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A ring collection spectrometer investigation of the decay of Sb 125 Payne, Frank Alden 1961

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A RING COLLECTION SPECTROMETER INVESTIGATION OF THE DECAY OF Sb 125 by FRANK ALDEN PAYNE B.A.Sc. The U n i v e r s i t y o f B r i t i s h Columbia, 1954 II.A.Sc. The U n i v e r s i t y o f B r i t i s h Columbia, 1957  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY i n the Department of PHYSICS  We accept t h i s the r e q u i r e d  THE  t h e s i s as conforming t o  standard  UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1961  In the  presenting  requirements  of  British  it  freely  agree for  that  available  I  copying  gain  shall  by or  not  of  agree  for  purposes  or  thesis  Qj^Jj  partial  degree  the  shall  reference  and  study.  I  extensive  may  be  publication be' a l l o w e d  of  copying  granted  this  v/ithout  by  of  the  .It thesis  PHVS^S Columbia,  make  further this  Head  is  of  thesis my  understood  for  my w r i t t e n  of  University  Library  for  J I M -  at  the  his-representatives.  <*  fulfilment  that  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a . Date  in  an. a d v a n c e d  permission  that  Department  for  Columbia,  scholarly  Department  this  financial  permission.  ii  ABSTRACT  A t h i n - l e n s beta-ray spectrometer  has been m o d i f i e d f o r  c o l l e c t i o n of beta-rays at the p o s i t i o n of the r i n g f o c u s . T h i s has i n c r e a s e d the g a t h e r i n g power/line width r a t i o ^  0.12  to ^ 0 . 8 .  The  f o c u s i n g p r o p e r t i e s of the  have been i n v e s t i g a t e d f o r v a r i o u s  from  instrument  geometries.  Using the m o d i f i e d spectrometer,  the decay scheme of  Sb 125 - Te 125 has been i n v e s t i g a t e d .  The  primary  beta  spectrum, p h o t o e l e c t r o n s p e c t r a and beta-gamma c o i n c i d e n c e s p e c t r a have been measured. From c o n v e r s i o n c o e f f i c i e n t measurements, the f o l l o w i n g r a d i a t i v e t r a n s i t i o n m u l t i p o l a r i t i e s were  determined  ( e n e r g i e s i n k e v ) : 176(E2+M1J, 428(E2+M1), 602(E2+M1) and  464(E2),  638(E2).  F i v e primary beta groups have been i d e n t i f i e d with p o i n t e n e r g i e s of 626,  450,  307,  unobserved t r a n s i t i o n s of 76,  246 and 133 kev.  143,  219,  355,  end  Previously  540 and 640  kev  have been i d e n t i f i e d . Based on a l l experimental evidence  the f o l l o w i n g s t a t e s  of Te 125 w i t h s p i n and p a r i t y assignments have been ground s t a t e 321 kev kev  ( S 1 / 2 + ) ,  (9/2-), 464  36 kev  kev  undetermined).  3  / 2 + ) »  1  4  (5/2+), 525 kev  (11/2- or 9/2-), 638 kev  parity  ( d  5  k  e  v  proposed:  ( ll/2"")-» n  (11/2- or 9/2-),  (5/2+) and 676  kev  (spin  and  540  iii  TABLE OF CONTENTS  CHAPTER I I. II.  IV. V. VI.  1  Beta Decay  3  Theory Selection Rules Comparative Lifetime Kurie Plot  11  Gamma Decay  13  Internal Conversion  15  Methods of Measurement i n Nuclear Spectroscopy  17  Beta-ray Spectrometers  23  a) Instrument Parameters b) Types of Instruments  23 25  RING FOCUS COLLECTION IN A THIN--LENS MAGNETIC SPECTROMETER  II. III.  IV.  3 7 9 10  e) O r b i t a l Electron Capture  CHAPTER II  I.  1  Introduction  a) b) c) d)  III.  NUCLEAR DECAY AND NUCLEAR SPECTROSCOPY  Introduction Preliminary  29 29  Investigation  31  The Modified Thin-Lens Spectrometer and Associated Apparatus a) General Mechanical Description b) The Detector c j The E l e c t r o n i c s i ) The control c i r c u i t i i j Beta spectra counting c i r c u i t  36 36 37 41 42 43  Experimental Investigation of Spectrometer Modification  44  a) Preliminary Procedures b) Experimental Measurements and Results  44 46  •  CHAPTER III I. II.  iv  THE GROUND STATE DECAY OF Sb 125  51  Previous Investigation  51  Present Investigation  56  a) Methods and Apparatus ( i ) Source preparation ( i i ) Apparatus - mechanical ( i i i ) Apparatus - e l e c t r i c a l  57 57 59 61  b) Results ( i ) The beta spectrum ( i i ) The internal conversion spectrum ( i i i ) The photoelectron spectrum (iv) Beta-gamma coincidence spectra (v) Synthesis of the gamma spectrum  62 63 67 68 69 71  'a)'The Decay Scheme d) The Consistency Argument e) Spin and Parity Assignments f ) Discussion  75 80 84 87  APPENDIX I  APPENDIX II  BIBLIOGRAPHY  INTENSITY MEASUREMENT OF CONVERSION LINES AND PRIMARY BETA GROUPS ITERATIVE METHOD OF CONVERSION LINE SEPARATION  91  94 99  V  LIST OF FIGURES AND  TABLES To follow page  CHAPTER I Figure 1  Third-order focusing p r i n c i p l e  27  Figure 2  Double focusing p r i n c i p l e  27  Figure 3  S e c t o r f i e l d and prism  27  Figure 4  The "Orange" spectrometer  27  Figure 5  Electron t r a j e c t o r i e s i n a h e l i c a l spectrometer  30  Figure 6  Graph i l l u s t r a t i n g the match of the r i n g focus exit s l o t for a given entrance s l o t  34  Figure 7  The modified thin-lens spectrometer  36  Figure 8  The detector assembly  39  Figure 9  Defocusing noise  41  Figure 10  Control c i r c u i t  42  Figure 11  Counting c i r c u i t  43  Figure 12  The v a r i a t i o n of peak shape with source position, s  46  Figure 13  The v a r i a t i o n of peak shape with exit s l o t width  47  Table I  Summary of results of ring focus collection  47  Table II  Comparison of some high h e l i c a l spectrometers  48  spectrometers  LPTER II  e f f e c t on photomultiplier  performance  vi  CHAPTER III Figure 14  Decay scheme of Siegbahn and F o r s l i n g  53  Figure 15  Moreau's decay scheme  54  Figure 16  Lazar's decay scheme  55  Figure 17  Photoelectron source  59  Figure 18  Beta-gamma coincidence modification  61  Figure 19  Beta-gamma coincidence c i r c u i t  61  Figure 20  Beta spectrum of Sb 125  63  Figure 21  Kurie analysis of beta spectrum of Sb 125  65  Table III  Summary of beta group i n t e n s i t i e s and end point energies  65  Figure 22  Internal conversion spectrum of Te 125  67  Table IV  Internal conversion l i n e i n t e n s i t i e s  68  Figure 23  Photoelectron spectrum  68  Figure 24  Singles gamma spectrum  69  Figure 25  Gamma-rays i n coincidence with N +N Gamma-rays i n coincidence with N-L+N2+N3 x  Figure 26 Figure 27  Gamma-rays i n coincidence with l 2 3 4 N  Figure 28  + N  + N  69 6  9  69  Gamma-rays i n coincidence with N +N +N +N +N5+N  69  Gamma-rays i n coincidence with the 174-176K conversion l i n e  71  1  Figure 30  + N  69  Gamma-rays i n coincidence with N +N +N +N +N5 1  Figure 29  2  2  2  3  3  4  4  6  Figure 31  Gamma-rays i n coincidence with the 428K conversion l i n e  Table V  Summary of beta-gamma coincidence results  Table VI  Relative gamma-ray i n t e n s i t i e s  Figure 32  Decay scheme proposed i n present investigation  Table VII  Conversion c o e f f i c i e n t s and (K/L+M) r a t i o s  APPENDIX I Figure 33  Method of measuring conversion l i n e intensity  APPENDIX II Figure 34  Separation of 109L and 109M conversion l i n e s  Figure 35  Intensity measurements of the 109K conversion l i n e  Table VIII  Intensity measurements of the conversion l i n e s of the 109 kev transition  ACKNOWLEDGEMENTS  The work involved i n t h i s thesis has been f a c i l i t a t e d by the advice and assistance of many people. I would l i k e to thank Mr. Alex Fraser and Mr. William Morrison  f o r their technical advice and f o r t h e construction  of parts of the apparatus. Thanks are also due t o Mr. H. R. Schneider for t h e use of h i s coincidence apparatus, Mr. I I . R . Schneider and Mr. E. D. Earle for their investigation o f t h e s e n s i t i v i t i e s of several photomultipliers and to Dr. J. B . 'barren f o r the use of the kicksorter. Most of a l l , to Dr. K. C. Mann, who suggested t h e research problem, I wish to express my sincere appreciation for h i s assistance throughout the experimental investigation and the analysis of the r e s u l t s . F i n a l l y I wish to thank the National Research Council for awarding me Studentships  during the period 1957-1959 and  the Defense Research Board for f i n a n c i a l support u n t i l the completion of t h i s thesis.  from 1959  CHAPTER I  NUCLEAR DECAY AND NUCLEAR SPECTROSCOPY  I.  Introduction Nuclear p h y s i c s may be d e f i n e d g e n e r a l l y t o be the study  of the p h y s i c a l p r o p e r t i e s o f the nucleus - i t s p h y s i c a l s t r u c t u r e , e l e c t r i c a l and mechanical p r o p e r t i e s , and modes of e x c i t a t i o n .  The main s t r u c t u r a l or mechanical p r o p e r t i e s  of the nucleus a r e mass, s i z e , shape and angular momentum w h i l e t y p i c a l e l e c t r i c and magnetic  properties associated  w i t h the nucleus a r e charge, magnetic e l e c t r i c quadrupole  moment.  d i p o l e moment and  There are, of course, many ways  whereby n u c l e a r p r o p e r t i e s may be i n v e s t i g a t e d .  One very  powerful method i s the i n v e s t i g a t i o n and c l a s s i f i c a t i o n o f the r a d i a t i o n s e m i t t e d by a r a d i o a c t i v e n u c l e u s .  This i s  the f i e l d o f n u c l e a r s p e c t r o s c o p y . I t i s observed that a nucleus can e x i s t i n v a r i o u s d i s c r e t e s t a t e s w i t h each of which i s a s s o c i a t e d a t o t a l energy  f o r the n u c l e u s .  t e d energy  .The s t a t e h a v i n g the lowest  associa-  i s c a l l e d the ground s t a t e of the nucleus w h i l e  -2-  s t a t e s o f h i g h e r energy a r e c a l l e d e x c i t e d s t a t e s .  If a  nucleus i s i n an e x c i t e d s t a t e , i t i s i n an u n s t a b l e conf i g u r a t i o n and i t decays  t o a s t a t e o f lower energy,  usually  g i v i n g up the excess energy by the e m i s s i o n o f electromagn e t i c r a d i a t i o n (gamma-rays).  In t h i s case i t e v e n t u a l l y  reaches i t s ground s t a t e which may o r may not be s t a b l e against  f u r t h e r decay.  I f the ground s t a t e c o n f i g u r a t i o n of  the nucleus i s a s t a b l e one, the nucleus i s then a nucleus of a s t a b l e i s o t o p e table.  of one of the elements  i n the p e r i o d i c  I f the ground s t a t e c o n f i g u r a t i o n i s not s t a b l e ,  the nucleus then decays  by one o f several p o s s i b l e  processes  w i t h a p o s s i b l e r e s u l t i n g change i n n u c l e a r charge.  This  means t h a t the o r i g i n a l nucleus becomes a d i f f e r e n t nucleus, i t s atom a d i f f e r e n t atom i n terms o f chemical  behaviour,  and i s c l a s s i f i e d as an i s o t o p e o f a d i f f e r e n t element i n the p e r i o d i c t a b l e . The  three most common processes by which the u n s t a b l e  ground s t a t e of a nucleus can decay are by the emission o f a negatron or p o s i t r o n o r by o r b i t a l e l e c t r o n c a p t u r e , a l l processes being c a l l e d beta decay and i n each case r e s u l t i n g i n a change of n u c l e a r charge.  The occurrence of these  types of decay i s p o s s i b l e i f : M(Z,A) > M(Z+1,A) M(Z,A)>M(Z-1,A) + 2m M(Z,A) > BI(Z-1,A)  f o r negatron e m i s s i o n G  f o r p o s i t r o n emission  |  f o r o r b i t a l e l e c t r o n capture J  (1)  where  m i s the mass of the e l e c t r o n and M(Z,A) i s the atomic  mass o f the n e u t r a l atom having Z protons and mass number A.  II.  Beta Decay  a) Theory Beta-rays  a r e e x p e r i m e n t a l l y i n d i s t i n g u i s h a b l e from  atomic e l e c t r o n s .  They d i s p l a y the same e/m value and the  same charge and are observed  not t o be captured by atomic  o r b i t s a l r e a d y occupied by e l e c t r o n s .  Thus they a r e excluded  from f i l l e d e l e c t r o n s t a t e s by the P a u l i p r i n c i p l e and hence they a r e i d e n t i c a l  particles.  Beta s p e c t r a a r e unique among n u c l e a r s p e c t r a i n that they a r e observed  t o be continuous  i n energy, approaching  i n t e n s i t y a t s m a l l e n e r g i e s , p a s s i n g through  zero  a maximum and  r e t u r n i n g t o z e r o i n t e n s i t y a g a i n a t some end p o i n t energy, E , which has been shown t o be the a v a i l a b l e decay energy. Q  T h i s f a c t appears t o v i o l a t e the law o f c o n s e r v a t i o n o f energy except a t the one energy E . Q  A l s o , i t i s observed  t h a t beta decay occurs between n u c l e a r s t a t e s whose angular momentum, measured i n u n i t s o f h , d i f f e r s by i n t e g r a l v a l u e s . T h i s i s not compatible  with the h a l f - i n t e g r a l s p i n a s s o c i a t e d  w i t h the e l e c t r o n and w i t h the law o f c o n s e r v a t i o n o f angular momentum.  These d i s c r e p a n c i e s a r e overcome by the n e u t r i n o  -4-  h y p o t h e s i s o f P a u l i , i n which i s p o s t u l a t e d the simultaneous e m i s s i o n of the n e u t r i n o and beta p a r t i c l e .  To preserve the  c o n s e r v a t i o n laws of angular momentum and energy, the n e u t r i n o i s assumed t o have an i n t r i n s i c s p i n of h/2, an energy  o f (E -Eg} and a very s m a l l o r z e r o mass.  The  0  quantum mechanical  theory of beta decay was f i r s t  f o r m a l i z e d by Fermi* i n 1934.  In i t s s i m p l e r form he made  the f o l l o w i n g assumptions: (a) The wave f u n c t i o n s o f the n e u t r i n o and e l e c t r o n may be approximated  by plane waves.  (b) The p r o b a b i l i t y of beta decay depends upon the e x p e c t a t i o n v a l u e of f i n d i n g the e l e c t r o n and the n e u t r i n o at  the n u c l e u s . (c)  The p r o b a b i l i t y o f e m i s s i o n depends upon unknown  f a c t o r s such as the matrix element H taken between the i n i t i a l and f i n a l s t a t e s of the nucleus and a c o n s t a n t f a c t o r , g, r e p r e s e n t i n g the s t r e n g t h of the c o u p l i n g g i v i n g r i s e t o the i n t e r a c t i o n . In  mathematical  language these assumptions take the  form: (a) I f tyg, p  g  and  , p  tf  a r e the wave f u n c t i o n s and  momenta r e p r e s e n t i n g the beta p a r t i c l e and n e u t r i n o r e s p e c tively,  then: If  ft  = N  e B H i p  R  #  i  - N  e >'T ±P  v  () 2  -5-  are the plane wave forms o f the wave f u n c t i o n s i n which Ng and N  v  are n o r m a l i z a t i o n f a c t o r s .  (b) The e x p e c t a t i o n value f o r f i n d i n g the beta p a r t i c l e and the n e u t r i n o a t the nucleus i s g i v e n by: N (0)l  2  B  • Wv(0)l  (3)  2  (c) The u n c e r t a i n t y w i t h r e g a r d t o the nature of the i n t e r a c t i o n c a u s i n g the decay permits H to be o f s e v e r a l p o s s i b l e forms.  Two such forms a r e : M =  ^ V f * ¥ i di:  M -  Jty * cf V  A  (4a) dt  (4b)  f o r the s c a l a r and t e n s o r i n t e r a c t i o n s r e s p e c t i v e l y , where V f and  a r e the wave f u n c t i o n s d e s c r i b i n g the f i n a l and  i n i t i a l s t a t e s o f the nucleus and the P a u l i s p i n m a t r i c e s .  <? i s a g e n e r a l i z a t i o n o f  Three other types o f i n t e r a c t i o n s  are a l s o p o s s i b l e , namely the p s e u d o s c a l a r , p o l a r v e c t o r and a x i a l vector interactions. evidence t o determine  I t remains  f o r experimental  which form of the matrix element and  t h e r e f o r e which type o f i n t e r a c t i o n best d e s c r i b e s the results  observed.  The momentum d i s t r i b u t i o n of e m i t t e d beta p a r t i c l e s based on the above assumptions  t u r n s out t o be:  2 2 2 p(p)dp = C IMI ( E p - E ) p dp  (5)  -6-  where  2 •V  E i s the t o t a l e l e c t r o n energy  i n u n i t s o f ratf'"  p i s the e l e c t r o n momentum i n u n i t s n» c 0  C = g /2 2  t t \  7  C  3  .  As p r e v i o u s l y noted, a plane wave s o l u t i o n f o r the e l e c t r o n wave f u n c t i o n has been assumed. is,  This  assumption  i n f a c t , too crude and i f the d i s t o r t i o n t o the e l e c t r o n  wave f u n c t i o n by the n u c l e a r coulomb f i e l d i s taken i n t o account by a f a c t o r "F"CZ,p) then e q u a t i o n (5) becomes: P(p)dp - C i B J l F(Z,p) 2  (E -E) 0  2  p dp  (6)  2  The coulomb e f f e c t on the wave f u n c t i o n o f an e m i t t e d effect e l e c t r o n i s , o f c o u r s e , d i f f e r e n t from the coulomb/for  posi-  t r o n e m i s s i o n because o f the d i f f e r e n c e i n s i g n of the charge o f the two p a r t i c l e s .  T h i s e f f e c t i s most marked a t  low e n e r g i e s where the negatron momentum d i s t r i b u t i o n i s increased because  and the p o s i t r o n momentum d i s t r i b u t i o n i s decreased  of the r e s p e c t i v e  a t t r a c t i o n and r e p u l s i o n of the  negatron and p o s i t r o n . In the c a l c u l a t i o n o f M i n the above treatment, each o f the wave f u n c t i o n s  i s expressed as a s e r i e s i n powers of  (R/X) where R i s the r a d i a l e x t e n s i o n o f the nucleus and % corresponds t o the wavelength  of the e m i t t e d beta p a r t i c l e .  I f one assumes z e r o e x t e n s i o n o f the nucleus as i n t h e above treatment, o r i n other words i f one c o n s i d e r s o n l y the f i r s t  -7-  terra i n the s e r i e s expansion o f the wave f u n c t i o n s ,  then the  momentum d i s t r i b u t i o n r e s u l t i n g i s that o f a s o - c a l l e d " a l l o w e d " beta t r a n s i t i o n f o r which M i s c o n s t a n t .  When  h i g h e r o r d e r terms a r e taken i n t o account, the matrix is becomes a f u n c t i o n  element  of momentum and thus M/no l o n g e r a c o n s t a n t .  The momentum d i s t r i b u t i o n s r e s u l t i n g from c o n s i d e r i n g  these  h i g h e r order terms a r e those of the s o - c a l l e d " f o r b i d d e n " t r a n s i t i o n s i n which f i r s t - f o r b i d d e n , s e c o n d - f o r b i d d e n and so on r e f e r to the i n c l u s i o n o f the second, order terms r e s p e c t i v e l y  t h i r d and h i g h e r  i n the s e r i e s expansion o f the wave  functions. b) S e l e c t i o n For  Rules  both a l l o w e d and f o r b i d d e n s p e c t r a ,  certain  t i o n r u l e s govern the change o f the two quantum t i c s , t o t a l angular momentum and p a r i t y .  I, o f the s t a t e .  wave f u n c t i o n  o f i t s s p a c i a l c o o r d i n a t e s and  i s s a i d to be odd i f the wave f u n c t i o n  spacial  o f h g i v e s the  P a r i t y d e s c r i b e s the nature of the  under i n v e r s i o n  spacial inversion  characteris-  The angular  momentum of a s t a t e when expressed i n u n i t s spin,  selec-  changes s i g n under  and even i f i t does not change s i g n under  inversion.  The s e l e c t i o n r u l e s which apply t o a p a r t i c u l a r beta ^ t r a n s i t i o n a r e dependent upon the nature o f the matrix element used to d e s c r i b e the t r a n s i t i o n .  F o r example, the  *  i  -8-  use  o f the m a t r i x element i n e q u a t i o n (4a) l e a d s t o the Fermi  s e l e c t i o n r u l e s which f o r an allowed spectrum a r e : AI...» 0  Fermi:  j "no"  T h i s i s a s h o r t hand n o t a t i o n meaning that takes p l a c e between n u c l e a r s t a t e s parity.  Hence  Al =0  the t r a n s i t i o n  of the same s p i n and  and there i s "no" change i n p a r i t y .  S i m i l a r l y , i f the matrix element has the tensor form, as i n e q u a t i o n (4b),  the r e s u l t i n g s e l e c t i o n r u l e s , or Gamow-Teller  s e l e c t i o n r u l e s , f o r an allowed t r a n s i t i o n a r e : G - T:  A I  = o,ll  Forbidden s p e c t r a  j  "no"  have a s s o c i a t e d  ; no 0->0. w i t h them d i f f e r e n t  s e l e c t i o n r u l e s governing s p i n change and p a r i t y change. Experimental evidence f a v o u r s the G-T s e l e c t i o n r u l e s and t h e r e f o r e supports the tensor form o f the i n t e r a c t i o n the s c a l a r  form.  I t s h o u l d be noted here that  the above treatment i s a  n o n - r e l a t i v i s t i c f o r m u l a t i o n and i s t h e r e f o r e an fication.  over  A complete r e l a t i v i s t i c  oversimpli-  treatment g i v e s r i s e to  d i f f e r e n t s e l e c t i o n r u l e s f o r the v a r i o u s types of i n t e r actions  and s e r v e s t o e x p l a i n  transitions.  a g r e a t many o f the observed  However, some t r a n s i t i o n s have been observed  which cannot be e x p l a i n e d by e i t h e r the Fermi o r GamowTeller selection rules.  The problem of f i t t i n g these  -9-  t r a n s i t i o n s i n t o the theory i s as y e t u n r e s o l v e d . the simple s e l e c t i o n r u l e s above cannot nature of f o r b i d d e n s p e c t r a which may relativistic  interactions.  One  In a d d i t i o n  hope t o e x p l a i n the  a r i s e from complex  e x c e p t i o n to t h i s , however,  i s p r e d i c t e d by the theory i n the case of t r a n s i t i o n s f y i n g the c o n d i t i o n s  ;  A l = n+1  n i s the degree of f o r b i d d e n n e s s .  t t ^ tt^ = ( - l ) , n  where  These t r a n s i t i o n s have a  unique energy dependence f o r each n and are c a l l e d " n bidden unique  satis-  t n  -for-  transitions".  c ) Comparative L i f e t i m e The  l i f e t i m e , t , of a beta t r a n s i t i o n i s determined  i n t e g r a t i n g equation  Twhere  (6) t o g e t :  C  f ( Z  'Pmax  ,  '  | M  2  ( 7 )  D  f  The  by  ^»Pmax) "  function 2  tabulated.  f  (Z,p  ''max \ o m a x  F  < >P> Z  (E -E) G  2  2 P dp  ) has been e x t e n s i v e l y c a l c u l a t e d  Thus the product  and  f t , known as the cq^paraJJ^e,  jyytet^Lme, i s e x p r e s s i b l e as:  ft  -  constant o— IMI  (8)  2  From t h i s e q u a t i o n i t can be seen t h a t the  comparative  l i f e t i m e i s a measure of the magnitude of the matrix element  -10-  a s s o c i a t e d with the t r a n s i t i o n .  In g e n e r a l terms, the matrix  element decreases w i t h i n c r e a s i n g order of forbiddenness  thus  making the f t - v a l u e a u s e f u l q u a n t i t y i n determining whether a t r a n s i t i o n i s allowed o r f o r b i d d e n . tity lpg  ft  1 0  i s used because the f t v a l u e s vary over such a  l a r g e range o f magnitudes.  log  In p r a c t i s e the quan-  Convenient  methods o f c a l c u l a t i n g 3  f t have been d e s c r i b e d by Moskowski.  d) K u r i e P l o t From e q u a t i o n  (6) i t can be seen t h a t the beta spectrum ,  approaches the end p o i n t energy £ difficult  t o determine.  0  t a n g e n t i a l l y making E  Q  T h i s problem i s overcome w i t h the  use of a K u r i e p l o t which i s simply a p l o t o f /H£p_i where N(p) i s the number o f beta p a r t i c l e s  v/pV  v  e  r  s  u  s  counted per u n i t momentum i n t e r v a l and i s , o f course, d i r e c t l y proportional to P(p).  F o r t h i s purpose F(Z,p) has 4  been e x t e n s i v e l y c a l c u l a t e d and t a b u l a t e d . spectrum  F o r the allowed  shape, i n which M i s c o n s t a n t , the K u r i e p l o t  r e s u l t s i n a s t r a i g h t l i n e w i t h energy  intercept E . Q  The  advantage o f the K u r i e p l o t l i e s i n the f a c t t h a t more weight may be p l a c e d on p o i n t s having g r e a t e r  statistical  accuracy than those near the end p o i n t . In  the case o f a f o r b i d d e n t r a n s i t i o n , the K u r i e p l o t 5  may not be l i n e a r and a shape c o r r e c t i o n f a c t o r duced t o make i t l i n e a r .  i s intro-  The degree of f o r b i d d e n n e s s o f  -li-  the t r a n s i t i o n can sometimes be determined shape f a c t o r w i l l  l i n e a r i z e the K u r i e p l o t .  by knowing which That i s , the  shape f a c t o r i n d i r e c t l y i s a c o r r e c t i o n f o r the momentum dependence of the matrix element M and t h e r e f o r e can i n d i c a t e whether a t r a n s i t i o n i s allowed o r f o r b i d d e n .  T h i s i s , how-  ever, not always a p o s i t i v e i n d i c a t i o n o f whether a t r a n s i t i o n i s allowed or f o r b i d d e n because there a r e many cases o f f o r bidden t r a n s i t i o n s haying momentum independent  matrix elements  and whose K u r i e p l o t s a r e t h e r e f o r e l i n e a r . e) O r b i t a l E l e c t r o n  Capture  The process of o r b i t a l e l e c t r o n capture takes p l a c e e n t i r e l y w i t h i n the atom and i s t h e r e f o r e d i f f i c u l t t o observe. or ing  I t m a n i f e s t s i t s e l f o n l y through s o f t x-ray  Auger e l e c t r o n e m i s s i o n a r i s i n g from the subsequent  emission fill-  of the h o l e i n the atomic s h e l l s t r u c t u r e caused by the  e l e c t r o n capture.  S i n c e the o r b i t a l e l e c t r o n i s captured  from a bound s t a t e , the n e u t r i n o e m i t t e d by the nucleus has a d i s c r e t e energy.  Thus, i n c o n t r a s t t o negatron  ron e m i s s i o n , the f i n a l determined  and p o s i t -  s t a t e s a v a i l a b l e i n phase space a r e  s o l e l y by the energy  o f the e m i t t e d n e u t r i n o .  Another d i f f e r e n c e a r i s e s i n the c a l c u l a t i o n o f the p r o b a b i l i t y f o r f i n d i n g an o r b i t a l e l e c t r o n a t the n u c l e u s .  In the  theory o f beta decay, the q u a n t i z a t i o n was formulated w i t h i n a box of volume V, and the p r o b a b i l i t y of f i n d i n g an e l e c t r o n  -12-  at the nucleus t h e r e f o r e depended upon the magnitude o f V. The p r o b a b i l i t y o f f i n d i n g an o r b i t a l e l e c t r o n a t the nucleus, on the o t h e r hand, i s independent the shape o f i t s o r b i t .  o f V and depends o n l y on  Thus the atomic e l e c t r o n wave f u n c -  t i o n s a r e used i n t h i s case. I t s h o u l d be noted t h a t most t r a n s i t i o n s of t h i s i n v o l v e the capture of an e l e c t r o n from the atomic  type  K-shell  because the K - s h e l l wave f u n c t i o n o v e r l a p s the n u c l e a r volume more than the wave f u n c t i o n s o f other s h e l l s .  L - s h e l l capture  i s o f course p o s s i b l e but much l e s s probable.  Under the con-  d i t i o n s t h a t the energy  i n a t r a n s i t i o n i s l e s s than the  b i n d i n g energy o f the K - s h e l l e l e c t r o n s , then L - s h e l l  capture  i s predominant, but t h i s c o n d i t i o n i s r a r e l y met. Whereas the d e n s i t y o f f i n a l s t a t e s f o r negatron and p o s i t r o n e m i s s i o n i s o f the form: 2  ?  (  E  o  3  )  I  A  4 TT fc 4  (Eo-E) 6  C  2  P °P 2  3  the c o r r e s p o n d i n g e x p r e s s i o n f o r K-capture i s : l  -  3  (Eo+m/jZ-E  )  2  (io)  2 where Eg i s the atomic  b i n d i n g energy  o f the c a p t u r e d  electron. As i n negatron and p o s i t r o n e m i s s i o n , i t i s p o s s i b l e to w r i t e an e x p r e s s i o n f o r the l i f e t i m e o f a K-capture  -13-  t r a n s i t i o n i n the form: i — where  = constant 3 »\" r  • f  (11)  k  , /*-2v2-  I t s h o u l d be emphasized t h a t Z i n e q u a t i o n to the parent nucleus and not the daughter negatron  III.  (12) r e f e r s  nucleus as i n  and p o s i t r o n e m i s s i o n .  Gamma Decay In g e n e r a l , r a d i o a c t i v e decay by e i t h e r beta e m i s s i o n  or e l e c t r o n capture l e a v e s the daughter state.  nucleus i n an e x c i t e d  T h i s s t a t e then decays by e i t h e r e l e c t r o m a g n e t i c  r a d i a t i o n or by the competing process of i n t e r n a l c o n v e r s i o n , to be d i s c u s s e d l a t e r . The  quantum theory of r a d i a t i o n c l a s s i f i e s gamma r a y s  i n t o e l e c t r i c and magnetic m u l t i p o l e r a d i a t i o n s c h a r a c t e r i z e d , j u s t as i n p a r t i c l e e m i s s i o n , by the quantum  mechanical  p r o p e r t i e s o f angular momentum, L, and p a r i t y , TT , o f the e m i t t e d photon.  In c l a s s i c a l analogy,  these r a d i a t i o n s  a r i s e from the o s c i l l a t i o n of e l e c t r i c and magnetic n u c l e a r m u l t i p o l e s which i n t u r n a r e the r e s u l t o f the d i s t r i b u t i o n o f e l e c t r i c charge  and c u r r e n t s i n the n u c l e u s .  When a  -14-  nucleus decays from one e x c i t e d TT j_ t o another s t a t e of s p i n i s emitted carrying $j =  away w i t h i t angular momentum TT = +1 and -1  f  denotes even and odd p a r i t y multipolarity  respectively.  of a t r a n s i t i o n i s d e f i n e d t o be 2  f o r both magnetic and e l e c t r i c t r a n s i t i o n s . f o r a t r a n s i t i o n between s t a t e s and  I i and p a r i t y  T T f , a gamma r a y  I f and p a r i t y  and p a r i t y TTV "TT , where  ITi - T f l  The  state of spin  f i s proportional  L  The p r o b a b i l i t y  having wave f u n c t i o n s V i  to jif j q  dx , where dro i s a  volume element and the o p e r a t o r q depends upon the type of transition.  In the case of e l e c t r i c d i p o l e  f o r example, q w i l l have the form function.  M(L)  ^.e^x^, which i s an odd  Thus E l r a d i a t i o n has odd p a r i t y  i n general E(L)  radiation (El)  r a d i a t i o n has p a r i t y  ( TT = -1) and  TT = (-1) *. 1  Similarly,  IT = - ( - l ) ^ . l n accord w i t h the  r a d i a t i o n has p a r i t y  even o r odd nature of q i n  qV^^ d t .  C o n s e r v a t i o n o f angular momentum demands that L =  \T  i  - If|  and i t f o l l o w s  \'I - I f ±  I  ^  L  therefore  ^ \l  ±  + If  In the theory of m u l t i p o l e r a d i a t i o n , decreases s h a r p l y with i n c r e a s i n g most cases L =  \ Ij_ - I f |  that:  1  (13)  transition probability  multipolarity.  = A l . This,  Thus f o r  coupled w i t h the  f a c t that  the p r o b a b i l i t y o f e l e c t r i c m u l t i p o l e r a d i a t i o n i s  generally  much g r e a t e r than the p r o b a b i l i t y of magnetic  -15-  multipole  r a d i a t i o n would l e a d one t o expect that a t r a n s i t i o n  i n v o l v i n g a s p i n change transition.  A I would be a 2 ^ - p o l e I  Parity considerations,  a 2^*-pole magnetic m u l t i p o l e The  electric  however, can sometimes make  t r a n s i t i o n more probable.  s e l e c t i o n r u l e s f o r gamma r a d i a t i o n d u r i n g the  t r a n s i t i o n V? ±—*"^f  may be summarized a s :  E(L)  radiations  -  AI = L ;  T T ^ TT^  = (-1)  L  M(L.)  radiations  -  AI = L }  TV T  = ~(-l)  L  No  0—»*0 t r a n s i t i o n s  ±  f  magnetic The  p a r i t y and L dependence of e l e c t r i c  and/multipole  r a d i a t i o n s a l l o w the p o s s i b i l i t y of mixed t r a n s i t i o n s i n which M(L) and E(L+1) a r e competing m u l t i p o l e s .  So f a r ,  only  E2+M1 mixtures have been e x p e r i m e n t a l l y observed. IV.  Internal  Conversion  Whenever a nucleus decays by m u l t i p o l e  r a d i a t i o n , the  competing process of i n t e r n a l c o n v e r s i o n i s a l s o  possible.  In t h i s process, the e x c i t a t i o n energy o f the t r a n s i t i o n i s g i v e n up t o one of the bound atomic e l e c t r o n s .  The e l e c t r o n  i s e m i t t e d w i t h an energy: E = E where  E  Q  Eg  Q  - Eg  i s the energy of the t r a n s i t i o n i s the b i n d i n g  energy of the e l e c t r o n i n  (14)  -16-  i t s atomic o r b i t . Internal  c o n v e r s i o n may take p l a c e through i n t e r a c t i o n  an e l e c t r o n  i n any o f the atomic l e v e l s but K - s h e l l  with  con-  v e r s i o n i s g e n e r a l l y the most probable, f o l l o w e d by L - s h e l l c o n v e r s i o n and s o on. I f an assembly o f n u c l e i decays from one e x c i t e d to another through  gamma t r a n s i t i o n s  conversion t r a n s i t i o n s ,  and N  e  internal  then N /N e  (15)  r  i s d e f i n e d to-be the i n t e r n a l c o n v e r s i o n c o e f f i c i e n t . the  c o n v e r s i o n e l e c t r o n s a r e e j e c t e d from d i f f e r e n t  shells,  Since  atomic  then N  and  state  e  .- N  6  k  + Ne  L  + N  e | |  +  (16)  the c o n v e r s i o n c o e f f i c i e n t may be d e f i n e d f o r the  v a r i o u s atomic s h e l l s a s : o<=o^ + o 4 K  where  and  L  + oL^ + ...  °<  = Ne /Ny, i s the K - s h e l l  «*L  =  K  K  (17)  conversion c o e f f i c i e n t  Ng^/iy i s the L - s h e l l c o n v e r s i o n c o e f f i c i e n t ,  so on. E x t e n s i v e t h e o r e t i c a l c a l c u l a t i o n s  of i n t e r n a l  c o n v e r s i o n c o e f f i c i e n t s have been undertaken and t a b u l a t e d "6 by Rose. Certain  g e n e r a l statements c o n c e r n i n g the nature o f  -17-  i n t e r n a l c o n v e r s i o n c o e f f i c i e n t s as t h e o r e t i c a l l y p r e d i c t e d may be l i s t e d as f o l l o w s : (a) c< i n c r e a s e s w i t h i n c r e a s i n g Z and L and d e c r e a s i n g transition  energy.  (b) F o r a g i v e n t r a n s i t i o n energy (c)  0 4  transition  e l  >  °^ mag°  j f / ^ L decreases w i t h i n c r e a s i n g L f o r g i v e n Z and energy.  (d) C . ° < / * L ) K  transition  and Z, ° <  e l  < (°^K  /0(  L^mag  f  °  r&  g  i  v  e  n  L  »  Z  a  n  d  energy.  Thus the i n t e r n a l c o n v e r s i o n c o e f f i c i e n t i s a v e r y u s e f u l measure o f the s p i n and p a r i t y changes a s s o c i a t e d w i t h a nuclear  V.  transition.  Methods o f Measurement  i n Nuclear  Spectroscopy  Many e x p e r i m e n t a l techniques have been d e v i s e d f o r the study of n u c l e a r r a d i a t i o n s , some o f which have  suggested  themselves  The develop-  through  theoretical considerations.  ment o f the s c i n t i l l a t i o n counter and advances i n photom u l t i p l i e r d e s i g n have been b a s i c t o the improvements a c h i e v e d i n gamma-ray s p e c t r o s c o p y . for  The same may be s a i d  a s s o c i a t e d e l e c t r o n i c c i r c u i t r y and i n p a r t i c u l a r f o r  the refinements made i n c o i n c i d e n c e t e c h n i q u e s .  In the  f i e l d o f b e t a s p e c t r o s c o p y , the improvements have been  -18-  mostly i n spectrometer d e s i g n and one such improvement i s the s u b j e c t o f p a r t of t h i s  thesis.  W i t h i n the c u r r e n t s t r u c t u r e of n u c l e a r theory, the g e n e r a l aim o f n u c l e a r s p e c t r o s c o p y i n the study of a p a r t i c u l a r n u c l e u s , i s t o e s t a b l i s h the energy sequence of the e x c i t e d s t a t e s of the nucleus and t o measure the energy, s p i n and p a r i t y a s s o c i a t e d w i t h each o f these s t a t e s .  There  are, of c o u r s e , o t h e r p r o p e r t i e s which may be a s s i g n e d t o each n u c l e a r s t a t e but those mentioned  a r e the ones of primary  concern i n n u c l e a r s p e c t r o s c o p y . The  two b a s i c t o o l s used i n b e t a - and gamma-ray s p e c t r o -  scopy a r e the magnetic  spectrometer and the s c i n t i l l a t i o n  c r y s t a l - p h o t o m u l t i p l i e r spectrometer. operate on c o n t r a s t i n g The magnetic  The two spectrometers  principles.  spectrometer w i l l be d i s c u s s e d i n d e t a i l  l a t e r , but i t i s u s e f u l t o note some of the b a s i c at t h i s time. magnetic  field,  principles  When a charged p a r t i c l e  (electron) enters a  i t experiences a force  F - — ( v x B) and c  thus d e s c r i b e s a t r a j e c t o r y whose c h a r a c t e r i s t i c s depend upon v and B.  I t i s p o s s i b l e t o d e s i g n magnets whose i n d u c -  t i o n B i s o f such a nature t h a t e l e c t r o n s o f a p a r t i c u l a r v e l o c i t y v a r e " f p c u s s e d " a f t e r t r a v e r s i n g the f i e l d B. E l e c t r o n s of other v e l o c i t i e s a r e d e f l e c t e d away from the focus.  Thus every v e l o c i t y has a c o r r e s p o n d i n g f i e l d s t r e n g t h  to achieve a f o c u s .  When arrangements a r e made such  that  -19-  o n l y the f o c u s s e d e l e c t r o n s are d e t e c t e d (or counted), then a graph o f the i n t e n s i t y versus B g i v e s the i n t e n s i t y t r i b u t i o n of e l e c t r o n momenta.  dis-  G e n e r a l l y such instruments  are c h a r a c t e r i z e d by h i g h r e s o l u t i o n and low e f f i c i e n c y o f detection. The s c i n t i l l a t i o n spectrometer on the other hand, makes use of the p r o p e r t i e s of c e r t a i n c r y s t a l s .  These c r y s t a l s  emit a p u l s e o f l i g h t when a charged p a r t i c l e o r electromagn e t i c r a d i a t i o n i s absorbed i n the c r y s t a l .  For p a r t i c l e  a b s o r p t i o n , the i n t e n s i t y o f the l i g h t p u l s e produced i s r o u g h l y p r o p o r t i o n a l t o the energy of the i n c i d e n t  particle.  For gamma-ray a b s o r p t i o n , the p u l s e h e i g h t output o f the c r y s t a l i s more c o m p l i c a t e d because of energy d i s s i p a t i o n f o r photons  o f the d i f f e r e n t modes  i n the c r y s t a l .  Another  p a r t of the s c i n t i l l a t i o n spectrometer i s the p h o t o m u l t i p l i e r made up of a l i g h t - s e n s i t i v e cathode and an e l e c t r o n m u l t i p l i e r f o r l i g h t detection.  For maximum response i t i s  necessary t h a t the s p e c t r a l s e n s i t i v i t y o f the cathode match the spectrum of the l i g h t e m i t t e d by the c r y s t a l .  The  measured spectrum o f p a r t i c l e e n e r g i e s i s s i m p l y the r e s u l t i n g p u l s e h e i g h t d i s t r i b u t i o n of the p h o t o m u l t i p l i e r output. G e n e r a l l y such spectrometers a r e c h a r a c t e r i z e d by low r e s o l u t i o n and h i g h d e t e c t i o n e f f i c i e n c i e s . The two types of spectrometers d e s c r i b e d above may be used s i n g l y or i n combination i n a number o f d i f f e r e n t ways  -20-  to o b t a i n u s e f u l data.  Very b r i e f l y , some of the methods used  i n b e t a - and gamma-ray spectroscopy  are as f o l l o w s :  (a J Gamma-ray spectrum - The s o - c a l l e d s i n g l e s gamma-ray scintillation  spectrum i s sometimes s u f f i c i e n t f o r the  energy d e t e r m i n a t i o n o f the gamma-rays e m i t t e d by a p a r t i c u l a r r a d i o a c t i v e nucleus but the i n h e r e n t l y poor r e s o l u t i o n o f scintillation  spectrometers  makes t h i s a d i f f i c u l t task i f the  spectrum i s a t a l l complex. (b) P h o t o e l e c t r o n spectrum - A more a c c u r a t e energy d e t e r m i n a t i o n f o r gamma-rays i s o b t a i n e d i n the p h o t o e l e c t r o n spectrum u s i n g a magnetic spectrometer. utilizes  This  technique  the p h o t o e l e c t r i c e f f e c t by a l l o w i n g gamma-rays t o  f a l l on a t h i n f o i l o f h i g h Z m a t e r i a l such as l e a d o r bismuth and a n a l y z i n g the e j e c t e d p h o t o e l e c t r o n s . i n t o account  the b i n d i n g energy o f the atomic  Upon t a k i n g  s t a t e s from  which the e l e c t r o n s a r e e j e c t e d i n the f o i l and the energy dependence o f 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 , both the t r a n s i t i o n e n e r g i e s and r e l a t i v e gamma-ray i n t e n s i t i e s may be determined  w i t h c o n s i d e r a b l e accuracy.  (c) Gamma-gamma c o i n c i d e n c e spectrum - The c o i n c i d e n c e technique, used e x t e n s i v e l y i n gamma-ray s p e c t r o s c o p y , i s u s e f u l both i n e s t a b l i s h i n g the sequence o f gamma emissions from a nucleus and i n energy d e t e r m i n a t i o n s  through  t i o n o f gamma-rays i n a c o i n c i d e n c e spectrum. t i o n spectrometers  separa-  Only s c i n t i l l a -  can be u s e f u l l y employed with t h i s method.  -21-  (d) Gamma-gamma angular c o r r e l a t i o n - Theory p r e d i c t s t h a t the angle between two gamma-rays e m i t t e d s u c c e s s i v e l y , or i n cascade,  i n a system o f three n u c l e a r l e v e l s depends  upon the s p i n s and p a r i t i e s o f the l e v e l s .  That i s , i f the  f i r s t gamma-ray i n the cascade, y ^ , i s emitted lar direction gamma-ray,  i n a particu-  the p r o b a b i l i t y o f emission o f the second  j^g* *  d i r e c t i o n 5g i s a f u n c t i o n o f the  n  angle between r-^ and ?£. method, u s i n g s c i n t i l l a t i o n c o i n c i d e n c e techniques  The gamma-gamma angular  correlation  c o u n t e r s , n e c e s s a r i l y employs  and i s u s e f u l i n s p i n  determinations.  T h e o r e t i c a l c a l c u l a t i o n s o f angular c o r r e l a t i o n s between both pure and mixed t r a n s i t i o n s have been done by Biedenharn and Rose.^ (e) Beta-gamma c o i n c i d e n c e spectrum - T h i s method e x p l o i t s the h i g h r e s o l u t i o n o f a beta-ray spectrometer and the h i g h t r a n s m i s s i o n a v a i l a b l e i n a gamma-ray spectrometer.  The o r d e r i n g o f t r a n s i t i o n s i s e a s i l y e s t a -  b l i s h e d by t h i s method thus f a c i l i t a t i n g decay scheme.  scintillation  the a n a l y s i s o f a  F u r t h e r i n f o r m a t i o n can o f t e n be o b t a i n e d  from c o i n c i d e n c e s between c o n v e r s i o n e l e c t r o n s and gamma-rays. T h i s technique  i s e q u i v a l e n t , i n a sense, t o the gamma-gamma  c o i n c i d e n c e technique with one channel  o f the apparatus  having very good r e s o l u t i o n . ( f ) Beta-ray  spectrum - A n a l y s i s o f a beta-ray  w i t h a magnetic spectrometer  g i v e s i n f o r m a t i o n about  spectrum level  -22-  e n e r g i e s through end p o i n t energy measurements.  In cases  where the degree of forbiddenness can be determined,  informa-  t i o n c o n c e r n i n g s p i n and p a r i t y changes i s a l s o o b t a i n e d . (g) I n t e r n a l c o n v e r s i o n spectrum s i o n spectrum  - The i n t e r n a l  conver-  i s the most a c c u r a t e method f o r determining  t r a n s i t i o n e n e r g i e s as i t i s measured under the c o n d i t i o n s of r e l a t i v e l y good r e s o l u t i o n i n h e r e n t i n beta-ray s p e c t r o meters.  From t h i s spectrum  and from gamma-ray i n t e n s i t y  measurements i t i s p o s s i b l e to c a l c u l a t e c o n v e r s i o n c o e f f i c i e n t s which, i f known a c c u r a t e l y enough, determine the m u l t i p o l a r i t i e s of the t r a n s i t i o n s . The a b s o l u t e d e t e r m i n a t i o n o f the i n t e r n a l c o n v e r s i o n c o e f f i c i e n t of a t r a n s i t i o n r e q u i r e s an a c c u r a t e knowledge of c e r t a i n geometric  parameters of the beta-ray  being used i n the experimental i n v e s t i g a t i o n , ,  spectrometer These parame-  t e r s a r e o f t e n d i f f i c u l t t o measure w i t h s u f f i c i e n t t o reduce  accuracy  the c o r r e s p o n d i n g u n c e r t a i n t y i n the c a l c u l a t e d  i n t e r n a l conversion c o e f f i c i e n t .  T h i s d i f f i c u l t y can be  avoided by measuring the s o - c a l l e d K/L r a t i o , o r the r a t i o of i n t e n s i t i e s o f the K - s h e l l c o n v e r s i o n e l e c t r o n s t o the L - s h e l l conversion electrons.  U n f o r t u n a t e l y , t h i s method i s  not as u s e f u l as was o r i g i n a l l y a n t i c i p a t e d because o f the experimental d i f f i c u l t y o f measuring the L - s h e l l c o n v e r s i o n i n t e n s i t y coupled with the r e l a t i v e i n s e n s i t i v i t y o f the K/L r a t i o t o the type o f m u l t i p o l e r a d i a t i o n .  The use of  -23-  r e f i n e d techniques t o measure the b e t a - r a y spectrometer geom e t r i c parameters can, however  p  overcome t h i s problem to a  large extent. An i n t e r e s t i n g case i s the 0:—*- 0 t r a n s i t i o n where s e l e c t i o n r u l e s f o r b i d an e l e c t r o m a g n e t i c t r a n s i t i o n .  Thus  o n l y i n t e r n a l c o n v e r s i o n can occur and the a s s o c i a t e d i n t e r n a l conversion c o e f f i c i e n t i s therefore  VI. a)  infinite,,  Beta-ray Spectrometers Instrument Parameters There a r e v a r i o u s parameters which c h a r a c t e r i z e the  f o c u s i n g p r o p e r t i e s o f a magnetic b e t a - r a y spectrometer. The two parameters most d e s c r i p t i v e o f spectrometer performance are t r a n s m i s s i o n and r e s o l v i n g power.  R e s o l v i n g power i s a  measure o f the s p h e r i c a l a b e r r a t i o n o f the instrument and i s d e f i n e d i n terms of how t h i s a b e r r a t i o n a f f e c t s the shape of the spectrum o f a r a d i o a c t i v e source of monoenergetic electrons.  In p r a c t i s e , t h i s i s accomplished by examining  an i n t e r n a l c o n v e r s i o n l i n e i n a spectrum.  The most common  P d e f i n i t i o n of r e s o l v i n g power i s R - - j — ^ , where p i s the mr  momentum of the e l e c t r o n s p r o d u c i n g the c o n v e r s i o n l i n e and A p i s the l i n e width measured a t h a l f i n t e n s i t y . become customary t o r e f e r t o the q u a n t i t y  I t has  as the  -24Ap " r e s o l u t i o n " o f the instrument but i n t h i s t h e s i s  "~p  will  be c a l l e d simply the l i n e width and w i l l be expressed as a percentage. Beta-rays a r e e m i t t e d , o f course, by the source i n t o 4TT s t e r a d i a n s but o n l y a s m a l l f r a c t i o n of them a r e d e t e c t e d . T h i s f r a c t i o n i s d e f i n e d t o be the transmission,, T.  A related  parameter i s the g a t h e r i n g power, « , which i s d e f i n e d t o be the f r a c t i o n o f 4"rr s t e r a d i a n s subtended b a f f l e s a t the source.  In other words, the entrance  make a v a i l a b l e f o r magnetic spectrometer  by the entrance baffles  a n a l y s i s and d e t e c t i o n by the  those b e t a - r a y s e m i t t e d by the source i n t o a  s o l i d angle of  4TT'W  steradians.  Unfortunately, a l l beta-  r a y s passed by the source-entrance b a f f l e system a n a l y s i s a r e not n e c e s s a r i l y focused.  T h i s means that T ^ u .  In some a p p l i c a t i o n s , other parameters i n d e s c r i b i n g instrument performance.  f o r magnetic  are a l s o u s e f u l  Two examples of these  are the d i s p e r s i o n and l u m i n o s i t y parameters. D i s p e r s i o n dx D, i s d e f i n e d as D = — — — - , where x i s a s u i t a b l e d(H ^ ) c o o r d i n a t e d e f i n i n g the p o s i t i o n of the focus and H^> e l e c t r o n momentum i n gauss-cm.  a  i s the  T h i s parameter i s a measure  of the a b i l i t y o f the instrument t o separate adjacent  lines  i n a spectrum. In order t o o b t a i n a good spectrum,  the source must be  kept t h i n t o reduce s c a t t e r i n g w i t h i n the source i t s e l f . to o b t a i n s u f f i c i e n t a c t i v i t y , source m a t e r i a l o f h i g h  Thus,  -25-  s p e c i f i c a c t i v i t y i s u s u a l l y r e q u i r e d , p a r t i c u l a r l y i f the source must a l s o he s m a l l .  In cases where t h i s i s not  p o s s i b l e and an extended source has  to be used t o o b t a i n  r e q u i r e d a c t i v i t y , the l u m i n o s i t y parameter;, A  , measures the  a b i l i t y of a spectrometer to make use of an extended Luminosity  i s d e f i n e d as  -A. =  0".  the source  and w i s the g a t h e r i n g power.  the  source.  where 0" i s the area of A more meaningful  parameter i n p r a c t i c e i s the " o v e r a l l l u m i n o s i t y " , L„ d e f i n e d to be L = 0" ° T. T,  From the r e l a t i o n s h i p between w  i t i s c l e a r that L 6 A  and  .  As f a r as t r a n s m i s s i o n and r e s o l v i n g power are concerned, one  o b v i o u s l y wishes t o have an instrument  m i s s i o n and h i g h r e s o l v i n g power.  with high t r a n s -  In a p a r t i c u l a r a p p l i c a -  t i o n , i t i s o f t e n d e s i r a b l e to o p t i m i z e e i t h e r the t r a n s m i s s i o n or the r e s o l v i n g power at the expense of other.  For example, a complex spectrum r e q u i r e s an  ment with h i g h r e s o l v i n g power to separate i n t e r n a l conversion  l i n e s whereas a low  r e q u i r e s a h i g h t r a n s m i s s i o n instrument time down to a reasonable  the  the  instru-  various  activity  source  to keep the  counting  level.  b) Types of Instruments 8 Gerholm beta-ray  has w r i t t e n an e x t e n s i v e  spectrometers,  a r t i c l e d e a l i n g with  so o n l y a b r i e f account of  v a r i o u s types of spectrometers  the  w i l l be g i v e n here f o r the  -26-  sake of completeness.  The one e x c e p t i o n t o t h i s w i l l be the  t h i n - l e n s spectrometer, a m o d i f i c a t i o n of which i s d i s c u s s e d later. Beta-ray spectrometers may magnetic  be very g e n e r a l l y d i v i d e d  into  f o c u s i n g instruments which are momentum s e l e c t i v e  and e l e c t r o s t a t i c f o c u s i n g instruments which are energy selective.  The l a t t e r type i s r a r e l y used mainly because i t  i s l i m i t e d by the range of e l e c t r o n e n e r g i e s that can be focused.  The p r o d u c t i o n and c o n t r o l of the very l a r g e  e l e c t r i c f i e l d s r e q u i r e d i n v o l v e t e c h n i c a l problems to  overcome.  produces of  By comparison„ a magnetic  f i e l d of 1000  the same r a d i u s of c u r v a t u r e as an e l e c t r i c  300 000 volts/cm„ s  Thus  9  difficult gauss field  the b e t a - r a y spectrometers i n  use today are almost without e x c e p t i o n those of the  magnetic  f o c u s i n g type. Magnetic  f o c u s i n g spectrometers may  be f u r t h e r  classi-  f i e d i n t o the s o - c a l l e d f l a t spectrometers and the h e l i c a l or  lens-type spectrometers  s  9  the d i s t i n c t i o n b e i n g that the  e l e c t r o n t r a j e c t o r i e s i n the former type l i e i n planes approximately p e r p e n d i c u l a r .to the magnetic  axis while  e l e c t r o n t r a j e c t o r i e s i n the l e n s - t y p e spectrometer l i e i n planes that c o n t a i n the magnetic t h a t c o n t a i n the magnetic  axis.  The phrase "planes  a x i s " should r e a l l y read " r o t a t i n g  planes t h a t c o n t a i n the magnetic  a x i s " because  i n the l e n s - t y p e spectrometer f o l l o w h e l i c a l  the e l e c t r o n s  trajectories  -27-  over p a r t o f the s o u r c e - d e t e c t o r d i s t a n c e . i) Flat  spectrometers  Great improvements have been made over the years in  the p r o p e r t i e s o f f l a t spectrometers, c h i e f l y by shaping  the magnetic  field.  One such improvement u t i l i z e s the  t h i r d - o r d e r f o c u s i n g p r i n c i p l e i l l u s t r a t e d i n F i g . 1 wherein a l l e l e c t r o n s e m i t t e d i n the same plane a r e f o c u s e d a t the same p o i n t .  A f u r t h e r improvement employs double  focusing,  as i n F i g . 2, i n which the e l e c t r o n s a r e focused i n both the h o r i z o n t a l and v e r t i c a l d i r e c t i o n s .  V a r i a t i o n s on the  f l a t spectrometer d e s i g n a r e the s o - c a l l e d prism and s e c t o r f i e l d spectrometers i n which both source and d e t e c t o r a r e o u t s i d e the r e g i o n of the magnetic  field,  as i n F i g . 3.  In  these spectrometers, the shape of the p o l e p i e c e s where the e l e c t r o n s e n t e r the magnetic  field  i s a v a r i a b l e which p e r -  mits the o p t i m i z a t i o n o f p a r t i c u l a r d e s i r e d p r o p e r t i e s .  A  n o v e l d e s i g n , i n F i g . 4, e f f e c t i v e l y employing s i x s e c t o r f i e l d spectrometers i n p a r a l l e l , i s the "orange" s p e c t r o Q meter o f Kofoed-Hansen i i ) Helical  E  L i n d h a r d and N i e l s o n .  spectrometers  As i n the case o f f l a t spectrometers;, s e v e r a l c h a r a c t e r i s t i c types a r e d e f i n a b l e i n the f a m i l y o f h e l i c a l spectrometers.  The s o l e n o i d a l spectrometer employs a  uniform magnetic lending i t s e l f  field  over the e n t i r e e l e c t r o n path, thus  t o simple computation  of e l e c t r o n  trajectories.  -28-  T h e o r e t i c a l c a l c u l a t i o n s have been made t o determine magnetic  f i e l d shape r e q u i r e d t o reduce the i n h e r e n t  aberrations.  Such a f i e l d shape i s approximated  l e n s spectrometer and the intermediate-image  the  focusing  i n the  long-  spectrometer.  Both of these spectrometers have the source and d e t e c t o r i n regions  of s t r o n g magnetic  field.  f a c t o r l i m i t s the f l e x i b i l i t y One type.  For some applications,, t h i s  of use of the spectrometer.  f u r t h e r type of h e l i c a l spectrometer i s the t h i n - l e n s  I t i s c h a r a c t e r i z e d by an i n h e r e n t l y l a r g e s p h e r i c a l  a b e r r a t i o n but a m o d i f i c a t i o n t o reduce t h i s l i m i t a t i o n be v e r y s i m p l y i n c o r p o r a t e d m o d i f i c a t i o n w i l l now  be  i n t o the instrument.  discussed.  Such a  can  -29-  CHAPTER I I  RING FOCUS COLLECTION IN A THIN-LENS MAGNETIC SPECTROMETER  I.  Introduction While the t h i n - l e n s spectrometer does not e x h i b i t  either  the h i g h t r a n s m i s s i o n or the r e s o l v i n g power t h a t can be a t t a i n e d w i t h v a r i o u s other instruments now  available, i t  does possess some a t t r i b u t e s which are worth d i s c u s s i n g here. I t i s an i n e x p e n s i v e instrument both to operate and c o n s t r u c t . T h i s , of course, d e r i v e s p a r t l y from the f a c t t h a t the power requirements are s m a l l and the a s s o c i a t e d c o n t r o l are few.  circuits  I t i s a l s o a m e c h a n i c a l l y simple instrument employ-  i n g o n l y a vacuum chamber and an a i r - c o r e magnet. The  t h i n - l e n s spectrometer i n t h i s l a b o r a t o r y , as  o r i g i n a l l y used; e x h i b i t e d o n l y a moderate t r a n s m i s s i o n (^0.4%) and r e s o l u t i o n  ( l i n e width <^3.0%).  These perform-  ance c h a r a c t e r i s t i c s are poor enough to s e t s e r i o u s l i m i t s  on  the u s e f u l n e s s of the instrument, p a r t i c u l a r l y i n the a n a l y s i s of complex decay schemes.  T h e r e f o r e , an  investiga-  t i o n i n t o the p o s s i b i l i t y of improving the instrument  was  -30-  undertaken. For many years i t was spectrometers  known that magnetic  lens-type  d i s p l a y e d a " r i n g f o c u s " of e l e c t r o n t r a j e c -  t o r i e s „ as i n F i g . 5, somewhat analogous to the of l e a s t c o n f u s i o n " i n an  "circle  ''. • Ring  o p t i c a l l e n s system.  This  ^ ^ ^ ^ >^  spherical aberration effect, and  focus  I^^n^  s  the e f f e c t of other  a b e r r a t i o n s , was reduced by u s i n g a symmetric  ^ x \ V  Figure 5 - Electron t r a j e c t o r i e s i n a h e l i c a l spectrometer.  geometry i n which the source  and d e t e c t o r were  p l a c e d equal d i s t a n c e s from the magnet on the magnetic a x i s . On  the other hand, s e v e r a l w o r k e r s ^ " ^ have taken advantage  of the r i n g focus p r o p e r t y by p l a c i n g b a f f l e s at the p o s i t i o n of the r i n g f o c u s , r e s u l t i n g i n an improvement of instrument  performance.  In once case**,  c a l c u l a t e d to i n c r e a s e by a f a c t o r two  the  the t r a n s m i s s i o n  was  f o r a given r e s o l v i n g  power. In an instrument  of t h i s type,  the e l e c t r o n t r a j e c t o r i e s  at the p o s i t i o n of the r i n g focus are d i v e r g i n g and c r o s s the magnetic a x i s a t w i d e l y separated makes i t d i f f i c u l t  This  t o c o l l e c t a l l the e l e c t r o n s with an  d e t e c t o r u n l e s s the spread from the source  points.  therefore  i n emergent angle  axial  of e l e c t r o n s  i s kept s m a l l , thus r e d u c i n g the  transmission.  -31-  The m o d i f i c a t i o n t o the instrument i n t h i s l a b o r a t o r y i t s t r a n s m i s s i o n i n two ways. at ing  First,  improved  the d e t e c t o r was p l a c e d  the p o s i t i o n of the r i n g f o c u s so that a l l e l e c t r o n s passthrough the r i n g f o c u s were c o l l e c t e d .  assymmetric  Second, an  geometry was used i n which the source to magnet  d i s t a n c e was decreased t o a l l o w the use o f t r a j e c t o r i e s having l a r g e r emergent a n g l e s .  That i s , the symmetric  geometry of the unmodified instrument l i m i t e d the maximum emergent angle a t the source because the vacuum chamber. net,  of the f i n i t e s i z e of  By moving the source c l o s e r t o the mag-  emergent angles i n the r e g i o n o f g r e a t e r geometric  acceptance became a v a i l a b l e and a l a r g e r t r a n s m i s s i o n was attained.  II.  Preliminary Investigation A s e r i e s o f t r a j e c t o r i e s were c a l c u l a t e d f o r us by the  Computation  Center a t the McLennan L a b o r a t o r y , U n i v e r s i t y o f  Toronto t o determine where the r i n g f o c u s was l o c a t e d and what degree of assymmetry c o u l d be employed.  These c a l c u l a -  t i o n s were based upon the method of Deutsch, E l l i o t t and 14 Evans  and used the f o l l o w i n g e q u a t i o n s : The e q u a t i o n d e f i n i n g the e l e c t r o n t r a j e c t o r i e s was: r"  (* -A ) - r ' A ^ (l r< ) 2  2  2  +  +  A ^  = ~  0  -32-  where  A i s the v e c t o r p o t e n t i a l per ampere of magnetizing current r  i s the r a d i a l  z i s the a x i a l  displacement displacement  k i s the e l e c t r o n momentum i n gauss-cm/ampere r ' and r " a r e time  derivatives.  The v e c t o r p o t e n t i a l A i s c a l c u l a t e d from the equation.  r r** ^ 5 ^ ^ A ( r , z ) = | H ( z ) - fg--£^2 H ( z ) + I s T 2  0  H  Q  °  (  Z  )  " °°°  where H ( z ) i s the a x i a l magnetic f i e l d g i v e n by: Q  B  i n which,  ° ' - lOUaV*!) ( Z  i B ( .  s  ) - B (  M  ) }  n i s the number of t u r n s i n the magnet = 2040 a^ i s the i n n e r r a d i u s of the magnet = 11.02 cm. &2 i s  t n  ^ outer r a d i u s of the magnet = 28.40 cm.  L i s the a x i a l l e n g t h o f the magnet = 17.61 cm. and the f u n c t i o n B i s g i v e n by: 2 1/2 , 2-, 1/2) ( a ) = Cz+|)ln{a+[a +(z ^) ] ] - (z-£)ln|a+ [a + (z-£) J j r  2  B  2  +  I t i s a t once apparent  t h a t there a r e many parameters  t h a t determine the nature and p o s i t i o n o f the r i n g f o c u s , and to o p t i m i z e completely  the performance o f the instrument,  parameter would have t o be i n d e p e n t e n t l y a d j u s t a b l e . parameters a r e :  each  These  -33-  (a) source-to-magnet  distance,  (b) the spread of emergent angles accepted from the source, (cJ r i n g detector-to-magnet d i s t a n c e , (d) r i n g d e t e c t o r r a d i u s , and (e) r i n g d e t e c t o r s l o t width. Independent  adjustment of each of these v a r i a b l e s  poses  a f o r m i d a b l e mechanical problem, s i n c e a l l adjustments have to be made i n vacuo.  T h e r e f o r e a compromise was adopted.  The s o u r c e - t o - d e t e c t o r d i s t a n c e ( l i m i t e d by the a v a i l a b l e tube l e n g t h ) was f i x e d a t 69.7 cm. in  Simultaneous  variation  (a) and ( c ) above was o b t a i n e d by s l i d i n g the tube  a x i a l l y through the f o c u s i n g magnet.  The mean r i n g d e t e c t o r  r a d i u s was kept f i x e d a t about 5 cm.  Parameters  (b) and (e)  were a l t e r e d manually by the use o f a s^et of a p p r o p r i a t e b a f f l e s of s l i g h t l y d i f f e r e n t  radii.  These r e s t r i c t i o n s a r e i l l u s t r a t e ^ i n F i g . 6, taken from the c a l c u l a t e d  t r a j e c t o r i e s , i n which the r a d i a l  displacements of t r a j e c t o r i e s i n the plane of the r i n g focus are plotted the  as a f u n c t i o n o f emergent a n g l e . F o r  case i l l u s t r a t e d ,  the mean emergent angle has a  tangent of about 0.32 and the g a t h e r i n g power i s 1.10%. T h i s c h o i c e o f entrance b a f f l e s produces a r i n g focus about 1 mm wide a t a mean r a d i u s of 5„15 cm. from the f i g u r e  I t i s apparent  that f o r a g i v e n source p o s i t i o n  there i s  /  -34-  6.0-  B o CD  a  5.5  Width of E x i t at Match  Slot  28  .32 Tangent  9  .40 i n  F i g u r e 6 - Graph i l l u s t r a t i n g the match of the r i n g e x i t s l o t f o r a g i v e n entrance s l o t . a unique p a i r of emergent angles which d e f i n e a r i n g of a g i v e n  focus  focus  width.  I t s h o u l d be noted here t h a t the instrument d i s p l a y s optimum performance when the width of the t r a j e c t o r y envelope a t the r i n g focus and the width of the annular a p e r t u r e are e q u a l .  exit  T h i s c o n d i t i o n w i l l be r e f e r r e d to as  -35-  a "match". exit  I f the c o n d i t i o n of a match does not e x i s t and the  / s l o t i s too wide, then the r e s o l v i n g power o f the instrument i s determined by the s l o t width. i s reduced i n s t e p s .  In t h i s case, the s l o t width  With each s t e p , the l i n e width de-  c r e a s e s with no l o s s of t r a n s m i s s i o n u n t i l the peak h e i g h t begins  to decrease.  T h i s p o i n t r e p r e s e n t s a match.  Con-  v e r s e l y , i f the e x i t s l o t i s too narrow, the r e s o l v i n g power i s determined by the width of the t r a j e c t o r y envelope a t the r i n g focus.  The s l o t i s then opened i n steps t o i n c r e a s e the  t r a n s m i s s i o n , w i t h no change i n l i n e width, u n t i l the match c o n d i t i o n i s reached. F i g . 6, i n a d d i t i o n t o i n d i c a t i n g the optimum width f o r a given p a i r o f source  slot  b a f f l e s , a l s o i n d i c a t e s the  optimum mean r a d i u s o f the e x i t s l o t .  I d e a l l y , t h i s means  t h a t the e x i t s l o t s h o u l d be o f v a r i a b l e mean r a d i u s as w e l l as v a r i a b l e width. instrument parameter. constant  A few t e s t s showed, however, that the  performance was very i n s e n s i t i v e to change i n t h i s T h e o r e t i c a l l y , t h i s means t h a t the instrument  k (gauss-cm/ampere) has been s l i g h t l y  w h i l e the c h a r a c t e r o f the focus i t s e l f changed.  decreased  i s p r a c t i c a l l y un-  Based upon the above c o n s i d e r a t i o n s , the r a d i u s of  the outer e x i t b a f f l e was made 5 cm and the i n n e r e x i t b a f f l e was changed t o vary the width of the e x i t s l o t , the e f f e c t of the s l i g h t change i n mean r a d i u s being  negligible.  -36-  III.  The M o d i f i e d Thin-Lens Spectrometer  and A s s o c i a t e d  Apparatus a) General mechanical  description  A schematic drawing of the spectrometer used i n t h i s l a b o r a t o r y i s shown i n F i g . 7.  The vacuum chamber i s  c o n s t r u c t e d o f 1/8" brass t u b i n g , i s 1 meter l o n g and has an outer diameter of 8".  The magnet i s made of f o u r  coils  of No. 8 gauge formex magnet wire each c o n t a i n i n g about 510 t u r n s and s e p a r a t e d from each other by c o o l i n g  coils.  The width o f the magnet s p o o l i s approximately 8 1/4" and the i n n e r and outer diameters of the s p o o l a r e 8 1/2" and 24" r e s p e c t i v e l y .  Compensation c o i l s a r e used t o c a n c e l  the v e r t i c a l component of the e a r t h ' s magnetic  field.  Accurate c e n t e r i n g o f the source i s e s s e n t i a l whenever narrow e x i t s l o t s a r e used or when the source i s s m a l l in size  ( i . e . < 2 mm d i a m e t e r ) .  The s o u r c e - c e n t e r i n g  mechanism a l l o w s the source t o be p o s i t i o n e d i n the plane which c o n t a i n s the source and which i s p e r p e n d i c u l a r t o the a x i s o f the vacuum chamber.  I t i s a simple r a c k and  p i n i o n arrangement and i s operated by c o n t r o l rods p a s s i n g through vacuum s e a l s i n t h e end p l a t e a t the source end of the spectrometer. ^  The entrance b a f f l e s a r e made from 1/8" aluminum  sheet and a r e mounted on s t a n d o f f s about 4 cm i n f r o n t of the source i n such a way as to move r i g i d l y w i t h the s o u r c e .  -37-  A l e a d b a f f l e i s s i t u a t e d i n the chamber t o s h i e l d the d e t e c t o r from d i r e c t gamma r a d i a t i o n from the source. l e a d b a f f l e s are p l a c e d  Other  i n the vacuum chamber t o d i m i n i s h  the number of s c a t t e r e d e l e c t r o n s and photons that reach the d e t e c t o r when an i n t e n s e source i s used. The  whole o f the d e t e c t o r  i s l o c a t e d i n s i d e the vacuum  chamber and as a r e s u l t care has to be taken that the vacuum i s "hard" enough t o prevent e l e c t r i c a l d i s c h a r g e i n the bleeder  supplying  V o l t a g e supply  the dynode v o l t a g e s  to the d e t e c t o r .  leads and s i g n a l leads a r e f e d i n t o the  vacuum chamber through three Kovar s e a l s i n the end p l a t e at the d e t e c t o r end o f the instrument. b) The d e t e c t o r A major m o d i f i c a t i o n necessary t o improve the performance of the t h i n - l e n s spectrometer was the d e s i g n and c o n s t r u c t i o n of a d e t e c t o r  able to c o l l e c t e l e c t r o n s a t  the p o s i t i o n of the r i n g f o c u s . being  The d e t e c t o r  currently  used i s one of many that have been t r i e d , the f i r s t  of which was b u i l t by J . A. L. Thompson i n t h i s i n 1953.  laboratory  I t c o n s i s t e d o f a l u c i t e l i g h t - c o n e arrangement  which conducted the l i g h t from the s c i n t i l l a t o r , s e t i n t o the p e r i p h e r y  of the l i g h t - c o n e , onto the f a c e of a 2" 15  photomultiplier.  Milley  improved the d e s i g n  of the l i g h t -  cone by c a l c u l a t i n g the s u r f a c e shape necessary to produce  -38-  critical  internal reflection.  During the c u r r e n t  investigation, several  designs were assembled and  tested.  The  detector  f i r s t of  these  embodied a f u r t h e r improved l i g h t - c o n e coupled to an EMI a 14-stage 2" p h o t o m u l t i p l i e r .  A plastic scintillator  employed i n t h i s d e t e c t o r which was  the one  used to  6262, was  deter-  mine the s e n s i t i v i t y of the r i n g focus width to the mean r a d i u s of the e x i t  slot.  At t h i s p o i n t i n the i n v e s t i g a t i o n 5" became a v a i l a b l e commercially and m u l t i p l i e r s were purchased.  photomultipliers  three Dumont 6364 photo-  D i f f i c u l t i e s had  been encountered  w i t h o p t i c a l c o u p l i n g at the c r y s t a l - l u c i t e and m u l t i p l i e r i n t e r f a c e s , and  f o r t h i s reason a d e t e c t o r  t e s t e d that c o n s i s t e d simply tor  of a r i n g of p l a s t i c  was  scintilla-  glued onto the face of a Dumont 6364 with R313.  detector was  lucite-photo-  This  proved to have a poor s i g n a l - t o - n o i s e r a t i o which  thought to a r i s e from the low s e n s i t i v i t y of the photo-  cathode of the 6364 a t i t s edge.  Subsequent i n v e s t i g a t i o n  i n t o the s e n s i t i v i t y of the photocathode of a 6364 showed that the peak s e n s i t i v i t y at the center  of the photocathode  c o u l d be s e v e r a l times l a r g e r than at the edge. s e n s i t i v i t y pattern also v a r i e d with d i f f e r e n t p l i e r s and was  The photomulti-  found to be markedly dependent on the  * A v a i l a b l e from C a r l H.  Biggs Co.,  Los Angeles, C a l .  voltages  -39-  a p p l i e d to the dynodes and The  above c o n s i d e r a t i o n s i n d i c a t e d t h a t a l i g h t  arrangement had fall  the f o c u s i n g e l e c t r o d e .  to be used to allow s c i n t i l l a t i o n photons to  on the c e n t e r p o r t i o n o f the photocathode where the  s e n s i t i v i t y was  greatest.  Various  t e s t e d , the best being the one designed has  pipe  l i g h t - p i p e designs were  shown i n F i g . 8.  It i s  f o r c r i t i c a l i n t e r n a l r e f l e c t i o n at the s u r f a c e  and  a diameter, at the l u c i t e - p h o t o m u l t i p l i e r i n t e r f a c e ,  equal  to the diameter of the photocathode.  The  the l i g h t - p i p e i s covered with aluminum f o i l l i g h t t h a t may  s u r f a c e of  to c o n t a i n  be t r a n s m i t t e d r a t h e r than r e f l e c t e d .  the l i g h t - p i p e i s h e l d c e n t e r e d  any  Finally,  over the photocathode by  means of a b a k e l i t e r i n g which i s f i x e d onto the f a c e of  the  p h o t o m u l t i p l i e r with Armstrong cement. The s c i n t i l l a t o r used i n t h i s d e t e c t o r i s anthracene. T e s t s showed t h a t the pulse output NE  101 was  o f the p l a s t i c  scintillator  o n l y about o n e - t h i r d t h a t of anthracene.  V a r i o u s o p t i c a l c o u p l i n g m a t e r i a l s were t e s t e d . l u c i t e - p h o t o m u l t i p l i e r i n t e r f a c e i t was  difficult  At  the  to pro-  duce a l o n g l a s t i n g c o u p l i n g with s i l i c o n e o i l .  Even when  u s i n g the very high v i s c o s i t y DC200 f l u i d i t was  found t h a t  t h i s o i l g r a d u a l l y d r a i n e d away from the i n t e r f a c e . t h i s s i t u a t i o n , a s i l i c o n e gum  (DC400) was  found very d i f f i c u l t  into a thin layer.  ing  the gum  to spread  t r i e d but By  To remedy was dilut-  with the o i l i t became p o s s i b l e t o produce a  -40-  t h i n l a y e r of c o u p l i n g f l u i d t h a t would not flowf e r e n t m a t e r i a l i s used to couple t o the l u c i t e .  The o i l ,  A dif-  the anthracene c r y s t a l s  gum and oil-gum  mixture were found  to be inadequate a t the c r y s t a l - l u c i t e i n t e r f a c e as they g e n e r a l l y c o n t a i n e d minute a i r bubbles which expanded under vacuum l i f t i n g the c r y s t a l s out of t h e i r s l o t .  While the a i r  d i d e v e n t u a l l y d i s s i p a t e , i t r e q u i r e d c o n s i d e r a b l e time t o do so and t h e r e f o r e other c o u p l i n g m a t e r i a l s were t r i e d . was decided  to use a mixture of g l y c e r i n e and Ivory soap f o r  a coupling material.  T h i s mixture,  i s d e s c r i b e d by Fleishman e t a l but  It  i s s o l i d a t room temperature.  the p r e p a r a t i o n of which  , flows r e a d i l y when warm These p r o p e r t i e s a l l o w  easy i n s t a l l a t i o n of the anthracene c r y s t a l s and e l i m i n a t e the a i r bubble problem. While the d e t e c t o r i s removed a reasonable  distance  from the magnet, a s u f f i c i e n t l y i n t e n s e r e s i d u a l magnetic f i e l d can e x i s t , even a t t h i s d i s t a n c e , to cause of the p h o t o e l e c t r o n s necessary,  w i t h i n the p h o t o m u l t i p l i e r .  defocusing It i s  t h e r e f o r e , t o i n c o r p o r a t e a magnetic s h i e l d i n t o  the d e t e c t o r assembly.  The magnetic s h i e l d , seen i n F i g . 8,  i s a c t u a l l y c o n s t r u c t e d of two s h i e l d s , both o f which a r e commercially  available.  The outer s h i e l d i s a F e r n e t i c -  C o n e t i c * s h i e l d s p e c i f i c a l l y designed  f o r 5" p h o t o m u l t i p l i e r s  * A v a i l a b l e from P e r f e c t i o n Mica Co., Chicago,  Illinois.  -41-  and  the i n n e r s h i e l d , made of mu-metal, i s a l s o a standard  s h i e l d f o r 5" p h o t o m u l t i p l i e r s .  The f a c e p l a t e  of the outer  s h i e l d was made i n t h i s l a b o r a t o r y from F e m e t i c and C o n e t i c sheet m a t e r i a l and was m a g n e t i c a l l y coupled t o the rest  of the outer s h i e l d by an i r o n r i n g .  Fig. 9 illustrates  a check on the e f f i c i e n c y of the magnetic  shielding  that was c a r r i e d out by measuring the v a r i a t i o n i n background c o u n t i n g r a t e w i t h magnetic 0  .1  .2  Potentiometer  .3  .4  .5  The  setting(volts)  field.  e x i t b a f f l e s are  made of 1/8" aluminum F i g u r e 9 - D e f o c u s i n g e f f e c t on photomultiplier noise. d i r e c t l y i n front  sheet and a r e mounted  of the anthracene c r y s t a l s .  The inner e x i t  b a f f l e i s h e l d r i g i d l y t o the outer e x i t b a f f l e by a s p i d e r l e g arrangement c o n n e c t i n g the two and the whole assembly mounted on the back o f the i r o n r i n g mentioned above.  A  tapped hole i n the c e n t e r o f the i n n e r e x i t b a f f l e and a h o l e i n the f a c e p l a t e  o f the magnetic s h i e l d a l l o w the i n t r o d u c -  t i o n o f a machine b o l t the  t o keep the l i g h t - c o n e pressed a g a i n s t  f a c e of the p h o t o m u l t i p l i e r and a l s o  r i g i d l y c e n t e r e d behind the e x i t s l o t .  t o keep the c r y s t a l s I  '  c) The e l e c t r o n i c s The  investigation  of the f o c u s i n g p r o p e r t i e s of the  -42-  modified  t h i n - l e n s spectrometer r e q u i r e s o n l y the standard  e l e c t r o n i c s a s s o c i a t e d with  any beta r a y spectrometer,  i ) The c o n t r o l c i r c u i t The  e l e c t r i c c u r r e n t used to produce the f o c u s -  i n g magnetic f i e l d was p r o v i d e d  by a 110 V d.c. source.  As shown i n F i g . 10, the c u r r e n t passed through a s e r i e s +110v  c i r c u i t c o n s i s t i n g of the magnet, a bank of  Rubicon Potentiometer  Magnet  38 6AS7's connected i n p a r a l l e l and a 0.1 ohm s t a n d a r d  Bias Control Circuit  resist-  ance made of manganin. T h i s c i r c u i t was 0.1 ohm 4r  F i g u r e 10 - C o n t r o l c i r c u i t  designed to handle c u r r e n t s up to 10 amperes.  A Rubicon  potentiometer s u p p l i e d an a c c u r a t e l y known v o l t a g e which the v o l t a g e developed a c r o s s by the magnet c u r r e n t was compared.  the s t a n d a r d  *  with  resistance  T h i s comparison was  c a r r i e d out i n the b i a s c o n t r o l c i r c u i t which f e d the r e q u i r e d b i a s onto the g r i d s of the 6A$7's.  The s e n s i t i v i t y  b i a s c o n t r o l c i r c u i t was 1 p a r t i n 1 0 . 4  achieved  of the  This s e n s i t i v i t y  was  u s i n g an a.c. a m p l i f i e r of frequency response from  10 c/s to 2000 c/s and a g a i n of 10,000 coupled c o n v e r t e r - f e d d.c. c o n t r o l a m p l i f i e r having  with a Brown  a frequency  -43-  response from 0 c/s t o 20 c/s and a g a i n of 30,000. i i ) Beta s p e c t r a c o u n t i n g In the counting  circuit  circuit,  shown i n F i g . 11, the  c o l l e c t o r output of the photomultiplier f e d a 6j6  Beta Detector  CathodeFollower  cathode f o l l o w e r used t o  3-  match the impedence of the s i g n a l cable.  The p u l s e s  Amplifier  Scalar  were then a m p l i f i e d by a Tracerlab amplifier,  F i g u r e 11 - Counting c i r c u i t  model RLA-1, and f e d t o a scalar.  The s c a l a r used was a standard  s c a l e o f 64 s c a l a r ,  model 101-M, a v a i l a b l e from Atomic Instruments High v o l t a g e  Corporation.  f o r the p h o t o m u l t i p l i e r was p r o v i d e d  model HV-4A power  by a TMC  supply.  A l l dynodes. of the p h o t o m u l t i p l i e r were s u p p l i e d from a bleeder made up of 500 Kfi 1st dynode stage which c o n t a i n e d  voltage  r e s i s t o r s except f o r the  a 2Mst  potentiometer.  tap p o i n t on the potentiometer s u p p l i e d the f o c u s i n g  The  screen  v o l t a g e f o r the p h o t o m u l t i p l i e r and with an H.T. o f 1350 V the optimum screen v o l t a g e was found to be 2.6 V above the photocathode.  -44-  IV.  Experimental I n v e s t i g a t i o n of Spectrometer  Modification  a) P r e l i m i n a r y procedures The source used throughout the i n v e s t i g a t i o n of the f o c u s i n g p r o p e r t i e s o f the t h i n - l e n s spectrometer u s i n g r i n g f o c u s d e t e c t i o n was Cs 137.  I t c o n t a i n s an i s o l a t e d  internal  c o n v e r s i o n l i n e of momentum 3381.28 gauss-cm (corresponding to the K-conversion l i n e of the 662 kev t r a n s i t i o n ) making i t i d e a l f o r t h i s study.  The source was o b t a i n e d from Chalk  R i v e r and was i n the chemical form of C s N 0  3  d i s s o l v e d i n HNO3.  A beta source was prepared by d e p o s i t i n g a drop of the s o l u t i o n on a t h i n  (240 ugm/cm ) aluminum f o i l , 2  a l l o w i n g i t to  evaporate to dryness and then c o v e r i n g i t w i t h a t h i n f i l m of c o l l o d i o n to c o n t a i n the a c t i v e m a t e r i a l . Two procedures that have t o be c a r r i e d out p r i o r to the measurement  of any spectrum with t h i s spectrometer are s o u r c e -  c e n t e r i n g and s e t t i n g the d i s c r i m i n a t o r v o l t a g e on the discriminator c i r c u i t .  S o u r c e - c e n t e r i n g i s accomplished  simply by r e c o r d i n g the v a r i a t i o n i n peak h e i g h t of an i n t e r n a l c o n v e r s i o n l i n e as a f u n c t i o n of source p o s i t i o n . T h i s maximizing procedure a p p a r e n t l y s e r v e s to b r i n g the r i n g focus i n t o c o i n c i d e n c e with the e x i t s l o t , but does not, i n g e n e r a l , n e c e s s a r i l y b r i n g the magnetic a x i s i n t o c o i n c i d e n c e w i t h the s o u r c e - d e t e c t o r a x i s .  The l a t t e r c o n d i t i o n i s of  course the most d e s i r a b l e one but w i t h the source diameters used, the s m a l l d e v i a t i o n s from i t produce o n l y second order  -45-  e f f e c t s which a r e w i t h i n experimental  error.  For a l l p r a c t i c a l purposes, e l e c t r o n s of a given momentum  g i v e r i s e t o a f i n i t e spread o f v o l t a g e p u l s e  about some mean v a l u e .  heights  Thus, a l l s i g n a l p u l s e s l i e above a  p a r t i c u l a r v o l t a g e l e v e l and i t i s s u f f i c i e n t t o count o n l y those p u l s e s which l i e above t h i s l e v e l thereby r e j e c t i n g the n o i s e p u l s e s o f l e s s e r amplitude  i n voltage.  In p r a c t i c e ,  the d i s c r i m i n a t i n g v o l t a g e i s determined by measuring the peak h e i g h t o f an i n t e r n a l c o n v e r s i o n l i n e as a f u n c t i o n o f d i s criminator setting.  As the d i s c r i m i n a t o r v o l t a g e i s decreased  to " d i g " out more s i g n a l p u l s e s , the peak h e i g h t o f the conv e r s i o n l i n e measured above background i n c r e a s e s t o some maximum value and f u r t h e r lowering o f the d i s c r i m i n a t o r s e t t i n g does not a f f e c t the s i g n i f i c a n t peak h e i g h t .  The  graph o f peak h e i g h t versus d i s c r i m i n a t o r s e t t i n g i s thus a plateau-shaped  f u n c t i o n , the knee of which determines the d i s -  c r i m i n a t o r v o l t a g e s e t t i n g t o be used e l e c t r o n s being focused.  a t the energy of the  I f e l e c t r o n s of g r e a t e r energy are  focused on the d e t e c t o r , they o f course generate l a r g e r amplitude  p u l s e s of  and t h e r e f o r e the same d i s c r i m i n a t o r s e t t i n g  allows the d e t e c t i o n of a l l of these e l e c t r o n s .  For e l e c t r o n s  of s u f f i c i e n t l y g r e a t e r energy, however, the d i s c r i m i n a t o r s e t t i n g may be r a i s e d without decrease  l o s s of s i g n a l p u l s e s t o  the background count r a t e .  Thus the d i s c r i m i n a t o r  s e t t i n g e s t a b l i s h e d a t a p a r t i c u l a r momentum, p , i s used Q  -46-  o n l y f o r the momentum i n t e r v a l  (p , P Q  +  Q  A p j and  changed t o a more advantageous s e t t i n g . A p decreases w i t h d e c r e a s i n g e l e c t r o n b) Experimental measurements and The  The u s e f u l  interval  energy.  results  three g a t h e r i n g powers of 0.7%,  a r b i t r a r i l y chosen  then  1.1%  and 1.6%  were  as r e p r e s e n t a t i v e of those t o be used i n  f u t u r e e x p e r i m e n t a t i o n f o r the i n v e s t i g a t i o n of the f o c u s i n g p r o p e r t i e s of the m o d i f i e d spectrometer. angles were a l s o chosen  Three mean emergent  f o r study and source b a f f l e s were made  to d e f i n e the p r e v i o u s l y mentioned g a t h e r i n g powers at these three angles. With each of the nine p o s s i b l e combinations  of g a t h e r -  i n g power and mean emergent angle, the source p o s i t i o n , s, was  optimized.  T h i s was  accomplished  by measuring  the change  i n l i n e width and peak h e i g h t of the Cs 137 c o n v e r s i o n l i n e as the vacuum chamber was  moved a l o n g i t s a x i s .  A t y p i c a l run  of t h i s type i s shown i n F i g . 12 i n which the l i n e width peak h e i g h t are both o p t i m i z e d f o r the same source P h y s i c a l l y t h i s means t h a t f o r t h i s p a r t i c u l a r  and  position.  source  p o s i t i o n , the width of the t r a j e c t o r y envelope a t the r i n g f o c u s i s a minimum. The next s t e p i n the procedure was the e x i t s l o t u n t i l a match was  to vary the s i z e of  achieved.  s t a r t i n g w i t h a very wide e x i t s l o t ,  T h i s was  done by  thus e n s u r i n g that a l l  To f o l l o w page 4 6  0)  a si  m  o CM  s o I a o r> ; • t> (0(O CO * II  a  o <Ha g •H +-p +» too m •H UJ a: at co oo a>+> CO o H -P s «W X) o «H iH (0 Ct & +» «H O O 0 O H +* a co O V «H al «H U ±> rfl +» -rl I ax CM U  •H  -47-  e l e c t r o n s i n the r i n g focus were p a s s i n g through the e x i t s l o t , and then d e c r e a s i n g the s l o t width i n s t e p s u n t i l the peak h e i g h t began to d i m i n i s h .  During t h i s procedure  the l i n e  width decreased up t o the p o i n t where the peak h e i g h t began to drop whereupon the l i n e width then remained results  of the matching  constant.  The  procedure seem t o support the i n t e r -  p r e t a t i o n , p r e v i o u s l y o u t l i n e d , as t o the p h y s i c a l nature o f the r i n g f o c u s .  The e f f e c t on the c o n v e r s i o n l i n e o f Cs 137  d u r i n g such a matching  procedure  A summary o f the r e s u l t s  i s i l l u s t r a t e d i n F i g . 13.  o f the i n v e s t i g a t i o n  i s given  Table I . Summary of r e s u l t s o f r i n g f o c u s c o l l e c t i o n i n a t h i n - l e n s beta r a y spectrometer taken a t three g a t h e r i n g powers w i t h three d i f f e r e n t mean emission a n g l e s . Large source diameter = 2.4 mm, s m a l l source diameter = 1.6 mm.  L i n e width (%)  Exit slot width (mm)  .«',(%)  Mean tangent  Large source  Small source  Large source  Small source  1.60  0.400  1.54  1.37  3.50  3.25  0.384  1.54  1.36  3.50  3.50  0.351  1.59  1.38  3.75  3.50  0.400  1.30  1.24  3.25  3.25  0.385  1.31  3.05  0.352  1.24  2.90  0.399  1.15  3.50  0.383  1.09  0.357  1.19  1.10  0.70  1.10  3.05 3.50  3.05  Exit slot width = 3.75 mm 3.50  F i g u r e 13 - E f f e c t of e x i t s l o t width on peak shape. Entrance b a f f l e s : 0.296 - 0.406 (w=1.6%).  -48-  i n Table I.  As may be seen from the t a b l e , two sources were  used d u r i n g the i n v e s t i g a t i o n .  The f i r s t source used was  approximately 2.4 mm i n diameter.  A complete  survey of mean  emergent angles and g a t h e r i n g powers was c a r r i e d out w i t h t h i s source. determine  A second source 1.6 mm i n diameter was made t o  the e f f e c t o f source s i z e on instrument  performance,  although t h i s was not done f o r a l l p o s s i b l e geometries.  The  s m a l l e r source d i s p l a y e d a s m a l l e r l i n e width than that of the f i r s t source by about 10%. The product wR i s u s e f u l as a rough measure of the o v e r a l l performance  of a spectrometer and i s l i s t e d f o r the  v a r i o u s spectrometers i n T a b l e I I i n which the m o d i f i e d t h i n l e n s spectrometer i s compared t o some h i g h performance  helical  spectrometers. The r i n g focus c o l l e c t i o n m o d i f i c a t i o n i n c o r p o r a t e d i n t o the t h i n - l e n s spectrometer i n t h i s l a b o r a t o r y has improved  i t s performance  by a c o n s i d e r a b l e f a c t o r making i t  once a g a i n a u s e f u l t o o l i n n u c l e a r s p e c t r o s c o p y .  This i s  p a r t i c u l a r l y t r u e i n the case of p h o t o e l e c t r o n s p e c t r a and beta-gamma c o i n c i d e n c e s p e c t r a which r e q u i r e f o r t h e i r measurement an instrument having p a r t i c u l a r geometric propert i e s i n a d d i t i o n to s i m p l y good performance.  F o r example, a  p h o t o e l e c t r o n spectrum g e n e r a l l y r e q u i r e s the use of an intense source.  T h i s i s a p r o h i b i t i v e requirement i n the  many spectrometers which have a c o n s i d e r a b l e amount of  To f o l l o w page 48  Table I I . spectrometers.  Comparison o f some h i g h performance h e l i c a l Most of the data taken from r e f e r e n c e 17.  Type  Iron  «.(%)  Solenoidal  No  2.  0.4  500  Intermediate image**  No  4.5  1.6  280  Long l e n s  Yes  6.3  2.4  262  Yes  3.  1.2  250  Yes  2.7  1.3  208  Yes  8.  4.  200  Intermediate imaged  Yes  10.  5.5  180  Long l e n s  No  11.  9.  122  Thin  No  1.37  118  a  c  Solenoidal^ Long l e n s  e  Intermediate  -  f image  lens*  1.6  1/B(%)  wRxlOO  a.  F. Schmidt, Rev. S c i . I n s t r . 23, 361 (1952).  b.  D. A l b u r g e r , Rev. S c i . I n s t r . 27, 991 (1956 J.  c.  H. de Ward, T h e s i s , Groningen  d.  T. Gerholm, Rev. S c i . I n s t r . 26, 1069 (1955).  e.  W. Z i l n t i , Helv. Phys. A c t a 21, 179 (1948).  f.  H. S l a t i s and K. Siegbahn,  g.  N i c h o l s , Pohm, Talboy, and Jensen, Rev. S c i . I n s t r .  U n i v e r s i t y , 1954.  Phys. Rev. 75, 1955 (1949).  26, 580 (1955). h.  H. Agnew and H. Anderson, Rev. S c i . I n s t r . 20, 869 (1949).  i.  Present  investigation.  -49-  s c a t t e r i n g m a t e r i a l i n the r e g i o n o f the source. t h i n - l e n s spectrometer  The m o d i f i e d  i s r e l a t i v e l y free of scattering  m a t e r i a l i n the r e g i o n o f the source and w i t h i t s improved performance can now adequately measure p h o t o e l e c t r o n s p e c t r a . S i m i l a r l y , the measurement o f beta-gamma c o i n c i d e n c e s p e c t r a r e q u i r e s h i g h performance from the beta spectrometer d i f f i c u l t y a r i s e s w i t h the gamma d e t e c t o r . i n many spectrometers  but a  I t i s impossible  t o i n c o r p o r a t e a gamma d e t e c t o r near  the source because i t i s i n a r e g i o n o f h i g h magnetic T h i s problem i s much reduced  field.  i n the t h i n - l e n s spectrometer i n  which the source does n o t l i e i n a h i g h f i e l d r e g i o n . gamma d e t e c t o r may then be adequately  The  s h i e l d e d t o prevent  magnetic d e f o c u s i n g . L i k e any other instrument, spectrometer  has i t s l i m i t a t i o n s .  the m o d i f i e d t h i n - l e n s One such l i m i t a t i o n i s the  thermal n o i s e o f the p h o t o m u l t i p l i e r used i n the d e t e c t o r assembly.  T h i s reduces  the low energy e f f i c i e n c y o f the  d e t e c t o r s i n c e l a r g e background c o u n t i n g r a t e s have t o be accepted i n c o u n t i n g the low v o l t a g e p u l s e s .  The h i g h energy  e f f i c i e n c y o f the present d e t e c t o r i s i n d i r e c t l y  limited  through magnetic d e f o c u s i n g i n the p h o t o m u l t i p l i e r .  Although  the p h o t o m u l t i p l i e r i s completely e n c l o s e d by a magnetic s h i e l d , i t s l a r g e s i z e makes i t s u s c e p t i b l e t o d e f o c u s i n g by weak magnetic f i e l d s .  The d e f o c u s i n g e f f e c t can be measured  and c o r r e c t e d f o r , but f o r s u f f i c i e n t l y l a r g e magnetic  fields  -50-  i t cannot be t o l e r a t e d any f u r t h e r .  Thus, w h i l e the present  d e t e c t o r i s u s e f u l f o r c o u n t i n g e l e c t r o n s up t o ^ 800 kev without  e x c e s s i v e c o r r e c t i o n s , an improvement i n the perform-  ance of the instrument defocusing e f f e c t .  c o u l d be made through r e d u c t i o n of the  T h i s may be achieved  by:  (a) moving the  d e t e c t o r f a r t h e r from the magnet, (b) improved magnetic s h i e l d i n g , and ( c ) u s i n g a s m a l l e r p h o t o m u l t i p l i e r .  The use  of a s m a l l e r p h o t o m u l t i p l i e r would reduce both the s h i e l d i n g problem , and the problem o f thermal n o i s e . 1  In s p i t e of these  l i m i t a t i o n s on the t h i n ^ l e n s s p e c t r o -  meter, the m o d i f i c a t i o n o f r i n g focus c o l l e c t i o n has much improved i t s performance i n other r e s p e c t s .  The u s e f u l n e s s  of the spectrometer i s demonstrated i n the next  chapter  where an account i s g i v e n of the i n v e s t i g a t i o n of the decay scheme of Sb 125.  CHAPTER I I I  THE  GROUND STATE DECAY OF Sb 125  With a spectrometer of the c h a r a c t e r i s t i c s d e s c r i b e d above, i t i s now p o s s i b l e t o attempt an a n a l y s i s of very complex decay schemes w i t h some hope of s u c c e s s . l a r l y complicated  A particu-  decay scheme i s that o f Sb 125 which has 18-25  been i n v e s t i g a t e d by other workers. general  agreement on some aspects of the decay i n p r e v i o u s l y  published other  While there i s  r e s u l t s , there i s c o n s i d e r a b l e  details.  disagreement on  In view of t h i s f a c t , an a n a l y s i s was per-  formed on the r a d i a t i o n s o f Sb 125 i n an attempt to r e s o l v e these d i f f e r e n c e s .  I.  Previous  Investigation  Several research  groups have s t u d i e d the decay schemes  of Sb 125 and Te 125 s i n c e 1949.  A review a r t i c l e on 26  isotopes  by Strominger, H o l l a n d e r ,  and Seaborg  l i s t s the  major c o n t r i b u t o r s i n the e a r l i e r i n v e s t i g a t i o n of t h i s  -52-  decay scheme and some o f these r e s u l t s w i l l now be o u t l i n e d . The i n t e n s i t y of X-ray e m i s s i o n from a sample o f Sb 125, known t o decay by negatron e m i s s i o n to Te 125, l e d F r i e d l a n d e r 18 et  al  to look f o r a h i g h l y converted isomeric  i n Te 125.  transition  They observed, a f t e r c h e m i c a l l y s e p a r a t i n g the  Te 125 from the Sb 125, that the Te 125 was r a d i o a c t i v e . From l i f e t i m e and a b s o r p t i o n measurements on the e m i t t e d conv e r s i o n e l e c t r o n s , they concluded that a t r a n s i t i o n of about 120 kev e x i s t e d i n Te 125m and that the t r a n s i t i o n was K 1Q probably 2 - p o l e . graphs  In a l a t e r paper by H i l l e t a l  A  , spectro-  a n a l y s i s of the c o n v e r s i o n e l e c t r o n s d i s c l o s e d K, L  and M i n t e r n a l c o n v e r s i o n peaks c o r r e s p o n d i n g t o a 109.3 kev t r a n s i t i o n from which they o b t a i n e d the i n t e n s i t y K/L = 1 . 5 and L/M = 3.5.  The t r a n s i t i o n was  M4 w i t h a p o s s i b l e 5% admixture of E5.  ratios,  i d e n t i f i e d as  Evidence f o r another  t r a n s i t i o n was a l s o observed through an i n t e r n a l c o n v e r s i o n l i n e a t 30.4 kev and the h a l f - l i f e of the metastable s t a t e was measured t o be 58 ± 4 days. A r a t h e r thorough i n v e s t i g a t i o n of the decay o f Te 125m 20 was made by Bowe and A x e l  , i n which they e s t a b l i s h e d two  l e v e l s a t 35.5 kev and 145.2 kev above the ground s t a t e . Branching r a t i o s f o r both the 110 kev and 35 kev t r a n s i t i o n s were determined and s i n g l e p a r t i c l e assignements of s-jy2« d  3/2  a n (  * ll/2 n  w  e  r  e  m  a  d  e  t  o  t  n  e  ground s t a t e , 35.5 kev l e v e l  and the metastable 145.2 kev l e v e l r e s p e c t i v e l y .  Comparison  -53-  of experimental c o n v e r s i o n c o e f f i c i e n t s with  theoretical  v a l u e s i d e n t i f i e d the 35 kev t r a n s i t i o n as Ml w i t h admixture  < 1%  of E2.  Kern e t a l * were the f i r s t 2  beta spectrum  of Sb 125.  to attempt  to measure the  They i d e n t i f i e d two beta groups a t  288 kev and 621 kev and from p h o t o e l e c t r o n and i n t e r n a l v e r s i o n s p e c t r a observed gamma-rays of 110, 609  and 646  kev.  431,  466,  A f t e r chemical s e p a r a t i o n of the Te  and i n v e s t i g a t i o n 110 kev  175,  con-  125  of the i n t e r n a l c o n v e r s i o n l i n e s of the  t r a n s i t i o n , they measured i t s K/L r a t i o to be  1.2. oo  Sb 51 74  1 2 5  SB  125 52 73 T  Siegbahn  and  Forsling  proposed  the decay  Te  scheme' i n F i g . 14, -lthie_" -637  f i r s t suggested scheme that  •465  •35 0 F i g u r e 14 - Decay scheme of Siegbahn and F o r s l i n g .  bears some  resemblance to the currently  145m  decay  accepted  scheme,for Sb 125. spectroscopic they observed groups at 128,  analysis three beta 299  spectrum  respectively.  and  616 kev which were  i d e n t i f i e d as being f i r s t - f o r b i d d e n , second-forbidden third-forbidden  By  and  From the i n t e r n a l c o n v e r s i o n  and the p h o t o e l e c t r o n spectrum, gamma-rays a t 35,  110,  175, 425, 465, 601 and 637 kev were i d e n t i f i e d and the  K/L+M r a t i o f o r the c o n v e r s i o n l i n e s of the 110 kev t r a n s i t i o n was measured t o be 1.1. Moreau ^ p o i n t e d out t h a t the i n t e n s i t y of the 175 kev 2  gamma-ray observed  by Siegbahn and F o r s l i n g c o u l d not be  f u l l y accounted f o r by t h e i r decay scheme.  He observed the  same gamma-rays as they d i d but by measuring beta-gamma c o i n c i d e n c e s between 175 kev gamma-rays and 320 kev b e t a r a y s he was a b l e t o e s t a b l i s h a l e v e l 175 kev above the metastable  state  (145 kev)  a t 320 kev.  Through gamma-gamma  c o i n c i d e n c e s between the 425-465 kev group and gamma-rays of  175 kev he confirmed  t i o n s i n Te 125.  the presence of two 175 kev t r a n s i -  Moreau's decay scheme, i n F i g . 15,  52 300 kev. (45%)  Te  125 73 -637  444 kev (12%)  •465  612 kev (14%)  -320  -14 5 * -35  F i g u r e 15 - Moreau's decay scheme.  -55-  i n c l u d e d f o u r beta groups although o n l y the 612 kev and 300 kev groups c o u l d be e a s i l y i d e n t i f i e d i n h i s beta spectrum.  Intense i n t e r n a l c o n v e r s i o n l i n e s obscured  the h i g h  energy ends of the 444 kev and 125 kev groups but the 320 kev ahd 637 kev l e v e l s t o which these beta groups decay were e a s i l y e s t a b l i s h e d through  the 320-175 kev beta-gamma  c o i n c i d e n c e measurement and the e x i s t e n c e o f the 601-637 kev gamma-ray group. In 1956,  L a z a r * , u s i n g s c i n t i l l a t i o n c o u n t e r s , made a 2  study o f the gamma r a d i a t i o n s o f Te 125 by i n v e s t i g a t i n g gamma-gamma c o i n c i d e n c e s .  He i d e n t i f i e d e l e v e n gamma  t r a n s i t i o n s , i n a d d i t i o n t o the 110 kev-35 kev cascade the metastable  125 52 73  proposed  T e  (See T a b l e I I I f o r beta i n t e n s i t i e s )  from  s t a t e , and  the decay scheme  shown i n F i g . 16. From h i s 677 637 -525 .463  measured gamma i n t e n s i t i e s and the h a l f - l i f e of 2.0 ± 0 . 2  value  years f o r  the ground s t a t e of -320 145'  Sb 125 he c a l c u l a t e d the i n t e n s i t i e s of the beta groups and t h e i r l o g f t  35 0 F i g u r e 16 - L a z a r ' s decay scheme,  values.  In the present  i n v e s t i g a t i o n some r e l i a n c e has been p l a c e d  ' -56-  on L a z a r ' s work c o n c e r n i n g the p o s i t i o n i n g o f the 676 kev l e v e l , but t h i s w i l l be d i s c u s s e d  later.  N a r c i s i ® has measured the beta spectrum and photo2  e l e c t r o n spectrum w i t h a d o u b l e - f o c u s i n g spectrometer as w e l l as gamma-gamma c o i n c i d e n c e s p e c t r a t h i s decay scheme.  i n the study of  H i s proposed decay scheme i s e s s e n t i a l l y  the same as L a z a r ' s up t o the 525 kev l e v e l but i n s t e a d o f the 637 kev and 6*77 kev l e v e l s , N a r c i s i has e s t a b l i s h e d l e v e l s a t 633.6, 639.7, 652 and 667.6 kev.  K-shell  i n t e r n a l c o n v e r s i o n c o e f f i c i e n t s were c a l c u l a t e d by N a r c i s i assuming t h a t the 428 kev t r a n s i t i o n was pure E2 and had a 27 c o n v e r s i o n c o e f f i c i e n t of .009 - from S l i v and Rand  II.  Present  Investigation  While i t i s r e a l i z e d t h a t a complete and comprehensive study o f any decay scheme must n e c e s s a r i l y i n v o l v e  extensive  i n v e s t i g a t i o n o f both beta and gamma r a d i a t i o n s , the emphasis i n t h i s work i s p r i m a r i l y on the beta r a d i a t i o n s . T h i s emphasis i s motivated p a r t l y by the f a c t t h a t the greater  p a r t of the work done on t h i s decay scheme up t o the  present time has been i n the study o f the gamma r a d i a t i o n s from Te 125. Sb  The beta spectrum o f the ground s t a t e decay of  125 has n o t been s t u d i e d  as e x t e n s i v e l y  mainly because  -57-  of i t s complexity.  For the same reason, few attempts  have  been made t o o b t a i n beta-gamma c o i n c i d e n c e s p e c t r a .  In the  present i n v e s t i g a t i o n the r e s u l t s o b t a i n e d i n the measurement of the three types of s p e c t r a mentioned above appear t o j u s t i f y the more e x t e n s i v e use, once a g a i n , o f the t h i n - l e n s spectrometer  i n n u c l e a r s p e c t r o s c o p y with the i n c o r p o r a t i o n  of the p r e v i o u s l y d e s c r i b e d m o d i f i c a t i o n . a) Methods and Apparatus ( i ) Source p r e p a r a t i o n A 1 m i l l i c u r i e Sb 125 source was o b t a i n e d from Oak Ridge.  I t was i n the chemical form of SbClg and SbOCl i n  6N HC1 s o l u t i o n and was c a r r i e r f r e e .  For source-backing  m a t e r i a l , the r e l a t i v e l y t h i n (240yW.g/em2) aluminum  foil  used f o r the Cs 137 source c o u l d not be used because of the nature o f the a c i d s o l u t i o n .  After investigating several  source-backing m a t e r i a l s i t was decided t o use a t h i n of c o l l o d i o n .  film  T h i n f i l m s were prepared by a l l o w i n g a drop'  of a v e r y d i l u t e e t h e r s o l u t i o n o f c o l l o d i o n t o spread over a water s u r f a c e .  A f t e r p i c k i n g up the f i l m from the water  s u r f a c e by means o f a simple wire frame and then a l l o w i n g it The  t o dry, the f i l m was mounted on an aluminum source  ring.  f i l m was then very t h i n l y a l u m i n i z e d by an e v a p o r a t i o n  technique t o prevent source c h a r g i n g .  A s m a l l drop of source  s o l u t i o n was d e p o s i t e d on the a l u m i n i z e d backing, allowed t o  evaporate t o dryness and then covered w i t h another t h i n of  film  c o l l o d i o n t o c o n t a i n the source and prevent the danger of  source m a t e r i a l f l a k i n g o f f and contaminating the spectrometer. Source backings o b t a i n e d i n t h i s way were t h i n enough t o produce white l i g h t f r i n g e s and t h e r e f o r e were f e l t adequate. in  t o be  The source prepared i n the above manner was used  the measurement o f the beta spectrum  and the beta-gamma  coincidence spectra. Very l i t t l e source s o l u t i o n was used t o prepare the beta source so t h a t c o n s i d e r a b l e a c t i v i t y was l e f t p a r a t i o n o f a p h o t o e l e c t r o n source.  f o r the p r e -  Experience i n t h i s  l a b o r a t o r y has emphasized the importance  of u s i n g a t h i n  e l e c t r o n absorber i n a p h o t o e l e c t r o n source so t h a t the a c t i v e m a t e r i a l may be p o s i t i o n e d as c l o s e l y as p o s s i b l e t o the c o n v e r t e r .  T h i s i s necessary so that reasonable  i n t e n s i t y may be o b t a i n e d i n the p h o t o e l e c t r o n spectrum. A c o m p l i c a t i o n i s i n t r o d u c e d through the f a c t that a t h i n absorber must o f course be made from a m a t e r i a l of higher Z than a t h i c k absorber i f each type i s to s t o p e l e c t r o n s of a g i v e n energy.  The t h i n absorber t h e r e f o r e becomes a  source o f p h o t o e l e c t r o n s i t s e l f s i n c e the c r o s s - s e c t i o n f o r the p h o t o e l e c t r i c e f f e c t i n c r e a s e s by a t l e a s t Z . 4  Thus the  u s u a l compromise must be made between the Z-value of the absorber and the t h i c k n e s s o f the absorber. The absorber used i n the p h o t o e l e c t r o n source f o r the  present i n v e s t i g a t i o n was 1/64" t h i c k copper sheet bonded to the s t a n d a r d type o f aluminum source r i n g used i n the spectrometer.  A s m a l l i n d e n t a t i o n was made i n the back o f the  absorber with a c e n t e r punch and the e n t i r e source s o l u t i o n was  d e p o s i t e d i n t h i s i n d e n t a t i o n drop by drop and evapora-  ted  t o dryness, sometimes a i d e d by h e a t i n g w i t h an i n f r a r e d  lamp.  C o l l o d i o n was then d e p o s i t e d i n e t h e r s o l u t i o n t o  keep the source m a t e r i a l i n the i n d e n t a t i o n . l/6'4* Cu sheet Pb c o n v e r t e r  illustrates  F i g . 17  the photo-  e l e c t r o n source. Both bismuth  and l e a d  c o n v e r t e r s were used t o Aluminum r i n g  obtain photoelectron spectra.  F i g u r e 17 - P h o t o e l e c t r o n source.  The bismuth  con-  v e r t e r was 4 mm i n diameter and 1.86 mg/cm  prepared by e v a p o r a t i n g bismuth  and was  onto an aluminum f o i l .  The  l e a d c o n v e r t e r was 4 mm i n diameter and 12 mg/cm t h i c k and 2  was  prepared by manually  r o l l i n g l e a d sheet i n t o a t h i n  foil. ( i i ) Apparatus  - mechanical  The spectrometer has been thoroughly d e s c r i b e d i n Chapter  I I and t h e r e f o r e o n l y the p a r t i c u l a r  parameters  chosen w i l l be noted here.  geometric  F o r a l l s p e c t r a the  -60-  f o l l o w i n g geometry was used i n the spectrometer: (a) E x i t b a f f l e diameters = 10,6 cm, 10.0 cm (b) Entrance b a f f l e s = a r c t a n .313, a r c t a n .390 (w=l.l%) (c) Source p o s i t i o n = 21.5 cm. Because o f the l a r g e f l u x o f gamma r a y s from the Sb 125 s o u r c e , p a r t i c u l a r l y from the p h o t o e l e c t r o n source, three l e a d b a f f l e s were p l a c e d i n the vacuum chamber t o reduce the c o u n t i n g r a t e due t o s c a t t e r e d photons  (see F i g . 7).  The b a f f l e s were e x p e r i m e n t a l l y p o s i t i o n e d t o a v o i d c u t t i n g i n t o the e l e c t r o n beam. that were exposed  Any l e a d s u r f a c e s on the b a f f l e s  t o the e l e c t r o n beam, thereby c o n s t i t u t i n g  a source o f s c a t t e r i n g i n t o the beam, were covered with Apiezon Q, whose low Z-value reduces t h i s type o f s c a t t e r i n g . One l e a d b a f f l e c o n s i s t e d o f an i n n e r and outer p o r t i o n s e p a r a t e d by an annular s l o t through which the e l e c t r o n beam passed.  T h i s b a f f l e was p l a c e d between the source and  d e t e c t o r t o s h i e l d the d e t e c t o r from d i r e c t gamma r a d i a t i o n from the s o u r c e .  Each of the other two l e a d b a f f l e s  s i s t e d o f an outer p o r t i o n o n l y .  con-  They were p l a c e d i n f r o n t  of the d e t e c t o r and the source b a f f l e s t o reduce the area o f the vacuum chamber w a l l s "seen'' by the source and d e t e c t o r and t h e r e f o r e t o reduce the s c a t t e r i n g from t h i s p a r t o f the apparatus. For beta-gamma  c o i n c i d e n c e s p e c t r a , a m o d i f i c a t i o n was  made t o the source end o f the spectrometer t o a l l o w the  -61-  p o s i t i o n i n g o f a gamma d e t e c t o r near the s o u r c e .  T h i s modi-  f i c a t i o n i s i l l u s t r a t e d i n F i g . 18. Because o f the p r o x i m i t y of  the source and magnet, a r a t h e r high magnetic f i e l d  i n the r e g i o n of the s o u r c e .  A 5 1/2" long l u c i t e rod, used  as a l i g h t - p i p e t o couple the 1 l/2"x 1" to  exists  Nal(Tl) crystal  the RCA 6342 p h o t o m u l t i p l i e r , removed the p h o t o m u l t i p l i e r  from t h i s h i g h f i e l d r e g i o n .  A l e a d s h i e l d w i t h a tapered  a p e r t u r e c o l l i m a t e d the photons a n d reduced radiation striking  the c r y s t a l .  the s c a t t e r e d  A d e t a i l e d account  o f the  beta-gamma c o i n c i d e n c e m o d i f i c a t i o n i s given by Schneider  .  ( i i i ) Apparatus-electrical The  c o u n t i n g c i r c u i t used t o measure the beta  spectrum and p h o t o e l e c t r o n s p e c t r a o f Sb 125 was e x a c t l y the same as the one used i n the i n v e s t i g a t i o n of the f o c u s i n g p r o p e r t i e s o f the m o d i f i e d spectrometer  This c i r c u i t i s  shown i n F i g . 11. The e l e c t r o n i c c i r c u i t r y used t o measure the beta-gamma c o i n c i d e n c e s p e c t r a i s shown i n b l o c k diagram form i n F i g . 19. B a s i c a l l y i t i s a standard f a s t - s l o w t r i p l e c o i n c i d e n c e  cir-  c u i t i n which f a s t r i s e - t i m e p u l s e s from the beta and gamma d e t e c t o r s a r e f e d i n t o a c o i n c i d e n c e u n i t along w i t h other beta p u l s e s which have f i r s t passed circuit. thereby  through  a discriminator  T h i s c i r c u i t r e j e c t s many o f the n o i s e p u l s e s , improving  the s i g n a l - t o - n o i s e r a t i o .  P u l s e s which  a r r i v e a t these three i n p u t s i n c o i n c i d e n c e generate  a gate  F i g u r e 18 - Beta-gamma c o i n c i d e n c e m o d i f i c a t i o n .  To f o l l o w page 61  1 y Detector  B Cathode Follower  Amplifier (x2)  I  Fast Driver  Coincidence  0o07//sL  Fast Drxver  Amplifier  Discriminate  Amplifier  1  Slow Coincidence  ro. Scaler  Amplifier  Kicksorter  Figure  Amplifier  Gate  U_nna Lus  19 - Block diagram of the beta-gamma coincidence c i r c u i t .  -62-  pulse which i s used t o open the gate a t the i n p u t o f the 100-channel k i c k s o r t e r .  S i g n a l p u l s e s from the gamma d e t e c t o r  are a l s o f e d t o the k i c k s o r t e r s o t h a t each time a gate  pulse  a r r i v e s , the gamma-ray s i g n a l p u l s e c o n t r i b u t i n g to the t r i p l e c o i n c i d e n c e i s allowed  t o pass through the gate t o be  analyzed and s t o r e d i n the a p p r o p r i a t e channel. slow c o i n c i d e n c e c i r c u i t  This  fast-  i s d e s c r i b e d i n d e t a i l by Schneider ® 2  Some minor changes i n the o p e r a t i n g v o l t a g e s used by Schneider  i n the above c i r c u i t should be noted,  however.  These d i f f e r e n c e s were: (a) w h i l e , f o r maximum g a i n the a  s c r e e n v o l t a g e o f the beta d e t e c t o r p h o t o m u l t i p l i e r was the same as the f i r s t dynode v o l t a g e , the H,T, was i n c r e a s e d t o 1500  V} (b] because of the low energy photons i n the Sb 125  spectrum, the gamma d e t e c t o r H.T. was i n c r e a s e d t o 1600 v°  s  and  ( c ) the h i g h e r H.T. on the gamma d e t e c t o r caused the  s i g n a l generated and  a t the e i g h t h dynode t o become n o n l i n e a r  the s i g n a l t a p p o i n t was thus moved to the seventh  dynode.  b) R e s u l t s The  r e s o l u t i o n o b t a i n a b l e with the instrument  geometry  chosen above v a r i e d with the p a r t i c u l a r source being s t u d i e d . T h i s was p r i m a r i l y due t o the source s i z e .  Cs 137 was used  t o c a l i b r a t e the beta spectrum of Sb 125 and had a l i n e width of 1.25% on the K - s h e l l i n t e r n a l c o n v e r s i o n l i n e of the 662 kev  transition.  The v a l u e used f o r the momentum o f t h i s  -63-  l i n e was  3381.28 gauss-cm.  In the Sb 125 b e t a spectrum  itself,  the s m a l l e s t l i n e width o b t a i n e d on an i n t e r n a l c o n v e r s i o n l i n e was  1.27%  on the 428 K peak, i n d i c a t i n g that the s i z e s  of the two sources must have been n e a r l y the same.  The  line  width o b t a i n e d on the s t r o n g e s t peak i n the p h o t o e l e c t r o n spectrum,  on the other hand, was  size  mm  (^4  the s i z e  diameter) was 1 mm  ( i ) The beta The  3.4%  but the e f f e c t i v e  source  of course c o n s i d e r a b l y g r e a t e r than  diameter) of the Sb 125 beta source. spectrum  beta spectrum  of Sb 125,  i n F i g . 20,  was  measured by p l o t t i n g the s i g n i f i c a n t count r a t e as a f u n c t i o n o f potentiometer s e t t i n g .  The s i g n i f i c a n t count r a t e was  the  observed count r a t e l e s s the background count r a t e c o r r e c t e d f o r magnetic  d e f o c u s i n g of the p h o t o m u l t i p l i e r .  With the a i d  of t a b l e s of Fermi f u n c t i o n s , a K u r i e a n a l y s i s of the beta spectrum was  undertaken.  I t must be admitted that before the a n a l y s i s was the prospect of determining r e l i a b l e i n t e n s i t i e s and  begun, end  p o i n t e n e r g i e s of a t l e a s t f i v e primary beta groups by  this  method, d i d not appear to be too h o p e f u l i n view of the • m u l t i p l e s u b t r a c t i o n s that the process r e q u i r e s .  The  however, are reasonably unambiguous and s u r p r i s i n g l y t e n t w i t h the requirements  imposed by other d a t a .  results, consis-  The  a n a l y s i s r e v e a l e d f i v e d i s t i n g u i s h a b l e beta groups, which f o r purposes  of d i s c u s s i o n w i l l be c a l l e d N j ,  N4  and  I  Potentiometer S e t t i n g  (volts)  w  -64r-  N5  i n d e c r e a s i n g order of energy. The K u r i e a n a l y s i s of the  f o r b i d d e n unique shape f a c t o r a straight  5  group r e q u i r e d the f i r s t a^ = W -1+(W -W) 2  l i n e , which i n d i c a t e d  squares c a l c u l a t i o n  2  Q  t o produce  A l = 2\ "yes".  was made on the data r e s u l t i n g  A least i n an end  p o i n t energy of 626.4 kev. A f t e r s u b t r a c t i o n o f the presence o f the N  2  group.  group, the r e s i d u e shows the  U n f o r t u n a t e l y , most of the e x p e r i -  mental p o i n t s o f t h i s group a r e not t o o r e l i a b l e s i n c e the b e t a spectrum i n t h i s r e g i o n i s almost e n t i r e l y covered by a group of i n t e r n a l c o n v e r s i o n l i n e s .  The p o i n t s used were i n  f a c t taken by making a reasonable e s t i m a t e of the beta b u t i o n under the c o n v e r s i o n l i n e s .  distri-  Only a r e l a t i v e l y s h o r t  momentum i n t e r v a l i n t h i s group was f r e e o f t h i s u n c e r t a i n t y . However, the end p o i n t energy o f t h i s group i s known w i t h r e s p e c t t o the gamma t r a n s i t i o n . the  N  2  end p o i n t energy through a c o n n e c t i n g Therefore  s  s i n c e we were unable t o t r u s t  data s u f f i c i e n t l y t o a c c u r a t e l y determine the shape o f  t h i s group, a l i n e a r K u r i e p l o t was drawn from the known end p o i n t , 450.4 kev, through the few p o i n t s that were a c c u r a t e l y known.  T h i s assumption o f a l i n e a r K u r i e p l o t f o r N  j u s t i f i e d of c o u r s e , so that the i n t e n s i t y  of t h i s  2  i s not  group  cannot be determined w i t h any accuracy. An attempt was made t o determine the p o s s i b l e extent of this uncertainty.  I f i t was assumed that the group was f i r s t -  -64a-  f o r b i d d e n unique and the a p p r o p r i a t e shape f a c t o r c o r r e c t i o n a p p l i e d to the u n r e l i a b l e data, then the group i n t e n s i t y dropped by approximately  40%.  The e f f e c t of t h i s was  p r i m a r i l y t o i n c r e a s e the i n t e n s i t y o f the next group N 3 by almost the same number of counts,  while groups N 4 and Ng  were e s s e n t i a l l y u n a f f e c t e d both i n i n t e n s i t y and end p o i n t energy.  That i s , the t o t a l N +N  t i v e l y constant  2  3  i n t e n s i t i e s remained e f f e c -  during t h i s manipulation  o f the s p e c t r a l  shape o f the N 2 group. A f t e r s u b t r a c t i n g the N  2  group ( l i n e a r K u r i e p l o t ) , the  i n t e n s e N 3 group d i s p l a y e d a l i n e a r K u r i e p l o t with end p o i n t energy of 309.3 kev.  S u b t r a c t i o n o f the N 3 group r e s u l t e d  i n a n o n - l i n e a r K u r i e p l o t f o r the weak N 4 group.  Applying  the f i r s t - f o r b i d d e n unique shape f a c t o r c o r r e c t i o n once again r e s u l t e d i n a K u r i e p l o t t h a t was l i n e a r w i t h i n e x p e r i mental u n c e r t a i n t i e s .  Independent support  f a c t o r c o r r e c t i o n t o the  f o r the shape  group was the e f f e c t i t had on  the end p o i n t energy of the i n t e n s e Nj. group which f o l l o w s i t i n the s u b t r a c t i o n process.  When the shape f a c t o r was not  a p p l i e d to the N 4 group, the measured end p o i n t energy of the N5  group and the end p o i n t energy estimated  were c o n s i d e r a b l y d i f f e r e n t . reduced t h i s d i s c r e p a n c y  evidence  A p p l i c a t i o n of the shape f a c t o r  t o a value more c o n s i s t e n t with the  e r r o r expected f o r a group as i n t e n s e as Ng. end  from other  The measured  p o i n t energy o f the N 4 group was 247.4 kev.  -65-  A f t e r s u b t r a c t i n g the N 4  group, the Ng group produced  a l i n e a r K u r i e p l o t with an end p o i n t energy of 132.8 Examination of the N 5 evidence f o r a s t i l l  kev.  K u r i e p l o t shows what appears to be lower energy beta group.  Unfortunately,  t h i s i s the energy r e g i o n wherein one can expect a b s o r p t i o n and s c a t t e r i n g from the source and source backing m a t e r i a l „ T h e r e f o r e no f u r t h e r c o n c l u s i o n s can be drawn r e g a r d i n g the presence of other beta groups.  Other workers have presented  i n d i r e c t evidence f o r a weak beta group,, Ng p o i n t energy between 90 kev and I00_kev.  i s q u i t e weak compared t o Ng.  w i t h an end  In t h i s r e g i o n , the  Ng K u r i e p l o t appears to be q u i t e l i n e a r . it  9  Hence i f Ng  exists,  I t has been e s t i m a t e d that  i t s h o u l d be observed as an i d e n t i f i a b l e group i f i t s i n t e n s i t y were g r e a t e r than about 4 % of the i n t e n s i t y of Ng.  One  must then admit the p o s s i b i l i t y of the e x i s t e n c e of Ng w i t h an i n t e n s i t y l e s s than t h i s l i m i t . ;  N5  The measured i n t e n s i t y of  would then i n f a c t be the i n t e n s i t y of Ng+Ng  combined.  The K u r i e a n a l y s i s p l b t s are shown i n F i g . 21. The i n t e n s i t i e s of the beta groups were determined by p l o t t i n g the momentum d i s t r i b u t i o n and measuring the area under each beta group and c o r r e c t i n g f o r xhe r e s o l u t i o n factor  (1.4%)  as d i s c u s s e d i n Appendix  I.  Because of the low  energy d e t e c t i o n l i m i t a t i o n s a l r e a d y mentioned, i n t e n s i t y of t h e Ng group was  the measured  assumed to i n c l u d e the Ng group.  The r e s u l t s of t h i s a n a l y s i s are summarized  i n Table I I I .  W ( u n i t s of njp2)  Table I I I . Summary of beta group i n t e n s i t i e s , end p o i n t e n e r g i e s (both measured and c o r r e c t e d ) and l o g f t values. Bracketed e n t r i e s are Lazar's results.  Group Nl N  2  N  3  N' 4 N  *  %  End Point Measured  Energy Corrected  Measured  Intensity Corrected  626.4 kev  627 kev  27,900c/m  27,900c/m  450.4  451  20,200  309.3  308  ) > 247.4 J  247  132.8  134  —  232  96  Relative  Log f t  12.6% (14.0%)  9.5 (9.3)  -13,375  6 0 4 (5.5)  9.3 (9.4)  80j500  ^87,325  39.42 (42.0)  8.0 (7.8)  ) ( 8,390 )  ) f 8,390  ) >84 400  )  o  ) V'3.79 (1.2)  ;  >8.6)  \(9.2)  >8.6;  >81,400  >36 75 (37.0)  <6.8  (6.7)  < 3,000  < 1,1.36 (0.17)  >7.9  (8.7)  f  c  -66-  I t was  r e c o g n i z e d , of course, as was  s t a t e d above, t h a t  a K u r i e a n a l y s i s i n v o l v i n g s e v e r a l s u b t r a c t i v e processes likely  imposes probable e r r o r s that i n c r e a s e w i t h each sub-  traction,  p a r t i c u l a r l y when the r e s i d u e s i n v o l v e weak groups.  Thus the end p o i n t e n e r g i e s and i n t e n s i t i e s o b t a i n e d i n t h i s manner are s u b j e c t to c o r r e c t i o n from other evidence. too,  i t i s d i f f i c u l t to make r e a l i s t i c  bable e r r o r s .  Then,  e s t i m a t e s of the p r o -  These e r r o r s s h o u l d be s m a l l e s t whenever the  beta i n t e n s i t i e s are g r e a t e s t but even t h i s i s s u b j e c t to q u a l i f i c a t i o n under c e r t a i n circumstances.  The data f o r the  group should be r e l i a b l e s i n c e i t i n v o l v e s no s u b t r a c t i o n s . The shape of the N  2  group i s based upon an estimate of the  primary beta spectrum version lines. of  the N  2  T h i s estimate a f f e c t s  and N 3 groups.  this effect of  under a group of i n t e n s e i n t e r n a l the measured  intensity  F o r t u n a t e l y , a n a l y s i s has shown that  on both the i n t e n s i t i e s and  the lower energy  the end p o i n t e n e r g i e s  beta groups i s s m a l l .  The N 4 group i s the weakest of a l l groups observed, it  i s not s u r p r i s i n g t h a t s t a t i s t i c a l  t h e i r g r e a t e s t e f f e c t here. t h i s group e x i s t s ;  con-  u n c e r t a i n t i e s have  However, there i s no doubt that  and s i n c e t h i s r e g i o n of the spectrum  f r e e of c o n v e r s i o n l i n e s , e s t i m a t e s of i t s i n t e n s i t y be r e a s o n a b l y c o r r e c t .  and  N 5 i s an i n t e n s e group and  o b t a i n e d from i t i s probably f a i r l y r e l i a b l e .  is  should  the data  The major  u n c e r t a i n t y i n N 5 of course comes from the p o s s i b l e i n c l u s i o n  -67-  in  the d a t a of a weak Ng Table I I I l i s t s  group.  two columns  p o i n t energy of each beta group.  f o r the i n t e n s i t y and end The f i r s t column g i v e s the  measured v a l u e s determined from the K u r i e a n a l y s i s w h i l e the c o r r e c t e d column  lists  the r e s u l t s of adjustments made to  these v a l u e s from other d a t a .  These data are the r e s u l t s of  c o i n c i d e n c e experiments i n which r a d i a t i v e and i n t e r n a l conv e r s i o n t r a n s i t i o n s between l e v e l s f e d by d i f f e r e n t beta groups e s t a b l i s h e s the end p o i n t energy d i f f e r e n c e s between these groups.  The t r a n s i t i o n e n e r g i e s are i n e r r o r by not  more than 0.5%.  I t i s s u p r i s i n g that the adjustments of end  p o i n t e n e r g i e s from the K u r i e a n a l y s i s to match the t r a n s i t i o n energy requirements are so s m a l l .  Thus, one can have  some c o n f i d e n c e i n the i n t e n s i t i e s r e s u l t i n g from the K u r i e analysis. are  The v a l u e s f o r the i n t e n s i t i e s of groups  and  the e x p e r i m e n t a l l y measured v a l u e s and no attempt has  been made t o c o r r e c t them.  The i n t e n s i t i e s of groups N^s  Ng,  N5  and Ng have been e s t a b l i s h e d from a c o n s i s t e n c y  to  be o u t l i n e d l a t e r , but they are c o n s i s t e n t w i t h the e x p e r i -  mental v a l u e s of  ( N 2 + N 3 )  and of  arguments,  ( N 5 + N 6 ) .  Log f t v a l u e s were c a l c u l a t e d from the beta i n t e n s i t i e s by assuming a h a l f - l i f e of 2 years f o r the ground s t a t e of Sb  125. ( i i ) The i n t e r n a l c o n v e r s i o n spectrum The i n t e r n a l c o n v e r s i o n spectrum, shown i n F i g . 22,  o H)  oH*  O  Potentiometer S e t t i n g  (volts)  •a $» TO CD o •J  -68-  was  o b t a i n e d by s u b t r a c t i o n of the primary beta spectrum.  As i n the case of the primary spectrum, the K - s h e l l  internal  c o n v e r s i o n l i n e of the 662 kev t r a n s i t i o n i n Cs 137 was f o r c a l i b r a t i o n purposes.  Transitions  e n e r g i e s of 109,  176,  380,  kev.  l i n e i n t e n s i t i e s are l i s t e d  Conversion  355,  428,  used  were i d e n t i f i e d a t  464,  540,  602 and  i n Table  638 IV  and were measured by the area method d i s c u s s e d i n Appendix I. Other methods of i n t e n s i t y measurement were a l s o employed on some of the c o n v e r s i o n l i n e s .  These methods are d e s c r i b e d i n  Appendix I I . ( i i i ) The  p h o t o e l e c t r o n spectrum  The p h o t o e l e c t r o n spectrum measured u s i n g the bismuth c o n v e r t e r was  of l i t t l e use f o r measuring r e l a t i v e  gamma-ray i n t e n s i t i e s but s e r v e d to i d e n t i f y gamma at 109,  176,  204  and 219 kev.  F i g . 23 shows t h i s spectrum  the p h o t o e l e c t r o n spectrum measured with the l e a d i n which t r a n s i t i o n s were i d e n t i f i e d .  a t 219,  transitions  380,  428,  464,  converter  602 and 638  The compton background was  and  kev  measured simply  by removing the c o n v e r t e r and r e p e a t i n g the spectrum measurements.  I t was  necessary  to " n o r m a l i z e " the compton back-  ground i n between peaks t o account which depend upon the presence The most important  kev, 602/638 key  was  effects  or absence of the c o n v e r t e r .  contribution  present i n v e s t i g a t i o n  for scattering  of t h i s spectrum to the  i n the measurement of the 428/464  and 380/428 kev  intensity  ratios.  To f o l l o w page 68  Table IV. I n t e r n a l c o n v e r s i o n l i n e i n t e n s i t i e s . v a l u e s are i n counts/minute. Total Area  Line  All  HalfSymmetry  Total Symmetry  Peak Height  109K  33,900  26,000  22,050  19,500  109L  22,000  19,600  18,470  16,400  109M  6,510  5,610  5,030  4,900  175K  2,250  1,980  1,888  1,780  516  175(L+M)  ^50  380K  692  692  428K 428(L+M)) 464K  )  330 ^ 45  464(L+M)  219  602K 602(L+MH 63 8K  )  159  T a b l e V. Gamma-rays i n c o i n c i d e n c e w i t h beta-rays and i n t e r n a l conversion electrons. Electrons  Coincidences  N i group  none  N2  group  176 kev  N3  group  143,  N4  group  -76,  N  group  602,  5  176, 428, 464 kev 428, 464 kev 638 kev; p o s s i b l e 428, 464 kev  175K l i n e  317 kev; p o s s i b l e 175 kev  428K l i n e  possible  640L l i n e  Te 125 K x-rays  ^ 76 kev  428K 250 Not a l l experimental p o i n t s are p l o t t e d  B i converter 1.86 mg/cn>2 4 mm d i a . 200  lsq-  Pb c o n v e r t e r 12 mg/cin 4 mm d i a .  CD  +> 3  sa  •H  2  150  S3 \  lOOJ- 174 176K  CO  +> c: 3 -O  o  100  50h  •-3 0  50 h  Ha  O  F i g u r e 23 - P h o t o e l e c t r o n spectrum.  O •O P  .05  10  15  .20  .25  .30  Potentiometer S e t t i n g  (volts)  .35  era <t> o> oo  -69-  ( i v ) Beta-gamma c o i n c i d e n c e s p e c t r a The  geometry o f the gamma d e t e c t o r f o r the b e t a -  gamma c o i n c i d e n c e measurements was determined by the minimiz a t i o n o f the l e a d x-ray produced by the gamma s h i e l d around the p h o t o m u l t i p l i e r . r a d i a t i o n from Sb 125,  Because o f the r a t h e r i n t e n s e gamma the x-ray c o u l d not be e l i m i n a t e d  a l t o g e t h e r , even with exact c o l l i m a t i o n .  Thus a few p r e l i m i n -  a r y s i n g l e s gamma s p e c t r a were measured with d i f f e r e n t  detec-  t o r geometries t o determine the p o s i t i o n s of the N a l ( T l ) c r y s t a l and the l e a d s h i e l d which gave the l e a s t interference.  x-ray  A t y p i c a l s i n g l e s gamma-ray spectrum i s shown  i n F i g . 24. F i g u r e s 25-29 i l l u s t r a t e the r e s u l t s o f the beta-gamma c o i n c i d e n c e measurements.  Coincidence  runs were taken  the magnet c u r r e n t s e t t o focus e l e c t r o n s o f e n e r g i e s beyond the end p o i n t o f each beta group.  with just  A s e r i e s of  c o i n c i d e n c e s p e c t r a were thus measured f o c u s i n g e l e c t r o n s from the  group o n l y , then from groups  from groups N^, N  2  2  only,  then  and N3 o n l y , and so on. The c o i n c i d e n c e  spectrum measured a t the potentiometer focused e l e c t r o n s o f group were no c o i n c i d e n c e s observed, the  and N  setting  .370 v, which  o n l y , i s not shown as there thus c o n f i r m i n g the f a c t t h a t  group feeds the metastable  145 kev l e v e l i n Te 125.  Throughout the course of a c o i n c i d e n c e run, the beta c o u n t i n g r a t e was monitored p e r i o d i c a l l y .  S i n g l e s gamma-ray  To f o l l o w page 69  F i g u r e 24 - S i n g l e s gamma spectrum.  174,176 kev  10  20  30  40  50 60 70 Channel No.  80  F i g u r e 25 - Gamma-rays i n c o i n c i d e n c e N N . 1 +  90  100  with  2  176 kev • -  •  r * »• * . 10 20 r  \ i 30  1  40  J  50  i  60  Channel No.  i  70  i  80  i  90  100  To f o l l o w page 69 F i g u r e 26 - Gamma-rays i n c o i n c i d e n c e w i t h '. N N +N . 176 kev 1+  2  3  a> +> at  a  3  O  (N +N )-1.08N 2  3  2  428,464 kev Pb x-ray I/--S  0  10  20  30  40  50  60  70  80  90  100  Channel No.  F i g u r e 27 - Gamma-rays i n c o i n c i d e n c e w i t h N 1 + N 2 + N 3 + N 4 .  176 kev 428,464 kev  CD +» a  03  +> a !3 O  o  |_ Pb x-ray +76 kev  721 N +2.155 N 2  10  20  30  3  40  50  60 i 70  Channel No.  80  90  100  To f o l l o w page F i g u r e 28 - Gamma-rays i n c o i n c i d e n c e w i t h N 3 + N 2 + N 3 + N 4 + N 5 .  174,176 kev • 428,464 kev -p +» a  3  .738N +2.9N +1.2N4 + ( s c a l e d Cs 137)  Pb x-ray +76 kev  2  3  O  o 602,638 kev  0  10  20  30  40  50  60  70  80  90  100  Channel No.  F i g u r e 29 - Gamma-rays i n c o i n c i d e n c e with UJ+N2+N3+N4+N5+N6. 174,176 kev  0  10  20  30 1  40  50  60  Channel No.  70  80  90  100  -70-  s p e c t r a were taken both b e f o r e and a f t e r each c o i n c i d e n c e run as a check on the system g a i n s t a b i l i t y and to measure the gamma c o u n t i n g r a t e i n each channel of the k i c k s o r t e r . The chance c o i n c i d e n c e r a t e was c a l c u l a t e d from the formula ^chance  =  2hin "C 2  »  w  n  e  r  e  n  i and »  a  r  2  e  t  n  e  counting rates  i n the two channels and "C i s the r e s o l v i n g time o f the coincidence c i r c u i t .  F o r the c o i n c i d e n c e runs i n the p r e s e n t  i n v e s t i g a t i o n , the r e s o l v i n g time was measured t o be 0.0975 yW.sec. By s u c c e s s i v e s u b t r a c t i o n s i t was p o s s i b l e t o determine the c o n t r i b u t i o n of each i n d i v i d u a l beta group t o the c o i n c i d e n c e spectrum.  That i s , from a knowledge of the i n t e n s i t y  of each beta group a t every potentiometer s e t t i n g , as obt a i n e d from the K u r i e a n a l y s i s , a s y n t h e s i s was made of the c o i n c i d e n c e spectrum t o be expected from any beta group a t the d e s i r e d potentiometer s e t t i n g .  For example, i n F i g . 26,  the s o l i d l i n e r e p r e s e n t s the t o t a l spectrum o f gamma-rays i n c o i n c i d e n c e w i t h e l e c t r o n s from groups N j , N the potentiometer s e t t i n g  2  and N 3 a t  .235 v and the dashed l i n e i s the  r e s i d u a l spectrum a f t e r s u b t r a c t i n g the expected c o n t r i b u t i o n of groups and N  2  and N . 2  The expected c o n t r i b u t i o n of groups  a t the potentiometer s e t t i n g  .235 v i s j u s t the  spectrum i n F i g . 25 c o r r e c t e d f o r the r e l a t i v e beta-ray i n t e n s i t i e s , the change i n the momentum "window" A p and c o u n t i n g time d i f f e r e n c e s .  Thus the r e s i d u a l  spectrum  -71-  r e p r e s e n t s the c o n t r i b u t i o n o f the N 3 group o n l y , a t the potentiometer The  setting  .235 v.  s p e c t r a shown i n F i g u r e s 30 and 31 measured the  c o i n c i d e n c e s between gamma-rays and the K - s h e l l i n t e r n a l conv e r s i o n l i n e s o f the 176 kev and 428 kev t r a n s i t i o n s . Another s e t o f beta-gamma c o i n c i d e n c e runs were measured w i t h the system g a i n i n c r e a s e d so that the 176 kev gamma-ray was  p o s i t i o n e d a t about channel  73 on the k i c k s o r t e r .  From  these "expanded s c a l e " c o i n c i d e n c e runs, weak t r a n s i t i o n s a t 76,  143, 219 and 640 kev were i d e n t i f i e d .  A beta-gamma  c o i n c i d e n c e r u n with the L - s h e l l i n t e r n a l c o n v e r s i o n e l e c t r o n s of the 638 kev t r a n s i t i o n focused showed c o i n c i d e n c e s the Te 125 K x - r a y s . 640  T h i s was i n t e r p r e t e d as evidence  with for a  kev t r a n s i t i o n between the 676 kev l e v e l and the 36 kev  level. Table V l i s t s  the d e f i n i t e c o i n c i d e n c e s and p o s s i b l e  c o i n c i d e n c e s a s s o c i a t e d with each beta group and each  conver-  sion line selected. (v) S y n t h e s i s o f the gamma spectrum The  gamma spectrum o f Sb 125 was analyzed  components by u s i n g both coincidence spectra.  into i t s  the s i n g l e s gamma spectrum and the  Cs 137 was i n s t a l l e d i n the s p e c t r o -  meter i n the same geometry as the Sb 125 source  t o measure  the compton c o n t r i b u t i o n of the 602-638 kev group.  Subtract-  i n g t h i s c o n t r i b u t i o n from the s i n g l e s gamma spectrum  (after  To f o l l o w page 71 F i g u r e 30 - Gamma-rays i n c o i n c i d e n c e w i t h the 174-176K c o n v e r s i o n l i n e . 174,176 kev  -  k I \— 1.497N+4... 07N +1. 2  3  -  8 I 6 N 4  428,464 kev  L \  •  1* J  -  Pb x-ray / +76 kev f *  1 •  i \ *i  V.317 kev / \  •  V <  Q  1  10  <  20  1  30  \  7  \  J  < 1  f  V 1  1  40 50 60 Channel No.  70  1  80  90  100  F i g u r e 31 - Gamma-rays i n c o i n c i d e n c e w i t h the 428K c o n v e r s i o n l i n e .  .352N  -1  10  i_  20  t  30 Channel No.  2  t_  40  50  -72-  a d j u s t i n g f o r energy d i f f e r e n c e s ) l e f t gamma-rays o f energy ^ 464 kev.  the spectrum o f the  I d e a l l y , another source w i t h  an i s o l a t e d gamma-ray of about 450 kev s h o u l d have been used t o determine the compton d i s t r i b u t i o n o f the 428-464 kev group but such a source was not a v a i l a b l e . method thus had t o be employed contribution.  An a l t e r n a t e  t o determine t h i s compton  The nature o f the decay scheme i s such that  the 464 kev l e v e l decays almost e n t i r e l y by the e m i s s i o n o f the 428 kev and 464 kev gamma-rays. c o i n c i d e n c e w i t h the N 3  Thus the gamma-rays i n  group only, determined by the method  of s u c c e s s i v e s u b t r a c t i o n s mentioned p r e v i o u s l y , r e p r e s e n t the gamma spectrum o f the 428-464 kev group.  The 464 kev  l e v e l a l s o decays by a 143 kev-176 kev cascade which o f course i s i n c o i n c i d e n c e w i t h the N 3 F i g . 26.  group as can be seen i n  F o r t u n a t e l y , t h i s cascade i s weak enough so that a  r e a s o n a b l y a c c u r a t e e s t i m a t e may be made o f the shape of the spectrum o f the 428-464 kev group a l o n e . A f t e r s u b t r a c t i n g the c o n t r i b u t i o n o f the two h i g h energy groups, the r e s i d u a l spectrum was a n a l y z e d i n t o i t s v a r i o u s components.  The l a s t gamma-ray of major  intensity  i n the r e s i d u a l spectrum was the 174-176 kev composite peak. The shape o f t h i s peak was assumed to be the same as that o f the known " c l e a n " peak o b t a i n e d i n the beta-gamma c o i n c i d e n c e spectrum i n F i g . 25.  S u b t r a c t i o n of the 174-176 kev peak  r e v e a l e d gamma r a y s a t 204, 219 and 380 kev.  A similar  -73-  treatment  of the expanded s c a l e s p e c t r a r e v e a l e d the 76  and 143 kev  kev  gamma-rays.  The r e l a t i v e i n t e n s i t i e s of the gamma-rays were  calcula-  ted by measuring the area under each peak w i t h a planimeter and c o r r e c t i n g  for photoelectric  geometry e f f i c i e n c i e s .  c r o s s - s e c t i o n and  The r e l a t i v e i n t e n s i t i e s of the  428 kev and 464 kev were determined under the composite  by d i v i d i n g  i n F i g . 23.  to the composite  the area  peak i n t o two component areas which  agreed w i t h the r e l a t i v e i n t e n s i t y r e s u l t s t r o n spectrum  A similar  of the p h o t o e l e c -  procedure was  taken as the d i f f e r e n c e  the measured r e l a t i v e i n t e n s i t y the weaker i n t e n s i t y  relative  between t h i s value  f o r the composite  peak.  and Of  gamma-rays, o n l y the 380 kev gamma-ray  produces a l i n e on the p h o t o e l e c t r o n spectrum. this analysis  kev  a d j u s t e d to agree w i t h the c o n v e r s i o n  c o e f f i c i e n t f o r an E2 t r a n s i t i o n and the 602 kev  of  applied  602-638 kev peak except that the 638  r e l a t i v e i n t e n s i t y was  i n t e n s i t y was  crystal  The  results  are summarized i n T a b l e VI i n which  son i s made w i t h the r e s u l t s  of both Lazar and  N a r c i s i has i d e n t i f i e d other gamma t r a n s i t i o n s  compari-  Narcisi. f o r which no  evidence has been found i n the present i n v e s t i g a t i o n .  These  are not i n c l u d e d i n T a b l e VI, I t s h o u l d be p o i n t e d out here that a n a l y s i s complex s c i n t i l l a t i o n gamma-ray spectrum  of a  has c e r t a i n  funda-  mental d i f f i c u l t i e s which make r e l i a b l e measurements of  -74-  T a b l e V I . R e l a t i v e gamma r a y i n t e n s i t i e s from present i n v e s t i g a t i o n compared t o the r e s u l t s o f Lazar and o f Narcisi.  Energy ^ 3 0 kev 76 143 174-176  Present Investigation ~1.0 ^.04 ~ .04 .209 t0% ±  204  ~ .03  219  < . 01  317  < .01  Lazar  Narcis:  -  .196  .196 .008  <.01  -  -  .0088  .026  .038  :039  1.000  1.000  380  .049 lo%  428  1.000 ±\o%  464  .355 ± 1 0 %  .31  .325  602  .709 * 5 %  .88  .617  638  .485 t 5 %  .23  .357  r e l a t i v e gamma-ray  ±  intensities difficult  to a c h i e v e .  Any  p o r t i o n o f the spectrum, with the e x c e p t i o n of the h i g h e s t energy  p o r t i o n , has a t any channel, c o n t r i b u t i o n s not o n l y  from p h o t o e l e c t r o n peaks, but from Compton processes gamma-rays of h i g h e r energy  as w e l l .  t i o n s are not easy to determine  from  The Compton c o n t r i b u -  p r e c i s e l y , and these must  be known b e f o r e the p h o t o e l e c t r o n r e s i d u e s can be estimated.  -75-  For  t h i s reason, weak gamma-ray i n t e n s i t i e s appearing i n  T a b l e VI are expected t o have very h i g h probable e r r o r s and s h o u l d not be taken too s e r i o u s l y .  The most r e l i a b l e  i n t e n s i t y data w i l l be those a s s o c i a t e d w i t h the 638, 602, 464 and 428 kev gamma-rays.  S i n c e the 380 kev gamma-ray  appears i n the p h o t o e l e c t r o n spectrum as a weak peak, i t can be compared w i t h the 428 kev gamma-ray photopeak, so that i t s r e l a t i v e i n t e n s i t y s h o u l d be r e a s o n a b l y c o r r e c t . The  i n t e n s i t y of the 174-176 kev composite  s c i n t i l l a t i o n s i n g l e s spectrum  peak i n the  i s measured a f t e r two s u b t r a c -  t i o n s i n v o l v i n g somewhat u n c e r t a i n Compton c o n t r i b u t i o n s . The r e l a t i v e i n t e n s i t y a s s i g n e d t o t h i s gamma-ray consequently cannot be as a c c u r a t e as the h i g h e r energy gamma-rays quoted. F i n a l l y , the x-ray-gamma peak a t approximately 30 kev appears i n the expanded s c a l e spectrum a t the lowest o p e r a t i n g channels of the k i c k s o r t e r .  An examination o f the peak shape  shows a d e c i d e d assymmetry, the low energy s i d e f a l l i n g o f f much more s h a r p l y than the h i g h energy s i d e .  There i s t h e r e -  f o r e a good chance that not a l l of t h i s peak i s accepted by the k i c k s o r t e r , as channels 1-3 on the k i c k s o r t e r are known to be i n o p e r a t i v e .  I f s o , then the r e l a t i v e  intensity  a s s i g n e d to t h i s peak i s d e f i n i t e l y too low. c ) The Decay Scheme The decay scheme i n F i g . 32 has been proposed from the  To follow page 75  The beta information, i n order, i s : energy i n kev, r e l a t i v e i n t e n s i t y , and log f t . The dashed t r a n s i t i o n s are those observed by Lazar but not i n the present investigation. 125 Te 52 73  96,<H.36%,> 7.9134> 36. 75%, <6.8 f  232,J  3  79  (>8.6  -676  35S  212  -638 5/2+  1711"* I 317  247,^-V:)>3.6  I  -540 5 z"525 l o r ^ 4 H/  308,39.42%,8.0  76  211 2cxf  -464 5/2+ W3  451,6.04%,9.3  380  V  176  627,12.6%,9.5  I IF  1'  5*0  «8  -321 9/2feq-o  4fc«t  -145m h  L36  *—36 d 3/2 -0  Figure 32 - Decay scheme proposed i n present  1 1 / 2  s 1/2  investigation.  -76-  present i n v e s t i g a t i o n w i t h no appeal t o other work except i n e s t a b l i s h i n g the 676 kev l e v e l as w i l l be noted cussion to follow.  i n the d i s -  A summary o f the i n f o r m a t i o n obtained from  the s p e c t r a i s g i v e n here  to f a c i l i t a t e  the d i s c u s s i o n of the  c o n s t r u c t i o n o f the decay scheme. ( i ) Primary  beta-gamma c o i n c i d e n c e r e s u l t s  N^ group:  No observed  N  In c o i n c i d e n c e with the 176 kev gamma-ray  2  group:  coincidences.  and Te 125 x-ray. N3  group:  In c o i n c i d e n c e w i t h 143, 176, 428 and 464 kev  gamma-rays and Te 125 x-ray. N  4  group:  In c o i n c i d e n c e w i t h 76, 428 and 464 kev  gamma-rays. N5  group:  In c o i n c i d e n c e with 602 and 638 kev gamma-  r a y s and the Te 125 x-ray and p o s s i b l y w i t h lower  energy  gamma r a y s . Ng group:  No observed  ( i i ) Conversion 174-176R:  coincidences.  electron-gamma c o i n c i d e n c e r e s u l t s  In c o i n c i d e n c e with 317 kev gamma-ray and  p o s s i b l y w i t h the 174-176 kev composite peak (weak). 428K:  P o s s i b l y i n c o i n c i d e n c e with the 76 kev gamma-ray.  638L:  In c o i n c i d e n c e with the Te 125 K x-ray.  ( i i i ) Photoelectron spectra T r a n s i t i o n s observed 464,  602 and 638 kev. (iv)  I n t e r n a l c o n v e r s i o n spectrum  T r a n s i t i o n s observed 540,  a t 109, 176, 204, 219, 380, 428,  602 and 638 kev.  a t 109, 176, 355, 380, 428, 464,  -77-  Probably  the most u s e f u l s p e c t r a i n determining  transi-  t i o n sequences i n a decay scheme are the beta-gamma coincidence spectra.  On  the b a s i s of the c o i n c i d e n c e  beta groups N-^, N 2 , N 3  the end p o i n t e n e r g i e s of the primary  and N 5 were a d j u s t e d to agree with the t r a n s i t i o n as measured i n the p h o t o e l e c t r o n and i n t e r n a l spectra. i n Table  The  conversion  ground s t a t e . kev  listed  l e v e l s f e d by these beta t r a n s i t i o n s  thus e s t a b l i s h e d a t 145,  and 602  energies  These are the c o r r e c t e d end p o i n t e n e r g i e s III.  results,  The 36 kev  321,  464  and 638 kev  are  above the  l e v e l i s e s t a b l i s h e d v i a the  t r a n s i t i o n s from the 464  kev and 638  kev  428  levels  respectively. From the spectrum of gamma-rays i n c o i n c i d e n c e with  the  174-176 K i n t e r n a l c o n v e r s i o n l i n e , a p o s s i b l e weak c o i n c i dence i s noted between the two 174-176 kev gamma peak.  components of the composite  Thus the weaker 174 kev  i s e s t a b l i s h e d between the 638 kev  and 464  same c o i n c i d e n c e spectrum, the 317  kev  kev  transition  levels.  t r a n s i t i o n observed  be i n c o i n c i d e n c e with the composite 174-176 K  kev  and  to  internal  c o n v e r s i o n l i n e must decay between the 638 kev and 321 l e v e l s r a t h e r than between the 464  In the  145 kev  kev  levels  because of i n t e n s i t y c o n s i d e r a t i o n s . The  143  kev  t r a n s i t i o n i s observed  i n the form of a  composite 143-176 kev peak i n the spectrum of gamma-rays i n c o i n c i d e n c e with the N 3 group.  The  e x i s t e n c e of the 143  kev  -78-  t r a n s i t i o n i s a l s o evidence  f o r the weak c o i n c i d e n c e between  the 174 kev and 176 kev t r a n s i t i o n s . observe  While Lazar d i d not  the 143 kev t r a n s i t i o n , i t i s not i n c o n s i s t e n t w i t h  h i s spectrum of gamma-rays i n c o i n c i d e n c e w i t h 175 kev gammar a y s i n which a weak c o n t r i b u t i o n e x i s t s a t ^ 160 kev that c o u l d be i n t e r p r e t e d as an u n r e s o l v e d 143-176 composite peak. He makes no comment on i t , low  however, presumably because o f i t s  intensity. As mentioned p r e v i o u s l y , an appeal t o L a z a r * s work i s  made i n e s t a b l i s h i n g the 676 kev l e v e l .  Lazar found gamma-  r a y s o f 175 kev and 214 kev ( c o r r e s p o n d i n g t o 174 kev and 212 kev i n the present decay scheme) i n c o i n c i d e n c e with the 428-464 kev gamma group.  The very d e f i n i t e 214 kev c o i n c i d e n c e  c o u l d o n l y be i n t e r p r e t e d as a t r a n s i t i o n from a l e v e l a t 677 kev as i n F i g . 16.  In the present i n v e s t i g a t i o n , evidence f o r  the e x i s t e n c e o f the 676 kev l e v e l i s the 355 K i n t e r n a l conv e r s i o n l i n e which from energy c o n s i d e r a t i o n s w i l l only f i t i n t o the decay scheme between the 676 kev and 321 kev l e v e l s . F u r t h e r evidence  i s the weak c o i n c i d e n c e between the 638L  i n t e r n a l c o n v e r s i o n l i n e and Te 125 K x-rays which i s i n t e r p r e t e d as a 640 kev t r a n s i t i o n between the 676 kev and 36 kev levels. The  observed  end p o i n t energy o f the N 4 group p l a c e s a  l e v e l of Te 125 a t 525 kev.  T h i s l e v e l s h o u l d be weakly  populated as i t i s f e d from the weak N 4 group.  Transitions  -79-  of 204 kev and 380 kev from t h i s l e v e l t o the 321 kev and 145 kev  l e v e l s r e s p e c t i v e l y are e a s i l y i d e n t i f i e d .  t i o n s a r e o f comparatively reason  low i n t e n s i t y and t h i s may be the  t h a t they a r e not observed  o b t a i n e d w i t h the N  4  These t r a n s i -  group.  i n the c o i n c i d e n c e  However, N  4  data  d e f i n i t e l y shows  c o i n c i d e n c e s w i t h a 76 kev t r a n s i t i o n and with the 428, 464 kev gamma group.  A t r a n s i t i o n between the 525 kev and 464 key  l e v e l s o f Te 125 would r e s u l t i n a 61 kev t r a n s i t i o n which i s d e f i n i t e l y not observed. and  In a d d i t i o n , the observed  540 kev t r a n s i t i o n s s t i l l The  s t r o n g evidence  76, 219  have not been accounted f o r .  t h a t the N  4  beta group i s i n c o i n -  c i d e n c e w i t h the 76, 428 and 464 kev gamma rays can most e a s i l y be accounted f o r i f the weak N composite o f two weak, u n r e s o l v e d  4  group i s i n f a c t a  beta groups of end p o i n t  e n e r g i e s o f 247 kev and 232 kev ( c o r r e c t e d v a l u e s ) , l e a d i n g to l e v e l s i n Te 125 a t 525 kev and 540 kev r e s p e c t i v e l y above the ground s t a t e . disappear.  With t h i s one assumption, a l l d i f f i c u l t i e s  Not o n l y a r e the c o i n c i d e n c e data e x p l a i n e d but  the 219 kev and 540 kev t r a n s i t i o n s f a l l n a t u r a l l y i n t o p l a c e . I f the assumption o f a composite N would be most d i f f i c u l t  4  group i s c o r r e c t , i t  t o r e s o l v e them i n a K u r i e a n a l y s i s .  T h e i r i n t e n s i t i e s a r e low and t h e i r end p o i n t e n e r g i e s by o n l y 15 kev.  differ  In a d d i t i o n , c o i n c i d e n c e attempts with  a s s o c i a t e d gamma-rays or i n t e r n a l c o n v e r s i o n l i n e s t o r e s o l v e the N  4  components would be almost impossible because o f  -80-  intensity  and r e s o l v i n g  power  limitations.  The o n l y gamma-rays observed in this investigation  by Lazar and not observed  are the 113 kev t r a n s i t i o n , presumably  between the 638 kev and 525 kev l e v e l s ,  and the 212 kev  t r a n s i t i o n between the 676 kev and 464 kev  levels.  d) The C o n s i s t e n c y Argument In any decay scheme the r a t e s of feed and decay t o and from a l l l e v e l s must, of course, be e q u a l . investigation,  In the present  the i n t e n s i t i e s of the i n t e r n a l  conversion  l i n e s and the primary beta groups have been measured. R e l a t i v e gamma-ray i n t e n s i t i e s have a l s o been measured i n the  u s u a l way.  Thus a m u l t i p l y i n g c o n s t a n t , K, must be  found which w i l l normalize the r e l a t i v e intensities  to the beta i n t e n s i t i e s .  t i o n of the i n t e r n a l immediately  Ideally,  conversion c o e f f i c i e n t s  the c a l c u l a -  then f o l l o w s  and no appeal has to be made to some known  conversion c o e f f i c i e n t intensity  gamma-ray  measurements.  to normalize the c o n v e r s i o n l i n e The value f o r K i s determined  from  a c o n s i s t e n c y argument which w i l l now be o u t l i n e d . The f o l l o w i n g equations w i l l be understood easily  more  i f r e f e r e n c e i s made to the decay scheme i n F i g . 32  and t o Tables I I I , IV and VI which l i s t intensity  measurements.  the r e l e v a n t  -81-  At each l e v e l , r a t e of f e e d .  the t o t a l decay r a t e i s equated to the  For example,  676 kev l e v e l  ,  (  Ng = (212)+ (355)+ (640)*- (212)+ (355)  (a)  where (212) r e p r e s e n t s the gamma decay r a t e p l u s the i n t e r n a l c o n v e r s i o n decay r a t e of the 212 kev t r a n s i t i o n .  Here, Ng i s  l e f t t o be determined from o v e r a l l c o n s i s t e n c y . 638 kev l e v e l N  5  =  (602)+(638)+(174)+(113)+(317)  = 1.194K+400+(174)+(113 )+(317)  (b)  where 1.194K = normalized decay r a t e of the 602 kev and 638 kev gamma-rays and 400 = t o t a l c o n v e r s i o n e l e c t r o n decay r a t e f o r these two t r a n s i t i o n s .  As p r e v i o u s l y mentioned,  the measured i n t e n s i t y of the Ng group was assumed to i n c l u d e the Ng group.  Thus from equations (a) and (b) we  have: Ng+Ng — 84,400*= 1.194K+400+( 174)+ (113 )+(317 )+(212)+(355 ) (c ) N4 l e v e l s - (both  components)  8390+(113) =  (76)+(219)+(204)+(540)+(380)  = (76)+(219)+(204)+(540)+.049K+80  (d)  -82-  464 kev l e v e l (lOO,700-N )+(174)+(212)+(76) = (428 )+ (464 )+ (143 ) 2  = 1.355K+1100+Q43 ) where i t has been estimated that  N 2 + N 3 -  (e)  100,700.  321 kev l e v e l N +(143)+(317)+(355)+(204)+(219) 2  = (176) = .209K+2765-U74)  since  (f)  (174,176)^ .209K+2765.  145 kev l e v e l 27,900+(176)+(3 80) = (109) (109) = ,258K-(174)+30,750 T o t a l decay.  (g)  ( T o t a l beta feed r a t e - t o t a l decay t o ground s t a t e )  221,390 = (109)+(640)+(540)+ 2, 548K+1500 (109) = 219,870-2.548K  (h )  A d e s c r i p t i o n o f the d e t a i l e d s o l u t i o n of equations ( a ) , to (h) i s t e d i o u s and i n f a c t not necessary t o the understandi n g of the decay scheme. I t i s apparent that w i t h i n  the l i m i t s s e t by the  measured data, c e r t a i n parameters may be v a r i e d - e.g. the  -83-  parameter K, the i n t e n s i t y o f Ng< 3000, e t c . Because of the complex nature of the decay, a poor c h o i c e of some parameters leads t o p r e d i c t i o n s about the beta and gamma t r a n s i t i o n s that a r e i n c o n s i s t e n t w i t h the experimental r e s u l t s .  I t turns  out, f o r example, t h a t the value o f K i s d e f i n e d w i t h i n narrow limits.  Thus, upper and lower l i m i t s on the K-value  determined  very simply.  For example, from e q u a t i o n  can be ( c ) one  obtains: K «  70,350 -  w h i l e from equation K - 61,910  +  (174 )+ (113 )+ (317 )+ (212)+ (355) —  (e) and ( f ) one o b t a i n s : 2(174)+(212)+(76)+(317)+(355)+(2Q4)+(219) j - ^ J  Thus 61,910 < K < 70,350.  A more d e t a i l e d a n a l y s i s o f the  equations shows that the i n t e n s i t i e s o f some o f the weak t r a n s i t i o n s a r e very s e n s i t i v e t o the K-value.  Hence the  c r i t e r i o n f o r i t s d e t e r m i n a t i o n was the c r e d i b i l i t y o f the p r e d i c t e d i n t e n s i t i e s f o r the low i n t e n s i t y gamma-rays. a c r i t e r i o n has l e d t o a K-value  of ^ 6 7 , 1 2 0 .  Such  Unfortunately,  l i t t l e knowledge can be gained c o n c e r n i n g the weak gamma-rays other than t o impose wide l i m i t s on t h e i r i n t e n s i t i e s .  How-  ever, r e a s o n a b l e estimates can be made on some of the adjustments  t o the beta i n t e n s i t i e s .  i n Table I I I .  These a r e a l r e a d y noted  -84-  Some c o n f i r m a t i o n f o r the i n n e r c o n s i s t e n c y of  equations  (a) t o (h) i s g i v e n by the p r e d i c t e d i n t e n s i t y of the 109 transition.  The  c o n s i s t e n c y argument p r e d i c t s (109) ^ 4 6 , 2 5 0  while e x p e r i m e n t a l l y the v a l u e i s 45,000-50,000, the t a i n t y being due  kev  uncer-  to the unknown source - s c a t t e r i n g  c o n t r i b u t i o n to the i n t e r n a l c o n v e r s i o n l i n e s i n t h i s r e g i o n of  the spectrum.  Appendix II g i v e s a d e t a i l e d account  e x p e r i m e n t a l measurement of the i n t e n s i t y of the 109  of the  kev  transition. e) S p i n and p a r i t y assignments Work i n other l a b o r a t o r i e s appears to have e s t a b l i s h e d w i t h some degree of c e r t a i n t y the decay of the 145 i s o m e r i c s t a t e i n Te 125. 36 kev The  The  109 kev  t r a n s i t i o n are i d e n t i f i e d as M4  kev  t r a n s i t i o n and  the  and Ml r e s p e c t i v e l y .  ground s t a t e of Te 125 has been measured t o be 1/2 -ft  which f i t s w e l l w i t h the s h e l l model assignment of an S j y 2 even p a r i t y s t a t e . the 145 kev  The 36 kev  l e v e l as ^ii/2~  o  n  l e v e l i s a s s i g n e d d^/2 *  n e  and  +  assumption t h a t f o r these  low e x c i t a t i o n e n e r g i e s , the n u c l e a r s t a t e s are genuine single particle states.  S i m i l a r l y , the ground s t a t e of Sb  125  i s d e s i g n a t e d gy/2+ » a l s o i n agreement w i t h s h e l l model pred i c t i o n s f o r a c o n f i g u r a t i o n r e p r e s e n t i n g one a f i l l e d magic number s h e l l .  proton above  I t i s h i g h l y u n l i k e l y that the  s i n g l e - p a r t i c l e model w i l l apply beyond these l e v e l s  as  -85-  higher e x c i t a t i o n e n e r g i e s w i l l probably cause c o n s i d e r a b l e configurational The 175,  mixing.  c o n v e r s i o n c o e f f i c i e n t s f o r the major t r a n s i t i o n s of  428,  464,  602  and 638 kev energy can now  u s i n g the K-value determined above.  be  estimated  from the c o n s i s t e n c y argument  As an example, the 602 kev  t r a n s i t i o n takes p l a c e  w i t h the emission of 219 K-conversion  electrons/minute.  gamma-ray i n t e n s i t y i s .709x67,120 = 47,590/min. o<  K  219 = 4 ^5^ 7  Rose's t a b l e s  0  = 4.64  x 10"  ) closest  E2 t r a n s i t i o n and 5.4  *3  .  The  x 10~  3  the r e s u l t s of s i m i l a r c a l c u l a t i o n s  possible  f o r an The  T a b l e VII g i v e s  f o r the major  a s s i g n e d to them.  (from  x 10  f o r an Ml t r a n s i t i o n .  assignment made i s an E 2 + M 1 7 2 % E 2 ) mixture.  and the m u l t i p o l a r i t y  Therefore,  t h e o r e t i c a l values  to t h i s value are 4.35  The  transitions  I t has a l s o been  to make an estimate of the c o n v e r s i o n c o e f f i c i e n t  f o r the 380 kev  t r a n s i t i o n but a m u l t i p o l a r i t y  u n i q u e l y a s s i g n e d as theory p r e d i c t s  cannot be  the same c o n v e r s t i o n co-  e f f i c i e n t f o r both E2 and Ml m u l t i p o l e s . From t h i s i n f o r m a t i o n , s p i n and p a r i t y assignments of 5/2+  have been made to the 464  i s consistent 464  kev and 638 kev  levels.  This  with coulomb e x c i t a t i o n experiments i n which the  kev and 638 kev  l e v e l s have been e x c i t e d .  Thus the  1?4  kev gamma-ray i s an Ml t r a n s i t i o n . The  composite i n t e r n a l c o n v e r s i o n l i n e of the 174-176 kev  Table V I I . transitions. .  Conversion c o e f f i c i e n t s and (K/L+M) r a t i o s f o r the major  Transition  Measured  K Theoretical  176 kev  <~ .14*15%  .18 (E2)  K/L+M Measured 4.36*5%  .13 (Ml) 380  *1.52xl0~  428  1.03xl0~  2  Theoretical  Multipolarity Assignment  3.19 (E2)  E2+M1  6.16 (Ml)  (^ 60%E2) E2orMl  1.55xlO~ (E2orMl) 2  + 30% 2  ' l . l x l O " (E2) 2  5.47 ± 5 %  5;01 (E2)  E2+M1  6.03 (Ml)  (~55%E2)  ±15%  [1.23xlO~ (Ml) 2  464  8.55X10"  3  (8.55xlO" (E2) 3  E2  ±20%  l O x l O " (Ml) 3  602  4.64xl0~  3  (4.35xlO~ (E2) 3  E2+M1  ±10%  5.4xlO~ (Ml) 3  638  3.7xl0~  3  i»5%  3.7xlO  -3  (E2)  4.75x10-3(Ml)  (- 72%E2) E2  -86-  t r a n s i t i o n i s made up almost e n t i r e l y of the 176 kev t r a n s i ts  t i o n so t h a t the c o n v e r s i o n c o e f f i c i e n t and the -^-rr L+M f o r the composite  peak are, f o r a l l p r a c t i c a l purposes,  of the 176 kev t r a n s i t i o n a l o n e . assignment  ratio those  The E2+M1 m u l t i p o l e mixture  to the 176 kev t r a n s i t i o n thus makes the 321 kev  l e v e l a 9/2- s t a t e which i s not i n c o n s i s t e n t w i t h the informat i o n o b t a i n e d from the beta  spectrum.  I t i s worth n o t i n g that the f i r s t - f o r b i d d e n unique shape of the  beta group supports the g7/2+ and  assign-  ments to the ground s t a t e of Sb 125 and the 145 kev i s o m e r i c s t a t e of Te 125 r e s p e c t i v e l y . The  l o g f t v a l u e s f o r the N* and N" beta groups are both 4 4 ,  > 8.6 i n d i c a t i n g that they are probably groups ( A I = 0,1,2J  "yes").  first-forbidden  T h i s i s c o n s i s t e n t w i t h the  Shape c o r r e c t i o n f a c t o r a p p l i e d t o the composite  N 4 group.  I f t h i s i s a proper c o r r e c t i o n , then e i t h e r both groups a r e e q u a l l y f o r b i d d e n o r one group i s f a r more i n t e n s e than the other.  T h e r e f o r e one might expect these l e v e l s t o have odd  p a r i t y and probably h i g h s p i n v a l u e s f o r reasons given i n the next s e c t i o n .  T h e r e f o r e , the assignments  o f 9/2- or 11/2-  to the N 4 l e v e l s a r e p r e f e r r e d . U n f o r t u n a t e l y there i s not enough i n f o r m a t i o n t o make a s p i n and p a r i t y assignment:  t o the 676 kev l e v e l .  The l o g f t  value f o r the Ng group ( > 7 . 9 ) c o u l d make the t r a n s i t i o n e i t h e r allowed or f i r s t - f o r b i d d e n .  Then too, i t s low  -87-  i n t e n s i t y p r e c l u d e s the p o s s i b i l i t y of m u l t i p o l a r i t y  assign-  ments t o r a d i a t i v e t r a n s i t i o n s o r i g i n a t i n g a t the 676 kev level.  The low i n t e n s i t y of the Ng group i s probably due to  the  low energy a v a i l a b l e f o r the t r a n s i t i o n (95 k e v ) .  f )  Discussion The apparent success o f the s i n g l e p a r t i c l e s h e l l model  i n p r e d i c t i n g the f i r s t i s somewhat s u r p r i s i n g .  two l o w - l y i n g  excited states  of Te 125  However, i t i s not t o be expected  that s i n g l e p a r t i c l e assignments can be made t o s t a t e s o f h i g h e r e x c i t a t i o n energy because i t i s h i g h l y probable that a few core nucleons w i l l begin t o c o n t r i b u t e tion defining  t o the c o n f i g u r a -  the s p i n and p a r i t y o f the s t a t e .  Some j u s t i f i c a t i o n f o r the s i n g l e p a r t i c l e assignments made to the f i r s t  two e x c i t e d s t a t e s  tion p r o b a b i l i t i e s predicted levels.  i s found i n the t r a n s i -  by the s h e l l model f o r these  For example, f o r a s i n g l e neutron, the t r a n s i t i o n  p r o b a b i l i t y , T, f o r an M4 t r a n s i t i o n may be r o u g h l y estimated to be (see page 391 of r e f e r e n c e 17): T = 1.5 x 1 0  - 4  A  2  Fy S ( 1 . 8 )  - 1  sec'  1  where A = n u c l e a r mass number, E^, = t r a n s i t i o n energy i n Mev and  S ( ^ l ) i s a s t a t i s t i c a l factor.  t r a n s i t i o n , T - 2.84 x 1 0 ~  9  sec  - 1  Thus f o r the 109 kev  .  T h i s may be r e l a t e d to the experimental  half-life,  -88-  h/2  b  *  :  _ T  where  exp  .693 t  =  1 / 2  (l+»( )  i s the i n t e r n a l c o n v e r s i o n c o e f f i c i e n t f o r the t r a n s i  20 F o r the 109 kev t r a n s i t i o n , ol ^  tion.  Therefore T the  e x  p—  .47 x 1 0  sec  - 9  - 1  .  293 and t j y g — 58 days  Thus the crude e s t i m a t e of  t r a n s i t i o n p r o b a b i l i t y d i s a g r e e s with" experiment by o n l y  a f a c t o r of about s i x . Te  125 has 52 protons and 73 neutrons.  predictions  I f we examine the  o f the s h e l l model i n these r e g i o n s , we f i n d a  cluster of close-lying l e v e l s ,  S^/2»  to the most e n e r g e t i c neutrons.  ^ 3 / 2  a n c  *  n  l l / 2  a v a  il °i a  e  S i m i l a r l y , above the Sj/2  s t a t e s which the outermost protons occupy, a r e two c l o s e - l y i n g levels, d § / 2  a  m  * ^11/2°  the h i g h e r e x c i t e d but that  l  states  i f they a r e not, a configuration  s  possible  of course, that i n  these l e v e l s are v i o l e n t l y d i s t u r b e d ,  then i t i s not unreasonable t o assume c o n s i s t i n g o f a few nucleons o f e i t h e r  k i n d , d i s t r i b u t e d amongst these a v a i l a b l e duce p o s i t i v e p a r i t y s t a t e s negative p a r i t y states made t o the e x c i t e d with t h i s rather  of low s p i n  of high spin  states  l e v e l s , would pro-  (1/2, 3/2, 5/2) or  (11/2).  The assignments  of Te 125 appear t o be  naive argument.  consistent  However, i f one compares  the r e s u l t s of coulomb e x c i t a t i o n experiments  i n which  t r a n s i t i o n p r o b a b i l i t y measurements have been made f o r the  -89-  464 kev and 638 kev t r a n s i t i o n s with the s i n g l e neutron d i c t i o n s , i t can be shown that  pre-  these l i f e t i m e s show a g r e a t e r  disagreement with the p r e d i c t i o n s  o f the s i n g l e p a r t i c l e  s h e l l model, the d i s c r e p a n c y being a f a c t o r o f <^30.  For  example, the t r a n s i t i o n p r o b a b i l i t y f o r an E2 t r a n s i t i o n i s g i v e n by: „ «. 214 + 1 T^(E2) = 1.23 x 1 0 ~ ( A E ) B(E2) i g + l 2  5  s  e  ,  c  2  where  A E i s the energy d i f f e r e n c e  and the coulomb e x c i t e d s t a t e and e x c i t e d  state  between the ground  i n kev, 1^ and I f are the ground  state spins respectively  and B(EX ) i s the o  reduced  state  t r a n s i t i o n p r o b a b i l i t y measured i n u n i t s e*(10  For the 464 kev t r a n s i t i o n , l  cm^) .  « 1/2, I f = 5/2 and B(E2) = .44.  ±  T h i s g i v e s Ty.(E2) — 38.8 x 1 0  O A.  —24  sec"*.  9  The corresponding  s i n g l e neutron estimate of the t r a n s i t i o n p r o b a b i l i t y i s : T - 1.6 x 1 0  8  A  Ey S ( 1 . 7 J " s e c '  4 / 3  1  Q  which leads to T — 1.27 x 10  1  - I  sec  and s i n g l e p a r t i c l e p r e d i c t i o n s  .  Experimental  results  f o r the t r a n s i t i o n p r o b a b i l i t y  thus d i s a g r e e by a f a c t o r o f about 30.  A s i m i l a r discrepancy  e x i s t s i n the case of the 638 kev t r a n s i t i o n .  At t h a t ,  d i s c r e p a n c y i s not t o be c o n s i d e r e d as v e r y l a r g e the crude nature o f the s i n g l e p a r t i c l e e s t i m a t e s .  this  i n view of In other  words, although undoubtedly s i n g l e p a r t i c l e assignments a r e not v a l i d here, there i s a p p a r e n t l y a f a i n t s u g g e s t i o n of  -90-  s h e l l model s t r u c t u r e . There a r e some aspects of the decay which s t i l l r e q u i r e verification.  From the evidence o b t a i n e d there seems to be  l i t t l e doubt of the s p i n and p a r i t y assignemnts made to the 145,  321,  464  and 638  kev l e v e l s .  The  525 kev and 540  l e v e l s do not i n s p i r e so much c o n f i d e n c e , although h i g h l y probable  t h a t they a r i s e from f o r b i d d e n  i t is  transitions.  T h i s means n e g a t i v e p a r i t y and presumably h i g h s p i n . weakly populated 676 kev the low  kev  The  l e v e l i s beyond our reach because of  i n t e n s i t y of the r a d i a t i o n s to and from i t .  I t would be u s e f u l to attempt a more a c c u r a t e  determina-  t i o n of the i n t e n s i t i e s of some of the weaker t r a n s i t i o n s to see i f m u l t i p o l a r i t i e s c o u l d be assigned which were c o n s i s t e n t w i t h the quantum d e s c r i p t i o n of the Te 125 connect.  l e v e l s which they  T h i s w i l l r e q u i r e a s t r o n g e r source than was  a b l e f o r t h i s experiment.  avail-  -91-  APPENDIX I  INTENSITY MEASUREMENT OF CONVERSION LINES AND PRIMARY BETA GROUPS  The r i n g focus c o l l e c t i o n m o d i f i c a t i o n t o the t h i n - l e n s spectrometer  has g i v e n i t a r a t h e r unique p r o p e r t y among  beta-ray spectrometers.  That i s , when the p r e v i o u s l y d i s -  cussed c o n d i t i o n o f a "match" i s r e a l i z e d , an i n t e r n a l c o n v e r s i o n l i n e d i s p l a y s a symmetric peak shape p r o v i d e d that it  i s o f s u f f i c i e n t l y h i g h energy to be out of the r e g i o n of  source-scattering.  T h i s symmetry p r o p e r t y i s u s e f u l , i n  f a c t , f o r i n d i c a t i n g the r e g i o n where s o u r c e - s c a t t e r i n g begins t o i n t r o d u c e peak d i s t o r t i o n i n t o the spectrum. As p r e v i o u s l y noted, a l l e l e c t r o n s p a s s i n g through the e x i t s l o t a r e counted  by the d e t e c t o r .  Thus, a t a match,  the peak h e i g h t of a c o n v e r s i o n l i n e on an N(p) versus p p l o t i s i n t e r p r e t e d as the i n t e n s i t y of the l i n e ; and one does not need t o appeal t o the u s u a l method o f measuring the a r e a under the l i n e on an *^P) versus p p l o t .  Such an i n t e n s i t y  Mr  measurement, of course, cannot be made on a continuous primary  beta spectrum or on c o n v e r s i o n l i n e s which have  -92-  s u f f e r e d from s o u r c e - s c a t t e r i n g .  I t i s u s e f u l to determine  the r e l a t i o n s h i p between the two types of i n t e n s i t y measurements on a c o n v e r s i o n l i n e  ( i . e . from peak h e i g h t s on an N(p)  versus p p l o t and from areas on an  J versus p p l o t ) , s i n c e  t h i s then g i v e s a simple method of measuring primary spectrum  intensities.  Let N  Q  be the peak h e i g h t of a " c l e a n " i n t e r n a l  s i o n l i n e having shape N ( p ) . magnetic spectrometers and  Ap  beta  conver-  S i n c e i t i s a p r o p e r t y of  t h a t A p = kp, where k i s a constant  i s the l i n e width a t h a l f h e i g h t , then, N(p) = n(p)  Ap  = n(p)  kp  where n(p) i s an e q u i v a l e n t momentum d e n s i t y d i s t r i b u t i o n r e s u l t i n g from i n s t r u m e n t a l behaviour.  Thus k must be  a d j u s t e d so t h a t  Jn(p) Reference  dp - N  c  = £  dp  t o F i g . 33 shows the g r a p h i c a l r e p r e s e n t a t i o n N(p)  of these e q u a t i o n s .  Curve A i s simply the p l o t of  ^ ' f  versus p while the r e c t a n g l e B i s the same h e i g h t as curve A and has an area equal t o the area under curve A.  5> ( Ap)* = fEi£l dp - kN p  J p  Q  That i s ,  -93-  Therefore,  *\ ( P)'|*  k  =  (Apr P  I f curve A were t r i a n g u l a r i n shape,  then  ( A p)' = Ap,  and k  would be i d e n t i c a l with the l i n e width  P  F i g u r e 33 - Method of measuring conversion l i n e i n t e n s i t y .  k = -£-P- . P Since conversion l i n e s from t h i s spectrometer are g a u s s i a n - l i k e i n shape,  and k i s always g r e a t e r than the l i n e width.  then ( A p) • > Ap F o r example, on  a Cs 137 i n t e r n a l c o n v e r s i o n l i n e having a l i n e width of 1.25%, k i s 1.37%.  In the present i n v e s t i g a t i o n , the 428 K c o n v e r s i o n  l i n e i n the Sb 125 beta spectrum d i s p l a y e d a l i n e width of 1.28% w h i l e the r e q u i r e d k t o make area and peak h e i g h t methods o f i n t e n s i t y measurements agree was 1.40%.  T h i s was  the r e s o l u t i o n f a c t o r used t o c a l c u l a t e the beta i n t e n s i t i e s i n Chapter I I a c c o r d i n g to the e q u a t i o n  -94-  APPENDIX II  ITERATIVE METHOD OF CONVERSION LINE SEPARATION  During the a n a l y s i s of the i n t e r n a l c o n v e r s i o n spectrum of Te 109M  125,  i t was  d e s i r e d to separate the u n r e s o l v e d 109L  conversion l i n e s .  e r r o r methods but  T h i s i s most o f t e n done by t r i a l  i t can  method which w i l l now  a l s o be  be  accomplished by  outlined.  the composite peak, S ( x ) , c o n s i s t of two  Ni(x)  and N ( x ) 2  l o c a t e d at x^ and x  " p o s i t i o n r a t i o " ^1 *1 By  s  a n d  t h e  p  e  a  height r a t i o  k  Let  the  - r. N2 0  may  be w r i t t e n  i n terms of Nj(x) N <*) - £ H i  S i n c e S(x)  i s the sum  of N^(x)  and N ( x ) ,  S(x)  «Ni(x) +  N (x)  « S(x)  2  r  therefore,  -%(§) 1  x  as:  (|)  2  and  component peaks  respectively.  2  34.  the constant r e s o l u t i o n p r o p e r t y of magnetic spectrometers,  N (x) 2  m  and  another  C o n s i d e r , f o r example, the composite peak i n F i g . Let  and  -  F  ,x\ N,(-)  then:  18 A - t o t a l l y symmetric curve B - half-symmetric curve  F i g u r e 34 - S e p a r a t i o n of 109L and 109M i n t e r n a l c o n v e r s i o n lines.  -95-  Repeated s u b s t i t u t i o n of t h i s e q u a t i o n i n t o i t s e l f  leads  to: N l  ( x ) = S(x) - p ( f ) S  +  ^  S (^2)  Thus N (x) may be e a s i l y determined f  - ~  S (^3) +  ...  when r and s are known.  In p r a c t i c e the p o s i t i o n r a t i o , s, can u s u a l l y be estimated w i t h reasonable accuracy by simple i n s p e c t i o n .  The peak h e i g h t  r a t i o , r , must, however, be a r r i v e d a t through an i t e r a t i v e process.  T h i s r e q u i r e s knowledge of the peak shape NjCx)  which may be gained from an adjacent completely r e s o l v e d conv e r s i o n l i n e i n the spectrum t i o n s from the composite In  peak  or by making r e a s o n a b l e  assump-  itself.  the present i n v e s t i g a t i o n , the c o n t r i b u t i o n s of the  109L l i n e a t the 109M p o s i t i o n and v i c e v e r s a were  determined  by assuming t h e i r shapes t o be the same as the 109K peak. f i r s t approximation,  the peak h e i g h t s of the 109L and 109M  peaks were taken t o be 17,000 c/m and 5200 c/m  respectively.  These v a l u e s were taken from the p o s i t i o n of the maxima on the composite  peak S(x) and are t h e r e f o r e too h i g h .  S u c c e s s i v e approximations 109L: 109M:  In  t o the peak h e i g h t s were:  17,000 } 16,467 ; 16,472 ; 16,473 5,200 J  4,900 j  4,931  J  Thus the peak h e i g h t r a t i o was 16,473/4,933  4,933 • 3.34 = r .  -96-  Using t h i s v a l u e f o r r and the measured v a l u e f o r s, the component peak shapes were e a s i l y determined  from  the e q u a t i o n  d e r i v e d above. Because the 109K,  L and M c o n v e r s i o n l i n e s l i e i n the  source-scattering region, intensity are s u b j e c t t o some u n c e r t a i n t y .  measurements by any method  The  low energy s i d e of each  c o n v e r s i o n l i n e has a l o n g t a i l c o n t a i n i n g e x t r a counts. There i s no way  to a c c u r a t e l y measure the s c a t t e r i n g  contribu-  t i o n to the l i n e i n t e n s i t i e s , although e s t i m a t e s can be made based on reasonable but r a t h e r a r t i f i c i a l example, the i n t e n s i t y  of the 109K  has been measured by f o u r d i f f e r e n t on an N versus p p l o t  postulates.  For  c o n v e r s i o n l i n e i n F i g . 35 methods.  The peak h e i g h t  i s 19,500 counts/minute  w h i l e the area  method, d i s c u s s e d i n Appendix I, g i v e s 33,900 c/m.  Obviously  the f i r s t v a l u e i s too low because of source a b s o r p t i o n and the second value i s too h i g h because of the excess under the peak.  Two  other completely a r b i t r a r y  been used t o estimate the peak i n t e n s i t y ,  counts  methods have  both measurements  being d e r i v e d from peak shape c o n s t r u c t i o n s .  One  method i s  to completely symmetrize the peak w i t h r e s p e c t to the edge. rizes  T h i s i s curve A i n F i g . 35.  The other method symmet-  the peak from the h a l f - h e i g h t p o s i t i o n  i s curve B. intensity  The  downwards.  This  t o t a l l y symmetric curve l e a d s to an  of 22,050 c/m  to an i n t e n s i t y  trailing  w h i l e the half-symmetric  of 26,000 c/m.  The  109L and 109M  l i n e s were t r e a t e d s i m i l a r l y and the r e s u l t i n g  curve l e a d s conversion  intensities  are  -97-  l i s t e d i n Table V I I I along w i t h the K/L and L/M r a t i o s .  The  Table V I I I . I n t e n s i t y measurements of the i n t e r n a l c o n v e r s i o n l i n e s o f the 109 kev t r a n s i t i o n by f o u r methods d e s c r i b e d i n the t e x t . Peak Height  Total Symmetry  HalfSymmetry  109K  19,500 c/m  22,050 c/m  26,000 c/m  33,900 c/m  109L  16,400  18,470  19,600  22,000  109M  4,900  5,030  5,610  6,510  Totals  40,800  45,550  51,210  62,410  L/M r a t i o  3.35  3.67  3.49  3.38  K/L r a t i o  1.190  1.194  1.327  1.540  t o t a l s l e a d t o the i n t e n s i t y  Total Area  estimate f o r the 109 kev t r a n s i -  t i o n of 45,000-50,000 c/m as noted i n the s e c t i o n d e a l i n g w i t h the c o n s i s t e n c y argument i n Chapter I I I . From T a b l e V I I I i t i s e a s i l y seen t h a t L/M r a t i o i s l i t t l e a f f e c t e d by the type of i n t e n s i t y T h i s i s undoubtedly  measurement employed.  due t o the p r o x i m i t y o f the 109L and 109M  l i n e s i n the spectrum.  The K/L r a t i o , on the other hand,  depends upon the type o f measurement employed.  The r a t i o  d e r i v e d from the t o t a l area method i s undoubtedly f o r reasons a l r e a d y e x p l a i n e d . of the half-symmetric  method.  too h i g h  The same may p o s s i b l y be s a i d The t o t a l l y symmetric method,  when a p p l i e d t o the K, L and M l i n e s shows a continuous  -98-  degradation i n l i n e width as n i g h t be expected absorption alone. crepancy  from  T h i s d e g r a d a t i o n tends t o reduce  source the d i s -  between the area method of i n t e n s i t y measurement and  the peak h e i g h t method on an u n d i s t o r t e d l i n e .  Thus the  t o t a l l y symmetric method may be a r e a s o n a b l y c l o s e measure of the a c t u a l i n t e n s i t i e s . of  ^1.2  published  I f s o , t h i s l e a d s t o a K/L r a t i o  and an L/M r a t i o o f results  2 0  '  2 2  .  ^3.5  i n f a i r agreement with  -99-  BIBLIOGRAPHY  1.  E. Fermi, Z e i t . f . Phys. 88, 161 (1934).  2.  E. Feenberg and G. T r i g g , R.BJ.P. 22, 399 (1950).  3.  S. A. Moszkowski, Phys. Rev. 82, 35 (1951).  4.  "Beta- and Gamma-Ray Spectroscopy" - Appendix I I , E d i t e d by K. Siegbahn.  5.  C. S. Wu, R.M.P. 22, 386 (1950).  6.  M. E. Rose, " I n t e r n a l C o n v e r s i o n C o e f f i c i e n t s " - NorthH o l l a n d P u b l i s h i n g Co.  7.  L. E. Biedenharn and M. E. Rose, R.M.P. 25, 746 (1953).  8.  T. R. Gerholm, Handbuch der P h y s i k - Volume XXXIII.  9.  Kofoed-Hansen, L i n d h a r d and N i e l s e n , K g l . Danske Ved. S e l s k . Matfys. Medd. 25, No. 16 (1950).  10.  Hornyak, L a u r i t s e n and Rasmussen, Phys. Rev. 76, 731 (1949).  11.  K e l l e r , Koenigsberg and P a s k i n , Rev. S c i . I n s t r . 21, 713  (1950).  12.  P r a t t , Boley and N i c h o l s , Rev. S c i . I n s t r . 22, 92 (1951).  13.  Jensen, L a s l e t t and P r a t t , Phys. Rev. 75, 458 (1949).  14.  Deutsch, E l l i o t t and Evans, Rev. S c i . I n s t r . 15, 178 (1944).  15.  D. C. 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