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UBC Theses and Dissertations

The production of neutron beams using the associated particle technique Tripard, Gerald Edward 1964

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THE PRODUCTION OF ]mJTR0N BEAMS USING THE ;  ASSOCIATED PARTICLE TECHNIQUE  by  GERALD EDWARD TRIPARD B So., University of B r i t i s h Columbia, 1962 0  A THESIS SUBMITTED IN PARTIAL FULFILMENT | F THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October* 1964  In the  presenting  r e q u i r e m e n t s f o r an a d v a n c e d  British  Columbia, I agree that  available mission  f o r reference  f o r extensive  representatives.  cation  w i t h o u t my w r i t t e n  . Department  of  SEPT  the L i b r a r y  and study-.  shall  I further  make i t f r e e l y  agree' t h a t  rJJy%/C-£. Columbia,  o r by  t h a t / c o p y i n g or p u b l i -  f o r f i n a n c i a l gain  permission*  per-  f o r scholarly-  by the Head o f my Department  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada Date  fulfilment of.  degree a t the U n i v e r s i t y o f  I t i s understood  of t h i s thesis  i n partial  copying of t h i s thesis  p u r p o s e s may be g r a n t e d his  this thesis  shall  n o t be a l l o w e d  ii  ABSTRACT A c c u r a t e l y o o l l i m a t e d monoenergetic f a s t n e u t r o n beams o f s m a l l a n g u l a r w i d t h were produced by bombarding heavy i c e t a r g e t s w i t h d e u t e r o n s , and o p e r a t i n g the n e u t r o n d e t e c t o r i n c o i n c i d e n c e w i t h a s e m i c o n d u c t o r d e t e c t o r d e t e c t i n g t h e He^ r e c o i l n u c l e i * U s i n g a bombarding  energy o f  " 50 i e ? a n e u t r o n beam o f energy  2,55 MeV and known a b s o l u t e i n t e n s i t y was p r o d u c e d . beam p r o f i l e agreed w i t h t h e t h e o r e t i c a l l y  The measured  calculated  profile.  beam was used t o measure the a b s o l u t e n e u t r o n d e t e c t i o n  The  efficiency  and the p u l s e spectrum o f a p l a s t i c s c i n t i l l a t i o n c o u n t e r bombarded by 2.55 Me? n e u t r o n s .  U s i n g a bombarding  energy o f E  4  * 2 Me? a  n e u t r o n beam o f energy 5.08 MeV was produced and t h e bearers p r o f i l e was measured«  vli  ACKNOWLEDGMENTS I w i s k t o express my g r a t i t u d e t o B r . B. L. White f o r h i s s u p e r v i s i o n and f o r much a p p r e c i a t e d i n completing t h i s wort. valuable  a s s i s t a n c e and encouragement  I am a l s o i n d e b t e d  t o Dr. G. Jones f o r  a s s i s t a n c e i n t h e d e s i g n and o p e r a t i o n 6 f some •• «&ec I w o u l d l i k e t o g i v e s p e c i a l thanks t o my coworker on t h e  p r o j e c t , Mr. I . F. M o n i e r , f o r t h e d e s i g n ,  c o n s t r u c t i o n , and  o p e r a t i o n o f much o f the equipment. I also appreciate the N u c l e a r P h y s i c s  t h e h e l p o f my f e l l o w graduate s t u d e n t s o f  Group, e s p e c i a l l y Mr. A. K e s t l e m a n , Mr. J .  Mac Donald, and Mr. M. Eeimann. I must e x p r e s s my deepest a p p r e c i a t i o n t o my mother, f a t h e r , and my w i f e , A n g e l i n e ,  f o r t h e i r l o v e and s u p p o r t d u r i n g my time o f  s t u d y , a l s o t o my f a t h e r f o r t h e p r i n t i n g o f t h i s t h e s i s and t o Angeline  for her typing. I als© g r a t e f u l l y acknowledge t h e r e c e i p t o f two s c h o l a r s h i p s  from t h e N a t i o n a l Research C o u n c i l .  iii  TABLE OF CONTENTS  Chapter I  - INTRODUCTION . . .. . . . . . .  Chapter I I - PRODUCTION OF .THE 2.55 MEV NEUTRON BEAM  ....  Chapter I I I - CALCULATION OF NEUTRON PROFILE AND COMPARISON WITH EXPERIMENT . . . . . . . . . A.  Introduction  B.  C a l c u l a t i o n s o f t h e Beam P r o f i l e  C.  The C e n t e r o f Mass and Y i e l d  D.  Number o f Neutrons T r a v e r s i n g (dx', dy' ) a t ( 3 c ' y ) f o r a T h i n Target . . . . . . . . . . . .  ^  .  .  o  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . . . . . . . .  . . . . . . . . . .  ?  s  E.  T r a n s f o r m a t i o n t o Lab C o o r d i n a t e s  . » . . • • . .  F.  Neutron P r o f i l e f o r a Thick Target .  G.  Comparison  w i t h Experiment .  o  O  O  Q  o  •  e  o  •  o  o  o  o  o  9  O  •'  O  Chapter IV - PRODUCTION OF THE 5 MEV NEUTRON BEAM A.  Introduction  B.  Choice o f Energy and Angle  C.  Target and Beam Arrangement  D.  Heavy I c e T a r g e t  E.  The Mass .Spectrometer io ii*  Fc  o  o  o  *  •  C a l i b r a t i o n o f t h e Mass S p e c t r o m e t e r by Coulomb S c a t t e r i n g o f P r o t o n s on Au o o . C a l i b r a t i o n o f the Mass S p e c t r o m e t e r w i t h a F l e x i b l e Wire • • ' • • " • • • o o « « . o  Search f o r H e  3 + +  Recoil Particles  i.  El.iotronic Pileup  ii.  P r o t o n s i n t h e Beam .  e  o  o  «  «  o  o  o  #  o  *  o  e  «  e  •  s  o  o  o  o  o  e  o  »  iv  page iii.  R e a c t i o n P r o t o n s a t t h e Target  . . . . . . . .  2§  . . . . . . . . . . . . . . . . .  23  6.  Fast Coincidence  H.  Neutron B e a m - P r o f i l e i. l.i  . .  24  *  24  The P r o f i l e »  iii. Chapter ¥  . . . . . .  Jll"b 6 IIS  o  o  «  «  o  e  «  «  o  o  o  «  o  o  a  «  »  }  *  Background  213 25  - MEASUREMENT OF THE ABSOLUTE NEUTRON DETECTION EFFICIENCY OF A PLASTIC SCINTILLATOR . ." . . >  27  Chapter VI - A RESUME OF THEORY AND EXPERIMENTS INVOLVING ' AND LEADING TO SMALL ANGLE SCATTERING OF NEUTRONS  29  A.  Introduction  29  B.  E a r l y Measurements  SO  C.  Schwinger S c a t t e r i n g  Do  Electric P o l a r i z a b i l i t y Scattering  E.  Neutron P o l a r i z a b i l i t y f r o m the Meson Theory  . . . . .  30  . . . . . . . .  32  and P h o t o p r o d u c t i o n o f P i o n s from P r o t o n s  36  F.  Other E f f e c t s  36  G.  Conclusions  37  Appendix A - SIMULATION OF CHARGED PARTICLE TRAJECTORIES WITH A CURRENT FLOWING IN A WIRE . . . . . . . Bibliography ,.•,»,.  38 4 1  V  LIST OF FIGURES to f o l l o w page 1.  Beam P r o p e r t i e s  2.  Response o f Semiconductor Reaction  1 D e t e c t o r t o D on D  . . . . . '"i .  •  3.  Geometry o f t h e Assembly  4.  B l o c k Diagram o f t h e E l e c t r o n i c s  5.  E x p e r i m e n t a l and C a l c u l a t e d Neutron Beam Profiles Geometry o f K i n e m a t i c s i n Center o f Mass Coordinates  6. 7. •8. 9.  8  9 . . . . . . . . .  9  • • • •  1Q' L2  V e c t o r Diagram o f V e l o c i t i e s o f R e a c t i o n Particles  i n t e x t p.14  C a l c u l a t e d I n t e n s i t y o f ' t h e Neutron Beam f o r a T h i n Target  16  Partial Profiles  16  10a. Target and Beam Arrangement .  18  10b.  Target and Beam Arrangement  18'  11.  Target T h i c k n e s s C a l i b r a t i o n  19  12.  P r o t o n s on G o l d a t 250 keV  13.  Spectrometer  20  . .  21  . . . .  21  F i e l d C a l i b r a t i o n w i t h Gaussmeter  14. .Energy C a l i b r a t i o n o f t h e Mass S p e c t r o m e t e r 15.  .  Semiconductor D e t e c t o r Spectrum f o r D on DgO with' Gold B a c k i n g  22  Semiconductor D e t e c t o r Energy Spectrum I n s i d e R e a c t i o n Chamber  23  17.  B l o c k Diagram o f F a s t E l e c t r o n i c s  24  18.  He  24  19.  Neutron P r o f i l e  16.  2  Spectrum .  24  to 20o  Neutron Spectrum i n P l a s t i c  21c  C a l c u l a t e d and. Measured E f f i c i e n c i e s o f a Plastic  Scintillator  Scintillator  . . . .  0  . . . . .  2 7  . . . . . '. . . . .  .22.  Cross-Sections f o r Scattering  23.  C u r r e n t Through a Wire i n a Magnetic Fie1ft  24.  C a l i b r a t i o n o f S p e c t r o m e t e r w i t h a Wire  25o  Energy as a F u n c t i o n o f D e t e c t o r P o s i t i o n  26o  Energy as a F u n c t i o n o f Spectrometer C u r r e n t  o f Neutrons  2 7  '. . . .  552  . . »  0  . . . . . . . . .  follow page  38 .  3 9 40  CHAPTER I INTRODUCTION Our u n d e r s t a n d i n g o f t h e p r o p e r t i e s o f t h e n u c l e u s has- come l a r g e l y from i n t e r p r e t i n g the r e s u l t s o f e x p e r i m e n t s i n w h i c h unbound p a r t i c l e s c o l l i d e w i t h n u c l e i t o produce a "nuclear  reaction".  is..necessary  To s t u d y n u c l e a r  reactions i n d e t a i l , i t  to. have .a q u a n t i t a t i v e , measure of. t h e . - , p r o b a b i l i t y  of a given nuclear  reaction.  The q u a n t i t y used f o r t h i s  purpose i s t h e c r o s s - s e c t i o n o f a n u c l e u s f o r a p a r t i c u l a r r & a c t i o n , u s u a l l y denoted by c w i t h an a p p r o p r i a t e  subscript.  I n o r d e r t o determine t h e c r o s s - s e c t i o n f o r a p a r t i c u l a r r e a c t i o n some o r a l l o f s e v e r a l p r o p e r t i e s o f t h e i n c i d e n t particles  ( o r beam o f p a r t i c l e s ) must be measured*  These a r e  as f o l l o w s (see f i g u r e 1)':. I.,  t h e average momentum o f the b e a m , ( K ) , 0  where  i s the momentum o f one o f the beam  particles. 2*  -  t h e s p r e a d i n t h e momentum o f t h e beam particles.  2.  the average f l u x o f the beam, I  4.  t h e f l u x d i s t r i b u t i o n o f the beam, I ( x , y ) — »  .  5.  t h e p o l a r i z a t i o n o f the beam, P]_  The q u a n t i t a t i v e v a l u e  o f t h e s e p r o p e r t i e s and t h e a c c u r a c y ,  w i t h w h i c h they can be measured d e t e r m i n e the u s e f u l n e s s o f theinformation  a v a i l a b l e from t h e n u c l e a r  reactions  involved.  Charged P a r t i o l e Beams Charged p a r t i c l e teams compared w i t h uncharged p a r t i c l e beams a r e more e a s i l y o b t a i n e d w i t h a w e l l momentum  K  Q  d e f i n e d average  and a f r a c t i o n o f a p e r c e n t s p r e a d i n the  momentum o f t h e beam p a r t i c l e s .  Such beams a r e r e a d i l y  able w i t h a v a r i e t y o f p a r t i c l e accelerators.  obtain-  The average  f l u x o f the beam can be measured a c c u r a t e l y by i n t e g r a t i n g the charge accumulated on a t a r g e t over a s p e c i f i e d time i n t e r v a l . The  f l u x d i s t r i b u t i o n , I ( x , y ) , i n most cases can be assumed t o  be u n i f o r m o v e r a c o n f i n e d a r e a determined by m a t e r i a l tors.  The p r o d u c t s o f n u o l e a r r e a c t i o n s have been found i n  several can  collima-  oases t o be p o l a r i z e d .  Measurements o f the p o l a r i z a t i o n  p r o v i d e i n f o r m a t i o n about t h e n u c l e a r energy l e v e l s  involved,  and, i n t h e case o f n u c l e i  aid i n distinguishing  c o n t a i n i n g few n u c l e o n s ,  between t h e p o s t u l a t e d t y p e s o f  nuoleon-nucleon i n t e r a c t i o n .  In p r i n c i p l e , the i n t e r a c t i o n s  t h a t g i v e r i s e t o p o l a r i z a t i o n c a n be used to determine t h e p o l a r i z a t i o n parameters f o r both charged and uncharged p a r t i c l e beams. leutron  Beams S i n c e i t s d i s c o v e r y i n 1922 t h e n e u t r o n has p r o v i d e d a  highly  useful  t o o l i n attempts't:o understand-th« nuciejus/:. ;  ,  However, t h e t y p e s o f n u c l e a r phenomenon, w h i c h can be s t u d i e d and  the n a t u r e o f t h e r e s u l t s o b t a i n e d a r e v e r y dependent on t h e  n e u t r o n beams a v a i l a b l e .  -3-  'The  e a r l i e s t experiments used sources t h a t depended on  the r e l e a s e o f n e u t r o n s from v a r i o u s n u c l e i when ©C-parti c l e s o r K-rays from n a t u r a l l y o c c u r r i n g r a d i o a c t i v e i n t e r a c t e d with' them.  These ( <*,,n) and  disintegrations  ( &',n). s o u r c e s have,  by p r e s e n t day s t a n d a r d s , low y i e l d s , broad energy and complex s t r u c t u r e .  spreads,  For example, the spectrum o f n e u t r o n s  from a Pu-Be source' shows p a r t i c l e s o f a l l  e n e r g i e s up to about  10 MeV,  and 7  w i t h peaks i n the v i c i n i t y o f 1,4,  MeV.  P h o t o n e u t r o n sources (A. Wattenburg) are used f r e q u e n t l y because the n e u t r o n s produced have a s m a l l e r energy s p r e a d .  The most  p o w e r f u l s o u r c e s o f neutrons are .those a s s o c i a t e d w i t h n u c l e a r reactors.  I f an e x p e r i m e n t a l h o l e i s opened through the r e a c t o r  s h i e l d and i n t o , t h e l a t t i c e i t s e l f , a beam o f n e u t r o n s r e p r e s e n t a t i v e o f the energy d i s t r i b u t i o n p r e s e n t i n the l a t t i c e i s obtained.  The most i m p o r t a n t c h a r a c t e r i s t i c r e l a t i n g t o a  r e a c t o r , as f a r as n e u t r o n r e s e a r c h i s concerned, i s the v a l u e o f the n e u t r o n f l u x . 5 x 10  13  An example of h i g h f l u x a v a i l a b l e i s the  / ? t h e r m a l n e u t r o n s /cm -sec from the Chalk R i v e r heavy  water r e a c t o r (F.W.  Gilbert)-.  with particle accelerators  (Hanson,  example, the r e a c t i o n D(d,n)He 3.268 MeV,  Neutrons  can a l s o be  produced  Taschek, and W i l l i a m s ) .  For"  i s e x o e r g i c , w i t h a Q,»value o f  and good n e u t r o n y i e l d s can"be o b t a i n e d w i t h d e u t e r o n  e n e r g i e s as low as 50=100 keV.  However, u n t i l r e c e n t  t e c h n i q u e s had been d e v e l o p e d , o n l y a p p r o x i m a t e l y  monoenergetic  n e u t r o n s c o u l d be o b t a i n e d w i t h even t h i s l a s t s o u r c e .  -4Because o f the n a t u r e o f t h e s o u r c e s d e s c r i b e d e x p e r i menters i n t h e p a s t d i d not. have a v a i l a b l e to them n e u t r o n beams w i t h b o t h a h i g h f l u x and a s m a l l momentum s p r e a d .  The  measurement o f t h e average f l u x o f the beam i s u s u a l l y  based  on t h e c o n v e r s i o n o f t h e energy o f n e u t r o n s t o t h a t o f charged p a r t i c l e s , which can be d e t e c t e d t h r o u g h t h e i r i o n i z a t i o n .  If  the charged p a r t i c l e s happen t o be p r o t o n s , t h e n an a c c u r a t e knowledge o f p r o t o n r e c o i l c r o s s - s e c t i o n over a wide range o f neutron energies i s necessary.  A l s o t h e geometry and  c o n s t i t u t i o n o f t h e d e t e c t i o n m a t e r i a l must be w e l l known.  As  a r e s u l t accurate determination of neutron f l u x e s , or at l e a s t t h e i r r e l a t i v e magnitude has been v e r y d i f f i c u l t .  Difficulty i n  a d e q u a t e l y c o l l i m a t i n g n e u t r o n s has been a n o t h e r problem i n t h e p r o d u c t i o n o f n e u t r o n beams.  Attempts t o c o l l i m a t e n e u t r o n s by  m e c h a n i c a l means u s u a l l y r e s u l t e d i n a h i g h background  o f neutrons  beyond t h e g e o m e t r i c c u t - o f f o f the c o l l i m a t o r r e s u l t i n g i n an undesireable f l u x d i s t r i b u t i o n , I(x,y), unsuitable f o r performing some experiments such as s m a l l a n g l e s c a t t e r i n g o f n e u t r o n s . R e c e n t l y a new t e c h n i q u e has been developed  (V.J. Strizhak,  V.V. Bobyr, and L. Y a . Grona) which a l l o w s the p r o d u c t i o n o f a c c u r a t e l y c o l l i m a t e d n e u t r o n beams o f s m a l l a n g u l a r w i d t h and known a b s o l u t e i n t e n s i t y and energy.  The beam i s produced by  d e t e c t i n g t h e a s s o c i a t e d r e c o i l n u c l e i , i n t h i s c a s e , He". The p r o d u c t i o n o f an a c c u r a t e l y c o l l i m a t e i i n e u t r o n beam of energy 2 . 5 5 MeV u s i n g the r e a c t i o n D(d,n)He^ w i t h bombarding  energy o f 50 keV i s d e s c r i b e d i n Chapter I I . applied at E calculation  d  The same  * 2 MeV i s d e s c r i b e d i n Chapter IV. A  technique theoretical  o f t h e beam p r o f i l e produced a t E4 = 5 0 KeV i s  d e s c r i b e d i n Chapter I I I . The use o f t h e 2.55 MeV beam t o measure 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 and p u l s e  spectrum o f a p i e c e o f p l a s t i c s c i n t i l l a t o r i s d e s c r i b e d i n Chapter V. To produce the 2 . 5 5 MeV beam a 50 keV a c c e l e r a t o r was used to bombard heavy i c e t a r g e t s w i t h 50 KeV d e u t e r o n s . from t h e r e a c t i o n were d e t e c t e d  i n time c o i n c i d e n c e  of m i c r o s e o o n d s ) w i t h t h e i r a s s o c i a t e d p a r t i c l e H e neutron beam.  The n e u t r o n s ( o f the o r d e r 2  and so t h e  det.ector was s e n s i t i v e o n l y "to those n e u t r o n s i n t h e The He  r e c o i l i o n s produced i n t h e r e a c t i o n were d e t e c t e d  w i t h 100$ e f f i c i e n c y i n a l o w n o i s e h i g h r e s o l u t i o n s e m i c o n d u c t o r counter  subtending  at the t a r g e t .  a s m a l l and a c c u r a t e l y d e f i n e d s o l i d angle  The a s s o c i a t e d n e u t r o n s were e m i t t e d i n a beam  whose a n g u l a r s i z e was determined o n l y by t h e geometry o f the t a r g e t spot and o f the semiconductor d e t e c t o r , and by t h e r e a c t i o n dynamics.  The n e u t r o n  beam was o f known a b s o l u t e  i n t e n s i t y s i n c e the number, o f n e u t r o n s i n the beam.is e x a c t l y the number o f r e c o i l i o n s d e t e c t e d .  The s p a t i a l d i s t r i b u t i o n o f t h i s  beam (the "Beam P r o f i l e " ) was measured. of the l i m i t a t i o n s o f t h e p a r t i c u l a r f l u x o f 180 mieroamps/cm Therefore  U n f o r t u n a t e l y , because  a c c e l e r a t o r used, a maximum  o f d e u t e r o n s c o u l d be put on t h e t a r g e t . .  t h e n e u t r o n beam was o f i n s u f f i c i e n t i n t e n s i t y t o per-  form a s c a t t e r i n g e x p e r i m e n t w i t h r e a s o n a b l e  statistics.  -6-  For two reasons t h e t e c h n i q u e was extended to produce a n e u t r o n team u s i n g t h e Van de G r a a f f a c c e l e r a t o r and d e u t e r o n . beams o f about 2 MeV energy.  F i r s t , i t was p o s s i b l e t o improve  the c r o s s - s e c t i o n f o r D(d,n)He^ r e a c t i o n which I s h i g h e r a t E& 2 -MeV t h a n a t E  d  • 50 keV.  Second, at E  n e u t r o n s would be p a r t i a l l y p o l a r i z e d  d  s  = 2 MeV the beam.of  ( M a r i o n and F o w l e r ) .  U s i n g 2 MeV deuterons,. however, -nroducer! n ".e^v ^roblem.  With  50 keV bombarding deuterons t h e r e was no problem w i t h Coulomb s c a t t e r e d deuterons s i n c e they were o f much l o w e r energy t h e He  recoil particles.  than  But w i t h 2 MeV bombarding deuterons  t h e r e was a p r o l i f i c number o f Coulomb s c a t t e r e d deuterons a t a l l angles which rendered impossible p l a c i n g s semiconductor d e t e c t o r i n s i d e t h e t a r g e t chamber to d e t e c t He ^ r e c o i l directly.  particles  Such a c o u n t e r would have been c o m p l e t e l y swamped by  scattered deuterons.  T h i s d i f f i c u l t y was overcome by p l a c i n g  an a n a l y s i n g magnet a t an a p p r o p r i a t e a n g l e w i t h r e s p e c t t o t h e i n c o m i n g d e u t e r o n beam and t h e r e b y s e l e c t i n g by momentum t h e 3 p a r t i c u l a r He  r e c o i l p a r t i c l e s g o i n g i n t o the r e q u i r e d  solid  a n g l e w h i l e a t the'same time r e j e c t i n g most o f t h e u n d e s i r e d scattered deuterons. t h i s experiment  The bep'm o f 5.08 MeV n e u t r o n s produced i n  subtended a s o l i d a n g l e o f .981 m i l l i s t e r a d i a n s ,  at a l a b angle o i 89° w i t h r t ^ e c x to .he d e u t e r o n beam.  Work  i s p r e s e n t l y b e i n g d i r e c t e d towards b u i l d i n g a moving heavy i c e t a r g e t which can take a 20 microampere beam o f deuterons  instead  o f t h e .3 microampere beam w i t h a f l u x o f 150 microampere s crn ' ;  used i n t h i s work.  A l s o o t h e r t e c h n i q u e s mentioned  i n this  2  thesis  - 7  w i l l be used t o improve t h e i n t e n s i t y o f the n e u t r o n beam and c u t down random c o i n c i d e n c e s o u t s i d e o f t h e beam t o a minimum.  This  w i l l produce a n e u t r o n beam o f s u f f i c i e n t i n t e n s i t y t o perform a s m a l l angle s c a t t e r i n g  experiment.  ^  The most i n t e r e s t i n g experiment  w h i c h c o u l d be done w i t h  the n e u t r o n beam i s - t o measure the s m a l l angle s c a t t e r i n g o f neutrons  by heavy n u c l e i .  o f p r e v i o u s experiments  The c o r r e c t . e x p l a n a t i o n and e v a l u a t i o n  i n t h i s f i e l d has not y e t t e e n mac"^.  study o f t h e s m a l l angle s c a t t e r i n g  o f neutrons  A  o f 5.08 MeV,  e i t h e r p o l a r i z e d - o r - u n p o l a r i z e d s h o u l d p r o v i d e data o f v a l u e i n r e s o l v i n g the e x i s t i n g confusion.  The e x p e r i m e n t a l  measurements  had n o t been made a t t h e time o f w r i t i n g t h i s t h e s i s ; because o f the i n t e r e s t o f t h e problem, t h e p r e v i o u s work i n t h i s f i e l d and the p o s s i b i l i t y o f a p p l y i n g t h e t e c h n i q u e d e s c r i b e d h e r e i n t o the problem have been d e s c r i b e d i n Chapter  V.  -8-  CHAPTER I I PRODUCTION OF THE 2.55 MEV NEUTRON BEAM The apparatus t o be described, uses t h e " A s s o c i a t e d p a r t i c l e t e c h n i q u e " i n c o n j u n c t i o n w i t h t h e D(d,n)He  reaction  t o produce an a c c u r a t e l y c o l l i m a t e d n e u t r o n beam o f known absolute i n t e n s i t y .  This technique u t i l i z e s the f a c t  that  whenever a n e u t r o n i s e m i t t e d i n a c e r t a i n angle w i t h r e s p e c t to the i n c o m i n g d e u t e r o n beam, s i m u l t a n e o u s l y a r e c o i l  nucleus  i s e m i t t e d I n a c o r r e s p o n d i n g a n g l e d e t e r m i n e d . o n l y by t h e k i n e m a t i c s o f the r e a c t i o n .  >  A major r e a s o n t h i s t e c h n i q u e was not e x p l o i t e d i n conjunction w i t h the  D(d,.h)H©^  r e a c t i o n u n t i l r e c e n t l y was  the d i f f i c u l t y o f p e r f o r m i n g a c c u r a t e s p e c t r o m e t r y on t h e r e c o i l n u c l e i and t h e n e u t r o n s .  I t must be p o s s i b l e t o  d i s t i n g u i s h t h e r e c o i l i o n from t h e p a r t i c l e s o f any competing reactions.  T h i s d i f f i c u l t y has been overcome by t h e development  of semiconductor c o u n t e r s w i t h t h i n windows, and w i t h energy r e s o l u t i o n and f r e q u e n c y r e s p o n s e .  adequate  F i g u r e 2 shows an  energy spectrum t a k e n w i t h an R.C.A. d i f f u s e d j u n c t i o n semic o n d u c t o r c o u n t e r type A-3-7f~2.0 f o r a bombarding energy f o r d e u t e r i u m o f 50 keV.  The He  and T groups a r e w e l l s e p a r a t e d .  The H©" r e c o i l energy i s o n l y 185 keV d i f f e r e n t from t h e energy 3  o f t h e T r e c o i l n u c l e i produced by t h e competing  reaction  D(d,p)T , so l o w window b r o a d e n i n g and system n o i s e were e s s e n t i a l i n o r d e r t o r e s o l v e the He  and T groups.  FIGURE  2  RESPONSE  OF  SEMICONDUCTOR  DETECTOR-TO  D  ON D  E d = 5 0 , keV  CHANNEL  NUMBER  REACTION  F i g u r e 3 shows t h e t a r g e t and beam arrangements•> deuterons were produced w i t h a 5 0 keV i o n a c c e l e r a t o r .  The The  bombardment took p l a c e i n s i d e an aluminium r e a c t i o n chamber from which the n e u t r o n beam emerged through a aluminium window  0 . 0 0 7  inch  The d e u t e r o n beam was m a g n e t i c a l l y a n a l y s e d  0  and f o c u s s e d w i t h an e l e c t r o s t a t i c s t r o n g f o c u s s i n g l e n s on a 1 . 0 3 3 mmo d i a m e t e r s t a i n l e s s s t e e l c o l l i m a t o r J u s t i n f r o n t o f the t a r g e t o used.  Target c u r r e n t s from 0 „ 5  t o 1 . 5 microamperes were  The angle c< between t h e normal t o t h e t a r g e t plane T  and t h e d e u t e r o n beam was 3 5 ° target spot.  g i v i n g r i s e t o an e l l i p t i c a l  The t a r g e t was D 0 f r o z e n onto a l / 3 2 g  inch  copper  b a c k i n g m a i n t a i n e d a t l i q u i d n i t r o g e n t e m p e r a t u r e s , and was t h i c k t o 5 0 keV d e u t e r o n s .  At the r e c o i l d e t e c t o r the t a r g e t  spot subtended an angle o f 1 . 1 8 ° an angle o f 1 . 7 8 °  i n the h o r i z o n t a l plane and  i n the v e r t i c a l plane.  The r e c o i l d e t e c t o r  c o l l i m a t o r was c i r c u l a r and was p l a c e d 5 0 mm. from the t a r g e t at an angle  ®jj 3 e  of  1 0 5 °  w i t h r e s p e c t t o t h e d e u t e r o n beam and  subtended an angle o f 1 . 3 5 ° placed 1 6 . 5 " by 1 7 / 8 "  a t t h e target„  from t h e t a r g e t a t an a n g l e 6  by 3 " b l o c k o f N E 1 0 2  a t t h e t a r g e t an a n g l e o f 0 . o 6o5 i n the v e r t i c a l plane.  8 7 °  The neutjgron d e t e c t o r n  o f 7 8 ° was a 1 / 4 "  scintillation plastic  i n t h e h o r i z o n t a l p l a n e and  F i g u r e 4 i s a b l o c k diagram o f the e l e c t r o n i c usedo  subtending  system  The p r e a m p l i f i e r f o r t h e s o l i d s t a t e d e t e c t o r had an  e q u i v a l e n t i n p u t n o i s e o f 6 keV.  The c o i n c i d e n c e r e s o l v i n g  time between.the semiconductor d e t e c t c r and t h e n e u t r o n  FIGURE  3  GEOMETRY 'OF  THE  ASSEMBLY  PHOTO  1  MULTIP H E R  <-e-  ,'  NEUTRON  V  ;  ^^>  SEMICONDUCTOR COUNTER  PLASTY C  SCINTILLATOR (NE-102)  CHA RGE SENSI"TIVE AMPLI FIER  AMPLIFIER  AMPLIFIER DISCRIMINATOR  SINGLE C H A N N E L P U L S E HEIGHT ANALYSER COINCIDENCE UNIT  LINEAR GATE SCALER /0O-CHANN£J_ PULSE H E I G H T ANALYSE R  FIGURE  4  BLOCK  DIAGRAM  OF  THE  ELECTRONICS  -10-  d e t e c t o r was 10  microseconds.  . The beam p r o f i l e was measured i n the h o r i z o n t a l p l a n e by m e a s u r i n g t h e number o f n e u t r o n He^ c o i n c i d e n c e s p e r u n i t i n c i d e n t beam charge as a f u n c t i o n o f the p o s i t i o n o f t h e n e u t r o n counter i n t h e h o r i z o n t a l p l a n e .  The r e s u l t s are  shown i n F i g u r e 5 . The c i r c l e s a r e t h e e x p e r i m e n t a l  results,  w i t h one t y p i c a l e x p e r i m e n t a l e r r o r f l a g shown, and t h e s o l i d l i n e i s t h e c a l c u l a t e d beam p r o f i l e as d e s c r i b e d i n t h e next chapter.  The count r a t e s were l o w o f t h e o r d e r o f two neutrons  per second p e r m i l l i s t e r a d i a n .  9 0 +  NEUTRON FIGURE  5  ANGLE  EXPERIMENTAL NEUTRON  8c  BEAM  (IN  DEGREES)  CALCULATED PROFILES  11CHAPTER I I I CALCULATION OF NEUTRON PROFILE AND COMPARISON WITH EXPERIMENT A.  Introduction The  'Associated  geometry o f t h e n e u t r o n team produced by t h e p a r t i c l e t e c h n i q u e ' i s d e f i n e d by the geometry o f  the t a r g e t spot and t h e r e c o i l d e t e c t o r , by the r e a c t i o n chosen, by t h e bombarding energy and by t h e t a r g e t m a t e r i a l . a l s o i n the d i s c u s s i o n o f some a s s o c i a t e d p a r t i c l e  I t may  experiments  be n e c e s s a r y t o take i n t o account s c a t t e r i n g o f t h e i n c i d e n t bombarding p a r t i c l e s i n t r a v e r s i n g t h e t a r g e t , and s c a t t e r i n g o f the r e c o i l n u c l e i i n l e a v i n g t h e t a r g e t , i n c a l c u l a t i n g t h e r e s u l t i n g neutron d i r e c t i o n . and- u n c e r t a i n ;  Such c a l c u l a t i o n s a r e d i f f i c u l t  f o r t u n a t e l y they do not seem to be n e c e s s a r y f o r  the d i s c u s s i o n o f the p r e s e n t experiment s i n c e the beam p r o f i l e calculated without Considering experiment.  such s c a t t e r i n g agrees w e l l w i t h  P r e v i o u s workers ( J . Rethmeier , C.G. Johfcer,  M o Rodenburg, J.W. Hovenien and D.R. v . d . Meulen) u s i n g  this  method and u s i n g the T-d r e a c t i o n were u n a b l e t o o b t a i n agreement between measured and c a l c u l a t e d n e u t r o n beam p r o f i l e s , p r o b a b l y because o f such s c a t t e r i n g i n t h e t a r g e t .  At t h e h i g h e r bombard=  i n g d e u t e r o n e n e r g i e s they u s e d , and w i t h t r i t i a t e d  zirconium  t a r g e t s , t h e e f f e c t s o f s c a t t e r i n g were much more s e r i o u s t h a n i n the p r e s e n t e x p e r i m e n t .  -12-  B.  C a l c u l a t i o n o f the Beam P r o f i l e The neutron'"beam p r o f i l e * ' i s the f l u x d i s t r i b u t i o n ,  I(x,y),  o f the neutrons measured i n the p l a n e o f m o t i o n o f the  neutron  d e t e c t o r (see f i g u r e 6 ) .  made o f  the n e u t r o n beam p r o f i l e . stages.  A t h e o r e t i c a l c a l c u l a t i o n was  This c a l c u l a t i o n proceeded i n two  F i r s t , as stoning an i n f i n i t e l y t h i n t a r g e t and a u n i f o r m  d e u t e r o n f l u x o f energy E, &E over the t a r g e t a r e a T, the number o f c o i n c i d e n t neutrons/em / i n c i d e n t deuteron d I { E , x l , y " ) t r a v e r s i n g an i n f i n i t e s i m a l n e u t r o n counter dx'dy' at ( x " y ) was c a l c u l a t e d ?  5  i n the c e n t e r o f mass c o o r d i n a t e s . Co  The  Center o f Mass and  Yield.  6 J J and <J>! are the a n g u l a r c o o r d i n a t e s o f the o r i g i n o f the o o , x'y' a x i s w i t h r e s p e c t t o th© c e n t e r o f the t a r g e t spot and ;  0 " and 0* o o are r e q u i r e d t o s p e c i f y the d i f f e r e n t i a l y i e l d i n the c e n t e r o f i n c i d e n t beam d i r e c t i o n i n t h e • c e n t e r o f mass f r a m e  0  mass c o o r d i n a t e s . YiE,e«,<&»)dE 0  0  s  y i e l d o f n e u t r o n s t r a v e l i n g i n the d i r e c t i o n 8£,(S>' i n the c e n t e r o f mass frame, per s t e r a d i a n , p^u? i n c i d e n t deuteron w i t h E^ between E and E-?1E  Because the t a r g e t and r e c o i l d e t e c t o r e o l l i m a t o r s i z e s were both s m a l l compared w i t h the d i s t a n c e d between them, th®  area of  i n t e r e s t on the n e u t r o n d e t e c t o r p l a n e , n, i n v o l v e s a n g l e s w h i c h d i d n o t d i f f e r s u f f i c i e n t l y from t i o n o f Y(E,e, ,4>») v a r y i n g w i t h x \ y ?  !  6'•,(!>  1  to r e q u i r e c o n s i d e r a -  f o r a g i v e n v a l u e o f E.  That  i s , f o r g i v e n E, we took the y i e l d over the r e g i o n o f i n t e r e s t i n the n p l a n e as a c o n s t a n t , equal t o Y ( E , 0^(D£), where ©^"^d  were the  a n g l e s i n the c e n t e r o f mass c o o r d i n a t e system cooresponding  to  E  0  DIRECTION  RECOIL  OF  D  BEAM  PARTICLE  DETECTOR  NEUTRON  PLANE,r  TARGET  t  PLANEj  DETECTOR  PLANE, n  RECOIL COLLIMATOR AREA,  R  PROJECTION OF  T  WITH  ON r  CENTER  OF PROJECTION AT  U/)  OU'S)  = AREA  OF  T = TARGET AREA FIGURE  6  GEOMETRY  OF  KINEMATICS  IN  CENTER  OF  MASS  OVERLAP OF  D  BEAM  COORDINATES  -13(Each -value o f E o f E^ gave r i s e t o a d i f f e r e n t c e n t e r o f mass system.) Do  lumber o f Neutrons T r a v e r s i n g (dx°,dy ) a t (x',y') f o r a !  T h i n Target,  .  I f a n e u t r o n l a t o he produced i n T w i t h d i r e c t i o n t o go through ( x , a x ' , y " , d y ) and f o r t h e a s s o c i a t e d r e c o i l 8  1  particle  t o go t h r o u g h E, o o l i n e a r i t y o f momentum i n t h e c e n t e r o f mass system demands t h a t the n e u t r o n  can he produced o n l y i n the a r e a  o f overlap', Q(x-',y'), [the o v e r l a p o f th® p r o j e c t i o n o f H on t , (center x  f t  y ' i w i t h t ] • flow dx'jyrj^ s s o l i d angle subtended a t t h e t a r g e t by .g2 dx'.dy'  where g i s t h e dia tance from T t o t h e n p l a n e and, ,, Qi£l»Xll T Therefore  ;s  the f r a c t i o n o f target area producing r e a c t i o n s which can t r a v e r s e dx'dy'.  t h e number o f c o i n c i d e n t n e u t r o n s d e t e c t e d i n dx'dy'  p e r i n e i d e n t d e u t e r o n w i t h E^ between E and E-4E I s d I ( E , x ,y»)dx'dy 8  E.  -Transformation  ~ i^" (E, ©^'(p*)dEJQ ( x y J g^T '  5  !  s  t o 'Lab C o o r d i n a t e s  The ' f o l l o w i n g t r a i l s format i o n s were made from the c e n t e r Of mass c o o r d i n a t e s • t o t h e l a b c o o r d i n a t e s . LAB  .  :  x  y  ^  ec ^ • - : - ~ >  C.O.M.  ,,  x ' ( x , E ) , ax'-'-- / d x \ d x ' sdxV  y.«(y,E')  , dy' - j | J ^ dy  e 0 'ie .E).. a e 0 - = 0  • 8  de«  -14-  •Therefore a t a p a r t i c u l a r v a l u e o f ;x y i n the l a h frame, the 9  ' i n t e n s i t y o f the  .(•%'= E,dE)  coincident  neutrons from a t h i n  i s d l f E , x,y)dxdy  then the t r a n s f o r m a t i o n o f x C o n s i d e r the  0  !  following fig&re  target  S i n c e x« l a almost equal to  g6°  t o x i s almost t h a t o f 0! t o 8« 7s  •P-ICRJEE 7.VeptQi> diagram o f v e l o c i t i e s o f r e a c t i o n particles» l a the c e n t e r o f mass' c o o r d i n a t e a (0-3.) E.'ine 0, , E , and E a r e the e n e r g i e s o f the He$ „ n e u t r o n , 33, illCS • and the'" two-deuterons r e s p e c t i v e l y o Q, ~ 3 S 6 8 Mafo Using, e q u a t i o n  +-  \  -  D  '(3.-1) w©  can o b t a i n P^ %  'St 2m  '  E.in<s  6m  +  13-2)  wher© P r e p r e s e n t s the magnitude o f the momentum o f the. p a r t i c l e and m i s a u n i t masso  I n the ©enter.-of mass system.  He n "becomes 2 h * l| i n c p  T h e r e f o r e 13«2)  p  3  C E  n  + 2m 2  .(3-3)  al,so  r  d  •=•'  (3=4 )  1 ino  U s i n g 4.3-3).- and •(••3-4) iwe have 3(E +• d) Is inc d t a k e s on i t s l a r g e s t v a l u e o f 0.025 Mev  (3-5)  i n o  E  ¥  %no  a t Ed -  SO  keV.  Therefor© vn v  n  [3(1 i - 130.72)] a t E ~  19.9,  more a t l o w e r  s  d  50  ke?  energies  Prom f i g u r e t a n 6'  ~  v sin 6 v^eos^+v^  tan 8»  -  tan 9  n  1  + ' d>_... ^'oos( y  -I  ;  T h e r e f o r e f o r 50 k e f e n e r g i e s , d6 i s a p p r o x i m a t e l y e q u a l t o and dx i s a p p r o x i m a t e l y e q u a l t o dx'.  &0'  This t r a n s f o r m a t i o n can he  written y C E ^ ^ j d E d i ^ ' O t x i ^ )  F.  ,Y(E;8 (^)dEeLxdyO(x' [E.x\ „y'.' ["E.y'j 0  Heutron p r o f i l e f o r a Thick Target The  second main s t e p i n the c a l c u l a t i o n was  neutron p r o f i l e f o r a t h i c k t a r g e t .  T h i s was  t o o b t a i n the  done by  integrating  the p a r t i a l p r o f i l e s ' o r n e u t r o n f l u x e s dI|E,x,y-J, c o r r e s p o n d i n g t o the bombardment o f t h i n t a r g e t s w i t h deuterons k i n e t i c energy, E&,  corresponding  r a n g i n g from 50 keV t© z e r o keV»  SO kftV  YJE.6 ,(D, |0(x» f E . x l .y' [E.yl )dE /  o f the  \  -16Thie  i n t e g r a l was a p p r o x i m a t e d by d o i n g a n u m e r i c a l summation,.  The l a r g e s t e r r o r i n ' t h e e v a l u a t i o n o f t h i s summation was i n t h e v a l u e s u s e d f o r t h e y i e l d , y('E^,(D ), a t v a r i o u s energies*. 8 IfE.x.y) = V ' y ( E ; , e 0 Q J 0(x«fa.. x l . v ' T E c y ! )dE,0  Some p a r t i a l p r o f i l e s a r e shown i n ' f i g u r e 9o Go  Comparison w i t h Experiment I n o r d e r t o make a comparison o f t h e c a l c u l a t e d b e a m ' p r o f i l e  w i t h t h e e x p e r i m e n t a l p o i n t s o b t a i n e d by experiment i n Chapter I I , i n t e g r a t i o n over a f i n i t e s i z e d n e u t r o n d e t e c t o r was p e r f o r m e d , The number o f c o i n c i d e n t n e u t r o n s / s e o / i n c i d e n t d e u t e r o n , S ( x , y ) , t r a v e r s i n g a f i n i t e d e t e c t o r o f a r e a A, c e n t e r e d a t .{x»y) would be 50keV/v-  //Y(E,9 ,@ )0jx'fE,x7 , y ' f E , y ] )dEdxdy 0  /  c  -This i n t e g r a l was a l s o a p p r o x i m a t e d by d o i n g a n u m e r i c a l summation,, Z(x,y) = V ^ T j =i  k=l  ^ 1=1  Y ( E i ,9 ;,(Do -)0(x fa ,xj"1 .y T E i ..YkI )dE(dxj d y r  0  8  (  S  K  2 t  The r e s u l t o f t h i s c a l c u l a t i o n i s shown i n f i g u r e 6 . The skewness o f t h e c a l c u l a t e d curve about t h e z e r o angle i s due t o t h e s p r e a d i n d e u t e r o n e n e r g i e s produced by the t a r g e t thickness»  I t can be  seen t h a t t h e agreement between experiment and c a l c u l a t i o n i s good.  FIGURE  8  CALCULATED TARGET  INTENSITY  OF  THE  NEUTRON  BEAM  FOR  A  THIN  -17CHAPTER I V PRODUCTION OF THE 5 Mev NEUTRON BEAM A.  introduction The  same t e c h n i q u e as d e s c r i b e d i n Chapter TI. was u s e d t o  produce a 5 ;Mev beam o f a c c u r a t e l y  collimated  neutrons.  Certain  changes were made i n t h e e x p e r i m e n t a l arrangement w i t h t h e i n t e n t i o n o f i m p r o v i n g t h e i n t e n s i t y and c o l l i m a t i o n o f t h e n e u t r o n beam and  i n v e s t i g a t i n g t h e p o s s i b i l i t y o f p r o d u c i n g a p o l a r i z e d beam  of neutrons. A beam o f n u c l e o n s i s p o l a r i z e d  i f the s p i n s a r e n o t  randomly d i s t r i b u t e d b u t have some p r e f e r r e d  orientation.  I f the  nuinber o f p a r t i c l e s i n t h e beam w i t h s p i n component p a r a l l e l t q this preferred  direction i s N  +  and t h e number w i t h a n t i p a r a l l e l  s p i n component i s N_, t h e p o l a r i z a t i o n i s d e f i n e d If or p a r t i o l e s ) as p a N  f  => N  o  spin  I f t h e p o l a r i z a t i o n o f a beam i s  known t o g e t h e r w i t h t h e p a r t i c l e t y p e , t h e momentum, and i n t e n s i t y d i s t r i b u t i o n o f t h e p a r t i o l e s t h e n t h e beam i s c o m p l e t e l y B.  specified*  Choice o f Energy and A n g l e A c c o r d i n g t o M a r i o n and F o w l e r , f o r t h e D(d,n)He  reaction,  toward h i g h e r bombarding e n e r g i e s t h e magnitude o f t h e p o l a r i z a t i o n o f t h e D=D n e u t r o n s i n c r e a s e s and seems t o approach a maximum near 3 Mevo  I t was d e c i d e d t h a t s i n c e 2 Mev was a p p r o x i m a t e l y t h e b e s t  energy f o r p r o d u c i n g maximum p o l a r i z a t i o n o f t h e n e u t r o n beam t h a t an attempt would be made t o p e r f o r m a n u c l e a r s c a t t e r i n g w i t h t h e n e u t r o n s produced a t t h i s bombarding energy.  experiment  However i t  -18was a l s o d e c i d e d t h a t the f i r s t attempt t o produce a n e u t r o n 3 •  team would be made c h o o s i n g t h e He d i f f e r e n t i a l r e a c t i o n c r o s s section.. a l a b angle o f 89  r e c o i l a n g l e f o r t h e maximum T h i s t u r n e d out t o be a t  w i t h r e s p e c t t o t h e i n c o m i n g P beam.  Higher  c r o s s - s e c t i o n s c o u l d be a t t a i n e d a t even s m a l l e r a n g l e s t h a n 89 but t h i s would reduce the a l r e a d y s m a l l energy o f 207 keV f o r t h e He  r e c o i l p a r t i c l e t o v a l u e s t o o s m a l l to' p e r f o r m a c c u r a t e  s p e c t r o m e t r y and f a s t c o i n c i d e n c e s > Co  Target and Beam Arrangements t  F i g u r e s 10a and 10b show t h e t a r g e t and beam arrangements,.. The d e u t e r o n beam was produced by t h e 3 MeV f a n de G r a a f f machine at  t h e U n i v e r s i t y o f B.C.  The bombardment took p l a c e i n s i d e a  b r a s s r e a c t i o n chamber from which t h e n e u t r o n beam emerged t h r o u g h .a •.'..006. i n c h aluminium window.  The d e u t e r o n beam was' magn'l^i.cally  a n a l y s e d and f a c u s s e d f i r s t with, a magnetic l e n s and then.an e l e c t r o s t a t i c s t r o n g f o c u s s i n g l e n s on a l/l&n  diameter tantulum  c o l l i m a t o r - f o l l o w e d - b y . a .954 cm d i a m e t e r s t a i n l e s s s t e e l . c o l l i m a t o r . The t a r g e t was DgO f r o z e n onto a .00025 i n c h aluminium f o i l mounted on a t h i c k copper r i m . n i t r o g e n temperatures  V 0  The copper r i m was m a i n t a i n e d a t l i q u i d I t was. n e c e s s a r y t o 'measure,'' the t a r g e t  c u r r e n t w i t h a Faraday cup p l a c e d b e h i n d t h e t a r g e t s i n c e the DgO i c e and aluminium f o i l were t h i n to 2 MeV d e u t e r o n s .  The  angle between t h e normal t o t h e t a r g e t p l a n e and t h e d e u t e r o n beam was 5 0  p o  The c o l l i m a t o r to the s p e c t r o m e t e r was b r a s s w i t h a l / 8 "  d i a m e t e r c i r c u l a r h o l e anil was p l a c e d 3 l l / l 6  R  from the t a r g e t a t an  angle o f 88°'31* 2' w i t h r e s p e c t t o the d e u t e r o n beam.  A theodolite  FIGURE  lOd  TARGET  AND  BEAM  ARRANGEMENT  NEUTRONS .006  TARGET CHAMBER  ALUMINIUM  FARADAY  WINDOW  CUP MASS (B  SPECTROMETER  OUT  OF  PAGE) SEMICONDUCTOR DETECTOR  TO  VACUUM  DISPENSER  DEUTERON  BEAM  COVAR TO  FIGURE  10b  TARGET  AND  BEAM  ARRANGEMENT  SEALS  DETECTOR  was used .to measure t h e a n g l e optically«  The c o l l i m a t o r s u h t e n t s a  s o l i d angle o f 9 8 1 m i l l s t e r a d i a n s a t t h e t a r g e t s 0  The r e c o i l  d e t e c t o r was l o c a t e d a t a d i s t a n c e o f 4 o 3 8 " a f t e r t h e the t r a j e c t o r y o f the r e c o i l .particle<>  c o l l i m a t o r on  The d e t e c t o r was an Ortec  Si'lio'bn S u r f a c e B a r r i e r D e t e c t o r SBEJ 050-60 w i t h diameter o f o S l ^ c The- n e u t r o n d e t e c t o r was p l a c e d 28 i n c h e s from the t a r g e t a t a l a b a n g l e o f 155 ' a 1 T/8  re  w i t h r e s p e c t t o the i n c o m i n g D beam  0  I t was  diameter, 1" deep b l o c k o f HE 102 s c i n t i l l a t i o n p l a s t i c ;  s u b t e n d i n g a t t h e t a r g e t a s o l i d angle, o f 3°4 m l l l i s t e r a d i a n s * ])„  Heavy l e e Target To p r o v i d e a d e u t e r o n t a r g e t a q u a n t i t y o f heavy water was  s p r a y e d onto the l i q u i d n i t r o g e n r e f r i g e r a t e d aluminium f o i l w i t h a DgO e v a p o r a t o r o  The d e t a i l s o f t h e o p e r a t i o n and. a photograph  o f a s i m i l a r d e v i c e i s g i v e n on page 18 o f L a r s o n ' s Thesis'(1957)» A c a l i b r a t i o n o f t h i s d e v i c e was made by measuring the 873 keV resonance o f ,F (p„cxK)0 19  16  the s h i f t o f  reaction a f t e r a given quantity  o f DgO vapor was d e p o s i t e d ' o n a t h i n c a l c i u m f l u o r i d e (Monier'g T h e s i s , 1957)<, of o i l ,  target  W i t h a p r e s s u r e c o r r e s p o n d i n g t o 10 cm  the t a r g e t was measured to be 14 keY t h i c k to.873 k e ? p r o t o n s ,  or 1746 keV deuterons o  The c a l i b r a t i o n measurement i s shown  i n f i g u r e 11 < > So  fhe Mass  Spectrometer  In o r d e r to prevent Coulomb s c a t t e r e d D from t h e t a r g e t ' a n d t a r g e t b a c k i n g from d i r e c t l y s t r i k i n g t h e He  r e c o i l c o u n t e r and  swamping the e l e c t r o n i c s w i t h counts i t was n e c e s s a r y t o d e s i g n a n d c a l i b r a t e a mass s p e c t r o m e t e r which would t r a n s m i t the d e s i r e d :  FIGURE  II  TARGET  THICKNESS  CALIBRATION  -20= energy He  p a r t i c l e s and r e j e c t t h e m a j o r i t y o f the s c a t t e r e d D  partioles.  The p a r t i c u l a r d e s i g n used f o r t h i s experiment was a  45° s i n g l e f o c u s i n g magnet w i t h a 10 cm r a d i u s o f c u r v a t u r e . i.  C a l i b r a t i o n , o f the Mass Spectrometer By Coulomb S c a t t e r i n g o f P r o t o n s on Au.  The semiconductor  c o u n t e r was c a l i b r a t e d w i t h a P l u t o n i u m  5.13 Mev a l p h a source and a r t i f i c i a l p u l s e s i n j e c t e d i n t o t h e semiconductor  c o u n t e r p r e a a p l i f i e r were used to i n t e r p o l a t e between  0 and 5.13 Mev, and to e s t a b l i s h the energy amplitude analysers.  c a l i b r a t i o n o f the pulse  A g o l d t a r g e t was p l a c e d i n t h e chamber and  bombarded w i t h 250 keV p r o t o n s from the f a n de G r a a f f . spectrum  An  energy  ( f i g u r e 12) was taken f o r v a r i o u s mass s p e c t r o m e t e r c u r r e n t s  w i t h the counter p l a c e d 0,4 i n c h e s from an a r b i t r a r y p o s i t i o n i n t h e - l i n e o f motion o f the c o u n t e r .  The p u l s e r c a l i b r a t i o n was  used t o determine where i n the spectrum 250 k e ? p r o t o n s would appear.  The s p e c t r o m e t e r c u r r e n t which produced a spectrum w i t h the  maximum i n t e n s i t y f o r 250 keV p r o t o n s a t t h i s p o s i t i o n was 4.6 ±.05 amps.  This was r e p e a t e d a g a i n f o r 200 keV p r o t o n s g i v i n g a maximum  i n t e n s i t y f o r 200 keV p r o t o n s a t a s p e c t r o m e t e r c u r r e n t o f 3.8±.05 amps.  To compare these v a l u e s a Gauss me t e r was used t o measure t h e  f i e l d a t v a r i o u s spectrometer c u r r e n t s .  F i g u r e 13 i s a graph o f  the f i e l d i n K i l o g a u s s as a f u n c t i o n o f t h e s p e c t r o m e t e r c u r r e n t i n amps.  U s i n g the r e l a t i o n s h i p 2  E<xB (where E i s the energy  o f the p a r t i c l e and B i s the f i e l d s t r e n g t h  o f t h e s p e c t r o m e t e r ) and t h i s graph i t can be shown t h a t a  m  o  x  NUMBER  OF  COUNTS  -21= s p e c t r o m e t e r c u r r e n t of 4.5 t o 3.78  amps f o r 250 keV p r o t o n s i s e q u i v a l e n t  amps f o r 200 keV p r o t o n s .  U s i n g t h i s r e s u l t and the graph  i n f i g u r e 13 t h e e n e r g i e s f o r the r e a c t i o n p a r t i c l e s which c o u l d be t r a n s m i t t e d through the s p e c t r o m e t e r were c a l c u l a t e d - f o r v a r i o u s spectrometer c u r r e n t s . u s i n g - /ImE q.  (4-1)  where q i s the r a d i u s o f c u r v a t u r e , m i s the mass o f the p a r t i c l e , , q i s the charge.  The r e s u l t s o f these c a l c u l a t i o n s are shown i n  f i g u r e 14, C a l i b r a t i o n Curves F o r the Mass s p e c t r o m e t e r . ii.  C a l i b r a t i o n of the Mass Spectrometer w i t h a F l e x i b l e • Wire  A c u r r e n t f l o w i n g i n a f l e x i b l e w i r e was used t o s i m u l a t e Z++ / . t h e t r a j e c t o r y of t h e He i o n (see Appendix A ) . The r e l a t i o n s h i p ' 3++ between the t r a j e c t o r y o f the He  i o n and the energy o f the i o n  was  determined by making measurements at a s p e c t r o m e t e r c u r r e n t o f  1.6  amperes.  U s i n g the graph i n f i g u r e 13 and  equation (4=1) f  these measurements were e x t r a p o l a t e d to v a l u e s f o r a s p e c t r o m e t e r c u r r e n t of 4.5  amps.  With t h e c o u n t e r p o s i t i o n e d as i n . the p r o t o n 3 + +  s c a t t e r i n g i t was  found t h a t the e n e r g i e s of the He  v a r i e d o v e r t h e d i a m e t e r o f the c o u n t e r (.314 t o 349 keV, a change of 66 keV. ke¥,  r e c o i l ions  i n c h e s ) from 293  The average energy would be  keV  321  a d e v i a t i o n o f o n l y 3$. from t h e 307 keV determined by p r o t o n  scattering.  1  SPECTROMETER  CURRENT  IN  AMPERES  400+  FIGURE  14  THE  ENERGY  MASS  CALIBRATION  OF  SPECTROMETER  300+  > 2  200+  p < Q.  li_ o 100+  cr u z QJ  1  2  SPECTROMETER  3 CURRENT  4 IN  AMPERES  5  =22= ,fFo  Search f o r He  3++  Recoil Particles  The f i r s t attempt t o see the He  r e c o i l p a r t i c l e s was made  "by bombarding a D 0 t a r g e t f r o z e n onto a l / l 6 i n c h Gold b a c k i n g . 2  F i g u r e 15 shows the. semiconductor d e t e c t o r spectrum taken f o r a s p e c t r o m e t e r s e t t i n g o f I. =,4.5 o f one micro-amp. microcoulombs.  amperes and a d e u t e r o n beam c u r r e n t  The i n t e g r a t e d c u r r e n t on t h e t a r g e t was S i n c e o n l y a few counts o f He  7.5  were expected i n  the r e g i o n o f 207 keV i t became i m m e d i a t e l y apparent t h a t they would be i m p o s s i b l e "to see i n such a l a r g e background.  T h i s background  was a t t r i b u t e d t o t h r e e p o s s i b l e s o u r c e s ; e l e c t r o n i c p i l e u p , p r o t o n s i n the beam, and p r o t o n s from a r e a c t i o n a t the t a r g e t . i.  Electronic Pileup  An experiment was performed to determine t h e extent' t o w h i c h p i l e u p was r e s p o n s i b l e f o r t h e h i g h background o f the spectrum.  i n the 240 keV r e g i o n  One s c a l e r was s e t to count t h e number o f p u l s e s 1  i n t h e 120 keV peak and a n o t h e r was s e t t o count t h e number o f p u l s e s H i n the 240 keV peak fsee f i g u r e 1 5 ) .  For p i l e u p the f o l l o w i n g r e l a -  t i o n s h i p s h o u l d holdd I' F"  (Beam C u r r e n t )  I t was f o u n d t h a t o n l y f o r beam c u r r e n t s above 100 nanoamps on Au d i i l p i l e u p become s i g n i f i c a n t o ii.  P r o t o n s i n t h e Beam  I f t h e r e were p r o t o n s i n the D would g i v e counts i n the 240 k e f ' p e a k . experiment was performed u s i n g Dp  beam a p p e a r i n g as Hg tfcey Therefore a s c a t t e r i n g  a t 2 Mev as the bombarding p a r t i c l e  J  -22= I n s t e a d o f atomic deuterium*.  There was no o b v i o u s d i f f e r e n c e between  the m a g n e t i c a l l y a n a l y s e d semiconductor d e t e c t o r spectra«.  The  D<jj  beam, cannot c o n t a i n protons as an i m p u r i t y i n d i c a t i n g t h a t t h e 240 k e y peak c o u l d n o t be due t o p r o t o n c o n t a m i n a t i o n i n t h e d e u t e r o n beam. iii.  R e a c t i o n P r o t o n s a t the Target  There a r e s e v e r a l p o s s i b l e s o u r c e s o f r e a c t i o n p r o t o n s vshieh c o u l d have been produced a t t h e t a r g e t , degraded and s c a t t e r e d i n t o the e n t r a n c e c o l l i m a t o r o f the a n a l y s i n g magnet .  Figure.16 i s an  energy spectrum o f t h e r e a c t i o n p a r t i c l e s from 2 MeV D on D g b a n d p o s s i b l e i m p u r i t i e s t a k e n w i t h , a semiconductor d e t e c t o r p l a c e d r i g h t i n the r e a c t i o n chamber a t a l a b angle o f 120° w i t h r e s p e c t ' t o : t h e i n c o m i n g beam.,  A .002 i n c h Aluminium f o i l was p l a c e d d i r e c t l y i n  f r o n t o f t h e d e t e c t o r t o c o m p l e t e l y degrade the He , T, and s c a t t e r e d Do  T h i s was r e p e a t e d a t 1.8 and 1.5 Mev bombarding e n e r g i e s .  From  the e n e r g i e s and c r o s s - s e c t i o n s i t was p o s s i b l e to determine t h e r e a c t i o n s r e s p o n s i b l e f o r the v a r i o u s peaks o 0 (aip)0 l 6  ! 7  , C  12  (d,p)C *, and D f d , p ) T  the DgO d i s p e n s e r .  13  0  The C  These were; 0 'Cd,p )0' , ,6,  was p r o b a b l y from  1 2  Thus we c o n c l u d e d t h a t t h e counts above the 120 keV  peak not a c c o u n t e d f o r by e l e c t r o n i c p i l e u p and p r o t o n c o n t a m i n a t i o n i n the beam c o u l d have been caused by r e a c t i o n p r o t o n s a t t h e t a r g e t a l t h o u g h t h i s was not c o n f i r m e d by f u r t h e r e x p e r i m e n t s . G.  Fast Coincidence^ z  S i n c e i t was not f e a s i b l e to see the He  directly with a  semiconductor d e t e c t o r because o f the l a r g e background,  the neutron  p u l s e s were used t o g a t e the k i c k s o r t e r f o r the semiconductor d e t e c t o r  -24= p u l s e s t h e r e b y a l l o w i n g o n l y those p u l s e s which were i n time c o i n c i d e n c e w i t h t h e n e u t r o n p u l s e s t o be a n a l y s e d by the k i c k s o r t e r . U s i n g o p t i c a l alignment the n e u t r o n d e t e c t o r was p l a c e d as a c c u r a t e l y as p o s s i b l e a t the p o s i t i o n where t h e n e u t r o n beam was c a l c u l a t e d t o pass fsee s e c t i o n C, Chapter 4 ) . F i g u r e 17 i s a b l o c k diagram o f the e l e c t r o n i c s w i t h a time r e s o l u t i o n o f the o r d e r o f 80 nanoseconds which was used to f i n d t h e He r e c o i l p a r t i c l e s .  With a s p e c t r o m e t e r  c u r r e n t o f 4.6 amps and a t o t a l charge o f 4000 microcoulombs on the t a r g e t ' t h e r e were 538 c o i n c i d e n c e s . spectrum i s shown i n f i g u r e 18.  The r e s u l t i n g He  The u n s a t i s f a c t o r y t h i n g  collected recoil  about  t h i s procedure was t h a t the a b s o l u t e n e u t r o n i n t e n s i t y was unknown 3  s i n c e t h e number o f He  r e c o i l p a r t i c l e s g o i n g i n t o the d e t e c t o r was  unknown as i n the experiment d e s c r i b e d i n Chapter I I . H. U e u t r o n Beam P r o f i l e i.  The P r o f i l e  U s i n g the e l e c t r o n i c arrangement shown i n f i g u r e 17 and the t a r g e t and beam arrangement shown i n f i g u r e 10a and 10b t h e n e u t r o n p r o f i l e was measured f o r an a n a l y s i n g magnet s e t t i n g o f 4.6 amps. The r e s u l t i n g n e u t r o n p r o f i l e i s shown i n f i g u r e 19.  Each p o i n t  r e p r e s e n t s the number o f time c o i n c i d e n t events which o c c u r r e d f o r 1000 microcoulombs  o f charge on the t a r g e t .  I n the plane o f the:  d e t e c t o r s t h e n e u t r o n beam's measured w i d t h a t h a l f maximum was 4^°. T h i s i s because the n e u t r o n d e t e c t o r i i t s e l f subtended an a n g l e o i 2 5/6' i n t h i s p l a n e .  I t w i l l be n e c e s s a r y t o use a t h i n s l a b t o  e s t a b l i s h the t r u e w i d t h o f the bsam which s h o u l d be c l o s e t o thie  SEMI CONDUCTOR DETECTOR  KICKSORTER  SCALAR  GATE  FAST TRIGGER  ZERO CROSSOVER  SCALAR  SINGLE CHANNEL PULSE HEIGHT ANALYSER  NEUTRON DETECTOR  FAST COINCIDENCE  DELAY  LIMITER  FAST TRIGGER  TIM E SOR1rER  DISCRIMINATOR  BLOCK  FIGURE  17  DIAGRAM  OF  FAST  ELECTRONICS  TPIGC . E R  NUMBER  OF  COUNTS  DI STANCE  FROM  SOURCE  DETECTOR  = 28 INCHES  ANGLE  SUBTENDED  IN  X  DIRECTION  +  +  BY *  TO  NEUTRON  NEUTRON DETECTOR  3° 50*  300.-  to  S  z LU Q  2004  O Z  o o o  5 Z  +  +  +  2 46 8 10 DISPLACEMENT OF NEUTRON DETECTOR IN X DIRECTION  FIGURE  19  NEUTRON  PROFILE  12'  -25o w i d t h o f t h e 2 subtended a t -fee t a r g e t by t h e s o l i d s t a t e c o u n t e r . ii.  Intensity  With the n e u t r o n d e t e c t o r l o c a t e d a t the p o s i t i o n o f maximum i n t e n s i t y o f the n e u t r o n beam the c o i n c i d e n c e r a t e was .3 microamp's. T h i s corresponds. 4d a p p r o x i m a t e l y one n e u t r o n p e r seoond i n the beam t a k i n g i n t o account the 30$ e f f i c i e n c y o f t h e n e u t r o n d e t e c t o r . Attempts were made t o put .6 mrc'r damps on t h e t a r g e t ' b u t ' t h i s d e c r e a s e d the to  yield rapidly.  A p p a r e n t l y t h e DgO was s u b l i m i n g o r m i g r a t i n g  d i f f e r e n t p a r t s o f the t a r g e t .  I t i s hoped t h a t w i t h a moving  . t a r g e t t h i s i n t e n s i t y can be i n c r e a s e d t o 33 n e u t r o n s p e r second for  a 10 mieroamp d e u t e r o n beam. iii.  .Background  •The random c o i n c i d e n c e r a t e was .032 counts p©r second compared w i t h t h e t r u e c o i n c i d e n c e r a t e o f .3 c o u n t s p e r second. These r a t e s were e s t i m a t e d by comparing t h e c o i n c i d e n c e r a t e a t t h e p o s i t i o n o f maximum i n t e n s i t y o f the n e u t r o n beam w i t h t h e r a t e a t a p o s i t i o n e n t i r e l y o u t o f t h e r e g i o n o f the beam.  T h i s background  i s much t o o h i g h t o perform ' u s e f u l s m a l l a n g l e s c a t t e r i n g experiments w i t h the n e u t r o n beam.  Three t h i n g s w i l l be done t o out down t h i s  random c o i n c i d e n c e rat® c o n s i d e r a b l y . the  F i r s t the'time r e s o l u t i o n o f  e l e c t r o n i c s w i l l be improved from 80 nanoseconds  i o about 5  nanoseconds 'by changing t h e s e t t i n g f o r the time s o r t e r and discrimenator i n the e l e c t r o n i c s .  Second, a p i l e u p  discriminator  w i l l reduce the number o f p u l s e s from t h e semiconductor d e t e c t o r p r e a m p l i f i e r which appear' t o t h e s u c c e e d i n g e l e c t r o n i c s as 240 kev" and 360 keV p u l s e s b u t which are merely 120 k e f s c a t t e r e d d e u t e r o n  pulses  coming i n v e r y r a p i d succession..  Even a t 65 microamps p i l e u p  c o n t r i b u t e d s i g n i f i c a n t l y t o t h e random c o i n c i d e n c e  r a t e since there 2 were 12 p i l e u p p u l s e s i n the energy r e g i o n o f t h e He r e c o i l p a r t i c l e s 3 f o r every He  pulse»  T h i r d , a gamma-ray d i s c r i m i n a t o r w i l l be put  i n t o the n e u t r o n c i r c u i t r y .  The c o u n t i n g r a t e o f t h e n e u t r o n  d e t e c t o r was 50,000 counts p e r second w i t h no c o l l i m a t i o n and 1,600 counts p e r second when the n e u t r o n d e t e c t o r was s h i e l d e d w i t h a l e a d and wax c o l l i m a t o r o by t h e i r n a t u r e ,  Experiments on s m a l l angle: s c a t t e r i n g cannot,  be done i f t h e n e u t r o n c o u n t e r i s c l o s e l y s h i e l d e d ,  t h e r e f o r e i t i s v e r y i m p o r t a n t t o e l i m i n a t e t h i s h i g h count r a t e o u t s i d e the c o l l i m a t o r w i t h a gamma-ray d i s c r i m i n a t o r o  = ' 2 7 " '  CHAPTER f MEASUREMENT OP THE ABSOLUTE IEUTRON DETECTION EFFICIENCY OF A PLASTIC SCIHTILLATOR She to  2 o 5 5  determine  Mev n e u t r o n beam, d e s c r i b e d i n Chapter  the absolute neutron d e t e c t i o n e f f i c i e n c y of a c y l i n d e r  of p l a s t i c s c i n t i l l a t o r HE 1 0 2 , diameter.  I I , was u s e d  o f 1 " t h i c k n e s s , and two i n c h e s  The n e u t r o n beam was i n c i d e n t n o r m a l l y a t t h e c e n t e r o f  th© p l a n e f a c e o f t h e c y l i n d e r .  The geometry was such t h a t t h e beam  was l o c a l i s e d w e l l w i t h i n t i i e a r e a o f t h e plane f a c e o f t h e s c i n t i l l a tor,  so t h a t the e f f i c i e n c y was g i v e n d i r e c t l y by t h e r a t i o o f t h e  number o f neutrons  counted i n c o i n c i d e n c e w i t h r e c o i l s , U , t o t h e e  number ©f r e c o i l s , N o r  H  0  was t a k e n to be e q u a l t o t w i c e t h e number  o f counts i n the n e u t r o n spectrum above energy 1 / 2 , where E i s t h e maximum energy g i v e n up by the n e u t r o n to the s c i n t i l l a t o r .  Figure  2 0 shows the p u l s e sp@ctrum from the n e u t r o n s p e c t r o m e t e r whent i t was o p e r a t i n g I n c o i n c i d e n c e i s o l i d l i n e ) and a l s o when i t was c o u n t i n g a l l neutrons  I n c i d e n t on i t , i . e . not o p e r a t i n g i n c o i n c i d e n c e  (totted l i n e ) .  The measured e f f i c i e n c y was .297  ( £ . 0 3 ) ;  this i s  ©ompgred i n f i g u r e 2 1 w i t h t h e e f f i c i e n c y c a l c u l a t e d u s i n g t h e a p p r o x i m a t i o n g i v e n by Swartz and Owen  0  The c a l c u l a t e d  efficiency  E ( c ) i s p l o t t e d as a f u n c t i o n o f L, t h e average d i s t a n c e t r a v e l l e d i n t h e s c i n t i l l a t o r by a n e u t r o n which has c o l l i d e d w i t h a carbon nucleus.  S i n c e double  s c a t t e r i n g o f neutrons  by hydrogen n u c l e i  was not c o n s i d e r e d i n the c a l c u l a t i o n o f E ( c ) , and s i n c e t h e s c i n t i l l a t o r i s s u f f i c i e n t l y t h i c k to require a reasonably  accurate  \ \  CHANNEL FIGURE  20  NEUTRON  NUMBER  SPECTRUM  IN  PLASTIC  SCINTILLATOR  0.25  \  I 1.0  1 2.0 VALUE  FIGURE  21  CALCULATED A  hOF  L  1 3.0 IN  v  4.0  CENTIMETERS  AND MEASURED  PLASTIC  1  SCINTILLATOR  EFFICIENCIES  OF  ~28~  t r e a t m e n t ©f s c a t t e r i n g ,  i t i s not f r u i t f u l t o t r y t o compare the  t h e o r y o f Swartss and Owen w i t h t h i s r e s u l t accuracyo  t o a h i g h degree o f  B a t h e r , t h i s t e c h n i q u e s h o u l d he used t o p r o v i d e t h e  experimental r e s u l t s  on which t o base t h e d e r i v a t i o n  a c c u r a t e t h e o r y of s c i n t i l l a t o r e f f i c i e n c i e s and  o f a more  spectra  0  CHAPTER V I A RESUME OP THEORY AID EXPERIMENTS INVOLVING  AND  LEADING TO SMALL ANGLE SCATTERING OF NEUTRONS A.  Introduction Several interactions  i n a d d i t i o n t o t h a t due t© a s i m p l e  o p t i c a l model p o t e n t i a l have been proposed t o e x p l a i n low a n g l e s c a t t e r i n g ©f n e u t r o n s .  Some o f the t h e o r y i n v o l v e d i n these  i n t e r a c t i o n s w i l l he d i s c u s s e d t o g e t h e r w i t h the r e l a t e d  experiments.  Of s p e c i a l i n t e r e s t i s t h e anomalous i n c r e a s e i n the d i f f e r e n t i a l cross-section at small angles.  Alelcsandrov and A l e k s a n d r o v ,  Anikin,  and S o l d a t o v observed t h i s e f f e c t f o r uranium and p l u t o n i u m w i t h neutrons of a broad energy s p r e a d t h a t averaged 2.8 Mev.  Dukarevich  and Dyumin u s i n g 14.2 Mev n e u t r o n s measured a s i m i l a r i n c r e a s e f o r uranium and t h o r i u m .  However, no such e f f e c t was observed f o r  s e v e r a l heavy n u c l e i a t average n e u t r o n e n e r g i e s o f 0.8 Mev Mev  or f o r uranium a t a n e u t r o n energy o f 0 . 5 7 Mev.  or  2.5  Because o f i t s  a n g u l a r dependence t h i s anomalous i n c r e a s e cannot be r e a d i l y a t t r i b u t e d t o the n u c l e a r f o r c e o r t© th®  spin-orbit  interaction  a r i s i n g from the m o t i o n o f the n e u t r o n magnetic moment i n th© n u c l e a r Coulomb f i e l d  (Sehwinger s c a t t e r i n g ) .  Aleksandrov s s  i n t e r p r e t a t i o n o f h i s r e s u l t s i s t h a t i f the n e u t r o n has a charge structure,  as p r e d i c t e d by the meson t h e o r y , t h e n t h e r e w o u l d be an  i n t e r a c t i o n between an i n d u c e d e l e c t r i c d i p o l e moment of the n e u t r o n and the e x t e r n a l e l e c t r i c f i e l d o f the s c a t t e r i n g n u c l e u s .  A  comparison i s made o f t h e p r e d i c t e d v a l u e s o f t h e n e u t r o n p o l a r i z a b l l i t y w i t h the v a l u e e s t i m a t e d by making use of d a t a on the  •*» 25 0*="  p h o t o p r o d u e t i o n o f p i o n s from p r o t o n s and w i t h t h e v a l u e c a l c u l a t e d by BarashenJxov from t h e meson t h e o r y . B.  E a r l y Measurements E a r l i e r measurements of the a n g u l a r d i s t r i b u t i o n o f f a s t  n e u t r o n s s c a t t e r e d from a l a r g e number o f elements were r e p o r t e d by K i x u e h l et« a l o and A m a l d i e t . a l o i n which th© main f e a t u r e s o f the  d i s t r i b u t i o n c o u l d be e x p l a i n e d as t h e d i f f r a c t i o n e f f e c t s due  to t h e s c a t t e r i n g o f n e u t r o n waves by s p h e r i c a l p a r t i c l e s . C»  Sohwinger  Scattering  In 1948 w i t h the i n t e n t i o n o f s u g g e s t i n g a new method f o r o b t a i n i n g p o l a r i z e d n e u t r o n s Schwinger d e s c r i b e d a s p i n - o r b i t  inter-  a c t i o n a r i s i n g from t h e motion o f the n e u t r o n i n t h e n u c l e a r Coulomb field.  S i n c e neutrons p o s s e s s a magnetic moment, they may be  a p p r e c i a b l y s c a t t e r e d by the i n t e n s e e l e c t r o s t a t i e f i e l d s o f heavy nuclei.  Because t h e magnetic moment and s p i n o f a n e u t r o n a r e  connected by t h e r e l a t i o n  where M i s the magnetic moment v e c t o r i n e r g g a u s s " , jyu^l t h e magnetic moment o f the n e u t r o n ~ 1.9155 n u c l e a r magnetons, eh i s t h e n u c l e a r magneton = 5.04929 x 1 0 "  2 4  e r g g a u s s , a n d c r i s the P a u l i m a t r i x , - 1  this scattering i s polarization sensitive.  The energy o f a n e u t r o n  —*•  moving i n an e l e c t r i c f i e l d , E, i s d e s c r i b e d by t h e f o l l o w i n g contribution to the neutron Hamiltonian;  where p i s the momentum o f the n e u t r o n  0  Consequently t h e d i f f e r e n t i a l  c r o s s - s e c t i o n f o r the s c a t t e r i n g o f a n e u t r o n beam w i l l be m o d i f i e d a t s m a l l angles by t h i s i n t e r a c t i o n where n u c l e a r f o r c e s w i l l n o t be significant«  Sehwinger used the Born a p p r o x i m a t i o n o f t h e r e s u l t i n g  Sohrodinger equation d e s c r i b i n g the motion o f the neutron;  where and  s  =  K  The r e s u l t i n g d i f f e r e n t i a l s c a t t e r i n g e r o s 3 - s e c t i o n may be w r i t t e n cr(e h)= )  \Ue)\  2  + f c o t  2  f  + f  p . FT  Imf (e)cot| 0  where f _ ( 8 ) i s the a m p l i t u d e of t h e n u c l e a r s c a t t e r i n g , P s p o l a r i z a t i o n v e c t o r o f i n c i d e n t beam, n = the u n i t v e c t o r normal to t h e p l a n e o f t h e r e a c t i o n , and  denotes  "imaginary p a r t of" .  Sample c l a i m s t o p r o v i d e a  more a c c u r a t e s o l u t i o n by c a l c u l a t i n g th® p e r t u r b a t i o n o f a " h a r d s p h e r e " wave f u n c t i o n due t o t h e electromagnet!© i n t e r a c t i o n . i s a s t r o n g resemblance  There  between t h e two o a l e u l t i o n s , t h e d i f f e r e n c e  b e i n g t h a t t h e p o l a r i z a t i o n dependent term i n Sample's c a l c u l a t i o n i s 25% l a r g e r t h a n S c h w i n g e r ' s o at  The d i v e r g e n c e o f t h e c r o s s - s e c t i o n  zero s c a t t e r i n g angle resembles t h a t i n R u t h e r f o r d s c a t t e r i n g ,  and may be removed i n t h e same way, by t a k i n g i n t o account t h e s c r e e n i n g by atomic electrons„  -32°  E a r l y attempts t o d e t e c t Sohwinger s c a t t e r i n g made by L o n g l e y and Sample were i n c o n c l u s i v e < > I n 1956 A l e k s a n d r o v p u b l i s h e d some c o n v i n c i n g r e s u l t s from h i s experiments w i t h f a s t emerging  from a r e a c t o r .  to 0.9 x 3»6 cm. t h i c k  neutrons  They were o o l l i m a t e d w i t h a s t e e l  collimator  A f t e r c o l l i m a t i o n the w i d t h o f t h e i r n e u t r o n  0  beam a t h a l f maximum was about .75 degrees..  The measured a n g u l a r  d i s t r i b u t i o n f o r the e l a s t i c s c a t t e r i n g o f n e u t r o n s compared v e r y f a v o u r a b l y w i t h Sohwinger "a t h e o r e t i c a l Do  Electric Polarizability  calculation,.  Scattering  I f the n e u t r o n has a charge s t r u c t u r e , perhaps  caused by a  " c l o u d " o f charged mesons around a c e n t r a l c o r e , t h e n i n an f i e l d E t h e r e may  electric  be i n d u c e d i n the n e u t r o n an e l e e t r i e d i p o l e moment  P p a r a l l e l t o the i n d u o i n g f i e l d .  Then f o r a weak f i e l d one  may  writes  where o t i s t h e p o l a r i z a b i l i t y .  T h i s s h o u l d show i t s e l f i n an  anomalous b e h a v i o r of the d i f f e r e n t i a l c r o s s - s e c t i o n o f s m a l l angle (Iu.o A. A l e k s a n d r o v and L L due  Bondarenko) o  The p e r t u r b i n g H a m i l t o n i a n  to the i n t e r a c t i o n o f t h e i n d u c e d n e u t r o n e l e c t r i c d i p o l e moment  w i t h the e x t e r n a l e l e c t r i c f i e l d i s then;  &«e  2  Thus i n the f i e l d o f a heavy n u c l e u s of charge Z, th© p e r t u r b i n g H a m i l t o n i a n may  be taken to be 7/{r)  vfeiere H s l»5x and  * p$otZ e r" 2  2  4  for  r>R  fermis,  9rir)«V/  f o r r<B  • 38-  where/Vis the nuclear Hamiltonian. One o f the f i r s t a t t e m p t s i n t h e l i t e r a t u r e  t o s e p a r a t e the  e f f e c t s o f d i f f e r e n t t y p e s o f s c a t t e r i n g was made i n a t h e o r e t i c a l paper by Barashenkov.  H i s e q u a t i o n f o r the energy o f t h e i n t e r a c t i o n  betweenMhe n e u t r o n and the n u c l e u s was;  9/rr) = V(r) -yu Ceh/2m c )a 2  2  •£ x p -  :  n  ocZVr"*  The f i r s t term was d e t e r m i n e d by p u r e l y n u c l e a r f o r c e s and by the assumption t h a t the i n t e r a c t i o n was s p i n Independent.  The s e c o n d t e n s  d e s c r i b e s the "Sehwinger s c a t t e r i n g " and t h e t h i r d term d e s c r i b e s t h e "Electric polarizability  scattering".  For the e v a l u a t i o n o f the  magnitude o f the p o l a r i z a t i o n s c a t t e r i n g Barashenkov uses the Born approximation. ential  He o b t a i n e d the f o l l o w i n g  e x p r e s s i o n f o r the d i f f e r -  c r o s s - s e c t i o n o f the e l a s t i c s c a t t e r i n g o f a beam o f n o n - p o l a r -  i z e d n e u t r o n s on the n u c l e u s (H„Ah crte) = I . T > ) f + i >  c t  [M{M)  9  2  f  + f(e) Re  f.( ) + i 9  f (e) z  (5-1)  where f O . ) i s the a m p l i t u d e o f t h e n u c l e a r s c a t t e r i n g 0  ( s o l i d sphere  approximation); f(e)zmc/Zef Where K s 4.44 X 1 0 / E i 2  and E  s  KR  I sin K R  energy o f the s c a t t e r e d n e u t r o n .  r e p r e s e n t i n g Barashenkov's c a l c u l a t i o n s o f the e l a s t i c  ,-f KR)  .  s i n (9/3) ,  the s o l i d sphere a p p r o x i m a t i o n was used.  section  +• cos K R  For the n u c l e a r  scattering,  F i g u r e 22 shows the c u r v e s o f the d i f f e r e n t i a l  cross-  s c a t t e r i n g o f n e u t r o n s o f energy E - 4 Mev  FIGURE  22  CROSS  SECTIONS  FOR  THE  SCATTERING  OF  NEUTRONS  -34-  and ex = 10  cm  ; 07  ,0~ ,(% a r e the c r o s s - s e c t i o n s of t h e n u c l e a r , 2  2 33  Sohwinger and p o l a r i z a t i o n s c a t t e r i n g on U  ;  From these curves i t i s e v i d e n t t h a t the p o l a r i z a t i o n s c a t t e r i n g as w e l l as the Sch w i n g e r s c a t t e r i n g , i s nan i f e s t i n t h e s m a l l angle s c a t t e r i n g of neutrons.  The range o f a n g l e s 6^3°  t o 10°  would be the most c o n v e n i e n t f o r measurements, where the n u c l e a r s c a t t e r i n g i s s t i l l o n l y s l i g h t l y dependent on the a n g l e , and the Sohwinger s c a t t e r i n g i s a l r e a d y n e g l i g i b l e .  Barashehfcow c o n c l u d e s ,  however, t h a t f o r comparison w i t h experiment  i t i s n e c e s s a r y t o have  a good knowledge o f the a b s o l u t e v a l u e o f t h e p u r e l y n u c l e a r s c a t t e r i n g s i n c e the s l o p e o f the curve CTO) c o n s t r u c t e d from f o r m u l a (5=1) i s s m a l l and q u a l i t a t i v e l y t h e c u r v e s <j{&) and 0~ (6) a r e 4  d i f f i c u l t to d i s t i n g u i s h . I n an attempt t o I n t e r p r e t the anomalous s c a t t e r i n g i n h i s own experiments  observed  o f 1958, A l e k s a n d r o v made c a l c u l a t i o n s on the  assumption t h a t the n u c l e u s c o u l d be approximated  as a s o l i d  sphere.  The a m p l i t u d e o f pure n u c l e a r s c a t t e r i n g was e s t i m a t e d by e x t r a p o l a t i n g h i s e x p e r i m e n t a l curves from the h i g h angle r e g i o n s i n t o t h e s m a l l angle r e g i o n s .  He i n t e r p r e t e d the anomalous b e h a v i o r o f the  d i f f e r e n t i a l e l a s t i c s c a t t e r i n g c r o s s - s e c t i o n f o r Pu (Z = 94) and U (Z - 92) to be caused by a n e u t r o n p o l a r i z a b i l i t y . o b t a i n e d was tx 5 (8.0 zfc 3 . 5 ) x 10  cm .  The v a l u e he  I n a more r e c e n t  paper  (1961) A l e k s a n d r o v r e t r a c t s h i s o r i g i n a l c o n c l u s i o n s about the s i z e  = 35'  o f the p o l a r i z a b i l i t y o f t h e n e u t r o n and c a u t i o u s l y concludes t h a t "The  d e t e c t e d phenomenon were n o t y e t s a t i s f a c t o r i l y e x p l a i n e d . " I n a paper p u b l i s h e d by T h a l e r (1959) t h e r e s u l t s o f a  s e r i e s o f more r e f i n e d measurements by Hangsdorf distribution  o f the angular  o f neutrons s c a t t e r e d from a v a r i e t y o f elements a t  low e n e r g i e s .  From h i s a n a l y s i s he a r r i v e s a t a v a l u e f o r the -41  e l e c t r i c p o l a r i z a b i l i t y of 0<<X<2X10  3  cm .  I t i s i n t e r e s t i n g to  note t h a t i n a f o o t n o t e of T h a l e r ' s paper he admits a n i n c o n s i s t e n c y i n h i s c a l c u l a t i o n s and c o n c l u d e s t h a t t h e observed e f f e c t s were p r o b a b l y the r e s u l t o f t h i c k t a r g e t s and poor energy r e s o l u t i o n i n the o r i g i n a l  data.  To i n v e s t i g a t e th®- o c c u r r e n c e o f s c a t t e r i n g r e s u l t i n g from the n e u t r o n p o l a r i z a b i l i t y Fossan performed an experiment t o measure the d i f f e r e n t i a l c r o s s - s e c t i o n f o r e l a s t i c s c a t t e r i n g o f 0.57 Me? neutrons by uranium a t seven a n g l e s between 3° and 18°.  Neutrons  w i t h an energy s p r e a d o f about 50 keV were produced by th© Li (p,n)Be 7  7  r e a c t i o n w i t h p r o t o n s from a Van de O r a a f f a c c e l e r a t o r  and c o l l i m a t e d by a b o r a t e d - p a r a f f i n and p o l y e t h y l e n e c o l l i m a t o r . I n the c a l c u l a t i o n o f o"(0), the n u c l e a r a m p l i t u d e was e v a l u a t e d from an o p t i c a l  model w i t h the n u c l e a r p o t e n t i a l parameters  Moore and Auerbach.  suggested by  From h i s r e s u l t s he concludes t h a t enhanced  s m a l l - a n g i a s c a t t e r i n g o f the magnitude observed a t h i g h e r e n e r g i e s , A l e k s a n d r o v (1958), (1961), D u k a r e v i c h (1963) does not o c c u r a t a n e u t r o n energy o f 0.57 MaV and t h a t t h e i n c r e a s e i n cr(6) p r e v i o u s l y observed i s not t h e r e s u l t o f a n i n d u c e d e l e c t r i c d i p o l e moment i n t h e  -26-  neutron. Eo  Neutron P o l a r i z a b i l i t y from the Meson Theory ana o f P i o n s from P r o t o n s . The p o l a r i z a b i l i t y of the n e u t r o n was  (1959) and t h e v a l u e o b t a i n e d was oc - 1 . 6 x 1 0  Photoproduction  c a l c u l a t e d by -42 3 cnf .  Thaler  This value i s  i n s u r p r i s i n g l y good agreement w i t h a me s o n - t h e o r e t i c c a l c u l a t i o n of -42  Barashenkov and Barashov, they o b t a i n e d o< - 1 . 8 X 1 0  3  cm .  Barashenkov and Barashov a l s o quote the v a l u e o f the p o l a r i z a b i l i t y o b t a i n e d by B a l d i n .  The v a l u e s quoted are -43  4X10  3  cm  y  ,  3  -AZ  - ex. i 1 . 4 X 1 0  oaf.  T h i s r e s u l t i s i n agreement w i t h an e s t i m a t e made i n d e p e n d e n t l y  by  F o l d y from the p i o n p h o t o p r o d u c t i o n d a t a , v i z . , cx £ EX 10 cm . Barashenkov, however, has o b t a i n e d ,a t h e o r e t i c a l v a l u e o f oc near -41  8 X 1 0  3  em  by i n c l u d i n g c o n t r i b u t i o n s from v i r t u a l e x c i t a t i o n s  p o s i t r o n and e l e c t r o n p a i r s .  A f u r t h e r r e s u l t o b t a i n e d by B r e i t —  R u s t g l from the p i o n p h o t o p r o d u c t i o n i s t h a t c< £ 2 X 1 0 F.  of  42  and  3  cm  .  Other E f f e c t s I n the paper w r i t t e n by B r e i t and R u s t g i (1959) o t h e r l e s s  u s u a l e f f e c t s are d i s c u s s e d w h i c h may anisotropy i n neutron s c a t t e r i n g .  account  f o r the  observed  The approximate f i t s t o d a t a  by means o f the o p t i c a l model p o t e n t i a l employing  a square w e l l  i n d i c a t e t h a t a t l e a s t a p a r t o f the a n i s o t r o p y i n low s c a t t e r i n g can be r e p r e s e n t e d i n t h i s manner.  angle  I t appears p r o b a b l e  t h a t employment o f p o t e n t i a l w e l l s w i t h t a i l s at l a r g e r r s h o u l d i t e a s i e r to f i t the d a t a .  Possibly direct interaction with  n u c l e o n s at the n u c l e u s produces  the observed asymmetry.  a l s o suggests these a n g u l a r e f f e c t s may  Breit  have t h e i r o r i g i n i n  n u c l e a r s t r u c t u r e and p o s s i b l e compound n u c l e u s phenomenon. G.  Gonolusion As can be seen from t h i s r e v i e w , t h e o r e t i c i a n s have had  considerable, d i f f i c u l t y i n e x p l a i n i n g r e c e n t low angle s c a t t e r i n g o f n e u t r o n s s i m p l y because o f the number o f p o s s i b l e i n t e r a c t i o n s i n v o l v e d and because o f t h e f a c t t h a t some o f these i n t e r a c t i o n s are not c o m p l e t e l y u n d e r s t o o d .  I n t r y i n g t o i s o l a t e one type o f  i n t e r a c t i o n such as the " e l e c t r i c p o l a r i z a b i l i t y " s c a t t e r i n g ,  one  must make seme u n j u s t i f i a b l e assumptions about the magnitude o f o t h e r i n t e r a c t i o n s and the adequacy o f the o p t i c a l model. I t i s now up t o the e x p e r i m e n t a l i s t t o improve the p r e s e n t s c a t t e r i n g experiments which have been inadequate u n t i l f o r two important r e a s o n s .  recently  These are the energy spread i n r e a c t o r  nexitrons and t h e r e l a t i v e l y poor c o l l i m a t i o n a t t a i n e d u s i n g m e c h a n i c a l methods.  The e l e c t r o n i c c o l l i m a t i o n o f n e u t r o n s over-  comes both of these d i f f i c u l t i e s and a l s o p r o v i d e s a means o f p r o d u c i n g a p a r t i a l l y p o l a r i z e d beam o f n e u t r o n s .  So f a r no work  has been done u s i n g t h i s t e c h n i q u e w i t h n e u t r o n s i n the r e g i o n o f 2.5 t o 5 MeY which i s a n t i c i p a t e d by t h i s t h e s i s .  The o n l y q u e s t i o n  r e m a i n i n g i s whether or not a beam can be produced o f s u f f i c i e n t l y h i g h i n t e n s i t y t o make a s i g n i f i c a n t c o n t r i b u t i o n t o the p r e s e n t scattering data.  -38-  APPENDIX A SIMULATION OF CHARGED PARTICLE  TRAJECTORIES  •WITH A CURRENT FLOWING IN A WIRE I t i s p o s s i b l e t o determine  t h e t r a j e c t o r y o f a charged  p a r t i c l e I n a u n i f o r m magnetic f i e l d by analogy w i t h a f l e x i b l e w i r e i n t h e same f i e l d under t e n s i o n I (amperes) . ( R i t s o n , Dewire, B a c h ) .  (dynes) c a r r y i n g a c u r r e n t I n f i g u r e 23 t h e f o r c e  dF (dynes) e x p e r i e n c e d by an element o f c u r r e n t - c a r r y i n g conductor i n a f i e l d o f u n i f o r m i n d u c t i o n B (webers meters  )  dF* - I d l X B where F i s i n Newtons, I i s ' i n amperes, 1 i s i n meters.  (A-l) From  f i g u r e 23 d l - qdc<  (A-2)  where q i s t h e r a d i u s o f c u r v a t u r e o f t h e w i r e and doc i s a n increment o f a n g l e .  The f i e l d B* i s p e r p e n d i c u l a r t o t h e p l a n e  of t h e w i r e , t h e r e f o r e ( A - l ) a n d (A-2) can be combined t o o b t a i n dF - I^BdoC .  (A-8)  Summing t h e y components o f the f o r c e over the w i r e i n the f i e l d one t h e n has  « Fy  or  F  v  M /  = J 2 I o B c o s ( ^M-oc)d<x ,  (A-4)  - 2IpBsin*M  (A-5)  .  U s i n g t r i g o n o m e t r y i t i s easy t o show t h a t Fv s- T s i n o ^ (A-6) Z ' 2 where T i s i n Newtons. Combining e q u a t i o n s (A-5) and ( A - 6 ) , we  =29-  obtain for a wire i n  equilibrium' •T - IBq  (A-7)  For a p a r t i e l e w i t h eharge q Coulombs and mass m K i l o g r a m s w i t h v e l o c i t y v meters sec  —I  i n a f i e l d B webers meters  -2  moving  , the  e q u a t i o n o f motion i s q-vB = mv q  (A~8)  2  where q i s the r a d i u s o f c u r v a t u r e i n meters .  But  mv = /2mT  (A-9)  w h i c h combined w i t h (A-8) becomes Bq - \/3mE~ . Substituting  (A-1G)  t h i s v a l u e f o r B^ i n t o ( A - 7 ) , f o r the t r a j e c t o r y  of  the p a r t i c l e and the w i r e t o be i d e n t i c a l T - I\[ZmE  In practice  .  (A-11.)  a v e r y f i n e w i r e i s c o n s t r a i n e d a t the s o u r c e ,  run  through the f i e l d to some p o s i t i o n , and then r u n over a p u l l e y  to  a weight  (Ritson).  T h i s i n t r o d u c e s an e r r o r due t o f r i c t i o n o f the  pulleyo  I n o r d e r t o o b t a i n an a c c u r a t e c a l i b r a t i o n f o r p a r t i c l e s  w i t h e n e r g i e s o f a few hundred M l o v o l t s a 2 t h o u copper w i r e  was  suspended from a d e l i c a t e s p r i n g w i t h a c o e f f i c i e n t o f s t i f f n e s s force 5586 dynes w h i c h gave a v e r t i c l e d e f l e c t i o n o f F i g u r e 24 shows the e x p e r i m e n t a l arrangement usedo  dynes/emo This provided  a means o f measuring t e n s i o n s o f the o r d e r o f 736$ dynes t o ±2 dynes.  The w i r e was  passed  i n t o the magnet box through the  c o l l i m a t o r and out through a c o l l i m a t o r w h i c h d u p l i c a t e d the  entrance position  //////////  FIGURE  24  CALIBRATION  DELICATE  SPECTROMETER A  SPRING  OF WITH  WIRE  2  ENTRANCE COLLIMATOR;  THOU  COPPER  WIRE  MAGNET BOX  MAGNET POLE  PIECES  SIMULATES SEMICONDUCTOR DEVICE ADJUSTING  IN WIRE  ////////////  FOR TENSION  DETECTOR  =40-  o f the semiconductor  deteetoro  The w i r e was t h e n anchored t o a  d e v i c e which was used f o r a d j u s t i n g t h e t e n s i o n i n t h e w i r e and f o r v a r y i n g t h e s l o p e o f t h e w i r e t o study the p a r t i c l e o r b i t s .  As a  check t h a t o t h e r f o r c e s d i d n o t i n f l u e n c e t h e w i r e p o s i t i o n t h e t e n s i o n and c u r r e n t were v a r i e d , k e e p i n g  I constant.  Corrections  were made f o r the w e i g h t o f t h e w i r e . F i g u r e s 85 and 36 show the r e s u l t s o f some measurements S++ o f t r a j e c t o r i e s f o r He keV.  p a r t i c l e s w i t h e n e r g i e s t o as low as 30  >  60--  ; to I  55--  FIGURE ENERGY  AS  FUNCTION  U.  25 A  OF  DETECTOR  POSITION  O  50iu z  ID  .3  .4  POSITION  .5 OF  .6  4-  J  .8  DETECTOR  IN  .9  INCHES  60..  >  50FIGURE  <u u. O  > o q: u z  ENERGY  26  AS A  FUNCTION OF  40-  SPECTROMETER  CURRENT  30  UJ  1.2 1.3 14 SPECTROMETER  1.5 1.6 1,7 CURRENT IN  AMPERES  - 4 1 -  BIBIIOGRAPHY A l e k s a n d r o v , Y . A . ( 1 9 5 7 ) , Zh. Eksperimo i Teor. F i z . 3 3 , ( t r a n s l a t i o n : S o v i e t P h y s . JETP 6, 2 2 8 (19587T.  2 9 4  A l e k s a n d r o v , Y . A . , A n i k i n , G.B., and S o l d a t o v , A..S. ( 1 9 6 1 ) , i Teor. F i z . 4 0 , 1 8 7 8 ( t r a n s l a t i o n : S o v i e t Phys. JETP 1 3 , 1 3 1 9 (19T1)). A l e k s a n d r o v , Y.A. and Bondarenko, I . I . ( 1 9 5 6 ) , Zh. Eksperimo i Teor. F i z . 3 1 , 7 2 6 ( t r a n s l a t i o n : S o v i e t Phys. JETP 4 ,  4 1 2  ( 1 9 5 7 7 ) .  A m a l d i , E., Ageno, H . , Phys. Rev. 7 1 ,  B o e e i a r e l l i , D., and T r a b a e e h i , G. 20.  ( 1 9 4 7 ) ,  B a l d i n , A.S. ( 1 9 5 7 ) , P r o c e e d i n g s o f t h e Padua-,Venice Conference on Fundamental P a r t i c l e s . Barashenkov, V , S . ( 1 9 6 3 ) , i n P r o c e e d i n g s o f t h e I n t e r n a t i o n a l Conference on Nucleon S t r u c t u r e a t S t a n f o r d U n i v e r s i t y , e d i t e d by R. H o f s t a d t e r and I . I . S c h i f f ( S t a n f o r d U n i v e r s i t y P r e s s , S t a n f o r d , C a l i f o r n i a , t o be p u b l i s h e d . ) 0  Barashenkov,  V o S  Barashenkov,  V  0  and Barbashov, B.M. ( t o be p u b l i s h e d ) .  c  and K a i s e r , H.J.  S .  B r e i t , G. and R u s t g i , M.I. Dukarevich, Y . V . Fiz. 4 4 ,  ( 1 9 5 9 ) ,  and Dyumin, A . I .  Fortsehr. Physik  ( 1 9 6 2 ) ,  Phys. 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