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A single crystal sodium iodide scintillation spectrometer for the investigation of gamma-ray spectra Azuma, Richard Ernest 1953

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A SINGLE CRYSTAL SODIUM IODIDE SCINTILLATION SPECTROMETER FOR THE INVESTIGATION OF GAMMA-RAY SPECTRA  by Richard Ernest Azuma  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF  ARTS  i n the Department of PHYSICS  We accept t h i s t h e s i s as conforming t o the standard required from candidates f o r the degree of MASTER OF  ARTS  Members of the Department of PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1953  ABSTRACT A s i n g l e c r y s t a l sodium i o d i d e spectrometer has been d e v e l oped f o r the i n v e s t i g a t i o n o f gamma-ray s p e c t r a . The spectrometer was t e s t e d w i t h the gamma-rays from the sources E u l 5 5 RaD,  N a , Z n , C o , and RdTh. 22  6 5  6 0  }  The spectra from these sources  have been obtained by a n a l y z i n g the pulse height d i s t r i b u t i o n from the s c i n t i l l a t i o n counter w i t h a s i n g l e channel d i f f e r e n t i a l discriminator. A c r y s t a l mounting technique i s described i n which the crys t a l s are mounted dry w i t h a l a y e r of magnesium oxide powder surrounding them t o provide d i f f u s e r e f l e c t i n g s u r f a c e s .  With  mountings of t h i s type, 7% energy r e s o l u t i o n has been achieved f o r gamma-ray energies o f approximately 1 MeV. The expected pulse height d i s t r i b u t i o n s have been c a l c u l a t e d and compared w i t h the experimental d i s t r i b u t i o n s .  The e f f e c t  of m u l t i p l e s c a t t e r i n g events on the shape of the d i s t r i b u t i o n s i s discussed,2and the e f f e c t o f c r y s t a l dimensions on the r e s o l u t i o n has been s t u d i e d .  I t has been found t h a t f o r the energy  region 0.5 t o 2.5 MeV the best r e s o l u t i o n i s obtained with s m a l l crystals. A search has been made f o r the presence o f low energy gammarays i n the decay o f t r i t i u m , and i t was found that w i t h i n the accuracy of t h e experiment no gamma-rays were present. A p r e l i m i n a r y r e p o r t i s presented on the i n v e s t i g a t i o n of p o s s i b l e s c i n t i l l a t i o n produced i n a i r by alpha p a r t i c l e s .  The  e f f e c t has been shown t o e x i s t but no systematic study has been made.  ACKNOWLEDGMENTS  The author wishes t o express h i s thanks t o Dr. J . B. Warren f o r suggesting t h i s research and f o r h i s advice and supervision i n performing the experiments. Thanks are a l s o due t o Mr. G. M. G r i f f i t h s f o r h i s many helpf u l discussions and suggestions. The author a l s o wishes t o thank the National Research Council f o r the Summer Research Grant and Bursary under which t h i s r e search was c a r r i e d out.  INDEX Page I. II.  \  INTRODUCTION  .  Compton E f f e c t Photoelectric Effect P a i r Production Process The Calculated Spectrum Shape .... Multiple Scattering Resolution of the S c i n t i l l a t i o n Counter ....  24  The Dry Box C r y s t a l Mounts D e t a i l s of Technique  25 26  THE GAMMA-RAY SPECTROMETER H.T. Power Supply Count-Rate Meter and Head A m p l i f i e r Power Supplies............. C. O s c i l l o s c o p e D. The P h o t o m u l t i p l i e r Tube E. The P r e - A m p l i f i e r F. The Single Channel Analyzer G. The Count-Rate Mete* H. The Brown Recorder EXPERIMENTAL RESULTS  29  A. B.  V.  5 11 14 16 17 20  CRYSTAL MOUNTING TECHNIQUES A. B. C.  IV.  .  THE INTERACTION OF GAMMA-RAYS WITH THE CRYSTAL AND THE SPECTRUM SHAPE A. B. C. D. E. F.  III.  .  A. B. C. D. E. F. G.  •  30 30 30 30 31 31 32  RaD and Eu 55 D i s t r i b u t i o n s Na Distributions Co60 D i s t r i b u t i o n s Zn ? D i s t r i b u t i o n s RdTh D i s t r i b u t i o n s Energy Resolutions..... The Search f o r Gamma-Rays From T r i t i u m .....  33 35 37 38 39 41 43  x  2 2  6  APPENDIX I - C a l c u l a t i o n of the Compton R e c o i l Electron D i s t r i b u t i o n  45  APPENDIX I I - The S c i n t i l l a t i o n of Alpha P a r t i c l e s In A i r . 1  46  ILLUSTRATIONS Figure Number I. II. III. IV.  V. VI. VII. VIII.  Facing Page  The Compton E f f e c t Showing Angular and EnergyNotations  6  Compton E f f e c t Cross-Sections  6  C a l c u l a t e d Compton E l e c t r o n D i s t r i b u t i o n s f o r 0.511 MeV and 1.28 MeV Gamma-Rays  10  Cross-Section vs. Energy f o r the Compton E f f e c t , P h o t o e l e c t r i c E f f e c t , and P a i r Production  12  E l e c t r o n Range v s . Energy Curve  13  C a l c u l a t e d Pulse Height D i s t r i b u t i o n 2 . 6 2 MeV Gamma-Rays • •  16  C a l c u l a t e d Pulse Height D i s t r i b u t i o n f o r 0 . 5 H MeV and 1.28 MeV Gamma-Rays  17  C a l c u l a t e d Pulse Height D i s t r i b u t i o n f o r the Go  b0  17  Gamma-Rays  IS.  The Mount f o r the C y l i n d r i c a l C r y s t a l s  26  X.  The Mount f o r the Rectangular C r y s t a l s  26  XI.  The Mount f o r the Thin " D i s c " C r y s t a l s  26  Block Diagram of the Spectrometer  29  The 2500 V Power Supply  29  XII. XIII. XIV.  XV. XVI. XVII. XVIII. XIX.  The P r e - A m p l i f i e r and the Schmitt C i r c u i t Input to the Count-Rate Meter  31  The Count-Rate Meter  32  Experimental Pulse Height and Eu!55 Experimental Pulse Height from the Large C r y s t a l Experimental Pulse Height from the Small C r y s t a l Experimental Pulse Height  D i s t r i b u t i o n s f o r RaD .... Distribution f o r Na  33  2 2  Distribution f o r Na  36  2 2  Distributions f o r Co^.  36 3S  Figure Number  Facing  XX.  Experimental Pulse Height D i s t r i b u t i o n f o r Zn°5 from the Large C r y s t a l  XXI.  Experimental Pulse Height D i s t r i b u t i o n f o r Zn ? from the Small C r y s t a l 5  XXII.  Experimental Pulse Height D i s t r i b u t i o n f o r RdTh  TABLES Number I.  II.  The Percent Probable E r r o r f o r the Count-Rate Meter a t Various Counting Rates and Time Constants Facing Page 32 Experimentally Achieved R e s o l u t i o n  Page 41  PLATES Number I.  Photograph of the dry box  Facing Page 24  I.  INTRODUCTION  The development of the s c i n t i l l a t i o n counter as an energy s e n s i t i v e detector has produced a powerful t o o l f o r the study of X-ray and gamma-ray s p e c t r a . Recent refinements i n technique have r e s u l t e d i n t h e design of spectrometers which are capable of measuring gamma-ray spectra from sources of the order of 10"^ c u r i e and w i t h r e s o l u t i o n , (measured as the r a t i o o f t h e f u l l width at h a l f maximum to energy a t peak), of approximately £ percent, f o r the energy r e g i o n 1 t o 3 MeV.  This d e f i n i t i o n of en-  ergy r e s o l u t i o n w i l l be used throughout the t e x t .  The r e s o l u -  t i o n a t t a i n a b l e , to date, f o r the energy r e g i o n below 1 MeV has been r e s t r i c t e d by the s t a t i s t i c a l v a r i a t i o n s a s s o c i a t e d with the p h o t o m u l t i p l i e r tubes, and below 100 KeV, these v a r i a t i o n s become dominant and a r e s o l u t i o n of about 40$ can be expected, g e t t i n g worse as the energy drops.  The poor r e s o l u t i o n i n t h i s  very low energy r e g i o n may quite o f t e n be t o l e r a t e d s i n c e the h i g h e f f i c i e n c y of the s c i n t i l l a t i o n counter makes p o s s i b l e the d e t e c t i o n and measurement of spectra from extremely weak sources. The use of t h a l l i u m - a c t i v a t e d sodium i o d i d e c r y s t a l s as a means of d i s t i n g u i s h i n g gamma-ray energies was f i r s t reported by R. Hofstadter i n 1943 ( 1 ) . This i n i t i a l report showed t h a t the f l u o r e s c e n t l i g h t output of sodium i o d i d e was considerably l a r g e r than that from most of the known organic phosphors, but not anthracene, and t h a t the i n t e n s i t y o f fluorescence was an i n c r e a s i n g f u n c t i o n of the i n c i d e n t gamma-ray energy.  A subsequent  publica-  t i o n by the same author (2) showed that sodium i o d i d e counters gave a c h a r a c t e r i s t i c pulse height d i s t r i b u t i o n f o r an i n c i d e n t  2 beam of monoenergetic gamma-rays.  This "spectrum" was charac-  t e r i z e d by the presence of a continuous d i s t r i b u t i o n with a sharp c u t - o f f at the high energy s i d e , and by. the presence of a number of sharp peaks.  The peaks were a t t r i b u t e d t o the i n t e r a c t i o n of  the gamma-rays w i t h the heavy component ( i o d i n e , z=53) of the c r y s t a l by means of the p h o t o e l e c t r i c and p a i r production processes, and the continuous d i s t r i b u t i o n was i n t e r p r e t e d as the r e s u l t of i n t e r a c t i o n s by the Compton e f f e c t .  The p o s i t i o n of t h e j h o t o -  e l e c t r i c and p a i r peaks i n the d i s t r i b u t i o n was reported t o be a l i n e a r f u n c t i o n of the i n c i d e n t gamma-ray energy.  This l i n e a r i t y  w i t h respect t o i n c i d e n t gamma-ray energy of the f l u o r e s c e n t output of the c r y s t a l , along w i t h the presence of sharp peaks i n the spectrum, and the high absorption e f f i c i e n c y has made sodium i o d i d e the i d e a l type of c r y s t a l t o use f o r the measurement of gamma-ray energies. Recent advances i n the design of p h o t o m u l t i p l i e r tubes have r e s u l t e d i n marked improvement i n the performance of the s c i n t i l l a t i o n counter.  Those f a c t o r s of p h o t o m u l t i p l i e r design which  are of most importance i n t h i s a p p l i c a t i o n are the f o l l o w i n g : (i)  High e f f i c i e n c y i n photocathode emission, and u n i f o r -  mity of emission over the whole photocathode surface, (ii) (iii)  High gain and low dark c u r r e n t , Large photocathode area to increase l i g h t c o l l e c t i o n e f -  ficiency. (iv) (v)  I n s e n s i v i t i t y of the gain t o stray magnetic f i e l d s Large output current pulse without a f f e c t i n g l i n e a r i t y  of the response or causing i o n feedback.  3 (vi)  Maximum e f f i c i e n c y i n c o l l e c t i o n of the electrons from  the photocathode. (vii)  Matching of the s p e c t r a l response of the photocathode  with that of the f l u o r e s c e n t r a d i a t i o n of the c r y s t a l . Although much research has been done t o improve these operating c h a r a c t e r i s t i c s , the s t a t i s t i c a l f l u c t u a t i o n s introduced by them, e s p e c i a l l y v a r i a t i o n s i n photocathode emission and g a i n , s t i l l account f o r approximately h a l f of the observed spread of the peaks. The spurious pulses produced by thermionic emission from the dynodes of the p h o t o m u l t i p l i e r are of the same magnitude as those pulses produced by very low energy gamma-rays and X-rays.  These  spurious pulses may be reduced both i n magnitude and i n number by c o o l i n g the tube t o l i q u i d a i r temperatures.  Hence the spectra  of very weak i n t e n s i t y , low energy gamma-rays, ( <£ 1 KeV) may be i n v e s t i g a t e d but t h i s method has not as yet been e x p l o i t e d t o i t s f u l l e s t extent. The e f f e c t of the u n i f o r m i t y of the c r y s t a l ( i . e . uniform f l u o r e s c e n t y i e l d from a l l parts of the c r y s t a l f o r a given of  gamma-ray energy), the s i z e of the c r y s t a l , the method mounting A  the c r y s t a l , and the degree of c o l l i m a t i o n of the i n c i d e n t gammaray beam on the energy r e s o l u t i o n of the counter has been desc r i b e d i n the l i t e r a t u r e (2,3,4).  I n v e s i t g a t i o n has shown that  aside from improved p h o t o m u l t i p l i e r tubes and u n i f o r m i t y i n c r y s t a l s , the l a r g e s t s i n g l e g a i n i n r e s o l u t i o n i s obtained by improved c r y s t a l mounting techniques. R.K. Swank has o u t l i n e d ( 5 ) a method of mounting sodium i o d i d e c r y s t a l s i n order t o ob-  4 t a i n optimum l i g h t input i n t o the m u l t i p l i e r and hence optimum resolution.  With t h i s method as a guide, a c r y s t a l mounting  technique has been developed which i s capable of producing a counter w i t h a r e s o l u t i o n , f o r example, of seven percent f o r  the  60  two p h o t o e l e c t r i c l i n e s i n the spectrum of Co The technique^ of s c i n t i l l a t i o n spectrometry as introduced above has been used i n the performance of many kinds of e x p e r i ments.  A few of the more w e l l known types of experiments  are  l i s t e d below: (i)  The d e t e c t i o n and measurement of gamma-ray spectra  ( e s p e c i a l l y i n the case of weak i n t e n s i t y spectra) produced by bombardment of t a r g e t m a t e r i a l s with a c c e l e r a t e d p a r t i c l e s . (ii) (iii)  The search f o r weak i n t e n s i t y gamma-rays from i s o t o p e s , The, determination of c r o s s - s e c t i o n s i n "bombardment"  experiments, and absolute f l u x measurement of l i n e gamma-rays. (iv) and  The determination of decay schemes by means of ov-Tf, (3-ir coincidences.  (v)  The measurements of i n t e r n a l conversion r a t i o s by measur-  i n g the r a t i o s of X-ray. f l u x . There are very many more s p e c i a l i z e d a p p l i c a t i o n s of t h i s t e c h nique to p a r t i c u l a r experiments.  So f a r t h i s technique has been  a p p l i e d by the author only to ( i i ) mentioned above.  5  II.  THE INTERACTION OF GAMMA-RAYS WITH THE CRYSTAL 'AND THE SPECTRUM SHAPE-. I t has been shown (3,4) t h a t the pulse height d i s t r i b u t i o n  obtained with a s c i n t i l l a t i o n counter f o r an i n c i d e n t beam of mono-energetic gamma-rays has a c h a r a c t e r i s t i c shape.  In order  t h a t the energy of the i n c i d e n t gamma-rays may be determined from t h i s d i s t r i b u t i o n an a n a l y s i s must be made of the e f f e c t on the shape of the spectrum of each of the three absorption processes: (i) (ii) (iii)  Compton e f f e c t , Photoelectric effect, P a i r production.  The c r y s t a l obtains i t s f l u o r e s c e n t energy from the energetic e l e c t r o n s which r e s u l t from the absorption processes.  The pulse  d i s t r i b u t i o n , i n i t s general aspects, i s then determined by the energy v s . number d i s t r i b u t i o n of these e l e c t r o n s . These d i s t r i butions are c a l c u l a t e d below f o r each of the absorption processes, from which the " i d e a l " d i s t r i b u t i o n can be c a l c u l a t e d . The " i d e a l " d i s t r i b u t i o n i s , of course, distorted due t o m u l t i ple s c a t t e r i n g events t a k i n g place i n the c r y s t a l , w a l l e f f e c t s , and by s t a t i s t i c a l f l u c t u a t i o n s introduced by the p h o t o m u l t i p l i e r tube.  These e f f e c t s are discussed below and a q u a l i t a t i v e argu-  ment i s presented o f these e f f e c t s on the shape of the d i s t r i b u t ion. A.  COMPTON EFFECT In c o n s i d e r i n g the Compton e f f e c t i t i s assumed t h a t the e l e c -  t r o n s i n the atom may be thought o f as f r e e and t h a t the photon c o l l i d e s with an e l e c t r o n and i s d e f l e c t e d , the e l e c t r o n r e c o i l i n g  SCATTERED PHOTON  W  INCIDENT PHOTON  RECOIL ELECTRON  FIGURE I The Compton E f f e c t , Showing Angular and EnergyNotations  c o  .Ol  -O  O.I PHOTON  ENERGY  IN  LO MEV  IO  FIGURE I I Cross-Sections v s . Energy f o r the Compton E f f e c t e<f the c r o s s - s e c t i o n f o r the number of photons s c a t t e r e d ; e Os the c r o s s - s e c t i o n f o r the energy of the scattered photons; e OS. the c r o s s - s e c t i o n f o r the energy absorbed by the e l e c t r o n s  4  6  i n a d i f f e r e n t d i r e c t i o n . I t i s the number v s . energy d i s t r i b u t i o n o f the r e c o i l electrons t h a t must be c a l c u l a t e d .  In the  c a l c u l a t i o n s that f o l l o w , i t i s assumed that only primary processes occur, i . e . , a l l degraded quanta escape from the c r y s t a l w i t h no f u r t h e r i n t e r a c t i o n s , and t h a t the e l e c t r o n s lose a l l t h e i r energy t o the c r y s t a l ( i . e . , no w a l l e f f e c t ) and r a d i a t e none i n the form of brehmstrahlung r a d i a t i o n . From the conservation of energy andnomentum i n the process, the r e l a t i v i s t i c equations f o r energy and mass, and the n o t a t i o n shown i n F i g . ( I ), the f o l l o w i n g expressions  U  =  I  <> f J  -l ny  *<rv &  where  =  J  can be obtained:  —  (3)  *  (4)  o( =  K l e i n and Nishina ( 6 ) have c a r r i e d out a quantum mechanic a l c a l c u l a t i o n of the process and have obtained the f o l l o w i n g equation f o r the f r a c t i o n of the gamma-ray energy scattered i n a given d i r e c t i o n : (5)  where l b = i n t e n s i t y of i n c i d e n t beam of gamma-rays, I  = i n t e n s i t y o f s c a t t e r e d beam at the angle Q and d i s tance mass nr.  from the s c a t t e r i n g e l e c t r o n of charge e and  7  I f k(0) = c r o s s - s e c t i o n f o r the number o f photons s c a t t e r e d per e l e c t r o n and per u n i t s o l i d angle i n the d i r e c t i o n 9, t'hen equat i o n (5) may be w r i t t e n I * - j ? ? - - ' W « 0 Sir  .  w h e r e k ( 9 )  M  ^  L  hv  ^ _±^  t  .  ^  ;  *  1  '  |  t  (  6)  |[|+<A(I-.  In the above equation  ^ - ( ^ ;  =  ^  eCt'O) = c r o s s - s e c t i o n f o r the number o f photons' s c a t t e r e d i n t o  the s o l i d angle <Ln. i n the d i r e c t i o n e • The c r o s s - s e c t i o n f o r the amount o f energy scattered per e l e c t r o n and per u n i t s o l i d angle i n the d i r e c t i o n e i s Combining equations (1) and (6) K{9) becomes (7)  where  ^Os(©) i s the cross s e c t i o n f o r the energy o f the photons  s c a t t e r e d i n t o s o l i d angle ASL i n the d i r e c t i o n & • I f the f o l l o w i n g definitions are made: (i)  e& = Compton t o t a l c r o s s - s e c t i o n i . e . , c r o s s - s e c t i o n f o r  the number o f photons scattered o r f o r the t o t a l amount o f energy removed from the beam. (ii)  = Compton s c a t t e r i n g c o e f f i c i e n t i . e . , c r o s s - s e c t i o n  f o r the amount o f energy r e t a i n e d by the scattered photons then gCT' and O ^ are obtained by i n t e g r a t i n g equations (6) and (7) e  r e s p e c t i v e l y over a l l p o s s i b l e d i r e c t i o n s . tions are:  The r e s u l t i n g equa-  etf = „ ^ ^ l ^ - ± U i + " ] * k * > + > 4 - $ f e ,<& - ^  ^(H-*O+- ^ ,  +  ^  x  +  3  \  <:,+*o*J  (8) (9)  Since c ^ i s the c r o s s - s e c t i o n f o r the t o t a l amount of energy r e e  moved from the i n c i d e n t beam, andgfl^ i s the c r o s s - s e c t i o n f o r the amount o f energy r e t a i n e d by the s c a t t e r e d photons, then <^ the e  c r o s s - s e c t i o n f o r the amount of energy absorbed by the r e c o i l i n g electrons i s  C M . Davisson ( 7 ) has c a l c u l a t e d values f o r these c r o s s - s e c t i o n s at various energies.  They are shown i n F i g . ( H ) .  Since the p r o b a b i l i t y that an e l e c t r o n w i l l be s c a t t e r e d i n t o JLJXJ  s i t u a t e d i n the d i r e c t i o n <b , i s the same as the p r o b a b i l i t y  t h a t a primary quantum w i l l be scattered i n t o the s o l i d angle Juji n the d i r e c t i o n ^ , ^ and being r e l a t e d by equation ( 4 ) , then A  J  r\  «*-*•«•  1  «*-*'  (10)  where k(0) and k((fr) have analogous meaning, but are f o r photons and electrons r e s p e c t i v e l y and where k(^) i s given by equation ( 6 ) . Now, i f equation (10) i s i n t e g r a t e d only over  (the polar angle  $ ) the r e s u l t obtained i s  isM,  „ ^ .  4  H«i&„  ( u )  where the prime on the <S i n d i c a t e s that the $ dependence has been i n t e g r a t e d out, and where  ^effV^O d 4>  ^  s  cross-section  . 9 f o r the number of e l e c t r o n s scattered between two cones whose h a l f angles d i f f e r by u n i t y . The q u a n t i t y of i n t e r e s t i s the d i f f e r e n t i a l c r o s s - s e c t i o n as a f u n c t i o n of e l e c t r o n energy, which might be thought o f as the number v s . energy d i s t r i b u t i o n s o f the e l e c t r o n s .  Mathematically  this i s dE*l  ~  d<t>  dEel  (12)  can immediately be found by d i f f e r e n t i a t i n g equation (3) and i t i s  x  d*  1  _  In order t o f i n d  d<P  [i+a<* -l- ( 1 + * ? W > J  (see equation (11)), - — ^ r d~&-  m  u  s  t  first  be c a l c u l a t e d . I f the polar coordinates  are R, 0 and S, and i f the s c a t t e r -  i n g angle & o r <f> i s associated with the polar angle 0, then the element o f s o l i d angle i s sin 9  the photondjO- =  for  f o r the e l e c t r o n JLa! « s i n 4 Thus  t  d4>  ^d-Cil =: a  de d $  <*4>  ^  srn>e<* $ d$ &  can be c a l c u l a t e d from equation (4)  The r e s u l t i s dxn  ~  [0+*?- *(i+o<)  (14)  W - * J *  On using equations (11), (12), (13), (14) the d i f f e r e n t i a l crosss e c t i o n per u n i t energy becomes  Mf^L  J™LUfo){  o+«f-* *~f4> x  l  z  (15)  FIGURE I I I Compton e l e c t r o n d i s t r i b u t i o n f o r i n c i d e n t gamma-ray e n e r g i e s o f 0.511 MeV and 1.28 MeV The d a s h e d c u r v e s show t h e s e d i s t r i b u t i o n s s p r e a d o u t t o 10$ r e s o l u t i o n .  10  in  Now, i f the energy o f the r e c o i l e l e c t r o n mc  2  i s expressed units of A  i . e . cXe|=  Then equation (15) can be s i m p l i f i e d , (See Appendix I) g i v i n g  where the maximum energy of t h e r e c o i l e l e c t r o n i s *el<—-)=-7^  (  Equation (16) has been c a l c u l a t e d  1  7  )  f o r the primary quanta energies  of 0.511 MeV abd 1.28 MeV (<* = 1 and 2.5 r e s p e c t i v e l y ) .  The r e -  s u l t s are graphed i n F i g . ( I I I ) . In any experimental case t h e measured d i s t r i b u t i o n w i l l be spread out due t o the f i n i t e energy r e s o l u t i o n o f the system. This spreading o f the d i s t r i b u t i o n can be c a l c u l a t e d  i n the f o l -  lowing way: (i)  The c a l c u l a t e d  d i s t r i b u t i o n i s divided up i n t o t h i n  vertical strips. (ii)  Each s t r i p i s put i n t o the form of a Gaussian of the  same area and with a width determined by the r e s o l u t i o n o f the system i . e . o" =  ^  where E  m  = mean energy o f the p a r t i c u lar strip  R  = resolution o f system as def i n e d i n the i n t r o d u c t i o n  cr = mean square d e v i a t i o n of the Gaussian. (iii)  The c o n t r i b u t i o n s from a l l the Gaussians are added up  11  and the r e s u l t a n t d i s t r i b u t i o n p l o t t e d . This has been done f o r the two d i s t r i b u t i o n s mentioned above assuming a r e s o l u t i o n of 10% which has been experimentally a t t a i n e d f o r energies of 1 MeV,  and the r e s u l t s are shown i n F i g . (HI).  In the Compton process, the e l e c t r o n with which the quanta i n t e r a c t s has up t i l l now been assumed to be f r e e .  Since the bind-  er i n g energy of the K e l e e t r o n i o d i n e i s approximately 29 KeV, A  this  assumption i s no longer v a l i d f o r i n c i d e n t quanta of energy l e s s than, say, 100 KeV.  I t would be expected then t h a t there should  be considerable m o d i f i c a t i o n s t o the Compton d i s t r i b u t i o n at these low energies.  Since the Compton d i s t r i b u t i o n i s r a r e l y  observed  at these energies due to the overwhelming presence of the e l e c t r i c peak, these e f f e c t s need not be considered.  photo-  In g e n e r a l ,  i t has been found experimentally t h a t the Compton d i s t r i b u t i o n i s not n o t i c e a b l e u n t i l i n c i d e n t quanta energies of s e v e r a l hundred KeV have been reached.  In. t h i s energy r e g i o n , and higher, then,  the above mentioned e f f e c t i s n e g l i g b l e . B.  THE PHOTOELECTRIC EFFECT The medium Z component (iodine Z - 53)  of the c r y s t a l shows  a reasonable p h o t o e l e c t r i c c r o s s - s e c t i o n f o r gamma-ray energies up to s e v e r a l MeV.  CM.  Davisson has c a l c u l a t e d ( % ) the  photo-  e l e c t r i c c r o s s - s e c t i o n as a f u n c t i o n of energy f o r various Z absorbers.  These c a l c u l a t i o n s are discussed i n d e t a i l and the ac-  curacy of the r e s u l t s i s s t a t e d f o r c e r t a i n energy ranges.  It  appears t h a t over the energy range considered the r e s u l t s should be accurate to w i t h i n 10%.  FIGURE IV  O S  I.O  1 5 E N E R G Y  2 . 0 O F  T H E  2.5 P H O T O N  3 . 0 ( M E V )  3 . 5  12  From the t a b l e s given i n t h i s report the c r o s s - s e c t i o n f o r sodium i o d i d e at various energies can be c a l c u l a t e d .  These values are  p l o t t e d i n F i g . ( I V ) . I t can be seen from t h i s curve tha t above 3 MeV the c o n t r i b u t i o n due t o the p h o t o e l e c t r i c effecjf i s n e g l i g i ble. When spectra of low energy gamma-rays are being i n v e s t i g a t e d i t i s p o s s i b l e that the gamma-ray energy may go through the K abs o r p t i o n edge o f i o d i n e (29 KeV).  I f t h i s happens, the same con-  s i d e r a t i o n s apply t o the c r o s s - s e c t i o n ( i . e . absorption c o e f f i c i e n t ) as those which apply i n the case o f X-ray absorption theory,which can be found i n any t e x t on X-rays.  I n e f f e c t , then, the c r y s t a l  j u s t becomes suddenly l e s s e f f i c i e n t when the gamma-ray energy passes through an absorption edge. In the p h o t o e l e c t r i c process an e l e c t r o n i s ejected from one of the i o d i n e (or sodium) s h e l l s , followed by the subsequent emission of an X-ray.  The photoelectron presumably loses a l l i t s en-  ergy t o the c r y s t a l (neglecting brehmstrahling and edge e f f e c t s ) , and the X-ray, due t o i t s low energy, i . e . , K X-ray of iodine i s 29 KeV, i s assumed t o be completely absorbed.  Consequently, two  or more e l e c t r o n s , one of which i s the o r i g i n a l photoelectron, simultaneously lose energy, where the t o t a l energy l o s t t o the c r y s t a l must equal the f u l l energy of the gamma-ray.  Hence, i n  e f f e c t , the number v s . energy d i s t r i b u t i o n of the photoelectrons can be assumed t o be a " l i n e " d i s t r i b u t i o n of e f f e c t i v e l y zero width, and corresponding t o the f u l l energy of the gamma-ray.  A  "photopeak" should thus occur i n the d i s t r i b u t i o n and the p o s i t i o n of t h i s peak can be taken as a measure of the energy of the i n c i d e n t gamma-ray.  FIGURE V  13 For a counter w i t h p e r f e c t r e s o l u t i o n t h e pulse height d i s t r i b u t i o n from the p h o t o m u l t i p l i e r should be a " l i n e " d i s t r i b u t i o n of zero w i d t h .  T h i s , of course, i s an i d e a l i z a t i o n and  hence c o r r e c t i o n must be made f o r the f i n i t e r e s o l u t i o n of the system.  This i s done by r e p l a c i n g the * l i n e " by a Gaussian o f  the appropriate width, where the area under t h e Gaussian  (i.e.,  the t o t a l number o f photoelectrons produced) i s compatible with the p h o t o e l e c t r i c c r o s s - s e c t i o n a t the given energy.  That the  a c t u a l photopeak i s Gaussian has been v e r i f i e d by experiment. I f the c r y s t a l dimensions are very s m a l l , then the p r o b a b i l i t y of escape o f the i o d i n e X-rays i s no longer n e g l i g i b l e .  An "es-  cape peak" should then appear i n the d i s t r i b u t i o n w i t h energy equal t o the d i f f e r e n c e between the energy of t h e i n c i d e n t quanta and o f t h e X-rays o f i o d i n e . With a very t h i n c r y s t a l i t might a l s o be p o s s i b l e t o have a peak a t 29 KeV which would r e s u l t i f many of the photoelectrons escaped completely from the c r y s t a l while the X-rays of i o d i n e were absorbed.  Hower, due t o " s t r a g g l i n g " i n the w a l l e f f e c t  and the f a c t t h a t the above sequence of events i s not too probable, t h i s e f f e c t may be neglected.  No peak at 2 9 KeV has y e t been  observed by the author, although escape peaks have. The magnitude of the w a l l e f f e c t depends on two f a c t o r s : 1)  The range i n Nal of the photoelectrons.  2)  The dimensions  o f the c r y s t a l .  The range vs. energy curve f o r the e l e c t r o n s has been c a l c u l a t e d from Feather*s r u l e and i s shown i n F i g . (V ). Mateosian and Smith ( 8" ) have o u t l i n e d a method f o r c a l c u l a t i n g the w a l l e f f e c t  but due t o the nature o f the experiments  so f a r performed by the  author i t has not been found necessary t o make t h i s c a l c u l a t i o n . C.  PAIR PRODUCTION PROCESS 2 At energies greater than 2 mc , i . e . , greater than 1.02 MeV,  absorption of gamma-rays by the process of p a i r production occurs. The c r o s s - s e c t i o n at d i f f e r e n t energies f o r t h i s process i n sodium i o d i d e can be c a l c u l a t e d from the t a b l e s published by Davisson (7 ). A graph o f these values i s shown i n F i g . ( I V ) . The absorption o f energy by the c r y s t a l due t o p a i r product i o n occurs i n the f o l l o w i n g manner: Consider an i n c i d e n t quantum of energy (i)  E  y  MeV  The quantamannihilates, producing an e l e c t r o n - p o s i t r o n  p a i r whose t o t a l k i n e t i c energy i s E y -1.02 MeV.  Both p o s i t r o n  and e l e c t r o n are assumed to l o s e a l l t h e i r energy t o the c r y s t a l . (ii)  The p o s i t r o n then a n n i h i l a t e s w i t h an e l e c t r o n , produc-  i n g two quanta each with energy 0.511 MeV. (iii)  Both the a n n i h i l a t i o n quanta may be absorbed by the c r y -  s t a l , only one may be absorbed with the other escaping, o r both may escape from t h e c r y s t a l . Hence, three peaks, designated P a i r I , P a i r I I , and P a i r I I I should appear i n the spectrum w i t h energies corresponding t o Ey (both a n n i h i l a t i o n quanta captured), E y - 0.511 MeV (only one a n n i h i l a t i o n quanttf/n captured) and t i o n quanta escape) r e s p e c t i v e l y .  - 1 . 0 2 MeV (both a n n i h i l a These peaks are i d e a l l y zero  width peaks, but due t o the f i n i t e r e s o l u t i o n of the counter they are subjected to the same c o n d i t i o n s of broadening as was i n d i -  15  cated f o r the p h o t o e l e c t r i c  peaks.  The r e l a t i v e heights of the three p a i r peaks depend c r i t i c a l l y on the dimensions of the c r y s t a l .  These r e l a t i v e heights can-  not be c a l c u l a t e d exactly as a f u n c t i o n of c r y s t a l dimensions but q u a l i t a t i v e l y , at l e a s t , some estimation can be made.  For example,  consider a c y l i n d r i c a l c r y s t a l whose dimensions are 3 cm. meter and  3 cm.  i n length.  Now  in dia-  i f i t i s assumed that a l l pairs  are produced and a n n i h i l a t e some^where along the a x i s of the s t a l or very close to i t ,  ( t h i s i s a f a i r assumption f o r  quanta energies up to 2 or 3 MeV  and f o r good c o l l i m a t i o n )  f o r an order of magnitude c a l c u l a t i o n i t may a n n i h i l a t i o n quanta have a 1 . 5  cm.  f o r e escaping from the c r y s t a l .  cry-  incident then  be assumed that a l l  path length on the average be-  Suppose i t i s f u r t h e r assumed  that i f an a n n i h i l a t i o n quantam s u f f e r s one  s c a t t e r i n g event i n  the c r y s t a l that i t i s then completely absorbed, otherwise i t escapes completely.  For a . 5 1 1 MeV  c i e n t i n Nal i s 0 . 3 4  cm~^.  quantum the absorption c o e f f i -  From t h i s value and the above assump-  t i o n s the f o l l o w i n g p r o b a b i l i t i e s f o r a p a i r of a n n i h i l a t i o n quant a can be found: (i) (ii) (iii)  P r o b a b i l i t y that both quanta escape =  0.36  P r o b a b i l i t y that only one quantum escapes = 0.4&* P r o b a b i l i t y that both quanta are absorbed =  Hence f o r these conditions  0.16  the three p a i r peaks should be i n the  ratio Pair I I I : Pair I I : Pair I = 0.36  : 0.1+B :  0.16  These three peaks, where the t o t a l area under them must be compat i b l e w i t h the cross-section  at the given energy, are  superimpos-  FIGURE VI Calculated pulse height d i s t r i b u t i o n f o r the 2.62 MeV gamma-ray of RdTh assuming a l l a n n i h i l a t i o n quanta escape. A r e s o l u t i o n of was assumed i n the c a l c u l a t i o n s . 500 Pair  III  Peak I..60 MEV  400 Compton Distrlbutin 1  i  300  UJ  200  <  tr  o z H Z  o  1 0 0  2.62 MEV Photopeak  u  1.0  3.0  2.0 ENERGY  IN  UNITS  OF  mc"  4.0 (i.e.  pulse  SO height)  6.0  16  ed upon the Compton and p h o t o e l e c t r i c resultant distributions.  At 0.511 MeV  d i s t r i b u t i o n s to g i v e the the a b s o r p t i o n i s mainly  by the Compton process,so that due to m u l t i p l e s c a t t e r i n g of the absorbed a n n i h i l a t i o n quanta,it would be expected t h a t there would be considerable broadening  of the P a i r I and P a i r I I peaks.  At high energies (e.g., > 10 MeV)  f u r t h e r broadening  effects  would r e s u l t from l o s s e s by brehmstrahling and by w a l l e f f e c t s . The rough c a l c u l a t i o n s presented above show t h a t the dimensions of the c r y s t a l are the most s i g n i f i c a n t f a c t o r i n determining p r e c i s e l y the d i s t r i b u t i o n due to p a i r production.  An i n -  crease i n o v e r a l l dimensions w i l l make P a i r I and P a i r I I the dominant peaks, and f o r very large dimensions only P a i r I should be significant.  For very small c r y s t a l s ( i . e . " d i s c " c r y s t a l ) only  P a i r I I I would be s i g n i f i c a n t , but i n t h i s case w a l l e f f e c t s are very important and considerable spreading of the d i s t r i b u t i o n due to t h i s e f f e c t would be probable.  Since no rigorous c a l c u l a t i o n  has been made f o r the r e l a t i v e heights of the three peaks the only diagram on the p a i r process F i g . ( VI ) i s constructed assuming t h a t only the P a i r I I I peak occurs" ( i . e . l i m i t i n g case f o r s m a l l crystals). D.  THE CALCULATED SPECTRUM SHAPE I t has been shown t h a t , assuming primary events only, and  n e g l e c t i n g other broadening  e f f e c t s each of the absorption proces-  ses give r i s e to a c h a r a c t e r i s t i c pulse height d i s t r i b u t i o n .  The  r e l a t i v e number of pulses f o r a given gamma-ray energy due t o each process can e a s i l y be found from t h e i r r e l a t i v e c r o s s - s e c t i o n s , i . e . , the r a t i o of the areas under the d i s t r i b u t i o n s must  FIGURE V I I Calculated pulse height d i s t r i b u t i o n s f o r gamma-ray energies 0.511 MeV and 1.28 MeV. The curves c a l c u l a t e d assuming p r i mary processes only and a r e s o l u t i o n of 10$.  FIGURE V I I I  x  be equal t o the r a t i o of the c r o s s - s e c t i o n s .  7  On t h i s b a s i s , the  expected pulse height d i s t r i b u t i o n has been c a l c u l a t e d f o r i n c i dent gamma-ray energies of 0.511 MeV, 1.28 MeV, and 2.62 MeV. The  f i r s t two d i s t r i b u t i o n s were c a l c u l a t e d assuming 10 percent  r e s o l u t i o n , and the t h i r d assuming 8" percent r e s o l u t i o n . d i s t r i b u t i o n s are shown i n F i g . (VI) and (VEI).  These  The pulse height  f\C\  d i s t r i b u t i o n .for the Co  gamma-rays (1.7 and 1.33 MeV i n cascade)  has a l s o been c a l c u l a t e d , assuming 10 percent r e s o l u t i o n , and i s shown i n F i g . ( V I I ) . The  c a l c u l a t e d d i s t r i b u t i o n s mentioned above hold only i n the  l i m i t i n g case of very small c r y s t a l s . are increased  As the c r y s t a l dimensions  these d i s t r i b u t i o n s w i l l only be an approximate i n -  d i c a t i o n of the shape.  The e f f e c t s of c r y s t a l dimensions and mul-  t i p l e s c a t t e r i n g w i l l be considered i n the next s e c t i o n . E.  MULTIPLE SCATTERING Figures ( V I ) , and (VII), and (VLLT) show t h e spectrum shape  c a l c u l a t e d on the assumption that m u l t i p l e s c a t t e r i n g events do not occur.  This assumption i s i d e n t i c a l t o the assumption that  the c r y s t a l i s very s m a l l .  Since experimentally,  the c r y s t a l s  are of f i n i t e dimensions, i t can be expected that with  increasing  dimensions m u l t i p l e s c a t t e r i n g events w i l l become more prominent. M u l t i p l e s c a t t e r i n g events play a n e g l i g i b l e r o l e i n the d i s t r i b u t i o n from the p h o t o e l e c t r i c e f f e c t (aside from the p o s s i b i l i t y of an escape peak and a 29 KeV peak mentioned e a r l i e r ) .  If  brehmstrahlung i s construed as a m u l t i p l e s c a t t e r i n g event, then at high energies t h i s e f f e c t w i l l become apprecistie, and pulses  18  w i l l be l o s t from the photopeak due to escape of radiation.  brehmstrahlung  This e f f e c t can be neglected except at f a i r l y high  energies. (>10  MeV)  The presence of three peaks i n the p a i r production d i s t r i b u t i o n has been demonstrated p r e v i o u s l y . The dependence of the r e l a t i v e heights of these peaks on the dimensions of the c r y s t a l has been i n d i c a t e d but no q u a n t i t a t i v e estimations have been made. The l a r g e s t c o n t r i b u t i o n to m u l t i p l e s c a t t e r i n g comes from the Compton process where a secondary quantum i s produced i n every collision.  Q u a l i t a t i v e l y , i t would be expected that many pulses  from t j i e region of the Compton peak w i l l be transferred t o the photopeak due to the capture of the s o f t back-scattered quanta. For example, again consider a c y l i n d r i c a l c r y s t a l 3 cm. i n d i a meter and 3 cm. i n length and a c o l l i m a t e d beam o f , say, MeV  gamma-rays i n c i d e n t upon i t .  be of the order of 300  KeV.  1.28  The back-scattered quanta w i l l  Assume t h a t a l l these quanta o r i g i n -  ate uniformly along the a x i s of the c r y s t a l , ( t h i s assumption i s v a l i d w i t h i n the accuracy d e s i r e d since the h a l f thickness i n Nal for  1.28  MeV  gamma-rays i n 4.3  cm.)  path l e n g t h of the quanta i s 1.5 c o e f f i c i e n t 0.6  cm""-*- f o r 300  cm.  and t h a t the average escape Then from the absorption  KeV quanta see F i g . (IV ) approxima-  t e l y 60% of the back-scattered quanta are absorbed, mostly the p h o t o e l e c t r i c process.  through  On t h i s simple c a l c u l a t i o n i t would  be expected that approximately 60% of the pulses i n the Compton peak would be s h i f t e d upwards to some extent.  A l l other quanta  which are s c a t t e r e d in a d i r e c t i o n other than back w i l l be subject to the same c o n s i d e r a t i o n s but with a correspondingly smaller e f -  19  feet.  Consequently, the photopeak w i l l have added to i t very  many pulses from the Compton d i s t r i b u t i o n .  Experimentally  been found that the photopeak i s much l a r g e r than the  i t has  cross-sec-  t i o n would i n d i c a t e , where the increase i s roughly i n agreement w i t h the above c a l c u l a t i o n s . These r e s u l t s w i l l be described  later  i n the s e c t i o n on experimental r e s u l t s . I t i s quite obvious from these arguments that there are  two  l i m i t i n g cases: (i)  Very small c r y s t a l s where a l l degraded quanta escape.  These c a l c u l a t i o n s have been c a r r i e d out e x p l i c i t l y i n the preceding  sections. (ii)  Very large c r y s t a l s where a l l the degraded quanta are  completely absorbed and the r e s u l t a n t d i s t r i b u t i o n c o n s i s t s of only one peak corresponding to the f u l l energy of the i n c i d e n t gamma-ray. As the c r y s t a l dimensions are v a r i e d from very small to very large between these two l i m i t s , t h e r a t i o of Compton peak height to photopeak height should decrease s t e a d i l y to zero.  The  cry-  s t a l dimensions which give the best r e s o l u t i o n cannot be p r e d i c ted unless the above c a l c u l a t i o n s are c a r r i e d out e x a c t l y . dimensions are determined experimentally  These  as w i l l be described i n  the s e c t i o n on experimental r e s u l t s . Whenever p o s s i b l e , experiments have been done using a p r e c i s e l y c o l l i m a t e d beam to reduce the broadening e f f e c t s of m u l t i p l e scattering.  I t i s quite easy to see how an uncollimated  beam would  r e s u l t i n very poor r e s o l u t i o n by assuming i n the argument above that scattered quanta could o r i g i n a t e at any point w i t h i n the c r y -  20 stal.  R. Hofstadter (2 ) has demonstrated very f o r c i b l y the e f -  f e c t of c o l l i m a t i o n  on the  resolution.  »  F.  RESOLUTION OF THE SCINTILLATION COUNTER The s t a t i s t i c a l spread i n the pulse height d i s t r i b u t i o n of a  s c i n t i l l a t i o n counter i s influenced by the f o l l o w i n g (i)  factors:  The number of photons emitted by the phosphor,  (ii)  The number of photons t r a n s m i t t e d to the  (iii)  The quantum e f f i c i e n c y of the  Xiv)  photocathode.  photocathode.  The number of photoelectrons reaching the f i r s t dynode.  (v)  The secondary emission r a t i o of the dynodes.  Each of these f a c t o r s has a s s o c i a t e d w i t h i t a s t a t i s t i c a l uncertainty.  P.W.  Roberts has deduced an expression ( 9  gives the spread of the d i s t r i b u t i o n due to these  ).which  uncertainties.  This expression i s  t  C=  where  f r a c t i o n a l variance i n pulse height d i s t r i b u t i o n  NI = number of photons emitted by the phosphor & = variance of N m i = gain of the f i r s t m  stage  - gain of each succeeding  stage  Bi = variance of the secondary emission r a t i o of the f i r s t stage S = variance of the secondary emission r a t i o of each succeeding stage 2  variance = (standard d e v i a t i o n ) f- = f r a c t i o n of photons t r a n s m i t t e d t o the photocathode  21 -/» = quantum e f f i c i e n c y o f the photocathode ^ = f r a c t i o n of photoelectrons which reach the f i r s t dynode A b i n o m i a l d i s t r i b u t i o n was assumed i n c a l c u l a t i n g the e f f e c t s of the f a c t o r s f , p, and q, and the expression has been a p p r o x i mated to the case of a l a r g e number of dynode stages. Equation (1) can be r e w r i t t e n R  =  J  where R  2  5 * | ^ J ? )  (  = [width of peak a t h a l f max. (MeV)] \ energy of peak (MeV) /  2  = (2 x 1.18 <S~)  2  )  2  The numerical f a c t o r i s t h a t one which converts the standard dev i a t i o n of.a Gaussian i n t o the f u l l width at h a l f maximum. » • *(•#-')  E = energy o f peak i n MeV _ N^Pfr—  _  n u m D e r  0  f photoelectrons per MeV reaching  the f i r s t dynode I f the number of photons per MeV produced by the i n c i d e n t gamma-ray i s assumed to f o l l o w a Poisson d i s t r i b u t i o n then the term A becomes zero. in  However, A has been found t o be non-zero,  most cases, but very small, so i t i s l e f t as a parameter to be  determined by experimental r e s u l t s .  This term, then, represents  the spread of the d i s t r i b u t i o n due t o non-uniform  response of the  crystal. Since the term A has been found to be very s m a l l , the second term only of equation (2) need be considered.  22 Then  a R  ~  s. £  I f the p h o t o m u l t i p l i e r gain per stage i s assumed t o be 3 , then B. i s approximately 4 / 3 . For an i n c i d e n t energy, say, o f 1 MeV  I t i s quite obvious that n, the e f f e c t i v e number of photoelectrons produced at the photocathode per MeV, determines the u l t i m a t e r e s o l u t i o n a t t a i n a b l e with the counter, e.g.  i f n = 500 then R ^ 12.2% I f n = 1000 then R »  3.7$  For a given c r y s t a l and p h o t o m u l t i p l i e r tube the only f a c t o r of which can be increased i s f , the f r a c t i o n of the photons which reach the photocathode.  I t i s e s s e n t i a l , then, that e f f i c i e n t  c r y s t a l mounting^ techniques are developed.  23  III.  CRYSTAL MOUNTING TECHNIQUES  I t has been shown that the l a r g e s t s i n g l e gain i n r e s o l u t i o n , aside from improved c r y s t a l s and p h o t o m u l t i p l i e r photocathode e f f i c i e n c i e s , can be obtained by improved c r y s t a l mounting techniques.  Considerable work has been done on improving the e f f i -  ciency of l i g h t c o l l e c t i o n of the mounts. Sodium i o d i d e c r y s t a l s are very deliquescent, the surfaces immediately  becoming d i s c o l o u r e d on contact with the water vapour  i n the atmosphere, so that any mount designed f o r the c r y s t a l must provide p e r f e c t p r o t e c t i o n against water vapour.  The  ori-  g i n a l method of mounting used by the author consisted of immersing the c r y s t a l i n a c l e a r , water f r e e , mineral o i l i n a l i g h t t i g h t aluminum c o n t a i n e r .  This container was h i g h l y polished on  the i n s i d e , and the o i l contact between the c r y s t a l and the cont a i n e r provided the necessary o p t i c a l coupling f o r optimum r e f l e c tion efficiency.  The o i l f i l m a l s o acted as a preservative f o r  the o p t i c a l p r o p e r t i e s of the c r y s t a l surfaces.  The r e s o l u t i o n  obtained with mountings of t h i s type was never very good. For mountings of t h i s type G i l l e t t e has shown (10) that the entrapment of l i g h t due to F r e s n e l r e f l e c t i o n s c o n s t i t u t e s a very serious l o s s i n the transmission of l i g h t to the photocathode. I t i s a l s o shown t h a t the transmission i s increased many times by using some form of d i f f u s e r e f l e c t i o n at the surfaces of the c r y stal.  Consequently, a method of c r y s t a l mounting was sought which  provided t h i s necessary R.K.  property.  Swank has reported (5 ) a method of mounting c r y s t a l s  PLATE I THE DRY BOX  24  u s i n g the h i g h l y e f f i c i e n t , d i f f u s e r e f l e c t i n g p r o p e r t i e s of powdered magnesium oxide.  This method r e q u i r e s that the c r y s t a l s  be mounted dry ( i . e . , completely f r e e from a l l t r a c e s o f o i l i n which they are stored) since the r e f l e c t i n g p r o p e r t i e s o f the magnesium oxide are destroyed i f t h e powder becomes "matted" with oil.  This has made the design and c o n s t r u c t i o n o f a "dry box" nec-  essary so t h a t a l l mounting operations can be c a r r i e d out in. a dry atmosphere, thus preventing the surfaces of the c r y s t a l from being d i s c o l o u r e d due t o contact with moisture.  The magnesium  oxide, i t s e l f , i s s l i g h t l y deliquescent so that i t must be baked for  s e v e r a l hours a t about 500°C before i t i s used.  A.  THE DRY BOX The "dry box" i s a large metal box, o f dimensions 3 0 " wide x  18"  deep x 2 0 " h i g h .  I t has a s l o p i n g f r o n t window 27" x 11" made  of p l e x i g l a s s . Construction i s o f aluminum sheet throughout, a l l j o i n t s are butt welded, and the whole enclosure i s made a i r - t i g h t . An a i r - t i g h t door i s provided on one side o f the box t o permit m a t e r i a l s t o be conveniently placed i n s i d e .  I l l u m i n a t i o n i s pro-  vided by a s m a l l , 15 watt f l u o r e s c e n t tube i n s i d e the box.  The  box contains a f l a t , removable t r a y 8" long x 11" wide x 1/2" deep i n which i s placed a mixture of sand and phosphorous pent o x i d e as the d r y i n g agent.  A small a i r blower i s so l o c a t e d that  the atmosphere w i t h i n the box i s c o n t i n u a l l y c i r c u l a t e d over the d r y i n g agent.  A Moisture i n d i c a t o r i s placed i n s i d e the box.  valves a r e s u p p l i e d , one on each end o f the box,  Two  so t h a t a c o n t i n -  uous flow of d r i e d nitrogen may be passed through the box.  This  2  5  ThiO' serves the purpose of sweeping out any organic vapours which may have accumulated due t o the f i n a l c r y s t a l p o l i s h i n g process c a r r i e d out i n s i d e the box. of the c r y s t a l q u i c k l y become  This i s necessary  since the surfaces  clouded on contact with most organ-  i c vapours. Work i s done i n the box through long sleeve rubber gloves which enter through glove ports i n the f r o n t panel.  The ends of  the gloves are attached t o these ports by an a i r t i g h t s e a l , but may r e a d i l y be removed and replaced. The d e t a i l s o f c o n s t r u c t i o n of the box are shown i n Plate.I B.  .  CRYSTAL MOUNTS The mounting f o r a sodium i o d i d e c r y s t a l must s a t i s f y the f o l -  lowing three (1)  requirements:  The gamma-rays must enter the c r y s t a l with l i t t l e absorp-  t i o n or s c a t t e r i n g . (2)  The f l u o r e s c e n t l i g h t must be extracted with a uniformly  high e f f i c i e n c y from a l l parts of the c r y s t a l . (3)  The mount must be l i g h t t i g h t and impervious t o water  vapour. (4)  O p t i c a l coupling t o photocathode of p h o t o m u l t i p l i e r must  be good. In a d d i t i o n , such obvious requirements as ruggedness and i n s e n s i t i v i t y t o o r i e n t a t i o n and temperature v a r i a t i o n s must be met. The f i n a l design, with which most of the r e s u l t s have been obt a i n e d , consisted of an aluminum container with a l u c i t e window. S u f f i c i e n t space i s l e f t between the c r y s t a l and the container so  FIGURE IX  Rubb  Mount f o r the c y l i n d r i c a l c r y s t a l drawn t o scale. The mount i s o p t i c a l l y coupled t o the photomultip l i e r tube with D.G. 200 s i l i c o n e ' o i l , and held i n place by a r i n g which f i t s i n the r e t a i n i n g r i n g groove.  FIGURE X  Al. Nal  foil top  held  in place  Rectangular  retaining  hold  ring  container  black  Duco paint  Crysta  I  Al.  with  with  Al.  flanged  foil  container  bottom  to  in  place Black Lucite  cylinder  D.C.200  Silicone  Duco  paint  oil  Mount f o r the rectangular c r y s t a l drawn t o s c a l e . The mount i s attached t o the p h o t o m u l t i p l i e r tube with black e l e c t r i c a l scotch tape using D.C. 200 s i l i c o n e o i l f o r o p t i c a l coupling.  FIGURE XI  Lucite  cylinder  Mount f o r the t h i n c y l i n d r i c a l c r y s t a l drawn to s c a l e . The mount i s attached t o the photo m u l t i p l i e r tube w i t h black e l e c t r i c a l scotch tape. Any places which may leak l i g h t are painted with black Ducco p a i n t .  26 that powdered magnesium oxide may be packed i n to form a r e f l e c t ing s u r f a c e .  The c r y s t a l i s o p t i c a l l y coupled to the l u c i t e win-  dow by the use of D.C. stokes v i s c o s i t y ) •  200 (Dow Corning) s i l i c o n e o i l (10^ c e n t i -  Movement of the c r y s t a l i s prevented by a l u -  c i t e p o s i t i o n i n g r i n g ( i n mounts f o r c y l i n d r i c a l c r y s t a l s only) and by t i g h t packing of the assembly. This basic design has been adapted f o r mounting three types of  crystals: (1)  Cylindrical  crystals.  (2)  Rectangular c r y s t a l s .  (3)  Thin "wafer"  crystals.  The d e t a i l s of the design of the mounts f o r each type of c r y s t a l are shown i n F i g . ( I X ), ( X  ), and ( X I ) r e s p e c t i v e l y .  Data par-  t i c u l a r t o each design are shown on the F i g u r e s . C.  DETAILS OF TECHNIQUE A l l rough p o l i s h i n g of the c r y s t a l i s done outside the dry  box.  This i s c a r r i e d out by using white b l o t t i n g paper soaked  i n acetone as the a b r a s s i v e s u r f a c e . A f t e r being rubbed on t h i s surface s e v e r a l times the c r y s t a l i s t r a n s f e r r e d to a piece of b l o t t i n g paper soaked i n mineral o i l on which i t i s rubbed t o r e move a l l t r a c e s of acetone.  This process i s repeated s e v e r a l times  u n t i l the surfaces of the c r y s t a l are q u i t e c l e a r .  The  crystal  i s then placed i n a bath of mineral o i l to preserve i t s s u r f a c e s . I t i s then t r a n s f e r r e d to the dry box, along w i t h the other t h o r oughly d r i e d out components.  A two hour "drying-out" time i s a l -  lowed so that the atmosphere w i t h i n the box can become thoroughly  27  dry.  The c r y s t a l i s then removed from i t s o i l bath, i t s surfaces  wiped completely f r e e of a l l t r a c e s of o i l , and i f necessary i s given a f i n a l p o l i s h i n g .  This i s done by "dry" p o l i s h i n g the  c r y s t a l on b l o t t i n g paper.  I t has seldom been found necessary  that f u r t h e r p o l i s h i n g w i t h organic s o l v e n t s i s required once the c r y s t a l i s placed i n the dry box. i n case t h i s i s necessary. are  However, p r o v i s i o n i s made  A f t e r the f i n a l p o l i s h i n g , the mounts  assembled, and any j o i n s i n the mount which may leak moisture  i n t o the c r y s t a l are covered w i t h a t h i n l a y e r of p a r a f f i n wax. These j o i n s are then painted over w i t h black "Due$o" paint t o form a permanent j o i n .  The mountings are then removed from the  box and attached t o the p h o t o m u l t i p l i e r tube, u s i n g D.C. 200 •technique  s i l i c o n e o i l as the o p t i c a l couple*  With t h i s arrangement and  the dry MgO, c r y s t a l s remain c l e a r and the ,ps^£orffiaa&e has not v a r i e d over a three month p e r i o d .  2%  IV.  THE GAMMA-RAY SPECTROMETER  I t has been shown ( 11) that a pulse amplitude d i s t r i b u t i o n curve obtained w i t h a d i f f e r e n t i a l analyzer i s subject to a small e r s t a t i s t i c a l u n c e r t a i n t y than the curve obtained by d i f f e r e n t i a t i n g an i n t e g r a l b i a s curve.  Hence, the simplest d i f f e r e n t i a l  analyzer was used f o r t h i s work, a "Single Channel K i c k s o r t e r " , i n which o n l y those pulses which l i e above a " b a s e l i n e " voltage and w i t h i n a "window" immediately above i t are counted.  E i t h e r the base  l i n e and window voltages can be adjusted separately, or as i s usu a l f o r most of the work of t h i s t y p e , i t i s more convenient to set the window width and s h i f t the b a s e l i n e . There are two main types of experiments which can be done with t h i s equipment: (a)  Experiments i n v o l v i n g bombardment of t a r g e t m a t e r i a l s  w i t h a c c e l e r a t e d p a r t i c l e s i n which case one has to use e i t h e r the i n t e g r a t e d t a r g e t current as a monitor, or a separate gamma-ray monitor as a r e f e r e n c e , or perhaps both. (b)  Experiments i n v o l v i n g the measurement of gamma-ray spec-  t r a from r a d i o a c t i v e sources of reasonably constant or slowly decaying a c t i v i t y . Most of the author's work consisted of experiments of the type ( b ) . For t h i s purpose the b a s e l i n e of the k i c k s o r t e r was d r i v e n a t a constant r a t e (with a f i x e d window width) by a synchronous motor through acsystem of gears.  The gear system i s so designed t h a t  three d r i v i n g speeds are p o s s i b l e (1 v o l t / 3 6 s e c , 1 v o l t / l min. 12 s e c , 1 v o l t / 6 min.).  The k i c k s o r t e r output  pulses are fed  FIGURE XII  H.T. Power Supply  P.M.  Preomp.  Scope  BLOCK  Pre—amp Power Supply  Pulse  Count  Height  Rate  Analyzer  Meter  Power Supply  Scaler  DIAGRAM  OF  THE  SPECTROMETER  Brown Pen Recorder  FIGURE  XIII  H,T. POWER. SUPPLY 2SOOV.  MAX.  29  i n t o a l i n e a r count r a t e meter, and the counting r a t e i s recorded on a "Brown" r e c o r d i n g potentiometer.  A block diagram of the sys-  tem i s shown i n F i g . (XEE). I t has been found t h a t f o r t h i s method t o give r e l i a b l e r e s u l t s the lowest counting r a t e ( f o r a given channel width) t h a t could be t o l e r a t e d was of the order of 1 0 counts per second.  In  any experiment the window width was set so t h a t t h i s minimum counti n g r a t e was always exceeded, with the added c o n d i t i o n t h a t the narrowest peak i n the d i s t r i b u t i o n should be at l e a s t three channels wide.  Measurements i n v o l v i n g very weak i n t e n s i t i e s cannot be  done by t h i s "continuous  d r i v e " method, and f o r these cases manual  operation of the k i c k s o r t e r would be  necessary.  A d e s c r i p t i o n of each element of the spectrometer,  along with  the operating c h a r a c t e r i s t i c s are given below. A.  H.T.  POWER SUPPLY  The gain of the p h o t o m u l t i p l i e r tube i s very s e n s i t i v e t o the voltage a p p l i e d across i t . type  6262)  I n the type of tube used (E.M.I,  the gain was found to increase by  tage change of 5 0 V.  50  percent f o r a v o l -  Consequently, a voltage supply of exception-  a l l y long term s t a b i l i t y i s r e q u i r e d .  A supply has been construc-  ted whose measured long term s t a b i l i t y was b e t t e r than 0 . 1 percent. The supply i s e l e c t r o n i c a l l y s t a b i l i z e d using a 1 5 0 V. b a t t e r y as reference and i s capable of d e l i v e r i n g volts.  10  m i l l i - a m p s . at  The c i r c u i t diagram i s shown i n F i g .  (xm).  2000  30 B.  COUNT-RATE METER AMD HEAD AMPLIFIER POWER SUPPLIES Both these s u p p l i e s are commercially b u i l t u n i t s obtained  from the "Lambda E l e c t r o n i c s " Corporation, and are designated "Model 2 8 " . A negative " r a i l " capable of d e l i v e r i n g 10 mill.-amps, at minus 150 v o l t s has been b u i l t i n t o each u n i t .  Both these sup-  p l i e s , and the H.T. supply are d r i v e n from a constant-voltage mains transformer. C.  OSCILLOSCOPE A model 5HD " T e t r o n i x " o s c i l l o s c o p e was used f o r i n v e s t i g a t -  i n g pulse shapes and s i z e s a t various points i n the c i r c u i t .  No  q u a n t i t a t i v e measurements were made with i t , and i t was used s o l e l y f o r convenience i n " s e t t i n g up" the apparatus. D.  THE PHOTOMULTIPLIER TUBE An E.M.I, type 6262 fourteen stage m u l t i p l i e r was used f o r  a l l the experiments.  The tube was operated between 1000V and  1400V depending on the spectra being i n v e s t i g a t e d .  The noise  background was found t o be n e g l i g i b l e a t a l l v o l t a g e s , but when measurements on gamma-rays of energy l e s s than 10 KeV were attempt e d the noise becomes overwhelming.  The maximum gain of these  m u l t i p l i e r s i s of the order o f 10? and the output was found t o be l i n e a r f o r pulses up t o 30 v o l t s a t l e a s t .  The s i g n a l was  taken from the l a s t dynode and not the f i n a l c o l l e c t o r since a p o s i t i v e pulse was r e q u i r e d t o d r i v e the a n a l y z e r . E.  THE PRE-AMPLIFIER The p r e - a m p l i f i e r c o n s i s t s of a cathode f o l l o w e r stage only  FIGURE  XIV  H.T. +.OOI  4:  OOI = ±  .390K  H.T. + 2 Q O V •500K  V/////DI2 ;500K  68O K  5500K  Collector  .Ol 6J6  From analyzer  .1  1/2 6 J 6  To .count rate meter  1/2 6 J 6  - W \ A 4 - 30K V C Ij  82K  p3 >47K  I Meg  -f pulses  PRE-AMPLIFIER  IOK  <5K 25  A\\\\\DI3 ,OOl=j=  200 V  •IOK  SCHMITT  CIRCUIT  INPUT  TO  COUNT-RATE  METER  31  (see F i g . (XIV)) f o r feeding i n t o a 100 ohm l i n e .  No a m p l i f i e r  stage was included since i t was f e l t t h a t the pulses a v a i l a b l e from the p h o t o m u l t i p l i e r tube were s u f f i c i e n t l y large f o r analyzi n g purposes. F.  THE SINGLE CHANNEL ANALYZER The analyzer i s a commercially b u i l t u n i t supplied by the  Atomic Instrument  Company, and designated "Model 5 1 0 " .  The operat-  i n g c h a r a c t e r i s t i c are given i n the pamphlet e n t i t l e d "Interim I n s t r u c t i o n Manual, Model 510 S i n g l e Channel Pulse Height Analyzer" obtainable from the Atomic Instrument  Company. The operating char-  a c t e r i s t i c s o f the analyzer were found t o be q u i t e adequate f o r handling the pulses obtained from a N a l ( T l ) s c i n t i l l a t i o n ( r i s e time  & 0.25 sec).  counter  The analyzer i s capable of handling p u l -  ses up t o 100 V maximum, and has a maximum window width of 7.5 V. The maximum pulse input r a t e i s 2500 c p s .  ( f o r 5f? l o s s ) .  G. THE COUNT RATE METER Elmore and Sands ( 12 ) give the theory of the operation of a count r a t e meter.  A d i s c u s s i o n of the l i n e a r i t y i s given and an  expression i s deduced f o r the f r a c t i o n a l probable e r r o r i n the counting r a t e .  I  This expression i s 6 = o.&7 j  where  n = average counting r a t e RC  = i n t e g r a t i n g time constant  Cooke-Yarborough has designed  ( 13 ) a count r a t e meter which  uses a 100% feedback D.C a m p l i f i e r t o ensure l i n e a r i t y .  A model  was b u i l t t o t h i s c i r c u i t and found to be l i n e a r t o b e t t e r than  .FIGURE  COUNT  RATE  X V  METER  TABLE I. Counting Rate f.s.d. 1 0 5  c.p.s.  Time Constant ( S ec) 4.8  X  24'  X  1 2 0  X  4 8 0  X  4S  c.p.s.  2 4 0  X X  10-3  10-3 10-3 10-3  10-3 10-3  c.p.s.  io  2  c.p.s.  10  c.p.s.  11  3.0 1.5 0.6 0.3  3.0 1.5  0.6 0.3  1.2 4.8  1C-3  % P.E. at H a l f Scale d e f l e c t i o n  4 8  X  2 4 0  X  10-3 10-3  1 0 . 0  5.0  1.2  2.0  4.8  1.0  0.2  1 5 . 0  1.0  6.7  5.0  3.0  2 0 . 0  1.5  0.2  47.0  1.0  2 1 . 0  5.0  1 0 . 0  2 0 . 0  5.0  This t a b l e shows the percent probable e r r o r f o r the count-rate meter at various counting rates and time constants.  32  one percent and t o possess excellent long time s t a b i l i t y .  The c i r -  c u i t diagram i s shown i n F i g . ( X V ) . The count r a t e meter has s i x ranges, from 1 c.p.s. t o 1 0 ^ c.p.s., w i t h v a r i a b l e time cons t a n t s f o r each range.  Table I shows the percent probable e r r o r  f o r the v a r i o u s time constants f o r each range. In h i s r e p o r t , Cooke-Yarborough  gives a d e t a i l e d a n a l y s i s of  the  c i r c u i t , and o u t l i n e s the procedure f o r "setting-up" the meter.  H.  THE BROWN RECORDER A Brown d i r e c t reading potentiometer Model  to record the output of the count r a t e meter.  No.153X12  i s used  Pulse height d i s t r i b u t i o n f o r RaD and E u ^ the t h i n c y l i n d r i c a l c r y s t a l . 1  obtained w i t h  33 V. EXPERIMENTAL RESULTS The pulse height d i s t r i b u t i o n s f o r the gamma-rays of Eu-^5^ RaD,  Na , Zn^ 22  and RdTh have been obtained with d i f f e r e n t s i z e  c r y s t a l s with a view to comparing the experimentally obtained , shapes with the c a l c u l a t e d shapes.  These d i s t r i b u t i o n s have  a l s o been used to determine the c o n d i t i o n s under which optimum r e s o l u t i o n i s obtainable with t h i s technique and to c a l c u l a t e from the s t a t i s t i c a l formula f o r r e s o l u t i o n  (equation (2)), page  6) the e f f e c t i v e number of photoelectrons produced at the photocathode per MeV of i n c i d e n t  energy.  The d i s t r i b u t i o n s f o r each source are considered i n d e t a i l below.  The c r y s t a l s w i t h which the d i s t r i b u t i o n s were obtained  are designated #1, #2, and #3 f o r the t h i n c r y s t a l (1/6*" t h i c k ness, 1-3/4" diameter), the 3/4" x 3/4" x 1-1/2" block, and the 1/2" cube A.  RaD AND  respectively. Eu  1 5 5  The d i s t r i b u t i o n s f o r these two sources are shown i n F i g . (XVI) and were obtained with c r y s t a l #1.  In the r e g i o n below  20 KeV the r e s o l u t i o n i s very poor, approximately 100%, so that the p r e c i s e determination of energy i s impossible.  From 20 KeV  upward, the r e s o l u t i o n r a p i d l y improves and i s about 50% f o r the 85 KeV l i n e i n Europium.  The c r y s t a l container was made as t h i n  as p o s s i b l e (see F i g . (X! )) to increase the d e t e c t i o n e f f i c i e n c y f o r low energy (<20  KeV) quanta.  The mounting technique f o r  t h i s case was very d i f f i c u l t and u s u a l l y r e s u l t e d i n a l o s s of e f f i c i e n c y of l i g h t c o l l e c t i o n and hence poorer r e s o l u t i o n .  More  34 work i s being done to improve this technique, and by sacrificing some detection efficiency i t should be possible to improve the resolution. The relatively large 13 KeV peak in the RaD  distribution shows  the detection efficiency possible in this region. resolution i t may  With better  be possible to resolve the escape peak which  should appear at approximately 17 KeV.  This would probably show  as a change of slope or a "bump" on the high energy side of the 13 KeV peak. ~"  The distribution for Eu-^5  shows the presence of the well  known gamma-ray at #5 KeV and of a 40 KeV X-ray resulting from K- conversion de-excitation of the #5 KeV  level in Gadolinium.  The 100 KeV gamma-ray has not yet been resolved, but with the possible increase in resolution mentioned above and by manual operation of the Kicksorter baseline so that improved statistics are possible, the peak should appear.  The distribution also  shows the presence of a peak at 10 KeV which i s presumably the escape peak due to photoelectric  absorption of the 40 KeV X-ray.  Mateosian and Smith (8) indicate a method of calculating the i n tensity of this peak.  However, since no attempt has yet been  made to measure absolute intensities, relative intensities, or conversion coefficients this calculation has not been carried through.  If experiments of this type are to be done a  correction  for the wall effect in this thin crystal must be made. An examination of Fig. (XVI) amount of non-linearity  shows that there exists a small  of response.  If the RaD  distribution i s 155 used as the calibration curve,it can be seen that the Eu dis-  35  t r i b u t i o n i s s h i f t e d a small amount ( & 5%) i n the low energydirection.  The r a p i d d e t e r i o r a t i o n of the MgO  r e f l e c t i n g sur-  face and hence the decrease i n l i g h t c o l l e c t i o n e f f i c i e n c y i s assumed t o be r e s p o n s i b l e f o r t h i s n o n - l i n e a r i t y , s i n c e considerable time elapsed between the runs on the two sources.  As has  been i n d i c a t e d above, f u r t h e r work i s i n progress to improve the technique i n t h i s energy region and i t i s f u l l y expected that the n o n - l i n e a r i t y w i l l be removed. Mateosian and Smith (8) describe a method obtaining A  spectra,  both gamma and beta, by using a sodium i o d i d e c r y s t a l which cont a i n s a small quantity of the source under i n v e s t i g a t i o n as an impurity.  This method removes the d i f f i c u l t i e s introduced by  the absorption of gamma-rays ( or beta p a r t i c l e ) i n the c r y s t a l container, and i n cases where source t h i c k n e s s i s important, a source of e f f e c t i v e l y zero thickness i s obtained.  In experiments  where t h i s i s not f e a s i b l e i t i s p o s s i b l e to place the source i n d i r e c t contact w i t h the c r y s t a l , both source and c r y s t a l being;, enclosed by the c o n t a i n e r . B.  Na  22  *  22  The spectrum of Na 0.511  c o n s i s t s of a 1.28  MeV a n n i h i l a t i o n r a d i a t i o n .  MeV gamma-ray and a  F i g . (VII) shows the  expected  pulse height d i s t r i b u t i o n f o r these two energies on the assumpt i o n that only primary processes occur.  The r a t i o s of the Compton  peak height to the photopeak height are 0.92 and 3 . 6 f o r the 0.511 MeV and 1.28 MeV r a d i a t i o n s r e s p e c t i v e l y . F i g s . (XVII) and (XVIII) show the experimentally observed  F I G U R E X V I I  500  O  5  IO  15 PULSE  20 HEIGHT -  25 VOLTS  30  35  FIGURE X V I I I  COUNTING RATE Arbitrary Units  O  5  IO  15  20  25 PULSE  30 HEIGHT  35 VOLTS  36  d i s t r i b u t i o n obtained with c r y s t a l s #2 and #3 r e s p e c t i v e l y . Both of these curves have an intense low energy (^r250 KeV) peak with the high energy side c o n s i s t i n g of two components o f d i f f e r e n t slope.  I t has been assumed that the point at which  t h i s change of slope occurs on each curve corresponds to the peak of the Compton d i s t r i b u t i o n .  The majority of the counts i n  these peaks, however, are assumed to be caused by back-scattered quanta (# 250 KeV f o r 1 MeV r a d i a t i o n ) o r i g i n a t i n g i n the w a l l s of the c r y s t a l mounting, the p h o t o m u l t i p l i e r tube, and surrounding o b j e c t s .  This second assumption can be supported by the f o l -  lowing experimental evidence: (i)  A peak of approximately 250 KeV appeared i n a l l the d i s -  t r i b u t i o n s whenever high energy (y 500 KeV) gamma-rays were present • (ii)  C o l l i m a t i o n of the i n c i d e n t beam reduced the irtensity  of the peak and changed i t s shape, but never e l i m i n a t e d i t . (iii)  Without c o l l i m a t i o n the peak shape could be changed con-  s i d e r a b l y (but not the r e l a t i v e i n t e n s i t y very much) by changing the p o s i t i o n of the source.  Under s i m i l a r conditions the Compton,  and p h o t o e l e c t r i c d i s t r i b u t i o n s always remained constant i n shape and r e l a t i v e i n t e n s i t y . (iv)  With s i m i l a r source geometry, the peak took on d i f f e r e n t  shapes f o r c r y s t a l s of d i f f e r e n t dimensions but, again, the Compton and p h o t o e l e c t r i c d i s t r i b u t i o n s remained e s s e n t i a l l y the same Aside from t h i s r a t h e r intense low energy peak the shape of the d i s t r i b u t i o n i s roughly that expected from previous considerations.  The r e l a t i v e i n t e n s i t i e s of the Compton and phtopeaks  37  has been shown to be c r i t i c a l l y dependent on c r y s t a l dimensions as the r e s u l t of m u l t i p l e s c a t t e r i n g  events.  This e f f e c t as a  f u n c t i o n of c r y s t a l dimensions i s q u i t e evident from the curves as can be seen i f the r a t i o r = Compton peak height f o r the 1.28 photopeak height MeV r a d i a t i o n  i s considered.  (The 0.511 MeV r a d i a t i o n  i s not con-  sidered since the Compton d i s t r i b u t i o n i s not w e l l d e f i n e d ) . The f o l l o w i n g (i) (ii) Uii)  values of r have been obtained:  Calculated d i s t r i b u t i o n (primary processes only) r = 3 * 6 C r y s t a l #2 r = 1.1 C r y s t a l #3 r = 1.25  The r a t i o increases as the dimensions become smaller thus v e r i f y ing the q u a l i t a t i v e arguments presented p r e v i o u s l y .  The r e s o l u -  t i o n a l s o improves but t h i s w i l l be discussed separately i n a following  section.  The t r a n s f e r r i n g  of pulses from the Compton peak t o the photo-  e l e c t r i c peak by m u l t i p l e s c a t t e r i n g  processes l i m i t s the accur-  acy of determining r e l a t i v e i n t e n s i t i e s by comparing areas under photopeaks.  Although the 0.511 MeV Compton d i s t r i b u t i o n i s not  w e l l defined there i s an i n d i c a t i o n that t h i s e f f e c t i s a f u n c t ion of energy as w e l l as c r y s t a l dimensions.  Consequently, a  rigorous c a l c u l a t i o n must eventually be rmade on the magnitude of t h i s process as a f u n c t i o n of energy and c r y s t a l dimensions C.  Co^  ,  The Co 1.17  spectrum i s known to c o n s i s t of two gamma-rays,  MeV and 1 . 3 3 MeV i n cascade.  The c a l c u l a t e d  distribution  (primary processes only) i s shown i n F i g . (VIII) and the e x p e r i -  FIGURE XIX COUNTING RATE  1  PULSE  HEIC HT  DISTRIBUT ION  FOR  ^60 C(  I  Arbitrary Units  t  \ \ \  /  /  \  10,000  \  * \ Compton  /  \  \ \ \ \ \  di .tribution (  7 MEV  Photop cak  IOOO  \  m  1.33 MEV f ^hotopeak  \D  IOO  i\\  ft  Curve  A  Curve  B Obtained  obtained  usir\q usir\q a  a  1/2  cub e  of  Nal  3/4 X 3/<4 X 1 1/2" block of  Nal  u  1  IO  10  15  20  25 PULSE  30 HEIGHT  35 VOLTS  FIGURE  XX  500  O  5  IO  15 PULSE  HEIGHT  20 -  VOLTS  25  30  FIGURE XXI  38  mental d i s t r i b u t i o n s i n F i g . (XIX).  An intense low energy peak  ( # 2 5 0 KeV) a l s o appears i n these d i s t r i b u t i o n s and i s i n t e r p r e 22  ted i n a s i m i l a r manner t o t h a t o f Na The  e f f e c t s of m u l t i p l e  i n the p r e v i o u s . s e c t i o n .  s c a t t e r i n g , again, are quite  evident,  and the values f o r the r a t i o r as defined i n the preceeding section  are: (i)  Calculated d i s t r i b u t i o n Ml.17  MeV) = 3 . 0  ^-(1.33 MeV) = 8 . 3  C r y s t a l #2  (ii)  A ( 1 . 1 7 MeV) = 1.05  A ( 1 . 3 3 MeV) = 1.45  C r y s t a l #3  (iii)  AU.17  MeV) = 1.4  A ( 1 . 3 3 MeV) = 2 . 1  These r a t i o s are l a r g e r f o r t h e smaller c r y s t a l , as expected, and t h e r e s o l u t i o n i s a l s o markedly improved as w i l l be described later.  The importance of c r y s t a l dimensions i s again emphasized  by these curves, p a r t i c u l a r l y by the increased height o f the photopeaks due t o t h e t r a n s f e r of Compton pulses.  The above  r a t i o s do not give a true p i c t u r e since two Compton d i s t r i b u t i o n s are superimposed and the r e s o l u t i o n was not s u f f i c i e n t l y good t o r e s o l v e them. D.  Zn^ There are two main r a d i a t i o n s i n the gamma-ray spectrum of  Zn : 6 5  The  a 1.114 MeV l i n e and 0.511 MeV a n n i h i l a t i o n r a d i a t i o n .  experimental d i s t r i b u t i o n s are shown i n F i g . (XX) and (XXI)  f o r c r y s t a l s #2 and #3 r e s p e c t i v e l y .  Q u a l i t a t i v e l y , these d i s -  t r i b u t i o n s are very s i m i l a r t o those o f N a  2 2  except t h a t the  F I G U R E  X X I I  39  r e l a t i v e i n t e n s i t y of the a n n i h i l a t i o n r a d i a t i o n i s much smaller Hence an i n t e r p r e t a t i o n f o r these curves, s i m i l a r t o t h a t 22  f o r Na  is valid.  I t w i l l be n o t i c e d t h a t the r a t i o r i s not  as d i f f e r e n t , ( i . e . r = 0.94 and 1.02^as would be E.  expected.  RdTh DISTRIBUTIONS The radio-thorium spectrum has a number of gamma-ray l i n e s  l e s s than 1 MeV MeV.  i n energy, and a reasonably strong one at  Since i t was f e l t t h a t the above r e s u l t s adequately  ..the ensrgy region below 1.5  MeV,  2.62 covered  the high energy end only of the  radio-thorium spectrum was i n v e s t i g a t e d . At 2.62  MeV the p a i r production c r o s s - s e c t i o n i n Nal i s s i g -  n i f i c a n t so t h a t the p a i r peaks should appear i n t h i s d i s t r i b u t i o n . Fig.  (XXII) shows the experimental d i s t r i b u t i o n obtained w i t h  c r y s t a l #2.  As was i n d i c a t e d on page 15 the r e l a t i v e i n t e n s i t i e s  of the three p a i r peaks cannot be predicted on any  reasonably  simple theory so t h a t no q u a n t i t a t i v e comparison with theory can be made.  Q u a l i t a t i v e l y , however, these three peaks a r i s e i n the  f o l l o w i n g manner: (i)  The low energy peak. This peak i s due e n t i r e l y to the P a i r I I I c o n t r i b u t i o n  and i s superimposed on the low e n e r g y . t a i l of the Compton d i s t r i bution.  I t s p o s i t i o n corresponds  (ii)  The medium energy peak.  to 1.60  MeV.  This peak i s the sum of two c o n t r i b u t i o n s : the Compton d i s t r i b u t i o n from the 1.2S distribution.  MeV  gamma-ray, and the P a i r I I  The p o s i t i o n of the peak cannot be p r e d i c t e d accura-  40 t e l y since the energy of the Compton peak i s not known p r e c i s e l y , the P a i r I I d i s t r i b u t i o n i s broadened an indeterminate amount by m u l t i p l e s c a t t e r i n g of the absorbed a n n i h i l a t i o n quanta, and  the  r e l a t i v e c o n t r i b u t i o n of each d i s t r i b u t i o n i s unknown (iii)  The high energy peak. This peak c o n s i s t s of three components:  the photoelec-  t r i c c o n t r i b u t i o n , the P a i r I c o n t r i b u t i o n , and the s c a t t e r i n g c o n t r i b u t i o n from the Compton peak. responds to 2.62  MeV  multiple  I t s p o s i t i o n cor-  and due t o . m u l t i p l e s c a t t e r i n g events the  low energy side would be expected to be broadened. The  presence of these three w e l l defined peaks i n the d i s -  t r i b u t i o n shows that when pair, production occurs an accurate energy measurement i s p o s s i b l e .  The use of a l a r g e r c r y s t a l w i l l  increase the r e l a t i v e i n t e n s i t y of the high energy peak as w e l l as i n c r e a s i n g t h e . e f f i c i e n c y of detection f o r high energy gammarays.  I f both the low and high energy peaks can be i d e n t i f i e d  i n an unknown d i s t r i b u t i o n , an energy c a l i b r a t i o n i s immediately possible since t h e i r d i f f e r e n c e i n p o s i t i o n corresponds to  1.02  MeV. The appearance of three peaks i n the p a i r production d i s t r i b u t i o n has the disadvantage that i f a spectrum consists of or more gamma-rays d i f f e r i n g i n energy by 1.2 MeV  two  or l e s s , the  r e s u l t a n t d i s t r i b u t i o n w i l l be very d i f f i c u l t to analyze, i . e . , for  two gamma-rays s i x peaks w i l l be i n a very small r e g i o n .  In  many experiments where t h i s occurs, the use of a s i n g l e c r y s t a l s c i n t i l l a t i o n counter i s u n s a t i s f a c t o r y and a l t e r n a t i v e schemes must be sought, e.g.,  the 3 c r y s t a l p a i r spectrometer  (15).  41  F.  ENERGY RESOLUTION One of the main reasons f o r undertaking t h i s work was to  f i n d the conditions under whin optimum r e s o l u t i o n i s achieved f o r a given energy range.  For the r e g i o n below 100 KeV i t was found  that a t h i n c r y s t a l gives the best r e s u l t s , both i n detection e f f i c i e n c y and i n r e s o l u t i o n .  With a d d i t i o n a l work, f u r t h e r im-  provements are expected i n t h i s energy region. In the energy range 0.5 MeV to 1.5 MeV i t has been found that the small c r y s t a l gave the b e t t e r r e s o l u t i o n .  Table I I shows  the r e s o l u t i o n i n % achieved with both c r y s t a l s #2 n d #3 f o r a  the peaks i n the N a , Zn^5 2 2  were assigned the 1.17  f  and Co^O d i s t r i b u t i o n s .  No values  MeV photopeaks i n the Go^° d i s t r i b u t i o n s  since i t was very d i f f i c u l t t o determine t h e i r h a l f  heights.  For the same reason, the r e s o l u t i o n assigned t o the 0.511  MeV  Ac  peaks i n .Zn ' i s subject t o considerable e r r o r . TABLE I I Crystal No.  Na22  .511 MeV Peak  Na^ 1.28. MeV Peak  ZnO MeV Peak  .511  #2  14.7  9.1  18.8  #3  12.7  8.0  12.2  The e f f e c t i v e number of e l e c t r o n s  Znt>5  1.114  Peak  Mev  Co°U i MeV Peak  1.33  11.3  9.3 7.0  8.0  produced a t the photocath-  ode per MeV of energy i n c i d e n t on the c r y s t a l has been c a l c u l a t e d from the Na  d i s t r i b u t i o n s using equation (2) page 2 1 .  The  values obtained are 680 and 930 f o r c r y s t a l s #2 and #3 r e s p e c t i v e l y .  42  The values of A (see page 21) were found to be zero w i t h i n ^ the accuracy of the c a l c u l a t i o n s . The smaller c r y s t a l gives b e t t e r r e s o l u t i o n as a r e s u l t of the f o l l o w i n g two (i)  effects.  Less broadening due to m u l t i p l e s c a t t e r i n g as has been  p r e v i o u s l y emphasized. (ii)  B e t t e r l i g h t c o l l e c t i o n due to the smaller dimensions  of the c r y s t a l . I t should be noted the "n", the e f f e c t i v e number of photocathode e l e c t r o n s per MeV  i s not a true values since the equat-  i o n f o r c a l c u l a t i n g i t does not include a f a c t o r accounting f o r broadening by m u l t i p l e s c a t t e r i n g . I t i s concluded from these r e s u l t s that to about 2 MeV,  the  best r e s o l u t i o n i s achieved with a c r y s t a l of rather small dimensions ( 4. 1/2"  cube).  A lower l i m i t , of course, i s set on the  dimensions by; 1.  The magnitude of the w a l l e f f e c t which increases with  decreasing dimensions and higher energies, 2.  and  by the i n t e n s i t y of the r a d i a t i o n being measured i n which  case the dimensions must be chosen so that a reasonable  counting  r a t e i s obtained. I t i s doubtful whether f u r t h e r s i g n i f i c a n t improvements i n r e s o l u t i o n w i l l be obtained by a d d i t i o n a l work on mounting techniques.  Improvements w i l l have to wait on the development of  more e f f i c i e n t phosphors and photocathode surfaces.  43  G.  THE SEARCH, FOR GAMMA-RAYS FROM TRITIUM The t r i t o n i s known t o decay (14) t o He3 by beta-emission  with an end point o f approximately l£ KeV and with a h a l f - l i f e of approximately 12 years.  A source of t r i t i u m  adsorbed i n z i r -  conium on a t h i c k tungsten backing was i n v e s t i g a t e d with the t h i n c r y s t a l t o determine the presence, i f any, o f a low energy gammaray. Since t r i t i u m decays by beta-emission, the pulse height d i s t r i b u t i o n would c o n s i s t mainly o f accontinuous d i s t r i b u t i o n , c u t t i n g o f f at IB KeV, as the r e s u l t of brehmstrahlung from the b e t a - p a r t i c l e s .  radiation  Any low energy peak would be superim-  posed on t h i s continuous d i s t r i b u t i o n .  With the r e s o l u t i o n  ach-  ieved w i t h the t h i n c r y s t a l , i t would be necessary f o r a gammaray t o be greater than 7 KeV i n energy and a t l e a s t  comparable  (to an order o f magnitude) i n i n t e n s i t y t o the brehmstrahlung radiation,to  be d e t e c t a b l e . To t h i s degree o f experimental ac-  curacy, there i s no i n d i c a t i o n o f the presence of a gamma-ray. The d i s t r i b u t i o n had a plateau a t a very low energy, obscured.by the large noise background. that t h i s plateau r e s u l t e d  partly  I t was thought a t f i r s t  from the presence of a gamma-ray.  However, by i n s e r t i n g t h i n aluminum absorbers (from . 0 0 1 " t o .015") between the source and the counter i t was found that the plateau developed i n t o a peak, and as the absorber thickness was i n creased the peak s h i f t e d upward i n energy t o a maximum o f IS KeV. The i n t e n s i t y , of course, dropped r a t h e r d r a s t i c a l l y . A  Since  Obtained from the Atomic Energy Commission of Canada.  44  the absorption of gamma-rays increases very r a p i d l y with a decrease i n energy the above phenomena was a t t r i b u t e d  to the i n -  creasing absorption of the lower energy quanta i n the continuous brehmstrahlung d i s t r i b u t i o n .  The f a c t that the upward s h i f t i n  peak energy ceased at IB KeV v e r i f i e s t h i s .  A s i m i l a r experiment  was done with the 13 KeV peak i n the RaD d i s t r i b u t i o n .  No s h i f t  i n the energy of the peak was n o t i c e d w i t h i n c r e a s i n g absorber thickness.  From t h i s , and the above argument i t was  concluded  that the plateau i n the t r i t i u m d i s t r i b u t i o n was not due to a low energy gamma-ray.  45 APPENDIX I Calculation  of the Compton E l e c t r o n D i s t r i b u t i o n ,  The formula obtained on page 9  f o r t h e Compton e l e c t r o n d i s t r i -  bution i s zans a>  i  (1)  where k(&) i s given by eqn. (6).page 7 This equation can be s i m p l i f i e d g i v i n g equation (16) page 10 by converting the u n i t s o f the e l e c t r o n energy t o c / ^ = (a)  The s i m p l i f i c a t i o n of cos <f> 2  £•/ ~ ki/j  £ e i v  —-—./  see eqn. (3) page .6  S o l v i n g t h i s equation f o r cos <^ , the r e s u l t i s 2  c o ^  =  ^ L  i ^ i l  (2)  (b)  A s i m i l a r s i m p l i f i c a t i o n f o r cos  (c)  *he expression f o r k(6) given on page 6 can be s i m p l i f i e d  with the  .iU.se  of equation  (3) above  0 gives  and the new energy u n i t s ,  giving k $ = ^ | ± i ^ o c ^ ^  Then u s i n g equations ( 2 ) and (4), equation (1) becomes de  cf  _  TTA>  ( ) 4  APPENDIX I I  46  THE SCINTILLATION OF ALPHA PARTICLES IN AIR As a p r e l i m i n a r y to the i n v e s t i g a t i o n of the s c i n t i l l a t i o n s produced by i o n i z i n g p a r t i c l e s i n gasses and vapours, the s c i n t i l l a t i o n s produced i n a i r by alpha p a r t i c l e s have been examined. •*  This i n v e s t i g a t i o n was c a r r i e d out i n the f o l l o w i n g manner: (i)  A polonium alpha source was mounted i n a l i g h t t i g h t  box. (ii)  The i n t e r i o r of the box was viewed with an R.C.A. 5^19  p h o t o m u l t i p l i e r so s i t u a t e d that any s c i n t i l l a t i o n s produced by the alpha p a r t i c l e s would be detected. (iii)  The source was so placed t h a t i t s self-luminescence  could not reach the p h o t o m u l t i p l i e r .  A s u i t a b l e shutter was con-  s t r u c t e d such that the alpha p a r t i c l e s could, when d e s i r e d , be prevented from t r a v e r s i n g the box. (iv)  The counting r a t e from the p h o t o m u l t i p l i e r was measured  with the shutter "covering" the source and with the shutter r e moved from the alpha p a r t i c l e beam. A s i g n i f i c a n t i n c r e a s e , approximately eight times the background, was observed when the alpha p a r t i c l e s were allowed t o t r a verse the box.  This increase was a t t r i b u t e d t o the s c i n t i l l a t i o n s  produced i n the a i r w i t h i n the box.  The pulse amplitudes were  s m a l l , of the same order as large noise pulses, but the l i g h t c o l l e c t i o n was not very e f f i c i e n t . This p r e l i m i n a r y i n v e s t i g a t i o n e s t a b l i s h e d the existence of the e f f e c t .  In view of the meagre information on the number of  photons and t h e i r energy produced by i o n i z i n g events i n gasses,  47  f u r t h e r work i s i n d i c a t e d ; namely the v a r i a t i o n of the e f f e c t w i t h pressure and with the nature of the gas.  The t h e o r e t i c a l  side o f t h i s problem, u n l i k e the a s s o c i a t e d one where i o n p a i r s are produced, has been l i t t l e discussed.  However, the p u b l i c a -  t i o n by Grun and Schopper (16) showed that t h i s l i n e of work was more advanced elsewhere, and since the author's main i n t e r e s t was i n the i n v e s t i g a t i o n of gamma-ray spectra w i t h s c i n t i l l a t i o n count e r s , the above work was discontinued. This e f f e c t could c l e a r l y be r e s p o n s i b l e f o r some of the strange r e s u l t s reported by Richards and Cole (1#) and Richards and Dee ( l g ) .  BIBLIOGRAPHY (1)  Hofstadter  P h y s i c a l Review  74,  100,  1948  (2)  Hofstadter and Mclntyre  P h y s i c a l Review  78,  617,  1950  (3)  Hofstadter and Mclntyre. P h y s i c a l Review  79,  389,  1950  (4)  Hofstadter  P h y s i c a l Review  80,  631,  1950  (5)  Swank and Moenich  Rev.Sci. Instruments 23, 5 0 2 ,  1952  (6)  K l e i n and N i s h i n a  Z.Physik  853,  1929  (7)  Davisson and Evans  Review of Modern Physics 79,  1952  52,  24, (8)  der Mateosian and Smith  P h y s i c a l Review  (9)  Roberts  P r o c . P h y s i c a l Society A,  (10)  Gillette  (11)  Westcott and Hanna  (12)  Elmore and Sands  Report f o r the Linde A i r Products Co. Tonawanda, New York. Rev.Sci.Instruments 2 0 , 1 8 1 , 1 9 4 9 McGraw H i l l , Electronics 1949  (13)  Cooke-Yarborough  Proc.Inst.Elect.Engs. Part I I  (14)  Langer and Moffat  P h y s i c a l Review  88,  689,  1952  (15)  Johansson  P h i l . Magazine  43,  249,  1952  (16)  Grun and Schopper  Z.Naturforsch.  6A,  698,  1951  (17)  Richards and Cole  Nature  167,  286,  1951  (IS)  Richards and Cole  Nature  169,  736,  1951  88,  98,  1186,1952  192 , 1 9 5 3  191,  1951  

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