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The efficiency of scintillation counters for gamma ray detection Leigh, John Laurence 1964

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THE EFFICIENCY OF SCINTILLATION COUNTERS FOR GAMMA. RAY DETECTION  b7  JOHN LAURENCE LEIGH B . S c . , U n i v e r s i t y o f B r i t i s h Columbia, 1962  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We accept t h i s t h e s i s as conforming t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October., 1964  In the  r e q u i r e m e n t s f o r an  British  mission  for reference  for extensive  p u r p o s e s may  be  cation  of  written  Department  of  and  by  for  the  study,  the  the  Library  I further  Head o f my  Testes Columbia,  University  agree for  that  of  of  or  c o p y i n g or  s h a l l not  per-  scholarly  Department  that  f i n a n c i a l gain  fulfilment  s h a l l make i t f r e e l y  this thesis  permission*  The U n i v e r s i t y of B r i t i s h V a n c o u v e r 8, Canada Date  degree at  I t i s understood  this thesis  w i t h o u t my  that  copying of  granted  representatives.  this thesis i n partial  advanced  Columbia, I agree  available  his  presenting  be  by publi-  allowed  ii  ABSTRACT  The e f f i c i e n c y of N a l ( T l ) s c i n t i l l a t i o n counters f o r the detection of gamma rays i s discussed and experimentally determined,, Experimental e f f i c i e n c i e s , based upon the number o f counts above a b i a s equal t o one-half the gamma ray energy and a s o l i d angle defined t o the c r y s t a l e f f e c t i v e centre, f o r a three-inch-diameter by t h r e e - i n c h long (3 x 3) c r y s t a l are given for gamma ray energies of 0.51, 1»275 and 6 3J+ MeV. B  Gamma ray spectra at 1 275 and 6„14 MeV are extrapolated t o zero energy B  i n order t o compare t h e o r e t i c a l e f f i c i e n c i e s , based upon the integrated primary absorption, w i t h the experimental results,,  These r e s u l t s show t h a t , w i t h  experience, one can expect accuracy t o b e t t e r than 5$ at these energies. Tables are given of the t h e o r e t i c a l e f f i c i e n c y f o r 3 x 3 , 2% x Ui» and 5 x 4 c r y s t a l s f o r s e v e r a l gamma ray energies and source-to-counter distances of from 0<,1 cm t o 1 m  0  viii  ACKNOWLEDGMENTS  I wish t o express my g r a t i t u d e t o Dr. G. M. G r i f f i t h s for h i s superv i s i o n o f the work which comprises t h i s t h e s i s  0  I am also indebted t o D r ,  J . B. Warren, D r . G. Jones and D r . B . L . White for many h e l p f u l suggestions and d i s c u s s i o n s . In p a r t i c u l a r I acknowledge the help o f my fellow graduate students of the Nuclear Physics Group - notably Mr. J . MacDonald, Mr, W. Falk, Mr. L . Monier and Mr. M. Relmann. To my mother and father, and t o my w i f e , I owe sincere thanks f o r much patience and encouragement throughout my years o f study.  iii  TABLE OF CONTENTS page Chapter I  - INTRODUCTION . . . .  Chapter I I  - EMPIRICAL DEFINITION OF SCINTILLATION COUNTER EFFICIENCY  0  0  . . . . . . .  0  0  0  0  0  0  0  0  . . . . . . . .  0  0  0  0  0  0  0  0  0  A.  The E m p i r i c a l E f f i c i e n c y D e f i n i t i o n . . . . . . . . . . .  B„  Experimental Measurement of the H a l f Energy Bias  .  1  0  6 6  .  7  1.  The S c i n t i l l a t i o n Counter . . . . . . . . . . . . . .  7  2.  The E f f i c i e n c y at 0.511 and 1.28 MeV . . . . . . . .  9  3.  The E f f i c  4.  The R a t i o of E f f i c i e n c i e s  5.  Summary of 3 x 3 C r y s t a l H a l f Energy B i a s  Ef f xc iency  .  .  .  0  0  E f f i c iency R6S*ul"bs  .  0  0  0  9  0  .  .  .  at 4.43 and 11,68  0  0  0  0  0  0  0  0  0  .  .  .  .  MeV . . .  19  0  21  0  0  0  0  22  Chapter I I I - THEORETICAL EFFICIENCIES . . . . . . . . . . . . . . A.  Theoretical Efficiency  B.  Experimental Studies of the T h e o r e t i c a l E f f i c i e n c y  . . .  23  1.  Theoretical Efficiencies  at 6.14 MeV . . . . . . . .  24  2.  Theoretical Efficiencies  at 1.28 MeV . . . . . . . .  30  3.  R a t i o of T h e o r e t i c a l E f f i c i e n c i e s Ho  C.  22  . . . . . . . . . . . . . . . . .  6S  M©V  0  0  0  0  0  0  0  0  0  0  0  at 4.43 and 0  0  0  0  E f f e c t i v e Centres from T h e o r e t i c a l E f f i c i e n c y Csilcizlcit ions 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  Chapter IV  0  0  0  0  0  0  32  . . . . . . 0  32  . . . . .  34  at 6.14 MeV . . . . . . . . . . . . . .  34  0  - STUDIES OF A Z% x k\ INCH N a l ( T l ) CRYSTAL  A.  The E f f i c i e n c i e s  B.  The Ratio of the E f f i c i e n c i e s  at 4.43 and 11.68  *  0  0  0  MeV . . .  Appendix A - REPRESENTATIVE SPECTRA FOR THE 3 x 3 CRYSTAL  . . . .  35 35  iv  page Appendix B - THEORETICAL EFFICIENCY OF N a l CRYSTALS .  38  A.  D e r i v a t i o n of the E f f i c i e n c y Equation  B.  Numerical I n t e g r a t i o n of the E f f i c i e n c y I n t e g r a l . . . . .  C.  Tables of T h e o r e t i c a l E f f i c i e n c i e s . . .  D»  The Computer Program  Bibliography  . . . . . . . . . .  . . . .  . . . . . . . . . . . . . . . . . .  0 0 . . . . . . . o . . . . . . . . . . . . . . . .  38 40 41 45 47  V  LIST OF TABLES page I  M a t e r i a l Between C r y s t a l Face and Container Face . o * e . . .  8  II  Resolution o f the S c i n t i l l a t i o n Detector  9  III  Properties of the Alpha Detector  IV  Alpha Detector P r e a n p l i f i e r Performance  V  Alpha Counter S o l i d Angle  VI  H a l f Energy Bias E f f i c i e n c y at 6.14 MeV . . o  VII  Half Energy B i a s E f f i c i e n c i e s - 3 x 3 C r y s t a l  VIII  T h e o r e t i c a l E f f i c i e n c y Extrapolations  IX  Photofraction  X  Comparison of A n a l y t i c and Experimental C ent res  XI  E f f i c i e n c i e s at 6 14 MeV - 2 f x 4 i C r y s t a l . . . o . . . . . .  35  XII  C r y s t a l , C o l l i m a t o r and Absorber Path Lengths  . . . . . . . .  40  XIII  Theoretical Efficiencies - 3 x 3 Crystal . . . . . . . . . . .  42  XIV  T h e o r e t i c a l E f f i c i e n c i e s - 2^ x kh Inch C r y s t a l  . . . . . . .  43  XV  Theoretical Efficiencies - 5 x 4 Crystal . . . . . . . . . . .  44  . . . . . . . . . .  . o o o o . o . . . . . . . . . . . . . . . . . .  . » . « o »  • . • .  14 15 16 18  . . . . . . . .  21  at 6.14 MeV . . . . . .  29  at 1.275 MeV . . . . . . . . . . a .  . . . . . .  31  Effective  0  vi  LIST OF FIGURES t o follow page 1.  S c i n t i l l a t i o n Counter Preamplifier , • .  8  2.  Caesium-137 Gamma Spectrum • , . , , . , » . . , . . . .  8  3.  Resolution Function of the 3-Inch-Diameter by 3-inchLong Nal(Tl) Sointillation Counter * * . » » . . »* . .  9  4.  Cobalt-60 Decay Scheme . * » • • « « • • » • * « « •  in text p.10  5.  Sodium-22 Decay Scheme . . , , . . . . . . • . , . *  In text p»12  6.  F^(pf°(  7.  Fluorine-19 Target Chamber . , . , . . » , . , . . , , .  14  8.  S o l i d State Detector Preamplifier  15  9.  5.3 MeV P o  » y  . . , . • • • « , . « , « « « , « ,  2 1 0  i n te:xt p»13  . . . . . . . . . . .  Alpha P a r t i c l e Spectrum  . . . . . . . . .  15  . , » , , , . , , . , , . , . . .  15  10*  Alpha P a r t i c l e Window  11.  F^(p,o<,  12.  1.85 MeV Alpha Spectrum  13.  6.14 MeV Gamma Ray Spectrum  l4»  "AAtt vs d - 6,14 MeV  )0"^ E x c i t a t i o n Function  .  16 16  . . . . . . . . . . . . . .  17 18  VN — 6  15.  Alpha Detector Background  16.  Gamma Ray Spectrum from B ^ p , i r ) C  17.  B ^ ( p , 2T ) C  18.  H a l f Energy B i a s E f f i c i e n c i e s ( 3 x 3 )  19.  Comparison o f 6 MeV Monte Carlo Spectrum and 6.I4 MeV Experimental Spectrum . . . . . . . . . . . . . . . . .  25  20.  T h e o r e t i c a l E f f i c i e n c y Extrapolations  26  21.  Zero Intercept Parameter  22.  Effect o f Lead S h i e l d i n g on Cobalt-60 Spectrum . . . . .  29  23.  Effect o f Lead S h i e l d i n g on the 6 . I 4 MeV Spectrum  29  1 2  . . . . . . . . . . . . . . . l 2  - Ep - 300 k e v . . *  . . . . . . . . . . . . . . . . . . .  JsJb  ^  18 . 1 9  i n text p . 19  . . . . . . » # .  at 6*14 MeV . . .  «.  21  28  » . *  vii  t o follow page 24.  Comparison of 1.275 MeV Monte Carlo Spectrum and Experimental Spectrum . . . . . . . . . . . . . . . . . .  30  25.  Inverse Square P l o t o f T h e o r e t i c a l E f f i c i e n c i e s (3 x 3) •  32  26.  T h e o r e t i c a l E f f i c i e n c y E x t r a p o l a t i o n at 6.14 MeV for the 2$ x 4^ Inch C r y s t a l  . . . . . .  34  . . . . . . . . . . .  37  . « . . « . . .  27.  Caesium—137 Gramma Ray . . . . . . .  28o  Sodium—22 Gamma Rays  . . . . . . . . . . . . . . . . . .  37  29.  Cobalt-60 Gamma Rays  . . . . . . . . . . . . . . . . . .  37  30.  Radio Thorium Gamma Rays  31.  B -(p, 2 T ) C , Ep = 300 kev, Gamma Rays  32.  P ^ p , * * , f)0 ^,  33.  . . . . . . . . . . . . . . . .  37  . . . . . . . . .  37  Ep = 340 kev, Gamma Rays . . . . . . . .  37  Geometry of C r y s t a l , C o l l i m a t o r , and Absorber for theoretical Efficiency Calculations . . . . . . . . . . .  38  1:i  12  1  CHAPTER I INTRODUCTION A l a r g e part of the work o f the U n i v e r s i t y of B r i t i s h Columbia Van de Graaff group has been concerned w i t h measuring the gamma rays produced by capture reactions and the inverse of t h i s , p h o t o d i s i n t e g r a t i o n .  To obtain q u a n t i t a t i v e  data on both processes i t i s necessary t o measure gamma ray f l u x e s .  More than  60 years a f t e r the discovery of gamma rays t h i s i s s t i l l a d i f f i c u l t t h i n g t o do w i t h high accuracy over much o f the energy range of nuclear gamma r a y s . The discovery of gamma rays can be a t t r i b u t e d t o V i l l a r d who, i n 1900, drew a t t e n t i o n t o the fact that radium gave out very penetrating r a d i a t i o n s which were detectable photographically and were non-deviable by a magnetic f i e l d .  These  r e s u l t s were confirmed i n the same year by Becquerel and again very c l e a r l y demonstrated i n 1903 by Mme. Curie i n a c l a s s i c experiment reported i n her t h e s i s t o the Faculty o f Science, P a r i s .  Rutherford studied the absorption of these  r a d i a t i o n s i n s e v e r a l materials by observing the i o n i z a t i o n produced i n a i r w i t h an electroscope.  Although given the name gamma rays, the nature of these  penetrating r a d i a t i o n s was i n doubt i n 1904 when Rutherford*s book " R a d i o - A c t i v i t y " was p u b l i s h e d .  Some favoured the hypothesis that they were Roentgen-like ether  waves w h i l e others b e l i e v e d them t o be cathode rays moving at a v e l o c i t y close t o t h a t of l i g h t .  Many subsequent experiments delineated the exponential absorption  of gamma rays i n d i s t i n c t i o n t o the d e f i n i t e range for alpha and beta rays i n matter.  With i n c r e a s i n g refinement, p a r t i c u l a r l y a f t e r the development o f the  Wilson cloud chamber, these experiments showed that gamma rays d i d not l o s e energy continuously i n t h e i r passage through matter but only when they transferred t h e i r energy t o e l e c t r o n s , e i t h e r by the p h o t o e l e c t r i c e f f e c t , when a l l the energy i s t r a n s f e r r e d , or by a s c a t t e r i n g process where only part o f the energy i s transferred.  Both processes at f i r s t suggested the p a r t i c u l a t e nature of the  -2-  gamma r a y s .  However, l a t e r more d e t a i l e d studies of the s c a t t e r i n g showed a  c l e a r analogy between gamma ray  s c a t t e r i n g and the Compton s c a t t e r i n g o f X - r a y s .  The l a t t e r were known t o be electromagnetic waves because of t h e i r interference and p o l a r i z a t i o n c h a r a c t e r i s t i c s .  The study of these processes helped t o  e l u c i d a t e the d u a l i t y of quantum and w a v e - l i k e properties o f electromagnetic r a d i a t i o n which were incorporated i n t o quantum mechanics a f t e r 1926. With the development o f quantum mechanics and the Dirac r e l a t i v i s t i c e l e c t r o n equation i t was p o s s i b l e t o describe i n very s a t i s f a c t o r y d e t a i l the angular p r o p e r t i e s , the energetics and the p r o b a b i l i t y of Compton s c a t t e r i n g by means o f the K l e i n N i s h i n a formula.  In a d d i t i o n the p h o t o e l e c t r i c absorption was w e l l understood  i n p r i n c i p l e , although accurate q u a n t i t a t i v e estimates o f the cross s e c t i o n required a more d e t a i l e d d e s c r i p t i o n of the bound atomic electrons than was a v a i l a b l e at the t i m e .  The t h i r d main process by which gamma rays i n t e r a c t w i t h  matter, namely the production of p o s i t r o n - e l e c t r o n p a i r s i n the f i e l d o f the nucleus was not discovered u n t i l a f t e r D i r a c s p r e d i c t i o n o f negative energy ?  electrons (p o sitrons ) and t h e i r discovery by Anderson i n 1932. In s p i t e o f d e t a i l e d experimental confirmation of the accuracy of a very complete theory f o r the main primary absorption processes f o r gamma rays i n matter over a wide range of energies (Davisson and Evans, 195?) the problem of determining gamma r a y . fluxes accurately has remained a vexed one f o r s e v e r a l reasons.  By whatever method detected, gamma rays are not observed d i r e c t l y but  only through the secondary electrons they eject from matter.  Each of the three  primary absorption processes produces a d i f f e r e n t primary e l e c t r o n spectrum. The r e s u l t i n g t o t a l spectrum i s i n general complex and d i f f i c u l t t o i n t e r p r e t quantitatively.  Further, the shape of the electron spectrum, the angular  d i s t r i b u t i o n of the electrons and the cross s e c t i o n are a l l continuous functions of the gamma ray energy.  Because of the range of the electrons i n matter and  -3-  subsequent absorption or escape o f scattered quanta the spectrum a c t u a l l y observed i s not the primary spectrum but one modified by secondary processes*  This i s  p a r t i c u l a r l y complicated for high energies where the electrons l o s e energy not only by i o n i z a t i o n but a l s o by the  emission of bremsstrahlung r a d i a t i o n  r e s u l t i n g i n a continuous secondary photon spectrum. The e a r l i e s t attempts t o obtain.other than r e l a t i v e i n t e n s i t i e s  of the  gamma rays emitted by r a d i o a c t i v e sources were c a l o r i m e t r i c ( E l l i s and Wooster, 1925).  The t o t a l energy due t o f  -rays was measured i n a d i f f e r e n t i a l c a l o r i -  meter and compared w i t h the t o t a l energy due t o  and p - r a y s .  These measure-  ments gave no information about the energy spectrum or the number of photons. A f t e r the r e c o g n i t i o n that gamma rays followed p a r t i c l e emission s e v e r a l attempts were p a r t l y successful i n obtaining absolute gamma ray fluxes by c o r r e l a t i n g them w i t h the number of p a r t i c l e s observed.  Other early experiments involved the  magnetic a n a l y s i s of photoelectrons ejected from r a d i a t o r s exposed t o the gamma rays using photographic d e t e c t i o n of the electrons and l a t e r d e t e c t i o n by means of geiger counters.  These d i d give some information about the energy spectrum  and i n t e n s i t y o f the gamma rays, t h i s information becoming more accurate as p h o t o e l e c t r i c cross sections became b e t t e r determined.  The e a r l i e r work determined  gamma ray energies by f i n d i n g the absorption c o e f f i c i e n t of the r a d i a t i o n or by measuring the energy of the secondary electrons i n a cloud chamber placed i n a magnetic f i e l d .  L a t e r work up t o 1948 tended t o concentrate on (3 - r a y  spectrometers for measuring the energy of the secondary electrons or on measuring absorption curves o f the secondary electrons w i t h t h i n window geiger counters.  The absolute y i e l d o f the  X~ -rays could be measured e i t h e r w i t h a  t h i c k w a l l e d i o n chamber (Gray, 1936) or w i t h a t h i c k w a l l e d geiger counter (Bradtet a l , 1946; B l e u l e r and Z u n t i , 1946).  Both methods depended on a knowledge  -4-  o f the range of a l l the secondary electrons i n the w a l l s of the chambers.  They  were not very u s e f u l for complex spectra as they gave no information on the energy of the gamma rays producing the i o n i z a t i o n .  A useful summary o f t h i s p r e -  s c i n t i l l a t i o n counter work i s given by Fowler, L a u r i t s e n and L a u r i t s e n (1948). The advent of the s c i n t i l l a t i o n counter produced a great advance i n the technique of measuring energies, i n t e n s i t i e s , and l i f e t i m e s of gamma ray transitions.  This detector received i t s i n i t i a l impetus from the work o f  Kallman (1947) who discovered that naphthalene was transparent t o l i g h t generated i n i t by fast moving charged p a r t i c l e s , and that the l i g h t could be detected and a m p l i f i e d many times using p h o t o m u l t i p l i e r tubes developed for t e l e v i s i o n . Following t h i s , organic phosphors such as anthracene,  s t i l b e n e , and s e v e r a l  p l a s t i c s and l i q u i d s were developed w i t h large volumes capable of very short time r e s o l u t i o n .  S e v e r a l attempts were made t o develop inorganic phosphors  w i t h components of higher atomic number f o r greater gamma ray absorption which were transparent t o t h e i r own fluorescent r a d i a t i o n . introduced sodium i o d i d e w i t h a t h a l l i u m a c t i v a t o r .  In 1948 Hofstadter Although t h i s has a slower  decay time than the organic phosphors i t has a large l i g h t output and a large gamma ray absorption and has become the standard detector used i n p r a c t i c a l l y a l l gamma ray work s i n c e , except for that r e q u i r i n g very high energy r e s o l u t i o n . As a r e s u l t i t i s important t o have accurate information on the gamma ray d e t e c t i o n e f f i c i e n c y of sodium iodide s c i n t i l l a t i o n counters. A great d e a l o f work has been done i n t h i s and other l a b o r a t o r i e s t o e s t a b l i s h the e f f i c i e n c y of s c i n t i l l a t i o n counters for gamma r a y s .  Accurate  absprption c o e f f i c i e n t s have been tabulated as a function of energy (Grodstein, 1957).  A method s u i t a b l e for machine c a l c u l a t i o n has been developed for  i n t e g r a t i n g the primary absorption over the c r y s t a l geometry (Rose, 1953) and s e v e r a l Monte Carlo type c a l c u l a t i o n s have been performed t o t r y and p r e d i c t  -5-  the spectrum shape t o be expected as a function o f gamma ray energy and c r y s t a l s i z e ( M i l l e r and Snow, I960; Zerby and Moran, 196l).  However, p a r t i c u l a r l y f o r  higher energy gamma rays i t remains d i f f i c u l t t o check the accuracy o f these calculations. The present work involves the measurements o f s c i n t i l l a t i o n counter e f f i c i e n c y ; f i r s t l y according t o an a r b i t r a r y d e f i n i t i o n o f e f f i c i e n c y and secondly according t o the integrated primary absorption i n the c r y s t a l .  -6-  CHAPTER I I EMPIRICAL DEFINITION OF SCINTILLATION COUNTER EFFICIENCY A.  THE EMPIRICAL EFFICIENCY DEFINITION Inspection of gamma ray spectra from sodium iodide ( t h a l l i u m activated)  c r y s t a l s shows one that i t i s i m p r a c t i c a l t o count a l l the pulses i n the spectrum.  In the low energy r e g i o n , room background and s c a t t e r i n g from s h i e l d s  and other equipment tends t o d i s t o r t the spectrum.  Also i t i s often necessary  t o eliminate the lower energy pulses i n order t o reduce e l e c t r o n i c dead time losses.  Therefore i t i s best t o count only those pulses which appear above a  convenient b i a s p o i n t .  For most a p p l i c a t i o n s i t has been found that a bias of  one h a l f the gamma ray energy i s convenient.  The spectra are g e n e r a l l y low and  f l a t i n t h i s region and small gain s h i f t s i n the e l e c t r o n i c system w i l l have l i t t l e effect upon the r e s u l t s obtained.  Also f o r energies at which p a i r  production i s s i g n i f i c a n t the p a i r peaks are w e l l above t h i s b i a s .  Thus an  e m p i r i c a l d e f i n i t i o n of e f f i c i e n c y i s conveniently based upon the h a l f energy bias. I f one measures source-to-counter distances t o a point w i t h i n the c r y s t a l , c a l l e d the e f f e c t i v e centre, i t i s found that the count rate v a r i e s as the inverse square of the d i s t a n c e .  One can then define a h a l f energy b i a s  efficiency,  , that i s distance independent provided any r e s i d u a l distance dependence i s included i n the e f f e c t i v e centre p o s i t i o n .  The number o f counts expected above  the h a l f energy b i a s , N , f o r a source-to-counter face distance d i s then c  N wheres  . •, jf  W  A (d + e )  - N  !±l*  i s the s o l i d angle defined t o the e f f e c t i v e centre, 2  -7-  A i s the cross s e c t i o n a l area of the c r y s t a l , and N^is the number of gamma rays emitted i n t o the sphere. It i s assumed that for d greater than the c r y s t a l length the e f f e c t i v e centre, e, i s distance independent.  I t should be emphasized that the above  d e f i n i t i o n i s s t r i c t l y e m p i r i c a l and i s dependent upon the source-counter geometry and s h i e l d i n g . Algebraic manipulation o f the preceeding equation leads t o the following expression;  This r e s u l t i s very convenient for experimental i n v e s t i g a t i o n f o r i t represents and source-to-counter face distance d intercept - e .  An experimentally determined p l o t of d vs ~\ / —  enables one t o  V No  c a l c u l a t e the h a l f energy b i a s e f f i c i e n c y and the e f f e c t i v e centre distance,  B.  EXPERIMENTAL MEASUREMENT OF THE HALF ENERGY BIAS EFFICIENCY 1,  The S c i n t i l l a t i o n Counter  The gamma ray detector employed was a standard three-inch-diameter by t h r e e i n c h - long ( 3 x 3 ) c y l i n d e r of N a l ( T l ) mounted on a selected Dumont 6363 photomultiplier.  The u n i t , Harshaw 12S12/E, obtained from the Harshaw Chemical  Company incorporates an e x t e r n a l magnetic s h i e l d . inches back from the container face. t h i s distance.  The c r y s t a l i s mounted 0.1375  Table I l i s t s the m a t e r i a l which makes up  -8-  TABLE I MATERIAL BETWEEN CRYSTAL FACE AND CONTAINER FACE  ' MATERIAL  DENSITY  THICKNESS  Packed aluminum oxide  67 mg/cm  2  Polyethylene d i s c  13 mg/cm  2  .006"  Neoprene sponge rubber  43 mg/cm  2  .050"  Aluminum container  129.9 mg/cm  .0625 "  2  .019"  The assembly i s coupled t o a t r a n s i s t o r i z e d head a m p l i f i e r the c i r c u i t diagram of which i s reproduced i n Figure 1„ The Harshaw Chemical Company has guaranteed a r e s o l u t i o n of 8% or b e t t e r for the 0.661 MeV gamma ray of caesium-137 for t h i s crystal-phototube  combination,,  Subsequent measurement has confirmed t h i s w i t h a r e s u l t of 8„01 i 0.24$.  (See  Figure 2) The r e s o l u t i o n over the energy range 0,511 MeV t o 6,14 MeV has been measured and the r e s u l t s are included as Table I I below. of r e s o l u t i o n  AE^Ey  where E  r  Figure 3 shows a p l o t  i s the gamma ray energy i n MeV, Also included  for comparison i s the r e s o l u t i o n function for a 3 X 3 c r y s t a l w i t h 7.8$ r e s o l u t i o n at 0,661 MeV taken from Yuan and Wu (1963), page 636.  Dumonl  6363  FIGURE 1  Scintillation  Counter P r e a m p l i f i e r  7E=> +  :4f  100 r* 100 ft  S-20pf  0C i c Q  8-^ Volts  A 100 K  6  8  X Out  100 Ft H  < /OOJl  220K< 100 M  T .£  2.N 38tj-"'-''''  2.N38*  + MOO. Volts QUI  /zooo  OOIy*f  FIGURE 2  MeV  137 Cs Gamma Spectrum  /GOOD 14-000 IZ0O0 •P IOOOO c  3 o  o- 18 5 (v-|eV  <  8-0/ %  O 8000  cooo 4ooo  2000 10  2.0  30  C h a n n e l Number  ¥0  50  (oO  -9-  TABLE I I RESOLUTION OF THE SCINTILLATION DETECTOR RESOLUTION GAMMA ENERGY FOR 3 X 3 CRYSTAL * 0.3  FROM YUAN AND WU  %  8.7%  0.511 MeV  8.9  0.661  8,01 ± 0.24  7.8  1.27  6.18 * 0.17  6.2  1.33  6.08 * 0.14  6.1  2.62  4.94 * 0.12  4.9  6.14  3.86 t o . l 6  The h a l f energy b i a s e f f i c i e n c y f o r t h i s c r y s t a l has been measured at 0.511, 1.28, and 6.14 MeV.  In a d d i t i o n an attempt t o measure the r a t i o of the  e f f i c i e n c y at 4.43 MeV t o that at 11.68 MeV has been made. 2.  The E f f i c i e n c y at 0.511 and 1.28 MeV  Cobalt-60 decays by (1~ emission t o the 2.505 MeV e x c i t e d s t a t e o f n i c k e l - 6 0 which subsequently decays t o the ground s t a t e by gamma ray cascade through the 1.332 MeV l e v e l (Nuclear Data Tables, I960 - see Figure 4 ) .  The two Cobalt-60  gamma rays w i t h energies of 1.332 and 1.173 MeV are i s o t r o p i c a l l y d i s t r i b u t e d .  1  I . I  I I  1  I  1  i  i  i  i  i  i  i  i  10  -  8  ^>  ^>  4  f r o m Yuan a n d Wu UBC  crystal  2 -  E n e r e v (MeV) i  0 0  i  •2  i  i i i 6-0 4 0 i i  4  i  i  i  20 i  •6  i  i -8  i  i 1-0  (Gamma Ray E n e r g y ) FIGURE 3  i i  i  t  1-2  i  14  i  i  1-6  (MeV)~^  R e s o l u t i o n F u n c t i o n o f the 3-Inch-Diameter by 3-Inch-Long N a l ( T l ) S c i n t i l l a t i o n Counter  -10-  FIGURE 4 COBALT-60 DECAY 2-505  SCHEME  I  1 Ni  1o 6 0  Singh (1959) has measured the f l u x o f gamma rays emitted by a cobalt-60 source (Co-60 #1) i n t h i s l a b o r a t o r y by a standard coincidence technique.  He  obtained a source strength value o f 0.0237 * 0.0006 m i l l i c u r i e s on A p r i l 22, 1958. By counting a l l pulses above the average h a l f energy b i a s i n the Co-60 #1 spectrum the detector e f f i c i e n c y at the average gamma ray energy 1.253 MeV was obtained.  A p l o t o f ~\ I^Ji vs d gave the e f f e c t i v e centre at t h i s same energy. VA/ The r e s u l t i s C  £^(1.25) = (  6 0  ' 5 5 * 1.61)$  e ( l . 2 5 ) = 3.50 ± 0.40 cm The e r r o r involved i s mainly due t o the o r i g i n a l uncertainty i n the source strength, w i t h a d d i t i o n a l small errors from the counting s t a t i s t i c s , distance measurement, and the a d d i t i o n a l uncertainty i n the source strength at the time of the present e f f i c i e n c y  measurements.  I f the o r i g i n a l source strength were I  Q  then, a f t e r a time t had elapsed,  the source strength would be I J I  0  exp(- t ln2)  H wheres  ti  i s the h a l f l i f e o f the n u c l i d e , i n t h i s case  -11-  5.27 ± 0.05 years (Nuclear Data Tables, I960), The uncertainty A I i n I i s given by  41 = I  A[exp(--L^2),  41 L /  [A LI Li  e x p ( - -j- J^Z)  2  \  t JUZ A t ' / *  where A t ^ i s the uncertainty i n the h a l f 2  (U Y Z  life.  The time t between the o r i g i n a l source strength measurement ( A p r i l 22, 1958) and the present e f f i c i e n c y measurements (August 3 , 1962) i s 4«28 y e a r s . P u t t i n g the numbers i n t o the above equation y i e l d s an uncertainty A i r 0.02591 f o r the source s t r e n g t h . The t o t a l e r r o r i n the e f f i c i e n c y measurement i s the root mean square o f the following errorss i. ii. iii.  Gamma ray source strength  2.59$  Counting s t a t i s t i c s  0.75  Distance measurements  0.90  Total  2,66$  The counting and distance errors quoted are for the worst case. In order t o determine the h a l f energy b i a s e f f i c i e n c y at 0.511 MeV i t was assumed that the s c i n t i l l a t i o n detector e f f i c i e n c y for the 1.275 MeV gamma ray from sodium-22 was equal t o that measured f o r 1.253 MeV using the c a l i b r a t e d cobalt-60 source. Sodium-22 decays t o the 1.275 MeV l e v e l i n neon-22 by the following scheme (Nuclear Data Tables, I960).  -12-  F3GURE 5  I N a 22 2  SODIUM-22 DECAY  •10 K Capture  1-275  SCHEME  o  Kreger (1954) has shown that 10$ o f the d i s i n t e g r a t i o n s t o the 1.275 MeV e x c i t e d s t a t e o f neon-22 take place by e l e c t r o n capture and 90$ by p o s i t r o n emission.  Thus, f o r a source enclosed i n a container one can expect, f o r every  1.275 MeV gamma ray, 1.8 0.511 MeV gamma rays due t o p o s i t r o n a n n i h i l a t i o n w i t h i n the source and the container w a l l s . By counting the number o f pulses above the 1.275 MeV h a l f energy b i a s , the known e f f i c i e n c y was used t o determine the f l u x o f 0.51 MeV gamma rays emanating from the sodium-22 source.  A p l o t o f -\ /tlr  vs d was then used t o determine  the e f f e c t i v e centre and the h a l f energy b i a s e f f i c i e n c y at 0.51 MeV.  The  r e s u l t s were2 £ , ( 0 . 5 1 ) = (75.1 ± 2.4)$ e ( 0 . 5 l ) = (2.96 i 0.50)cm In a d d i t i o n t o the e r r o r due t o the e f f i c i e n c y uncertainty at 1.28 MeV . t h e r e are a d d i t i o n a l errors introduced.  The largest i s that due t o u n c e r t a i n t i e s  introduced by the s u b t r a c t i o n o f the 1.28 MeV gamma ray t a i l from the 0.51 MeV spectrum.  Distance measurement contributes errors of 1% or l e s s .  e r r o r i s given by the root mean square of the f o l l o w i n g e r r o r s l  The t o t a l  -13-  i. ii. iii.  E r r o r i n 1.28 MeV e f f i c i e n c y S t a t i s t i c a l errors Measurement errors Total  2.66$ 1.5 $ 1.0 % 3.21$  The E f f i c i e n c y at 6.14 MeV  3.  The h a l f energy b i a s e f f i c i e n c y at 6.14 MeV was determined by s i m u l taneous counting o f the alpha p a r t i c l e s and gamma rays from the w e l l known reaction  F^(p «,TC)0t  at a proton bombarding energy of 340 k e v .  This method  has been used and reported p r e v i o u s l y (Van A l l e n and Smith, 1941} G r i f f i t h s , 1958;  G r i f f i t h s et a l , 1962). At 340 kev bombarding energy, protons are resonantly captured by f l u o r i n e - 1 9 ,  forming neon-20 i n a h i g h l y e x c i t e d s t a t e .  The neon-20 decays by alpha p a r t i c l e  emission t o any one of three states of oxygen-16 (See Figure 6 ) , i e  t o the  6.15 MeV l e v e l , o( t o the 6.91 MeV l e v e l , and eXj t o the 7.12 MeV l e v e l . z  FIGURE 6 F  1 9  (p,^,^)0  ,16  :  /32(3  Curt Nt Ground.  10  Stite)  -14-  Alpha groups ©<o t o the ground s t a t e and <*tt t o the p a i r emitting s t a t e at 6.06 MeV i n oxygen-16 are not seen at t h i s bombarding energy.  The 6 14» 6.91, 0  and 7»12 MeV l e v e l s of oxygen-16 subsequently decay by gamma ray emission t o the ground s t a t e (Ajzenberg-Selove and L a u r i t s e n , 1959)» ?t * y  The i n t e n s i t y r a t i o  - 0.024 (Freeman, 1950) i n good agreement w i t h the gamma ray r a t i o  » * *»  = 0.023  t  .002 (Dosso, 1957).  The work o f Devons and Hine (1949)  and Chao (1950) has shown that the gamma rays and alpha p a r t i c l e s are  separately  i s o t r o p i c at the 340 kev resonance. The t a r g e t chamber as p r e v i o u s l y used by Larson (1957) was employed for the measurements but was modified t o incorporate a s o l i d s t a t e nuclear p a r t i c l e detector (RCA diffused j u n c t i o n detector type C-3-25-2.0) for counting the alpha p a r t i c l e s rather than the p r o p o r t i o n a l counter p r e v i o u s l y used. i l l u s t r a t e d i n Figure 7.  The chamber i s  The RCA C-3-25-2.0 unit was chosen simply because of  i t s low cost and r e l a t i v e l y l a r g e s e n s i t i v e area.  The most important  properties  of the detector are given i n Table I I I .  TABLE I I I PROPERTIES OF ALPHA DETECTOR Mat e r i a l  phosphorus diffused i n t o n-type silicon  Resistivity  1000 ohm-cm  Window Thickness  2 microns  S e n s i t i v e area  20 mm'  Operating voltage  25 v o l t s  Leakage Current (measured)  .02yaamps  Resolution (5.3 MeV alphas)  50 kev  A semiconductor p r e a m p l i f i e r was b u i l t as i l l u s t r a t e d i n Figure 8.  This  p r e a m p l i f i e r i s extremely easy t o b u i l d , i s very compact, and i s i d e a l for a p p l i c a t i o n s not r e q u i r i n g low noise l e v e l s or exceptional r e s o l u t i o n .  The  noise figures for the p r e a m p l i f i e r w i t h no c a p a c i t i v e loading are given i n Table IV.  The spectrum for the 5.3 MeV polonium-210 alpha p a r t i c l e s i s shown  i n Figure 9.  The p r e a m p l i f i e r incorporated the 2N930 t r a n s i s t o r s when the  spectrum was t a k e n .  TABLE IV ALPHA DETECTOR PREAMPLIFIER PERFORMANCE TRANSISTOR  TYPE  NOISE FIGURE  P h i l l i p s AFZ-11  PNP  .0060  84.6 kev  $ 4.22  Motorola 2N2218  NPN  .0070  98.7  $ 5.80  Texas Instruments 2N930  NPN  .0025  35.2  $18.00  *  EQUIVALENT FWHM *  COST*  * Pulses t o stimulate 5.3 MeV alpha p a r t i c l e s ** Approximate as o f J u l y , 1964  The alpha p a r t i c l e s were counted i n an accurately defined geometry at 135° t o the Van de Graaff generator proton beam d i r e c t i o n and at 90° t o the target face.  The s o l i d angle subtended by the alpha detector was defined by  a s t a i n l e s s s t e e l window w i t h an accurately measured diameter (Figure 10) which incorporated a 25/* inch sheet o f Grade C n i c k e l f o i l obtained from The Chromium Corporation o f America which was required t o reduce the scattered proton f l u x reaching the d e t e c t o r .  The measurements required t o determine the alpha  FIGURE 8  Solid  State Detector  Preamplifier  o Out  2-  COO  FIGURE <?  2NfSO  5 3 MeV P o Alpha P a r t i c l e Spectrum 2 1 0  500  1*00.  +->  FWHM 2 . 3 8 % (134 kev)  § 300 O O ZOO  IO0  150  i(,o  iro  C h a n n e l Number  lao  ^  5* 2-56  /6  -2/t  /6  1  T 32  /6  25/* i n Nickel  2a = 3 . I 960 ± . 000Z,. mm  8' Inches  11 lb  &  Z7" 32'  FIGURE 10 Alpha P a r t i c l e Window  -16-  detector s o l i d angle were made as i n d i c a t e d i n Table V . Refer t o Figure 7 for an explanation of the symbols used.  TABLE V ALPHA COUNTER SOLID ANGLE DISTANCE MEASURED  HOW MEASURED  RESULT  Window diameter (2r)  3.1960 * .0004 mm  T r a v e l l i n g microscope over 15 diameters  Distance A  4.227 * .001 i n  P r e c i s i o n c a l i p e r depth gauge  Distance B  0.9533 * .001 i n  P r e c i s i o n depth gauge  Target backing  0.014  Micrometer  Detector window t o t a r g e t face R = A - B - t  3.2597 * .0025 i n  S o l i d Angle  * .0005 i n  (1.170 * .002) x 1 0 " steradians  3  The errors quoted are a l l root mean square e r r o r s . The gamma rays were counted at 180° t o the alpha p a r t i c l e detector and c o r r e c t i o n s t o the number o f counts obtained were made i n order t o account for time dependent background, 6.91 and 7.12 MeV gamma rays and a l s o f o r the absorption i n the 0.014 inch copper target backing and the 1/32 inch aluminum gamma ray window.  The f l u o r i n e t a r g e t s were prepared by evaporation of powdered calcium  f l u o r i d e under vacuum ( « 5 x 10""'' mm Hg) onto the h i g h l y p o l i s h e d copper backings 0.014 inches t h i c k .  E i g h t y - s i x amperes of current passed through a  tantalum boat containing ^ 0 . 0 3 grams o f CaF2 formed a target 9 kev t h i c k t o 340 kev protons at a distance o f 25 cm from the boat.  A l l t a r g e t s were found t o be  FIGURE 12 1.85 MeV A l p h a Spectrum  85 MeV  /zoo  /ooo\  at •P C 3 O  FWHM \tfo  O 4001  ¥oo  V  Noi se  zoo\ \ 316  Generating  332 3H0 3¥Q Voltmeter Reading (Uncorrected) (kev ) . 3Z¥  b  to  :  *  ZO  Channel  30  Number  ¥0  -17-  v i s u a l l y uniform over t h e i r whole surface and e x c i t a t i o n functions (Figure 11) taken at various p o s i t i o n s and times during the runs confirmed the r e s u l t s of the v i s u a l i n s p e c t i o n . Measurements of the alpha p a r t i c l e and gamma ray fluxes were made by bombarding the t a r g e t s w i t h protons of <~ 340 kev energy from the UBC Van de Graaff a c c e l e r a t o r .  I t was necessary t o keep the beam current down t o approxi-  mately one microampere i n order t o prevent- too r a p i d target d e t e r i o r a t i o n .  When  the alpha count r a t e i n d i c a t e d that the t a r g e t was d e t e r i o r a t i n g badly the t a r g e t holder was r a i s e d or lowered i n order that a new part of the target be exposed t o the beam.  A t y p i c a l alpha spectrum i s shown i n Figure 12 w h i l e a  gamma ray spectrum appears as Figure 13.  The proton beam s t r i k i n g the target  was confined t o a beam spot o f 2 mm diameter by the c o l i i m a t i n g arrangement shown i n Figure 7»  This ensured that corrections t o the alpha counter s o l i d  angle due t o f l u c t u a t i o n s i n the beam spot p o s i t i o n and due t o the f i n i t e beam spot s i z e were n e g l i g i b l e . Pulses from the alpha counter were fed i n t o 128 channels of a Nuclear Data Type 101 256-ehannel k i c k s o r t e r w h i l e those from the gamma counter went t o 256 channels o f a Nuclear Data Type 120 512-chanhel k i c k s o r t e r and a l s o t o a type UBC NP-11 s c a l e r biased so as t o count only those pulses appearing above the h a l f energy b i a s . A p l o t o f ~\ / — distances d .  vs d was made for f i v e d i f f e r e n t source-to-counter  Here N ^ i s the number of alpha p a r t i c l e s detected w h i l e N  the number of gamma counts above the h a l f energy b i a s .  face c  The s t r a i g h t l i n e  obtained (Figure 14) gives the e f f e c t i v e centre distance for the 6 . I 4 MeV gamma ray. The h a l f energy e f f i c i e n c y i s given by  £  =  N L7°< C  is  O  20  ¥0  60  80  IOO  C h a n n e l Number  FIGURE 13  6.14 MeV Gamma Ray Spectrum  I20  /VO  I60  IQO  -18-  wheres  , N  are as p r e v i o u s l y defined  c  C^/* • tJy  a  r  e  the alpha and gamma detector s o l i d angles.  The gamma detector s o l i d angle i s defined t o the e f f e c t i v e  centre,  e(6.14) = 3.75 ± 0.25 cm, and i s given by  (j  -  A (d • •  2 where A i s the c r y s t a l cross s e c t i o n a l area = 45.606 cm . The r e s u l t s for the f i v e d i f f e r e n t t r i a l s are given i n Table V I .  TABLE V I HALF ENERGY BIAS EFFICIENCY AT 6.14 MEV  d  d + e  £^  PROBABLE ERROR  32.85 * .20 cm  36.60 *• .45 cm  56.03$  ± 1.15$  56.25 ± .20  60.00 ± .45  58.44  ± 0.88  74.40 ± .20  78.15 ± .45  58.33  ± 0.86  57.83  ± 0.82  57.76  ± 1.00  57.84  ± 0.94  106.00 ± .20  109.75  130.00 ± .30  133.75 ± .55  ±  .45  Weighted average  The errors quoted include c o n t r i b u t i o n s from distance measurement, alpha counter s o l i d  angle and counting s t a t i s t i c s .  The accuracy of the counting  s t a t i s t i c s was reduced by the s u b t r a c t i o n of appropriate background c o r r e c t i o n s . Time dependent background i n the alpha counter was n e g l i g i b l e at the p o s i t i o n of the alpha peak but beam dependent background emanating from the target  MeV  1. 8 5  o  200  ,  Beam Dependent Time Dependent  • •  1  160  120  i| ii 1 1 ,  Cour  >>  l  5 . 3 MeV o  l  1!  80  X  i 2?  0 /  1 1 1  -  1 1 \  /  \  Ilo />c I c  /  0 0  i  10  \  \ o  \  0  \  \o \  o \ oo 0 o ^  °°^o°° -°°-^ o 0  J  20  II  "  n  »  n  t  X « »  , » « " T «" »x * x X  50  30 Channel  FIGURE 15  \°  \  *y - " w .iT"H Miri *. • *«1« *H  Alpha D e t e c t o r Background  ?)  o  I  \ \  / °  0 0  / p  /  o°o  2 K  \  «/ o  \  /  0  (Po  o /o"oo\\ o 1  1  ,  MeV  1  » °  *  60  Number  j»o  X  o /  y  "K 1  70  l  80  90  /  -19-  amounted t o approximately 2% of the counts i n the alpha peak.  This background  was uniformly spread over a l l channels up t o approximately 4 MeV where a very broad peak was evident (Figure 15)•  Runs o f f the resonance gave.the same r e s u l t s  f o r the background. 4.  The R a t i o of E f f i c i e n c i e s at 4.43 and 11.68 MeV 11  The r e a c t i o n B  12 (p, t  )C  bombarding energy of 163 kev.  has a w e l l known low l y i n g resonance at a proton (Ajzenberg-Selove and L a u r i t s e n , 1959)#  This  populates the 16.11 MeV l e v e l of carbon-12 which decays by gamma emission e i t h e r d i r e c t l y t o the ground s t a t e or by cascade through the intermediate low l y i n g 4.43 MeV l e v e l (Ajzenberg-Selove and L a u r i t s e n , 1959* Figure 16). lilt Q"+ f  (fy* t(>3 Key)  FIGURE 17 B (p, n  r)G  12  Uf3  There i s a one t o one r e l a t i o n between the t o t a l number o f 4»43 MeV gamma rays and the t o t a l number o f 11.68 MeV gamma rays given o f f .  The angular d i s t r i b u t i o n  of the 11.68 MeV gamma ray has been found t o be p r o p o r t i o n a l t o 1 + (0.26 0.0l)cos*6 w h i l e that of the 4.43 MeV gamma ray i s p r o p o r t i o n a l t o 1 + (0.16 ± 0.02)cos 9 (Grant et a l , 1954) i n good agreement w i t h the t h e o r e t i c a l predictions.  -20-  The number o f counts expected above the h a l f energy b i a s , N , q  and so the r a t i o o f the 4.43 MeV t o 11.68 MeV e f f i c i e n c y 64(4.43) ££(11.68)  =  is N  £ ^ u,  Q =  is  N ( 4 . 4 3 ) N / 1 1 . 6 8 ) u^(4.43) c  N,(4.43) M ( 11.68) c  ty.(11.68)  where the s o l i d angles are defined t o the appropriate e f f e c t i v e centres.  It i s  t o be expected that t h i s r a t i o i s l e s s than one since the t o t a l absorption c o e f f i c i e n t o f N a l f o r 11.68 MeV gamma rays i s l a r g e r than that for 4.43 MeV gamma rays due t o the r a p i d increase i n the p a i r production cross s e c t i o n i n t h i s energy range (Grodstein, 1957). Measurements at 118° ± 2° t o the proton beam were made by bombarding a t h i c k (550 «g/cm^) target o f boron-11 obtained from Harwell, England, w i t h protons //  of 280-300 kev energy.  A representative spectrum i s shown i n Figure 17 w i t h the  background subtracted. The spectra were analyzed by s u b t r a c t i n g background and an average c o n t r i b u t i o n from the 16.11 MeV gamma ray t a i l which was assumed t o be f l a t through t o zero energy t o obtain the composite  4.43 + 11.68 gamma ray spectrum. An  average 11.68 MeV t a i l was then subtracted from the 4*43 MeV p o r t i o n o f the spectrum t o o b t a i n a completely separated 4.43 MeV gamma ray spectrum.  The  numbers o f counts above the r e s p e c t i v e h a l f energy biases were taken and corrected f o r the d i f f e r i n g angular d i s t r i b u t i o n s .  The e f f e c t i v e centre o f the c r y s t a l at  4.43 MeV was taken t o be equal t o t h a t at 11.68 MeV.  Investigation of t h e o r e t i c a l  e f f i c i e n c y p l o t s showed that t h i s introduced an e r r o r o f l e s s than 1% (see Chapter 3 ) .  Thus U {4.43) t  = (j/H.68).  The r a t i o obtained was 1.055 * .029 which i s much higher than expected. From the r a t i o s o f the absorption c o e f f i c i e n t s and t h e o r e t i c a l e f f i c i e n c i e s at 31.5 cm one expects a r e s u l t c l o s e t o 0.95.  -21-  Because of the r e s u l t obtained i t was decided t o repeat the  measurement  for a 2-3/4 x 4-1/2 inch c r y s t a l that had been p r e v i o u s l y i n v e s t i g a t e d .  Here  again the r a t i o was found t o be greater than one and more measurements,  using  a d i f f e r e n t t a r g e t and b e t t e r beam c o l l i m a t i o n , were made. r e s u l t s are presented i n Chapter 4.  D e t a i l s of the  S u f f i c e i t t o say at t h i s point that the  inconsistency o f the r e s u l t s i s very d i s t u r b i n g . 5.  Summary of 3 x 3 C r y s t a l H a l f Energy E f f i c i e n c y Results  The r e s u l t s and probable errors are tabulated i n Table V I together w i t h the measured e f f e c t i v e centres.  A l l e f f e c t i v e centres are for distances  compared w i t h the c r y s t a l l e n g t h .  Figure 18 i s a p l o t o f the  large  results.  TABLE V I I HALF ENERGY BIAS EFFICIENCIES - 3 x 3 CRYSTAL  ENERGY  HALF ENERGY EFFICIENCY  PROBABLE ERROR  0.511  75.1  ± 2.40  2.96 ± 0.50  1.253  60.55  ± 1.61  3.50 ± 0.40  6.14  57.34  * 0.94  3.75  EFFECTIVE CENTRE (cm)  * 0.25  0  I  I  O  I  I Z  I 3  I  I  I  I  I  I  k  S  G  7  &  1  Gamma Ray E n e r g y  (MeV)  l _ _ 10  L II  -22-  CHAPTER I I I THEORETICAL EFFIGIENGIES  A.  THEORETICAL EFFICIENCY Gamma rays of i n i t i a l i n t e n s i t y I , a f t e r t r a v e r s i n g a thickness of 0  m a t e r i a l , ^ , are found t o have an i n t e n s i t y T S/^\ 0  Thus a f r a c t i o n / -  e-^^  of the gamma rays have undergone at l e a s t a s i n g l e primary i n t e r a c t i o n , t r a n s f e r r i n g an amount of energy t o the m a t e r i a l depending upon the type of i n t e r a c t i o n , whether Compton s c a t t e r i n g , p h o t o e l e c t r i c absorption or p a i r production. I f the m a t e r i a l i s a N a l ( T l ) s c i n t i l l a t i o n detector then each gamma ray undergoing a primary i n t e r a c t i o n w i l l contribute a pulse t o the spectrum.  The  p o s i t i o n of the pulse i n the spectrum w i l l depend upon the energy t r a n s f e r r e d t o an e l e c t r o n i n the primary i n t e r a c t i o n s plus subsequent secondary i n t e r a c t i o n s and losses that take p l a c e .  Since the h a l f energy b i a s e f f i c i e n c y p r e v i o u s l y  discussed depends upon the secondary i n t e r a c t i o n s , i t i s not e a s i l y c a l c u l a b l e and therefore i t i s not p o s s i b l e t o achieve accuracies b e t t e r than 15 or 20$ by use of theory at the present t i m e .  The author feels t h a t , at t h i s t i m e , i t  should be pointed out that i t i s erroneous t o compare measured h a l f energy b i a s e f f i c i e n c i e s defined t o the e f f e c t i v e centre distances d i r e c t l y w i t h the semie m p i r i c a l theory o f P. P. Singh (1959) as was done i n h i s and other theses. The best that one can do i s t o determine i f the e f f i c i e n c y defined i n terms of a s o l i d angle subtended by the front face of the c r y s t a l approaches Singh*s value as the s o u r c e - t o - c r y s t a l face distance increases t o s e v e r a l c r y s t a l lengths. The t o t a l number of counts w i t h i n the spectrum i s not dependent upon the secondary i n t e r a c t i o n s t a k i n g p l a c e but depends only upon the number of primary interactions.  I t i s r e l a t i v e l y easy t o c a l c u l a t e the number of counts expected  -23-  i n the complete gamma ray spectrum and one can base an e f f i c i e n c y d e f i n i t i o n on the t o t a l spectrum i f one makes some assumptions about the spectrum shape i n those regions that cannot be d i r e c t l y observed. We define the t h e o r e t i c a l e f f i c i e n c y as the t o t a l p r o b a b i l i t y that a gamma ray w i l l i n t e r a c t w i t h the c r y s t a l .  For a broad p a r a l l e l beam impinging  perpendicular t o the c r y s t a l face the t h e o r e t i c a l e f f i c i e n c y i s 1 _  e  -/^  £  where! yiA i s the t o t a l absorption c o e f f i c i e n t for N a l at a gamma ray energy E y . i s the c r y s t a l l e n g t h . For an i s o t r o p i c point source s i t u a t e d on the c r y s t a l a x i s  the t h e o r e t i c a l  e f f i c i e n c y i s given by  o where!  r i s the c r y s t a l r a d i u s . d i s the s o u r c e - t o - c r y s t a l face d i s t a n c e . £(<p) i s the gamma ray path length w i t h i n the c r y s t a l . i s the angle the gamma ray makes w i t h the c r y s t a l a x i s .  This expression i s derived i n Appendix B which includes a d i s c u s s i o n o f the computer program w r i t t e n t o c a r r y out the i n t e g r a t i o n and t a b l e s of r e s u l t s obtained f o r three d i f f e r e n t c r y s t a l s i z e s and s e v e r a l gamma ray energies.  B.  EXPERIMENTAL STUDIES OF THE THEORETICAL EFFICIENCY As mentioned i n Chapter 2 i t i s not u s u a l l y p o s s i b l e t o observe a gamma ray  spectrum accurately down t o zero energy.  Thus t o determine the t o t a l number o f  counts i n a spectrum i t i s necessary t o extrapolate the observed spectrum.  The  -24-  next s e v e r a l pages are concerned w i t h the accuracy which one might expect by such an extrapolation,, 1.  T h e o r e t i c a l E f f i c i e n c i e s at 6.14 MeV  Since the gamma ray f l u x i s known most accurately at 6.14 MeV t h i s case s h a l l be discussed f i r s t . As w i t h most gamma ray spectra, the 6,14 MeV spectrum from e x h i b i t s a reasonably f l a t t a i l over much of the lower part of the spectrum. At energies from 0 t o 500 kev however, backscattering from lead s h i e l d i n g , room w a l l s and equipment d i s t o r t s the spectrum.  One u s u a l l y sees a c h a r a c t e r i s t i c  backscattering peak at an energy o f about 250 kev or l e s s , the height depending upon the geometry o f the s h i e l d i n g and other experimental d e t a i l s .  Also p a i r  production i n the lead s h i e l d gives r i s e t o a n n i h i l a t i o n gamma rays of 0.51 MeV at higher incident gamma ray energies which contribute t o the experimentally viewed spectrum. The f i r s t e x t r a p o l a t i o n that comes t o mind i s t o extend the f l a t  tail  through t o zero energy; the next i s t o draw a l i n e t o the o r i g i n of the axes from some convenient p o s i t i o n on the f l a t t a i l .  I t has been noted that many  i n v e s t i g a t o r s ( f o r example Mainsbridge, I960) have done just t h i s and assumed t h a t the t r u e number o f counts l i e s somewhere between these e x t r a p o l a t i o n s . In the present study extrapolations of these two types give r e s u l t s f o r e f f i c i e n c i e s that are much too high and were thus deemed u n s u i t a b l e . Monte Carlo c a l c u l a t i o n s of spectrum shape by M i l l e r and Snow (i960) and Zerby and Moran (1961) i n t h i s energy range have been i n good agreement w i t h experimental r e s u l t s f o r that part o f the spectrum comprising the three p a i r peaks.  At energies below these peaks the c a l c u l a t i o n s are much lower than  experimental r e s u l t s .  The t o t a l number o f counts i n the Monte Carlo spectra i s  -25-  i n agreement w i t h the t h e o r e t i c a l e f f i c i e n c y as defined above.  It seems evident  then that i n an experimental s i t u a t i o n there i s much unexplained s c a t t e r i n g adding counts t o the lower end o f the spectrum and i f any e x t r a p o l a t i o n i s t o agree w i t h the t h e o r e t i c a l e f f i c i e n c y i t must be such as t o remove these extra counts. I t was hoped that the Monte C a r l o spectrum o f Zerby and Moran for a 3 x 3 c r y s t a l at 6 MeV would give a guide by which the experimental curve at 6.14 MeV could be extrapolated t o zero energy.  Figure 19 shows a comparison between  t h e i r spectrum f o r a c r y s t a l w i t h 0.661 MeV r e s o l u t i o n of 7*64$ and an e x p e r i mental spectrum taken w i t h the UBC 3 x 3 c r y s t a l ( r e s o l u t i o n at .661 MeV of 8.01$).  It i s i n t e r e s t i n g t o note that the r e s o l u t i o n of the UBC c r y s t a l at  6.14 MeV (3»86$) i s b e t t e r than that for the Zerby and! Moran c r y s t a l at 6.14 (4.3$)•  The gross difference between the spectra cannot be explained by reso-  l u t i o n alone, for the experimental spectrum shows f a r fewer counts i n the p a i r peaks than the Monte Carlo spectrum.  I t would then seem j u s t i f i e d t o have an  extrapolated t a i l containing a l a r g e r percentage o f the counts than would be i n d i c a t e d by the Monte Carlo spectrum. Figure 20 shows the 6.14 MeV gamma ray spectrum w i t h f i v e d i f f e r e n t  extra-  p o l a t i o n s t o zero energy; I. II.  Extension of the f l a t t a i l t o zero energy. A s t r a i g h t l i n e e x t r a p o l a t i o n from the o r i g i n tangent t o the experimental spectrum.  III.-V.  Curved l i n e s drawn smoothly i n t o the p a i r peak and passing  through an approximate a n a l y t i c zero i n t e r c e p t . The zero intercept can be determined i n the f o l l o w i n g manner. I f one considers a l l i n t e r a c t i o n s w i t h i n the c r y s t a l , i t i s evident that Compton s c a t t e r i n g i s the only i n t e r a c t i o n that can contribute pulses t o the  T  Energy  F i g u r e 19  (MeV)  Comparison o f 6 MeV Monte C a r l o Spectrum and 6.14 MeV E x p e r i m e n t a l Spectrum Note adjustment o f energy s c a l e s so t h a t photopeaks c o i n c i d e a t 6 MeV.  -26-  f i r s t channel o f the k i c k s o r t e r spectrum and then only i n the l i m i t of a s i n g l e s t r a i g h t ahead scattering,,  I t i s necessary t o determine the p r o b a b i l i t y that an  incident gamma ray w i l l undergo one s t r a i g h t ahead Compton s c a t t e r i n g and no other i n t e r a c t i o n i n t r a v e r s i n g the c r y s t a l . I f we denote ( d [ ) as the absorption c o e f f i c i e n t per u n i t energy i n t e r v a l for ^ dE o Compton Forward S c a t t e r i n g (CFS) then the gamma ray beam i n t e n s i t y change A I due t o t h i s type of s c a t t e r i n a distance AI where  =  A x is  I Ax  dE  I i s the o r i g i n a l beam i n t e n s i t y .  Thus the p r o b a b i l i t y per u n i t energy i n t e r v a l of the photon undergoing a CFS i n a distance  A x i s given by  \dL\  [AI I  Ax  represents the p r o b a b i l i t y per u n i t energy per u n i t path length of  and  the gamma ray undergoing a CFS. I f the t o t a l path length i s p r o b a b i l i t y of obtaining only a s i n g l e CFS event i n  then the  i s equal t o the p r o b a b i l i t y  of obtaining a CFS times the p r o b a b i l i t y of obtaining no other absorption processes.  Thus the p r o b a b i l i t y per MeV of a s i n g l e CFS i n a distance £  diE lo  We can obtain  cLE  is  X  by t a k i n g the l i m i t of the K l e i n - N i s h i n a equation i n  the ca3e of forward s c a t t e r . The number-energy d i s t r i b u t i o n f o r Compton electrons per t a r g e t e l e c t r o n i s given by dE  \  2.TC  d(T\  cLSl  ^ mc 2  2  z 0  2  -  ,  cK ( £ + * ) C O S ( p 2  FIGURE 20  T h e o r e t i c a l E f f i c i e n c y E x t r a p o l a t i o n s at 6.14  MeV  -27-  wheres  (ft i s the e l e c t r o n s c a t t e r i n g anglec ok =  mc  = ,5108 MeV, the e l e c t r o n r e s t mass,  and  o< (i - cosef 2  dcr  / +- COS 0 + Z  i + o<(/ - cose)]  2  i -f- <^(i - cose)  i s the niuiiber-angle d i s t r i b u t i o n of Compton e l e c t r o n s , 9 i s the photon s c a t t e r i n g r  c  angle  i s the c l a s s i c a l e l e c t r o n r a d i u s .  See, for example, Davisson and Evans (1952); Evans (1955)<> For the Compton forward s c a t t e r 6 = 0°  and (p i s found from the r e l a t i o n  cot (p = (/ + ° < ) t a n f which gives (f = 90°. : Thus  / <jer  dSl  CFS  and  dE  2  CFS  2  This i s the cross s e c t i o n per MeV per e l e c t r o n f o r CFS, M u l t i p l y i n g by the e l e c t r o n density N gives  dU.  Thus  dl dE  ZTTr. Nmc z  z  for Nal  -28-  It follows then t h a t the p r o b a b i l i t y o f an event appearing i n the f i r s t  ^J=± ^tjtT^"^  channel o f the k i c k s o r t e r i s given by the average value o f  m u l t i p l i e d by the channel width i n energy u n i t s and the f r a c t i o n of events appearing i n the first^ channel i s the above d i v i d e d by the p r o b a b i l i t y that a gamma ray entering the c r y s t a l w i l l undergo any s c a t t e r i n g  process.  For 100$ accuracy i t would be necessary t o do a numerical i n t e g r a t i o n over a l l path lengths i n the c r y s t a l .  However, since Jsj/^^te  function over the range of i n t e r e s t  not a r a p i d l y varying  (Figure 21) and since the extrapolation  shapes only approximate the t r u e shapes o f the Compton t a i l , a rough estimate of the zero intercept was made. The number of counts i n the spectrum was taken as that defined by l i n e I I , Figure 20 and the f r a c t i o n o f counts i n the f i r s t channel was taken t o be  where •£> i s the c r y s t a l , l e n g t h .  This i s the t r u e f r a c t i o n for a  parallel  beam incident at r i g h t angles t o the c r y s t a l face. A l l extrapolations were made t o the zero intercept c a l c u l a t e d by t h i s method. The intercept i s probably correct t o 15$ for the distances used i n t h i s study. The experimental r e s u l t s obtained for the t o t a l e f f i c i e n c i e s , based upon the extrapolations of Figure 20, for the f i v e distances used t o determine the h a l f energy b i a s e f f i c i e n c y , are given i n Table V I I I . container i s l e s s than 1$ and has been neglected.  Absorption i n the c r y s t a l  T h e o r e t i c a l r e s u l t s obtained  by numerical i n t e g r a t i o n of the t o t a l absorption are a l s o shown, as w e l l as deviations from the t h e o r e t i c a l for the "best" e x t r a p o l a t i o n .  It i s evident  that a wide v a r i a t i o n i n r e s u l t s i s p o s s i b l e due t o the a r b i t r a r i n e s s of  T  Path Length  Z  (cm)  -29-  extrapolation.  As was expected the l i n e g i v i n g best r e s u l t s shows a l a r g e r  percentage of the counts i n the Compton t a i l than would be expected from the spectrum of Zerby and Moran.  TABLE V I I I THEORETICAL EFFICIENCY EXTRAPOLATIONS AT 6.14 MEV  EXTRAPOLATION  & d  32.85  ( x l O ) AT DISTANCE d (cm) 56.25. 74.40 106.0 - 3  t h  130.0  I  21.22  8.24  4.85  2.44  1.64  II  17.8  6.93  3.99  2.05  1.38  III  16.6  6.45  3.79  1.91  1.28  IV  14.7  5.70  3.36  1.69  1.13  —  V ANALYTIC ERROR IN "BEST" CURVE ( I I I ) .  Very  poor  —  17.38  6.37  3.74  1.89  1.27  -4.49$  1.26$  1.34$  1.05$  0.79$  In order t o determine i f s c a t t e r i n g from the lead s h i e l d i n g surrounding the c r y s t a l - p h o t © m u l t i p l i e r unit contributed g r e a t l y t o the spectrum, runs were made for both the 6.14 MeV r a d i a t i o n and for cobalt-60 r a d i a t i o n w i t h the counter i n and out o f the s h i e l d i n g .  The spectra obtained are p l o t t e d i n Figures 22 and 23.  I t i s evident that at 6.14 MeV the lead s h i e l d i n g does not contribute g r e a t l y t o the number of counts above 1 MeV and consequently the h a l f energy b i a s e f f i c i e n c y at t h i s energy i s not g r e a t l y dependent upon the lead c a s t l e s h i e l d i n g . At gamma ray energies of 1.17 MeV and 1.33 MeV the s c a t t e r i n g from the lead i s important i n c o n t r i b u t i n g counts t o the whole spectrum and i f one i s t o use the  FIGURE 22 E f f e c t o f Lead S h i e l d i n g on Cobalt-60 Spectrum  5000  I 17  t-000  3000  CO c zs o o 1000  Ift Pb  IOOOX  •5"  E n e r g y (MeV)  /'0  — — fo  5"ooo L  fo  6(83  0-5/ MfeV '  FIGURE 23  E f f e c t o f Lead S h i e l d i n g on t h e 6.14 MeV Spectrum  -p c  3 O  o  2000  /oooU  20  JO vo E n e r g y (MeV)  -30-  h a l f energy b i a s e f f i c i e n c y at these energies i t i s imperative that the s h i e l d i n g be comparable t o that used i n these measurements,. Since removal o f s h i e l d i n g does not reduce the 6.14 MeV t a i l , the g r e a t l y increased number o f counts above that expected from the t h e o r e t i c a l e f f i c i e n c y must be due t o other s c a t t e r i n g i n the room and i n the c r y s t a l container i t s e l f . 2.  T h e o r e t i c a l E f f i c i e n c i e s at 1.28 MeV  An attempt was made t o f i t curves s u i t a b l e for t h e o r e t i c a l efficiencycomparisons t o the spectrum o f the 1.28 MeV gamma ray from sodium-22. The gamma f l u x was determined by using the measured h a l f energy b i a s e f f i c i e n c y at the same energy (Chapter 2)  and the extrapolations were made using the  approximate zero i n t e r c e p t .  The r e s u l t s are e s s e n t i a l l y the same as for the  6.14 MeV r a d i a t i o n , that i s , i t i s p o s s i b l e t o get w i t h i n 2$ for a s u i t a b l y drawn curve but the range o f curves gives a range of r e s u l t s which vary about the c a l c u l a t e d t h e o r e t i c a l e f f i c i e n c y by 12$. The Monte Carlo spectrum of Zerby and Moran at an energy of 1.275 MeV has a photopeak r e s o l u t i o n o f 6.25$ which i s equal t o that o f the UBC 3 x 3 c r y s t a l at the same energy (6.18 £ .12$). i l l u s t r a t e s t h i s fact very w e l l .  Comparison of the two spectra (Figure 24) It would seem then that the  extrapolations  used t o compare w i t h the t h e o r e t i c a l e f f i c i e n c i e s should follow the Monte Carlo spectrum very c l o s e l y and indeed such an e x t r a p o l a t i o n gives good r e s u l t s . Because o f the obvious prominence of the photopeak i t was f e l t that i t would be easier t o use the photofraction f  p  Counts i n photopeak T o t a l counts  - N_ Nq  as the c r i t e r i o n for t h e o r e t i c a l e f f i c i e n c y c a l c u l a t i o n s .  The number o f counts  i n the photopeak was found, and from the c a l c u l a t e d absolute e f f i c i e n c y and the  ~i  :  n  n  ;  n  h275  Energy EIGURE 24  (MeV)  Comparison o f 1.275 MeV Monte C a r l o Spectrum and E x p e r i m e n t a l  Spectrum  -31-  known gamma ray f l u x I , the photofraction was c a l c u l a t e d so as t o give agree0  ment between the t o t a l counts i n the spectrum given by  and that expected from the t h e o r e t i c a l e f f i c i e n c y N  c = *o£th  The r e s u l t s for four d i f f e r e n t distances are shown i n Table IX „ There was no evidence of any change i n the spectrum shape over t h i s range of distance,.  TABLE IX PHOTOFRACTION AT 1.275 MEV  d  £  t  PHOTOFRACTION  h  50.0 cm  .961 1 0  - 3  .377 * .011  75.0  .400 1 0  - 3  .412 ± .012  125.0  .169 1 0 "  3  .381 ± .012  150.0  .119 1 0 "  3  .399 * .014  Weighted average  .391 * .012  Zerby and Moran  .404 * .012  The good agreement between experimental and Monte Carlo r e s u l t s  indicates  that one can use the photofraction 0.391 *.012 t o obtain the t o t a l number o f counts i n a 1.28 MeV gamma ray spectrum t o about 3.5$ accuracy p r o v i d i n g s t a t i s t i c s are good. I t i s necessary t o point out that the photofraction l i s t e d above for the  -32-  Monte Carlo spectrum i s not that l i s t e d i n Table 1, page 13, of the report by Zerby and Moran (1961) but represents the r a t i o o f the area under the photopeak of Figure 22, page 37, o f the same a r t i c l e t o the t o t a l area i n the spectrum.  3.  R a t i o o f T h e o r e t i c a l E f f i c i e n c i e s at 4.43 and 11.68 MeV  Because o f the wide v a r i a t i o n o f r e s u l t s obtained f o r the r a t i o of —^  -  i t was f e l t that any attempt t o extrapolate these curves t o zero  energy i n order t o o b t a i n ——  '•— would be meaningless,  (see Chapter 4 ) .  £tk0/-68)  C.  EFFECTIVE CENTRES FROM THEORETICAL EFFICIENCY CALCULATIONS I f one p l o t s - a / — v s d for large distances d ( y 25 cm) one obtains a  V  Otk  s t r a i g h t l i n e which crosses the negative d a x i s at the e f f e c t i v e centre o f the crystal.  For smaller distances the graph deviates from the s t r a i g h t l i n e and  consequently the e f f e c t i v e centre changes.  At close d i s t a n c e s , d  Q  say, the  e f f e c t i v e centre i s that point at which the s t r a i g h t l i n e tangent t o the vs d curve at d = d , crosses the negative d a x i s . 0  ^/-pr  I t i s expected that the  e f f e c t i v e centre w i l l move c l o s e r t o the c r y s t a l face as the source moves c l o s e r t o the face, f o r more s c a t t e r i n g events w i l l take place i n the front p o r t i o n o f the c r y s t a l .  Figure 25 shows a p l o t o f  vs d for the 3 x 3 c r y s t a l V <StK~  for energies of 6 . I 4 , 1.28 and .50 MeV.  For l a r g e distances the l i n e s are  remarkably s t r a i g h t and indeed, on the smaller s c a l e , no d e v i a t i o n from the s t r a i g h t l i n e i s evident over the whole range o f d i s t a n c e s .  The i n s e r t i n  Figure 25 shows the d e v i a t i o n from the s t r a i g h t l i n e f o r small values o f d f o r a gamma ray energy of 6.14 MeV. I f one i s t o use the measured h a l f energy b i a s e f f i c i e n c i e s for a s c i n t i l l a t i o n detector at short source-to-counter face distances i t i s important  0  10  20  30  40  50  Source DCstance  60 (cm)  70  80  90  100  -33-  t h a t the change i n e f f e c t i v e centre be taken i n t o account.  I t should be pointed  out t h a t , when one assumes that e f f e c t i v e centres as c a l c u l a t e d from absolute e f f i c i e n c y data may be a p p l i e d d i r e c t l y t o h a l f energy b i a s data, i t i s automatically assumed that the gamma ray spectra shape does not change w i t h distance. change  This should not be so, for edge losses and secondary effects should as source distances change.  However, i n t h i s study, no spectrum shape  change for any gamma ray was observed over a range of distances from 5 cm t o 2.5 m.  Thus the assumption i s probably a good one t o w i t h i n 1$.  Table X shows a comparison between the e f f e c t i v e centres measured i n the l a b o r a t o r y , corrected f o r the 0.1375 inches of m a t e r i a l between the c r y s t a l face and container face, and the a n a l y t i c e f f e c t i v e centres f o r l a r g e distances.  The r e s u l t s agree t o w i t h i n the rather large experimental e r r o r s .  TABLE X COMPARISON OF ANALYTIC AND EXPERIMENTAL EFFECTIVE CENTRES (3, x 3 CRYSTAL)  E^ 0.511  EFFECTIVE CENTRE EXPERIMENTAL ANALYTIC 2.61 ±0.50 cm  2.16 cm  1.28  3 . 1 5 * 0.40  3.13  6.14  3.40*0.25  3.15  -34-  CHAPTER IV STUDIES OF A 2-3/4 x 4-1/2 INCH Nal(Tl) CRYSTAL Many researchers i n the Nuclear Physics Group at UBC have employed a 2-3/4 x 4-1/2 inch N a l ( T l ) c r y s t a l for the study of capture gamma rays and photodisintegration»  The h a l f energy b i a s e f f i c i e n c y for t h i s detector has been  p r e v i o u s l y measured at 0.51> 1.28 and 6.14 MeV by the method o u t l i n e d i n Chapter 2, ( G r i f f i t h s , 1958; Singh, 1959; G r i f f i t h s et a l , 1962). A.  THE EFFICIENCIES AT 6.14 MEV Results o f recent important experiments on the p h o t o d i s i n t e g r a t i o n of  helium-3 depend g r e a t l y upon a knowledge of the e f f i c i e n c y of t h i s counter and i t was decided t o check the previous measurements at 6.14 MeV and t o see i f t h e o r e t i c a l e f f i c i e n c y extrapolations were consistent w i t h those o f the 3 x 3 crystal. The h a l f energy b i a s e f f i c i e n c y was remeasured by the method f u l l y d e t a i l e d i n Chapter 2.  The r e s u l t obtained i s £ | ( 6 . 1 4 ) =(76.7 * 1.8)%  which compares extremely w e l l w i t h the previous r e s u l t of ( 7 6 . 1 - 1 . 1 ) $ . Figure 26 shows a t y p i c a l 6.14 MeV spectrum w i t h a s i n g l e e x t r a p o l a t i o n t o the approximate a n a l y t i c zero intercept drawn i n .  This was the only extrapo-  l a t i o n drawn for t h i s c r y s t a l and the r e s u l t s , tabulated i n Table X I , show that experience i s very important i n obtaining accurate r e s u l t s .  +000  3Z00  6 . 1 4 MeV-  ZHOO  I bOO  800 _  <40  0  I  SO  60  Channel  Number  2 Energy  FIGURE 26  Theoretical E f f i c i e n c y Extrapolation  (MeV)  a t 6.14 MeV f o r t h e 2-3/4 x 4-1/2 I n c h C r y s t a l  -35-  TABLE X I THEORETICAL EFFICIENCIES AT 6.14 MEV 2-3/4 x 4-1/2 CRYSTAL £th EXPERIMENTAL  29.25 cm  20.28 1 0 "  PROBABLE ERROR IN EXPERIMENTAL  ANALYTIC  4  20.85 10~  4  6.91 1 0 3.62 1 0  53.90  7.18 10~  76.30  3.66 10-*+  DIFFERENCE BETWEEN £«.(exp) & 6«.(anal.)  ±3.00$  2.73$  - 4  ±2.05$  3.90$  - 4  ±2.20$  1.10$  4  The estimated e r r o r i n the experimental r e s u l t s i s based upon the assumption that the e x t r a p o l a t i o n i s the correct one and only s t a t i s t i c a l and measurement  errors are i n c l u d e d .  S t a t i s t i c a l errors include both gamma ray and  alpha p a r t i c l e s t a t i s t i c s since the gamma ray f l u x used t o c a l c u l a t e c?th ^ based upon the number of alpha p a r t i c l e s counted.  s  Absorption i n the c r y s t a l  container i s l e s s than 1$ and i s neglected. B.  THE RATIO OF THE EFFICIENCIES AT 4.43 AND 11.68 MEV Several attempts were made t o determine the r a t i o o f the h a l f energy bias  e f f i c i e n c i e s at 4.43 and 11.68 MeV. On three separate runs, comprising at l e a s t two d i f f e r e n t t r i a l s at d i f f e r e n t distances, r e s u l t s were consistent w i t h i n themselves but deviated g r e a t l y from r e s u l t s of the other runs and from the r e s u l t s expected by comparison of the c a l c u l a t e d t h e o r e t i c a l e f f i c i e n c i e s and by comparison of the respective absorption c o e f f i c i e n t s i n sodium i o d i d e ; (11.68) «, .139 c m ~ , ^ ( 4 . 4 3 ) - .128 c m " . 1  1  /  Two d i f f e r e n t t a r g e t s o f boron-11, not p r e v i o u s l y used, o f thicknesses  -36-  550/4 g/cm 300 k e v .  and 380 ^g/cm , were bombarded w i t h protons o f energies from 280 t o /  Measurements were made at 9 0 ° and 4 5 ° t o the proton beam.  I t i s evident that a d e t a i l e d study, i n c l u d i n g angular d i s t r i b u t i o n s , must be made i n order t o determine the cause o f the d i s c r e p a n c i e s .  -37-  APPENDLX A REPRESENTATIVE SPECTRA FOR THE 3 x 3 CRYSTAL  The following pages contain representative spectra taken w i t h the 3 x 3 N a l ( T l ) c r y s t a l for the gamma rays l i s t e d below.  The ordinate i s given i n  r e l a t i v e counts per MeV which represents the number o f counts at energy E i n a u n i t channel at t h i s energy.  Each spectrum has been normalized t o 10 at a  convenient peak.  FIGURE  GAMMA RAY SOURCE  ENERGY OF GAMMA RAYS  27  Caesium-137  0.661 MeV  28  Sodium-22  0.511, 1.275  29  Cobalt-60  1.173, 1.332  30  Radio Thorium  31  B - ( p , a O C ^ , Ep=300 kev  4.43, 11.68  32  F 9( , < , ^ ) o l ,  6.14  2.615, . 8 6 0 , .729 .511, . 8 3 0 , .583 .239, .040  1J  1  6  p  0  Ep=340 k ev  Relative O  •  0  I  C o u n t s P e r MeV  -J>  >Vi  I  I  I  ^\<,  i O  03 O  —  CO  . .  Co  Cn i  "  ^  o  (J  Relative  i  O  o  i  I  f\j  i  I  C o u n t s P e r MeV  i  i  i  i  i  i  i  O  i  i  o o 0 o  CD  o o  C  2  ft  OO  On  -4>  —  '  o -  -<  V *  0  O O  o flj -s  O O o o  0  £  <• CD  o  o  pj  -5  o o  , Energy ( M e V )  o o  -i  o  DP  o 'O o o o  _  o o  CD  t<  o  O  o  o . ' .  o  _  o o  o o  O  o°  CD  v  o 0 o o  fy^^^^^  .  ^  ^  ^  o  o o o 0  >  3  > V  to to  M  ErJ  1  > :  1  1  -  1  1  1  1  1  1  1  1  to co  1  do  1  O  FIGURE 27  H *  Caesiutn-137  o  1  »Tl  OO.  O  CO  1  1  1-0  o o o ~o° o  1  •  1  1  •!  .1  1  ¥•¥•3  10  J .  >  FIGURE 31  |  B (p,/)C n  1 2  8  a  2:  1.  <0  Q.  CO  6  £ 3  O C_) <0 Li > 1  •_J  +->  (0  0  <—<  *  •  /  \  <o " 2 V  •.  . 0  0  1  1  2  . <i  .  ..^i^i 0  e  \  •  0  6 1  I  .  * 6 " a ^4 1  1  1  8  10  Energy (MeV) ; 1  1  V  N  12 .1  10 FIGURE 32  F  1 9  (p,^,jr)0  M  1 6  >  8  1  « Z s. (1)  «->  1  6  c 3  O O >  •P  (0  0  r-l  CO  "~  e 0  0 • . . • • < , • • • . • • „ . • .  0  • "  •  1 Q  0  *  —  I  '  \  0  I  2  I  3  •  1  1  b  Energy  5 (MeV)  1  6  0  „  -38-  APPENDLX B THEORETICAL EFFICIENCY OF N a l CRYSTALS A.  DERIVATION OF THE EFFICIENCY EQUATION The t h e o r e t i c a l e f f i c i e n c y of N a l c r y s t a l s for gamma ray detection i s  defined as the t o t a l p r o b a b i l i t y of a gamma ray emitted by the source l o s i n g energy i n t h e c r y s t a l by Compton s c a t t e r i n g , the p h o t o e l e c t r i c effect or by p a i r production. For a point source s i t u a t e d on the a x i s of the c o l l i m a t o r - a b s o r b e r - c r y s t a l system of Figure 33 the gamma ray path lengths i n each m a t e r i a l are functions of the angle o f emission cf .  The f l u x of a beam of gamma r a y s , emitted at an  angle (P , s t r i k i n g the c r y s t a l i s  where the subscripts a and c r e f e r t o the absorber and c o l l i m a t o r r e s p e c t i v e l y , I  0  i s the i n i t i a l i n t e n s i t y o f the source assuming i s o t r o p y i n kTt geometry,  and dSl i s the element of s o l i d angle subtended by an element o f c r y s t a l .  The  gamma ray i n t e n s i t y l e a v i n g the c r y s t a l w i l l be  where the unsubscripted l e t t e r s r e f e r t o the c r y s t a l .  Thus the number of counts  expected i n the c r y s t a l i s  The t o t a l number o f counts i s obtained by summing a l l c o n t r i b u t i o n s from such elementary beams and i s given by  Col1imator  h—TCOL^ ZCOL  H  TABS H  TCRY  H -ZCRY  FIGURE 33  h  Geometry o f C r y s t a l , C o l l i m a t o r , and  H  Absorber f o r T h e o r e t i c a l E f f i c i e n c y C a l c u l a t i o n s  -39-  /\/ . = rjs.ll t  (,  HTTr  dSl  and the p r o b a b i l i t y that a gamma ray leave a pulse i n the spectrum i s  The i n t e g r a l over © may be done immediately since the path lengths do not depend upon t h i s v a r i a b l e due t o the symmetry of the geometry.  -  (JJ.  A 4- JI.  /..)  .  Thus  .. t  <d(p  where ft = t a n " £ 1  where r i s the c r y s t a l radius and z i s the source-to-counter  face d i s t a n c e . The path lengths i n the c r y s t a l ( • / ) , c o l l i m a t o r (-/ ) and absorber (-/ ) c  given as functions o f (f i n Table X I I .  a  are  In t h i s t a b l e r , z , t represent the c r y s t a l  r a d i u s , s o u r c e - t b - c r y s t a l distance and c r y s t a l length r e s p e c t i v e l y w h i l e subs c r i p t s c and a r e f e r t o the c o l l i m a t o r and the absorber.  -AC-  TABLE X I I CRYSTAL, COLLIMATOR AND ABSORBER PATH LENGTHS  A. CP > t a n (D i  2  _ L _  - 1  tan"  CRYSTAL  z + t r z + t  1  1  r  c c  ^  1  (/>  (f  _ t sec # c  £= 0 c  c  £S_  tan"  r  1  z C. for a l l (/>  B.  t sec  =  sec  0  1  tan-  + z  COLLIMATOR  z  ^ 4 tan~ _Jc zc + t  v C3C(P  ^ B.  > tan"  -  c  c  a  _ (  t p  +  J t a n <P - r, c s i n (/>  z  + t ABSORBER ^  - t s e c </> a  NUMERICAL INTEGRATION OF THE EFFICIENCY INTEGRAL The t h e o r e t i c a l e f f i c i e n c y i n t e g r a l was programmed for numerical  i n t e g r a t i o n be Simpson*s r u l e for 100 i n t e r v a l s of dx = cos <p by the IBM 1620 Computer i n the Fortran language.  The program has been subsequently a l t e r e d so  as t o be compatible w i t h the requirements for running i t on the UBG IBM 7040 Computer. Data input i s i n the form of a s i n g l e card for each energy and each geometry for which the t h e o r e t i c a l e f f i c i e n c y i s d e s i r e d .  I t was f e l t that  -4i-  t h i s method would give the greatest v e r s a t i l i t y o f input although i t i s not best s u i t e d for t a b l e p r i n t o u t s . The v a r i a b l e s i n the program are named as f o l l o w s ; r  3  RCRY  r  z  =  ZCRY  z  t  5  TCRY  t  =  UCRY  = RCOL  c  = ZCOL  c  =  TOOL  t  / L 5  UCOL  ju*  c  c  E  a  = TABS =  UABS  = ENERGY  and data i s punched i n F7.0 format on a s i n g l e card i n the following order: Card Columns  1-7  8-14  15-21  22-28  29-35  36-42  Variable  TCRY  TCOL  TABS  RCRY  RCOL  ZCRY  Card Columns  43-49  50-56  57-63  64-70  71-77  78-80  Variable  ZCOL  UCRY  UCOL  UABS  ENERGY  blank  Distances should be i n centimetres, absorption c o e f f i c i e n t s i n inverse centimetres and gamma ray energy i n MeV. R e s u l t s . a r e p r i n t e d i n the form o f a t a b l e for each card of input data. The t a b l e l i s t s the geometry o f the c r y s t a l , c o l l i m a t o r , and absorber together w i t h the energy and c a l c u l a t e d e f f i c i e n c y . The time taken on the IBM 7040 i s approximately 54 seconds for compilation p l u s 0.9 seconds for each data card, A l i s t i n g o f the a c t u a l program appears at the end of t h i s appendix.  -42-  C.  TABLES OF THEORETICAL EFFICIENCIES The following t a b l e s include t h e o r e t i c a l e f f i c i e n c i e s for N a l c r y s t a l s  w i t h no gamma ray c o l l i m a t o r or absorber.  TABLE X I I I THEORETICAL EFFICIENCIES - 3 x 3 CRYSTAL  SOURCE DISTANCE (cm)  0.50  1.28  4.43  0.50  297.0  217.0  169.1  168.7  179.9  1.00  235.2  170.7  132.7  132.4  141.2  2.00  155.8  113.0  87.91  87.66  93.49  5.00  60.32  44.64  35.10  35.00  37.24  10.00  21.79  16.63  13.25  13.21  14.02  20.00  6.680  5.238  4.226  4.216  4.461  30.00  3.189  2.532  2.055  2.050  2.166  60.00  .8583  .6921  .5653  .5640  .5952  100.00  .3185  .2586  .2119  .2114  .2229  Notes  GAMMA RAY ENERGY 6.14.  11.68  A l l values i n the above t a b l e must be m u l t i p l i e d by 10~° t o obtain the t h e o r e t i c a l e f f i c i e n c y .  TABLE XIV THEORETICAL EFFICIENCIES - 2-3/4 x 4-1/2 Inch Crystal SOURCE DISTANCE (cm)  GAMMA RAY ENERGY - MeV 0.50  1.28  4.43  6.14  8.06  9.17  11.68  0.10  356.1  262.9  206.2  205.7  209.5  212.2  219.0  0.50  281.4  205.5  160.7  160.2  163.3  165.4  170.7  1.00  219.0  159.4  124.7  124.3  126.7  128.3  132.4  2.00  , 141.4  103.5  81. 39  81.17  82.66  83.70  86.34  5.00  52.92  40.20  32.25  32.17  32.72  33.10  34.06  10.00  18.98  15.09  12.39  12.36  12.55  12.69  13.02  20.00  5.835  4.849  4.072  4.063  4.120  4.160  4.259  30.00  2.797  2.374  2.014  2.010  2.037  2.056  2.102  55.00  .8955  .7777  .6663  .6748  .6806  .6950  75.00  .4935  .4322  .3719  .3765  .3797-  .3875  100.00  .2824  .2489  .2148  .2174  .2192  .2237  Note:  .2152  —3 A l l values in the above table must be multiplied by 10 to obtain the theoretical efficiencies.  TABLE XV THEORETICAL EFFICIENCIES - 5 x 4 CRYSTAL  SOURCE DISTANCE (cm)  GAMMA RAY ENERGY - MeV 0.50  1.28  4.43  6.14  11.68  2.00.  261.9  205.5  166.8  166.4  175.8  4.00  163.3  127.6  103.4  103.2  109.0  8.00  76.02  60.17  49.16  49.04  51.72  12.00  42.54  34.21  28.16  28.1G  29.59  20.00  18.47  15.19  12.64  12.61  13.25  80.00  1.421  1.221  1.037  1.Q35  1,082  Notes  A l l values i n the above t a b l e must be m u l t i p l i e d by 10~  J  to  obtain the t h e o r e t i c a l e f f i c i e n c i e s .  The t o t a l absorption c o e f f i c i e n t s used i n the c a l c u l a t i o n s were taken from a graph of the values given i n the t a b u l a t i o n by Grodstein (1957) and are l i s t e d below. ENERGY  ^.(cnr ) 1  0.50  1.28  4.43  6.14  8.06  9.17  .331  .185  .128  .127  .130  .133  11.68  .139  -45-  D.  THE COMPUTER PROGRAM  $D) 0923 J . LEIGH ^FORTRAN C THIS PROGRAM CALCULATES GAMMA RAY DETECTION EFFICIENCIES FOR C SCINTILLATION CRYSTALS. PRINT 500 500 FORMAT (/44H CALCULATED EFFICIENCIES FOR GAMMA DETECTION) PRINT 700 700 FORMAT (//27X,7HCRYSTAL.7X,10HCOLLIMATOR,4X,8HABSORBER) DIMENSION Y(101), Z ( l O l ) C GEOMETRY DATA INPUT 1000. READ 1,TCRY,TCOL,TABS,RCRY,RCOL,ZCRY,ZCOL,UCRY,UCOL,UABS,ENERGY 1 FORMAT (11P7.0) PRINT 401,RCRY,RC0L 401 FORMAT (/10HRADIUS(CM),16X,F10.5,4X,F10.5) PRINT 400, TCRY,TCOL,TABS 400 FORMAT (13HTHICKNESS(CM),13X,F10.4,4X,F10.5,4X,F10.5) PRINT 402, ZCRY,ZCOL 402 FORMAT (19HS0URCE DISTANCE(CM),7X,F10.5,4X,F10.5) PRINT 403,UCRY,UCOL,UABS 403 FORMAT(22HABS0RPTI0N COEF.(CM-l),4X,F10.5,4X,F10.5,4X,F10.5) PHIMAX = ATAN(RCRY/ZCRY) PHIA o ATAN(RCRY/(ZCRY + TCRY)) CMAX COS(PHIMAX) H = ( 1 . 0 - CMAX)*.01 CA = COS(PHIA) C I F TCOLL IS ZERO THE NEXT STEPS ARE SKIPPED IF (TCOL)1000,301,302 302 PHIB = ATAN(RCOL/ZCOL) PHIBB - ATAN(RCOL/(ZCOL + TCOL)) GB . COS(PHIB) CBB . COS(PHIBB) C . CALCULATION OF INTEGRAND VALUES WILL PROCEED. 301 DO 320 I , 1, 101 AI I COPHI - CMAX + (AI - 1.0>H SIPHI = SQRT(1.0 - C0PHI*»2) IF(SIPHI) 303,304,303 303 SIIN . 1.0/SIPHI 304 COIN = 1.0/COPHI C IT IS NOW NECESSARY TO FIND THE GAMMA PATH LENGTHS IN EACH C ABSORBER, THE PATH LENGTH IN THE CRYSTAL IS DETERMINED FIRST. IF (COPHI - CA) 3,4,4 3 YCRY = 1.0 - EXP(-UCRY*(RCRY*SIIN - ZCRY»COIN)) GO TO 51 4 YCRY . 1.0 - EXP(-UCRY*TCRY*COIN) C IF NO COLLIMATOR THE FOLLOWING CALCULATIONS ARE SKIPPED. 51 IF (TCOL ) 1000,9,- 5 5 IF (COPHI - CBB) 6,9,9 6 • IF (COPHI -CB) 7, 7, 8 7 YCOL . EXP(-UCOL*TCOL*COIN) =  =  -46-  8 9 C 10 40 41 C 320 C  11  GO TO 10 YCOL = EXP(((TCOL + ZC0L)*SIPHI*C0IN - RC0L)*SIEJ*(-UC0L)) GO TO 10 ICOL = 1.0 IF THERE IS NO ABSORBER THE EXPONENTIAL CALCULATION IS SKIPPED IF (TABS) 1000,41, 40 YABS = EXP(-UABS*TABS»COIN) GO TO 320 YABS . 1 . 0 INTEGRAND IS NOW FORMED Y ( I ) = YABS* YCOL* YCRY INTEGRATION BY SIMPSON,S RULE STARTS SUMI = 0.0 DO 11 J • 1, 49 N . 2*J M - N + 1 SUMI . SUMI + 4.0*Y(N) - 2.0*Y(M) HI = H*.33333333 AREA1 = H1*(Y(1) + SUMI + 4»0*Y(lOO) + Y ( l O l ) ) EFFIC . 5*AREA1 PRINT 12,ENERGY,EFFIC FORMAT(13HEFFICIENCY AT,F9.4,7H MEV IS,E14.8) GO TO 1000 END =  12  $DATA 7.62  0.0  0.0  3.81  0.0  10.0  0.0  . 212  0.0  0.  1.0  -47-  BBLIOGRAPHT  Ajzeriberg-Selove, F. A. and L a u r i t s e n , T. (1959), Nuclear Physics 11,  1.  B l e u l e r , E . and Z u n t i , W. ( 1 9 4 6 ) , Helv. Phys. Acta 19, 375. &-adt» H . , Gugelot, P. C , Huber, 0 , , Medicus, H . , Preiswerk, P . and Scherre, P. ' ( 1 9 4 6 ) , H e l v . Phys. Acta l j , 77. Chao, C. Y . ( 1 9 5 0 ) , Phys. Rev. 80, 1035. Davis son, C. M. and Evans, R. D. ( 1 9 5 2 ) , Rev. Mod. Phys. 2Zj., 79. Devons, S. and Hine, M. G. N . (1949), P r o c . Roy. Soc. (London) 199A, 56. Dosso, H . H. ( 1 9 5 7 ) , M. A. Thesis, U n i v e r s i t y o f B r i t . C o l . E l l i s , C. D . , Wooster, W. A. and Dodds, J . M. ( 1 9 5 2 ) , P h i l , Mag. j>0, 521. Evans, R. D. (1955), The Atomic Nucleus, McGraw-Hill Book C o . , I n c . , New Y o r k . Fowler, W. A . , L a u r i t s e n , C. C , and L a u r i t s e n , T. ( 1 9 4 8 ) , Rev. Mod. Phys. 2 0 , 236. Freeman, J . M. ( 1 9 5 0 ) , P h i l . Mag. 4_1, 1225. Grant, P. <J., F l a c k , F. C , Rutherglen, Phys. Soc. A67, 751.  J . G. and Deuchars, W. M. ( 1 9 5 4 ) , Proc.  Gray, L . H. ( 1 9 3 6 ) , P r o c . Roy. Soc. A15_6, 578. G r i f f i t h s , G. M. (1958), Proc. Phys. Soc. 72, 337. G. M . , Larson, E . A. and Robertson, L . P. ( 1 9 6 2 ) , Can. J . Phys.  Griffiths,  46, 4 0 2 .  Grodstein, G. W. ( 1 9 5 7 ) , N a t » l Bureau o f Standards C i r c . 583. Hofstadter, R. ( 1 9 4 8 ) , Phys. Rev. 7Jt, 1 0 0 . Kallman, H. ( 1 9 4 7 ) , Natur u Technik. Kreger, W. E . ( 1 9 5 4 ) , Phys. Rev. 96, 1554. Larson, A G. L . ( 1 9 5 7 ) , M. A . T h e s i s , U n i v e r s i t y o f B r i t . C o l . 0  Main3bridge, B . ( i 9 6 0 ) , A u s t r . J . Phys. 13, 2 0 4 . Mainsbridge, E . ( i 9 6 0 ) , Nuclear Physics 2 1 , 1. M i l l e r , W. F. and Snow, W. J , ( i 9 6 0 ) , Rev. S c i . I n s t . 3_1, 39.  -48-  Rose, M. E . (1953), Phys. Rev. 91, 610" Singh, P. P. (1959), Ph. D. Thesis, U n i v e r s i t y o f B r i t . C o l . Van A l l e n , J . A. and Smith, H. M. (1941), Phys. Rev. 69, 501. V i l l a r d , P. (1900), Comptes Rendue 130. 1178. Yuan, L . C. L . and Wu, C. (1963) E d . , Methods of Experimental Physics, V o l . 5, Nuclear P h y s i c s , Pb. A. Zerby, C. D. and Moran, H. S. (1961), Oak Ridge N a t i o n a l Laboratory Report 3169 <-  

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