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Conversion electron and low energy gamma-ray spectrometer. Johnson, John Richard 1970

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A CONVERSION ELECTRON AND LOW ENERGY GAMMA-RAY SPECTROMETER  by  JOHN RICHARD JOHNSON B.Sc,  U n i v e r s i t y o f B r i t i s h Columbia,  1967  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We a c c e p t t h i s required  thesis.as  conforming to the  s t a n d a r d from c a n d i d a t e s f o r the  degree of MASTER OF SCIENCE  THE UNIVERSITY OF BRITISH COLUMBIA April,  1970  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree tha  permission for extensive copying of this thesis  for scholarly purposes may be granted by the Head of my Department or by his representatives.  It is understood that copying or publication  of this thesis for financial gain shall not be allowed without my written permission.  Department of  PL.tys t-c <,  The University of British Columbia Vancouver 8, Canada  D a t e  r<  7 o  ABSTRACT  A c o n v e r s i o n e l e c t r o n and low e n e r g y developed using a s i l i c o n  lithium-drifted  meter has a r e s o l u t i o n of  2 Kev f o r  optimum  conditions.  be e s t i m a t e d standard  The  e n e r g i e s of  t o -.1 K e v ,  sources  100  and  their  gamma-ray s p e c t r o m e t e r semiconductor  Kev  detector.  been  The  e l e c t r o n s and photons  these electrons  spectro-  under  and g a m m a - r a y s  i n t e n s i t i e s t o w i t h i n ^67o w i t h  can the  available. 153  The  has  e l e c t r o n c a p t u r e decay of  this  spectrometer.  Kev,  97.4  The  branching  153 Gd —>  Eu was i n v e s t i g a t e d  capture r a t i o s  to  the  172.9  using  Kev,  103.2  153 a n d 11%,  Kev,  respectively. 5  Kev  level,  for  the 97.4  with  and 0 Kev  those  /2  +  Kev  3  or  +  /2  l e v e l s of  Possible for  the  Eu w e r e f o u n d values  103.2  Kev  l e v e l have been a s s i g n e d .  f o u n d by o t h e r  investigators.  of  -V2  level,  and  t o b e 11%, or T  "V 2 -  /2,  These v a l u e s  39%,  for c  are  -  /2,  in  the or  39% 172.9 7  /2  -  agreement  TABLE'OF  CONTENTS Page  ABSTRACT  i i  LIST OF TABLES  v  LIST OF FIGURES  vi  ACKNOWLEDGEMENTS CHAPTER I  CHAPTER I I  CHAPTER I I I  viii  NUCLEI AND RADIOACTIVE DECAY 1.  Introduction  2.  B e t a Decay  3.  E x c i t e d S t a t e Decay  . . .  1  . . .  3 . . . . .  SEMICONDUCTOR DETECTORS 1.  The P-N J u n c t i o n  18  2.  The P - I - N  20  3.  Semiconductor C r y s t a l s as P a r t i c l e D e t e c t o r s  Crystal . . .  21  . . . .  25  LITHIUM ION DRIFTED SILICON DETECTORS 1.  S i ( L i ) Detectors  2.  Associated  3.  Inherent  f o r Photons and E l e c t r o n s  32  Electronics  R e s o l u t i o n o f the D e t e c t o r - A n a l y s e r 39  System 4. CHAPTER IV  CHAPTER V  9  Other C o n t r i b u t i o n s  to the R e s o l u t i o n  . . . . . . .  45  ANALYSIS OF SPECTRA 1.  Computer A n a l y s i s  54  2.  Energy C a l i b r a t i o n  58  3.  Separation  4.  Efficiency Calibration  DECAY OF 1.  153  o f E l e c t r o n and Photon S p e c t r a  . . . .  64 65  GADOLINIUM 70  Introduction i i i  CHAPTER V  (Continued) 2. 3.  CHAPTER VI  Source P r e p a r a t i o n 1 5 3  Gd  70  Spectra  .  4.  Conversion  5.  Capture Branching  6.  S p i n and P a r i t y Assignments  CONCLUSIONS  Coefficients  . .  72 76  Ratios  78 82 . .  83- .  APPENDIX A  86  REFERENCES  90  iv  LIST OF TABLES Page  I II  Gamow-Teller S e l e c t i o n  Rules f o r Beta Decay  6  C l a s s i f i c a t i o n o f Gamma T r a n s i t i o n s  15  III  Characteristics  o f the P u l s e Shaper  37  IV  Characteristics  o f the Two D e t e c t o r s  47  V VI VII VIII IX X  XI XII  Change i n E r r o r w i t h System G a i n Energy  C a l i b r a t i o n Sources  Energy L o s t i n Dead L a y e r o f Photon  57 59  Detector  E f f i c i e n c y C a l i b r a t i o n Data  63 68  Peak I d e n t i f i c a t i o n and I n t e n s i t i e s  75  Conversion C o e f f i c i e n t s  77  <* /<*  7  K  7  L  Capture B r a n c h i n g R a t i o s  81  v  LIST OF FIGURES Page 1  T y p i c a l Shapes of  2  Decay Scheme  10  3  Impurity Levels  19  4  Energy Loss i n Semiconductor  5  Si(Li) Crystals  6  jQ*  5  Distributions  23  Crystals .  '  26 27  £ v s . Temperature  7  Range of E l e c t r o n s i n S i  27  8  Energy Loss i n Dead Layer  28  9  P a r t i a l Energy Loss P r o c e s s e s  28  10  Photon Cross S e c t i o n f o r S i l i c o n  30  11  S y s t e m a t i c of E l e c t r o n i c s '  33  12  E q u i v a l e n t C i r c u i t f o r Detector-Preamp.  34  13  P u l s e Shaper Network  36  14  T y p i c a l Low  38  15  C r y s t a l Chamber  16  P l o t of Temperature  Energy Spectrum  43 v s . Optimized R e s o l u t i o n f o r  44  Two D e t e c t o r s 17  E f f e c t of Source T h i c k n e s s on R e s o l u t i o n  46  18  S u b l i m a t i o n Chamber  48  19  Pulser C i r c u i t  49  20  Two  51  Types o f Source H o l d e r s and T h e i r E f f e c t on Low Energy Photon  Resolution  21  E f f e c t s of Dead L a y e r on Low  22  Composite Peak  55  23  Components of Peak i n F i g . 22  56  vi  Energy E l e c t r o n s  52  LIST OF FIGURES ( c o n t ' d . ) Page 24  Energy C a l i b r a t i o n Curves  25  A b s o r p t i o n Curve f o r Photons i n Aluminum Absorber  26  Photon E f f i c i e n c y of S^ D e t e c t o r  27  Main T r a n s i t i o n s  28  Conversion E l e c t r o n  29  Photon Spectrum of  i n the Decay of Spectrum of 153  Gd  vii  60, 61, 66 - 69 153 153  Gd  Gd  71 73 74  62  ACKNOWLEDGEMENTS  I w i s h to express my g r a t i t u d e to Dr. K. C. Mann f o r guidance and encouragement throughout I would a l s o l i k e cussions  t h e . c o u r s e o f t h i s work.  to thank Mr. P. Tamminga f o r the many h e l p f u l  of the problems t h a t a r o s e d u r i n g  dis-  the development o f the s p e c t r o -  meter. T h i s p r o j e c t was s u p p o r t e d by a G r a n t - i n - A i d - o f - R e s e a r c h t o Dr. K. C. Mann by the N a t i o n a l Research  C o u n c i l of Canada.  I a l s o wish  to acknowledge the f u r t h e r a s s i s t a n c e o f the N a t i o n a l Research through awards to me o f N. R. C. B u r s a r i e s .  viii  Council  CHAPTER I NUCLEI AND  1.  RADIOACTIVE DECAY  Introduction be  N u c l e i are known to  a s s e m b l i e s of f a s t - m o v i n g heavy p a r t i c l e s  c a l l e d n u c l e o n s , which i n c l u d e b o t h neutrons number o f nucleons  is called  of p r o t o n s , which determines number Z .  The  the mass number A, w h i l e the t o t a l the n u c l e a r charge,  is called  the  total, number atomic  those w i t h  isobars.  i n t e r n a l motion  p e r t i e s as energy, and magnetic nucleons  protons.  N u c l e i w i t h the same Z are termed i s o t o p e s , and  the same A, The  and  o f the nucleons  a n g u l a r momentum X ( o r  g i v e s the n u c l e u s such  pro-  s p i n ) , p a r i t y TT , and  electric  moments, the. v a l u e s of which are measures of the way  a r e arranged  the  i n a n u c l e u s ; o r i n o t h e r words, of the n u c l e a r  structure. S i n c e a n u c l e u s i s a quantum m e c h a n i c a l i n c e r t a i n d i s c r e t e energy  moments. except  The  latter  two  Each energy  s t a t e may  be u n i q u e l y  s p i n , p a r i t y , and by i t s e l e c t r i c and p r o p e r t i e s are d i f f i c u l t  the lowest or ground s t a t e , and  a r e n o r m a l l y used  i t can o n l y e x i s t  s t a t e s , each c o r r e s p o n d i n g to a p a r t i c u l a r  i n t e r n a l nucleon c o n f i g u r a t i o n . c l a s s i f i e d by i t s energy,  system,  magnetic  to measure i n any  so the f i r s t  three q u a n t i t i e s  state alone  to d e f i n e a s t a t e .  R a d i o a c t i v e decay i s the p r o c e s s by which a n u c l e u s can r e a c h a s t a t e of lower its  internal  t o t a l energy.  I t may  do so by merely  a rearrangement  c o n f i g u r a t i o n w i t h no change i n the numbers or k i n d s of -1-  of  nucleons is  present  usually,  though not  may d e c a y b y results  to  the  always,  e m i s s i o n of  nuclear species.  type where a proton,  tive  state  decay).  or  a proton  excited  called state  Or  to  decay,  that  case the excess  by a gamma-ray  finally,  is  nucleons which to  constant, The  emitted  and t h i s  but  a  a neutron  particular  to  posi-  type  the work d e s c r i b e d i n  of  converts  p a r t i c l e s are  the decay p r o c e s s , f o l l o w e d  is relevent  It  t h e r a d i o a c t i v e d e c a y may b e  a neutron.  This  energy  quantum.  the r e s i d u a l n u c l e u s belongs  e l e c t r o n s and n e u t r i n o s , beta-decay.  this  a nucleon or a c l u s t e r of  t h e m a s s number A r e m a i n s  or negative  decay i s  In  carried off  i n a change i n A so t h a t  different the  (excited  of  by  this  thesis. Of alter  course,  the  energy,  Measurements of  a l l such decays a l t e r a n g u l a r momentum,  on the e m i t t e d  the n u c l e a r s t a t e s  the n u c l e o n c o n f i g u r a t i o n and h e n c e  parity,  r a d i a t i o n give  involved.  This  is  and moments  of  the  i n f o r m a t i o n on the  the f i e l d of  nuclear  nucleus. properties spectro-  scopy. All by  r a d i o a c t i v e decay f o l l o w s  the w e l l - k n o w n  the u s u a l s t a t i s t i c a l  rule  defined  equation  dt w h e r e f\} the decay  is  t h e number  constant.  Jve  is  usual  d e f i n i t i o n of  parent  n u c l e i present at  Integration  N where  of  then  t i m e t and  present  is  gives  = & e  t h e number  "A  (i - i ) at t  t h e mean l i f e  This  = O •  time  T  =  equation  '/-N  and  leads  the  to  the  half-life  3 2.  Beta Decay T h i s p r o c e s s , mentioned  the f o l l o w i n g  ,  b r i e f l y p r e v i o u s l y , may be d e s c r i b e d by  three e q u a t i o n s : a)  p —>  n  +  e  b)  n _>. p  +  e  c)  p  —>  n  +  e  +  +  V  p o s i t r o n decay (  + \>  where n, p, e , e , \? , and V +  n e g a t r o n decay  (S') /  ( I - 2) (E.C)  + V  o r b i t a l e l e c t r o n capture  refer  t o the n e u t r o n , p r o t o n , p o s i t r o n ,  n e g a t r o n , n e u t r i n o , and a n t i n e u t r i n o r e s p e c t i v e l y .  Only p r o c e s s b)  o c c u r s f o r f r e e p a r t i c l e s , b u t a l l may occur i n s i d e the n u c l e u s i f the t o t a l energy of the system  i s lowered  i n the p r o c e s s .  I t i s obvious  t h a t the e m i t t e d p a r t i c l e s  i n b e t a decay a r e the p o s i t i v e and n e g a t i v e  e l e c t r o n s and the n e u t r i n o s . The  energy requirements  f o r the t h r e e b e t a decay p r o c e s s e s a r e  a)  E„  = M(Z,A)c  2  b)  E„  = M(Z,A)c  c)  E  = M(Z,A)c  D  - M(Z-l,A)c  2  2  - M(Z+l,A)c  2  2  - M(Z-l,A)c  2  - I - 2 m - i '>  2 c c  >  0  0  - B (Z) - I" > 0 e  /?+  j8~ E.C.  I n these e q u a t i o n s E  e  = t o t a l energy r e l e a s e d i n the decay  M(Z,A)  = atomic mass o f the atom whose n u c l e u s has atomic number Z, and mass number A  I  = d i f f e r e n c e i n i o n i z a t i o n energy between p a r e n t and daughter•atoms  m„  = e l e c t r o n r e s t mass  B (Z) e  = b i n d i n g energy o f the atomic e l e c t r o n b e f o r e capture.  I t can be seen ignored. In fact,  This i s a v a l i d  approximation  o f the daughter  atom has been  except f o r the v e r y l i g h t  the f a c t o r I i s a l s o c u s t o m a r i l y i g n o r e d except where E  also small. E„  t h a t the r e c o i l energy  I n the c o n t e x t of these approximations  then,  nuclei. is  e  the energy  w i l l be shared s t a t i s t i c a l l y between the b e t a p a r t i c l e and the  n e u t r i n o i n the f i r s t  two p r o c e s s e s , w h i l e i n the t h i r d ,  i s emitted monoenergetically with  total  energy  the n e u t r i n o  E„ .  P o s i t r o n and Negatron Decay The energy  d i s t r i b u t i o n of e l e c t r o n s i n j3  P(E)  2 dE = -S-r  E(E -M.c )^ 2  2  (E.-E)  +  2  • 12 decay i s g i v e n by ' F(E^Z) | M | dE  (I - 4)  2  2 TT J where:  + P(E)  dE  = p r o b a b i l i t y o f e m i s s i o n of a ^ " p a r t i c l e t o t a l energy  g E„  with  between E and E+dE  = c o u p l i n g c o n s t a n t o f the i n t e r a c t i o n = energy  of the decay  F(E,+Z) = the c o r r e c t i o n to the d i s t r i b u t i o n f u n c t i o n a r i s i n g from  the i n t e r a c t i o n between the o u t g o i n g  jQ * p a r t i c l e and the n u c l e a r coulomb M  = n u c l e a r m a t r i x element i n v o l v e d i n the t r a n s i t i o n .  T h i s e q u a t i o n i s due o r i g i n a l l y  to F e r m i .  I t assumes t h a t r e s t  mass of the n e u t r i n o i s z e r o , and the r e c o i l o f the daughter and  field  nucleus  the d i f f e r e n c e i n i o n i z a t i o n e n e r g i e s between the p a r e n t and  daughter  atoms a r e n e g l i g a b l e .  + T y p i c a l shapes of/9  d i s t r i b u t i o n s a r e shown i n F i g .  The square o f the n u c l e a r m a t r i x element, jM/  1.  , can be expanded i n  FIG. Typical  Shapes of  1.-Distributions  6 a series  of terms i n k  where k =  R,  E/C+N  and  i s the n u c l e a r  R  Each term i n the e x p a n s i o n r e p r e s e n t s the c o n t r i b u t i o n involving  particular  a n g u l a r momentum and p a r i t y  from  changes.  radius.  transitions Selection 12  rules  g o v e r n i n g these t r a n s i t i o n s  and w i l l be summarized The f i r s t  have been deduced  theoretically  term i n the e x p a n s i o n r e p r e s e n t s 1  ATT  = No.  ' ' ,  later.  and l a r g e s t  to Gamow-Teller  4  selection  rules  ) a transition  i n which  T h i s i s c a l l e d an a l l o w e d t r a n s i t i o n .  (according  + A J = 0, 1 and  I f the  transition  2 is  of t h i s  type the f i r s t  I f not, the f i r s t  term i n | M |  i s dominant  is  I f the t r a n s i t i o n  dominant.  1).  term v a n i s h e s .  The second term i n the e x p a n s i o n of i n which A J = 0, * 1 , *2 and £ TV = Yes. transition.  (assuming k R «  i s of t h i s  2 |M| represents a t r a n s i t i o n This i s c a l l e d a f i r s t forbidden 2 type, the second term i n | M )  I f n o t , the second term v a n i s h e s .  In fact,  the  first  non-zero term i n the e x p a n s i o n always dominates, and determines the degree of f o r b i d d e n n e s s of a The Gamow-Teller are  listed  transition.  selection  rules  f o r the f i r s t  few t r a n s i t i o n  types  i n Table I. Table I Gamow-Teller  Degree of Forbiddenness  Selection  Parity Change ( ATT)  Allowed  No  1st  forbidden  Yes  2nd  forbidden  No  Rules f o r B e t a Decay Ang. Mom. Change (AJ)  3 0, +1  +  2  - 6  6 -  10  >10  + The h a l f - l i f e of/2  Approx. log f t value  decay i s g i v e n by  7  h - ¥ 2  and on  -  *  f »  •  2  tt  - 5)  P(E) d E  E  Jm„ c  i s s t r o n g l y dependent on E jM|  ' "  r E  ( t % v a r i e s approximately  0  , which i s i n c l u d e d i n the i n t e g r a l .  as E^  and  I f we d e f i n e a f u n c t i o n  f  as f =  \ °m c 2  E(E -» 2  2  c  4  )  (I - 6)  (E„ - E ) F(E,+Z) dE  %  2  0  + which i s the i n t e g r a l over  thej8  state,  ^ j E(E -M „ 2 tt»c  then  spectrum  2  CE°  Si  2-n is a function called  c ) *(E -E)  2  4  0  In 2 tk = —^  J  ^m. c  E(E -« 2  2  independent  2  e  c  4  )  %  (E -E)  2  a  o f the n u c l e a r  F(E,+Z) dE  F(E,+Z) |M|  2  dE  2  the comparative  half-life,  or f t value.  The f u n c -  3 t i o n f has been c a l c u l a t e d and t a b u l a t e d by T r i g g and Feenburg . The u s e f u l n e s s o f c a l c u l a t i n g an f t v a l u e i s t h a t i t i s almost ent o f E„, but r e t a i n s  2 the s t r o n g dependence on \M\ .  independ-  I t i s therefore a 2  measure o f the f o r b i d d e n n e s s o f a t r a n s i t i o n . r a p i d l y w i t h i n c r e a s i n g degrees increase rapidly also. to  use t h e i r Typical  That  i s , s i n c e {M|  o f f o r b i d d e n n e s s , the f t v a l u e  S i n c e f t v a l u e s a r e l a r g e , i t i s more  decreases  will convenient  logarithms. l o g f t v a l u e s f o r the d i f f e r e n t degrees  of forbiddenness  + of /3  t r a n s i t i o n s are included i n Table I .  The l o g f t v a l u e i n i t s e l f ,  while  u s e f u l i n a s s e s s i n g the f o r b i d d e n n e s s o f a t r a n s i t i o n ,  p l e t e l y d e f i n i t i v e s i n c e o v e r l a p s o f these v a l u e s a r e f a i r l y  i s n o t comcommon.  Orbital Electron  The  only emitted p a r t i c l e i n o r b i t a l e l e c t r o n capture i s a  n e u t r i n o , which i n t e r a c t s almost  Capture  v e r y weakly with m a t t e r ,  i m p o s s i b l e to d e t e c t .  of t r a n s i t i o n must come from Bremsstralung,  gamma-rays,  T h e r e f o r e any secondary  and  is  consequently  i n f o r m a t i o n about t h i s  effects  type  (x-rays, i n t e r n a l  etc.). 1 2 21  The  p r o b a b i l i t y f o r e l e c t r o n capture i s g i v a i  by  ' '  2 Pi  =  f i (Zo, Z) |M|  (1-7)  Z  2TT where  P  = the p r o b a b i l i t y of an e l e c t r o n b e i n g c a p t u r e d atomic  M  from  orbital i .  = i s the same n u c l e a r m a t r i x element t h a t i s i n v o l v e d i n fi  decay and  +  t h e r e f o r e o r b i t a l e l e c t r o n capture  by c l a s s i f i e d by the degrees  may  of f o r b i d d e n n e s s g i v e n i n  Table I. fi  (E„,Z)  = a f u n c t i o n t h a t depends on the a n g u l a r momentum,  p a r i t y , and b i n d i n g energy  o f the e l e c t r o n b e i n g  tured.  the change i n s p i n ,  and  I t a l s o depends on  energy  Numerical  between the p a r e n t and  where.  >  =  0  3  and  by  Zyryanoya  f o r e l e c t r o n c a p t u r e i s g i v e n by  \ 2ii  parity,  nuclei.  v a l u e s of f i ( E , Z ) have been t a b u l a t e d by  T r i g g and Feenburg The h a l f - l i f e  daughter  cap-  2  2  f i (E ,Z) | M | 2 TT  the summation b e i n g over a l l o r b i t a l  electron  states.  21  9  In  a s i m i l a r manner  f  =  <£, i  then the f t value  it  f i  Decay  +  d e c a y we c a n d e f i n e  (E„,Z)  =  l  n  i  2  f —  strongly  (E,,Z)  i  £  f i  (I  (E„,Z)  M  -  8)  2  £  2 on | M ) as i n the  + - case.  Schemes When a n u c l e u s u n d e r g o e s  represented  b e t a decay  + Cu) was c h o s e n as i t decays by 0  competition. transitions  t h e d e c a y s e q u e n c e may b e  s c h e m a t i c a l l y a s shown i n F i g . 2 .  64 (  a f u n c t i o n f as  is  21TJ w h i c h depends  toft  It will  be noted  are allowed.  This  particular  example  -  ,  j2>  a n  d E.C.,  a l l of which are i n  from s p i n and p a r i t y  Included  changes  that a l l  o n the d i a g r a m a r e f t v a l u e s and 18  relative  decay p r o b a b i l i t i e s w h i c h have been deduced from  These v a l u e s 3. Excited  a r e c o n s i s t e n t w i t h the allowed c h a r a c t e r of the decays. S t a t e D e c a y (Gamma D e c a y a n d I n t e r n a l Conversion)  . T h e r e a r e two m a i n p r o c e s s e s i n e x c i t e d s t a t e the of  emission of e l e c t r o - m a g n e t i c the decay energy  (internal initial The  experiments  T h e two p r o c e s s e s , when  and f i n a l s t a t e s ,  E„ E„  (gamma r a y s ) ,  by an atomic e l e c t r o n w i t h  conversion).  energy  quanta  are always  requirements  decay.  They a r e  and t h e a b s o r p t i o n  i t s subsequent they  involve  emission t h e same  i n competition.  f o r these processes are  4 9 0 = M (Z,A) c - M(Z,A) c > 0 gamma ( X ) * 2 2 = M ( Z , A ) c - M ( Z , A ) c - B e (Z) > 0 internal conversion (I.C.)  ( 1 - 9 )  10 FIG.  2.--  D e c a y Scheme  In  this  equation  the  the b i n d i n g energy are defined  refers  of  the  to  electron before  i n Equation  first  transition probability  order  energy  state  conversion.  a n d Be  The  (Z)  other  is  symbols  1 - 4 .  Gamma The  the h i g h e r  approximation)  Decay for  the  i s g i v e n by  e m i s s i o n of  a gamma r a y  (to  a  4 5 '  K k In  this  equation uJtf = t h e p r o b a b i l i t y gamma r a y w i t h K  = is a  per u n i t energy  E  time f o r = k  e m i s s i o n of  a  c  constant. the  initial  and f i n a l wave f u n c t i o n s  of  the  nucleus. = is  the r a d i u s  of  £ + W Z •=  represents  the i n t e r a c t i o n c a u s i n g the  R  £  the  nucleus.  i s e l e c t r i c i n o r i g i n and h a s  even  radiation.  parity. 4  rffl This for  i s magnetic  expression for  £Jy i s o f t e n  i n o r i g i n and has odd p a r i t y quite  inaccurate but  d e s c r i b i n g t h e m e t h o d b y w h i c h gamma r a d i a t i o n i s The  term e  - i  k  R  c a n be expanded  t Then the  first  is  .  useful  classified.  i n the u s u a l f o r m .  That  is:  =1 term  in \  (I -  ID  represents  the  transition probability  quadrapole  radiation,  O n l y terms  of  expansion unless  for  dipole radiation,  the  second  etc.4'"''^.  the  lowest  the energy  order  of  the  i n k R n e e d be c o n s i d e r e d i n emitted  gamma r a y  is  the  large.  For  example: taking  R  = 1.2  k  = 5.05 x  where A i s the  gamma r a y  Since E unity  cm A  1010  <=: 6 x 1 0 " 3  and o n l y  -13  E  1/3  cm"1 of  the nucleus  and E  is  the  energy  of  Mev.  is usually  following  10  t h e mass number  in  Then k R  x  A  less  terms  of  discussion is  E  than the  10 M e u ,  lowest  limited  to  k R i s u s u a l l y much l e s s  order this  than  i n k R need be r e t a i n e d .  The  case. 0  The ition  a n g u l a r momentum o f  is 2 with  referred  .  respect  If  to  and  the o r i g i n  are  the nucleus r e s p e c t i v e l y ,  a gamma r a y  the  then  r e s u l t i n g from a 2  to w h i c h  initial  the  -pole  the m u l t i p o l e  and f i n a l  is  a n g u l a r momenta  Q. due  r e s t r i c t i o n s on  to  trans-  of  conservation  o f momentum a r e  \j  f  - J.i =  J „ 4.  a  j  <  + J  f  ±  4 Because of  the  transverse  nature  of  electro-magnetic  r a y s m u s t h a v e a n g u l a r momentum g r e a t e r for  Jc  and i f set  than or  equal  radiation to one.  ,  gamma Therefore,  = 0  Jf  limits  = J^  = 0,  no gamma r a d i a t i o n  on the a l l o w e d v a l u e s  of  £  can o c c u r . in  the  These r e s t r i c t i o n s  expansion of  e  ^  Terms i n the i n t e g r a l  i n e q u a t i o n I - 11 w i l l v a n i s h u n l e s s and TV. have o p p o s i t e p a r i t y ,  have even p a r i t y .  Because  £  non-zero term w i l l  contain  £ i f the f i r s t  they  the second  c o n t a i n s w( , and v i c e  versa.  r a t i o ^ o f 77l to ^ i s o f the same o r d e r o f magnitude as k R.  The  That  is  ffl  6 Therefore, if  -3 -2/3 5 x 10 A '  ^  the f i r s t  the f i r s t  and second  contains  Only  terms a r e o f the same o r d e r o f magnitude these  two terms need be r e t a i n e d  as  2 contributions Similarly,  from a l l o t h e r  i f the f i r s t  Transitions electric  gamma r a y .  has  term c o n t a i n s ^ , a l l o t h e r terms may be i g n o r e d .  involving  the e m i s s i o n of gamma rays a r e c l a s s i f i e d as  There a r e two d i s t i n c t types o f t r a n s i t i o n s .  the p r o d u c t o f the i n i t i a l  parity  (-1)^  change).  transitions.  Such t r a n s i t i o n s  this  J  .  favored.  These a r e c a l l e d  parity  Transitions  i s g i v e n by  terms i n e q u a t i o n I - 11 a r e zero o r n e g l i g a b l e compared to  term. If  +1 = No, there  Both cases a r e d i s c u s s e d below.  transition probability  other  change,  are called p a r i t y  change o f - ( - 1 ) ^  P a r i t y Favored The  F o r the f i r s t  and f i n a l wave f u n c t i o n s o f the nucleus  (-1 = Yes, there i s a p a r i t y  second type has a p a r i t y  unfavored  All  smaller.  to U))( , and by the a n g u l a r momentum ( s p i n ) of the e m i t t e d  is not a parity The  (k R)  (E) o r magnetic (M) a c c o r d i n g to which a r e the dominant terms  contributing  type,  terms a r e a t l e a s t of o r d e r  0  Transitions =0  o f t h i s type a r e c l a s s i f i e d  the t r a n s i t i o n p r o b a b i l i t y  as E J .  i s g i v e n by  0  ;  Transitions  of  the percentage  ^ =  K k | ^ / [  this  type are  of  the  of  this  M J6 Jft  Unfavored  type are + c'  = 0 the  E J  The itions  of  classified  relative  the  -  11  An e x a c t  can be  which  spin,  classified  emitted  i s given  to  check the  1  as  El.  t r a n s i t i o n p r o b a b i l i t i e s of of  of  approximate  as the e r r o r  The in  that w i l l  the n u c l e u s .  give  The  t h e number  the r e q u i r e d  experimental of  involving changes  value  gamma r a y s w i t h source,  of  and C o n v e r s i o n  changes of  is often  Coefficients  a t r a n s i t i o n c a n be d e d u c e d f r o m  in  LUy  energy  such a model.  Conversion  S p i n and p a r i t y  trans-  are given i n Table I I .  J„  t i m e f r o m a known r a d i o a c t i v e  adequacy of  Internal  by  COy r e q u i r e s a n u c l e a r m o d e l  the nucleons  and p a r i t y  per u n i t  character.  considerable.  c a n be o b t a i n e d b y m e a s u r i n g  E  a  of  c represents  as  t i d r i  few v a l u e s  c a l c u l a t i o n of  the rearrangement  where  by  t r a n s i t i o n p r o b a b i l i t i e s are only  equation I  energy,  first  2  +1  6  type are  in  14  Transitions  c l a s s i f i c a t i o n and r e l a t i v e  involving  as M 1 + c E 2 ,  transition probability  this  '  k R) ^ j ^ i d i r l  i s given  = Kk|(^f* 6 Transitions  (-i  classified  transitions probability  Transitions  If  +  t r a n s i t i o n t h a t i s E2  Parity The  ^  '  the  used  ,  15  Table I I C l a s s i f i c a t i o n o f Gamma  P a r i t y Favored J  0  Parity  Change  Transitions  Case Class  0 (0-T~>.0)  No  1  Yes  El  1  2  No  E2  (k R)  3  Yes  E3  P a r i t y Unfavored  Ml +  (E2)  Approx. R e l a t i v e Value of 10% (k R )  2  2  Case  0 (0 -/> 0)  Yes  1  No  Ml +  (E2)  (k R )  2  2  Yes  M2 +  (E3)  (k R )  4  3  No  M3 +  (E4)  (k R )  6  El  1  internal is  conversion  defined  coefficients  iOz. i s  the  s h o u l d be n o t e d  transition  (E. c.e.  time;  -  and  probability  for  N  B-;)  c.e.  -(E.  -  K, Lj,  and N y ( E p ) *  refer  energy  -  internal and  the  Ea  version ition  denote  transfer  conversion  to  t h e number  B^ a n d E 0  It  conversion  respectively,  electrons  emitted  per  +  probability  atomic  the n u c l e u s  and  orbitals. the  i n t e r a c t i o n between  f i e l d which otherwise  contains for  different  between  a gamma r a y ^ .  therefore  the  is a direct  same m u l t i p o l e  e m i s s i o n of  conversion.  that  L J J , . . .  energy  internal  1  v  The  transition  B.)  fjJt= u + u. + u, where  a  that  and gamma r a y s w i t h unit  of  "Iu7"  =  . . Ue.  N  I.C.C.  -  *  where  The  as J  where  (I.C.C.).  atomic  the bound  transition  probability  for  the  same n u c l e a r w a v e f u n c t i o n s  in  internal as  in  electron  would have r e s u l t e d  The  gamma  electron  the  the con-  trans-  radiation. 12  It  h a s b e e n shown  wave f u n c t i o n s cients. the  The  initial  transition,  The  cancel in  I.C.C.'s and f i n a l and on the  electron being  that  '  the  then  ,  to  a close approximation,  c a l c u l a t i o n of  depend  states,  only  on the  internal  on the  energy  s p i n and p a r i t y  a n g u l a r momentum,  parity  converted.  internal  coefficients  can be w r i t t e n  as  the  nuclear  conversion  coeffi-  difference  between  change of  and b i n d i n g  the  energy  of  the  17  where  etc. These i n d i v i d u a l compared  coefficients  can be c a l c u l a t e d  and t h e i r v a l u e s  to those o b t a i n e d e x p e r i m e n t a l l y to deduce the s p i n and  parity  change of a t r a n s i t i o n . Theoretical  internal  by S l i v and Band^.  c o n v e r s i o n c o e f f i c i e n t s have been  They have c a l c u l a t e d  number between 33 and 98 and  o(  T  I atomic numbers between 41 and 98.  >  L  for multipolarities unfavored  up to J ,  transitions.  =5  Similar  I n v e s t i g a t i o n s of i n t e r n a l to knowledge of the s p i n decay of' a n u c l e u s .  K d  f o r nuclei with  atomic  ck-, (AT nuclei with II III I n b o t h cases c a l c u l a t i o n s were done a n  L  r  o  r  L  f o r both p a r i t y calculations  f a v o r e d and  therefore  changes i n v o l v e d i n the  Such i n v e s t i g a t i o n s  parity  g have been done by Rose .  conversion c o e f f i c i e n t s  and p a r i t y  calculated  require a suitable  lead  radioactive spectrometer  c a p a b l e of measuring e n e r g i e s and i n t e n s i t i e s of e l e c t r o n s and gamma rays.  A s p e c t r o m e t e r w i t h these f e a t u r e s was  lithum-drifted of  semiconductor d e t e c t o r .  constructed using a  The development and  silicon  characteristics  t h i s s p e c t r o m e t e r are the main t o p i c of Chapters I I , I I I and IV.  18  CHAPTER  II  SEMICONDUCTOR DETECTORS  1.  The P - N As  Junction  i s w e l l known,  to m o b i l e  carriers,  electrical  s u c h as e l e c t r o n s  or vacancies or "holes" of  an e x t e r n a l  number equal  of  electric field.  impurities  When t h i s  depending  upon whether  These i n e q u a l i t i e s duce l e v e l s h i g h bands.  becomes  tion.  Hence  forbidden  the  of c a r r i e r holes  the (p) a r e  t h e c o n d u c t i o n and  temperature. can cause an i n e q u a l i t y  the electrons  (n) o r h o l e s  between  semiconductor,  (p) a r e more  numerous.  f o r example,  t h e i m p u r i t i e s may i n t r o -  i n the forbidden  zone between  t h e c o n d u c t i o n and v a l e n c e  impurities  while  the h o l e  of t h i s  zone,  near  Other  behind  these  are trapped.  levels  from  semiconductor.  i n posi-  semiconductors.  as they " d o n a t e "  lead to l e v e l s  Valence  are called  the valence band, The e n e r g y  electrons  lying  leaving mobile holes  These i m p u r i t i e s  as they a c c e p t e l e c t r o n s  the conduction  i s trapped  to N-type  impurities  impurities  into  the top of the valence band.  into  of a P-type  left  type lead  a r e c a l l e d donor  the e l e c t r o n s  formation  influence  a r i s e because,  c a n e a s i l y be e x c i t e d  impurities  band,  the  crystal,  i s s o we h a v e a n N - t y p e o r a P - t y p e  the conduction band.  while  gap b e t w e e n  i n the c r y s t a l  a carrier,  These i m p u r i t i e s  conduction  semiconductor  An e l e c t r o n f r o m s u c h a l e v e l , when e x c i t e d  band,  i s due  w h i c h move u n d e r  ( n ) a n d t h e number  and o n t h e c r y s t a l  n and p .  the  I n a pure  and depend o n l y on t h e energy  However,  i n the u n f i l l e d  i n the valence band,  carrier electrons  valence bands,  to  conduction i n semiconductors  level  low i n electrons  behind, acceptor  leading  to  structures  19 FIG.  3.--  Impurity Levels  ?  ^L&y  Electron injected c o n d u c t i o n band Impurity  into  Conduction Band  level  V a l e n c e Band  Donor  Impurity  Conduction Band  I Electron Energy —  Impurity l e v e l  (for accepting electrons) Valence  Acceptor  Impurity  Band  20 for  both It  types  of  impurities  i s p o s s i b l e to  diffusing material  a donor  convert  impurity  c a n be c o n v e r t e d  d i f f u s i o n process extends different  regions.  junction.  type r e g i o n i n t o r e p u l s i o n from effect  is  called  the  to  10  However,  layers  the  cm  absence of  generated  by  the  crystal.  2.  The  or  donor  and c o n v e r s e l y ,  part  way,  the  j u n c t i o n between  these regions  the  balances  free  If  continue  is  of  two  called a from  until  the d i f f u s i o n  the  have  electrons  j u n c t i o n , 'a r e g i o n free These l a y e r s  N-type  diffusion.  crystal will  by  the  P-N  the  Coulomb  forces.  charge  are very narrow,  N-  The  carriers,  being  9  a reverse bias  causes a great  i n c r e a s e depending  have been a c h i e v e d . The  only  external  agitation,  the  These d e p l e t i o n  events, a process  junction  (negative  i n c r e a s e i n the w i d t h  on the v o l t a g e  contribution  ionizing  to  to are  the  the  Depletion  l a y e r s have  conduction  those  that  applied.  of  extremely  current,  electron-hole  can be r e d u c e d by  in  pairs cooling  Crystal c r y s t a l i s made b y d i f f u s i n g an a c c e p t o r  to be d i f f u s e d added  only  layer.  thermal  P-I-N  A P-I-N crystal,  at  the  3 mm  crystal,  to N-type m a t e r i a l  to P - t y p e by a c c e p t o r  charge b u i l d u p  high r e s i s t i v i t y . the  the  the a p p l i c a t i o n of  layer, >  P-type material  into  on the P - t y p e s i d e )  depletion  3.  the P - t y p e r e g i o n which w i l l  create,  -6  shown i n F i g .  t h e n be a d i f f u s i o n o f  depletion  typically  voltage  The  There w i l l  are  into  the  electrons  the P-type m a t e r i a l ,  impurity crystal  compensate leaving  into (say for  a donor  impurity  an N-type c r y s t a l .  into  a  P-type  The  impurity  P - t y p e ) m u s t be c h o s e n s o t h a t the a c c e p t o r  a r e g i o n w i t h no f r e e  the  l e v e l s which existed charge  carriers  in  other  •21 than  t h o s e due t o If  proper  material  resistivity for The  diffusing  on one s i d e of  on the o t h e r  tacts  thermal  side w i l l compared  applying  to  agitation. techniques  the  remain uncompensated. the  between  a reverse  j u n c t i o n under  that  width  (>2 of  The called  carrier free  compensated r e g i o n of i n the p a s t .  An e n e r g e t i c crystal will following  The  raise i t  The  energy of  a P-I-N  of  a P-I-N  compensated crystal  difference  c r y s t a l c a n be made much a P-N  junction.  crystal i s only  Hence  c r y s t a l has  Also  the  slightly  incorrectly  t h e name P - I - N  as P a r t i c l e  the  and t h e  the  been  crystals.  Detectors a  semiconductor  c r y s t a l and l o s e e n e r g y  i n one o f  the  9 ways.  the  conduction band,  the p r i m a r y  the energy  shared randomly  con-  bias.  c h a r g e d p a r t i c l e may i m p a r t to  low  addition,  the o n l y  charged p a r t i c l e that penetrates  interact with  three  to  Crystals  N-type m a t e r i a l  Therefore a P-I-N  reverse bias,  a P-I-N  In  region,  junctions.  r e g i o n of  on the a p p l i e d r e v e r s e  Semiconductor  width  P-N  than the d e p l e t e d r e g i o n of  intrinsic  a)  like  compensated r e g i o n , of  cm)  the  dependent  3.  the  P-type  These l a y e r s have a  t h e P - t y p e and c o m p e n s a t e d  a P-N  of  bias.  will  like  of  layer  c o m p e n s a t e d r e g i o n a n d a c t as e l e c t r i c a l  act  larger  a thin  c r y s t a l and a t h i n l a y e r  and N - t y p e r e g i o n s ,  being  only  compensated r e g i o n has a h i g h r e s i s t i v i t y .  junctions  act  are used,  leaving a hole  to  an  i n the v a l e n c e  p a r t i c l e i s r e d u c e d b y a n amount e q u a l  gap b e t w e e n  between  s u f f i c i e n t energy  the  the primary  two b a n d s . particle,  The the  electron band. to  the  remaining energy  secondary e l e c t r o n ,  is and  the secondary h o l e . processes b)  a),  b)  The  Each  or  of  these w i l l  p r i m a r y p a r t i c l e may  lattice itself.  optical  a n d a c o u s t i c a l modes o f  loss  of  lose  their  energies  by  c).  crystal  this  then  energy,  These  will  l o s e energy by i n t e r a c t i n g w i t h  interactions vibration.  continue  to  excite The  the  lattice  primary  the  in  particle,  l o s e energy by p r o c e s s a ) ,  after b),  or  c). c)  When a p a r t i c l e h a s i n s u f f i c i e n t e n e r g y  processes, lattice  i t must  l o s e i t s remaining energy  o v e r a l l energy  loss  When a r e v e r s e b i a s p r o d u c e d b y p r o c e s s a) increase.  It  the  l o s t by  energy  in later  of  the  l o s s e s to  above the  p r o c e s s i s shown s c h e m a t i c a l l y i n F i g .  i s a p p l i e d to a c r y s t a l ,  above  cause the  current  the primary  particle.  the  This  e l e c t r o n s and h o l e s  a c r o s s the  current will  4.  crystal  increase,  to  to deduce  be d e s c r i b e d i n m o r e  sections. of  electron-hole pairs  =  E/£  that  contribute  to  the  current  is  by n  where £  by t h e r m a l  i s p o s s i b l e , by m e a s u r i n g t h i s  T h e number given  either  material.  The  detail  for  E is  is  the  the energy average  The v a l u e germanium or  energy £  i n the required  depends  silicon),  to  produce  the  on the s e m i c o n d u c t o r m a t e r i a l primary  f l u c t u a t i o n i n t h e number  of  electron-hole pairs  the  crystal  an e l e c t r o n - h o l e  of  of  on the  c a r r i e r f r e e r e g i o n of  type  temperature The  of  lost  particle,  and  pair.  (usually  and on  the  crystal. i s given  by  9  23 FIG. E n e r g y  L o s s  i n  4.--  S e m i c o n d u c t o r  P r i m a r y  P a r t i c l e  E n e r g y  E x c i t a t i o n to  3  =  =  =  E  O p t i c a l  band.  E n e r g y  p ( E - E , ) /  i s  l a r g e  p  i s  the  become  p r i m a r i e s  Loss  f o r  f u t u r e  3  )  E  /2  g e n e r a t i o n  i f  t h e i r  enough.  f r a c t i o n  of  e n e r g y  l o s t  by  the  E  p r i m a r y  p a r t i c l e .  -  E  r  P a r t .  Energy  Energy P(E- E  =  P r i m a r y  E l e c t r o n  2  =  now  a c c o u s t i c a l  E n e r g y  ) ( l - p )  These  or  e x c i t a t i o n  E„  H o l e  P a r t .  E n e r g y ( E - E  L o s s  =  e l e c t r o n  c o n d u c t i o n  E n e r g y  P r i m a r y  of  C r y s t a l s  = ,  e n e r g y  24 < An> where  n_>  factor; of  is  previously,  )  (E/6  h  F  t h e RMS f l u c t u a t i o n s  a statistical  F = 0 would  =  imply  while  factor that  a value  i n n and F  i n t r o d u c e d by U.  no e n e r g y was of  F = 1 would  p r o d u c i n g an e l e c t r o n - h o l e  pair  is  two e x t r e m e s ,  somewhere  0 and  1.  between  these  is  the  Fano^  so-called  i n 1946.  l o s t by p r o c e s s e s b) imply  approaches  that  zero.  the value  the  Since of  A or  Fano value c)  probability the  true  F m u s t be  given of  picture between  CHAPTER I I I LITHIUM ION DRIFTED SILICON DETECTORS  1.  S i ( L i ) Detectors  f o r Photons  and E l e c t r o n s  A l i t h i u m i o n d r i f t e d s i l i c o n detector o p e r a t e d under r e v e r s e b i a s . l i t h i u m ions high  (a donor  temperature.  the P-type  These c r y s t a l s a r e made by d i f f u s i n g  impurity)  i n t o a c r y s t a l of P-type s i l i c o n a t a  The l i t h i u m compensates f o r the a c c e p t o r  s i l i c o n as d e s c r i b e d  The N- and P-type r e g i o n s contacts.  ( S i ( L i ) ) i s a P-I-N c r y s t a l  earlier,  creating a carrier free region.  a r e h i g h l y doped and s u p p l y  F i g . 5 schedmatically  impurity i n  good  electrical  shows some f e a t u r e s of a S i ( L i )  detector. The average energy r e q u i r e d  to produce an e l e c t r o n - h o l e p a i r i n  s i l i c o n by e l e c t r o n s depends o n l y on the temperature o f the c r y s t a l T h i s dependence i s shown i n F i g . 6.  1 1  .  The number o f e l e c t r o n - h o l e p a i r s  produced i n the c a r r i e r f r e e r e g i o n i s l i n e a r w i t h e l e c t r o n energy provided  the e l e c t r o n l o s e s a l l i t s energy i n t h i s r e g i o n .  minimum t h i c k n e s s layer  (window)  sets a  f o r the compensated r e g i o n and a l s o r e q u i r e s a dead  thin  enough t h a t no a p p r e c i a b l e  as the e l e c t r o n passes through i t . i n s i l i c o n as a f u n c t i o n o f energy  amount o f energy i s l o s t  F i g . 7 shows the range o f e l e c t r o n s  12  energy i n s i l i c o n p e r m i c r o n o f dead energy  This  .  Fig.  8 shows the l o s s i n e l e c t r o n  l a y e r as a f u n c t i o n o f e l e c t r o n  12 .  An i n c i d e n t e l e c t r o n may be s c a t t e r e d o u t o f the compensated of  the d e t e c t o r ,  as shown i n F i g . 9.  The " b a c k s c a t t e r e d "  have l o s t o n l y p a r t o f i t s energy i n the d e t e c t o r . -25-  region  electron w i l l  2,1: I t has been shown '  26 FIG. Si(Li)  5.— Crystals  P-layer (grounded)  N  Incident particles  (+  Dead l a y e r (window)  layer voltage applied)  a)  Physical  b)  C o n c e n t r a t i o n of carriers  c)  E l e c t r i c f i e l d due to applied bias  FIG. £  6.--  27  v s . Temperature  T in  FIG.  °K  7.--  Range of E l e c t r o n s i n S i  Range i n S i l i c o n  (microns)  28  FIG. 8.-Energy Loss i n Dead L a y e r  t  10  Electron Energy Loss (Kev/micror ) 1  10  100  1000 E l e c t r o n Energy  FIG.  10,000  (Kev)  9.--  P a r t i a l Energy Loss P r o c e s s e s  Compensated r e g i o n of detector  Backscattered Electron  >  Incident Electrons  'Backscattered" Electron  E l e c t r o n too e n e r g e t i c to be stopped by t h i s t h i c k n e s s of c r y s t a l  29  t h a t the f r a c t i o n of e l e c t r o n s s c a t t e r e d out o f a S i ( L i ) d e t e c t o r does n o t depend on e l e c t r o n energy.  I t depends o n l y on the s o u r c e - d e t e c t o r  geometry used. The d e t e c t i o n of photons detector requires  (gamma r a y s or x - r a y s ) w i t h a S i ( L i )  t h a t the photon's  (or e l e c t r o n s ) , and  energy be t r a n s f e r r e d  that the e l e c t r o n be d e t e c t e d .  to an  electron  T h i s t r a n s f e r of  energy can be accomplished by t h r e e p r o c e s s e s ; they are a)  Photo-electric  effect.  The photon, w i t h energy b i n d i n g energy E„. Eg  - Eg.  The e l e c t r o n i s e j e c t e d from the atom w i t h energy  The x - r a y or auger e l e c t r o n e m i t t e d due  atomic s h e l l w i l l b)  , i s absorbed by an atomic e l e c t r o n w i t h  Compton  interact  to the vacancy i n the  also.  scattering.  The photon s u f f e r s an i n e l a s t i c c o l l i s i o n w i t h an atomic e l e c t r o n , l o s i n g energy E  £  to the e l e c t r o n .  I f E^ i s g r e a t e r  than the b i n d i n g  energy o f the e l e c t r o n , i t w i l l be e j e c t e d from the atom. l e f t w i t h reduced energy and may c)  undergo f u r t h e r  The photon i s  interactions.  Pair production. 2 •  If  the photon energy i s g r e a t e r than 2 m  e l e c t r o n r e s t mass, the photon may  0  c , where m  0  i n t e r a c t w i t h the coulomb f i e l d  the n u c l e u s , c r e a t i n g an e l e c t r o n - p o s i t r o n p a i r .  of  The photon i s c o m p l e t e l y  absorbed and the excess energy i s shared by the e l e c t r o n and 2 The excess energy i s E = E j - 2 m, c , The  i s the  positron.  c r o s s - s e c t i o n s as f u n c t i o n s of photon energy f o r these t h r e e  p r o c e s s e s i s shown i n F i g . 10. The measurement of the energy of a photon w i t h a S i ( L i )  detector  FIG.  10.—  Photon Cross S e c t i o n f o r S i l i c o n  Photon Energy i n Kev  31  r e q u i r e s t h a t a known f r a c t i o n o f i t s energy be t r a n s f e r r e d  to the  e l e c t r o n s , and t h a t the e l e c t r o n s be c o m p l e t e l y stopped i n the compensated region. I n Compton s c a t t e r i n g detector after electron. measuring  the photon i s u s u a l l y s c a t t e r e d out o f the  t r a n s f e r r i n g an unknown f r a c t i o n of i t s energy to the  For this  r e a s o n the Compton p r o c e s s i s n o t a u s e f u l means o f  the photon's  energy.  The p h o t o - e l e c t r i c e f f e c t and p a i r p r o d u c t i o n , on the o t h e r hand, t r a n s f e r a l l o f the photon's  energy to e l e c t r o n s .  p h o t o - e l e c t r i c p r o c e s s , the f u l l by measuring is  I n the case o f the  energy o f the photon can be determined  the energy o f the p h o t o - e l e c t r o n produced, p r o v i d e d t h a t i t  stopped i n the compensated r e g i o n .  The p r o b a b i l i t y  t h a t the x - r a y  caused by the vacancy i n the atomic s h e l l w i l l escape w i t h o u t undergoing a p h o t o - e l e c t r i c i n t e r a c t i o n i n the compensated r e g i o n i s n e g l i g i b l e as 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 f o r t h i s energy  ( < 2 Kev f o r s i l i c o n )  is very large. The p o s i t r o n and e l e c t r o n produced i n the p a i r p r o c e s s l o s e energy i n the u s u a l way.  The p o s i t r o n , once i t has l o s t  their  i t s energy,  will  i n t e r a c t w i t h an atomic e l e c t r o n to form two photons, each w i t h energy 2 m„  c .  These photons may i n t e r a c t i n the compensated r e g i o n by e i t h e r  the p h o t o - e l e c t r i c o r the Compton s c a t t e r i n g p r o c e s s e s , o r they may escape.  A known f r a c t i o n o f the i n c i d e n t photon's  energy w i l l be  d e p o s i t e d i n the d e t e c t o r p r o v i d e d n e i t h e r o f these two secondary undergo  Compton s c a t t e r i n g .  photons  Ey i s d e p o s i t e d i f both photons produce 2 photo-electrons, E^ - m c i s d e p o s i t e d i f one photon escapes and . 2 the o t h e r produces a p h o t o - e l e c t r o n , and E ^ -. 2 m c i s d e p o s i t e d i f 0  b  32  b o t h escape. The c o l l e c t i o n , a m p l i f i c a t i o n and a n a l y s i s o f these produced by the energy l o s s i n S i ( L i ) d e t e c t o r s  charge-carriers  may be used to produce  an energy spectrum of the i n c i d e n t r a d i a t i o n .  2.  Associated  Electronics  The e l e c t r o n i c s r e q u i r e d  to c o l l e c t ,  amplify  and a n a l y z e the f r e e  charge c a r r i e r s produced i n the compensated r e g i o n o f a S i ( L i ) are  shown d i a g r a m m a t i c a l l y i n F i g . 11.  The e l e c t r o n i c s d e s c r i b e d a r e  those used i n t h i s r e p o r t and a r e o f " s t a t e - o f - t h e - a r t " The p r e a m p l i f i e r amplifier  i s a high  low n o i s e ,  (Tennelec, model 135 M) t h a t u t i l i z e s  impedance and low n o i s e valent  gain,  of a f i e l d - e f f e c t  c u r c u i t f o r a S i ( L i ) detector  shown i n F i g . 12.  and  resistance respectively.  R  g  and C  g  quality.  charge s e n s i t i v e the i n h e r e n t  t r a n s i s t o r (FET).  coupled  represent  detector  high  input  The e q u i -  to an FET p r e a m p l i f i e r i s  the c r y s t a l c a p a c i t a n c e and  a r e the r e s i s t a n c e  and c a p a c i t a n c e  i n the c o n n e c t i o n s between the c r y s t a l and the p r e a m p l i f i e r .  R^ i s the  9 l o a d r e s i s t a n c e o f the b i a s v o l t a g e parallel  combination o f  supply  (typically  10  ohms).  The  and R^, i s the feedback impedance o f the charge  s e n s i t i v e stage of the p r e a m p l i f i e r . If R  g  i s small  and R^ and R^ a r e l a r g e , the o u t p u t v o l t a g e  V„  is  g i v e n by  •  '  _Q_A_ C, + C + CL. (A+l) d s F  where A i s the open loop deposited  g a i n o f the p r e a m p l i f i e r  and Q i s the charge  on C^; t h a t i s , Q i s the f r e e charge c a r r i e r s produced i n the  FIG.  11.—  Schematic o f E l e c t r o n i c s  ?  High v o l t a g e s u p p l y (0-» - 1000  Pulse Shaper  V)  Main Amp.  Baseline  Biased  Pulse  Amp.  Stretcher  Restorer  Crystal  To M.C.A. <-  FIG.  12.—  E q u i v a l e n t C i r c u i t f o r Detector-Preamp.  1  A\*  FE.T.  Cf  =  R  6i :  C  s  =  -w/  i  •p-  compensated r e g i o n o f the d e t e c t o r . I f A i s l a r g e , the output  v The  v o l t a g e reduces t o  JL  p u l s e shaper i s the i n t e g r a t i n g d i f f e r e n t i a t i n g network shown  i n F i g . 13.  I t s c h a r a c t e r i s t i c s are given i n Table  III.  The p u l s e  from  the p r e a m p l i f i e r i s shaped to g i v e the b e s t s i g n a l to n o i s e g a i n i n the main a m p l i f i e r . The main a m p l i f i e r i s a N u c l e a r  Chicago, Model 27001.  I t s gain i s  c o n t i n u o u s l y v a r i a b l e from 6 to 400. The  b a s e l i n e r e s t o r e r i s an O r t e c , Model 438.  i n s u r e t h a t a p u l s e i s n o t superimposed on the t a i l that i s , i t prevents The  biased  pulses  restored The  of a preceding  pulse;  p i l e - u p o f the i n d i v i d u a l s i g n a l s .  a m p l i f i e r ( O r t e c , Model 408) d i s c r i m i n a t e s a g a i n s t  p u l s e s below a g i v e n v o l t a g e . All  I t s f u n c t i o n i s to  This discriminator voltage  i s adjustable.  above t h i s v o l t a g e a r e a m p l i f i e d l i n e a r l y and t h e i r  baseline  to z e r o . pulse  compatible  s t r e t c h e r ( O r t e c , Model 411) i n s u r e s t h a t the p u l s e s a r e  with  the i n p u t t o the m u l t i - c h a n n e l  analyser  (MCA), a  Nuclear  Data, Model 110. The  MCA  consists of a a n a l o g - t o - d i g i t a l converter,  memory (128 c h a n n e l s ) .  I t s readout i s v i s u a l  and a 128 word  ( N u c l e a r Data 410 D i s p l a y ) ,  or by a t e l e t y p e p r i n t e r and paper tape puncher. A t y p i c a l output a c t i v e source  o f t h i s system i s shown i n F i g . 14.  The r a d i o -  used was "^Co, which decays by e l e c t r o n c a p t u r e  to "^Fe.  FIG.13.-P u l s e Shaper  Network  0«.-v ( ?oS>  T1  T3  T4  T0  Tr  are  are  2N4124 2N4126  37  Table I I I Characteristics  of the P u l s e Shaper  Integration  Differentiation  Time Const.  C  l  Time Const. (A sec.)  C  2  (Msec.)  (pf)  0.2  20  0.2  .002  0.47  47  0.5  .005  1.0  100  l.o  .01  2.0  200  2.0  .02  4.7  47  5.0  .05  10.0  1000  10.0  Amplification R  3  (ohms)  Gain  22  2  47  4  100  8  (,*f)  .1  T y p i c a l Low Energy  Spectrum  Source:  L+M+ K  121.4  ~^Co  Detector:  S^  Kev/chan:  .378  •121.9  Y-121.9  r  I  •  ,»-o  /\ K  136.3  ©  FWHM  /  L-2.7-jJ FWHM  3.3-  \  /  / «  L+M+  /  \  \  30  40  50  / 60  /  I  •136.3  K-136.3  \ 70  80  Channel Number  90  100  110  120  39 The f o u r peaks  a r e due to the gamma r a y s and c o n v e r s i o n e l e c t r o n s  the 136.3 and 121.9 Kev t r a n s i t i o n s  i n "^Fe.  The f i r s t  peak i s due to  the K c o n v e r s i o n e l e c t r o n s from the 121.9 Kev t r a n s i t i o n . due  to gamma r a y s from this t r a n s i t i o n ,  The second i s  as w e l l as the L+ M+  v e r s i o n e l e c t r o n s whose energy i s o n l y s l i g h t l y r a y ' s energy.  from  con-  lower than the gamma  The t h i r d and f o u r t h a r e due to the K c o n v e r s i o n e l e c t r o n s  and gamma r a y s p l u s L + M +  c o n v e r s i o n e l e c t r o n s from the 136.3 Kev  transition.  3.  I n h e r e n t R e s o l u t i o n o f the D e t e c t o r - A n a l y s e r System The peaks  particles  i n F i g . 14 r e p r e s e n t t o t a l energy l o s s by mono-energetic  i n the compensated r e g i o n of the d e t e c t o r .  The w i d t h o f these  peaks a t h a l f maximum (FWHM-full-width-half maximum) i s c a l l e d the r e s o l u t i o n LO , and i s due to f l u c t u a t i o n s  i n the r e s p o n s e o f the  d e t e c t o r - a n a l y s e r system to these mono-energetic  particles.  The  f l u c t u a t i o n s i n the response have two independent causes.  a)  S t a t i s t i c a l f l u c t u a t i o n s i n the number o f e l e c t r o n - h o l e  They  are  produced  i n the d e t e c t o r .  The r e l a t i o n s h i p between the FWHM and the  f l u c t u a t i o n s i n the number o f p a i r s U> assuming  c  =  pairs  ^An> is  9  2.35 £ < A n >  t h a t the peak i s g a u s s i a n shaped.  From e q u a t i o n I I - 1 the  FWHM becomes L^c b)  =  2.35 ( E £ ) ^ F  F l u c t u a t i o n s due to n o i s e generated i n the d e t e c t o r and a s s o c i a t e d  electronics.  9 A d e t a i l e d a n a l y s i s of n o i s e has been done by G o u l d i n g .  40  He shows t h a t t h e r e a r e three main sources o f n o i s e , which may be summ a r i z e d as f o l l o w s .  The f i r s t ,  shot n o i s e , r e s u l t s from  p a i r s generated by thermal e x c i t a t i o n i n the d e t e c t o r .  electron-hole I t s contribution  to LO i s g i v e n by lO  The  2 J( K C T R S ) s T eq s  =  s  2  second, f l i c k e r n o i s e ,  flowing  i s generated by f l u c t u a t i o n s i n the c u r r e n t  i n t o the i n p u t stage of the p r e a m p l i f i e r , and i t s c o n t r i b u t i o n  is F  W  =  ( K  F  C  T F S  ) X  "  Finally,  leakage n o i s e  detector  and i t s c o n t r i b u t i o n i s  W  L  "  (  I n the above e q u a t i o n s ,  i s caused by c u r r e n t s over the s u r f a c e o f the  K  L  i  L  S  )  1  "  the K's a r e c o n s t a n t s ,  of c r y s t a l and i n p u t stage,  T i s the c r y s t a l  i s the t o t a l  temperature  capacitance  ( i n °K), R  is  the e q u i v a l e n t n o i s e r e s i s t a n c e o f the p r e a m p l i f i e r i n p u t , the S's a r e factors  t h a t depend upon the shape o f the p u l s e s ,  and i i s the leakage  current. Since  these n o i s e sources a r e independent of each o t h e r ,  dent o f the number o f e l e c t r o n - h o l e p a i r s ,  and indepen-  the t o t a l r e s o l u t i o n i s g i v e n  by = For  ( K  s T C  T  R  eq s S  +  ^  °T F S  +  \  1  S  L  +  £ ^ (2.35 f ) V  good r e s o l u t i o n , each term i n t h i s e q u a t i o n must be made as s m a l l as  possible. R  i s s e t by the type o f i n p u t  to the p r e a m p l i f i e r used.  I t cannot  be  changed w i t h o u t The  r e d e s i g n i n g the p r e a m p l i f i e r .  f a c t o r s S can be  i n the p u l s e shaper.  lowered  The  by the proper  u s u a l procedure  c h o i c e of time  for finding  s t a n t s i s to m i n i m i z e the r e s o l u t i o n by changing shaper  constants  the b e s t time  and  con-  i n the p u l s e  a f t e r a l l o t h e r parameters have been f i x e d .  C  can be  lowered  by u s i n g low  c r y s t a l and p r e a m p l i f i e r , and by  c a p a c i t a n c e connectors  the proper  between the  c h o i c e of d e t e c t o r .  c a p a c i t a n c e of a S i ( L i ) d e t e c t o r , assuming i t can be  The  t r e a t e d as a p a r a l l  plate capacitor, i s C  where  £  d  i  =  A/W  i s the p e r m i t t i v i t y of s i l i c o n . C  d  =  1.05  A/W  Therefore  picofarads  Here A i s the a r e a of the d e t e c t o r i n square  centimeters  and W i s the  t h i c k n e s s of the compensated r e g i o n i n c e n t r i m e t e r s . The  r e l a t i o n s h i p between n o i s e and  t o t a l i n p u t c a p a c i t a n c e f o r the  135 M p r e a m p l i f i e r i s ^ U) =  1.5  The Fano f a c t o r material.  Kev +  .018  Kev/pf  (in silicon)  (F) i n the e q u a t i o n f o r  I t i s very d i f f i c u l t  L*J  c  depends on the  crystal  to measure a c c u r a t e l y , but most r e p o r t s  9 17 g i v e v a l u e s f o r s i l i c o n r a n g i n g from .2 to .4 ' The for  U)^.  temperature o f the c r y s t a l e f f e c t s Decreasing  r e s o l u t i o n due  three terms, i n the  the temperature decreases  equation  the c o n t r i b u t i o n to the  to shot n o i s e by d e c r e a s i n g the number of thermally, pro-  duced e l e c t r o n - h o l e p a i r s .  I t a l s o decreases  the c o n t r i b u t i o n due  to  leakage  c u r r e n t by d e c r e a s i n g i , but  fluctuations £  6).  leakage  the c r y s t a l .  current also varies with  The  the r e v e r s e b i a s a p p l i e d to  b i a s v o l t a g e must be h i g h enough to a c c e l e r a t e the  e l e c t r o n s and h o l e s away from each o t h e r b e f o r e Unless  to  i n the number of e l e c t r o n - h o l e p a i r s produced by i n c r e a s i n g  (see F i g . The  i n c r e a s e s the c o n t r i b u t i o n due  g r e a t care i s taken  they are a b l e to r e u n i t e .  i n the p r e p a r a t i o n of the c r y s t a l  ing  the^ s u r f a c e of the c r y s t a l f r e e from contaminates,  ing  the leakage  current w i l l  dominate over  a n d . i n keep-  the term i n v o l v -  a l l the o t h e r s and w i l l  effect-  i v e l y s e t the minimum r e s o l u t i o n o b t a i n a b l e . S i n c e the c r y s t a l  i s u s u a l l y c o o l e d much below room temperature,  i t must be p l a c e d i n a vacuum chamber to i n s u r e t h a t no add  condensation  o c c u r s on  the c r y s t a l s u r f a c e , as t h i s w i l l  to the s u r f a c e  current.  F i g . 15 shows the vacuum chamber used f o r c o o l i n g the  I n summary, once the d e t e c t o r - a n a l y s e r system has are o n l y  three adjustments  leakage crystal.  been chosen,  there  t h a t can be made to improve the r e s o l u t i o n .  They a r e i ii iii In order  Temperature of the  crystal  Bias voltage Time c o n s t a n t s  of the pulse shaper.  to determine the b e s t r e s o l u t i o n o b t a i n a b l e w i t h  d e t e c t o r - a n a l y s e r system d e s c r i b e d i n S e c t i o n I I I - 2, temperature was each s e t t i n g , c o u p l e s , and  v a r i e d by  measured by  the r e s o l u t i o n o p t i m i z e d The  crystal  changing the l e n g t h of the c o l d - f i n g e r .  the temperature was  the time c o n s t a n t s .  the  the  copper-constantin  thermo-  by a d j u s t i n g the b i a s v o l t a g e  r e s u l t s of t h i s procedure f o r the two  At  and  crystals  FIG; Crystal  15.— Chamber  to vacuum pump  Liquid Nitrogen Chamber  Cold  Finger Crystal  c  -O  FIG. P l o t o f Temperature v s . Optimized  16.-R e s o l u t i o n f o r Two  Detectors  45  used a r e shown i n F i g . 16. g i v e n i n T a b l e IV.  The optimum r e s o l u t i o n f o r the  reached a t T = 190°C The  The c h a r a c t e r i s t i c s o f these c r y s t a l s a r e  V = 400 v o l t s ,  optimum r e s o l u t i o n f o r the  and time c o n s t a n t s o f 2  4.  /(sees.  d e t e c t o r was reached a t T = -100°C,  V = 350 v o l t s and time c o n s t a n t s o f 2 121.9  d e t e c t o r was  Xsecs.  The peak used was the  Kev gamma peak o f ~^Co.  Other  C o n t r i b u t i o n s to the R e s o l u t i o n  Peaks due to monoenergetic  p a r t i c l e s may be broadened  by e f f e c t s  o t h e r than the f l u c t u a t i o n s i n the response o f the d e t e c t o r a n a l y s e r system.  These e f f e c t s a r e source c h a r g i n g , source a b s o r p t i o n , s c a t t e r i n g  from s u r r o u n d i n g m a t e r i a l s , and dead l a y e r a b s o r p t i o n . Sources  t h a t emit e l e c t r o n s w i l l  q u i c k l y charge  (and sometimes f l u c t u a t i n g ) p o t e n t i a l s , emitted e l e c t r o n s . The  thus a l t e r i n g  The s o u r c e must t h e r e f o r e be w e l l  e f f e c t o f too t h i c k a source i s to degrade  e l e c t r o n s coming from below the s u r f a c e by c o l l i s i o n absorption).  themselves  T h i s adds a low energy  r e s u l t i n g i n a greater width. the s o u r c e must be k e p t t h i n ,  grounded.  the energy o f losses  (source  to the peak,  To keep t h i s peak b r o a d e n i n g  to a minimum,  the maximum t h i c k n e s s depending  s o u r c e a b s o r p t i o n i s shown i n F i g . 17. v e r s i o n peak o f "^Co.  the energy o f the  component, o r t a i l ,  s o u r c e m a t e r i a l and the e l e c t r o n energy.  to h i g h  on the  An example of peak b r o a d i n g due to The peak i s the 114 Kev K con-  The S^ d e t e c t o r was used  to o b t a i n both  spectra.  T h i n s o u r c e s may be made i n a number o f d i f f e r e n t ways^, b u t those used i n t h i s experiment were p r e p a r e d by s u b l i m i n g the s o u r c e m a t e r i a l onto a t h i n aluminum  b a c k i n g , as e x p l a i n e d below.. The s u b l i m a t i o n  chamber i s shown i n F i g . 18.  A drop o f a s o l u t i o n of the source m a t e r i a l  FIG. E f f e c t of  Thick  1000  f  17.-  Source T h i c k n e s s on  Resolution  Thin  Source  A  Source  Peak i s a t 114.8 Kev  3.3  Kev  M  k  2.5  Kev  0  • » • k  tt  r, ° 9  _ » o  30  40  50  60  30  40  50  60  T a b l e IV Characteristics  o f the Two D e t e c t o r s  Simtec type KQ2  D e t e c t o r S\  Obtained from Simtec L t d . i n October, 1968  Recommended r e v e r s e b i a s  400-800 v o l t s  Thickness  2 mm  (W)  2 Area  (A)  50 mm  Window (Dead L a y e r )  Detector Kj  .2 microns  Kevex type A80-5  Obtained from Kevex C o r p o r a t i o n i n F e b r u a r y , 1968  Recommended r e v e r s e b i a s  300-700 v o l t s  Thickness  5 mm  (W)  2 Area  (A)  Window (Dead L a y e r )  80 mm 5 microns  FIG. 18.-Sublimation  Chamber  Glass viewer  z  Source b a c k i n g  Source M a t e r i a l Tungsten ribbon  To vacuum pump  Tungsten Copper'  ^ Ceramic feed through  To p u l s e r •9-  Ribbon  FIG. Pulser  49  19.—  Circuit  2.N  SSS  no v//j.d  --w—0— SooJl  To V a r i a c 60 VAC) o_  To Tungsten Ribbon I  hi S"  i s d e p o s i t e d on  the t u n g s t e n r i b b o n .  infra-red  lamp and  i s pulsed  through  The m a t e r i a l i s then d r i e d w i t h  the chamber evacuated. the r i b b o n , and  A l a r g e c u r r e n t (-10  as a r e s u l t a l o c a l h o t - s p o t  i n the r e g i o n of the d r o p l e t where the r i b b o n w i d t h has been The  source m a t e r i a l i s sublimed  backing.  The  o f f the r i b b o n and  t h i c k n e s s of the source  c u r r e n t p u l s e s used,  in Fig  0  develops reduced.  can be v a r i e d by the number of  The  the amount of  current pulse generator  source h o l d e r , e t c . does not n o r m a l l y broaden a peak.  s c a t t e r i n g through looks l i k e a f u l l in  source  i s shown  19.  S c a t t e r i n g of e l e c t r o n s or photons from the chamber w a l l s , backing,  Amps)  onto the aluminum  the l e n g t h of the p u l s e s , or by  m a t e r i a l d e p o s i t e d on the r i b b o n .  s m a l l angles  source Compton  can, on o c c a s i o n , produce a peak t h a t  energy peak.  the s c a t t e r i n g p r o c e s s e s  In most cases, however, the energy  lost  l e a v e s a r e s i d u e t h a t appears a t c o n s i d e r a b l y  lower  e n e r g i e s than the u n d i s t o r t e d peak and  i s u s u a l l y smeared over  lower  energy background as a continuum.  e x c e p t i o n to t h i s  of low-energy photons, which may a slight  l o s s i n energy.  F  i  where E'^  and  E^  i s the  be s c a t t e r e d a t l a r g e angles w i t h  From the Compton p r o c e s s one  only  * ^  (  1  "  C  o  S  e  )  i s very  Q  i s the s c a t t e r i n g a n g l e .  l a r g e f o r E$  <£.  100  Kev  and  The 20°<  i n c i d e n t gamma  cross-section for ©  < 100°.  Hence  l a r g e mass c o n c e n t r a t i o n s s h o u l d be k e p t as f a r away from the source d e t e c t o r as p o s s i b l e . 20(b)  case  can deduce t h a t  are the e n e r g i e s of the s c a t t e r e d and  r a y s r e s p e c t i v e l y and t h i s process  The  the  _  1  Fig.  an  F i g . 20(a)  shows t h e i r e f f e c t on  shows two  types of source h o l d e r s  the 41 Kev  x-ray peak of europium.  and and  FIG. Two  20.-  Types of Source H o l d e r s and T h e i r E f f e c t Low  Energy Photon  on  Resolution  Detector 'Thin Afi. w i t h s o u r c e sublimed onto i t Ring holder a)  Ae or lucite ring  Electrical y  contact  Thin  Ai Cardboard  Cardboard h o l d e r  b)  70  : SO  90  Too  110  Channel No.  120 *•  E f f e c t s of B a c k s c a t t e r i n g from Source H o l d e r on 41 Kev X-Rays  FIG. 21 a ) . — E f f e c t s of Dead Layer on Low Energy E l e c t r o n s  53  Fig.  8 showed t h e energy l o s s o f e l e c t r o n s p a s s i n g through the dead  l a y e r of a S i ( L i ) d e t e c t o r .  F i g s . 21 shows the e f f e c t o f the dead  layers  153 of t h e Ki  and S-^ d e t e c t o r s on a p o r t i o n o f the  The spectrum taken w i t h t h e K-^ d e t e c t o r  Gd e l e c t r o n  spectrum.  (21(a)) shows the two gamma peaks  a t 97.4 and 103.2 Kev and a degraded e l e c t r o n peak a t lower energy. spectrum taken w i t h the  detector  ( 2 1 ( b ) ) has three e l e c t r o n peaks, two  of which a r e superimposed on the gamma peaks. itself, is  The  The gamma spectrum by  taken w i t h the e l e c t r o n s absorbed by a t h i n aluminium a b s o r b e r ,  i n c l u d e d f o r comparison o f the two s p e c t r a .  CHAPTER IV ANALYSIS OF  1.  Computer  Analyses  A computer program was obtained with explained  SPECTRA  w r i t t e n to s i m p l i f y the a n a l y s i s of  the d e t e c t o r - a n a l y s e r  in detail  system d e s c r i b e d above.  i n Appendix A.  = 1 i s i n d i c a t i v e of a good f i t ,  As  spectra  It is  s t a t e d t h e r e , a v a l u e of  although  i t was  found  X  2 /(n-m)  experimentally  2 t h a t f i t s w i t h v a l v e s of 'X /(n-m) between 0 and _  3 still  f i t the f u n c t i o n  2  G[  to the d a t a v e r y w e l l .  I f "X /(n-m) was  r e r u n u s i n g d i f f e r e n t p o r t i o n s of the fit  greater  than 3,  t o t a l spectrum, as  the f i t was  the goodness of  i s v e r y s e n s i t i v e to any n o n - l i n e a r i t y i n the background.  It  found t h a t a l l the s p e c t r a a n a l y s e d w i t h t h i s program c o u l d be 2 w i t h a goodness of f i t parameter, /\. /(n-m), l e s s than 3. The  program i s capable  of s e p a r a t i n g peaks t h a t o v e r l a p ;  peaks whose energy d i f f e r e n c e i s l e s s Fig.  22 shows two  such peaks.  fitted  that i s ,  than the r e s o l u t i o n of the  They are the  and  was  x-ray  system.  peaks of  109 silver  t h a t r e s u l t from the e l e c t r o n capture  energies  are  22.1  and  25.0  of the f u n c t i o n f i t t e d  Kev  respectively.  to t h i s d a t a .  of 4.64  their  check the a c c u r a c y i n t e n s i t i e s was  given i n reference  FT  =  <-  5 5  Cd.  solid and  Their  curve  23(b)  i s a plot  are  compared w i t h  This r a t i o i s  -  3 ) R  -54-  the com-  the computer program.  of the s e p a r a t i o n of these peaks, the  found and 18.  The  F i g s . 23(a)  ponents of t h i s composite peak g i v e n by To  decay of  the accepted  ratio  value  of  FIG. 22.--  Charmel No.  FIG. 23.-Components of Peak i n F i g . 22  b)  a) 3000 /\  component  component  500  Counts 400  2000  300  200  1000  100  i « «  10  20  '  30  40 Channel No.  10  20  30  to"  c o r r e c t i o n f a c t o r f o r the d i f f e r e n c e i n e f f i c i e n c y of the S\ .  R i s the  d e t e c t o r f o r the two +  .05  d i f f e r e n t energies.  (see F i g . 26).  The  This c o r r e c t i o n f a c t o r i s  r a t i o of t h e i r i n t e n s i t i e s  which i s i n agreement w i t h  the v a l u e  i s t h e r e f o r e 4.9  peaks and fitting  on  the r e l i a b i l i t y  routine.  The  of the i n t e n s i t y e s t i m a t e s the  114.9  peak r e s u l t i n g from the e l e c t r o n capture  Kev  g i v e n by  K-conversion  decay of ~*^Co.  The  p o s i t i o n and  the same.  The  i n t e n s i t y are g i v e n i n T a b l e  Table  s p e c t r a of  (Channel)  setting  r e s u l t s f o r the e r r o r i n V.  System  Gain  Peak U n c e r t a i n t y  (Kev/Channel)  Intensity Error  (Kev)  (Percent.)  2.0  +5.6  1.0  t.2  +.2  +4.0  0.5  + .1  + .05  +3.0  0.3  + .1  ±.03  +2.0  + .03  +2.0  0.1  From T a b l e V i t can be  seen t h a t a g a i n s e t t i n g of .3 Kev/Channel  w i l l m i n i m i z e the e r r o r i n the i n t e n s i t y and the MCA  the  V  Change of E r r o r w i t h Gain  the  electron  t h i s peak were taken f o r the same l e n g t h of time f o r each g a i n so the i n t e n s i t i e s would be  to  the u n c e r t a i n t y i n the p o s i t i o n of  peak used was  +  quoted above.  D i f f e r e n t v a l u e s of g a i n of the a m p l i f i e r system were used determine the e f f e c t of g a i n on  .9  has  amplifier  128  p o s i t i o n of a peak.  channels the b e s t r e s u l t s are o b t a i n e d  i s set.so  t h a t a range of 35 —> 45 Kev  i f the  i s covered  by  Since  biased the  MCA.  58  2.  Energy  Calibration  T h i s work i s m a i n l y  concerned  t h a t i s , w i t h e n e r g i e s up biased amplifier  w i t h low energy e l e c t r o n s and  to a p p r o x i m a t e l y  120  s e t t i n g s are needed to cover  Kev.  Three  photons;  different  t h i s range of e n e r g i e s i f  the minimum e r r o r p o s s i b l e i n peak p o s i t i o n and  intensity  i s to  be  obtained. Each of these  t h r e e s e t t i n g s was  c a l i b r a t e d u s i n g as many photon  s o u r c e s of known energy as were a v a i l a b l e . s e t t i n g , and are l i s t e d in Figs.  the sources  energy range of each  a l o n g w i t h the e n e r g i e s of t h e i r photon peaks  i n T a b l e VI.  24(a),  The  The  r e s u l t s of these c a l i b r a t i o n s are  plotted  ( b ) , and ( c ) . 2  A l e a s t square was  done on  f i t u s i n g a f u n c t i o n of the form  the c a l i b r a t i o n d a t a .  The  LJ = a + bx +  v a l u e s of a and b found  cx  f o r each  s e t t i n g a r e g i v e n on was  found  the c a l i b r a t i o n curves ( F i g s . 24). The v a l u e of c 4 to be a t l e a s t a f a c t o r of 10 s m a l l e r than the v a l u e of b f o r 2  each s e t t i n g . approximately  S i n c e the maximum e r r o r i n i g n o r i n g the x .04  Kev  (which  most c a l i b r a t i o n s o u r c e s ) s h o u l d be noted  i s less  t h a t the e r r o r s a s s o c i a t e d w i t h the v a l u e s of a and  procedure,  calibration The  and  of  are o n l y the s t a t i s t i c a l  e r r o r s of  do not c o n t a i n the p o s s i b l e e r r o r s i n the  It  b the  quoted  energies.  energy of c o n v e r s i o n e l e c t r o n peaks can be o b t a i n e d from  c a l i b r a t i o n curves  d e t e c t o r of  these  i f the energy l o s t by an e l e c t r o n i n the dead l a y e r of  the d e t e c t o r i s known.  Si  than the e r r o r i n the e n e r g i e s  the c a l i b r a t i o n curves were assumed l i n e a r .  g i v e n on the c a l i b r a t i o n curves fitting  term i s then  Simtec quotes a v a l u e f o r the dead l a y e r of  .2 m i c r o n s .  T h i s v a l u e was  checked u s i n g the  the  conversion  T a b l e VI Energy C a l i b r a t i o n Sources  Source Setting  5 7  Co  1 0 9  Cd  1 3 3  Ba  Gd  1 5 3  Energy 1.  2 4 1  Gd  .05  (K* )  22.1  +  .1  (K^)  25.0 t ' . l  (K« )  30.9  - .1  (K* )  35.1  ± .1  (K* )  41.3  - .1  (K,)  47.3  ± .1  41.3  +  .1  (K^ )  47.3  +  .1  Setting 3  1 3 3  Ba  154  5 7  Eu  Co  18 Ag x - r a y s  Cs x - r a y s  Eu x - r a y s  Energy Range 38 -* 85 Kev  (K„ )  Ba  Reference  6 -•50 Kev  +  Ara  1 3 3  Energy Range  14.35  Setting 2 1 5 3  (Kev)  59.54 * 81.0  Eu x - r a y s  .02  18  - .2  22  Energy Range 75 -* 128 Kev  81.0  *  .2  22  + 86.9 . - .2  22  105.3  - .2  122.9  *  .2  121,91 - .05  ' 18  FIG. 24 a ) . - S e t t i n g #1  FIG. 2.4 b ) . - Setting  #2  133 a = 38.33 Kev +  01 + b = .3631 Kev/Ch. - .0005  80  70 Energy (Kev)  Energy (Kev) = .3631 (Channel No.) + 38.33  "141  Am  60  50 Gd  40  Gd K*  10  20  30  40  50  60 Channel No.  70  80  90  100  110  T  FIG. 24  c).—  S e t t i n g #3  63  e l e c t r o n standards l i s t e d  i n Table VII.  peaks were found from F i g s . 2 4 , and and  those g i v e n by Reference  dead l a y e r  The  apparent e n e r g i e s of  their  the d i f f e r e n c e between these e n e r g i e s  18 was  used to deduce the t h i c k n e s s of the  (see F i g . 8 ) .  T a b l e VII Energy L o s t i n Dead L a y e r of S\ D e t e c t o r  Energy (Kev) from Ref. 18  Source  1 0 9  1 0 9  5 7  5 7  Cd  (K _  .,)  62.2  Cd  (L  .,)  84.2 ±  Co  (K  1 2 2  Q  )  114.9  Co  (K ,  0  )  129.2  Q  Q  1 0  ±  +  +  .2  61.9 ±  .2  84.1  .2  114.6  .2  E (Kev)  Energy (Kev) from F i g . 24  129.2  +  +  +  .1  .3 - .3  .1  .1  +  .3  .1  +  .3  .3  +  .3  .3  +  .3  +  .3  +  .3  .1  .1  0.  A v e r a g i n g these v a l u e s g i v e s a dead l a y e r of which i s i n agreement w i t h the v a l u e o f  .175 +  .2 microns  the t h i c k n e s s more a c c u r a t e l y .  used  to f i n d I t was  0.  +  .3  .3 m i c r o n s ,  i t was  Simtec.  i m p o s s i b l e to  .2 microns was t h e r e f o r e  the c o r r e c t i o n to the e l e c t r o n e n e r g i e s . found  by as much as one  t h a t the p o s i t i o n of the c a l i b r a t i o n peaks c o u l d change channel due  a g a i n s t t h i s happening were performed e n e r g i e s was  The v a l u e of  .3  quoted by  S i n c e b e t t e r e l e c t r o n s t a n d a r d s were not a v a i l a b l e , find  Dead Layer (microns)  to changes i n e l e c t r o n i c g a i n .  w h i l e a spectrum was  F o r each spectrum used, new  d i s c a r d e d and  runs  c o n t a i n i n g peaks of unknown  I f the s h i f t i n the c a l i b r a t i o n peaks was  than .2 c h a n n e l s , the d a t a was  guard  being taken, c a l i b r a t i o n  b e f o r e and a f t e r each spectrum  taken.  To  the spectrum  greater  taken a g a i n .  v a l u e s of a and b were c a l c u l a t e d f o r the  64  calibration The  curves.  maximum p o s s i b l e  e r r o r i n the energy of unknown peaks was  e s t i m a t e d by summing the d i f f e r e n t e r r o r s p o s i t i o n from the f i t t i n g  involved.  procedure ranged from  peaks to .2 Kev f o r weak peaks.  The e r r o r i n peak  .03 Kev f o r  intense  The e r r o r i n the c a l i b r a t i o n curves was  e s t i m a t e d to be a maximum o f .2 Kev (.15 Kev f o r the e r r o r due to energy uncertainty  o f the c a l i b r a t i o n peaks and .05 Kev f o r t h e i r  uncertainty).  The maximum e r r o r i n e l e c t r o n energy due to an e r r o r i n  the v a l u e used f o r the t h i c k n e s s .24  Kev f o r 100 Kev e l e c t r o n s  o f the dead l a y e r of the d e t e c t o r  and .5 Kev f o r 20 Kev e l e c t r o n s  a maximum e r r o r i n the t h i c k n e s s the  position  o f .3 m i c r o n s ) .  e n e r g i e s o f unknown peaks i s t h e r e f o r e  .9 Kev f o r 100 and 20 Kev e l e c t r o n s  was  (assuming  The maximum e r r o r i n  .4 Kev f o r photons and .6 and  respectively.  The a c t u a l e r r o r i n  measured e n e r g i e s i s p r o b a b l y much l e s s than these v a l u e s f o r a l l b u t v e r y low  3.  i n t e n s i t y peaks.  S e p a r a t i o n o f E l e c t r o n and Photon S p e c t r a Quite often  e l e c t r o n and photon peaks o v e r l a p  convenient therefore spectra.  to be a b l e  i n a spectrum.  It is  to s e p a r a t e the e l e c t r o n and photon  The p r o c e d u r e used was as f o l l o w s :  First  t a i n i n g b o t h e l e c t r o n and photon peaks was taken.  a t o t a l spectrum conAn aluminum absorber  19 t h i c k enough to s t o p a l l e l e c t r o n s and  detector  was then p l a c e d  and a spectrum c o n t a i n i n g  only  between the s o u r c e  photon peaks was taken.  The  i n t e n s i t i e s o f the photon peaks was c o r r e c t e d  f o r the absorber and sub-  t r a c t e d from the t o t a l  peaks due to e l e c t r o n s .  The  spectrum, l e a v i n g o n l y  photon peaks were c o r r e c t e d  e q u a t i o n o f the form  f o r the a b s o r b e r by an e m p i r i c a l  I  Here  =  A, B, and E  J-o  exp (A/(E - E ) )  are constants that are v a r i e d  a b s o r p t i o n d a t a , I and I respectively,  IV - 1  a  to f i t e x p e r i m e n t a l  a r e the reduced and i n i t i a l  and E i s the photon energy.  F i g . 25 i s a p l o t of t h i s  f u n c t i o n a l o n g w i t h the e x p e r i m e n t a l a b s o r p t i o n d a t a . E  = 7, and B = 1.5 g i v e a s a t i s f a c t o r y f i t I t s h o u l d be noted t h a t t h i s  intensities  The v a l u e s A = 5,  to the e x p e r i m e n t a l d a t a .  c o r r e c t i o n f u n c t i o n cannot be used to  c o r r e c t the t o t a l photon spectrum f o r the a b s o r b e r .  That i s , one cannot  the counts found i n each channel by the v a l u e of I/l0  multiply  a t the  energy c o r r e s p o n d i n g t o t h a t channel and g e t the same spectrum as one would  f i n d w i t h o u t the a b s o r b e r .  photons  The r e a s o n i s t h a t the monoenergetic  t h a t pass through the a b s o r b e r w i t h o u t l o s i n g any energy  (fraction  I / I o ) w i l l have a spread i n energy due to r e s o l u t i o n and a low energy continuum this  r e s u l t i n g from Compton s c a t t e r i n g .  c o r r e c t i o n c o n t i n u o u s l y the peaks would  on the lower energy s i d e would  be d i s t o r t e d  The lower energy continuum  T h e r e f o r e the v a l u e o f l / l  0  the d a t a over t h a t peak r e g i o n a f t e r the background  from the t o t a l spectrum. t a i n s the background  4.  Efficiency  to c o r r e c t  from h i g h e r energy  Only the peaks w i t h o u t background  were s u b t r a c t e d  The r e s u l t i s t h a t the e l e c t r o n spectrum  from photons  would  c o r r e s p o n d i n g to  the energy o f each peak was found and t h i s v a l u e was used  photons was s u b t r a c t e d .  as the c o r r e c t i o n  be too l a r g e and the c o r r e c t i o n on the  h i g h e r energy s i d e would be too s m a l l . a l s o be much too l a r g e .  T h e r e f o r e i f one a p p l i e d  as w e l l as the background  from  con-  electrons.  Calibrations  The e f f i c i e n c y o f the S i d e t e c t o r f o r photons as a f u n c t i o n o f photon energy was found u s i n g s t a n d a r d s o u r c e s o b t a i n e d from I.A.E.A.,  66 FIG.  25.--  A b s o r p t i o n Curve f o r Photons i n Aluminum Absorber  10  20 •  30 Energy  40 (Kev)  50  60 *  70  80  Vienna.  The r e l e v a n t c h a r a c t e r i s t i c s o f these s o u r c e s a r e l i s t e d i n  T a b l e IX.  The s o u r c e s a r e h e a t s e a l e d between two t h i n p l a s t i c d i s c s and  cold-welded between two t h i n aluminum d i s c s .  The f r a c t i o n o f the i n t e n -  s i t y o f the photon peaks absorbed by t h i s i n c a p s u l a t i o n was found by measuring  the d e c r e a s e i n i n t e n s i t y when one s i d e o f a dummy (no source)  c a p s u l e was p l a c e d between the source and the d e t e c t o r .  These f r a c t i o n s  were used  the s o l i d  to c o r r e c t the number o f photons  radiated into  angle  -3 of the d e t e c t o r (8.2 x 10 These i n t e n s i t i e s  Std) per u n i t time f o r each  c a l i b r a t i o n peak.  a r e i n c l u d e d i n T a b l e IX.  The r a t i o o f the a c t u a l i n t e n s i t y per u n i t  time o f a g i v e n  photon  peak as measured w i t h the S-^ d e t e c t o r to the c a l c u l a t e d i n t e n s i t y f o r t h a t peak i s the i n t r i n s i c e f f i c i e n c y o f t h i s d e t e c t o r f o r t h a t photon energy.  This r a t i o  i n T a b l e IX.  i s p l o t t e d i n F i g . 26 f o r the f i v e e n e r g i e s  The low energy p o r t i o n o f t h i s  peaks  listed  curve ( <30 Kev) i s e x t r a -  p o l a t e d to match curves g i v e n i n r e f e r e n c e 12. The e f f i c i e n c y of the S\  d e t e c t o r f o r e l e c t r o n s was assumed c o n s t a n t  (see Chapter I I I - 1 ) . I t has n o t been measured f o r t h i s d e t e c t o r .  A  v a l u e o f 80 * 57o i s assumed, which i s i n agreement w i t h measurements made 23 by v a r i o u s groups  25 '  '  .  Low energy e l e c t r o n s t a n d a r d s have o n l y  r e c e n t l y become a v a i l a b l e t o t h i s l a b o r a t o r y and t h i s e f f i c i e n c y be measured i n the near  will  future.  The e r r o r i n the photon  e f f i c i e n c y curve i s e s t i m a t e d to be 2? 5°L.  T h i s v a l u e i s the sum o f the e r r o r s i n the source s t r e n g t h , i n the f r a c t i o n of  t o t a l r a d i a t i o n r e p r e s e n t e d by a peak, and i n the measured  of  t h a t peak.  The t o t a l e r r o r may be l a r g e r  calculated solid  a n g l e subtended  intensity  than 5"L as any e r r o r i n the  by the d e t e c t o r has n o t been i n c l u d e d .  68  T a b l e VTII Photon E f f i c i e n c y C a l i b r a t i o n Source  Strength* (Mc)  t%  Cs  10.4  + .2  30. 5 years  Am  10.4  + .1  432. 9 years  203 Hg  20.3  + .2  46. 8 days  1 3 7  u  Data  Energy of C a l . peak (Kev) 32., l  . l  +  59.,54  5.,7 ± .2  .02  +  72.,873  +  .001  279,,191 * Co  11.4  + .1  271. 6 days  .008  121.,97 ± .03  a t January 1,1970; 00:00 U n i v e r s a l  Source  Energy  (Kev)  P e r c e n t of disintegration  A b s o r p t i o n (%) by c a p s u l e  35.,9 ± .6 9.,7 ± .5 81.,55  .15  +  85.,0 ±  1.7  time  Intensity"' (photons/sec)  1 3 7  Cs  32.1  +  .1  6.5  1300  2 4 1  Am  59.54  +  .02  3.8  8974  2 0 3  Hg  72.873 - .001  5 7  2 0 3  2.8  28188  Co  121.97  +  .03  2.1  23918  Hg  279.19  +  .008  1.4  21059  Intensity calculated the d e t e c t o r , a f t e r  to be r a d i a t e d i n t o  the s o l i d a n g l e subtended by  c o r r e c t i o n s have been made f o r the l i f e - t i m e of the  s o u r c e and a b s o r p t i o n by the c a p s u l e .  CHAPTER V DECAY OF  1.  153  GADOLINIUM  Introduction The  153  e l e c t r o n c a p t u r e decay of  p r e v i o u s l y by a v a r i e t y of 18 Lederer et a l . from disagreement  techniques  Gd  to  153  26-30  Eu has  been i n v e s t i g a t e d  The decay scheme deduced  these measurements i s g i v e n i n F i g . 27.  There i s a  between the v a l u e s g i v e n by d i f f e r e n t authors f o r the  capture branching r a t i o s ,  e s p e c i a l l y to the ground s t a t e .  I t was  there-  f o r e decided  t h a t a r e - i n v e s t i g a t i o n of t h i s decay u s i n g the  spectrometer  d e s c r i b e d i n the p r e v i o u s c h a p t e r s would be i n f o r m a t i v e .  2.  Source  by  Si(Li)  Preparation  153 The  Gd  s o u r c e m a t e r i a l was  c h e m i c a l form was  o b t a i n e d from Union C a r b i d e Corp.  GdCC ^ d i s s o l v e d i n 1 N. HCt  .  The  specific  Its  activity  153 of  Gd  i n the m a t e r i a l was  5.46  millicuries/ milligram. 2  Source m a t e r i a l was  sublimed  onto  i n the manner d e s c r i b e d e a r l i e r .  found  (.8 mg/cm )  The maximum t h i c k n e s s of source m a t e r i a l  t h a t would not degrade the low energy was  a t h i n aluminum b a c k i n g  e l e c t r o n peaks by source a b s o r p t i o n  e x p e r i m e n t a l l y by p r e p a r i n g s u c c e s s i v e l y t h i n n e r sources  no improvement i n peak shape was  noted.  T h i s t h i c k n e s s was  until  estimated  to  2 be  cs10  strength  M. gm/cm  ( ^  from  the s p e c i f i c a c t i v i t y  50 x C i ) , and  the source a r e a  ( ^  (5.46 m Ci/mgm), the 2 1.5  cm ) .  The  source  aluminum  b a c k i n g was mounted on cardboard (see F i g . 20) to reduce b a c k s c a t t e r . S i n c e GdC& ^ i s h y g r o s c o p i c , sources must be kept i n a vacuum, i n 22 a d e s i c c a t o r , or covered w i t h c o l l o d i o n so t h a t they do not absorb -70-  71  FIG. Main Transitions  in  27.— the  Decay of  153  Gd  =  5.8  E,  =  70  Kev  =  6.5  E „ = 139.8 Kev  =  6.6  E„  =  =  8.4  E„  =  =  7.8  E,,  = 243  145.6 Ke/ 159.6 Kev Kev  72 moisture  from the atmosphere and t h e r e f o r e become t h i c k e r .  c o u l d n o t be covered w i t h c o l l o d i o n as t h i s would absorb e l e c t r o n s passed  through  when n o t i n the c r y s t a l  3.  153  it.  The sources  energy as the  They were t h e r e f o r e s t o r e d i n a d e s i c c a t o r  chamber.  Gd S p e c t r a 153  The  total  spectrum and t h e photon spectrum of  three b i a s e d a m p l i f i e r s e t t i n g s , a l o n g w i t h were taken w i t h the Si  detector.  Gd f o r each of the  the energy c a l i b r a t i o n  The i n t e n s i t y of the peaks i n the photon  s p e c t r a were c o r r e c t e d f o r the absorber  (see Chapter  IV) and s u b t r a c t e d  from the t o t a l s p e c t r a to g e t the t h r e e e l e c t r o n s p e c t r a . s p e c t r a were n o r m a l i z e d taken over  data,  to the same time  These  three  (the l e s s i n t e n s e r e g i o n s were  longer p e r i o d s of t i m e ) , matched i n energy u s i n g the o v e r l a p  between the s e t t i n g s , and then p l o t t e d as one composite spectrum i n F i g . 28.  The same matching procedure  spectrum The  (Fig.  was used to o b t a i n the composite photon  29).  e n e r g i e s o f the peaks i n these  energy c a l i b r a t i o n d a t a and the channel the computer f i t t i n g program.  two s p e c t r a were found  p o s i t i o n of the peaks as g i v e n by  The e n e r g i e s of the e l e c t r o n peaks were  c o r r e c t e d f o r the a b s o r p t i o n i n the dead l a y e r o f the Si energies are included i n F i g s . The  u s i n g the  detector.  These  28 and 29.  o r i g i n s o f the e l e c t r o n peaks were deduced by s u b t r a c t i n g the  b i n d i n g e n e r g i e s o f the K-, L-, o r M+N- s h e l l atomic  e l e c t r o n s of europium  from the e n e r g i e s o f the gamma peaks and comparing these v a l u e s w i t h t h e e n e r g i e s of the e l e c t r o n peaks.  The o r i g i n s o f the gamma peaks were  deduced by comparing t h e i r e n e r g i e s w i t h the decay scheme ( F i g . 27).  the t r a n s i t i o n e n e r g i e s g i v e n on  Both the e l e c t r o n and photon peaks,  along  FIG.  28.—  Conversion E l e c t r o n Spectrum of  Setting  153  Gd  Setting  1  Setting  3  2  54.6  r  ,'  21.1  95.4  x4 48.9  .,  r  36.5  61.9  89.5 i  101.5  68.1  2  L  20  -tor  "10T5  1213  WT~ Channel  180  200  220  240  260  No, LO  FIG.  29.--  Photon Spectrum of  153  Gd  Setting 1  Setting 3 Setting 2  K-  97.4  112 41.3 10  103.2 x 20  64.8  r  4  r  40  60  80  100  47.3  120 Channel  140 No.  160  180  200  220  240  75  T a b l e IX Peak I d e n t i f i c a t i o n and I n t e n s i t i e s  21.1  K  69.7  36.5  Auger1  48.9  K, 97.4 K  54.6 61.9  103.2  L  69.7  69.7  89.5 L  95.4 101.5  J  97.4  103.2  + M f N  97.4  ^103.2  41.3  K  8 0 - 5  10516 *  5.3%  80  + T  37702 *  2.3%  80  * 5  1866 * 12.3%  80  * 5  2333 * 17%  80  +  , 250 * 45%  47127 -  7.3%  + 2336 - 10%  4.8%  8 0 - 5  7789 *  3.1%  80  * 5  1886 *  4 . 8 %  80  t  51230*  1.5%  30.6*1.5  *8768 *  8.1%  2357'- 10%  5  3%  .  18.6*  .9  5.8*  .3  103.2  97.4  166000 ±  6.5%  42200 *  8%  3892 * 20%  1810 -  3.6%  2.0-  .1  65990 -  8.6%  1056 *  4.1%  1.75*  . 09  46200 *  9.17=  0  103.2  after  13145 - 10%  5  1894 -  298 * 15%  103.2  16384 * 12%  7.3%  x-rays  69.8  97.4  Corrected Intensity  13107 -  7943 *  172.9  (%)  x-rays  47.3 K  Eff.  200 * 40%  M+N  68.1  S-^ D e t e c t o r  Intensity (Counts)  Peak Origin  Peak Energy (Kev)  0  the M„_, , c o n v e r s i o n e l e c t r o n s were s u b t r a c t e d . 97.4  76 w i t h t h e i r deduced o r i g i n s , The  T a b l e X. to  listed  peak i n t e n s i t i e s found by  intensities  due  are  corrected for  The  the  M  the  contribution  to  the  i n Table  X.  f i t t i n g program, and  detector e f f i c i e n c y ,  are  the  95.4  intensity  of  the  97.4  c o n v e r s i o n e l e c t r o n s from the  Kev  their  included Kev  in  electron  t r a n s i t i o n was  peak  cal-  g culated using the  the M  t r a n s i t i o n was  conversion c o e f f i c i e n t s El.  from o t h e r t r a n s i t i o n s Conversion The  were c a l c u l a t e d  S l i v and  and  Band^.  r e q u i r e t h a t the  E2.  69.7  t r a n s i t i o n be  The  Kev  E l , and  efficiencies  the  peaks  of  the the  Kev are  the  That i s , the  c o n t a i n the  and  ratio  °^K/  a l o n g w i t h the  transitions  percentage E2  was  calculated  be  coefficients 97.4  the  a m i x t u r e of Ml  rather  and  large  admixture i n the  from these r a t i o s  and  s h o u l d be more e x a c t as  These r a t i o s  The  can  E2,  S;[ d e t e c t o r f o r photons  transition,  g i v e n i n T a b l e XII  coefficients  i n agreement w i t h these assignments.  of L - c o n v e r s i o n e l e c t r o n s from t h a t  °^L.  background.  K-conversion  ^L  i s equal  number of K - c o n v e r s i o n e l e c t r o n s from a t r a n s i t i o n d i v i d e d  °^K/  resulting  transitions  t r a n s i t i o n be  103.2  these c o e f f i c i e n t s  c a n c e l out.  are  the  coefficients  theoretical  the  e f f i c i e n c y of  r a t i o of  the  Comparison of  L-conversion c o e f f i c i e n t s  i n the  L-conversion  a m i x t u r e of Ml  K-  The  that  to g i v e  of  t r a n s i t i o n be  The  electrons.  and  multipolarities  L-conversion c o e f f i c i e n t s  uncertainties  substracted  observed above the  compared to  The  and  assuming  Coefficients  a s s i g n e d from these comparisons.  Kev  and  Intensities  were too weak to be  K-conversion c o e f f i c i e n t s  ( T a b l e XI) g i v e n by  was  of L-^Q-J ^ c o n v e r s i o n e l e c t r o n s .  intensity  4.  This contribution  of Rose  by  as measured by  69.4  to be  theoretical Kev 07, — *  and  to  the  these the  number  the  detector.  values  103.2  207, and  of  Kev 167> — *  327,  77  Table X K-Conversion C o e f f i c i e n t s  Transition Energy (Kev)  4.2  97.4  .2  103.2  Theoretical  Measured Values  69.7  1.02  1.3  +  97.4 103.2  .60  M2  4.6  2.85  50.0  Ml  .64  +  .04  .26  1.6  1.2  13.0  +  .17  .24  1.43  1.07  11.0  5.34  64.0  +  035 18  Values E2  El  L-Conversion C o e f f i c i e n t s  69.7  ( pO K  +  ( o( ) 1~J  .22  .09  ,65  .007  .039  .25  .830  3.4  .03  .034  .209  .860  3.2  Theoretical  Values  T a b l e XI  Transition Energy (Kev)  Measured Values  69.7  7.0  97.4  5.6 t  103.2  5.3  El  1.2  +  +  1.1  Ml  E2  7.07  1.55  6.84  1.24  6.67  78  respectively. ably higher  The admixture o f E2 i n the 103.2 Kev t r a n s i t i o n i s c o n s i d e r -  than the v a l u e o f 1.7% g i v e n by r e f e r e n c e 18.  The 97.4 Kev  t r a n s i t i o n i s assumed to be pure E l as t h e n e x t a l l o w e d m u l t i p o l e has a 4 t h a t i s reduced by a f a c t o r o f (kR) (see T a b l e I I ) .  transition probability 5.  Capture Branching R a t i o s The f r a c t i o n o f t o t a l  capture t r a n s i t i o n s  t h a t go to a g i v e n l e v e l i n  the daughter n u c l e i i n e l e c t r o n c a p t u r e decay i s c a l l e d ing r a t i o  to t h a t  level.  Defining  the terms  N  Number o f c a p t u r e t r a n s i t i o n s  =  E  E above the ground s t a t e i n I (E ) e  =  0  =  c  to the e x c i t e d s t a t e a t energy  153 Eu  I n t e n s i t y o f the e = K, L, M+N+ c o n v e r s i o n e l e c t r o n s from  the E 1^ ( E )  the capture branch-  transition i n  0  153 Eu  I n t e n s i t y o f the gammas from the E  transition i n  0  153 Eu.  Then from the i n t e n s i t i e s g i v e n i n T a b l e X t h e number o f c a p t u r e transitions  N  to the e x c i t e d l e v e l s o f  172.9  =  *  X  =  N  103.2  =  9 7  T  &  N  ^172 9  7 )  +  -  2 )  9 7  4  to g e t N^^^  a  S  S  ( 6 9  '  7 )  \  +  \  ( 1 0 3  -  U  D  t  r  a  c  t  e  2  ( 6 9  -  7 )  ( 1  ° -  +  I  ( 9 7 K  '  +  M+N+  I  ( 6 9  '  7 )  4  2 )  4 )  (8.15 - .71) x 1 0  ^  a  K  +  ( ' >  c  W  X  Eu a r e  +  h  = (8.1 - 1.2) x 1 0  1 7 2 > 9  1  =  transition  ( 1 0 3  = 't  .4  -  (2.33 - .32) x 1 0  N,  ( 6 9  153  +  h  ( 9 7  3  2 )  +  VNf  ( 1 0 3  '  2 )  4  '  4 )  +  W  ( 9 7  '  4 )  4  from the t o t a l r a d i a t i o n from the 103.2 Kev s  t  ^  i e  172.9 Kev l e v e l feeds the 103.2 l e v e l v i a  the 69.4 Kev t r a n s i t i o n . The number o f c a p t u r e t r a n s i t i o n s be deduced from  to the ground s t a t e  the i n t e n s i t y o f the K x - r a y s .  t h a t the f r a c t i o n o f K-capture  yield  of  153  153  Eu can  This c a l c u l a t i o n requires  to L+M+N+ - c a p t u r e t r a n s i t i o n s  t h a t the number o f K x-rays r e s u l t i n g from c a p t u r e to the ground s t a t e  of  i s known,  t r a n s i t i o n s o t h e r than K-  Eu i s known, and t h a t the K - f l u o r e s c e n t  (W ) of europium i s known. K The K - f l u o r e s c e n t y i e l d i s the f r a c t i o n of v a c a n c i e s i n the K-atomic  shell The  t h a t r e s u l t i n K x-rays  ( t h e r e s t g i v e r i s e to Auger  K - f l u o r e s c e n t y i e l d o f europium i s .92 The  to the ground s t a t e  from a l l t r a n s i t i o n s multiplied  and the K-capture  33  transitions  by the K - f l u o r e s c e n t y i e l d .  can be c a l c u l a t e d  and by Zyryanova  I f a l l the c a p t u r e  transitions  f o r b i d d e n non-unique ( A J = 0, +1;  .  that are  from p r o b a b i l i t y r a t i o s g i v e n by Brysk and These r a t i o s a r e .  Q - E - B 1x2 .128 (• Q - E - B ' •  Ui-Lj. U  21  than  to a l l o t h e r l e v e l s ,  *1) , then the f r a c t i o n o f the t o t a l c a p t u r e t r a n s i t i o n s  K-captures Rose  t r a n s i t i o n s other  i s the sum o f the K - c o n v e r s i o n e l e c t r o n s  a r e assumed to be a l l o w e d o r f i r s t =  1  18  i n t e n s i t y o f K x-rays r e s u l t i n g from  K-capture  electrons ).  L  = K  R  (ignoring  II (J^  ,041  l^M+N ' U) L  L^.^  T  I  b i n d i n g energy)  = + u) II T  the d i f f e r e n c e  229  (  Q  "  E  " ^ N ) ?  Q - E -  L  -  capture i s not allowed.  B  L  i n the L s h e l l  80 these e q u a t i o n s (jJe  In  i s the p r o b a b i l i t y of an e l e c t r o n  atomic s h e l l b e i n g c a p t u r e d , Q i s the energy d i f f e r e n c e states state of  153  of  Gd and  153  Eu (= 243 Kev  the c a p t u r e t r a n s i t i o n s  the e atomic s h e l l  18  i n the e  between the ground  ), E i s the energy o f the e x c i t e d  i s g o i n g t o , and  i s the b i n d i n g  energy  i n Eu. 153  The number o f K-capture t r a n s i t i o n s W  N (K)  =  E  N  E  / ( l  to any l e v e l  L T +  ^ ( l  ^ +  T  N  ^ ) ( l  +  -  in %  7  Eu i s  N  ^ ) )  The number o f K x - r a y s that do not r e s u l t from the K-capture to the ground  state i s N(K x-ray) = ( N  1 7 2 < 9  (K) + N  1 0 3 > 2  (K) + N  9 ? < 4  ( K ) + I (69.7) + R  + I (103.2))W K  R  4 = (19.2  +  2.1) x 10  The number of K x - r a y s r e s u l t i n g from the K-capture t r a n s i t i o n s to the  ground  state i s N  u  + N  - N(K x-ray) = (1.6 * 1.6) x 1 0  The number of K-capture t r a n s i t i o n s N (K) = 0  1  f  2  ^ =  to the ground  ( 1 . 8 * 1.8) x 1 0  4  state i s  4  . K and  the number o f c a p t u r e t r a n s i t i o n s  =  (2.3  +  to the ground  ^LT  ^LTT  K  J-iJ  2.3) ± 1 0  state i s ^M+N  Li  4  153 The therefore  t o t a l number of c a p t u r e t r a n s i t i o n s  to a l l l e v e l s i n  Eu i s  I (97.4) R  81  N=N  = The  +  172.9  (2.09 *  N  103.2  .25)  +  x  N  10  +  97.4  N  o  5  = N /N.  c a p t u r e b r a n c h i n g r a t i o s are t h e r e f o r e g i v e n by f E  These v a l u e s , expressed  as percentages,  w i t h those found by o t h e r  E  are g i v e n i n T a b l e X I I I , a l o n g  investigators.  Table XII Capture  Branching  Ratios  Measured y  (log f t values i n brackets)  Ref.  L e u t z (1960) from Ref. 26  26  Ref.  172.9  11 * 3  (5.8)  17  11  12  103.2  39 *  (6.6)  32  50  32  (6.6)  40  35  30  9  4  24  10  97.4  39 * 8  0  11 *  The  reduced  i i  lifetimes  (7.3)  ( f t v a l u e s ) of the c a p t u r e  c a l c u l a t e d u s i n g these c a p t u r e b r a n c h i n g r a t i o s and p r o b a b i l i t i e s g i v e n by Zyryanova ft =  21  .  (1.683 (Q - E - B ) K  transitions  the e l e c t r o n  2  +  .2196  (Q - E - B ^ )  2  +  .0092  2  2^ in  LlI  "/\  = E  7\  i s d e f i n e d by t\  N X / N E  =  Q,n  tr\0c  2  i s i n sec \  2/-^  v a l u e s are g i v e n i n T a b l e X I I I .  = 242  E  , and  days.  The  l o g a r i t h m of  be  capture  They are  ( Q - E - B )')42 where the e n e r g i e s are i n u n i t s of  can  these  These l o g f t v a l u e s i n d i c a t e t h a t  the  30  82 e l e c t r o n c a p t u r e t r a n s i t i o n s are a l l o w e d or f i r s t 6.  forbidden.  S p i n and P a r i t y Assignments 153 The  of  J "  ground s t a t e s of = 5/2+  7 7  and  3/2+  153 Eu and  Gd have been a s s i g n e d  re s p e c t i v e l y by atomic  beam  the v a l u e s  experiments  153 The +  103.2  and  the 69.7  Kev  transitions  in  A J = 0, *1;  (E2) i n c h a r a c t e r , r e q u i r e t h a t  t r a n s i t i o n , being E l i n character requires that These requirements  g i v e the p a r i t y of the 103.2  Eu, as they are Ml ATT = 1. AJ  The  97.4  = 0, *1; ATT  and  172.9  Kev  Kev =  -1.  l e v e l s of  153 Eu as p o s i t i v e and  the p a r i t y of the 97.4  Kev  l e v e l as n e g a t i v e .  T h e r e f o r e t h e r e i s no p a r i t y change between the ground s t a t e of 153 and to  the 172.9, 103.2  and  0 Kev  l e v e l s of  Eu.  The  these l e v e l s i s t h e r e f o r e assumed to be allowed  as the next second  type of t r a n s i t i o n s  capture  153  Gd  transitions  ( A J = 0, *1; A T f  =  1)  t h a t does not have a p a r i t y change i s  forbidden with a log f t  >  10.  The  capture  transition  to the  97.4  153 Kev  l e v e l of  be f i r s t  Eu i n v o l v e s a p a r i t y change and  f o r b i d d e n ( A J = 0, * 1 , *2; A TT  w i t h the l o g f t v a l u e of  i s t h e r e f o r e assumed to  = - 1 ) , which i s i n agreement  6.6. 153  The  possible J * 1  97.4  Kev  103.2  Kev  172.9 Kev These v a l u e s of j "  v a l u e s of the e x c i t e d s t a t e s of J*  =  3  /2",  =  3  /2+  5  /2  7/2"  +  j"" = /2 /2 are i n agreement w i t h those g i v e n on F i g . 27. 3  -  5/2",  Eu are t h e r e f o r e  +  5  +  CHAPTER VI CONCLUSIONS  The ful  s p e c t r o m e t e r d e s c r i b e d i n p r e v i o u s c h a p t e r s has proved  i n i n v e s t i g a t i n g low energy  decays.  success-  t r a n s i t i o n s r e s u l t i n g from e l e c t r o n  A l t h o u g h i t s r e s o l u t i o n does n o t compare f a v o u r a b l y w i t h  o b t a i n e d by l a r g e magnetic  spectrometers f o r e l e c t r o n s  2  , or bent  capture  that crystal  28 s p e c t r o m e t e r s f o r low energy  gamma r a y s  , i ti s sufficient  to s e p a r a t e  the K-, L-, and M+N c o n v e r s i o n e l e c t r o n peaks and the gamma r a y peaks r e s u l t i n g from  the e x c i t e d s t a t e t r a n s i t i o n s a s s o c i a t e d w i t h these  I t has, however, t h r e e advantages l a r g e p o r t i o n s o f the energy  over  spectrum  these s p e c t r o m e t e r s .  decays.  Namely, t h a t  can be taken a t one time,  t h a t the  e l e c t r o n and gamma r a y s p e c t r a can be taken u s i n g the same s o u r c e  and  the same geometry, and t h a t the e f f i c i e n c y i s c o n s i d e r a b l y g r e a t e r . I t s h o u l d be noted  t h a t much b e t t e r r e s o l u t i o n  ( < . 4 Kev compared 34  to 2 Kev) f o r low energy x - r a y s has been o b t a i n e d u s i n g S i ( L i ) d e t e c t o r s To a c h i e v e t h i s r e s o l u t i o n cooled with l i q u i d stage.  the i n p u t stage of the p r e a m p l i f i e r must be  n i t r o g e n to reduce  The c r y s t a l must have a s m a l l s u r f a c e a r e a and a l a r g e  r e g i o n to reduce  the i n p u t c a p a c i t a n c e of the p r e a m p l i f i e r .  chamber must be evacuated  to a t l e a s t  on the s u r f a c e s of the c r y s t a l blems i n v o l v e d w i t h t h i s changed  the e l e c t r o n i c n o i s e o f the i n p u t  (since  the advantages  10  7  Torr.  to a minimum.  to reduce  It isfelt  And the condensation  t h a t the pro-  type of system when s o u r c e s o r a b s o r b e r s a r e  they must be p l a c e d i n s i d e the chamber) would of achieving better  can be improved by  i n s t e a d o f s i l i c o n as the average  -83-  nullify  resolution.  The r e s o l u t i o n o f the type o f spectrometer used u s i n g germanium c r y s t a l s  compensated  energy  required  84 to produce an e l e c t r o n - h o l e p a i r i n germanium (2.9G\/) i s l e s s than i n (3.7ev).  silicon  Germanium i s not used, however, as  be k e p t a t a temperature l e s s than - 3 0 ° C or out of  the  compensated r e g i o n .  c r y s t a l s f r e e of s u r f a c e  these c r y s t a l s must  the l i t h i u m i o n s w i l l  I t i s therefore very  drift  d i f f i c u l t to keep  c o n d e n s a t i o n when sources or a b s o r b e r s are  these  being  changed. The a better  uncertainty  c a l i b r a t i o n of  done y e t as and  i n the  the  i n t e n s i t y of photon peaks can be  the e f f i c i e n c y of  experiments s i n c e t h a t uncertainty  been i n almost c o n s t a n t  i n the  deduced from b a c k s c a t t e r  one  the d e t e c t o r  rather  The  e l e c t r o n spectrum w i l l  energy l o s s K - c o n v e r s i o n e l e c t r o n s and the b a c k s c a t t e r e d the peak to the  than u s i n g  1969,  f r a c t i o n of  be p o s s i b l e to o b t a i n  reduced a  value  The  efficiency  t h a t are  i n coin-  decay t h a t o n l y  involves  c o n t a i n a peak due  The  r a t i o of  i n t e n s i t y i s the e f f i c i e n c y of  Once the b a c k s c a t t e r will  been  i n other  to  a lower energy continuum due  K-conversion e l e c t r o n s .  total  use  experiments done by o t h e r workers.  the K x - r a y s of an e l e c t r o n capture  excited state.  not  December  i n t e n s i t y of e l e c t r o n peaks can be  can be measured by d e t e c t i n g the K - c o n v e r s i o n e l e c t r o n s with  by  time.  by measuring the e f f i c i e n c y of  cidence  T h i s has  c a l i b r a t i o n sources were not r e c e i v e d u n t i l  the e l e c t r o n i c equipment has  The  the d e t e c t o r .  reduced  to  the i n t e n s i t y  the  of  detector.  the S i ( L i ) d e t e c t o r  spectra with  full  i s known, i t  t h i s s p e c t r o m e t e r and  to  23 c o r r e c t these s p e c t r a f o r b a c k s c a t t e r i n g  .  separate  i n a decay by  J&  the d i f f e r e n t j£ groups i n v o l v e d  particles  that de-excite  t h a t are different  i n coincidence l e v e l s of  with  It will  a l s o be  possible  detecting  to  those  the r a d i a t i o n from t r a n s i t i o n s  the daughter  nucleus.  85 A new two  crystal  chamber has  S i ( l i ) detectors.  been b u i l t  It will  f a c i l i t i e s f o r mounting  T h i s chamber w i l l be used to measure the back-  s c a t t e r f r a c t i o n of e l e c t r o n s using, the above.  with  c o i n c i d e n c e method  described  a l s o be used to determine the sequence of t r a n s i t i o n s  i n v o l v e d i n a g i v e n decay by measuring c o i n c i d e n c e s  between r a d i a t i o n  r e s u l t i n g from the d i f f e r e n t t r a n s i t i o n s . This  chamber has  a liquid  keep the S i ( L i ) d e t e c t o r s to ~3  n i t r o g e n c a p a c i t y of 15  cooled f o r approximately three  hours f o r the chamber d e s c r i b e d  This w i l l  allow  longer  needed p r e v i o u s l y .  The  between the s o u r c e and  l i t r e s , and  runs to be  days  (compared  i n Chapter I I I ) w i t h o u t r e f i l l i n g .  taken w i t h o u t the c o n s t a n t  chamber a l s o has  attention  f a c i l i t i e s f o r i n s e r t i n g absorbers  d e t e c t o r s w i t h o u t opening the  r e q u i r e warming the c r y s t a l s to room temperature.  chamber, which would  It will  therefore  much more s u i t a b l e f o r i n v e s t i g a t i n g r a d i o a c t i v e n u c l e i than the described  i n this thesis.  can  be  chamber  86  APPENDIX A Fitting  The purpose of a l e a s t P , which minimize  R  In  square  f i t i s to f i n d v a l u e s o f the parameters  the f u n c t i o n  (y  =  2  Routine  - y. ( P ^ P ,  ±  . .., P J )  2  t h i s e q u a t i o n the summation i s over a l l d a t a p o i n t s .  experimental  d a t a , the ^ ' a  s  a  r  e  t  n  weights  e  (A - 1)  2  The y^'s a r e the  a s s o c i a t e d w i t h the y^' > s  the y^'s a r e the v a l u e s o f the f u n c t i o n t h a t i s used  an  &  to r e p r e s e n t the d a t a .  2 A n e c e s s a r y and s u f f i c i e n t c o n d i t i o n f o r R  to be a minimum, as a  f u n c t i o n of the P,'s, i s k  4~ These equations  =0  f o r a l l k.  can be s o l v e d e x a c t l y i f y ( P p P  f u n c t i o n o f the P ' s .  2 >  ••••> P ) i s a l i n e a r  I f n o t , no e x p l i c i t s o l u t i o n e x i s t s .  In this  case,  K.  a method o f l i n e a r i z a t i o n can be used.  One such method i s t h a t o f Gause  31  T h i s method c o n s i s t s o f l i n e a r i z i n g the f u n c t i o n y w i t h r e s p e c t to a set  o f parameters  P, = P ° + k  SP, by u s i n g a t r u n c a t e d T a y l o r ' s s e r i e s .  SP, , where P° i s the i n i t i a l k  k  \  ^  Here  y  =  y (P^ P  y° = r  2 >  P^)  (p;, p°, . . . p*) 1 2  —  (~^P~^  m  if  e s t i m a t e of the parameter P, , then k  k  m  That i s ,  ^ k P  +  k*§  n e r  derivitives  87  and  the d e r i v a t i v e s a r e e v a l u a t e d a t the i n i t i a l  meters.  e s t i m a t e s o f the para-  The f u n c t i o n  i s a l i n e a r f u n c t i o n o f the  S P, ' s. and k  *' - Z ^ - y r - ^ K , ' 2  i  .k  1  U  k  P  j  o  (A -  2)  i s a minimum when  ,.2 d  R  d  (o\)  These e q u a t i o n s P^ ( P  1  s  =  0  f o r a l l k.  can be s o l v e d f o r  P° +  o P^.) used  can be c o n t i n u e d u n t i l  e x a c t l y and a new e s t i m a t e f o r  i n equation  SP^. ^  ( A - 3)  ^ f°  r A  ( A - 2) . H  This i t e r a t i o n  ^ simultaneously.  process  A ^ is  u s u a l l y chosen so t h a t  y. <PJ, P*. .... P ^ . y . (Pj  P  ^  +  A  2  for a l l i . E q u a t i o n s A - 3 can be w r i t t e n as a m a t r i x Writing B = ( B ^ B ,  , B^)  2  =  C  =  £ . .  (  7  .  l  T  i  , ( ^ \  n x n matrix  v  £k  SP  l  =  —  ~ ri v ^ P j t  o  ( SP., £ P , 9  1  2  a  y  SP m  P )  K  equation.  P^ A^ +  88 Then e q u a t i o n s A - 3 become  c £P  =  B  which has s o l u t i o n s  P =  A B  where A i s the i n v e r s e o f the m a t r i x C. The  "sample s t a n d a r d d e v i a t i o n " i n the f i n a l  meter P. xs k  e s t i m a t e o f the para-  32  n-m where ^  2  2  i s the v a l u e o f R  f o r the f i n a l  parameters,  d a t a p o i n t s , m i s the number o f parameters, of  and A^  n i s the number o f  i s the d i a g o n a l element  the m a t r i x A. The  "goodness o f f i t " can be e s t i m a t e d by the q u a n t i t y  2  .  _ i I f (a^) 2  i s a good e s t i m a t e o f the s t a n d a r d d e v i a t i o n i n y^, and the e x p e r i m e n t a l _ 2 p o i n t s a r e a c t u a l l y r e p r e s e n t e d by the f u n c t i o n y, ~)C w i l l have an approximately 2 '"X /n-m (y/)  2  if  J-  c h i - s q u a r e d d i s t r i b u t i o n w i t h n-m degrees  should  then be a p p r o x i m a t e l y  (the s t a n d a r d d e v i a t i o n i n y^) ,  y. —> i The  unity  31  .  o f freedom and  Then i f one puts a^  2  ~)C /n-m w i l l  be a p p r o x i m a t e l y  f u n c t i o n used  unity  to r e p r e s e n t p o r t i o n s of s p e c t r a c o n t a i n i n g peaks peaks superimposed on a l i n e a r background.  is 2  \  =  exp ( 41n 2 ( j = 1  this  =  y. f o r a l l i . i  was the sum o f G a u s s i a n  In  2  )  )+ a + ib  j  equation J  =  number o f peaks i n the p o r t i o n o f  spectrum  That  89  H..  =  th h e i g h t of the j — peak  i  =  channel  j =  p o s i t i o n of the  = a +  number  FWHM of the  ib  =  peak i n channels peak i n channels  l i n e a r background.  A computer program was  w r i t t e n to f i t t h i s f u n c t i o n to the e x p e r i -  mental d a t a u s i n g the method d e s c r i b e d above.  The  program are the number of channels,  the counts  i n each channel,  of  and  peaks, the convergence c r i t e r i a ,  lu y  The The  me t e r s It exp  program e s t i m a t e s  initial  the i n i t i a l  v a l u e s f o r Ry  o u t p u t of the program c o n t a i n s the f i n a l U.,  u).,  J  H.,  J  J  channel,  U).  e s t i m a t e s of a and  of  /i^  and  b.  e s t i m a t e s of the para-  K  =*) )  (the f i t t e d  the v a l u e of y.. =  H.  peak minus background) f o r each  J  the i n t e n s i t y of each peak ( I . = (• Y 0) J 4 In 2  h  H.  j  w i t h i t s s t a n d a r d d e v i a t i o n , and  the  the number  a and b, a l o n g w i t h t h e i r s t a n d a r d d e v i a t i o n s , 0"", .  a l s o c o n t a i n s the v a l u e of y. a t each channel, (4 In 2 (  i n p u t requirements  VO.) j the goodness of f i t parameter, "%  2  /n-m.  90  REFERENCES  1  Siegbahn,  K. (Ed.);  Beta- and Gamma-Ray S p e c t r o s c o p y ,  North-Holland  P u b l i s h i n g Co. (1955). 2  Siegbahn,  K. (Ed.);  A l p h a - , Beta-, and Gamma Ray S p e c t r o s c o p y ,  North-  H o l l a n d P u b l i s h i n g Co. (1965) 3  Feenberg,  E., and T r i g g , G.;  4  F e r m i , E.; N u c l e a r P h y s i c s ,  5  De B e n e d e t t i , S.;  6  Evans, R. D.;  7  S l i v , L. A. and Band, I . M.;  Rose, M. E. :  The Atomic Nucleus,  G o u l d i n g , F. S.;  (1949).  John W i l e y and Sons  McGraw-Hill  (1964).  (1950).  C o e f f i c i e n t s of Internal  Conversion of  Academy o f S c i e n c e s , U. S. S. R.  I n t e r n a l Conversion C o e f f i c i e n t s ,  Publishing 9  399 (1950).  U n i v e r s i t y o f Chicago P r e s s  Nuclear I n t e r a c t i o n s ,  Gamma R a d i a t i o n , 8  Rev. Mod. Phys. _22  North-Holland  Co. (1958). N u c l . I n s t r . and Meth. 43  10  Fano, U.;  11  P e h l , R. H. , G o u l d i n g , F. S., L a n d i s , D. A., and L e n z l i n g e r , M.;  12  Phys. Rev. 70  1 (1966).  44 (1946), and Phys. Rev. 72  N u c l . I n s t r . and Meth. 54  45 (1968).  A P r a c t i c a l Guide to Semiconductor  Detectors;  26 (1947).  T e c h n i c a l Measurements  Corp. 13  Bothe, W.;  Z. N a t u r f . , 4a  14  Planskoy,  15  Kevex T e c h n i c a l Report,  16  Tennelec Sale  17  Dalby,  18  L e d e r e r , C. M., H o l l a n d e r , J . M. and Perlman, I . ;  B.;  D. A.;  N u c l . I n s t r . and Meth. 61  285 (1968).  November 1967.  Sheet. M.Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h  Sixth Edition, 19  542 (1949).  Columbia. Table of Isotopes  John W i l e y & Sons.  Wapstra, A. H., N i j g h , G. J . , and Van L i e s h o u t , R.; Spectroscopy Tables,  Nuclear  N o r t h - H o l l a n d P u b l i s h i n g Co.  91  20  Handbook of Chemistry and P h y s i c s ,  21  Zyryanova, L. N.;  Chemical Rubber P u b l i s h i n g  Once F o r b i d d e n B e t a - T r a n s i t i o n s ,  S e r i e s of Monographs on N u c l e a r Energy, 22  Ng, L. K. ;  Ph.D.  23  Charoenkwan, P.;  24  Bosch, H.,  N u c l . I n s t r . and Meth. 34  79  R e s t e r , D. H.  93  International  Pergamon P r e s s  U n i v e r s i t y of B r i t i s h  Krmpotic, F., and P l a s t i n o , A.;  23 25  Thesis,  Co.  (1963).  Columbia. (1965).  N u c l . I n s t r . and Meth.  (1963). and Rainwater, W.  J.;  Nucl. Instr.  and Meth. _41  51  (1966). 26  B l o k , L., Goedbloed, 993  W.,  Mastenbroek,  E., and Blok, J . ;  P h y s i c a 28  (1962).  27  C r e t z u , T., Holmuth, K.,  and Winter, G.;  28  A l e x a n d e r , P.;  29  Graham, R. L. and G e i g e r , J . S.;  30  Boyer, P. Chedin, P. and Oms,  31  Helmer, R. G.,  Phys. Rev.  Heath,  134  B499  B u l l . Am.  J.;  32  Freund, J . E.;  33  Brysk, H.  34  N u c l e a r Equipment Corp.;  46  E.;  Phys.  Soc. JJ.  N u c l . Phys. A99  (1964).  213  369  and Gipson, D. H.;  Rev. Mod. Technical  Prentice-Hall  Phys.  Report.  30  1169  (1966).  (1967). Nucl.  (1967).  Mathematical S t a t i s t i c s ,  and Rose, M.  415  (1964).  R. L., Putnam, M.  I n s t r . and Meth. J57  N u c l . Phys. _56  (1962).  (1958).  

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