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A measurement of the Panofsky ratio in helium-3 Corriveau, François 1977

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1  A MEASUREMENT OF THE PANOFSKY RATIO IN HELIUM-3 by FRANCOIS CORRIVEAU B.Sc,  U n i v e r s i t y L a v a l , 1975  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE  FACULTY OF GRADUATE STUDIES (Physics)  We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d  THE  standard  UNIVERSITY OF BRITISH COLUMBIA August, 1977  (c) F r a n c o i s  C o r r i v e a u , 1977  In p r e s e n t i n g t h i s  thesis  an advanced degree at  further  agree  fulfilment  of  the  requirements  the U n i v e r s i t y of B r i t i s h Columbia, I agree  the L i b r a r y s h a l l make i t I  in p a r t i a l  freely  available  for  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 copying o f  of  this  representatives. thesis for  It  financial  this  thesis  The  of  gain s h a l l not  Date  PHYSICS '  U n i v e r s i t y o f B r i t i s h Columbia  2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5  or  i s understood that copying o r p u b l i c a t i o n  written permission.  Department  that  r e f e r e n c e and study.  f o r s c h o l a r l y purposes may be granted by the Head of my Department by h i s  for  be allowed without my  i  ABSTRACT  The Panofsky  ratio  i n H e , P =a)(TT~ He-> HiT )/u(Tr~ He^ HY) , has 3  3  3  0  3  3  3  been measured e x p e r i m e n t a l l y f o r a b s o r p t i o n of n e g a t i v e p i o h s a t r e s t .  _  A 30 MeV TT beam was degraded and stopped target.  The high-energy  i n a 1.9 cm t h i c k l i q u i d  3  He  photons, from t h e i n f l i g h t TT°-^YY decay and  the r a d i a t i v e c a p t u r e c h a n n e l s , were d e t e c t e d by a l a r g e N a l ( T l ) c r y s t a l (46 cm (j) x 51 cm). and  The l a r g e d i s t a n c e (2.8 meters) between t h e c r y s t a l  t h e h e l i u m t a r g e t p r o v i d e d a good t i m e - o f - f l i g h t  photons, w i t h a n e g l i g i b l e n e u t r o n c o n t a m i n a t i o n . 135.8  A 4.5% r e s o l u t i o n a t  MeV was a c h i e v e d by t h e d e t e c t o r and made p o s s i b l e a good s e p a r a t i o n  between t h e r a d i a t i v e break-up channels interest presented  (dny + pnny) and t h e peak of  3 5 ( Hy)• About 1.1 x 10 photon events were observed  i n t h e data  i n t h i s work. After  s u b t r a c t i o n o f t h e t a r g e t empty backgrounds, t h e t h e o r e t i c a l  l i n e shapes were f o l d e d w i t h t h e e x p e r i m e n t a l to t h e d a t a . and  s e l e c t i o n of the  The Amado model was used  thus e x t r a c t t h e Panofsky  ratio.  energy  r e s o l u t i o n and f i t t e d  t o r e p r e s e n t t h e break-up  channels  A v a l u e o f P^ = 2.83 ± 0.07 was 3  determined,  n o t i n c l u d i n g t h e i n f l i g h t c o r r e c t i o n s and assuming f o r He  the i n t e r n a l c o n v e r s i o n r a t e o f hydrogen. A general p i c t u r e of the r a d i a t i v e pion capture processes i n 3 3 n u c l e i i s a l s o g i v e n , i n which •.i-itHeKt i s a t e s t case f o r t h e impulse approximation  and t h e h y p o t h e s i s of p a r t i a l c o n s e r v a t i o n of a x i a l - v e c t o r  current i n n u c l e i . Moreover, a second cesses  r a t i o , B^, between t h e r a d i a t i v e c a p t u r e  ( r a t i o o f t h e break-up channels  measured t o be' Bt. = 1.35 ± 0.11.  t o t h e e l a s t i c channel)  pro-  has been  ii  TABLE OF CONTENTS  ABSTRACT TABLE OF CONTENT LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENT < CHAPTER 1  INTRODUCTION  1.1 .1 .2 .3 1.2 .1 ,2 .3 1.3 CHAPTER 2  THE EXPERIMENT  2.1 2.2 2.3 .1 .2 2.4 CHAPTER 3  The P i o n Beam The Helium T a r g e t Equipment Set-up Electronics The N a l c r y s t a l SPECTRA  3.1 .1 .2 3.2 .1 .2 3.3 .1 .2 .3 3.4  Stopped p i o n a b s o r p t i o n Hydrogen Deuterium A > 2 Nuclei Helium^ ir Capture P r o c e s s e s ^ The Eanofsky R a t i o i n He R a d i a t i v e Break-up Previous Results  The Time S p e c t r a The RF s i g n a l Time-of-flight The "T2 n e u t r o n " Contamination Helium-3 Runs Background and Contamination Raw S p e c t r a Cuts on time Energy S p e c t r a Random Events Scalers  iii  Page CHAPTER 4  DATA ANALYSIS  4.1 .1 .2 .3 4.2 .1 .2 .3 4.3 .1 .2 .3 CHAPTER 5 5.1 5.2 5.3 BIBLIOGRAPHY  Target Empty Run E s t i m a t e s f o r each k i n d o f background 50 T2 Neutron Background N o r m a l i z a t i o n 53 Empty Target Background N o r m a l i z a t i o n 57 F i t t i n g of the Spectra 59 Low-Energy Background^ 60 L i n e s from t h e IT + He R e a c t i o n s 65 The 4 - l i n e F i t s 66 E r r o r P r o c e s s i n g and Panofsky. R a t i o C a l c u l a t i o n 7 0 C o r r e c t i o n s and Sources o f E r r o r s 70 The Panofsky R a t i o - P 78 The R a t i o B 83 3  3  CONCLUSIONS A b s o l u t e Rates Delayed Events The F u t u r e o f the Panofsky R a t i o  85 86 87 90  iv  LIST OF TABLES Page  Table I  E x p e r i m e n t a l b r a n c h i n g r a t i o s f o r IT c a p t u r e on  Table I I  F r a c t i o n o f the photons missed  Table I I I  Random and photon c o u n t i n g r a t e s  T a b l e IV  S c a l e r s f o r t h e experiment  Table V  E x t r a p o l a t i o n method f o r T2 neutrons  Table VI  E v a l u a t i o n o f e r r o r s i n v o l v e d i n the T2  3  He .  13 43  by t h e TOF c u t s  48 ........  .....  49 54  neutron  background w i t h r e s p e c t t o the t a r g e t empty r u n  56  Table V I I  N o r m a l i z a t i o n f a c t o r s f o r t h e t a r g e t empty background  58  Table V I I I  Comparison of reduced  chi-squares f o r electron  fits  between 17 and 79 MeV f o r r u n #164  64  T a b l e IX  D e s c r i p t i o n of the f i t s  69  Table X  Example o f e r r o r and c a l c u l a t i o n procedures  71  T a b l e XI  Sum i n each c a p t u r e channel f o r each r u n ............  77  Table X I I  External conversion c o r r e c t i v e factors  80  Table X I I I  I n d i v i d u a l Panof sky r a t i o s f o r each r u n  T a b l e XIV  I n d i v i d u a l r a d i a t i v e r a t i o s f o r each r u n  T a b l e XV  Summary o f e x p e r i m e n t a l and t h e o r e t i c a l r a t i o s  f o r t h e f i v e runs  . ....  81 83  ......  88  V  LIST OF FIGURES  Page Figure  (1.1)  Radiative capture spectra i n helium  Figure  (1.2)  P o l e model diagram f o r r a d i a t i v e TT c a p t u r e  12  Figure  (2.1.1)  Lay-out of the M9 c h a n n e l  16  Figure  (2.3.1)  Lay-out o f the t a r g e t a r e a and c r o s s - s e c t i o n of the h e l i u m t a r g e t  5  ....  19  Figure  (2.3.2)  Diagram of the e l e c t r o n i c s  Figure  (2.4.1)  129 MeV  Figure  (2.4.2)  N a l t i m i n g r e s p o n s e i n r u n 168  Figure  (3.1.1)  Time of f l i g h t  Figure  (3.1.2)  T i m e - o f - f l i g h t s e p a r a t i o n i n r u n 169  33  Figure  (3.1.3) . Energy s p e c t r a f o r v a r i o u s time c u t s  34  Figure  (3.2.1)  Figure  (3.2.2)  Figure  (3.2.3)  Figure  (3.2.4)  photon from n-y c o i n c i d e n c e  22 .............  f o r beam p a r t i c l e s  26 28  •  31 •  Time-energy d i s t r i b u t i o n of n e u t r a l events from a p a r t i a l He r u n (#169) .......... Contour p l o t of f i g u r e (3.2.1) D e t a i l e d contour p l o t f o r photon events i n r u n 168  36 3  7  38  Time-energy d i s t r i b u t i o n of events from the t a r g e t empty r u n  40  Figure  (3.2.5)  Contour p l o t of f i g u r e (3.2.4)  41  Figure  (3.3.1)  Raw photon spectrum o f r u n 169  46  Figure  (3.3.2)  G a i n s h i f t e d photon spectrum of r u n 169  Figure  (4.1.1)  T a r g e t empty photon spectrum  Figure  (4.2.1)  Time-energy d i s t r i b u t i o n of e l e c t r o n s f o r a partial He r u n (#169) . .  — . . •  47 51  61  vi  Page Figure  (4.2.2)  E l e c t r o n energy spectrum f o r r u n 164  Figure  (4.2.3)  F i t of r u n 169 a f t e r s u b t r a c t i o n of t h e  '  63  backgrounds .....................................  67  F i g u r e (4.2.4)  C o n t r i b u t i o n s t o t h e f i t o f f i g u r e (4.2.3)  68  F i g u r e (5.3)  V a l u e s o f t h e Panofsky r a t i o i n helium-3  88  vii  ACKNOWLEDGEMENTS  Je t i e n s a exprimer ma v i v e r e c o n n a i s s a n c e au p r o f e s s e u r M i c h a e l D. H a s i n o f f pour l ' a i d e et 1 encouragement p a t i e n t q u ' i l m'a 1  a p p o r t ^ s l o r s de l a p r e p a r a t i o n e t de l a r e d a c t i o n de c e t t e t h e s e . J e r e m e r c i e a u s s i t o u t spfacialement l e p r o f e s s e u r D.F. Measday e t l e d o c t e u r J . E . S p u l l e r pour de nombreux e n t r e t i e n s au c o u r s d e s q u e l s i l s ont su m ' 6 c i a i r e r sur l e s v e r i t a b l e s problemes de 1'experience f a i r e appr£cier l a s i g n i f i c a t i o n Que  e t m'en  physique.  l e s a u t r e s membres du groupe, D. B e r g h o f e r , T. Suzuki e t  l e s d o c t e u r s R. MacDonald, J-M. P o u t i s s o u , R. P o u t i s s o u e t M. Salomon, q u i par l e u r temps e t l e u r t r a v a i l ont rendu p o s s i b l e l e succes de c e t t e e x p e r i e n c e t r o u v e n t i c i l e u r j u s t e p a r t de m£rite e t s o i e n t remerci£s de c e t i n a p p r e c i a b l e a p p o r t . Je s u i s dgalement r e c o n n a i s s a n t au c o n s e i l n a t i o n a l de r e c h e r c h e du Canada pour son a p p u i f i n a n c i e r au cours de c e s deux ann£es d'dtudes a Vancouver.  1  Chapter 1  §1.1  Introduction  Stopped  Pion Absorption  N e g a t i v e p i o n s brought r e d by an atomic  to r e s t i n a m a t e r i a l are g e n e r a l l y captu-  system i n a l a r g e quantum number s t a t e to form p i o n i c  atoms. The pioris then q u i c k l y cascade down by X-ray or Auger  electron  e m i s s i o n to lower l e v e l s from which they i n t e r a c t w i t h the n u c l e u s . case of a m o l e c u l a r t a r g e t , m o l e c u l a r p i o n i c  s t a t e s may  In the  e x i s t but they a r e  v e r y u n l i k e l y because o f the s m a l l o r b i t a l r a d i u s r e q u i r e d by the mass o f the p i o n .  Moreover, i t has been observed t h a t when d i f f e r e n t atoms e n t e r  i n the c o m p o s i t i o n of a m o l e c u l e , t h e r e i s a p r e f e r e n t i a l c a p t u r e by h e a v i e r atoms. l i c h et a l . ,  T h i s p r o c e s s has been measured f o r example [see J.A.  1972]  i n hydrogenous compounds on the b a s i s of the c h a r g e -  exchange r e a c t i o n TT p gen and helium-3: is a direct  Bistir-  TT°n which i s suppressed i n most atoms except  the d e c r e a s e of t h i s r a t e w i t h r e s p e c t t o pure  hydro-  hydrogen  i n d i c a t i o n of the e f f e c t .  P i o n a b s o r p t i o n o c c u r s m a i n l y from 3s and 4s o r b i t s f o r hydrogen isotopes  [M. Leon and H.A.  Bethe, 1962], I s and 2p o r b i t s f o r o t h e r  low-  mass n u c l e i but c o n t r i b u t i o n s from h i g h e r o r b i t s become more and more imp o r t a n t as A i n c r e a s e s .  Because the cascade time and a b s o r p t i o n time  -12 ( ^10  sec) IH.W.  Baer et a l . , 1977]  a r e much s m a l l e r than the m e a n - l i f e  —8 time of the f r e e p i o n (2.6 x 10 absorbed.  s e c ) , most of the stopped p i o n s a r e  2  §1.1.1  Hydrogen The  s i m p l e s t and l o g i c a l f i r s t c h o i c e o f t a r g e t f o r t h e study of  stopped p i o n r e a c t i o n s w i t h n u c l e i i s hydrogen.  The a b s o r p t i o n from t h e  ns o r b i t s proceeds e s s e n t i a l l y through two c h a n n e l s : IT  + p  ->  n + TT°  charge-exchange  TT  + p  ->  n + y  r a d i a t i v e capture  The r a d i a t i v e c a p t u r e r e a c t i o n was one o f t h e f i r s t methods used t o d e t e r mine t h e mass o f the p i o n .  The n e u t r a l p i o n from t h e charge-exchange  —16 r e a c t i o n decays m a i n l y i n two photons et  a l . [W.K.H. Panofsky e t a l . ,  ( T - 10  s e c ) . I n 1951, Panofsky  1951] f i r s t measured t h e r a t i o P^ o f t h e  rates o f the strong i n t e r a c t i o n to the electromagnetic i n t e r a c t i o n : o)(ir p -»• mr°) P  l  =  to (IT p  ny )  They were f o l l o w e d by many o t h e r e x p e r i m e n t e r s . last  Among these r e s u l t s , t h e  two b e s t d e t e r m i n a t i o n s of t h e r a t i o were done by C o c c o n i et a l .  [V.T. C o c c o n i e t a l . ,  1961] and S p u l l e r e t a l . [ J . E . S p u l l e r e t a l . , 1977]  who found 1.533 ± 0.021 and 1.546 ± 0 . 0 0 9 ' r e s p e c t i v e l y , both u s i n g a N a l ( T l ) photon  spectrometer method.  Anderson that  and Fermi  [H.L. Anderson  and F. Fermi, 1952]  showed  a l i n k e x i s t s between t h e l e w ^ e n e r g y - p i e n - r e a c t i o n s ( i . e . s c a t t e r i n g  l e n g t h s ) and t h e p i o n p h o t o p r o d u c t i o n amplitude a t t h r e s h o l d .  The e x p e r i -  mental Panofsky r a t i o can t h e r e f o r e be used a s a t e s t o f t h e charge i n d e pendence p r i n c i p l e of t h e s t r o n g i n t e r a c t i o n , t h e d e t a i l e d b a l a n c e sis  hypothe-  f o r t i m e - r e v e r s e d r e a c t i o n s and procedures o f e x t r a p o l a t i o n a t zero  energy.  3  §1.1.2  Deuterium In deuterium,  the charge-exchange r e a c t i o n proceeds by  e m i s s i o n of the neutrons and a TT°.  the  For n e g a t i v e p i o n s (odd p a r i t y )  c a p t u r e d from the ns o r b i t s , the P a u l i p r i n c i p l e r e q u i r e s t h a t the  two  3 neutrons be e m i t t e d i n an a n t i s y m m e t r i c s t a t e , i . e . i n a  P s t a t e and  t h e r e f o r e the TT° must be e m i t t e d i n a p-wave t o c o n s e r v e s p i n and S i n c e the ir° has a k i n e t i c energy o f o n l y 1 MeV, suppressed  parity.  the r e a c t i o n i s g r e a t l y  ( r e l a t i v e to hydrogen, where the ir° has 2.9 MeV  and i s emitted  i n an s-wave. On the b a s i s o f the low b i n d i n g energy of the n u c l e u s , the  impulse  a p p r o x i m a t i o n and the Panofsky r a t i o i n hydrogen were used to o b t a i n f u r t h e r r e l a t i o n s h i p s between the low-energy  pion reactions.  c a p t u r e r e a c t i o n a l s o r e p r e s e n t s a two-neutron s c a t t e r i n g l e n g t h (a  The  radiative  system f o r which the  n-n  ) c o u l d be d e r i v e d i n the a p p r o x i m a t i o n of the  momentum d i f f e r e n c e between the n e u t r o n s .  low  T h i s a p p r o x i m a t i o n i s based  the e x p e r i m e n t a l o b s e r v a t i o n t h a t the photons  on  a r e s h a r p l y peaked towards  high energies.  §1.1,3  A > 2  Nuclei 3  For n u c l e i h e a v i e r than  He,  charge exchange appears  p r e s s e d even when i t i s e n e r g e t i c a l l y a l l o w e d .  to be  There a r e a l s o many more  p o s s i b l e c h a n n e l s open f o r the p i o n i n t e r a c t i o n , w i t h the p o s s i b l e of one or more n u c l e o n s . of about gen  ejectior  The r a d i a t i v e c a p t u r e r e a c t i o n has a p r o b a b i l i t y  2% f o r the medium-mass n u c l e i i n comparison  [V.T. C o c c o n i et a l . ,  sup-  1961], 24.7%  f o r deuterium  w i t h 39.5% [J.W.  f o r hydro-  Ryan, 1963]  and  4  14.0%  f o r He J  The  I P . T r u o l et a l . , 1974]. e x i s t e n c e of r a d i a t i v e c a p t u r e p r o c e s s e s i n complex n u c l e i  o f f e r s the p o s s i b i l i t y of c o n s i d e r i n g the p i o n i n t e r a c t i o n w i t h a p r o t o n s i d e of the n u c l e u s r a t h e r than w i t h the n u c l e u s as a whole.  The  study of  photon s p e c t r a , f o r which the e x p e r i m e n t a l energy r e s o l u t i o n i s f a r b e t t e r than f o r the n e u t r o n s , r e p r e s e n t s a way s t r u c t u r e and  of i n v e s t i g a t i o n g both the n u c l e a r  the mechanisms of p i o n a b s o r p t i o n .  For h i g h - r e s o l u t i o n d e t e c t o r s , such as the p a i r at H.W.  the Lawrence B e r k e l e y L a b o r a t o r y  spectrometer  [J.A. B i s t i r l i c h e t a l . ,  Baer e t a l . , 1973], which has a 2.0 MeV  used  1972;  (FWHM) r e s o l u t i o n , i t i s a l s o  p o s s i b l e to study the e x c i t e d s t a t e s of the r e s i d u a l n u c l e i i n r a d i a t i v e c a p t u r e r e a c t i o n s and  t e s t the p a r t i a l c o n s e r v a t i o n of a x i a l v e c t o r c u r r e n t  (PCAC) i n the s o f t p i o n  limit.  4 Such e x c i t a t i o n s have been s t u d i e d i n  He.  The spectrum  obtained  4 by B i s t i r l i c h e t a l . f o r r a d i a t i v e c a p t u r e i n [J.A. B i s t i r l i c h et a l . , 1970]  He was  detector for  reproduced  by assuming the e x i s t e n c e of t h r e e e x c i t e d  s t a t e s whose p o s i t i o n s a r e i n agreement w i t h 4-nucleon analyses.  well  system p h a s e - s h i f t  T h e i r c a l c u l a t e d c u r v e , f o l d e d w i t h the r e s o l u t i o n of t h e i r (but w i t h t h e i r e f f i c i e n c y f a c t o r removed) i s shown i n f i g u r e ( l . l a )  purpose of u n d e r s t a n d i n g  the sources of background i n v o l v e d i n our  experiment. A g e n e r a l r e v i e w of r a d i a t i v e p i o n c a p t u r e has been g i v e n r e c e n t l y by H.W.  Baer, K.M.  Crowe and P. Trub"l [1977].  5 F i g u r e (1.1)  RADIATIVE CAPTURE SPECTRA IN HELIUM I  : 1  1  1  :  1  (a)  4  He(iT  ,y)  >— cr. CE  cr. (b) cn  CY.  3  CE  0  HeOT,Y)  2 5  TT° photons  5 0  7 5  break-up  1 0 0  135.8. MeV  1 2 5  1 5 0  PHOTON ENERGY (MEV) He; the theoreF i g u r e (1.1) . R a d i a t i v e c a p t u r e s p e c t r a i n h e l i u m . (a) m t i c a l c u r v e , f o l d e d w i t h the r e s o l u t i o n o f t h e i r d e t e c t o r , i s from J.A. B i s t i r l i c h e t a l . [ 1 9 7 0 ] . . (b) i n He; the break-up channels a r e r e p r e s e n t e d by the Amado model [A.C. P h i l l i p s and F. R o i g , 1974].  6  §1.2  Helium-3  3 The  He n u c l e u s , the s u b j e c t of the p r e s e n t e x p e r i m e n t a l work,  r e p r e s e n t s a l i n k between the s i m p l e s t b a s i c n u c l e i complex ones and  i s t h e r e f o r e a t e s t case f o r the a p p l i c a t i o n of the  impulse a p p r o x i m a t i o n addition  (H and D) and more  (IA).  T h i s i s a l s o the o n l y o t h e r n u c l e u s , i n  to hydrogen, f o r which the charge-exchange r e a c t i o n  occur s i g n i f i c a n t l y and  i s known to  f o r which the r a d i a t i v e y i e l d i s s t i l l  even w i t h the presence of n o n - r a d i a t i v e break-up c h a n n e l s .  important,  Moreover, a l l  the p r o c e s s e s r e s u l t i n g from p i o n a b s o r p t i o n have been observed  for this  3-nucleon system:  coherent  t h i s i s e s p e c i a l l y h e l p f u l i n o r d e r to get a  p i c t u r e of the system and t b s t e s t i t h e v a l i d i t y of i t s t h e o r e t i c a l descriptions.  §1.2.1  Capture  TT  Processes  The f o l l o w i n g  channels a r e allowed by the c o n s e r v a t i o n laws f o r  the c a p t u r e of n e g a t i v e p i o n s a t r e s t i n  TT  He  +  TT  - ^ 3„  He  +  ->  3  ->  3  3 ir TT~  + 3  +  iT + TT"  He  +  3  3  H, + H  3F+  +  He  ^°  + y  3  He:  charge-exchange  (1)  e l a s t i c r a d i a t i v e capture  (2)  (3)  n + Y } r a d i a t i v e break-up  p + n + n + Y  (4)  d + n  He  -»-  He  ->  (5) p + n + n  } absorption  (6)  7  The n e u t r a l p i o n emitted i n t h e charge-exchange  r e a c t i o n has a  k i n e t i c energy o f 3.89 MeV from t h e d i f f e r e n c e i n masses, l e s s t h e b i n d i n g energy o f t h e TT i n t h e K - s h e l l l i f e o f 0.83 x 10 ^  (0.016 MeV).  The TT° decays w i t h a mean-  s e c . The main decay modes a r e [ P a r t i c l e Data Group,  1976] : TT°  +  y Y  TT°  ->  Y e  +  e"  (98.85 ± 0.05 %)  (a)  ( 1.15 ± 0.05 %)  (b)  The o t h e r modes, i n c l u d i n g TT° -»- e e e e , a r e a t l e a s t f o u r o r d e r s of +  +  magnitude lower i n p r o b a n i l i t y than t h e predominant f o r e neglected here.  YY mode and a r e t h e r e -  The photons from t h e two main channels a r e e m i t t e d  i s o t r o p i c a l l y i n t h e c e n t e r o f mass o f t h e TT°, but as t h e TT° has a velocity  v = 0.24 c, they a r e D o p p l e r - s h i f t e d i n t h e l a b o r a t o r y frame t o  y i e l d a u n i f o r m energy d i s t r i b u t i o n between t h e two l i m i t s , g i v e n by mc  2  0  E  =[.,  |  Y  (i ± e) where B = v / c , c i s t h e speed o f light  Y = l//(l-.{3 ) 2  m c 0  2  = 134.96 MeV, mass o f the TT°.  i . e . 53.1 and 85.7 MeV f o r H e . 3  3 The e l a s t i c  Hy c h a n n e l y i e l d s a high-energy gamma-ray a t 135.8 MeV  w h i l e t h e endpoints f o r t h e two o t h e r r a d i a t i v e c a p t u r e p r o c e s s e s a r e 129.8  and 127.7 MeV f o r r e a c t i o n s  possibility,  (3) and ( 4 ) , r e s p e c t i v e l y .  One f u r t h e r  t h e i n t e r n a l c o n v e r s i o n o f t h e photon from r e a c t i o n  to be c o n s i d e r e d .  F o r hydrogen,  ( 2 ) , has  t h e p r o b a b i l i t y (O(TT p->ne e )/CO(TT p-*ny)  has been c a l c u l a t e d t o be about 1% by Joseph 3 r a t e i s n o t known f o r He.  +  [D.W. Joseph, 1960], but t h i s  8  §1.2.2  The Panofsky  R a t i o i n ^He  3 The Panofsky  r a t i o P^ i n He i s d e f i n e d t h e same way as i t i s i n  hydrogen, i . e . the r a t i o o f t h e s t r o n g i n t e r a c t i o n t o t h e e l e c t r o m a g n e t i c interaction;  however, t h e i n t e r n a l c o n v e r s i o n p r o c e s s i s u s u a l l y not  3 i n c l u d e d f o r He:  _„ p. = 3  CO(TT  „  He  -*•  a)(Tr" He + 3  3  HTT°) Hy  (1)  =  )  (2)  There have been, t o t h i s time, two e x p e r i m e n t a l  determinations  of t h i s number.  3 Zaimidoroga  e t a l . [O.A. Zaimidoroga  et a l . ,  1965] used an  He  d i f f u s i o n chamber operated a t p r e s s u r e s of 17.5 and 6.5 atm. t o observe  3 the r e c o i l t r i t o n .  In the r a d i a t i v e capture r e a c t i o n  (2) t h e  H  energy  3 i s 3.28 MeV but i n t h e charge-exchange r e a c t i o n ( 1 ) t h e 0.19 MeV.  H energy  i s only  F o r c o n s i s t e n c y , because o f the r e s u l t i n g s h o r t t r a c k s , they  determined P^ a t d i f f e r e n t p r e s s u r e s . P = 2.28 ± 0.18  T h e i r measurements y i e l d e d  3  Trub'l e t a l . [P. Truo'l e t a l . , u s i n g a 180° p a i r spectrometer 129.4  1974] repeated t h e experiment  w i t h a r e s o l u t i o n o f 2.0 MeV  (FWHM) a t  MeV, p r o v i d i n g a good s e p a r a t i o n o f t h e break-up channels and t h e  e l a s t i c peak i n t h e photon spectrum.  The e f f i c i e n c y o f t h e i r d e t e c t o r  was low i n t h e charge-exchange r e g i o n and v e r y s e n s i t i v e t o t h e spark 3 chamber performance, so t h a t they r a n t h e l i q u i d  He t a r g e t i n t e r c h a n g e a -  b l y w i t h a hydrogen t a r g e t , f o r which the Panofsky w e l l known.  They measured a v a l u e , P^ =2.68  p r e s e n t e d an impulse a p p r o x i m a t i o n  r a t i o P^ was a l r e a d y  ± 0.13, w i t h which they  calculation.  T h i s a n a l y s i s , based on  9  the assumption  by E r i c s o n and F i g u r e a u [M. E r i c s o n and A. F i g u r e a u ,  1967]  t h a t the r a d i a t i v e c a p t u r e comes m o s t l y from the I s s t a t e o f the TT , i n v o l v e s a r e n o r m a l i z e d Panofsky t i c a l v a l u e was comparison 2.68  a l s o used  r a t i o f o r hydrogen;  was  done by P h i l l i p s and Roig  2p TT  w i t h t h e i r measured v a l u e  impulse approximation  calculation  [A.C. P h i l l i p s and F. R o i g , 1 9 7 4 ] .  a n a l y s i s , d i f f e r e n t percentages the 3-nucleon  wave f u n c t i o n s .  t i e s 1(1.8%,0%),  In t h i s  of S' and D s t a t e s were p o s t u l a t e d f o r A f t e r c o r r e c t i o n s f o r c a p t u r e from  s t a t e , v a l u e s of P^ o b t a i n e d f o r d i f f e r e n t p a i r s of S',D  respectively.  the  c o n s i d e r e d as a d i r e c t t e s t of the IA c a l c u l a t i o n .  F o l l o w i n g t h i s paper, another was  theore-  i n t h e i r e x p e r i m e n t a l d e t e r m i n a t i o n of P^,  of the c a l c u l a t e d v a l u e of 2.49  ± 0.13  but as t h i s  11(1.6%,5%) and  111(1.4%,9%) were 2.51,  2.79  the  probabiliand  2.98,  The advantage o f u s i n g the r a t i o of the two c a p t u r e r a t e s  i s t h a t the u n c e r t a i n t y of the i n i t i a l channels and can be n e g l e c t e d i n P^.  s t a t e i n t e r a c t i o n a p p l i e s to both They estimated t h a t the c o r r e c t i o n s  to these c a l c u l a t i o n s would be of the same order as the e f f e c t s of the v i r t u a l meson i n t e r a c t i o n i n the IA c a l c u l a t i o n f o r the B-decay of i . e . between.0% and 12%, Other  tritium,  i n agreement w i t h T r u o l ' s v a l u e .  IA c a l c u l a t i o n s have been performed  by M i z u t a et a l .  [M. M i z u t a et al.., 1975], y i e l d i n g a 2.63-3.06 range f o r the v a l u e of the Panofsky  ratio. The p a r t i a l c o n s e r v a t i o n of a x i a l - v e c t o r c u r r e n t (PCAC)  has a l s o been used  to determine  t h e o r e t i c a l l y the Panofsky  M. Erieson-,and A. F i g u r e a u , 1967,  1969;  ratio  M . E r i c s o n and M. Rho,  approach [see  1972].  T h i s h y p o t h e s i s o r i g i n a t e s from the a p p l i c a t i o n of weak i n t e r a c t i o n to  10  the s t r o n g i n t e r a c t i o n .  The v e c t o r p a r t of the h a d r o n i c c u r r e n t of the  weak i n t e r a c t i o n i s conserved, but the a x i a l p a r t cannot  be, as the mass  of the p i o n , f o r the p i o n decay, would have to be z e r o , thus the i d e a of p a r t i a l c o n s e r v a t i o n from a s m a l l c o r r e c t i o n t o t h i s c o u p l i n g c o n s t a n t . U s i n g the s i m i l a r i t i e s w i t h the weak i n t e r a c t i o n i n u and D.J. H a l l , 1961], the IT  capture  c a p t u r e i s c o n s i d e r e d , i n the  l i m i t , as the i n v e r s e of low-energy p h o t o p r o d u c t i o n . f i n a l n u c l e i a r e t r e a t e d as elementary  particles.  value  s o f t - p i o n ) used The  [1967]), a r e 1.9  and  2.1,  Fujii  soft-pion  Both i n i t i a l  and  Results obtained  these methods, a f t e r c o r r e c t i o n f o r the p-meson exhange (from = 2.70  [A.  by  their  depending on the method  (IA o r  to c a l c u l a t e the charge-exchange c r o s s - s e c t i o n .  g o a l of t h i s experiment  was  to redetermine  the Panofsky  ratio  3 in  He w i t h a 100%  e f f i c i e n t N a l d e t e c t o r which would reduce  the experimen-  t a l e r r o r i n the charge-exchange energy r e g i o n and h o p e f u l l y improve the a c c u r a c y of the r a t i o i t s e l f .  S i n c e theatwo e x i s t i n g v a l u e s d i s a g r e e by  c o n s i d e r a b l y more than t h e i r quoted should a l l o w one  e r r o r s , a t h i r d a c c u r a t e measurement  of the e a r l y measurements to be  rejected.  11  §1.2.3  Radiative Break-up Due to the overlap of the charge-exchange and the e l a s t i c r a d i a -  t i v e capture channels with the break-up channels, especially after folding in the experimental Nal resolution, a good  knowledge of a l l l i n e shapes  i s necessary to ascertain their respective contributions. In the Amado model [R.D. Amado, 1963], the f i n a l 3-nucleon  state  1 comes as a solution of the Faddeev equations i n which separable 2-nucleon interactions are assumed.  3 SQ and S^  In these states, one considers a "pair  of nucleons with respect to the t h i r d nucleon.  Both states imply a zero  o r b i t a l angular momentum between the t h i r d nucleon and the pair i t s e l f , but i n the f i r s t case the spins of the nucleons of the pair are a n t i p a r a l l e l while they are p a r a l l e l i n the second case.  P h i l l i p s and Roig  [A.C. P h i l l i p s and F. Roig, 1974] used t h i s model to calculate the r e l a t i v e rates for the break-up and e l a s t i c channels and to obtain the shape of the photon energy spectrum.  A comparison with experimental data of Truolet a l .  [1974] shows a good agreement i n the absolute rate and the energy bution (through the r a t i o s and shape).  distri-  However, for energies below M.10 MeV,  the agreement i s poor due to the o f f - s h e l l .part df the interaction ( i . e . the conservation of energy and momentum i s momentarily broken).  The good f i t  i n the high-energy region does not y i e l d , moreover, any evidence of a 3- nucleon resonance. A general approach f o r the r a d i a t i v e break-up channels has also been developed by Dakhno and Prokoshkin [L.G. Dakhno and Yu.D. Prokoshkin, 1968].  This"pole-model" (figure 1.2) involves the capture of a negative pion  by a quasi-free proton inside of the nucleus.  This model seems to provide  a much better description of the photon continuum than the Fermi-gas model  12  or a simple phase-space distribution.  It was used by B i s t i r l i c h et a l .  [J.A. B i s t i r l i c h et a l . , 1972], in conjunction with excited states of the final nucleus, to describe the photon spectra for ir absorption on nuclei with 5<A<41. However, there are s t i l l important uncertainties in the knowledge of i n i t i a l - and final-state interaction between particles or groups of particles involved in the description.  Figure (1.2) Pole model diagram for radiative TT capture with neutron emissioni:n neutroa emission.  No pole-model calculation was available to us at the time of this work, but the results of such a calculation were presented in 1974 by Truol et a l . , along with their experimental spectrum. Although a comparison between the information obtained using both the pole model and the Amado model would have been preferable to illustrate the model-dependent effects in the determination of P^, the Amado model described by Phillips and Roig was used in this analysis.  It provided a very good f i t to the data in the  high-energy region. The individual and summed shapes of the break-up channels are shown in figure (1.1b) together with the charge-exchange and elastic radiative capture spectral functions. The low-energy part of the radiative break-up channel (<90 MeV) i s an extrapolation by the polynomial method described in section (4.2.1) from the data in the 90-120 MeV region.  Further comments on this choice w i l l be given later in the analysis. In relation to these radiative break-up channels, another ratio,  B , i s defined between the radiative capture channels, namely the ratio of Q  13  the two break-up channels r a t e t o the r a t e f o r e l a s t i c c a p t u r e a t 135.8 as a u s e f u l parameter of the 3-nucleon f i n a l (3) + (4) 3  -3 O)(TT  He  (2)  states. dny) +  CO(TT  w(Tr" He -> 3  3  -3 He -> pnny)  Hy)  Depending on the S' and D c o n t r i b u t i o n s i n the 3-nucleon P h i l l i p s and.Roig o b t a i n e d v a l u e s f o r B (see l a s t  §1.3  3  MeV,  wave f u n c t i o n ,  o f 0.84(1), 1.10(11) and  1.27(111)  section).  Previous Results  T a b l e I summarizes p r e v i o u s experimental r e s u l t s f o r the d i f f e r e n t b r a n c h i n g r a t i o s f o r TT' a b s o r p t i o n i n  Table I  3  He.  E x p e r i m e n t a l b r a n c h i n g r a t i o s f o r TT c a p t u r e on  Final state  Zaimidoroga  et a l .  3  (2)  3  HTT°  H  Y  15.8  pnny  (5)  dn  • 15:9?± 2.?3i  (6)  pnn  57.8 ± 5.4  B  3  = [(3)+(4)]/(2)  ±  2.3  6.6 ± 0.8  3.6 ± 1.2  (4)  = (l)/(2)  17.8  6.9 ± 0.5  dny  3  [1974]  ±0.8  (3)  P  He  Trub'l e t a l .  11965, 1967]  (1)  3  2.28  ± 0.18  }  7.4 ± 1.0  }  68.2 ± 2.6  2.68  ±  0.13  1.12 ± 0.05  14  Chapter 2  The  Experiment  The Panofsky r a t i o i n helium-3  Is d e f i n e d as the r a t i o of the  - 3 3 r e a c t i o n TT + He -> H+TT° over the - 3 3 r a t e of the r a d i a t i v e , c a p t u r e r e a c t i o n TT + He -> H+y. In o r d e r t o determine t r a n s i t i o n r a t e of the charge-exchange  t h i s v a l u e e x p e r i m e n t a l l y , a beam of n e g a t i v e p i o n s was  stopped i n a l i q u i d  3 He t a r g e t . the  photons  A l a r g e N a l c r y s t a l was  used to o b t a i n the energy spectrum of  emitted from the t a r g e t , and they were d i s t i n g u i s h e d  neutrons by a t i m e - o f - f l i g h t t e c h n i q u e .  Thus, good t i m i n g response  r e q u i r e d from the d e t e c t o r and, because o f the presence of two break-up how  from  c h a n n e l s , the energy r e s o l u t i o n of the c r y s t a l was  was  radiative  critical  as  w e l l a l l the d i f f e r e n t channels would be s e p a r a t e d o u t . T h i s experiment was  i n many ways s i m i l a r to the v e r y p r e c i s e  re-measurement of the Panofsky r a t i o i n hydrogen done r e c e n t l y by J . E . S p u l l e r i n the same l o c a t i o n . a n d u s i n g b a s i c a l l y the same e x p e r i m e n t a l (See J.E. S p u l l e r , 1977). ristic  H i s energy s p e c t r a a l s o e x h i b i t e d the c h a r a c t e -  box from 55 to 83 MeV,  reaction  TT  +p  n+Tr°,  i n d i c a t i n g the events due to the  charge-exchange  as w e l l as a high-energy e l a s t i c peak a t 129.5  from the r a d i a t i v e c a p t u r e r e a c t i o n TT +p -»- n+y, break-up c h a n n e l .  equipment.  MeV,  but without of c o u r s e any  I s h a l l t h e r e f o r e r e f e r the r e a d e r to h i s work f o r a  more d e t a i l e d d i s c u s s i o n of some p o i n t s r e l a t i v e to the equipment a n a l y s i s procedures.  and  15  §2.1  The P i o n Beam T h i s experiment  Meson F a c i l i t y meson h a l l . cyclotron.  was  performed  i n March 1977  (TRIUMF) P r o j e c t u s i n g i t s stopped  H  a t the T r i - U n i v e r s i t y  ir/y channel  i o n s were a c c e l e r a t e d up to 500 MeV  (M9)  i n the  by the s e c t o r - f o c u s s e d  A change of c u r v a t u r e i n the t r a j e c t o r i e s of the i o n s  was  induced when the e l e c t r o n s were s t r i p p e d o f f the i o n s by a t h i n carbon at  an outer r a d i u s of r e v o l u t i o n . > . T h e  w i t h an e f f i c i e n c y of almost  100%  p r o t o n beam was  foil  extracted this  a l o n g the beam l i n e 1 (BL1).  c u r r e n t i n t h i s l i n e d u r i n g the c o r s e of the experiment  The  way  proton  v a r i e d between 12  t y p i c a l l y 3 and  lOuA, i . e . a f l u x of about from 20 to 60 x 10  protons/sec.  At the end of the l i n e the protons were f o c u s s e d onto a 10 cm B e r y l l i u m t a r g e t (T2), which produced per i n c i d e n t p r o t o n . A secondary  a r e l a t i v e l y l a r g e number of n e g a t i v e p i o n s  p i o n beam was  taken a t a 135° backward a n g l e w i t h r e s p e c t  to  the i n c i d e n t p r o t o n beam, as can be seen on f i g u r e  M9  channel was  composed of a s u c c e s s i o n of f i v e quadrupole  bending magnets as shown on the diagram. at  the second  30 MeV  TT  (2.1.1).  focus f o r t h i s channel.  beam (96.3 MeV/c).  c y c l o t r o n magnet, was  magnets and  two  The helium-3 t a r g e t was p o s i t i o n e d  A l l the magnets were s e t to c a r r y a  The l a s t d i p o l e magnet B3, a 30 cm  not used  This  i n t h i s experiment  gap  but imposed a 30  tons  p h y s i c a l c o n s t r a i n t to the p o s i t i o n of the N a l d e t e c t o r . H o r i z o n t a l and v e r t i c a l  slits  between the two  bending magnets B l 2  and B2 were s e t t o 2 and  10 cm r e s p e s t i v e l y , r e s u l t i n g i n a vLOxlO  cm  image of the p r o d u c t i o n t a r g e t a t the h e l i u m t a r g e t p o s i t i o n , w i t h a momentum spread a s s o c i a t e d to the w i d t h of the v e r t i c a l  slits.  Those  15%  17  c o n d i t i o n s were n o t o p t i m a l w i t h r e s p e c t to t h e dimensions of t h e '"'He 2 co n t e n t o f t h e t a r g e t (^80 cm ) , but on t h e other hand enabled  a h i g h beam  f l u x o f about 5x10'' p a r t i c l e s / s e c . Neutrons were removed from "the beam by the c u r v a t u r e of t h e channel but c o n t a m i n a t i o n s  by u  96 MeV r e s p e c t i v e l y ) .  and e  were s t i l l p r e s e n t  ( w i t h e n e r g i e s o f 37 and  I t was e s t i m a t e d , from e a r l i e r experiments w i t h t h e  same momentum f o r t h e beam p a r t i c l e s t h a t t h e r e were about 20% o f t h e p a r t i c l e s , o f t h e beam which were e l e c t r o n s w h i l e t h e muons r e p r e s e n t e d of  6%  them. The macro-duty c y c l e of t h e machine i s e s s e n t i a l l y 100%, but t h e  m i c r o - c y c l e i s o f about 7%. i n b u r s t s a t each 43.3 nsec  T h i s means t h a t the p r o t o n beam onto T2 comes f o r 3.0 nsec a t each time.  t h i s experiment was a r a d i o - f r e q u e n c y beam t o be used l a t e r §2.2  (RF) s i g n a l a s s o c i a t e d w i t h t h e  i n the a n a l y s i s .  The Helium T a r g e t The l i q u i d h e l i u m  J.S. Vincent, and W.R.  t a r g e t used i n t h i s experiment was developed  Smith [ J . S . V i n c e n t and W.R.  by  Smith, 1974] f o r e i t h e r  4  3 He or in  Also available f o r  He s c a t t e r i n g experiments.  The primary  t a r g e t c e l l was c y l i n d r i c a l  shape (10.6 cm ())• x 1.905 cm), i t s a x i s i n t h e same plane as t h e c h a n n e l ,  thus o f f e r i n g a 80 cm  face area.  f i l m o f s u p e r f l u i d Sle  i n the entrance and e x i t double windows (0.0125 cm)  of  the c e l l .  Good thermal  s h i e l d i n g was p r o v i d e d by a  A t an o p e r a t i n g p r e s s u r e o f about 135 mm Hg, these windows were 3  s l i g h t l y domed to g i v e t o t h e  He a c e n t r a l t h i c k n e s s of about 2.0 cm.  L a t e r a l " t h e r m a l s h i e l d i n g was a c h i e v e d by two c o n c e n t r i c copper  shields  18  each wrapped w i t h a few l a y e r s o f 10 microns a l u m i n i z e d s h e e t s . figure  In  (2.3.1) i s reproduced a c r o s s - s e c t i o n o f t h e chamber. The two copper s h i e l d s were t h e c o n t i n u a t i o n o f two r e s e r v o i r s  l o c a t e d over t h e t a r g e t .  The e x t e r n a l tank was f i l l e d by l i q u i d  nitrogen,  and t h e i n n e r one by l i q u i d Ste, b r i n g i n g t h e s h i e l d s to 77°K and 20°K r e s p e c t i v e l y , by c o n d u c t i o n .  Still  3  i n s i d e , a t h i r d pumped l i q u i d  v o i r was connected t o t h e t a r g e t by an heat exchanger i s cryopumped down t o t h e t a r g e t c e l l .  through which  He r e s e r 3 He gas  By t h i s system, t h e heat l o a d o f t h e  t a r g e t was about 10 mW a t 2°K. The c e l l i t s e l f was surrounded by a 10 ^ t o r r vacuum i n s i d e another l a r g e r chamber w i t h 20 cm diameter double windows on each s i d e . r e p r e s e n t e d an o v e r a l l d e n s i t y of 100 mg/cm 120 mg/cm For  2  (P3jje  2  Windows  w h i l e l i q u i d helium-3  averaged  3 A 3 0-08 g/cm ) . The He c o n t a m i n a t i o n o f t h e He gas was 1%.  =  t h e n e c e s s a r y empty t a r g e t r u n , i t was p o s s i b l e t o evaporate out o n l y 3  the  He c o n t e n t o f t h e t a r g e t , l e a v i n g the mylar windows, a d j a c e n t m a t e r i a l  and t h e 2 mm o f §2.3  He s u p e r f l u i d s h i e l d i n g f i l m on each  side.  Equipment  §2.3.1  Set-up A diagram o f t h e l a y - o u t o f t h e e x p e r i m e n t a l a r e a i s shown i n  figure  (2.3.1).  Upstream to t h e h e l i u m t a r g e t was a t e l e s c o p e o f t h r e e  p l a s t i c c o u n t e r s (NE102A) C l , C2 and C3 used t o d e f i n e t h e beam. s i z e o f C3 (8.8 cm  ensured t h a t t h e incoming p a r t i c l e s would be d i r e c t e d  onto t h e He c o n t e n t of t h e 10.6 cm < | >cell. the  The s m a l l  t a r g e t , was used as a v e t o c o u n t e r .  The counter C4, l o c a t e d behind  The C5 c o u n t e r , between t h e f r o n t  ™ 1 meter i  i J  C4  He  CH  C3  C2  2  Cl  Lead collimator OQ C  Lead collimator  i-i  ro  to  Figure  (2.3.1)  Lay-out o f the t a r g e t a r e a  and c r o s s - s e c t i o n o f the h e l i u m t a r g e t . The c o u n t e r s C1,C2 d e f i n e the beam; the  and C3 were used to C4 was. used as a v e t o i n  stop d e f i n i t i o n and C5 as a charge  The S i - L i d e t e c t o r was  identifier.  used by another group f o r mesic X-ray  studies  h-  1  vo  20  f a c e of t h e N a l d e t e c t o r particle  identifier. The  t a r g e t was a c t u a l l y r o t a t e d by a s m a l l a n g l e w i t h r e s p e c t  beam d i r e c t i o n ; increased two  t h i s was p e r m i t t e d  the e f f e c t i v e thickness  detectors  detector  and i t s l e a d c o l l i m a t o r , was used as a charged  present  o f t h e t a r g e t by about 15% and enabled t h e  t o view t h e t a r g e t as w e l l as p o s s i b l e .  The S i - L i  Our experiment was p a r a s i t i c to t h e i r s and t h e r e was no  room t o have t h e N a l d e t e c t o r  tly,  This also  l o c a t e d a t backward a n g l e was used by another group f o r mesic  X-rays s t u d i e s .  order  by i t s l a r g e v i e w i n g a n g l e .  to the  a t a l a r g e angle with respect  t o t h e beam i n  t o reduce the background due to simple s c a t t e r i n g e f f e c t s .  Consequen-  i t was put a t t h e best a v a i l a b l e p o s i t i o n , i . e . a t 14° from t h e beam  a x i s and w i t h t h e r e a r end o f i t s 15 cm &) c o l l i m a t o r a t 280 cm from t h e center  o f t h e t a r g e t , thus sustending  a s o l i d a n g l e o f 2.3 m s t r .  A 2.70 cm t h i c k CH^ degrader was p l a c e d order  t o stop t h e n e g a t i v e  pions i n the t a r g e t .  m i s s i o n measurements was done c o n c e r n i n g rough e s t i m a t e was made u s i n g rator i t s e l f , i n helium.  No o p t i m i z a t i o n by t r a n s -  t h e chosen t h i c k n e s s  but o n l y a  t h e energy l o s s e s i n t h e t e l e s c o p e ,  t h e mode-  t h e windows o f t h e t a r g e t and from t h e range o f n e g a t i v e  I t had been observed i n e a r l i e r experiments o f t h i s  [ J . E . S p u l l e r , 1977; R. MacDonald, 1977; large  i n t h e beam t e l e s c o p e i n  F. C o r r i v e a u ,  pions  type  1977] t h a t w i t h the  (15% FWHM) momentum spread o f t h e beam t h e s t o p p i n g  distribution i s  q u i t e u n i f o r m o r s l o w l y v a r y i n g , w i t h i n the range of t h e mean energy  pions.  T h i s i s e s p e c i a l l y t r u e f o r a t h i n t a r g e t such as we had i n t h e p r e s e n t periment so t h a t t h e exact  c h o i c e o f t h i c k n e s s was o f no r e a l  ex-  concern.  Many o f t h e incoming p i o n s , however, c o u l d be r e g i s t e r e d as s t o p s , without s t o p p i n g  i n the  3 He c o n t e n t of t h e t a r g e t , but i n t h e windows, o r  21  i n t h e s u r f a c e o f t h e v e t o counter ( t h a t i s , not deep enough to f i r e  it).  An empty t a r g e t r u n should c o r r e c t f o r t h e s e e f f e c t s .  §2.3.2  Electronics A diagram of t h e e l e c t r o n i c s used i n t h i s experiment  figure  (2.3.2).  The d a t a a c q u i s i t i o n system proceeded  i s shown on  i n three steps:  i d e n t i f i c a t i o n o f an event, o n - l i n e p r o c e s s i n g by a PDP 11/40 computer and r e c o r d i n g o f t h e d a t a on magnetic  tape.  The r e q u i r e m e n t s f o r an event were Cl.C2.C3.C4.Nal;  i . e . a possible  stop i n t h e t a r g e t a s s o c i a t e d w i t h a count i n t h e N a l c r y s t a l .  This  dence c o n d i t i o n was n o t s t r i n g e n t enough t o r e j e c t beam contaminant  coinciassocia-  ted events but t h i s problem was d e a l t w i t h i n t h e o f f - l i n e a n a l y s i s . the d e l i b e r a t e l y l a r g e  Indeed,  (70 nsec) C1.C2.C3.C4 gate was chosen t o have a b e t t e r  knowledge o f random events over an extended p e r i o d and proved v e r y u s e f u l in later analysis.  The t i m i n g of t h e N a l anode s i g n a l was p r o v i d e d through  an ORTEC 463 c o n s t a n t f r a c t i o n d i s c r i m i n a t o r . was  The event d e f i n i t i o n  logic  used b o t h t o open a f a s t 250 nsec gate f o r a LRS 2248" ADC CAMAC module  and t o s t a r t t h e c l o c k o f t h e LRS 2228 TDC CAMAC module.  The ADC i n t e g r a t e d  the N a l anode s i g n a l as a r e a d i n g o f t h e k i n e t i c energy d e p o s i t e d i n t h e crystal.  Three stop s i g n a l s were r e c o r d e d by t h e TDC:  t h e RF t i m i n g a s s o -  c i a t e d w i t h t h e p r o t o n beam, t h e C3 c o u n t e r and t h e N a l d e t e c t o r . of f l i g h t was d e f i n e d as t h e time f i f f e r e n c e between t h e N a l time and C3, p l a c e d j u s t  The time signal  i n f r o n t o f t h e t a r g e t and a c t i n g as stop time d e f i n i t i o n .  Furthermore, t h e c o i n c i d e n c e b u f f e r r e g i s t e r e d i f t h e p a r t i c l e e n t e r i n g t h e c r y s t a l was charged, as t h e c o u n t e r C5 would have f i r e d .  C5 Charge I d e n t i f i e r  .node, s i g n a l s Nal a  Beam Counters:  C4  C2  C3  Cl  RF s i g n a l  Cerenkov Monitor  "BEAM" Fan I n LRS 127B "STOP" Fan Out LRS 128  Disc.  Fast  Amp.  LRS 133B  LRS 621  Const. Frac Disc. ORTEC 463  1 Logic  Disc.  Disc.  LRS 621'BL  LRS 621  Coincidence Buffer  LRS 621  LRS 429  C i-f  LRS 465  "EVENT" D e f i n i t i o n  Logic Unit LRS 365  Disc. tLRS 621  stop  istop  start  CAMAC ADC  CAMAC TDC  LRS 2249  LRS 2228  OJ  1  /k-J  gate  Fan Out  veto Logic U n i t  Unit  Disc.  *  T3  LRS 465  strobe  LRS 621  Disc. LRS 621  Attetauator  Disc.  Visual Scaler  stop Output Register  CAMAC S c a l e r s E l l i o t - S R 1608  4 PDP 11/40 COMPUTER  Figure  (2.3.2)  Diagram o f t h e e l e c t r o n i c s .  N3 N3  23  To summarize, each event c o n t a i n e d t h e f o l l o w i n g  digital  information: 1.  RF time,  w i t h r e s p e c t t o an event s t a r t  2.  C3 time  3.  N a l time,  4.  N a l energy  5.  N a l charge b i t p a t t e r n (0 or 1)  signal  The PDP 11/40 computer c y c l e s t a r t e d w i t h a LAM from t h e s t a r t of t h e TDC.  A l l CAMAC modules were then i n h i b i t e d  to r e a d them i n . event t a k i n g .  signal  i n o r d e r f o r t h e computer  T h i s was f o l l o w e d by a r e s e t t i n g o f t h e u n i t s f o r t h e next  B e f o r e e n a b l i n g t h e system a g a i n , t h e computer p r o c e s s e d t h e  a c t i v e event by adding i t t o d i f f e r e n t time and energy histograms w i t h t h e p o s s i b i l i t y o f imposing c u t s on some o f t h e parameters.  T h i s o n - l i n e ana-  l y s i s was e s s e n t i a l i n f o l l o w i n g t h e p r o g r e s s of t h e experiment and gates t o t h e study o f energy  s h i f t s o r background  of g a i n s  changes due t o modi-  f i c a t i o n s i n the s h i e l d i n g . Up  t o 74 events were r e c o r d e d i n a b u f f e r by t h e computer.  Each  b u f f e r a l s o c o n t a i n e d t h e s c a l e r i n f o r m a t i o n p r o v i d e d by t h e CAMAC S c a l e r (Elliot  SR 1608 u n i t s ) , both a t t h e b e g i n n i n g and a t t h e end o f t h e group  of 74 e v e n t s .  T h i s procedure was s e t t o minimize t h e p o s s i b i l i t y o f l o s s  of i n f o r m a t i o n on t h e d i f f e r e n t count r a t e s .  ^ proportional to p  1.  Cerenkov  2.  C1.C2.C3  beam p a r t i c l e s  3.  C1.C2.C3.C4  stops  4.  Nal  counts i n d e t e c t o r  5.  C1.C2.C3.C4.Nal  events  6.  Real  in  time  monitor  The s c a l e r s were:  seconds  beam i n t e n s i t y  24  These proved u s e f u l o n - l i n e and a f t e r w a r d s , i n the o f f - l i n e a n a l y s i s , as a g e n e r a l u n d e r s t a n d i n g of e x p e r i m e n t a l c o n d i t i o n s and.as first  e s t i m a t e s f o r the background F i n a l l y , once f i l l e d ,  a amgnetic  §2.4  c o n t r i b u t i o n s and the counts r a t e s .  the b u f f e r was  t r a n s f e r e d d i r e c t l y onto  tape, i n c o m p a t i b i l i t y w i t h the o f f - l i n e a n a l y s i s  system.  The N a l C r y s t a l The d e t e c t o r used i n t h i s experiment was  a large  cylindrical  N a l ( T l ) c r y s t a l e n c l o s e d i n a s e a l e d aluminium can.  I t was  the  I t s diameter i s 45.7  Harshaw Chemical Co. o f C l e v e l a n d , Ohio, U.S.A.  and i t s l e n g t h 50.8  cm.  The d e t e c t o r was  e s p e c i a l l y d e s i g n e d f o r an  c i e n t d e t e c t i o n o f photons up to a few hundreds MeV. of  the p h o t o - s e n s i t i v e a r e a o f l a r g e tubes [M.D.  seven RCA  purchased from  Due  cm.  effi-  to n o n - u n i f o r m i t i e s  Hasinoff et a l . ,  1974],  4522 phototubes were used to view the c r y s t a l and t h e i r anode  p u l s e s were summed t o produce a p u l s e w i t h a 50 nsec r i s e - t i m e . J.E. S p u l l e r  See  [1977] f o r a f u l l d e s c r i p t i o n of the b a l a n c i n g of the tubes  w i t h cosmic r a y s .  I t s h o u l d be noted here t h a t e l e c t r o n i c s h i f t s were o b s e r -  ved however, which caused changes i n the energy c a l i b r a t i o n of the s p e c t r a . T h i s problem had t o be handled a f t e r w a r d s i n the d a t a a n a l y s i s , as w i l l  be  seen i n c h a p t e r 3. Two at  k i n d s o f i n f o r m a t i o n were r e q u i r e d from t h e d e t e c t o r :  the time  which the r e c o r d e d photon reached the c r y s t a l w i t h r e s p e c t to a stop  s i g n a l i n the t a r g e t and the energy o f the y-ray.  Hence the experiment  r e l i e d h e a v i l y on the performances of the d e t e c t o r , namely i t s energy and timing responses.  25  The energy response o f the N a l c r y s t a l was i n v e s t i g a t e d a t the time of the measurement o f the Panofsky r a t i o i n hydrogen by J . E . S p u l l e r , w i t h the same apparatus i n t h r e e d i f f e r e n t c o n d i t i o n s .  The l i n e shape was ob-  t a i n e d e x p e r i m e n t a l l y f o r the 129.5 MeV photons o f the 7r p ->• ny r e a c t i o n by demanding a c o i n c i d e n c e between the N a l d e t e c t o r and a n e u t r o n c o u n t e r (13 cm <j) x 5 cm NE213 l i q u i d  s c i n t i l l a t o r ) p l a c e d on e i t h e r s i d e o f the  t a r g e t , both a t r i g h t angles!torn the T T beam d i r e c t i o n .  Two c o n f i g u r a t i o n s  -  were used:  w i t h a 25 cm $ l e a d c o l l i m a t o r a t a d i s t a n c e o f 91 cm from the  t a r g e t f o r Run(l) and w i t h a 15 cm i f c o l l i m a t o r a t 193 cm f o r Run(2). FWHM r e s o l u t i o n s a c h i e v e d were o f 6.0% and 4.9% r e s p e c t i v e l y .  The  Both response  f u n c t i o n s e x h i b i t e d a c l e a r low-energy  t a i l which was a l s o c o n f i r m e d by  l o o k i n g d i r e c t l y a t the mono-energetic  11.7 MeV photons from the  n  B(p,Y)  1 2  C*  reaction.  The e m p i r i c a l l i n e shape o f the above mentioned in figure  (2.4.1).  Run(2) i s reproduced  I t was e s t i m a t e d t h a t a f t e r removing  the a c c i d e n t a l  c o i n c i d e n c e s , l e s s than 0.16% o f the response f u n c t i o n was below 90 MeV. For the purpose o f t h i s experiment, where the r a d i a t i v e break-up  channels  of the TT He r e a c t i o n have t o be s e p a r a t e d as w e l l as p o s s i b l e from the 3  r a d i a t i v e c a p t u r e p r o c e s s a t 135.8 MeV, the s m a l l 15 cm <j> l e a d was chosen.  Although t h e energy was s l i g h t l y d i f f e r e n t ,  collimator  i t was assumed t h a t  the 129.5 MeV l i n e shape c o u l d reproduce the response o f the d e t e c t o r i n t h i s experiment, c o n s i d e r i n g the s m a l l s h i f t i n energy. used l a t e r f o r the f o l d i n g o f the t h e o r e t i c a l energy  T h i s was the l i n e  shape  distributions.  The t i m i n g response o f the N a l d e t e c t o r f o r t h i s experiment showed t h a t the 135.8 MeV photons were d e t e c t e d w i t h a 1.8 nsec r e s o l u t i o n ,  compared  26 Figure  PHOTON-NEUTRON  (2.4.1)  COINCIDENCE  FOR  RUN2  300  250  200  CO 150  100  " I  50  •n 0  PHOTON Figure  (2.4.1)  photons.  Response  125  100  75  50  ENERGY  150  (MEV)  f u n c t i o n of t h e N a l c r y s t a l t o 129 MeV mono-energetic  The data were o b t a i n e d  r e a c t i o n f o r stopped p i o n s .  by n-y c o i n c i d e n c e measurement i n t h e TT p-Hry  See [ J . E . S p u l l e r , 1977].  27  to 2.2  nsec f o r the i r ° photons (53-85 MeV),  T h i s good t i m i n g r e s o l u t i o n ,  as i l l u s t r a t e d  1.0  (2.4.2).  t o g e t h e r w i t h the 280 cm d i s t a n c e of the N a l  from the h e l i u m t a r g e t , p e r m i t t e d an e f f i c i e n t flight  i n figure  a p p l i c a t i o n of the t i m e - o f -  t e c h n i q u e to d i f f e r e n t i a t e between photons and n e u t r o n s .  nsec walk from h i g h to low energy was  The  small  a t t r i b u t e d t o the e l e c t r o n i c  t i m i n g of the c o n s t a n t f r a c t i o n d i s c r i m i n a t o r  (ORTEC 463).  28 Figure (2.4.2) Nfll  0  TIMING  10  RESPONSE  20 CHANNEL  Figure  (2.4:2)  on t h e graph.  Nal timing  (see s e c t i o n 3.2).  30  RUN  40  168  50  NUMBER  response i n r u n 168.  The bump a t t h e l e f t  IN  FWHM r e s o l u t i o n s a r e g i v e n  of t h e TT° photons a r e "T2 n e u t r o n s "  29  Chapter 3  Spectra  The d a t a were d i s t r i b u t e d  i n r u n s , a c c o r d i n g to changes i n the  s h i e l d i n g or when more degrader was put i n the beam f o r t h e i n v e s t i g a t i o n of mes-ic X-rays from muon s t o p s i n the t a r g e t .  We r e l i e d on the p o s i t i o n of  the TT° photons and of the e l a s t i c r a d i a t i v e peak to o b t a i n the energy b r a t i o n of the s p e c t r a .  cali-  However, t h i s was not p o s s i b l e f o r t h e empty t a r g e t  run and t h e r e f o r e t h i s r u n was f o l l o w e d by a r u n w i t h a s o l i d L i H (9.0 cm x 11.5 cm <j>) t a r g e t s e a l e d i n a s t a i n l e s s s t e e l c a n . et a l . , for  1972] c a p t u r e r a t e on the hydrogen  The 3.7% [J.A. B i s t i r l i c h  provided a s a t i s f a c t o r y  spectrum  calibration. The o f f - l i n e a n a l y s i s was c a r r i e d a t the U n i v e r s i t y o f B r i t i s h  Columbia  Computing C e n t e r .  The d a t a magnetic  w i t h the IBM 370 system a v a i l a b l e t h e r e .  tapes were d i r e c t l y  compatible  A s e t of FORTRAN programs were  w r i t t e n and developed to p r o c e s s and handle the d a t a by means o f h i s t o g r a m s . T h i s c h a p t e r w i l l d e a l w i t h the e x p e r i m e n t a l r e s u l t s per se, p r e s e n t e d i n the form o f time and energy  §3.1  spectra.  The Time S p e c t r a E s s e n t i a l l y two types of time i n f o r m a t i o n were a v a i l a b l e through the  TDC CAMAC module i n t h i s experiment.  Both were used to s o r t out the events  of i n t e r e s t f o r the Panofsky r a t i o measurement.  The stop s i g n a l o f C3, the  counter p r e c e d i n g t h e t a r g e t , was used as t h e r e f e r e n c e time of the event.  30  §3.1.1  The RF Signal Associated with each proton burst onto the T2 pion production  target was an RF signal that was used to select the stopped pion events i n helium.  The time difference between t h i s signal and the C3 signal was,  within a constant, the time of f l i g h t of the negative p a r t i c l e s along the 8.4 meters of the M9 channel.  The spectra of figure (3.1.1) show how the  electrons, muons and pions, a l l having the same 96.3 MeV/c momentum but d i f f e r e n t speeds are positioned r e l a t i v e to each other.  I t was therefore  easy to check d i r e c t l y from the spectra the length of the channel (or v i c e versa) , by simple kinematics.  The spectra do not, however, represent a  v a l i d estimate of the beam contamination as theysare produced f o r stopped p a r t i c l e events only and the d i f f e r e n t thicknesses of the degrader were chosen to stop mostly pions (or muons), as seen on the graphs. The 70 nsec width of the stop gate i n the electronics was large enough to include some events related to the next proton burst (43.3 nsec later).  This provided a means of c a l i b r a t i n g the TDC module. In the f i r s t step of the analysis, the RF p o s i t i o n of the main pion  peak was checked a l l through the corresponding runs because i t was observed that the phase of the RF signal with respect to the proton beam changed during the experiment with d i f f e r e n t tunings of the cyclotron beam. The extent of the s h i f t was determined for each run and s u f f i c i e n t l y large cuts were made on the C3-RF histograms.  I t was -estimated that less than 0.4%  of the t o t a l number of neutral events (C5 not f i r e d ) were muon associated, which i s negligeable f o r the purpose of this experiment.  F i g u r e (3.1.1)  TIME OF FLIGHT FOR BEAM PARTICLES  CO  2  5  0  0  2  0  0  0  h  1 5 0 0  °  1 0 0 0  5 0 0  -  0  10000  Q000  6  0  0  0  4  0  0  0  2  0  0  0  h  0 -  2  5  .  0  -  1  5  .  0  -  5  .  0  5 . 0  1 5 . 0  2  5  .  RELATIVE TIME Figure  (3.1.1)  3  5  .  0  4  5  .  0  5  5  .  0  6  The d a t a  I n a muon r u n ( a ) , a 5.4 cm  degrader was i n t h e beam, compared t o 2.70 cm f o r a p i o n r u n ( b ) .  T h i s amount o f degrader reduces the IT f l u x  5  (NSEC)  Time o f f l i g h t f o r beam p a r t i c l e s i n t h e M9 c h a n n e l .  were o b t a i n e d f o r stopped p a r t i c l e events o n l y . thick  0  considerably.  .  0  32  §3.1.2  Time-of-flight  (TOF)  The l a r g e d i s t a n c e between the t a r g e t and the N a l c r y s t a l , i n a d d i t i o n to the good t i m i n g response of the d e t e c t o r , were of g r e a t use i n d i s t i n g u i s h i n g photons from neutrons by a simple t i m e - o f - f l i g h t t e c h n i q u e . T h i s was  e s s e n t i a l i n view o f the l a r g e y i e l d o f neutrons from the f o u r  3 d i f f e r e n t break-up  Figure apparent 2.7  channels of  (3.1.2) i s a TOF  He.  3  spectrum f o r one of the  r e s p e c t i v e l y ) w i t h the 1.0  (2.3  and ^1.8  a non-negligible f l a t  random e v e n t s .  T h i s was  energy s t r u c t u r e which moved towards  of the photons  i n the t a r g e t .  first  attri-  I t turned out t h a t i m p o s i t i o n of c u t s on  time i n those r e g i o n s r e v e a l e d , as i l l u s t r a t e d i n f i g u r e  nanoseconds l a t e r . -  achieved  random time d i s t r i b u t i o n  b e f o r e and a f t e r the time of a r r i v a l o f the photons. buted t o s t r i c l y  nsec  nsec walk i n the t i m i n g r e s p o n s e , as seen b e f o r e .  can see t h a t a good s e p a r a t i o n of the photon peak was  but i t i s superimposed  val  The  nsec r e s o l u t i o n of the gamma-rays i s a combination of the r e s o -  l u t i o n s o f the TT° box and r a d i a t i v e c a p t u r e photons  One  He r u n s .  The time z e r o was  (3.1.3), a d e f i n i t e  low e n e r g i e s f o r c u t s taken a  few  defined, as b e i n g the mean time o f  i n the c r y s t a l , i . e . 9.3  nsec a f t e r a stopped TT  Because o f i t s r a t h e r u n i f o r m time d i s t r i b u t i o n ,  arri-  reaction  the s t r u c -  t u r e c o u l d not be n o t i c e d o n - l i n e on the a v a i l a b l e p r o j e c t i o n h i s t o g r a m s . The next s e c t i o n d e a l s w i t h the s t e p s taken to i d e n t i f y the n a t u r e of the problem.  TIME-OF-FLIGHT  SEPARATION  IN  RUN  169  10000  8000  6000  -  4000  2000  0 -20  -15  -10  -5  RELATIVE Figure  (3.1.2)  10  0 TIME  15  (NSEC)  T i m e - o f - f l i g h t s e p a r a t i o n i n r u n 169 f o r stopped p i o n  events.  20  25  30  34 Figure ENERGY SPECTRA  (3.1.3) FOR  VARIOUS  TIME  CUTS  ISO  o  CJ  t= 11.6 ns  (g)  t= 7.6 ns  (f)  t= 3.6 ns  (e)  neutrons  75  /  150  75  O  150  TT° photons §  CD  75  I  break-up  \  CJ  —L  500  I  136 MeV  --I  I  t= -0.4 ns .  1o  (d)  250 .p-...«" i  50 L CD  CJ  T  1  As  (c)  t= -8.4 ns  (b)  t= -12.4ns  (a)  t= -4.4  25  50  o  25  CJ SO  CJ  25  r i  10  30  • •  „  •  i  50  70 ENERGY  90  110  130  150  IMEV)  Figure (3.1.3) Energy spectra f o r various time cuts i n run 164. A l l cuts are 2.4 nsec large and taken at 4.0 nsec i n t e r v a l s . Time zero i s defined as the mean time of a r r i v a l of low-energy photons. One can see a structure moving i n energy for t<0 ("T2 neutrons").  35  §3.2  The "T2 Neutron"  §3.2.1  Contamination  Helium-3 Runs In o r d e r t o observe the b e h a v i o u r o f the energy s t r u c t u r e , I  d e c i d e d to l o o k a t a two-dimensional  (2D) r e p r e s e n t a t i o n of the events,  p l o t t i n g the time of f l i g h t of the p a r t i c l e emitted from the. t a r g e t a g a i n s t i t s energy f o r each n e u t r a l p a r t i c l e e n t e r i n g the N a l d e t e c t o r , thus c r e a t i n g a 2D g r i d where the events were d i s t r i b u t e d .  Such a d o t - p l o t f o r a  3 partial  He r u n i s reproduced from a computer p r i n t o u t i n f i g u r e  (3.2.1).  For reasons of c l a r i t y , a contour p l o t of the same d a t a i s a l s o p r e s e n t e d in figure  (3.2.2).  As f a r as the computations a r e concerned, the d a t a  were always handled i n t h e i r r e a l b i n n i n g . The f e a t u r e s observed on t h i s p l o t a r e , a t the s o - d e f i n e d time z e r o , the energy d i s t r i b u t i o n of the photons  (enlarged i n f i g u r e  i n t h i s r e g i o n of i n t e r e s t ) , w i t h the c l e a r ir° box, h i l l and the r a d i a t i v e c a p t u r e peak.  the  (3.2.3)  breaknup.channels  At l a t e r t i m e s , a r e observed a l a r g e  number of neutrons r e c e e d i n g i n energy as the time goes on, c o n s i s t e n t w i t h k i n e m a t i c s and t i m i n g r e s p o n s e . between photons and n e u t r o n s .  One  can a g a i n see t h e c l e a r time s e p a r a t i o n  Random events a r e v i s i b l e a l l over the p l o t  a t h i g h energy, and these i s o l a t e d events a r e m o s t l y due t o cosmic T h e i r number seems to i n c r e a s e towards low e n e r g i e s . f a c t a low-energy negative times:  background  rays.  However, t h i s i s i n  t h a t can be d i s t i n g u i s h e d c l e a r l y o n l y f o r  t h e s e events w i l l be accounted f o r l a t e r i n the a n a l y s i s .  The main f e a t u r e of concern i n the d a t a i s t h i s t a i l g o i n g a c r o s s the photons w i t h a d e f i n i t e time-energy  relationship.  36 Figure (3.2.1) TIME-ENERGY DISTRIBUTION OF NEUTRAL EVENTS ( H e run)  i 1 30 a  l  V  X  w V  u T  s  R  0 P 0 tt H L  K  J 1 H G F E D C B A  V 8  7 6 5  4 i 2 1  37 36 35 3* 33 32 31 30 29 28 27 26 25 24 23 22 21 20  1  l>X»CB553 2 11 31 1 lfl«*ll-98511 1 1? 1 1 13»«kE92423 1 2 1 1 1 1 1 S » « » J 5 » b l l 3 16*»*FFB73111 6U'*IHA622 6««»IAG514  2 1 1  1 31  11  14S»«Cl)KC733 1 7 - * « C j r ) 0 6 3 1 12  1  2 i  1 l  l  3 S » » 1 K G 9 6 3 32 1 1  1  5 » » » l M C ; i 1141 211 1 2 P « . Y U C F 9 4 ! I 3 <34 I l l  11 1 1  18 17 16 15 1* 13 12 11 10 9 8 7  1  1 1  1  1 2  11  I  1 1  1  1  1  11 t  1 21 1 1  1  1 1 1  1 1  1  I  I  1  1 2 1  1  1 21  I 1  1  11 2  1 1  1  11  1  11 11  1  1 l  1 1  1  1 H « « . « * » » 2 Y « I I SI P.LFFFPeC573433 I 1 1DU»<«*»»*•*RNJCC0FGH9?597722 3111 7 j . « , . . . . . . I . V L ; L K E J H D E D I E 6 5 7 8 3 121 I 1 I C P 4 « « » * . « . « » « Y O V K P N h F F 8 K G 5 0 e 9 t 251 3 15X»»»»»*»<«»**»*XRPC0IA7EILF9A9452 I 52»<•»»*..«•»z«»Y1SSCIN0»FFGDC74672  . . . . . . . . tt...  I  I  1  T  1 1  1 1  1  1  1  1  12  1  1  11  1  I  I1 1 1  1 1  1  1  6A« • • » « « SHF I G A P 4 A 3 5 2 2 3 lC««<»»XhlJ9C6F.8Eti97364l 2 B « < < < > TCRKHH9 [ E 9 : l / i n A 5 5 2 1 1 lF»1««»«..VPHEHCKCnF5624232  It  l 211  1  11 2 1  1  4 J . . . P G C 4 9 3 6 3 1 21 1 € P « » « » L M E 4 5 4 31 2 I I 1 11 5 M " » I J D « C 7 « 1 2 n i l 2 12N«<«UJND97363513 11 3 L « « < « « H K C f 583 84 2 4 3 11 1 4 C » « < « « X f C A 8 B 6 6 6 4 2 1 11 3r»«.««l.KGGDF39778121  l  11  1 1  2 1111 11 1 1 t  M i 111 1 2 1  I 1  r  1  12  1  1  1  1  1 1  1  1 1  55 123  1 1  1  1  1  2 21  . • ' « * * S N O P P P P R N c e P C 786  1  211K<« «*»<».*»*««S»«*CR-2»k^CFlJIC F9598533161 131 X « • . » . . . . * . « . « « • • • • • . . t < x l l C C M G F L D 9 8 9 5 5 3 5 1 1  1  62 123  112  1  11  5DR««***««*«*****»*»**"< «YRHSI'LHIJN*1N7FFG083562 1 1 1 1 1 3E0<<««.».*.«..«*.»«......»kXYZSP»V.JJLLBE9CF88'.<.<.2 . 1 4 C H « « * . . . . . . . . . . . . . . . . . . . kz Z U " C U C L C J K 0 E L E F C A 8 4 4 4 4 5 2 1 2 1 2 5 9 C < « * » . . . . . * . » » » . » Z « . « « . X Z f J . I C S U H h U O N I C G 3 I 0 G 8 3 6 8 733911 1 121 :  6 5  1  3 2 1  1 1  4  1  1  1 1 1  l279.a**.***Z"*Y.*RTRYTJVXUJXWCSG"-SGTRCLAFnFEI7C69975C376321 I 6 5 A N > « k ' T : P V » Z C V 0 1 F K X V G S \ k t f D J L P » C F J U D ! K C H « 0 r . 3 C F . e 3 C 8 6 7 9 6 38 33 2 5 6 6 E I < l v . < K J L I - I W C K C C C I 1 G C 8 C C 8 7 C 3 8 B C : C C 5 C E E C G C G B P P. 8 9 9 5 7 2 A 3 1 2 4 2 3 3A 1  2  ,  3274«JJlGDCND8HGA77F9a3»AA49ABB5a3»C68C9P,73995B8557(>76875154333 2 122 1 29P.eHECCC.70P6 7A4543468352'. ;E2384927494634332612>4464 I 44 I 3 2 5 2 ? 6 5 2 1 2 4 I 1 11 5 7 4 ' . 7 G 8 9 7 9 6 3 4 5 4 I 3 1 1 2 3 3 3 4 2 1 4 2 3 1 3 2 2 2 ? 3 5 3 5 3 3 3 1 2 6 4 1 2 3 1 -, 3 1 3 3 5 5 2 1 ? ? 1 322 2 22113213 11 212111 1 1213 311 U 6 2 7 4 C 5 F 2 7 5 4 4 3 2 4 2 1 1 12 1 1 2 1 2 11 21 21 11 12 1UAS7767436512 1 1 22 2  0  1 23 2(3772361 2 1 1 I ' l l 1 11 112732555542212 1 1 5555422711 3 1 1 1 476262252 1 1 H i l l 1 112C5212321 2 122122 2 1 11154234512 311111 1 1 1 2 1 4 5 8 1 1 1 1 1 2 2 131 23 1 1 I U l 1 214583462442212 1 1 1 2 2 2 U 2 « 5 3324224 212 U l II 221 3 7E554753721 1 3351 221 1 1 12122 111 121844 335353364 353323 1 836262441  11 1 12 2 1 11 2  1  2  112 1  61115  2211  1 U 2 6 5 4 C 1 4 E 6 A 8 3 3 2 3 5 2 3 3 3 24 3 5 8 A D A 9 7 B C 8 F S 6 E 6 9 6 1 3 2 2 4 6 6 1  1  11 1 1  1  I  13 3 II 13 21 11 11211 11 1 11 I 1  2l^765t9338?3355333147656EBNUSFPKOPS'IFGM(I<FFEe78A43  1 1 1 11 III  1 1  1111111  1 1121 1222  121 1 1  1  1 2 1 1 11  32151 1  41 13  2  111  121E86426321S35644266161 f.70TXCJ« »I»W»YRXX»VS»MYPH73I 54223434 3)->414314' 45' 2 3 3 4 2 4 6 3 4 1 Ii J P 1 I L VM J V M J O H C Y XMP<- U 3 J E 9 4 22 5 5 2 1 5 I 112 34 2 3 3 4 1 2 4 2 1 3 322 1 3 - 4 4 6 4 5 6 ^ A 9 6 E eB609CCEFAC 5 C A 9 1 3 4 4 2 5 24 12 1 2 112 1 2 1 1 2 2 4221231 1 2- 1 1 2- 221511 2 21 2 1 I 21 •  44237665 887975 6892 867999671 6 7 3 7 74 F C DC 2 B F C L C F 6 6 0 E E I S K N C 1 1 1 2 3 3 1 4 5 6 8 B 6 0 C H A E A B A 8 9 6 A - < KR 7 9 1 1 1 1 1 -2 4 1 4 5 2 2 3 3 4 7 2 3 2 2 3 7 B A 5 2 1 121 11 1 1 2 22 1  11  ;  211 2 21 11 4 1 1 14111242211221 1 1 221 4 1 1 111 2 2 1 1 1 1 1 1 1 2 1 I 111 I • 1 2 2 3 132 512351 1232 11 2 1 2 11 1 1 1 1 It 3 121 113 341 2 4 1 1 2 2 1 1 11211232 13223 2 12 21 2 1 3 2 2 2 22 1 5 4 2 4 3 3 3 1 2 1 1 3 3 1 2 1 2 2 1 11 23 U l 3 1 1 1 1 1 1 2 1 2 1 3 1 3 2 4 2 1 1 2 1 11 1 4 1 3 1 2 3 11131 1 11 1 11 1 1 1 1 1 2 1 1 3 1 3 2 2 1 1 2 1 1 1 1 1 1 I 1 • 2 1211 1 111 1 2322 31 11 24231 111 U l 1 1 . 1 2 12 1 1 11 1 1 1 4 5 2 2 4 1 2 1 2 1 1 3 1 2 1 1 1 1 1 2 11112 1 1 12 1 22 2 1 1 ? 21143 21I1I1 121 1 21 1 121111 1 1 1 1 2 134 1 121 2 2 2 2 1 1 111 1 1 12 2123 2 U l 1 21 1 1 1 2 2 2311 223 1 1 2 1 1 1 11212 1 1 1 11 11 1 212 2 111 1 11 I 11 212 I 1 12 11 1 1 1 2 1 2} 1 1 1  _J  20  I  .  40  1  60  I  80  L  100  1  1  120  1—  140  ENERGY (MeV) Figure (3.2.1) Time-energy d i s t r i b u t i o n of neutral events from a p a r t i a l He run (#169) i n the form of a computer printout. The symbols f o r the number of counts i n each b i n are explained at the top l e f t side of the graph.  ENERGY Figure  (3.2.2)  Contour p l o t of f i g u r e  (MeV) (3.2.1).  The  superimposed dashed  l i n e s i n d i c a t e the shape o b t a i n e d f o r <fctie-3"T2':neutroh" data taken w i t h Bl dipole o f f .  the  D e t a i l e d contour p l o t f o r photon T  1  i 20  1  i 40  1  i 60  events  r  1  1  i  i  1  80  100  120  r  1  1  140 ENERGY  Figure  (3.2.3)  Detailed  c o n t o u r p l o t f o r photon events i n run  168.  (MeV)  39  §3.2.2  Background and  Contamination  S i m i l a r two-dimensional p l o t s f o r both t a r g e t f u l l empty ( f i g u r e s 3.2.4  and 3.2.5) runs l e a v e no doubt  and  target  t h a t the t a i l  cannot  3 be due t o  He, nor to s c a t t e r i n g from m a t e r i a l around  A s i d e from t h i s problem,  the t a r g e t body.  the t a r g e t empty r u n a l s o e x h i b i t e d many neutrons  (with a s l i g h t l y d i f f e r e n t o v e r a l l time-energy shape due to the d i s a p p e a 3 4 ranee of the He break-up channels) and the r a d i a t i v e high-energy He c h a n n e l , a t time z e r o , as expected. Consequently, i t was  b e l i e v e d t h a t the observed c o n t a m i n a t i o n  c o u l d o n l y come from the p i o n p r o d u c t i o n t a r g e t not  (T2).  This feature  was  seen a t the time of the measurement of the Panofsky r a t i o i n hydrogen  s i n c e then, the p r o t o n c u r r e n t onto T2 was  increased  (from 0.8  uA to about  5 uA) and a f a r l a r g e r number o f the n e u t r o n s b o i l i n g o f f the t a r g e t go through the 4.4  meters of s h i e l d i n g  (see f i g u r e 2.1.1).  but,  could  But a t the same  time the TT beam r a t e , a n d hence the stop r a t e i n the h e l i u m t a r g e t , i s i n c r e a s e d so t h a t many more of these T2 neutrons a r e r e g i s t e r e d as events when they e n t e r the N a l c r y s t a l .  Indeed, a two-dimensional p l o t f o r a r u n  taken a t a p r o t o n c u r r e n t of 10 uA shows such a c o m p a r a t i v e l y l a r g e increase. There were two ways of c h e c k i n g t h i s h y p o t h e s i s . time-energy  s l o p e of the f e a t u r e , i t was  F i r s t , from the  p o s s i b l e t o v e r i f y t h a t the  tail  agrees by simple k i n e m a t i c s f o r neutrons w i t h the d i s t a n c e of the d e t e c t o r from T2.  Secondly, another background  r u n w i t h the B l d i p o l e o f f (see  f i g u r e 2.1.1) confirmed c o n v i n c i n g l y the T2 n e u t r o n c o n t a m i n a t i o n . l a s t datum i s a l s o i n d i c a t e d i n f i g u r e  (3.2.2) f o r comparison.  This  40 F i g u r e (3.2.4) TIME-ENERGY DISTRIBUTION OF EVENTS FROM THE TARGET EMPTY RUN(#183) T •  I  3 0  4Q**««««l<>75 IT»**«.*|<771 2K«'«»«XC1957 ! » » « • « . I 9 J 7 *..»..|(151  •> 37 36 35 34 33 3? 31 30 29 2S 27 26 25 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7  6  5 4 3 2 1  0  i  L  N  11  2 I * * * « « * X 9 7 2 7 4 2 3 1 2 3 1 312 1 11 21 13 1 I 121 1 lj..4*..*P54432 2 3 2 1 2 2 11 11 1 1 11 S»*«««»YG87331 321 3 3 3 1 2 1 2 111121 , ( C 5 4 3 4 1 1231 1 23 2 132 2 1 2 « » « « « , . 0 0 9 7 3 5 4 2 1 1 2 3 1 2 11 I 1 2 1 1 N**««**»»C6C6 1 2 2 23 1 1 2 2 3 1 1 1 2 2 2 1111 1 2 1 .**4<a..NLE 7 6 5 2 1 2 5 3 2 1 2 1121 1 1 2 1 1 1 1 11  T  \  1 11 11 11112 11 1 2 11 11 111 1 1 2 221 12 1 1113111 121121 1 I I 2111 1 1 1 1 1 1 I 1 31 1 2 21 U l 1 21 11 I 1 1 1 1 I 12 11 1 11 I 1 II 1 U l 12 1 I 1 1111 1 11 I 1 11 11 11 2 1121 21 11 1 122 1 1 11 1 I 1 II 2 3 11 1 1 11 1 1 1  12 2 21 1 1 1 1 1 1 1 2 2 1 1 1 2 12 31 11131 1 1 21 1 2 3 2 2 1 2 3 3 1 1 1 1 2 1 1 1 1 1 1 141 3 2 2 3 3 1321 2 2 1 11 2 1 1 1 3 1 1 4 1 2 2 13135341 31 I 1111111131112 1 41 2 3 ) 31122222 22 1 4 2 2 1 32 I 221 2 m 2 2 2 13 1 2 1 4 2 12 2 1 1 1 1121 12 1 I  3 * * * 186421121 1 1 1 21 2 S * * . * 4 K f 3 9 4 2533123 3 1 4 2  ^39  T  T  1122 1 1121 2112 2 1 21 2 1 1 1 1 11 211 1 2 1 3 1 1 2 I 121 11 1 3 1 11 1B*»**.**»*PH354331413 131 1 2 1 3 1 2 1 12 3 11 1 1 1 32 1 1 1 1 [6 )*»* **•* •* ** •* *. .»XWZ 0J 1F C A 43 26 14 34 2211 U 1 1 11 2 1 12 1 0G i i1 m1 i n2 1 1 1 1 11 1 1 3 2 1 1 11 6 * * * * » « * * » * * S H C H 8 5 5 3 4 1 2 1 1 1 2 21 Ul 1 11 11 1 112 11 12 1 21 12 1 1 A * » « 4 » 4 * * * * * » X P K 9 2 4 42 3 3 2 1 11 1 2 2 111 21 3 1 1 7 * « * . 4 . * * * • * , . U S P C C 5 4 1 13 1 41 U l 2 2 1 1 2311 1221 1 1 1 1 2 22212 A * * * * * * * * * * * * * * * M N E 4 6 5 2 2 I 1 21 2 11 1 2 R * » . « « * * * . * * « * « » U N C G 8 4 2 3 1 1 1 3 2 1 2 2 1 1 1 1 2 21 121 U 1 1 12 1 2 3 3 2 1 1 2 1 1 1 1 1 1 1 1 1 l Y * * * * * * * * * * * « * * » * a / R 6 C 3 2 3 23 12 1 1 1 11 1  0  8  E  2112  1 1111 2 12 1 11 11 2 1 11 1 1 1 1 11 1 1 11 1 1 1 11 1 2 1 1121 1 3 a * « * * * * * * * * * * f t * * * » * 0 T C C 9 3 3 5 2 2 21 1 1 1 11111 2 1 1 1 1 2 1 0 * * * 4 * * * * . 4 . * • * » * * . * a W L D 8 4 4 1 1 1 12 1 1 11 2 1 2F.« * * 4 4 * * * * « t * . . . . . . . . . . p G 7 3 3 1 2 1 3 U l 1 211 1 11 1 1 2 1 2 1 11 1 1 Q * * » * » * * * » . « • * * * . « . * « « » * V 0 R J 8 6 3 2 1 2 2 4 1 I 221 2 1 1 1 1 1 1 1 11 4 | * * » 444* 44**«*»****.*******SN'E6742 2 1 2 31 2 1 22 1 111 11 1 lw 1 12 1 C**»44*«*«*«*****.***«**..*•ZNJIC63222 22 14211 31 11 1 2 2 1 2 I 1 1 11 1 2 A * « « * * » * * * * * * * » > * * « * * * * « » * * * * * * P R E E 5 9 2 3 4 1 2 2 1 1 1 1 1 11 1 11 11 11 1ig».4* » * * * * • * * * * * * * * * * * . * * * « * * * « * « » X F 0 F 8 4 5 1 2 3 2 U l 1 1 2 1 111 1 2 3 S * * * * * * * * * * * * * * * * * * * - * » * » » * * * * * * * Z Y J O B C 5 1 A 2 1 1 1 21 1 2 U l 1 1 1 1 1 1 I 11 3V*4*****.***4*«********4**********.*VRTFDC3231323ll 11 11 1 1 21 1 2 2 2 6 J * « * * * * * * * * * * * . * « : • * * . * « * » * « * . * » « * * » * . * « T J F E 4 5 5 1 6 4 2 22 12 1 1 11 22 U l 24M*« * * * * * * * * * * * * * * * * * * * * * » » . » * * + « « * * « * *«*»PLfiKE684a 42 I 1 1 1 11 3 3 J 4 > * * * * * « * • * • * * * « « » . * . * * . * * * * * * • * * * * . * * * * * * * . C ] N K 5 84 744 1 2 1 1 1 2 111 1 I 1 11 .*»«.»,«*»*HKEA0E778344111 1 1 I 3 a * * * * » * * * * * « * * * . « * . 1 -J. , I B f f * * * * * * * * * * * * * * * . * « * * • * * * * » . « « * * « * * * . * * * * * * * Z X K Z W M N A H 9 9 2 3 3 2 1 212 1 1 1 1 2 1 2 9 N * * * * * * * * * * * * * * * * * *.«**4**«.****.*****.-.*******.*WXt.»JDCC896462 1 1 1 1 12 . . . • . • f t * * * * * * * * * * * **»*.** + . t f Y V Z O U V U H 9 5 8 5 E 5 7 7 4 3 3 1 1 2 2 C9 V * 4 ******** »>.**** 12 1 1 1 2 2 4 P . C n 44444******. * * • * * * * * * * * ' * * * * *•» * * * * * * * « Y * * » / * X Z Y * T N C P 1 ) S Q I L 7 G 8 C 6 6 4 3 4 1 1 1 2 2 3 1 1 | 76CW«***********Z*»0tf**** <***«-**TVtfC9UUNTUTRSH7<TMLHRQG JHlHFlAr)9B256831??3! | j 1 1 L  f  i  1 1 5 6 J S * « * * 21 3759G** • * 114 566FV<»s I222558AUZTZ  * * * * * SZ*« N O R O P U S M I M L O L J F J H J M . T K 0 K C 0 9 0 n K K 9 8 F 1 F K 9 D 7 C 5 C 8 E B D 9 8 7 32 5 5 4 1 3 2 2 1 1 111 * * * U V 0 " 1 G C 9 Ji)9B< E 7 E 8 C 7 9 9 A 9 B 7 A F C 7 B C 9 9 9 6 8 6 B 5 8 7 A 8 5 9 6 E 9 4 6 3 2 3 2 2 3 5 6 4 3 1 1 2 1 4 ti»HJK98656356352447515 56225444553855358431453443434224 14224212 2 3 1 1 1 V P J E C U 7 A 5 C 7 4 3 U - 1 3 4 2 2 1 3111 3 1 2 4 3 3 4 4 1 2 42 U 2 1 12 1313 3 2 1 1 3 1 1 1 1 1 1 2 1 1 2 1 1 1 3 1 2 2 i i l l 2 i111 2 22JC.JSXWK.-.F0F5533753 3 .J 1 ; U 1 21 ! I 1 21 1 1 1121 12 1 ! !. 1 2 1 11 11 3 3 U l 23 694 3 I I HD7 83 3 3 4 ^ 2 3 1 1 1 2 1 2 1112 2 1 3 4 4 3 4 3 3 C J J 3 I C 5929H644T«21 2 1 1 1 2 1 1 1 1 1 12.2 2 2 11212 1 4344e757CF7CG797761Aaai>>Jl 2 323 1 1 22 1 1 121 11 U l 2 1 1 I 1329551 7 C C G F A 9 6 9 5 3 4 5 ? 3 2 2 l \ 2 2 42 1 1 1 1 1 11 1 1 11 11 1 1 21 1 I 2 11 1 U408744BCE9FA B6746246 3 1 1 22 2 1  U  1  3 3 4 6 4 9Pl.N'CE.'". 5 7 ' 8 7 4 ? 3 2 1  I  1  2 1 1  s  f*k/i  1 11 2 U l 1 1 1 446276365A67e977785927543240U"t^2322 12 1 1 2 1 1 1 3 1212 1 2 1 I 11 1 6 3 3 6 4 9 A 7 7 B E 1 8 6 B 8 3 5 9 5 7 4 4 4 7 2 4 2 2 2 2 >J. 2 4 214232 2 21 2 231243111 2 1 1 1 ! 11 2 1 3 4 4 5 9 5 E 5 E 7 6 8 7 G 8 3 6 9 6 9 C A 9 4 3 A 8 6 7 4 2 V 3J4J225 222213221222212 26157263231743565348A966787B59962331 1 1 1 111 1 2 2 3 2 5575 3 I 3 3 7 D 6 D C E E 37 7 8 E 4 A A C 5 83 7 8 5 J 6 8 8 0 5 5 6 9 7 A 5 D A 3 B D C A 7 9 8 7 F F X H F I K D E C E 5 6 6 3 2 4 2 2 1 13 1 |~1 5 5 3 2 5 55 4 81 6 3 47 4 6 F D 3 9 C 6 A A E F AE 3 A 7E7OTB3"' <IHFOGCPMIEH3FA2S11 111 fcF94496BBG7CGC6FDKF0NKI 2 2 4 >*"<3 0 5 A 6 A 6 4 6 7 0 E 8 A 9 E 8 9 A 0 G E E 8 9 9 9 I A E 3 A 9 ' 1 3 2 4 > ^ 6 7 4 45 5 4 4 A 4 7 9 8 9 0 8 6 F B 5 A C F A C H B C H 9 D S 8 A 6C O R s ^ B 9 7 5 7 B7 I L"!HI_ K H T J E M S K I H - R T * * M JK O C A F 6 C 3 I 4 1 4 4 4 1 5 T O J K I 3 3 2 3 7 1 8 8 7 5 9 A 9 6 5 A CD 5 AF64851C79789S«5>^B79756F2769GFHGK8GLHHOLYVHPC730C3551 1 2 4 3 3 7 4 7 2 l S ^ i 3 3 2 7 4 6 3 6 6 5 6 9 A 3 6 A t > 9 C 9 4 A D 8 5 5 84 i3 1 2 3 ^ 5 2 \ ^ 3 712 12 73 B15 4 53 3 3 6 4 C 5 9 3 C D 4 7 5 4 2 93 2 4 1366732 6362?§S23423428575AC7538964637653523352Z 13 112 U l 16441525513 4 3 1 1  -8  531t85206CA97B755 8AB592 532 I 2 3 U I II 1551315315243 IK 226697214222 554524564D2U9CC66957C777 3441 1 2JTV 1 1 2 5 5 6 4 1521 12 5212" 348554E7e75f;99G29ACDS75B31 3 3 3 3 > I t 11 1 28661123751 23133J 455A5985C3E883f,C78464542 123 5 ^ ? " 1 1 1 5 2 3 4 2 2 3 5 3 1 1 1 2 2 3 2 1 2'»4 32 3 5 4 6 5 9 9 6 5 8 5 3 5 7 3 A 6 7 6 B A 2 5 2 3 2 1 21 2 5 2 1 4 3 1 1 32233211 1 3 34*<76 37877458C88A976345685211 2 2 2 5 4 i ; i 4221 1 1 1 1 I 1 1 3 3 3 T S 2 5 4 6 6 5 2 e A 76» B8 6 3 3 4A2 454 4 4 3 1 2 3 1 1 11554 1223431 4 1 1 2 2 1 11 1 1 3 2 3 2 1 ^ 2 3 1 2 5 4 2 6 14 9A4 7 4 33 A 2 3 3 6 2 5 3 3 3 2 1 4 4 1 6 4 2 5 1 1 11 2 1 2 1 131 31 1 1 I 3 1 2 1>1£2 1 7 3 7 4 3 8.567 2 5 5 3 5 4 5 5 5 7 4 4 1 2227 5 2 3 2 4 2 2 1 3 11 1111 113121 1 1 2 I 2 2 2 > ^ 3 1 4 63 3 7 9 3 59 5 9 5 6 8 9 9 5 2 3 4 4 72 1 1 1 " 1 4 4 6 6 8 2 4 5 2 6 6 2 14 4 2 2 2 2 2 2 2 1 2 1 1 1 1 2 2 1 I U ^ 2 5 5 4 3 1 6 4 5 B 5 2 3 5 4 4 4 3 4 4 7 6 1 3 2 1 3TN?V 544542242 32221 1 342 12212 1 2211 132i r V , l 132 1 U 3 2 5 U 2223223223 2 1326245411123 2224 11 11 22 U 1 1 1 ^ * < 2 1 31232143122 2 3 1 2 2 1 " 212353556732132 22212 2 31 1 2 1 2 2 1 1 1 11 I 1 1 2 1 1 11 111 3 21 2 2 2 2 1 1 f-281416377452632141 1 1 11 3 1 1 2 11 11 3 2 2 1 31 2 ^ * 2 1 1 112 1 2 21 131 2 1 3 3 1 2 N 22143542222321234 321 3212 1 1 1 11 2 1 2^*, 11 111 1 11 2 2 <  ,  -16  111121237 1311244611  1 2 3 12 3 1 3  1 11 1 1  40  20  1 1  2 1 2 21212  12 111  60  1 1  1 1  2 1  1 1 1  80  1  100  120  140  ENERGY (MeV) Figure  (3.2.4)  in t h i s run. RF s h i f t .  Time-energy d i s t r i b u t i o n o f events from the t a r g e t empty r u n (#183). The s o l i d l i n e s ^ i e f i n e t h e shape o f the T2 n e u t r o n t a i l The dashed l i n e s r e p r e s e n t t h e t a i l i n r u n 169, thus showing t h e  20  40  60  80  100  ENERGY (MeV) Figure  (3.2.5)  Contour p l o t of f i g u r e  (3.2.4)  120  140  42  Such a background  happened t o be q u i t e troublesome, even once  u n d e r s t o o d , and turned out to be t h e most important source o f u n c e r t a i n t y i n t h i s experiment. its  subtraction.  I will detail  i n t h e next c h a p t e r t h e means used t o do  Furthermore, i t s h o u l d be noted h e r e t h a t t h e r e i s a l s o ,  i n t h i s c o n t a m i n a t i o n , a time s h i f t  independent o f t h e time o f f l i g h t o f  3  the photons and n e u t r o n s from t h e  He t a r g e t .  Moreover, t h i s s h i f t i s  3  s i g n i f i c a n t l y v a r i a b l e from one target-empty r u n . the experiment  He r u n t o a n o t h e r , w i t h r e s p e c t t o t h e  T h i s was a l s o a t t r i b u t e d  t o t h e RF i n s t a b i l i t y  during  so t h a t the T2 n e u t r o n s were a t d i f f e r e n t p o s i t i o n s i n  time from one r u n t o another when the TOF c a l i b r a t i o n was kept c o n s t a n t . This i s i l l u s t r a t e d  i n figure  (3.2.4).  43  §3.3  Raw  §3.3.1  Spectra  Cuts on Time U s i n g the TOF  how  spectrum  ( f i g u r e 3.1.2), i t c o u l d not be seen e x a c t l y  t o make the time c u t s i n o r d e r to produce  the energy s p e c t r a f o r gamma-  r a y s and a t the same time e s t i m a t e the c o n t a m i n a t i o n of r e a l events by neutrons. how  However the two-dimensional p l o t s  the d a t a were d i s t r i b u t e d .  ( f i g u r e s 3.2's) showed d i r e c t l y  A c c o r d i n g l y , the c u t s were made t i g h t  enough to reduce the c o n t r i b u t i o n from the T2 neutrons as much as p o s s i b l e without l o s i n g more than a v e r y s m a l l f r a c t i o n o f t h e r e a l e v e n t s . compromise, a 7.6 nsec wide time c u t was  chosen.  As a  The c u t was c e n t e r e d  d i f f e r e n t l y from low t o h i g h e n e r g i e s to account f o r the time walk but  was  m a i n t a i n e d a t the same w i d t h f o r c o n s i s t e n c y i n n e u t r o n and random back3 grounds between the  He runs and the t a r g e t empty r u n .  An e s t i m a t e of t h e  v a l i d i t y o f the c u t s was made by p r o d u c i n g time s p e c t r a f o r photons  i n the  TT° box r e g i o n and f o r the h i g h e r - e n e r g y gammas (as f o r f i g u r e 2.4.2). R e s u l t s a r e shown i n the next  Table I I  table:  F r a c t i o n of the photons missed by the TOF  Energy r e g i o n : (MeV)  c u t s ( i n %)  50-88  88-130  r u n 164  .06  .03  .04  r u n 168  .14  .10  .03  r u n 169  .11  .03  .04  r u n 170  .05  .02  .03  r u n 173  .05  .04  .04  r u n 183  .13  .04  1  130-145  44  In a d d i t i o n to t h e s e v e r y s m a l l c o r r e c t i o n s f o r photons which l i e o u t s i d e of the time c u t s , the TOF c u t s a l s o i n c l u d e d some neutrons from r e a l events. answer:  F o r t h i s problem, the two-dimensional p l o t s g i v e a d i r e c t  above 30 MeV,  n e u t r o n background to l e s s than 0.2%  the s e p a r a t i o n i n time i s such t h a t the p o s s i b l e  i n the time c u t i s n e g l i g i b l e .  The TOF neutrons sum  up  o f a l l the events i n the c u t s , and they a r e a r e the low-  energy end of the s p e c t r a , so t h a t t h e i r c o n t r i b u t i o n to the photon counts from the charge-exchange  §3.3.2  reaction i s negligible.  Energy S p e c t r a The time c u t s f o r each r u n were determined from the sum of the d a t a  i n that run.  The d a t a , however, were a n a l y s e d by s l i c e s i n s i d e each r u n  a f t e r i t had been observed, d u r i n g the o n - l i n e a n a l y s i s , t h a t s h i f t s i n energy were o c c u r i n g .  A two-dimensional p l o t was  significant  produced f o r  each s l i c e and the time c u t s were a p p l i e d on the i n d i v i d u a l p l o t s .  A  slice  of t y p i c a l l y f o r t y thousand events would produce a photon spectrum w i t h sufficient  s t a t i s t i c s t o e v a l u a t e the energy s h i f t but not so l a r g e t h a t  good energy r e s o l u t i o n would be worsened by g a i n s h i f t s d u r i n g t h i s Statistically data.  s p e a k i n g , the r a t i o  (events/photons) was  t y p i c a l l y 10 i n our  T h i s s l i c i n g procedure c o n f i r m e d the important changes  c a l i b r a t i o n , which were i n one c a s e as l a r g e as 5 MeV peak (135.8 MeV).  i n the energy  f o r the h i g h e s t - e n e r g y  To compensate f o r the s h i f t s i n the e l e c t r o n i c s of the  a p p a r a t u s , a g a i n - s h i f t i n g procedure was s p e c t r a of the sub-runs.  I t was  a p p l i e d b e f o r e adding  individual  n e c e s s a r y to keep as good energy  a s p o s s i b l e i n o r d e r t o s e p a r a t e out the 135.8 channels.  sub-run.  MeV  resolution  peak from the break-up  45  The This was  energy response of the Nal d e t e c t o r i s e s s e n t i a l l y  linear.  confirmed a f t e r w a r d s when the f i t t i n g of the s p e c t r a produced a  self-consistent linear calibration.  Two  numbers, d e f i n e d as the " z e r o "  (channel #) and the sgainVt(channels/MeV)  can then d e s c r i b e t h i s  c o r r e c t l y f o r the energy h i s t o g r a m s .  " g a i n " i t s e l f c o u l d riot be  The  calibration esti-  mated f o r a sub-run because of the low s t a t i s t i c s , but the summed s p e c t r a proved a f t e r w a r d s t h a t i t remained c o n s t a n t w i t h i n 0.5%.  It was  also  felt  t h a t a c l e a n s e p a r a t i o n a t h i g h e n e r g i e s was more important and t h a t , i f needed, a l i t t l e worse r e s o l u t i o n c o u l d be t o l e r a t e d a t low e n e r g i e s to account f o r keeping the " g a i n " c o n s t a n t .  The g a i n s h i f t i n g p r o c e d u r e c o n s i s -  ted then i n f i n d i n g the c e n t r o i d of the high-energy e l a s t i c peak f o r a l l the s l i c e s of a r u n , s h i f t i n g them a c c o r d i n g l y by a f r a c t i o n a l number of channels and f i n a l l y adding them up t o g e t h e r . i n the computation  ( l e s s than 0.1%)  Losses or mathematical b i a s  were n e g l i g i b l e . Two  sub-runs, r e p r e s e n -  t i n g 6% o f the t o t a l a n a l y s e d d a t a , had t o be d i s c a r d e d i n the p r o c e s s because of s h i f t s w i t h i n themselves t h a t were judged u n a c c e p t a b l e due t o l a r g e d r i f t s i n the e l e c t r o n i c s . Figure (3.3.2) r e p r e s e n t s the raw spectrum thus o b t a i n e d f o r one  3 of the f i v e figure  He runs c o n s i d e r e d i n t h i s t h e s i s .  A comparison w i t h  (3.3.1) shows t h a t t h e r e i s a c o n s i d e r a b l e improvement i n the  o v e r a l l energy r e s o l u t i o n w h i l e the g a i n s h i f t i n g , a t low e n e r g i e s ,  produces  a slight  never  smoothing e f f e c t .  In any c a s e , the energy r e s o l u t i o n was  worsened and, i n f a c t , a 4.5% Nal d e t e c t o r .  performance had been c l e a r l y a c h i e v e d by the  RAW  PHOTON  SPECTRUM  5 0  7 0  OF  RUN  169  500  400  300  200  -  100  h  0  10  3 0  PHOTON Figure  (3.3.1)  Raw  ENERGY  photon spectrum of r u n 169.  9 0  11 0 (MEV)  1 3 0  GHINSHIFTED  PHOTON  SPECTRUM.  RUN  169  400  300  CO  ZD O LJ  200 09 C H  UJ OJ  s •  100  rO  V  0 10  30  50 PHOTON  Figure  (3.3.2)  70  90 ENERGY  110  130  150  (MEV)  G a i n s h i f t e d photon spectrum o f r u n 169. The d a t a g i v e n below a r e estimates of t h e "T2 n e u t r o n " and " t a r g e t empty" backgrounds, a p p r o p r i a t e l y s h i f t e d and n o r m a l i z e d w i t h r e s p e c t t o the .target empty r u n they a r e taken from ( s e c t i o n 4.1).  48  §3.3.3  Random Events The random events, i . e . events which originate externally to the  experimental set-up as a whole, are mainly cosmic rays.  They are easy to  see at high energies on the two-dimensional plots where they are spread out  uniformly. At lower energies, there are other accidental counts but  their o r i g i n i s d i f f e r e n t and they w i l l be treated i n the next chapter.  The  two-dimensional plots were used to estimate the number of random events by merely counting the events scattered at high energies outside of the photon or neutron structures.  One then gets their average number per unit time  per unit energy, f o r l a t e r corrections to the Panofsky r a t i o . l i s t e d i n table I I I , where AE = 1 MeV and At = 1 nsec. agreement w en the rardom rate increases with v  They are  Th^rt  t o t a l pno--cn  xate.  Table I I I  Random and photon counting rates (per unit energy/per unit time)  Run no.  *  Photons  0.241  23.7  168  0.464  28.7  169  0.312  23.9  170  0.443  32.6  173  0.305  23.5  183(BKG)  0.238  5.0  164''  *:  Randoms  the stop gate was narrower f o r this run  49  §3.4  Scalers The scalers recorded .for.each run'during the experiment are  summarized i n table IV. Although they generally cannot be r e l i a b l e f o r precise calculations, they provide a good idea of the experimental conditions, given the set-up.  Table IV  Run# Target  Scalers f o r the experiment  Real Time  Cerenkov Beam Monitor  Incident Beam 1.2.3  "Stops"  (sec)  xlO  xlO  xlO'  9  9  Nal Events Counts total i n photon 1.2.3.4* rate stop.Nal TOF cuts xlO  164  3  He  5210  1.444  1.542  1.099  1.304  241960  25745  168  3  He  14747  2.933  4.401  2.045  2.331  371595  31925  169  3  He  5176  1.824  2.558  1.380  1.557  260023  26197  170  3  He  8712  2.271  3.120  1.729  1.809  337876  35718  173  3  He  4290  1.653  2.254  1.248  1.298  285297  25766  183  empty  10632  1.697  5.090  1.550  1.730  163375  5425  50  Chapter 4  §4.1  Data Analysis  Target empty Run  §4.1.1  Estimates f o r each kind of background The same physical configuration as described i n section 2 was  used f o r a l l the runs.  The only minor changes were the addition of some  shielding of the beam telescope on the side of the S i - L i detector and the 3 repositioning, also after the f i r s t counter. Nal  (#164) of our He runs, of the veto  A large electron contamination was expected and observed at the  detector due to i t s small 14° angle from the beam d i r e c t i o n .  The main  concern about the background was however the target i t s e l f , with i t s s t e e l and CH^ rings, copper side thermal shielding and mylar windows, as well as 4 3 the He superfluid f i l m on the entry and exit windows of the He c e l l . 3 It was possible to remove the He content of the target and the r e s u l t s of the run taken with an "empty" target are presented i n figure (4.1.1).  The spectrum displays c l e a r l y both the low-energy T2 neu-  tron.- contamination and the high-energy gammas from the target i t s e l f . compared to the Ste spectrum observed by B i s t i r l i c h  et a l . [J.A., B i s t i r l i c h  et a l . , 1970] (see figure 1.1a), the target empty background of contributions from other materials.  further flattened on the low-energy  shows evidence  These are mainly carbon and nitrogen  in the windows and the CR^ r i n g surrounding the target c e l l . n u c l e i are heavier and more complex than  When  As  these  He, their photon d i s t r i b u t i o n i s  side, but their contributions remain  less important due to the low p r o b a b i l i t y of r a d i a t i v e capture (^1% f o r A=25).  TARGET  10  30  EMPTY  PHOTON  70  90  50 PHOTON  Figure  (4.1.1)  ENERGY  T a r g e t empty photon spectrum (run 183).  SPECTRUM  1 10  130  150  (MEV) The two l i n e s a r e estimates of t h e shapes  of the T2 n e u t r o n and t a r g e t empty backgrounds.  52  The main problem a r i s e s i n c o n s i d e r i n g the background s u b t r a c t i o n . There a r e two backgrounds here, o f equal importance  but o f d i f f e r e n t  o r i g i n s , thus r e q u i r i n g d i f f e r e n t n o r m a l i z a t i o n s w i t h r e p e c t t o each of t h e target f u l l runs.  The number of photons coming d i r e c t l y from t h e t a r g e t  i s p r o p o r t i o n a l t o the number o f TT stops ( e x c l u d i n g t h e s c a t t e r e d p i o n s which miss t h e v e t o counter) w h i l e t h e number o f T2 neutrons  detected  depends d i r e c t l y on t h e p r o t o n beam by means o f the a c c i d e n t a l c o i n c i d e n c e rate.  The two backgrounds had t h e r e f o r e t o be separated from each other  i n their overlapping region. S e v e r a l time c u t s i n r e g i o n s where o n l y t h e T2 neutrons a r e p r e sent showed t h a t w i t h i n s t a t i s t i c s t h i s c o n t r i b u t i o n c o u l d be r e p r e s e n t e d by a g a u s s i a n energy assumption  f u n c t i o n (see f i g u r e 3.1.3).  It i s a  reasonnable  f o r t h i s i s a l s o about t h e shape o f t h e p r o t o n beam  profile.  4 The low-energy s i d e o f t h e  He r a d i a t i v e c a p t u r e spectrum  was e s t i m a t e d by  4 generously f o l d i n g the  He shape [J.A. B i s t i r l i c h e t a l . ,  N a l response  This s a t i s f i e d  function.  many r e a c t i o n s o f t h a t type 1973]  1970] w i t h t h e  t h e common slow decrease  [J.A. B i s t i r l i c h e t a l . ,  1972; H.W.  and p r o v i d e d a good e x t e n s i o n o f the a c t u a l shape.  f e a t u r e from Baer e t a l . ,  A s m a l l low-  energy backgroung c o n t r i b u t i o n was e s t i m a t e d from t h e t a r g e t empty d a t a and removed i n a manner d e s c r i b e d i n s e c t i o n  (4.2.1) o f t h i s c h a p t e r .  r e s u l t s o f these e s t i m a t i o n s a r e superimposed t o t h e t a r g e t empty r u n data, i n f i g u r e  (4.1.1).  The  53  §4.1.2  T2 Neutron Background N o r m a l i z a t i o n T h i s type o f background, i n v o l v e d n o t o n l y a n o r m a l i z a t i o n problem  but  a s h i f t ambiguity as w e l l .  The shirfr/ o f t h e RF s i g n a l , mentioned i n  s e c t i o n (3.1.1), meant t h a t a l t h o u g h t h e TOF c u t s were o f t h e same w i d t h 3 i n the  He runs and i n t h e targetcempty r u n , they d i d n o t s e l e c t t h e same  energy T2 n e u t r o n s w i t h r e s p e c t t o the RF. lateral  (time and energy:  T h e r e f o r e t h e l o n g i t u d i n a l and  see the two-dimensional p l o t s ) k i n e m a t i c ex-  pansions of t h e T2 n e u t r o n t a i l a r e a l s o d i f f e r e n t a t t h a t c u t . The changes o f c a l i b r a t i o n from one r u n t o another a r e p a r t o f t h e observed shift. I t was not p o s s i b l e t o make a proper RF c u t f o r t h i s  background  because o f even g r e a t e r c o m p l i c a t i o n s when t h e t a i l mixes w i t h r e a l neut r o n s from t h e t a r g e t .  Because o f t h e l o w - s t a t i s t i c s o f t h e t a i l  and t h e e v i d e n c e of o n l y slow changes m a t i c expansion was n e g l e c t e d . for  itself  i n i t s d i s p e r s i o n , t h e double k i n e -  The r e l a t i v e time s h i f t was compensated  by a c o r r e s p o n d i n g energy s h i f t f o l l o w i n g t h e same assumptions and  knowing t h a t a g a u s s i a n shape remains  (see f i g u r e  3.1.3).  As a check to i n s u r e o f t h e v a l i d i t y o f those assumptions, t h e 3 n o r m a l i z a t i o n f a c t o r s f o r each t i o n on t h e t a i l  He r u n were c a l c u l a t e d u s i n g t h e i n f o r m a -  i t s e l f p r o v i d e d by t h e two-dimensional time-energy p l o t s .  I t was easy t o i d e n t i f y t h e t a i l b e f o r e t h e time o f a r r i v a l o f t h e photons s i n c e i n t h a t r e g i o n i t was w e l l s e p a r a t e d from t h e low-energy  background.  I n t e r p o l a t i o n t o t h e photon a r r i v a l time u s i n g both t h e " e a r l y " time and the of  " l a t e " time d a t a was u n f o r t u n a t e l y n o t p o s s i b l e because o f t h e a r r i v a l n e u t r o n s from r e a l t a r g e t a s s o c i a t e d events r i g h t a f t e r w a r d s and  54  because o f t h e m i x i n g w i t h low-energy e x t r a p o l a t i o n was f e a s i b l e .  background.  However, some k i n d o f  The neutrons o f t h e t a i l were counted f o r  each time b i n , t h e r a t i o s o f these v a l u e s w i t h t h e c o r r e s p o n d i n g time b i n of t h e t a r g e t empty r u n were found and e x t r a p o l a t e d down to t h e m i d d l e o f the low-energy one r u n .  Table V  time c u t . T a b l e V i s an example o f t h e s e c a l c u l a t i o n s f o r  Time z e r o i s the time o f a r r i v a l of the photons.  E x t r a p o l a t i o n method f o r T2 neutrons  ( r u n #169)  Time b i n (nsec)  Run 169 ( He)  Run 183 (BKG)  -10.2  109  124  .88 ± .12  -9.4  124  166  .74 ± .09  -8.6  120  177  .68 ± .08  -7.8  144  167  .86 ± .10  -7.0  136  216  .63 ± .07  -6.2  132  227  .58 ± .06  -5.4  144  191  .75 ± .08  -4.6  136  198  .68 ± .08  extrapolation  .53 ± .22  0.0  3  linear  Ratio  55  S i m i l a r l y , the estimate l a t i n g the c e n t r o i d of the t a i l the time c u t .  along  t h e time b i n s down t o t h e m i d d l e o f  T h i s method d e a l t d i r e c t l y w i t h c h a n n e l s ,  the changes i n c a l i b r a t i o n . 200  o f t h e energy s h i f t was done by e x t r a p o -  The u n c e r t a i n t y was - 3 or 4 c h a n n e l s over  c h a n n e l s f o r t h e whole spectrum, i . e . about 2.5 MeV.  large value  thus d i s r e g a r d i n g  This rather  i s an i n e v i t a b l e consequence o f t h e low s t a t i s t i c s and t h e  f l a t n e s s of the t a i l . A second method used t o o b t a i n t h e n o r m a l i z a t i o n f a c t o r was t o c o n s i d e r i t a s a f r e e parameter and o p t i m i z e parameters i n t h e f i t t i n g program.  i t w i t h respect to the other  Here we f i n d an i n c o n s i s t e n c y , as t h e  v a l u e s e x t r a c t e d i n t h i s way a r e s y s t e m a t i c a l l y about one standard  devia-  t i o n lower than t h e e x t r a p o l a t e d numbers f o r which t h e f i t i s poorer i n the low-energy r e g i o n . pancy:  Three f a c t o r s c o u l d p a r t i a l l y e x p l a i n t h e d i s c r e -  t h e problem o f d e t e r m i n i n g  t h e a c t u a l amount o f low-energy photon  background i n t h e l a r g e bump o f t h e T2 neutrons,  the width of the t a i l ,  which c o u l d v a r y from one r u n t o another due t o t h e i n s t a b i l i t i e s o f t h e RF  s i g n a l (indeed, r u n 173, t h e s h o r t e s t r u n but w i t h t h e h i g h e s t  current,  shows a c l e a r remnant o f a bump a t t h e e x t r a p o l a t e d p o s i t i o n , t h a t cannot be c o m p l e t e l y  e l i m i n a t e d i n t h e background s u b t r a c t i o n ) , and f i n a l l y t h e  p o s s i b i l i t y of an u n c l e a r along  time-dependent e f f e c t on t h e shape o f t h e t a i l  t h e time b i n s a s t h e f a c t o r t h a t a g r e e s b e s t w i t h t h e e x t r a p o l a t e d  3 v a l u e comes from t h e l o n g e r  He r u n (#168).  I chose t o use t h e f a c t o r s  y i e l d e d by t h e parameter method, as they never c o m p l e t e l y the p r e d i c t e d ones. two  values.  concerning  disagreed  with  The e r r o r s were a s s i g n e d a s t h e d i f f e r e n c e between t h e  I t was d e c i d e d  t o add l i n e a r l y , l a t e r on, a l l u n c e r t a i n t i e s  t h e T2 neutrons ( i n t h e energy s h i f t and n o r m a l i z a t i o n ) .  56  The  numbers o b t a i n e d  a r e a l s o compared w i t h the r a t i o s of  Cerenkov s c a l e r s , as a rough i n d i c a t i o n of the k i n d s were expected.  As  the Cerenkov monitor was  t a r g e t i n the beam l i n e ,  the s c a l e r s should  t y of the p r o t o n beam, but focussed  of n o r m a l i s a t i o n  l o c a t e d near the  onto the T2 t a r g e t , from which the ir  that  production  be p r o p o r t i o n a l to the  they a l s o depend on how  summarizes the e s t i m a t e s of e r r o r s i n v o l v e d  the  intensi-  w e l l the beam i s  beam emanates.  i n the whole T2  T a b l e VI  neutron  procedure.  T a b l e VI  Run  no.  E v a l u a t i o n of e r r o r s i n v o l v e d i n the T2 n e u t r o n background w i t h r e s p e c t to the t a r g e t empty run (#183)  RF s h i f t (nsec)  Compensation ( i n energy ch.)  Cerenkov ratios  Extrapolated Norm,, f a c t o r  Fitted Ratios  164  2.0  -12  + 3  0.85  1.1  + .3  .77  +  .33  168  2.9  -18  + 4  1.73  1.0  + .4  .93  +  .33  169  1.0  -7 + 3  1.08  0.5  + .2  .31  +  .22  170  2.5  -15  + 4  1.34  1.6  +  .4  1.05  + .45  173  2.9  -18  + 4  0.97  2.0  + .5  1.55  + .45  57  §4.1.3  Empty Target  Background  Normalization  T h i s background a l s o r e q u i r e d energy c a l i b r a t i o n from one  run  some s h i f t i n g due  to a n o t h e r .  But  to the changes i n  as those f l u c t u a t i o n s  were w e l l known ( s e c t i o n 3.3.2, feed-back method), the proper d i s p l a c e ment c o u l d be a c c u r a t e l y made. An  e s t i m a t e of the n o r m a l i z a t i o n  the s c a l e r s .  I t was  a v a i l a b l e through  not p o s s i b l e to e s t i m a t e d i r e c t l y how  stopped i n the empty t a r g e t because j t was  f a c t o r s was  expected to be d i f f e r e n t due  many p i o n s  the s c a t t e r i n g of the p a r t i c l e s  to the absence of a l a r g e p a r t of  the  3 scattering material. when the t a r g e t was  However, the s m a l l t h i c k n e s s full,  content stopping  the f a c t t h a t the beam moderator was  to l e t the s l o p e of the s t o p p i n g  a l l o w e d us to use  He  the c o r r e s p o n d i n g slow change i n the  d i s t r i b u t i o n f o r the p i o n s , and sufficient  of the  not  d i s t r i b u t i o n change s i g n  the C1.C2.C3 s c a l e r s , i . e . the number of incoming  cles, for normalization. The  The  s t a t i s t i c a l uncertainty  empty d a t a was  2%.  mated shape on  i t s low-energy s i d e , was  of the  parti  target  c h o i c e of the f u n c t i o n , e s p e c i a l l y f o r i t s e s t i a s c r i b e d a 3% e r r o r , added  linearly. Another method of f i n d i n g the c o r r e c t n o r m a l i z a t i o n again  through the f i t t i n g  itself.  where the background i s observed three c o n t r i b u t i o n s : peak and  was  In the energy r e g i o n above the TT° box (95-125 MeV),  t h e r e are e s s e n t i a l l y  the break-up c h a n n e l s , the t a i l  the background.  factor  o f the 135.8  MeV  A f i t to reproduce the data i n t h i s r e g i o n  i m p r a c t i c a l not because of the s t a t i s t i c s , but m o s t l y the s l i g h t l y  was  unre-  l i a b l e low-energy behaviour of the t h e o r e t i c a l break-up channels shape [A.C.  P h i l l i p s , 1977].  The  a l t e r n a t e s o l u t i o n I chose c o n s i s t e d  in  58  i t e r a t i v e f i t t i n g o f t h e whole energy spectrum w i t h v a r i a t i o n of o n l y t h e parameter of i n t e r e s t .  The n o r m a l i z a t i o n f a c t o r was then g i v e n by the  b e s t g e n e r a l f i t i n t h i s r e g i o n f o r each s e r i e s , w h i l e  i t s u n c e r t a i n t y was  a s c e r t a i n e d by t h e v a r i a t i o n needed t o observe a d e v i a t i o n o f about one of t h e l o c a l x method).  2  ( i t h e 110-125 MeV r a n g e ) . n  this  The r e s u l t s a r e shown i n t a b l e V I I f o r t h i s n o r m a l i z a t i o n of t h e  high-energy background. initial  (See next s e c t i o n about  estimates  The e x t r a c t e d v a l u e s a r e seen t o check w i t h t h e  o f t h e beam s c a l e r s .  The former, b e i n g more r e l i a b l e ,  were used i n t h e e r r o r a n a l y s i s .  Table V I I  Normalization  f a c t o r s , f o r t h e t a r g e t empty background  F a c t o r from  fits  Run no.  Ratio of s c a l e r s  164  .30 ± .02  .30 ± .04  168  .86 ± .04  .85 ± .05  169  .50 ± .03  .50 ± .03  170  .61 ± .03  .58 ± .03  173  .44 ± .02  .44 ± .02  59  §4.2  F i t t i n g of the Spectra In order to o b t a i n  the Panofsky r a t i o ,  simultaneous f i t t i n g of  a l l of the l i n e s i n v o l v e d was n e c e s s a r y so t h a t the s i g n i f i c a n c e of t h e overlaps  c o u l d be estimated q u a n t i t a t i v e l y .  The s u b t r a c t i o n of the two  t a r g e t empty backgrounds was done f i r s t , i n the manner e x p l a i n e d  i n the  3 last  section  spectrum:  (4.1).  Four remaining l i n e s were then c o n s i d e r e d  i n the  He  a low-energy background, the TT° square box, the break-up  channels and the r a d i a t i v e c a p t u r e peak. as c o r r e c t i o n s and a r e d e s c r i b e d  Other c o n t r i b u t i o n s were t r e a t e d  i n the f o l l o w i n g s e c t i o n  I s h a l l comment here on t h i s p r o c e d u r e . knowledge of t h e background n o r m a l i z a t i o n  (4.3).  Due t o the poor i n i t i a l  f a c t o r s and the s e l f - c o n s i s t e n c y  of the d a t a , i t was not p o s s i b l e t o c a r r y out the a n a l y s i s i n a s t r a i g h t forward f a s h i o n . could  Only by u s i n g  the i n f o r m a t i o n  o b t a i n e d i n the a n a l y s i s  the energy c a l i b r a t i o n converge on i t s c o r r e c t v a l u e and the norma-  l i z a t i o n s a s c e r t a i n t h e i r own ranges.  The former was important i n the  computation of the a r e a under each l i n e r e s o l u t i o n ) w h i l e the l a t t e r The  fitting  stressed  (by the c h o i c e  t h e u n d e r s t a n d i n g of the backgrounds.  program used was d e r i v e d  squares" method d e s c r i b e d  of the f o l d i n g  by P.R. B e v i n g t o n  were two parameters a s s i g n e d to each l i n e :  from the " n o n - l i n e a r  least  [P.R. B e v i n g t o n , 1969].  There  i t s amplitude ( i . e . i n t e g r a t e d  area) and i t s p o s i t i o n i n terms of i t s channel number i n the 200 channel histograms.  The p o s i t i o n parameters were used a t f i r s t to get the c o r r e c t  c a l i b r a t i o n and i n the end were f i x e d a t the r i g h t energy. neously f i t t i n g  the f o u r l i n e s , the program a l s o p r o v i d e d  By  simulta-  e r r o r s on the  d i f f e r e n t parameters, c o r r e s p o n d i n g to a change of one i n the t o t a l c h i square when a parameter " a " was v a r i e d by an amount equal t o i t s s t a n d a r d  60  d e v i a t i o n " 0 " , i . e . such t h a t A l s o , as each l i n e was pseudo-analytical expressions  §4.2.1  a+  X (a) 2  r e q u i r e d to be had  +  !•  continuous,  to be p r o v i d e d  analytical  or  for i t .  main source of the low-energy background i n t h i s  the l e a d c o l l i m a t o r s .  data,  2  Low-Energy Background The  was  x ( °")  T h i s was  deduced  experiment  [ J / E . S p u l l e r , 1977]  when  taken w i t h d i f f e r e n t l e a d arrangements around the t a r g e t , were  analysed:  i t turned out  to be e s p e c i a l l y dependent on the s i z e o f  l e a d c o l l i m a t o r f o r the f r o n t f a c e of the N a l c r y s t a l .  T h i s i s because  the f r a c t i o n o f the edge o f the c o l l i m a t o r (of r a d i u s " r " ) over subtended s o l i d angle f o l l o w s a 1/r  the  the  r e l a t i o n s h i p ; hence the i n c r e a s e i n  the low-energy background f o r a s m a l l c o l l i m a t o r . Most of these photons, r e g i s t e r e d i n c o i n c i d e n c e w i t h a stop are l i k e l y due  to the i n t e r a c t i o n of high-energy gamma-rays i n the  t h e r e i s mainly p a i r p r o d u c t i o n , and  positron.  The  high-energy e l e c t r o n s of the beam a l s o produce bremsv e r y s e n s i t i v e because o f i t s f o r -  these counts were r e j e c t e d by  a s s o c i a t e d events on the b a s i s of the RF to e l e c t r o n s and  lead:  f o l l o w e d by b r e m s s t r a h l u n g o f the e l e c t r o n  s t r a h l u n g to which the N a l d e t e c t o r was ward p o s i t i o n , but  gate,  signal.  the s e l e c t i o n of As  the phenomena r e l a t i v e  low-energy background photons are l i n k e d , i t was  t h a t they wbuMihave a s i m i l a r energy dependence and e l e c t r o n shape c o u l d be used to r e p r e s e n t  pion  assumed  therefore that  the  t h i s background.  A two-dimensional p l o t ( f i g u r e 4.2.1) was same s l i c e of events as f o r f i g u r e (3.2.1),  but  produced f o r e x a c t l y t h i s time w i t h  requirement of a charged p a r t i c l e e n t e r i n g the d e t e c t o r .  The  the  the  opposite  considerable  61 Figure  (4.2.1)  TIME-ENERGY DISTRIBUTION OF ELECTRON EVENTS  I  •  ^39 38 * 37 36 35 34 33 32 31 30 29 20 27 26 25 24 23 22 21 20 19 IB 17 16 15 14 13 12 11 10 9  t  112 21 1 12 3 13 12 312 1 11 1 31 1311 221 232 i 12 1 24 12 1213 33 2 131 1 1 341 1 235431 1 1 1 12 2 11 11 1 I 112 11 1 1 21 1223 1 1 1232 2131 11 1 31 3 11 1 2 1  T  1 11 221 1  11  34222313111111 1 1123213123 1112311 1672212112 4121 112 11 112413524 211211 2 13 1  11  233233  1114152  31221311 2212  I  111421  1  12  3  2  1  222  1  1  231  11  212  151  1  1  1112  1 311  2  1 11  I 1 1  13 3 3 2 12 223 21 1242311151 2222 2111111  1112231311 1222211 12 1 123 32 11242 111 11  1  212 3 1  2111 1 212 1  12 1  1  12 1 1 1 1 1 3 1 2 I 1 1 1 13 1 1 1 1 22 2 1 1 1 1 11 1 3 2 111 21 12 1 1 121 1 1 11 1 1 1 1 1 1 11 1 1 1 1 11 11 21 2 122 II 1 1 13 1 1 1 11312 1 2 2 1 122221 1 1 215 122 11 2441361 21 34 1 1 1 1 1344512354451 . 3 1 1 2 2 3 2 1 1 1 1 243445352 155696  1 11  t  1  2  1  1  21.  1 1  1 1  21  22  1  5221222  12 2 3 1 2 II 1 1 2 11 2  237 12  1353234422326421235222314112 22  3  1  21  12  1 1 1 1 2  121 1 t 1  1  1  1  3 49745113352121  1141451135245 17533223325255442263234423211 22  I  T  1121  1112  1123  It  12212 2 12  2  2  1 1 1 1  31 1 2 1  1 1 1 11 1 1 11 1 1 21 1 1 1 1  1  -8  L  1 1  -16  20  40  _L  60  80  100  120  140  ENERGY (MeV) Figure  (4.2.1)  Time-energy d i s t r i b u t i o n  of e l e c t r o n s f o r a p a r t i a l  based on t h e same d a t a as i n f i g u r e charged p a r t i c l e  requirement.  He r u n  (3.2.1) except f o r t h e  62  drop i n the count r a t e i n t h e n e u t r o n r e g i o n , compared t o the s u b s t a n t i a l d i s t r i b u t i o n i n the photon TOF c u t , shows how t h e former a r e p r o b a b l y a l l random events but i t c o n f i r m s t h e c o n n e c t i o n o f t h e l a t t e r  t o t h e low-  energy photon background. The e l e c t r o n events were r e c o r d e d on tape d u r i n g t h e experiment but of  they were a s s i g n e d a s p e c i a l b i t - p a t t e r n . the e l e c t r o n s p e c t r a f o r a f u l l r u n .  No s i g n i f i c a n t c o n t r i b u t i o n from  e x t e r n a l c o n v e r s i o n o f t h e photons o f t h e I T TT°  ->  ye e~ +  F i g u r e (4.2.2) shows one  0  decay o r d i r e c t l y from t h e  decay c o u l d be observed i n any o f the r u n s .  c o n v e r s i o n (mostly by p a i r p r o d u c t i o n ) would  The e x t e r n a l  take p l a c e i n the m a t e r i a l  3 l y i n g between t h e He content o f the t a r g e t and the d e t e c t o r , i . e . t h e  4 superfluid  He f i l m i n the w a l l o f the e x i t s i d e o f the t a r g e t , the mylar  windows and t h e v e t o counter (see s e c t i o n 4.3.2). ment, J.E. S p u l l e r  I n an e a r l i e r  experi-  [1977] observed, w i t h much b e t t e r s t a t i s t i c s , a d e f i n i t e  bump i n t h e e l e c t r o n energy spectrum, i n t h e r e g i o n of t h e charge-exchange TT° photons.  These e l e c t r o n s were a t t r i b u t e d t o m o s t l y e* p a i r s from the  TT° •+ y e e ~ decay b u t t h e presence o f e l e c t r o n s from e x t e r n a l +  and the importance o f t h e low-energy background i t s e l f  conversion  d i d n o t permit the  d e d u c t i o n o f an a c c u r a t e b r a n c h i n g r a t i o f o r t h e s p e c i a l decay. In  t h i s experiment the c o n t a m i n a t i o n l e v e l o f the low-energy  photons was c o n s i d e r a b l y h i g h e r because o f the p o s i t i o n o f t h e N a l d e t e c tor  and i t s s m a l l c o l l i m a t o r and t h e r e was no s i g n i f i c a n t e v i d e n c e o f  the  two phenomena mentioned above.  Accordingly, a simple f i t to the  e l e c t r o n data was done i n order t o e x t r a p o l a t e the low-energy background under t h e ir° photon box. w e i g h t s , was f i r s t  A few parameter p o l y n o m i a l , g i v e n  statistical  t r i e d , b u t i t never reproduced t h e slow decrease o f t h e  ELECTRON  0  25  ENERGY  50 ELECTRON  Figure  (4.2,2)  SPECTRUM  75 ENERGY  FOR  RUN  100  164  125  150  (MEV)  E l e c t r o n spectrum f o r r u n 164. The t h r e e l i n e s a r e d i f f e r e n t See t a b l e V I I I for. an e x p l a n a t i o n o f the symbols.  f i t s to t h e d a t a .  64  data towards h i g h e n e r g i e s w e l l enough.  I d e c i d e d to use an e x p o n e n t i a l  form of t h e p o l y n o m i a l w i t h , f o r s i m p l i c i t y ,  e q u a l l y weighted p o i n t s .  The  r e s u l t s were g r e a t l y improved and indeed t h e b e s t or n e a r l y b e s t f i t f o r each r u n was p r o v i d e d by t h e e x p o n e n t i a l o f a c u b i c (exp(a + bx + c x  2  + d x ) with four parameters). 3  e f f e c t s of t h e d i f f e r e n t f i t s of  polynomial;  T a b l e V I I I shows t h e  on the. e l e c t r o n spectrum.  The e x p o n e n t i a l  a f o u r t h o r d e r p o l y n o m i a l was not r e t a i n e d because o f t h e c r i t i c a l  smallness o f t h e f i f t h parameter i n the  Table V I I I  Comparison of reduced c h i - s q u a r e s f o r e l e c t r o n f i t s between 17 and 79 MeV f o r r u n #164 (85 data p o i n t s )  Number of parameters "ti"  Figure  computations.  Polynomial. "Pn"  EXP(poly.) "En"  2  4.94  0.70  3  1.08  0.51  4  0.52  0.39  5  0.42  0.38  (4.2.2) shows t h e r e s u l t s o f t h r e e of t h e s e f i t s ,  the n o t a t i o n used i n t a b l e V I I I .  i d e n t i f i e d by  65  L i n e s from the IT  §4.2.2  + He R e a c t i o n s 3  There a r e f o u r r a d i a t i v e channels f o r helium-3, i n t h r e e l i n e s of the energy  spectrum.  and  they show up  The D o p p l e r - s h i f t e d photons  the TT° decay i n the charge-exchange r e a c t i o n have a u n i f o r m energy t r i b u t i o n between 53.1  and 85.7  MeV.  The  t i v e p i o n c a p t u r e r e a c t i o n TT + He 3  3  from dis-  e l a s t i c photons from the r a d i a -  H + y occur a t 135.8  MeV.  The Amado model, f o r reasons g i v e n i n the i n t r o d u c t i o n , was to r e p r e s e n t the break-up c h a n n e l s . o b t a i n e d by f i t t i n g polynomial-type  chosen  A p s e u d o - a n a l y t i c f u n c t i o n f o r i t was  the t h e o r e t i c a l shape [A.C. P h i l l i p s , 1977]  with  e x p r e s s i o n s i n segments c l o s e l y a d j o i n i n g each o t h e r .  Few-parameter p o l y n o m i a l s or e x p o n e n t i a l s of such were t r i e d , f o l l o w i n g the method d e s c r i b e d i n l a s t  section.  was  Two  taken f o r each segment.  reproduce  Whichever f i t t e d  the t h e o r y b e s t  f u n c t i o n s were a c t u a l l y s u f f i c i e n t  the a c c u r a c y of the t h e o r e t i c a l d a t a a v a i l a b l e :  the e x p o n e n t i a l  of a c u b i c p o l y n o m i a l c l o s e l y f o l l o w e d the curve between 119 and and  i t s smooth decrease  to p r a c t i c a l l y zero a t zero energy was  low-energy e x t r a p o l a t i o n (see f i g u r e 1.1b); reproduced  the 119-128 MeV  region.  a f o u r t h order  to  90  MeV  taken as a  polynomial  The e r r o r s a s s o c i a t e d w i t h t h i s  break-  up l i n e come i n the low-energy p a r t of the model which i s s e n s i t i v e to the high-momentum components of the 3-nucleon F. R o i g , 1974].  wave'function  These e r r o r s a r e d i s c u s s e d i n s e c t i o n  The low-energy background shape was  [A.C. P h i l l i p s  and  (4.3.1).  not f o l d e d w i t h the r e s o l u t i o n  f u n c t i o n because, b e i n g d e r i v e d from the d a t a , i t a l r e a d y c o n t a i n e d i t ;  3 but the t h r e e  He l i n e s were.  To account  towards low e n e r g i e s , the response  f o r the g r a d u a l l o s s o f r e s o l u t i o n  f u n c t i o n was  widened by a s m a l l amount  66  through a simple s t r e c h i n g fits  W i t h i n 0 . 1 % d i f f e r e n c e s , the best  process.  r e v e a l e d a 4 . 5 % r e s o l u t i o n f o r the 1 3 5 . 8 MeV  photons, 5 . 2 % f o r t h e  break-up c h a n n e l s and 6 . 2 % a t t h e TT° box, r o u g h l y a g r e e i n g l i n e a r l y w i t h the  7 . 7 % r e s o l u t i o n observed f o r monoenergetic 1 1 . 7 MeV  [J.E. S p u l l e r ,  photons  1 9 7 7 ] .  The chosen response f u n c t i o n was  the one o b t a i n e d by n-y c o i n c i -  dences, taken w i t h the same c o l l i m a t o r and shown i n f i g u r e was  slightly  folding. good  ( 2 . 4 . 1 ) .  smoothed to p a r t i a l l y compensate f o r the s t a t i s t i c s , b e f o r e  The e l a s t i c peak from the ir p  statistics,  ny s i n g l e experiment, w i t h i t s  c o u l d not be used because of e v i d e n c e of g a i n s h i f t s  during t h i s r u n ( 2 ) ,  which r e s u l t e d  i n the d i s t o r t i o n o f t h e l i n e  shape.  The e r r o r i n the c h o i c e of the response f u n c t i o n l i e s m a i n l y i n the and i s f u r t h e r d i s c u s s e d  i n the next  tail  section.  I t e r a t i v e f i t t i n g s made p o s s i b l e resolutions  It  the adjustment of the f o l d i n g  f o r each l i n e i n each r u n and the convergence of the  calibration.  The 4 - l i n e  § 4 . 2 . 3  One target  Fits  of t h e s e b e s t f i t s  i s shown i n f i g u r e  empty backgrounds have been s u b t r a c t e d .  w i t h t h e d a t a i s seen to be q u i t e good. and the f o u r o t h e r s i s g i v e n i n t a b l e IX. of the l i n e s to the f i t a r e a l s o  a f t e r the  ( 4 . 2 . 3 ) , .  The o v e r a l l  agreement  A descriptive l i s t for this f i t The i n d i v i d u a l  shown i n f i g u r e  ( 4 . 2 . 4 ) .  contributions  FIT  OF  RUN  169  MINUS  BACKGROUND  400  300  -  200  -  100  h  CO  o  0 10  30  50 PHOTON  Figure  (4.2.3)  70  90  ENERGY  110  130  150  (MEV)  F i t of r u n 169 a f t e r s u b t r a c t i o n o f the T2 n e u t r o n and t a r g e t empty backgrounds.  CONTRIBUTIONS  PHOTON Figure  (4.2,4)  Contributions  TO  ENERGY  THE  F I T  (MEV)  t o t h e f i t of f i g u r e (4.2.3) by the f o u r l i n e s :  the low-energy background,  the TT° photons, t h e break-up channels and the 136 MeV photons, a l l f o l d e d w i t h t h e e x p e r i m e n t a l response - f u n c t i o n .  69  T a b l e IX  Run no.  D e s c r i p t i o n o f the f i t s f o r t h e f i v e runs  S h i f t i n channels N o r m a l i z a t i o n f a c t o r s Number o f f r e e Reduced T2 n e u t r o n T a r g e t empty parameters v T2 n e u t r o n s  164  -12 ± 3  0.77 ± .33  0.30 ± .04  169  1.083  168  -18 ± 4  0.93 ± .33  0.85 ± .05  159  0.875  169  -7 ± 3  0.31 ± .22  0.50 ± .03  161  0.677  170  -15 ± 4  1.05 ± .45  0.58 ± .03  163  1.068  173  -18 ± 4  1.55 ± .45  0.44 ± .02  167  0.634  The program  c a l c u l a t e d .theaajreaeunderheachtbf t h e a f o l d e d - ' t h e o r e t i c a l  l i n e s , t a i l s i n c l u d e d , but i t was judged b e s t t o go i n t o the computation i n an h y b r i d e way.  The low-energy background  and t h e break-up  shapes were used d i r e c t l y and s u b t r a c t e d from the d a t a .  channels  Because o f t h e  d i f f i c u l t y o f f o l d i n g r e s o l u t i o n p r e c i s e l y , and i n o r d e r t o reduce t h e b i a s due t o t h e response f u n c t i o n a s much a s p o s s i b l e , t h e two l i n e s r e m a i n i n g in  the " s u b t r a c t e d f i t " (charge-exchange and e l a s t i c r a d i a t i v e c a p t u r e  c h a n n e l s ) were determined from t h e r e m a i n i n g d a t a . the  A problem a r i s e s i n  t a i l c o n t r i b u t i o n s because o f the enhancement o f s t a t i s t i c a l  and t h i s lower p a r t was c a l c u l a t e d from t h e knowledge o f t h e t a i l in  t h e f i t , i . e . t h e n o r m a l i z e d f o l d e d l i n e shape  (see f i g u r e  effects computed  4.2.4).  Thus t h e r e s u l t s a r e n o t c o m p l e t e l y independant o f t h e c h o i c e o f t h e response f u n c t i o n .  70  §4.3  E r r o r P r o c e s s i n g and Panofsky R a t i o C a l c u l a t i o n  In o r d e r to compute the Panofsky r a t i o ,  the c o n t r i b u t i o n s from  the charge-exchange and r a d i a t i v e c a p t u r e c h a n n e l s ,  i n c l u d i n g the  r e n t c o r r e c t i o n s and  In t h i s  e r r o r s , have to be e v a l u a t e d .  s e c t i o n , the  e r r o r s on the backgrounds p r e v i o u s l y d i s c u s s e d i n s e c t i o n (4.1) presented. f o r one  An  of the  §4.3.1  runs.  Sources of E r r o r s  the f i t The  three l i n e s considered  exchange (CE) , the break-up(BU) and numbers a r e g i v e n by the f i t s folded  are  example of the procedure f o l l o w e d i s g i v e n i n t a b l e X  C o r r e c t i o n s and  Step 1:  diffe-  i n t o each l i n e  v i d e d by the f i t s and  i n the photon s p e c t r a a r e : the e l a s t i c peak(EP).  the  charge-  Their basic  of the s p e c t r a w i t h the proper r e s o l u t i o n  (section  4.2.2). The e r r o r s quoted a r e the ones pro  they c o n t a i n the s t a t i s t i c a l u n c e r t a i n t y and  the  c o r r e l a t e d e r r o r f o r each l i n e w i t h r e s p e c t to the t h r e e o t h e r s u s i n g the standard d e f i n i t i o n  Step 2:  of a change of 1 i n the t o t a l x  (see s e c t i o n  4.2)  the s u b t r a c t e d f i t To m i n i m i z e the b i a s due  the l a s t s e c t i o n ) , a p a r t i a l l y e l a s t i c peak l i n e s was numbers.  2  I t was  to the l i n e shape (as commented upon i n  s u b t r a c t e d f i t f o r the charge-exchange and  used to p r o v i d e an a b s o l u t e c o r r e c t i o n to  estimated  that t h i s  the  " s u b t r a c t e d f i t " method covered  an  71  Table X  Step no.  Example o f e r r o r and c a l c u l a t i o n p r o c e d u r e s  RUN  #169  1  F i t ( x =0.677)  2  Subtracted f i t  3  Response  4  TOF  5  2  function  Break-up  Q,L  Chargeexchange  Q  14226 ± 130  +21 ±  48  Q  +16 ±  5  Low-energy background  Q  ±  21  6  High-energy randoms  Q  7  T a r g e t empty norm.  Q  8  T2 n e u t r o n s h i f t  L  9  T2 n e u t r o n norm.  L  10  Break-up f u n c t i o n  L  11  Inflight corrections  ?  12  SUM  +  +1 ±  1  -50 ±  +4 ± 19  +1 ±  1  9  -32 ±  6  ± 61  ±  5  ± 44  ±  1  ±  1  ± 138  ±  1  ±  0  +  -17 ±  7  17  +55 ± 55 ?  2524  3720  14259 ± 141  ±123  ± 62  L  ± 199  ± 57  ±  ir° decay f a c t o r  x  1.0058  Internal conversion  x  External  x  linear  14  +6 ± 73  Q  quadratic  13  2543 ± 58 +8  +13  Q  corrections  3708 ± 77  Radiative capture  errors  errors  conversion  1  ? .993(H) 1.0052  1.0059  1.0060  72  average of 9 6 % of the counts i n the charge-exchange the  e l a s t i c peak r e g i o n .  The remainder had to be e s t i m a t e d from the  due to s i g n i f i c a n t o v e r l a p s of the  Step 3:  the response The  r e g i o n and 8 3 % i n  shapes.  function  s t a t i s t i c a l e r r o r of the response f u n c t i o n i t s e l f ,  i n a n-y c o i n c i d e n c e measurement applies f u l l y  fits  to the break-up  (see s e c t i o n 2 . 4 ) , was  line.  For the o t h e r two  obtained  1 . 9 6 % and i t l i n e s , the u n c e r t a i n -  t y a s s o c i a t e d w i t h the response f u n c t i o n i s the s t a t i s t i c a l e r r o r of the fractional  c o n t r i b u t i o n s o b t a i n e d from the f i t s  (^4% f o r CE, M.7%  times t h i s f r a c t i o n a p p l i e d to the t o t a l number of counts under line  f o r EP),  the  ( i . e . -an average of 0.4% of the t o t a l f o r CE, 0.9% f o r E P ) ( e r r o r s ) . Moreover,  a c o r r e c t i o n must be made due to the f a c t  t h a t the r e s -  ponse f u n c t i o n m i s s e s about 0 . 1 5 % o f the events i n i t s low-energy An u n c e r t a i n t y of 3 0 % was It  should be.noted  a s s i g n e d to t h i s c o r r e c t i o n t h a t t h i s l i n e shape was  c o i n c i d e n c e measurement a t 1 2 9 . 4 MeV  w i t h hydrogen,  tail.  [J.E. Spuller,  1977].  o b t a i n e d from a but we chose to use i t 3  on the b a s i s of the s m a l l energy d i f f e r e n c e w i t h the (EP) and  events missed by TOF In  in  section  experiments.  cuts  ( 3 . 3 . 1 ) , i t was  e s t i m a t e d t h a t the t i g h t  the t i m e - o f - f l i g h t t e c h n i q u e used to s e p a r a t e photons  caused a s m a l l f r a c t i o n the  MeV  the good agreement w i t h the d a t a i n a l l the runs i n s p i t e of the  1 2 months time l a p s e between the two  Step 4:  He l i n e a t 1 3 5 . 8  charge-exchange  of the events to be missed:  cuts necessary  from neutrons  t y p i c a l l y 0.08% f o r  box, and 0.04% f o r both the break-up  and the e l a s t i c  73  structures.  The a s s o c i a t e d e r r o r s r e p r e s e n t the range of the unsure  which c o u l d be r e a l or random, and  t h i s should a l s o account  f o r the  events, over-  l a p s of the t h r e e l i n e s .  Step 5:  the low-energy background An argument based on the s i m i l a r i t y of the energy dependence  was  g i v e n i n s e c t i o n ( 4 . 2 . 1 ) f o r the use o f the e l e c t r o n shape to r e p r e s e n t the low-energy background.  Although  t h i s seems p l a u s i b l e and  there i s  good agreement i n the f i t s , no experiment has been performed to c o n f i r m i t decisively  and  the f u n c t i o n . typically)  t h e r e may  The  be a s y s t e m a t i c u n c e r t a i n t y i n the c h o i c e of  f i t s gives a correlated error f o r t h i s l i n e  as f o r the t h r e e o t h e r l i n e s , as i n s t e p ( l ) .  the c h o i c e of t h i s background f u n c t i o n , i t was double  thought  (V3.2%,  To account reasonnable  for to  i t , i . e . to add a g a i n the u n c e r t a i n t y i t b r i n g s to the counts  of  the charge-exchange c h a n n e l .  Step 6:  the high-energy The  randoms  low-energy background l i n e extend  contribution-.becomes the high-energy  v e r y s m a l l under the e l a s t i c peak.  random events, m a i n l y  cant source of background. dot-plots buted  to h i g h e r e n e r g i e s but i t s  I t was  At t h a t p o i n t ,  cosmic r a y s , a r e the most  observed,  by l o o k i n g a t  signifi-  two-dimensional  ( s e c t i o n 3.3.3), t h a t these events were q u i t e u n i f o r m l y  i n energy and  time and  c o u l d be r e p r e s e n t e d by a f l a t  i n s i d e the r e g i o n of the TOF. c u t s .  distri-  distribution  74  I d e a l l y , i t would have been p r e f e r a b l e to s u b t r a c t t h e s e random events b e f o r e the f i t ,  but i t was not p o s s i b l e t o determine t h e i r  distri-  b u t i o n a t lower e n e r g i e s because of the low s t a t i s t i c s and the dependence on the count r a t e s , nor c o u l d t h i s c o n t r i b u t i o n be f i t t e d by e x t e n d i n g the low-energy background  a t a c o n s t a n t l e v e l p a s t the p o i n t where both  a r e about equal (-100  MeV)  was  and was  g i v e n by the f i t ,  because the low-energy background therefore variable.  to d i s t r i b u t e the random c o n t r i b u t i o n above 90 MeV  amplitude  The procedure used  was  between the break-up  and the e l a s t i c c h a n n e l s a c c o r d i n g to t h e i r r e l a t i v e importance and t o s u b t r a c t from t h e s e e s t i m a t e s the c o r r e s p o n d i n g p a r t s of the background  line.  The e r r o r s a r e a q u a d r a t i c combination of the u n c e r t a i n -  t i e s on the cosmic r a y s and on the low-energy background  Step 7:  i n this  region.  the t a r g e t empty n o r m a l i z a t i o n The e r r o r on t h i s background  fits,  low-energy  s u b t r a c t i o n was  o b t a i n e d from the  i . e . the e f f e c t on the d i f f e r e n t channels o f the change i n the n o r -  m a l i z a t i o n f a c t o r which i n c r e a s e d the l o c a l x w i t h the p r e d i c t i o n s from the s c a l e r s  2  by 1.  A l l f a c t o r s agreed  ( s e c t i o n 4.1.3).  The d i f f e r e n c e s i n  the c o n t r i b u t i o n s of the l i n e s were taken as the c o r r e s p o n d i n g e r r o s f o r each c h a n n e l .  Steps. 8&9:  the "T2 n e u t r o n " background  There was production target  a s i g n i f i c a n t number of n e u t r o n s coming  from the p i o n  (T2) through the c o n c r e t e s h i e l d i n g and r e g i s t e r i n g a  c o i n c i d e n c e w i t h a stop s i g n a l .  The problem of removing  t h e s e events  75  involved a two-fold uncertainty, i n the correction of the RF s h i f t and i n the extraction of the normalization factor.  Both evaluations were made  by the extrapolation method, and since the flatness of the T2 neutron energy d i s t r i b u t i o n made the s h i f t d i f f i c u l t to estimate and for reasons given i n section (4.1.2), a consistent discrepancy was observed between the predicted normalization factors and the ones obtained by the f i t s . The uncertainties due to these two problems were given by the difference between f i t s for each l i n e when the input s h i f t or factor was changed by an amount equal to i t s standard deviation.  Because there i s no doubt  that these errors are systematic i n nature, both were treated l i n e a r l y i n further computation,  Step 10:  instead of i n quadrature.  the choice of the break-up function  The two break-up channels were represented by the Amado model. In our data as for the data from Berkeley [see A.C. P h i l l i p s and F. Roig, 1974], the agreement i s good for energies above ^105 MeV but the theoret i c a l l i n e consistently l i e s a l i t t l e too low i n the 90-100 MeV region (see figure (4.2.3) and section (1.2.3) for comments).  In an attempt to  correct for t h i s model dependant discrepancy, an average difference was calculated above 93 MeV, where the charge-exchange contribution i s n e g l i g i b l e , and over a range of about 8 MeV, main region of the v i s i b l e d i f f e rence.  The r e s u l t was an increase between 14% and 19% i n t h i s region f o r  a l l the runs and was applied to the break-up from 100 MeV to zero energy, corresponding to a t o t a l increase of 1.2-2.1% for the break-up l i n e .  This  also brought a negative correction to the t o t a l number of counts i n the charge-exchange channel, ranging from 0.09% to 0.17%, depending on the run.  76  One might argue on the hazards  o f t h i s method and t h e a l r e a d y  e x t r a p o l a t e d shape o f t h e break-up from 90 MeV down t o z e r o . the second p o i n t , t h e shape we used and which i s reproduced  Concerning i n figure  (1.1b)  shows t h a t below 100 MeV t h e r e i s about 12% o f t h e t o t a l number under t h e l i n e , which i s s m a l l and s u b j e c t t o minor changes o n l y w i t h the c o n d i t i o n of c o n v e r g i n g  t o zero a t 0 MeV, and t h e r e f o r e a c c e p t a b l e f o r a M.5% i n -  crease i n t h i s region.  F i n a l l y , t h i s was judged  compensate f o r t h e observed  discrepancy.  t h e b e s t p r a c t i c a l way t o  I t was d e c i d e d however t o  a s c r i b e t h e v a l u e of t h e c o r r e c t i o n t o t h e e r r o r and t o add l i n e a r l y t h i s u n c e r t a i n t y i n a l l c a l c u l a t i o n s as i t i s of a s y s t e m a t i c k i n d .  Step 11:  the i n f l i g h t c o r r e c t i o n s  They were n o t done i n t h i s experiment s i n c e they were found t o be <0.5% i n t h e hydrogen c a s e .  Step 12:  t h e sum f o r each  channel  The number o f counts under each l i n e i s t h e s t a r t i n g number from the f i t ,  t o which a r e added a l l t h e c o r r e c t i o n s l i s t e d above (see t a b l e X ) .  The d i f f e r e n t  e r r o r s a r e summed s e p a r a t e l y depending on whether they a r e  s t a t i s t i c ( Q ) o r s y s t e m a t i c ( L ) i n n a t u r e , as e x p l a i n e d above: ones a r e added i n quadrature  the f i r s t  and t h e o t h e r s l i n e a r l y , which produces two  numbers f o r each o f t h e t h r e e channels a t t h e end o f t h i s step i n t a b l e X. Furthermore, t a b l e XI summarizes these r e s u l t s runs.  f o r the f i v e  3 He  77  T a b l e XI  Run no.  Sum i n each c a p t u r e channel f o r each r u n  Charge-exchange. Q L  Break-up  164  13984  ±145 ±140  3402  ±122 ±83  2467  ±63  ±1  168  16044  ±157 ±223  3938  ±148 ±80  2809  ±63  ±2  169  14259  ±141 ±199  3720  ±123 ±57  2524  ±62  ±1  170  19457  ±177 ±217  4453  ±151 ±89  3472  ±76  ±1  173  12877  ±142 ±214  2640  ±144 ±39  2239  ±60  ±1  Q  L  Radiative capture Q L  78  The Panofsky R a t i o - P^  § 4 . 3 . 2  3 section  The Panofsky r a t i o f o r IT a b s o r p t i o n i n He has been d e f i n e d i n ( 1 « 2 . 2 ) as the r a t i o of the charge-exchange r a t e t o the e l a s t i c  radiative rate:  _ OJ(TT  p  3  He +  [TT°^YY  HTT°,  =  .  (TT  -3  (98.8%),  T\°+ye e  (1.2%)])  3  He ->  Hy)  (la) + (lb) (2)  as numbered i n s e c t i o h ( 1 . 2 . 1 ) .  If  the number of 1 3 5 . 8 MeV  i n the charge-exchange l i n e and N f i r s t a p p r o x i m a t i o n f o r P^ would  i s d e f i n e d as the number o f photons photons, a  be:  (0.5)x(N /N )  P' =  1  2  where the 0 . 5 f a c t o r a c c o u n t s f o r the two photons i n t h e TT° decay c h a n n e l a f t e r charge-exchange. N N  Step 1 3 :  =  x  2  =  2  But what we r e a l l y have i s : (la) + (lb) (2)  i n h e r e n t c o r r e c t i o n s to P^  The Panofsky r a t i o , w i t h simple a l g e b r a , can be r e w r i t t e n i n terms of P' and a m u l t i p l i c a t i v e c o r r e c t i o n .  1 P  + p'  = P' x {  } 1  3  where p ' i s the r a t i o  +  (p'/2)  ( l b ) / ( l a ) so t h a t  plicative correction.  = P' x C P  becomes the p i o n decay m u l t i -  From the P a r t i c l e Data Group  tables  [ 1 9 7 6 ] ,  one  f i n d s t h a t the r a t i o of the two main decay mode p r o b a b i l i t i e s f o r the neut r a l pion gives p'  =  0 . 0 1 1 6 3 ,  hence a m u l t i p l i c a t i v e f a c t o r  =  1 . 0 0 5 7 8 .  79  One can also show that the introduction of the r e l a t i v e rate of  3 internal conversion for photons i n  to (IT p =  r  OJ(IT  -  3  He,  He -> H  e  3  3  3  He.  H  y  +  e ) )  introduces another m u l t i p l i c a t i v e correction Panofsky r a t i o P^. Joseph ID.W.  Joseph, 1960]  He.  e  This branching r a t i o p has been calculated by i n the hydrogen case (p  D.W.  = 0.00710) but i t i s  H  3 not known for  = (1/(1+P3^ )) to the  Nevertheless, i t was decided, i n a f i r s t  approximation,  to assume the hydrogen value for P3g as a minimum correction to e  P^.  Therefore the correction factor used i s C. = 0.99295. l  Step 14:  external conversion The photons produced i n the target had a small p r o b a b i l i t y of  undergoing external conversion by pair production i n the materials placed in their path to the Nal detector.  3  These were the mylar windows of the  He target, the thermal shielding f i l m of superfluid  4 He i n the walls of  the c e l l and the veto counter through which the photons had to pass.  This  effect i s small (0.5%) compared to the f i n a l errors, but non-negligible i n t h i s experiment. Let N be the number of counts i n any one of the channels.  By pho-  ton absorption i n a given material, N i s changed by a m u l t i p l i c a t i v e factor exp(-a£), where a i s the cross-section i n terms of the inverse of the r a d i a t i v e length (L^) and I the thickness of material i n units of r a d i a t i v e length.  From the P a r t i c l e s Data Group tables [1976], one  finds:  80  E * 70 MeV, Y E ^ 120 MeV, Y E ^ 136 MeV, Y T h e r e f o r e each m a t e r i a l i n t r o d u c e s for  ratio.  The c o r r e c t i v e f a c t o r s C  e  a = 0.57 L  1  r a =  0.65 L  a =  0.66 L  -  1  r _  1  r a m u l t i p l i c a t i v e f a c t o r t o the Panofsky f o r external conversion are w r i t t e n at  the bottom o f t a b l e X , f o r each c h a n n e l .  T a b l e X I I summarizes those  calcu-  l a t i o n s , f o r which t h e net c o r r e c t i o n o b t a i n e d f o r P^ i s o n l y  C*  0 t  = ( 1 - 0.00082).  Table X I I  External conversion c o r r e c t i v e  Material  Thickness (cm)  mylar windows l i q u i d He v e t o counter (NE102A)  p  755  0.32  the r a t i o  Using (C  28.7  0.20  4  Step 15:  0.04  Radiative l e n g t h (cm)  P  42.9  factors  Corrective f o r B„  factors f o r P,  (1 - 0.00001)  (1 - 0.00013)  (1 -  )  (1 - 0.00002)  (1 - 0.00007)  (1 - 0.00067)  -  3  t h e two m u l t i p l i c a t i v e f a c t o r s o b t a i n e d i n t h i s s e c t i o n  f o r TT° decay and C  e  f o r e x t e r n a l c o n v e r s i o n ) , a t h i r d one (C., f o r i  i n t e r n a l c o n v e r s i o n ) b e i n g unknown but g i v e n , i n f i r s t a p p r o x i m a t i o n ,  the  v a l u e f o r hydrogen, t h e Panofsky r a t i o i n helium-3 i s simply t h e r a t i o , d i v i d e d by 2, o f t h e charge-exchange c o n t r i b u t i o n to t h e r a d i a t i v e sum of s t e p ( 1 2 ) .  81  Due t o t h e s y s t e m a t i c n a t u r e o f some o f t h e u n c e r t a i n t i e s , t h e errors are s t i l l  t r e a t e d s e p a r a t e l y i n the d i v i s i o n :  t i c a l e r r o r s ( Q ) a r e added i n quadrature a r e added l i n e a r l y .  Table XIII  The r e s u l t s  P„  statis-  and t h e r e l a t i v e s y s t e m a t i c e r r o r s  f o r t h e f i v e runs a r e l i s t e d  I n d i v i d u a l Panofsky  Run no.  the r e l a t i v e  i n table XIII.  r a t i o s f o r each r u n  Statistical uncertainties  Systematic uncertainties  164  2.828  + 0.078  (2.76%)  + 0.030  (1.04%)  168  2.850  + 0.070  (2.45%)  + 0.042  (1.46%)  169  2.819  + 0.075  (2.64%)  + 0.042  (1.47%)  170  2.796  + 0.066  (2.37%)  + 0.032  (1.14%)  173  2.870  + 0.082  (2.90%)  + 0.049  (1.71%)  Based on a r e a s o n a b l e c o n f i d e n c e i n t h e e s t i m a t e s o f t h e u n c e r t a i n t i e s , and on t h e good agreement o f t h e r e s u l t s w i t h themselves, i t was d e c i d e d t o take t h e i r weighted  average.  However, because o f t h e  s m a l l i n c o n s i s t e n c y i n the T2 n e u t r o n h a n d l i n g , t h e d i s t i n c t i o n was maint a i n e d between s t a t i s t i c a l and s y s t e m a t i c e r r o r s . ge o f t h e Panofsky  F o r t h e weighted  avera-  r a t i o , with the corresponding r e d u c t i o n of the s t a t i s -  t i c a l e r r o r , t h e f o l l o w i n g v a l u e was o b t a i n e d :  P^ = 2.830 ± 0.033  To t h i s o v e r a l l s t a t i s t i c a l e r r o r was added t h e average  (1.17%).  of the systematic  82  uncertainties, weighted by themselves:  ± 0.037 (1.29%) to finally obtain,  adding the two errors linearly: P  3  = 2.83 ± 0.07  (2.46%)  This result i s considered to be f a i r l y r e a l i s t i c .  For the purpose  of comparison only, i f the errors of individual runs had been added linearly before taking a weighted average, we would have obtained which i s considered to be too optimistic.  P^ = 2.83±0.05,  Furthermore, i f the internal  conversion factor (C/) had been completely ignored in this calculation (instead of assuming the hydrogen value), a l l individual and final ratios would have been increased by 0.020 and we would have obtained P^ = 2.85. The main sources of errors in this experiment were the T2 neutrons:  there  were too few of them to extract them well but too many of them to be considered negligible.  83  §4.3.3  The R a t i o B A second  in section channel  3  r a t i o between t h e r a d i a t i v e c a p t u r e p r o c e s s e s was  (1.2.3), namely t h e r a t i o o f t h e break-up r a t e s  defined  to t h e e l a s t i c  rate: O)(TT B  -3 -3 He -> dny) + to (IT He -> pnny) I3  =  3  wOrr  3  He ->• Hy)  (3) + (4)  as numbered  i n section  (2) (1.2.1).  The i n t e r n a l c o n v e r s i o n p r o c e s s e s have  not been c o n s i d e r e d a t - ^ a l l here due t o t h e absence o f any knowledge o f t h e 3  i n t e r n a l c o n v e r s i o n p r o b a b i l i t y f o r r a d i a t i v e c a p t u r e on t h r e e channels  involved  i n the r a t i o B^.  He i n any o f t h e  The v a l u e s c a l c u l a t e d f o r B^  from t h e numbers o b t a i n e d i n step(12) and w i t h c o r r e c t i o n f a c t o r s  from  steps(13&14) a r e l i s t e d  i n the  i n t a b l e XIV.  same double way as i n t h e l a s t  T a b l e XIV  The e r r o r s were c a l c u l a t e d  section.  I n d i v i d u a l r a d i a t i v e r a t i o s f o r each r u n  Run no.  B„  Statistical uncertainties  164  1.379.  + 0.061  (4.40%)  + 0.034  (2.48%)  168  1.402  + 0.061  (4. 38%)  + 0.030  (2.10%)  169  1.474  + 0.061  (4.12%)  + 0.023  (1.57%)  170  1.283  + 0.052  (4.04%)  + 0.026  (2.03%)  173  1.179  + 0.072  (6.08%)  + 0.018  (1.52%)  c  Systematic uncertainties  84  The unmistakably l a r g e spread i n the d a t a i s such t h a t a weighted average was  not a p p l i c a b l e .  The reason f o r t h i s wide range of v a l u e s i s  l i k e l y to be the f a c t t h a t , a p a r t from r e l a t i v e l y s m a l l c o r r e c t i o n s , b a s i c number f o r the c o n t r i b u t i o n i n the break-up fit.  I t was  channel comes from the  p o s s i b l e t o a p p l y the s u b t r a c t e d f i t method ( s e c t i o n 4.2.3)  to a l l l i n e s but t h i s one and t h e r e f o r e i t might be a f i t t i n g  problem.  T h i s h y p o t h e s i s i s confirmed by the c l o s e n e s s of the i n d i v i d u a l ratios within  the  Panofsky  themselves.  That the simultaneous f i t t i n g of f o u r l i n e s does not g i v e s e l f c o n s i s t e n t numbers emphasizes the need f o r a b e t t e r i n i t i a l knowledge o f the l o n g low-energy  p a r t of the break-up  channel to a v o i d the c o r r e l a t e d  d i s c r e p a n c i e s , which were d i s c u s s e d e a r l i e r and among which t h e r e might be p a r t of the T2 neutron n o r m a l i z a t i o n problem.  T h i s would of course  a l s o a v o i d the " c o r r e c t i o n s " t o the break-up channel>.0(step For for  these reasons, a l t h o u g h a weighted  of 1.348, i t was  10) .  average p r o v i d e d a v a l u e  d e c i d e d the maximum o f the encountered  errors for  both the s t a t i s t i c a l and the s y s t e m a t i c u n c e r t a i n t i e s , so t h a t adding the two of them l i n e a r l y f i n a l l y B  3  = 1.35  gives: ±  0.11  85  Chapter 5  §5.1  Conclusions  Absolute  Rates  3 Of the s i x main channels a c c e s s i b l e i n t h i s experiment:  f o r tr a b s o r p t i o n on  He,  two  the n o n - r a d i a t i v e a b s o r p t i o n  y i e l d e d n e u t r o n s which were d e t e c t e d  from the r a d i a t i v e break-up c h a n n e l s . p l a c e d a t 20 MeV  counted i n the  processes  i n the N a l c r y s t a l , but i t was  p o s s i b l e to e x t r a c t these neutrons from a l l the o t h e r neutron  was  were not  not  yields  Also, a discriminator threshold  to reduce the n o i s e and  the low-energy background  ADC. 3  In order to get the a b s o l u t e s t o p p i n g r a t e i n the  He content  of  the t a r g e t , complete range c a l c u l a t i o n s would have to be done, u s i n g approximate knowledge o f the momentum d i s p e r s i o n of the beam and t h i c k n e s s e s of the degrader m a t e r i a l s . and not computed a c c u r a t e l y , we  had  But as t h i s was  only  to r e l y on the s c a l e r  the  the  estimated  information  (see s e c t i o n 3.4). I t turned out t h a t t h i s was l i a b i l i t y of the " s t o p " s i g n a l . stopping  a l s o i m p o s s i b l e because of the u n r e -  Although  most of the beam p a r t i c l e s  i n the t a r g e t a r e a c t u a l l y p i o n s , many of them, and  number of muons and  e l e c t r o n s , a r e s c a t t e r e d by the t a r g e t m a t e r i a l and  do not f i r e the v e t o counter  C4  ( l e s s than 4ir c o v e r a g e ) .  c a l c u l a t i o n s i m p o s s i b l e i s the important when the t a r g e t i s empty r a t e normalized  also a large  What makes the  d i f f e r e n c e i n the s c a t t e r i n g  compared to when i t i s f u l l .  For a  stop  to the number of beam p a r t i c l e s from the t a r g e t empty r u n  86  to any of the He J  r u n s , the number o b t a i n e d , f o r example, i n the e l a s t i c  r a d i a t i v e c a p t u r e channel y i e l d s an a b s o l u t e b r a n c h i n g r a t i o of with a r e l a t i v e l y small d i s p e r s i o n  2.21%  (not u n c e r t a i n t y ) of ± 0.14%.  This  means t h a t the s c a l e r s concerned a r e s e l f - c o n s i s t e n t but t h a t t h e i r  abso-  l u t e i n f o r m a t i o n i s not v a l i d . -3  3  I f we assume however t h a t the b r a n c h i n g r a t i o f o r the TT He ->  Hy  r e a c t i o n i s of the o r d e r o f the v a l u e measured by Zaimidoroga et a l . (6.9±0.5%) [O.A.  Zaimidoroga et a l . ,  1965]  or. by Trub'l e t a l . (6.6±0.8%) 9 _  [P. T r u o l e t a l . , 1974], t h i s p r o v i d e s a rough e s t i m a t e o f 1.1  x 10  TT  3 stops i n §5.2  He f o r the f i v e runs p r e s e n t e d i n t h i s work. Delayed  I t was  Events  suggested to our group t h a t the p o s s i b i l i t y of d e l a y e d  events i n the TT a b s o r p t i o n should be c o n s i d e r e d [R.M.  Pearce,  1977].  These would be caused by the t r a p p i n g o f a few p e r c e n t of the n e g a t i v e p a r t i c l e s i n a slow cascade c h a n n e l of a h i g h quantum number atomic state  ( n , l ) i n such a way  conds l a t e r .  t h a t the a b s o r p t i o n would occur a few nanose-  Indeed, t h i s c o u l d be a s i g n i f i c a n t c o r r e c t i o n t o the abso-  l u t e r a t e s , but i t does not a f f e c t the Panofsky r a t i o , P^ o r the r a d i a tive ratio,  B^.  The problem i n u s i n g p i o n s i n t h i s experiment ( i n the mesic X-rays experiment)  i n s t e a d of muons  i s the i m p o s s i b i l i t y o f s e l e c t i n g o n l y  c i r c u l a r o r b i t s f o r which the d e l a y i s expected to be l a r g e and a l s o  the  l i f e - t i m e of the TT (26 nsec) , which i s of the same o r d e r as the k i n d of delay  sought.  87  To make sure t h a t no neutrons would e n t e r t h e d a t a , a c u t was a p p l i e d over t h e energy  range o f 130-140 MeV and t h e t i m e - o f - f l i g h t  trum was s t u d i e d f o r p o s s i b l e delayed e v e n t s . observed  spec-  No s p e c i a l s t r u c t u r e was  a f t e r t h e time o f a r r i v a l o f photons ( d e f i n e d as t h e time z e r o ) .  There was a s m a l l i n c r e a s e from t h e random events b e f o r e and a f t e r t h e zero time b u t i t c o u l d not be a t t r i b u t e d t o aby d e l a y e d events beyond t h e 1.5%  level.  The main r e a s o n i s t h a t t h e same k i n d o f d a t a taken w i t h b a -  s i c a l l y t h e same equipment was a v a i l a b l e f o r hydrogen, i n which case no d e l a y e d events a r e p o s s i b l e , and a time t a i l was s t i l l n o t i c e a b l e , v e r y l i k e l y due t o t h e e l e c t r o n i c response  o f t h e equipment.  The s e a r c h f o r  d e l a y e d events w i t h p i o n s was t h e r e f o r e i n c o n c l u s i v e .  §5.3  The F u t u r e o f t h e Panofsky  Ratio  A summary o f e x p e r i m e n t a l and t h e o r e t i c a l r e s u l t s f o r t h e Panofsky r a t i o , P^ and the r a d i a t i v e r a t i o , in figure section  (5.3).  i s g i v e n i n t a b l e XV and p i c t u r e d  F o r a b r i e f d i s c u s s i o n , the r e a d e r i s r e f e r e d t o t h e  (1.2.2) o f t h e i n t r o d u c t i o n .  88 Figure  (5.3)  V a l u e s of the Panofsky r a t i o i n helium-3  E2  I  •  1  El  T4  o Tl  169]'  o  o  (5.3)  T a b l e XV  Tl  2.2  2.0  1.8  Figure  2*  2.4  [67]  3.2  3.0  2.8  2.6  V a l u e s of t h e Panofsky r a t i o i n helium-3  Summary of e x p e r i m e n t a l ( E ) and t h e o r e t i c a l ( T )  E,T  Group  El  Zaimidoroga  ratios  Technique D i f f u s i o n chamber  2.28±0.18  E2  et a l . [1965] T r u O l et a l . [ 1 9 7 4 ]  Pair  2.68+0.13  1.12±0.05  E3  T h i s work  Nal  2.83±0.07  1.35±0.11  Tl  E r i c s o n et F i g u r e a u [1967] [1969]  PCAC h y p o t h e s i s no p-exch. c o r r e c t i o n  T2  T r u o l et al.[1974]  Impulse a p p r o x i m a t i o n  T3  P h i l l i p s and Roig [1974]  T4  M i z t u t a et a l . [1975]  [1977]  spectrometer spectrometer  IA f o r P„ Amado f o r B„ IA  I II III  2.70 1.9, 2.1 "2.49" 2.51 2.79 2.98 2.63-3.06  0.84±0.08 1.10±0.08 1.27±0.08  89  While t h i s new derably  measurement of the Panofsky r a t i o i s a g a i n c o n s i -  l a r g e r than the v a l u e o f Zaimidoroga et a l . , i t i s a l s o  l a r g e r than the v a l u e of T r u O l et a l . .  A clear increase  from t h e i r s u r p r i s i n g l y good r a t i o B^.  The  slightly  i s a l s o observed  agreement of the two  numbers  o b t a i n e d the 3-nucleon wave f u n c t i o n s w i t h non-zero S' and  D state proba-  b i l i t i e s i s excellent.  of the pnny  Naively,  i t seems t h a t an i n c r e a s e  c o n t r i b u t i o n to the t o t a l break-up c h a n n e l s would h e l p low-energy disagreement and Experimentally,  two  b r i n g up  to e x p l a i n  s l i g h t l y the comparative r a t i o  straightforward  modifications  to the  would, w i t h the same b a s i c a p p a r a t u s , improve our r e s u l t s . minimize the a c c i d e n t a l d e t e c t i o n of the the N a l d e t e c t o r should be put  should be  increased,  but  "T2  s i g n i f i c a n t l y i n c r e a s i n g the r e a l event r a t e .  l u a t i o n of the s t o p p i n g rates.  set-up  In order  even more important the  equipment would be to have a t h i c k s t o p p i n g  B^.  to  n e u t r o n s " , the s h i e l d i n g of  c l o s e r to the t a r g e t , keeping a good TOF  s c a t t e r i n g t a r g e t , to i n c r e a s e  the  The  separation,  detector thus  obvious change i n  the  target instead of a t h i n  the count r a t e and  allow a precise  r a t e i n o r d e r t o o b t a i n the a b s o l u t e  eva-  absorption  90  BIBLIOGRAPHY  H.L. Anderson and E. Fermi, Phys. Rev. 86,  794,(1952).  H.W. Baer, J.A. B i s t i r l i c h , K.M. Crowe, N. deBotton, J.A. Helland, and P. Truol, Phys. Rev. C i8, 2029 (1973). ar.  H.W. Baer, K.M. Crowe, and P. Truol, in Advances in Nuclear Physics, vol. 9 edited by M. Baranger and E. Vogt, Plenum Press^(1977). P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences McGraw-Hill (1969). J.A. B i s t i r l i c h , K.M. Crowe, A.S.L. Parsons, P. Skarek, P. Truol, and C. Werntz, Phys.. Rev. Lett. 25_, 689 (1970). J.A. B i s t i r l i c h , K.M. Crowe, A.S.L. Parsons, P. Skarek, P and P. Truol, Phys. Rev. C 5_j 1867 (1972).  i r u.  V.T. Cocconi, T. Fazzini, G. Fidecaro, M. Legros, N.H. Lipman, and A.W. Merrison, Nuovo Cimento 22^, 494 (1961). F. Corriveau, M.D. -Hasinoff, D.F. Measday, M. Salomon, J-M Poutissou, and J.E. Spuller, to be published. L.G. Dakhno and Yu.D. Prokoshkin, Sov. J. of Nucl. Phys. ]_,• 351 M.. Ericson and A. Figureau, Nucl. Phys. 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