a «=> E^/mc and E 2  D  i s t h e average compton photon  energy c o r r e s p o n d i n g To e s t i m a t e  to part  D.  t h e secondary I n t e r a c t i o n s o f t h e  compton photons i n the c r y s t a l i t was assumed t h a t a l l t h e compton I n t e r a c t i o n s o f t h e i n c i d e n t r - r a y s i n a p a r t i c u l a r subsection take place at the centre of the subsection.  Since  the i n c i d e n t photon, t h e compton s c a t t e r e d photon and t h e  -  89  -  c o r r e s p o n d i n g e l e c t r o n are i n the same p l a n e , from the knowledge o f the s c a t t e r i n g a n g l e s o f the cornpton photons, the p a t h l e n g t h , x, o f t h e s e photons i n the c r y s t a l were geometrically obtained.  F o r t h e c e n t r a l r i n g a l l the p l a n e s  through the a x i s are t h e same, but f o r the o u t e r two  rings,  the v a r i o u s p l a n e s making d i f f e r e n t a n g l e s w i t h the v e r t i c a l p l a n e , ab ( F i g . 1 9 a ) ,  have d i f f e r e n t d i m e n s i o n s and c o n t a i n  a d i f f e r e n t d i s t r i b u t i o n of p a t h l e n g t h s .  To take t h i s  e f f e c t i n t o c o n s i d e r a t i o n , f o r the r i n g s B and C, t h e p a t h l e n g t h s i n the p l a n e s a t 0 ° ,  30*,  60° and 90° .to the v e r t i c a l  were c a l c u l a t e d and an average p a t h l e n g t h was determined f o r  -  each.of the f o u r average photon e n e r g i e s c o r r e s p o n d i n g t o t h e 4 p a r t s o f t h e cornpton t a i l .  U s i n g the known 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 , ^ , f o r each o f the average  cornpton  photon e n e r g i e s , the f r a c t i o n "k" o f the photons from  each  p a r t o f t h e spectrum which f u r t h e r i n t e r a c t i n t h e c r y s t a l was determined from the s i m p l e r e l a t i o n k = (1 - e  )  These f r a c t i o n s were c a l c u l a t e d f o r each o f the 12 s u b s e c t i o n s and then an average f r a c t i o n (kj, k-j-j, k j n  and kjy)  was  d e t e r m i n e d f o r each o f the f o u r s e c t i o n s ( I , I I , I I I and I V ) . These f r a c t i o n s were t h e n n o r m a l i z e d t o the number o f p r i m a r y cornpton i n t e r a c t i o n s i n each s e c t i o n , and a f i n a l f r a c t i o n K o f t h e cornpton photons which f u r t h e r i n t e r a c t e d i n the c r y s t a l was d e t e r m i n e d .  Thus knowing m, k and d the t o t a l f r a c t i o n b  -  90  -  can be d e t e r m i n e d from t h e e q u a t i o n ( 2 ) . Prom t h e e s t i m a t e d v a l u e s o f ' a ' , b* and 'c», \ 1  the  known v a l u e s o f ir, «r, T and /* and t h e d i m e n s i o n s o f  the  c r y s t a l , the e f f i c i e n c y of N a l c r y s t a l s f o r counts  above t h e h a l f energy b i a s , €i/2>  w  a  determined u s i n g  a  equation (5).  the  (iv)  Gamma Ray E f f i c i e n c i e s - E x p e r i m e n t a l . The y - r a y e f f i c i e n c i e s o f t h e N a l c r y s t a l were  e x p e r i m e n t a l l y d e t e r m i n e d a t 0 . 5 1 Mev and 1.25 Mev by u s i n g Na  2 2  and Co^° s o u r c e s , which were c a l i b r a t e d i n d e p e n d e n t l y  as d e s c r i b e d below, and a l s o a t 6.14 Mev by u s i n g t h e reaction P ^ 1  ( , a y). O ^. 1  p  I n t h e l a s t case a b s o l u t e  c a l i b r a t i o n was o b t a i n e d by t h e s i m u l t a n e o u s c o u n t i n g o f a - p a r t i c l e s by a p r o p o r t i o n a l c o u n t e r (see L a r s o n , 1957) and 7 - r a y s by t h e s c i n t i l l a t i o n c r y s t a l s .  Relative  efficiencies  were d e t e r m i n e d a t 4 Mev and 12 Mev by o b t a i n i n g 4 Mev and 12 Mev 7 - r a y s f r o m t h e r e a c t i o n B the  1 1  (p, 7) C . 1 2  To o b t a i n  e f f i c i e n c y a t 12 Mev, t h e f l u x o f t h e s e 7 - r a y s was  d e t e r m i n e d by t a k i n g t h e e f f i c i e n c y a t 4 Mev from t h e a p p r o p r i a t e e f f i c i e n c y c u r v e ( P i g . 21) and assuming a one t o one r a t i o o f 4 t o 12 Mev 7 - r a y s f r o m t h e above r e a c t i o n .  (1)  C a l i b r a t i o n o f Co*  30  Sources.  The a b s o l u t e 7-ray f l u x f r o m a weak Co^° source  - 91 ( r e f e r r e d t o as C o "  # l ) was  0  coincidence technique  d e t e r m i n e d by means of  (Siegbahn,  c o i n c i d e n c e system (Jones, 58,  1955)  59).  standard  using a fast  slow  T h i s system c o n v e r t s  t i m e d e l a y spectrum i n t o a p u l s e a m p l i t u d e i n t r i n s i c time r e s o l u t i o n o f 5 x IO"*  11  spectrum w i t h  sec.  a an  This "time-sorter"  method p o s s e s s e s s e v e r a l advantages o v e r the d i r e c t  coincidence  method i n which the p u l s e s f r o m the two c o u n t e r s are f e d i n t o a coincidence a scaler.  c i r c u i t and the output p u l s e s are r e c o r d e d  The most i m p o r t a n t  advantage i s t h a t one  by  obtains a  complete p u l s e h e i g h t spectrum i n w h i c h the f l a t l e v e l on e i t h e r s i d e of the prompt peak c o r r e s p o n d s  t o the c o u n t s  due  t o random c o i n c i d e n c e s , o b s e r v e d s i m u l t a n e o u s l y w i t h the t r u e c o i n c i d e n c e s as shown i n P i g . 20.  Therefore,  one can make the  random c o i n c i d e n c e c o r r e c t i o n by i n t e r p o l a t i n g the f l a t l e v e l under the peak.  A l s o the measurements t a k e n w i t h t h i s  arrange-  ment are l e s s s e n s i t i v e t o g a i n s h i f t s because one can see e f f e c t o f such changes i n b r o a d e n i n g  o f the peak and  so  the  can  c o r r e c t f o r such changes. I f N i s the number o f d i s i n t e g r a t i o n s p e r s e c . f r o m t h e source p l a c e d between the two d e t e c t o r s , t h e n the number o f p u l s e s produced "in the two c o u n t e r s , N^ and Ng, N  x  N  2  »  2 N  - 2 N  where £^ and £g  a r e  ^' W 1  «  2  ,  W  1  2  per  sec.  per  sec.  are  (6)  t h e e f f i c i e n c i e s o f the two c o u n t e r s f o r  d e t e c t i n g 7 - r a y s and 0 ^ and  a r e the s o l i d a n g l e s  subtended  - 92 by the counters at the source and the f a c t o r 2 accounts f o r the f a c t that there are two 7-rays of almost the same energy f o r each d i s i n t e g r a t i o n of Co^°. Since both the 7-rays are so nearly the same,in energy (1.333 and 1.173 Mev) i t was assumed that the counter e f f i c i e n c i e s were the same f o r both 7-rays.  The coincidence counting rate, N, H  where  i s then given by  C  = 2 N  c  CjJ 2  l **2 (  ()  P  P (6) =.B C (1 + A c o s  P  0  2  ER  S E C  -  (7)  0 ) , and B Is the f a c t o r !  which takes into account the f i n i t e s o l i d angle of the .  \ \  counters, (1 + A c o s  1  9) i s the angular c o r r e l a t i o n function  2  f o r the two 7-rays, and C i s the normalizing constant such that. JG  (1 + A c o s  which gives  C = ^  2  1  6) dw  +  A  /  j  = 1  )  From (6) and (7) we get N  »  NT  (0.)  N  P  (0)  2 N (0)  c  B  (1  +  A  c o a  fl)  2  (8)  c  Equation (8) can be used to f i n d N from the knowledge of the other f a c t o r s .  Measurements were taken with 90° and 180°  between the counters i n order to determine a value f o r the parameter A.  From (8) we can write  A * N N  c  C  (180) NX (90) N2 (90) B. (90) _ (90) NX (180) N (180) B (180) 2  x  - 93 From 12 measurements made w i t h a n g u l a r s e p a r a t i o n s o f 90° and 180° between t h e c o u n t e r s an average v a l u e o f A = O.I67 +_ 0.003 was d e t e r m i n e d .  T h i s agrees very w e l l w i t h  the e x p e r i m e n t a l v a l u e , A = -.167 + 0.001 o f S t e f f e n ( a s r e p o r t e d by Siegbahn,  1955, p. 553) and w i t h t h e t h e o r e t i c a l  v a l u e o f A = O.1667.  A v a l u e O . I 6 7 was used f o r A i n t h e  f o l l o w i n g work. The  c o u n t s observed  by each d e t e c t o r ,  were c o r r e c t e d f o r combined dead time o f t h e s i d e and t h e s c a l i n g u n i t s w h i l e t h e observed  and Ng, channels  coincidence  counts  were c o r r e c t e d f o r l o s s e s l n t h e f a s t and slow c o i n c i d e n c e circuits. t o 0.5$.  These c o r r e c t i o n s were a l w a y s l e s s t h a n o r e q u a l The c o u n t e r s o l i d a n g l e c o r r e c t i o n f a c t o r B was  e v a l u a t e d by making a g r a p h i c a l average o v e r t h e known a n g u l a r c o r r e l a t i o n f u n c t i o n f o r t h e two a n g u l a r s e p a r a t i o n s and amounted t o a + 0.3$ c o r r e c t i o n a t 90° and a - 0.7$ c o r r e c t i o n a t 180°. A f t e r having a p p l i e d the v a r i o u s c o r r e c t i o n s to the observed  q u a n t i t i e s , t h e v a l u e o f N was c a l c u l a t e d u s i n g  equation (8).  The average o f 12 measurements, each one  i n v o l v i n g about 40 m i l l i o n s i n g l e c h a n n e l c o u n t s and about 20 thousand c o i n c i d e n t c o u n t s , gave a v a l u e o f N = 876.9 x 10^ o r a source  d i s i n t e g r a t i o n s per sec.  s t r e n g t h o f 0.0237 + 0.0006 mc on 22nd A p r i l , 1958.  - 94  -  The e r r o r s t a t e d I s the r o o t mean square e r r o r from the 12  separate runs.  The  s t r e n g t h o b t a i n e d compares v e r y w e l l  w i t h the NiR.C. c a l i b r a t i o n o f t h i s s o u r c e .  This calibration  was done by s c i n t i l l a t i o n c o u n t e r comparison of t h i s (Co  6 0  #1) w i t h a C o  source  source of about 1 mc," (#3) which had been  6 0  p r e v i o u s l y compared w i t h the Canadian radium s t a n d a r d by i o n i z a t i o n chamber measurements (N.R.C. c e r t i f i c a t e No C-121). These measurements i n d i c a t e d a s t r e n g t h f o r Co^° #1 o f +_ 0.002 mr/hr. a t 1 meter on 25th A p r i l , t h i s t o d i s i n t e g r a t i o n r a t e at 1.33 1 mc of Co^°  1956.  0.041  Converting  mr/hr. a t 1 meter f o r  g i v e s a source s t r e n g t h of 0 . 0 3 0 8 + 0 . 0 0 1 5  C o r r e c t i n g f o r the decay, the s t r e n g t h on 22nd A p r i l , becomes 0.0236 + 0.0010 mc,  mc.  1958,  which i s i n e x c e l l e n t agreement  w i t h t h e s t r e n g t h o b t a i n e d above I n d e p e n d e n t l y .  (2)  C a l i b r a t i o n of N a  Source.  2 2  The f l u x of 0.51  Mev  quanta f r o m a N a  2 2  source  was d e t e r m i n e d by s c i n t i l l a t i o n c o u n t e r comparison w i t h the Co^° #1 s o u r c e . w i t h 0.51  Mev  Since N a  2 2  g i v e s out 1.28  Mev  7-rays along  quanta, produced by the decay o f t h e p o s i t r o n s  l n the h o l d e r , 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 c o v e r i n g an energy range o f 0.2 Mev geometry, f o r a N a  2 2  to 1.5  Mev were t a k e n , under i d e n t i c a l  source and f o r t h e c a l i b r a t e d Co^°  S i n c e the mean e n e r g i e s of t h e 7 - r a y s from the Co^°  source.  and the  2.9  h i g h energy 7 - r a y from Na  u  are almost e x a c t l y the same, i t  was assumed t h a t the e f f i c i e n c y o f the N a l f o r t h e s e 7 - r a y s i s t h e same.  By comparing  the c o u n t s above the h a l f energy  bias  - 95 i n t h e 1.28 Mev 7-ray spectrum f r o m N a 1.28 Mev 7-ray f l u x was d e t e r m i n e d . scheme o f N a  Ne  2 2  2 2  2 2  and from Co^°, t h e  Prom t h e known decay  (90$ (3+ and 10$ e l e c t r o n c a p t u r e  b o t h t o t h e 1.28 Mev s t a t e i n N e  2 2  - A j z e n b e r g and L a u r i t s e n ,  1959) and t h e f a c t t h a t each p o s i t r o n p r o d u c e s two a n n i h i l a t i o n quanta, the f l u x o f t h e 0.51 Mev 7 - r a y s f r o m t h e Na determined  was  absolutely. The e x p e r i m e n t a l e f f i c i e n c y , £1/%,  k 1/2  -  4 7 r  r 2  i s d e f i n e d as  N s  A N  Where Ns i s t h e number o f c o u n t s o b s e r v e d above t h e h a l f energy b i a s i n a c e r t a i n time t , N i s t h e number o f 7 - r a y s e m i t t e d by t h e source i n t h e same t i m e , r i s the d i s t a n c e f r o m t h e source 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 r y s t a l and A I s the area of the f r o n t f a c e of the N a l c r y s t a l .  The  e f f e c t i v e c e n t r e I s t a k e n as t h a t p o i n t i n the c r y s t a l  from  which measurements o f source t o c r y s t a l d i s t a n c e a r e made i n o r d e r t o :give an i n v e r s e square r e l a t i o n between c o u n t i n g r a t e and d i s t a n c e .  (V)  RESULTS The e x p e r i m e n t a l and t h e o r e t i c a l e f f i c i e n c i e s at  h a l f energy b i a s f o r 7 - r a y e n e r g i e s i n t h e range o f 0.5 t o 12 Mev a r e shown i n P i g . 21. p o i n t s a r e a l s o shown.  Mev  The e r r o r s i n the e x p e r i m e n t a l  The agreement between the t h e o r y and  t h e e x p e r i m e n t s i s q u i t e good.  Not o n l y does t h e t h e o r y g i v e  t h e e f f i c i e n c y as a f u n c t i o n o f energy i n good agreement w i t h  - 96 -  t h e shape o f t h e e x p e r i m e n t a l curve but a l s o t h e a b s o l u t e v a l u e s have agreed to, b e t t e r t h a n 10$ i n a l l c a s e s c a l c u l a t e d . 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