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

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A CONVERSION ELECTRON AND LOW ENERGY GAMMA-RAY SPECTROMETER by JOHN RICHARD JOHNSON B.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s thesis.as conforming to the required standard from candidates f o r the degree of MASTER OF SCIENCE THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1 970 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree tha permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of PL. ty s t-c <, The University of Br i t ish Columbia Vancouver 8, Canada D a t e r< 7 o ABSTRACT A c o n v e r s i o n e l e c t r o n a n d l o w e n e r g y g a m m a - r a y s p e c t r o m e t e r h a s b e e n d e v e l o p e d u s i n g a s i l i c o n l i t h i u m - d r i f t e d s e m i c o n d u c t o r d e t e c t o r . T h e s p e c t r o -m e t e r h a s a r e s o l u t i o n o f 2 K e v f o r 100 K e v e l e c t r o n s a n d p h o t o n s u n d e r o p t i m u m c o n d i t i o n s . The e n e r g i e s o f t h e s e e l e c t r o n s a n d g a m m a - r a y s c a n b e e s t i m a t e d t o -.1 K e v , a n d t h e i r i n t e n s i t i e s t o w i t h i n ^67o w i t h t h e s t a n d a r d s o u r c e s a v a i l a b l e . 153 153 T h e e l e c t r o n c a p t u r e d e c a y o f Gd —> E u was i n v e s t i g a t e d u s i n g t h i s s p e c t r o m e t e r . T h e b r a n c h i n g c a p t u r e r a t i o s t o t h e 1 7 2 . 9 K e v , 1 0 3 . 2 153 K e v , 9 7 . 4 K e v , a n d 0 K e v l e v e l s o f E u w e r e f o u n d t o b e 11%, 3 9 % , 39% a n d 11%, r e s p e c t i v e l y . P o s s i b l e v a l u e s o f -V2 o r "V 2 f o r t h e 1 7 2 . 9 5 + 3 + T - c - 7 -K e v l e v e l , / 2 o r / 2 f o r t h e 1 0 3 . 2 K e v l e v e l , a n d / 2 , / 2 , o r / 2 f o r t h e 9 7 . 4 K e v l e v e l h a v e b e e n a s s i g n e d . T h e s e v a l u e s a r e i n a g r e e m e n t w i t h t h o s e f o u n d b y o t h e r i n v e s t i g a t o r s . TABLE'OF CONTENTS Page ABSTRACT i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i i CHAPTER I NUCLEI AND RADIOACTIVE DECAY 1 . Introduction . . . . . . 1 2 . Beta Decay 3 3 . Excited State Decay . . . . . 9 CHAPTER II SEMICONDUCTOR DETECTORS 1 . The P-N Junction 18 2 . The P - I-N C r y s t a l 20 3 . Semiconductor Crystals as P a r t i c l e Detectors . . . 21 CHAPTER I I I LITHIUM ION DRIFTED SILICON DETECTORS 1 . S i ( L i ) Detectors f o r Photons and Electrons . . . . 25 2 . Associated E l e c t r o n i c s 32 3 . Inherent Resolution of the Detector-Analyser System 39 4 . Other Contributions to the Resolution . . . . . . . 4 5 CHAPTER IV ANALYSIS OF SPECTRA 1 . Computer Analysis 54 2 . Energy C a l i b r a t i o n 58 3 . Separation of E l e c t r o n and Photon Spectra . . . . 64 4 . E f f i c i e n c y C a l i b r a t i o n 65 153 CHAPTER V DECAY OF GADOLINIUM 1 . Introduction 70 i i i CHAPTER V (Continued) 2. Source Preparation 70 3. 1 5 3 G d Spectra . 72 4. Conversion C o e f f i c i e n t s 76 5. Capture Branching Ratios 78 6. Spin and P a r i t y Assignments 82 CHAPTER VI CONCLUSIONS . . . . 83- . APPENDIX A 86 REFERENCES 90 i v LIST OF TABLES Page I Gamow-Teller S e l e c t i o n Rules f o r Beta Decay 6 II C l a s s i f i c a t i o n of Gamma Transitions 15 III C h a r a c t e r i s t i c s of the Pulse Shaper 37 IV C h a r a c t e r i s t i c s of the Two Detectors 47 V Change i n Error with System Gain 57 VI Energy C a l i b r a t i o n Sources 59 VII Energy Lost i n Dead Layer of Detector 63 VIII Photon E f f i c i e n c y C a l i b r a t i o n Data 68 IX Peak I d e n t i f i c a t i o n and I n t e n s i t i e s 75 X Conversion C o e f f i c i e n t s 77 XI <*K/<*L 7 7 XII Capture Branching Ratios 81 v LIST OF FIGURES Page 1 T y p i c a l Shapes of jQ* D i s t r i b u t i o n s 5 2 Decay Scheme 10 3 Impurity Levels 19 4 Energy Loss i n Semiconductor Crystals 23 5 S i ( L i ) Crystals . ' 26 6 £ vs. Temperature 27 7 Range of Electrons i n S i 27 8 Energy Loss i n Dead Layer 28 9 P a r t i a l Energy Loss Processes 28 10 Photon Cross Section f or S i l i c o n 30 11 Systematic of E l e c t r o n i c s ' 33 12 Equivalent C i r c u i t f o r Detector-Preamp. 34 13 Pulse Shaper Network 36 14 T y p i c a l Low Energy Spectrum 38 15 C r y s t a l Chamber 4 3 16 P l o t of Temperature vs. Optimized Resolution f or 4 4 Two Detectors 17 E f f e c t of Source Thickness on Resolution 46 18 Sublimation Chamber 4 8 19 Pulser C i r c u i t 49 20 Two Types of Source Holders and Their E f f e c t on Low 51 Energy Photon Resolution 21 E f f e c t s of Dead Layer on Low Energy Electrons 52 22 Composite Peak 55 23 Components of Peak i n F i g . 22 56 vi LIST OF FIGURES (cont'd.) Page 24 Energy C a l i b r a t i o n Curves 60, 61, 62 25 Absorption Curve for Photons i n Aluminum Absorber 66 26 Photon E f f i c i e n c y of S^ Detector - 69 153 27 Main Transitions i n the Decay of Gd 71 153 28 Conversion El e c t r o n Spectrum of Gd 73 153 29 Photon Spectrum of Gd 74 v i i ACKNOWLEDGEMENTS I wish to express my gratitude to Dr. K. C. Mann for guidance and encouragement throughout the.course of t h i s work. I would also l i k e to thank Mr. P. Tamminga for the many h e l p f u l d i s -cussions of the problems that arose during the development of the spectro-meter. This p r o j e c t was supported by a Grant-in-Aid-of-Research to Dr. K. C. Mann by the National Research Council of Canada. I also wish to acknowledge the further assistance of the National Research Council through awards to me of N. R. C. Bursaries. v i i i CHAPTER I NUCLEI AND RADIOACTIVE DECAY 1. Introduction Nuclei are known to b e assemblies of fast-moving heavy p a r t i c l e s c a l l e d nucleons, which include both neutrons and protons. The t o t a l , number of nucleons i s c a l l e d the mass number A, while the t o t a l number of protons, which determines the nuclear charge, i s c a l l e d the atomic number Z . Nuclei with the same Z are termed isotopes, and those with the same A, isobars. The i n t e r n a l motion of the nucleons gives the nucleus such pro-p e r t i e s as energy, angular momentum X ( o r s p i n ) , p a r i t y TT , and e l e c t r i c and magnetic moments, the. values of which are measures of the way the nucleons are arranged i n a nucleus; or i n other words, of the nuclear str u c t u r e . Since a nucleus i s a quantum mechanical system, i t can only e x i s t i n c e r t a i n d i s c r e t e energy states, each corresponding to a p a r t i c u l a r i n t e r n a l nucleon configuration. Each energy state may be uniquely c l a s s i f i e d by i t s energy, spin, p a r i t y , and by i t s e l e c t r i c and magnetic moments. The l a t t e r two properties are d i f f i c u l t to measure i n any state except the lowest or ground state, and so the f i r s t three quantities alone are normally used to define a state. Radioactive decay i s the process by which a nucleus can reach a state of lower t o t a l energy. I t may do so by merely a rearrangement of i t s i n t e r n a l configuration with no change i n the numbers or kinds of -1-n u c l e o n s p r e s e n t ( e x c i t e d s t a t e d e c a y ) . I n t h i s c a s e t h e e x c e s s e n e r g y i s u s u a l l y , t h o u g h n o t a l w a y s , c a r r i e d o f f b y a g a m m a - r a y q u a n t u m . I t may d e c a y b y t h e e m i s s i o n o f a n u c l e o n o r a c l u s t e r o f n u c l e o n s w h i c h r e s u l t s i n a c h a n g e i n A s o t h a t t h e r e s i d u a l n u c l e u s b e l o n g s t o a d i f f e r e n t n u c l e a r s p e c i e s . O r f i n a l l y , t h e r a d i o a c t i v e d e c a y may b e o f t h e t y p e w h e r e t h e m a s s n u m b e r A r e m a i n s c o n s t a n t , b u t a n e u t r o n c o n v e r t s t o a p r o t o n , o r a p r o t o n t o a n e u t r o n . The e m i t t e d p a r t i c l e s a r e p o s i -t i v e o r n e g a t i v e e l e c t r o n s a n d n e u t r i n o s , a n d t h i s p a r t i c u l a r t y p e o f d e c a y i s c a l l e d b e t a - d e c a y . T h i s i s t h e d e c a y p r o c e s s , f o l l o w e d b y e x c i t e d s t a t e d e c a y , t h a t i s r e l e v e n t t o t h e w o r k d e s c r i b e d i n t h i s t h e s i s . Of c o u r s e , a l l s u c h d e c a y s a l t e r t h e n u c l e o n c o n f i g u r a t i o n a n d h e n c e a l t e r t h e e n e r g y , a n g u l a r m o m e n t u m , p a r i t y , a n d moments o f t h e n u c l e u s . M e a s u r e m e n t s o n t h e e m i t t e d r a d i a t i o n g i v e i n f o r m a t i o n o n t h e p r o p e r t i e s o f t h e n u c l e a r s t a t e s i n v o l v e d . T h i s i s t h e 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 . A l l r a d i o a c t i v e d e c a y f o l l o w s t h e u s u a l s t a t i s t i c a l r u l e d e f i n e d b y t h e w e l l - k n o w n e q u a t i o n d t w h e r e f\} i s t h e n u m b e r o f p a r e n t n u c l e i p r e s e n t a t t i m e t a n d "A i s t h e d e c a y c o n s t a n t . I n t e g r a t i o n t h e n g i v e s N = & e (i - i) w h e r e Jve i s t h e n u m b e r p r e s e n t a t t = O • T h i s e q u a t i o n l e a d s t o t h e u s u a l d e f i n i t i o n o f t h e m e a n l i f e t i m e T = ' / - N a n d t h e h a l f - l i f e 3 2 . Beta Decay This process, mentioned b r i e f l y previously, may be described by the following three equations: a) p —> n + e + + V p o s i t r o n decay ( , b) n _>. p + e + \> negatron decay ( /S') (I - 2) c) p + e —> n + V o r b i t a l e l e c t r o n capture ( E . C ) where n, p, e +, e , \? , and V r e f e r to the neutron, proton, positron, negatron, neutrino, and antineutrino r e s p e c t i v e l y . Only process b) occurs f o r free p a r t i c l e s , but a l l may occur i n s i d e the nucleus i f the t o t a l energy of the system i s lowered i n the process. I t i s obvious that the emitted p a r t i c l e s i n beta decay are the p o s i t i v e and negative electrons and the neutrinos. The energy requirements for the three beta decay processes are a) E„ = M(Z,A)c 2 - M(Z-l,A)c 2 - I - 2 mc c 2 > 0 / ? + b) E„ = M(Z,A)c 2 - M(Z+l,A)c 2 - i ' > 0 j8~ c) E D = M(Z,A)c 2 - M(Z-l,A)c 2 - B e(Z) - I" > 0 E.C. In these equations E e = t o t a l energy released i n the decay M(Z,A) = atomic mass of the atom whose nucleus has atomic number Z, and mass number A I = d i f f e r e n c e i n i o n i z a t i o n energy between parent and daughter•atoms m„ = e l e c t r o n r e s t mass B e(Z) = binding energy of the atomic e l e c t r o n before capture. I t can be seen that the r e c o i l energy of the daughter atom has been ignored. This i s a v a l i d approximation except f o r the very l i g h t n u c l e i . In f a c t , the f a c t o r I i s also customarily ignored except where E e i s also small. In the context of these approximations then, the energy E„ w i l l be shared s t a t i s t i c a l l y between the beta p a r t i c l e and the neutrino i n the f i r s t two processes, while i n the t h i r d , the neutrino i s emitted monoenergetically with t o t a l energy E„ . Positron and Negatron Decay + • 1 2 The energy d i s t r i b u t i o n of electrons i n j3 decay i s given by ' 2 P(E) dE = -S-r E(E 2-M.c 2)^ ( E . - E ) 2 F(E^Z) | M | 2 dE (I - 4) 2 TTJ where: + P(E) dE = p r o b a b i l i t y of emission of a ^ " p a r t i c l e with t o t a l energy between E and E+dE g = coupling constant of the i n t e r a c t i o n E„ = energy of the decay F(E,+Z) = the c o r r e c t i o n to the d i s t r i b u t i o n function a r i s -ing from the i n t e r a c t i o n between the outgoing jQ * p a r t i c l e and the nuclear coulomb f i e l d M = nuclear matrix element involved i n the t r a n s i t i o n . This equation i s due o r i g i n a l l y to Fermi. I t assumes that r e s t mass of the neutrino i s zero, and the r e c o i l o f the daughter nucleus and the d i f f e r e n c e i n i o n i z a t i o n energies between the parent and daughter atoms are negligable. + T y p i c a l shapes of/9 d i s t r i b u t i o n s are shown i n F i g . 1 . The square of the nuclear matrix element, jM/ , can be expanded i n F I G . 1 . - -T y p i c a l S h a p e s o f D i s t r i b u t i o n s 6 a s e r i e s of terms i n k R , where k = E / C + N and R i s the nuclear radius. Each term i n the expansion represents the co n t r i b u t i o n from t r a n s i t i o n s i n v o l v i n g p a r t i c u l a r angular momentum and p a r i t y changes. S e l e c t i o n 1 2 4 rules governing these t r a n s i t i o n s have been deduced t h e o r e t i c a l l y ' ' , and w i l l be summarized l a t e r . The f i r s t and l a r g e s t term i n the expansion represents (according 1 + to Gamow-Teller s e l e c t i o n rules ) a t r a n s i t i o n i n which A J = 0, 1 and ATT = No. This i s c a l l e d an allowed t r a n s i t i o n . I f the t r a n s i t i o n 2 i s of t h i s type the f i r s t term i n |M | i s dominant (assuming k R « 1). I f not, the f i r s t term vanishes. 2 The second term i n the expansion of |M| represents a t r a n s i t i o n i n which A J = 0, *1, *2 and £ TV = Yes. This i s c a l l e d a f i r s t forbidden 2 t r a n s i t i o n . I f the t r a n s i t i o n i s of t h i s type, the second term i n |M ) i s dominant. I f not, the second term vanishes. In f a c t , the f i r s t non-zero term i n the expansion always dominates, and determines the degree of forbiddenness of a t r a n s i t i o n . The Gamow-Teller s e l e c t i o n rules f o r the f i r s t few t r a n s i t i o n types are l i s t e d i n Table I. Table I Gamow-Teller S e l e c t i o n Rules for Beta Decay Degree of Forbiddenness P a r i t y Change ( ATT) Ang. Mom. Change (AJ) Approx. log f t value Allowed No 3 - 6 1st forbidden Yes 0, +1 + 2 6 - 10 2nd forbidden No >10 + The h a l f - l i f e of/2 decay i s given by 7 h - ¥ - - r E ' " 2 • tt - 5) 2 * f E » P(E) dE Jm„ c and i s strongly dependent on E 0 ( t % v a r i e s approximately as E^ and on jM| , which i s included i n the i n t e g r a l . I f we define a function f as f = \ 2 E(E 2-» 2 c 4 ) % (E„ - E ) 2 F(E,+Z) dE (I - 6 ) ° m 0 c + which i s the i n t e g r a l over thej8 spectrum independent of the nuclear state, then ^ „ 2 In 2 tt»c tk = —^ j 0 E(E 2-M 2 c 4 ) * ( E e - E ) 2 F(E,+Z) dE Si C E ° E ( E 2 - « 2 c 4 ) % ( E a - E ) 2 F(E,+Z) |M|2 dE 2-n J 2 m^. c i s a f u n c t i o n c a l l e d the comparative h a l f - l i f e , or f t value. The func-3 t i o n f has been calculated and tabulated by Trigg and Feenburg . The usefulness of c a l c u l a t i n g an f t value i s that i t i s almost independ-2 ent of E„, but ret a i n s the strong dependence on \M\ . I t i s therefore a 2 measure of the forbiddenness of a t r a n s i t i o n . That i s , since {M| decreases r a p i d l y with increasing degrees of forbiddenness, the f t value w i l l increase r a p i d l y also. Since f t values are large, i t i s more convenient to use t h e i r logarithms. T y p i c a l log f t values f o r the d i f f e r e n t degrees of forbiddenness + of /3 t r a n s i t i o n s are included i n Table I. The log f t value i n i t s e l f , while u s e f u l i n assessing the forbiddenness of a t r a n s i t i o n , i s not com-p l e t e l y d e f i n i t i v e since overlaps of these values are f a i r l y common. O r b i t a l E l e c t r o n Capture The only emitted p a r t i c l e i n o r b i t a l e l e c t r o n capture i s a neutrino, which interacts very weakly with matter, and i s consequently almost impossible to detect. Therefore any information about t h i s type of t r a n s i t i o n must come from secondary e f f e c t s (x-rays, i n t e r n a l Bremsstralung, gamma-rays, e t c . ) . 1 2 21 The p r o b a b i l i t y for e l e c t r o n capture i s givai by ' ' 2 P i = f i (Zo, Z) |M|Z ( 1 - 7 ) 2 T T where P = the p r o b a b i l i t y of an e l e c t r o n being captured from atomic o r b i t a l i . M = i s the same nuclear matrix element that i s involved i n fi+ decay and therefore o r b i t a l e l e c t r o n capture may by c l a s s i f i e d by the degrees of forbiddenness given i n Table I. f i (E„,Z) = a f u n c t i o n that depends on the angular momentum, p a r i t y , and binding energy of the e l e c t r o n being cap-tured. I t also depends on the change i n spin, p a r i t y , and energy between the parent and daughter n u c l e i . Numerical values of f i (E 0,Z) have been tabulated by 3 21 T r i g g and Feenburg and by Zyryanoya The h a l f - l i f e f o r e l e c t r o n capture i s given by \ 2 2 where. > = 2i- f i (E ,Z) | M | i 2 TT the summation being over a l l o r b i t a l e l e c t r o n states. 9 + I n a s i m i l a r m a n n e r toft d e c a y we c a n d e f i n e a f u n c t i o n f a s f = < £ , f i ( E „ , Z ) i t h e n t h e f t v a l u e i s ( E , , Z ) i t = l n 2 i £ i f f i ( E „ , Z ) 2 1 T J £ — ( I - 8) M 2 2 + w h i c h d e p e n d s s t r o n g l y o n | M ) a s i n t h e - c a s e . D e c a y Schemes When a n u c l e u s u n d e r g o e s b e t a d e c a y t h e d e c a y s e q u e n c e may b e r e p r e s e n t e d s c h e m a t i c a l l y a s s h o w n i n F i g . 2 . T h i s p a r t i c u l a r e x a m p l e 64 + -( Cu) was c h o s e n as i t decays by 0 , j2> a n d E . C . , a l l o f w h i c h a r e i n c o m p e t i t i o n . I t w i l l b e n o t e d f r o m s p i n a n d p a r i t y c h a n g e s t h a t a l l t r a n s i t i o n s a r e a l l o w e d . I n c l u d e d o n t h e d i a g r a m a r e f t v a l u e s a n d 18 r e l a t i v e d e c a y p r o b a b i l i t i e s w h i c h h a v e b e e n d e d u c e d f r o m e x p e r i m e n t s T h e s e v a l u e s a r e c o n s i s t e n t w i t h t h e a l l o w e d c h a r a c t e r o f t h e d e c a y s . 3 . E x c i t e d S t a t e D e c a y (Gamma D e c a y a n d I n t e r n a l C o n v e r s i o n ) . T h e r e a r e two m a i n p r o c e s s e s i n e x c i t e d s t a t e d e c a y . T h e y a r e t h e e m i s s i o n o f e l e c t r o - m a g n e t i c q u a n t a (gamma r a y s ) , a n d t h e a b s o r p t i o n o f t h e d e c a y e n e r g y b y a n a t o m i c e l e c t r o n w i t h i t s s u b s e q u e n t e m i s s i o n ( i n t e r n a l c o n v e r s i o n ) . T h e two p r o c e s s e s , w h e n t h e y i n v o l v e t h e same i n i t i a l a n d f i n a l s t a t e s , a r e a l w a y s i n c o m p e t i t i o n . The e n e r g y r e q u i r e m e n t s f o r t h e s e p r o c e s s e s a r e 4 - 9 0 E „ = M ( Z , A ) c - M ( Z , A ) c > 0 gamma ( X ) * 2 2 ( 1 - 9 ) E „ = M ( Z , A ) c - M ( Z , A ) c - B e (Z) > 0 i n t e r n a l c o n v e r s i o n ( I . C . ) 10 F I G . 2.--D e c a y Scheme I n t h i s e q u a t i o n t h e r e f e r s t o t h e h i g h e r e n e r g y s t a t e a n d Be ( Z ) i s t h e b i n d i n g e n e r g y o f t h e e l e c t r o n b e f o r e c o n v e r s i o n . T h e o t h e r s y m b o l s a r e d e f i n e d i n E q u a t i o n 1 - 4 . Gamma D e c a y T h e t r a n s i t i o n p r o b a b i l i t y f o r t h e e m i s s i o n o f a gamma r a y ( t o a 4 5 f i r s t o r d e r a p p r o x i m a t i o n ) i s g i v e n b y ' I n t h i s e q u a t i o n uJtf = t h e p r o b a b i l i t y p e r u n i t t i m e f o r e m i s s i o n o f a gamma r a y w i t h e n e r g y E = k c K = i s a c o n s t a n t . K k t h e i n i t i a l a n d f i n a l w a v e f u n c t i o n s o f t h e n u c l e u s . R = i s t h e r a d i u s o f t h e n u c l e u s . £ + W Z •= r e p r e s e n t s t h e i n t e r a c t i o n c a u s i n g t h e r a d i a t i o n . £ i s e l e c t r i c i n o r i g i n a n d h a s e v e n p a r i t y . 4 rffl i s m a g n e t i c i n o r i g i n a n d h a s o d d p a r i t y . T h i s e x p r e s s i o n f o r £Jy i s o f t e n q u i t e i n a c c u r a t e b u t i s u s e f u l f o r d e s c r i b i n g t h e m e t h o d b y w h i c h gamma r a d i a t i o n i s c l a s s i f i e d . T h e t e r m e - i k R c a n b e e x p a n d e d i n t h e u s u a l f o r m . T h a t i s : t =1 T h e n t h e f i r s t t e r m i n ( I - I D \ r e p r e s e n t s t h e t r a n s i t i o n p r o b a b i l i t y f o r d i p o l e r a d i a t i o n , t h e s e c o n d q u a d r a p o l e r a d i a t i o n , e t c . 4 ' " ' ' ^ . O n l y t e r m s o f t h e l o w e s t o r d e r i n k R n e e d b e c o n s i d e r e d i n t h e e x p a n s i o n u n l e s s t h e e n e r g y o f t h e e m i t t e d gamma r a y i s l a r g e . F o r e x a m p l e : - 1 3 1/3 t a k i n g R = 1 . 2 x 10 cm A k = 5 . 0 5 x 1 0 1 0 E c m " 1 w h e r e A i s t h e m a s s number o f t h e n u c l e u s a n d E i s t h e e n e r g y o f t h e gamma r a y i n M e v . T h e n k R <=: 6 x 1 0 " 3 A E S i n c e E i s u s u a l l y l e s s t h a n 10 M e u , k R i s u s u a l l y m u c h l e s s t h a n u n i t y a n d o n l y t e r m s o f t h e l o w e s t o r d e r i n k R n e e d b e r e t a i n e d . The f o l l o w i n g d i s c u s s i o n i s l i m i t e d t o t h i s c a s e . 0 T h e a n g u l a r momentum o f a gamma r a y r e s u l t i n g f r o m a 2 - p o l e t r a n s -i t i o n i s 2 w i t h r e s p e c t t o t h e o r i g i n t o w h i c h t h e m u l t i p o l e i s r e f e r r e d . I f a n d a r e t h e i n i t i a l a n d f i n a l a n g u l a r m o m e n t a o f t h e n u c l e u s r e s p e c t i v e l y , t h e n t h e r e s t r i c t i o n s o n Q. d u e t o c o n s e r v a t i o n o f momentum a r e \ j f - J . i = J „ 4. a < j f + J± 4 B e c a u s e o f t h e t r a n s v e r s e n a t u r e o f e l e c t r o - m a g n e t i c r a d i a t i o n , gamma r a y s m u s t h a v e a n g u l a r momentum g r e a t e r t h a n o r e q u a l t o o n e . T h e r e f o r e , f o r J c = 0 a n d i f J f = J ^ = 0 , no gamma r a d i a t i o n c a n o c c u r . T h e s e r e s t r i c t i o n s s e t l i m i t s o n t h e a l l o w e d v a l u e s o f £ i n t h e e x p a n s i o n o f e ^ Terms i n the i n t e g r a l i n equation I - 11 w i l l vanish unless they have even p a r i t y . Because £ and TV. have opposite p a r i t y , the second non-zero term w i l l contain £ i f the f i r s t contains w( , and v i c e versa. The r a t i o ^ of 77l to ^ i s of the same order of magnitude as k R. That i s ffl -3 -2/3 ^ 5 x 10 A ' 6 Therefore, the f i r s t and second terms are of the same order of magnitude i f the f i r s t contains Only these two terms need be retained as 2 contributions from a l l other terms are at l e a s t of order (k R) smaller. S i m i l a r l y , i f the f i r s t term contains ^ , a l l other terms may be ignored. Tra n s i t i o n s i n v o l v i n g the emission of gamma rays are c l a s s i f i e d as e l e c t r i c (E) or magnetic (M) according to which are the dominant terms contributing to U))( , and by the angular momentum (spin) of the emitted gamma ray. There are two d i s t i n c t types of t r a n s i t i o n s . For the f i r s t type, the product of the i n i t i a l and f i n a l wave functions of the nucleus has p a r i t y (-1)^ (-1 = Yes, there i s a p a r i t y change, +1 = No, there i s not a p a r i t y change). Such t r a n s i t i o n s are c a l l e d p a r i t y favored. The second type has a p a r i t y change of - ( - 1 ) ^ . These are c a l l e d p a r i t y unfavored t r a n s i t i o n s . Both cases are discussed below. P a r i t y Favored Tr a n s i t i o n s The t r a n s i t i o n p r o b a b i l i t y i s given by A l l other terms i n equation I - 11 are zero or negligable compared to this term. Tr a n s i t i o n s of th i s type are c l a s s i f i e d as EJ 0 . If J0 = 0 the t r a n s i t i o n p r o b a b i l i t y i s given by ; ' ' 14 ^ = K k | ^ / [ ^ + ( - i k R ) ^ j ^ i d i r l 2 T r a n s i t i o n s o f t h i s t y p e a r e c l a s s i f i e d a s M 1 + c E 2 , w h e r e c r e p r e s e n t s t h e p e r c e n t a g e o f t h e t r a n s i t i o n t h a t i s E2 i n c h a r a c t e r . P a r i t y U n f a v o r e d T r a n s i t i o n s T h e t r a n s i t i o n s p r o b a b i l i t y i s g i v e n b y T r a n s i t i o n s o f t h i s t y p e a r e c l a s s i f i e d a s M J 6 + c ' E J 6 +1 I f J f t = 0 t h e t r a n s i t i o n p r o b a b i l i t y i s g i v e n b y = K k | ( ^ f * 6 t i d r i 1 T r a n s i t i o n s o f t h i s t y p e a r e c l a s s i f i e d a s E l . T h e c l a s s i f i c a t i o n a n d r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s o f t r a n s -i t i o n s i n v o l v i n g t h e f i r s t f e w v a l u e s o f J„ a r e g i v e n i n T a b l e I I . T h e r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s a r e o n l y a p p r o x i m a t e a s t h e e r r o r i n e q u a t i o n I - 11 c a n b e c o n s i d e r a b l e . A n e x a c t c a l c u l a t i o n o f COy r e q u i r e s a n u c l e a r m o d e l i n v o l v i n g t h e r e a r r a n g e m e n t o f t h e n u c l e o n s t h a t w i l l g i v e t h e r e q u i r e d c h a n g e s i n e n e r g y , s p i n , a n d p a r i t y o f t h e n u c l e u s . T h e e x p e r i m e n t a l v a l u e o f LUy , w h i c h c a n b e o b t a i n e d b y m e a s u r i n g t h e number o f gamma r a y s w i t h e n e r g y Ea e m i t t e d p e r u n i t t i m e f r o m a k n o w n r a d i o a c t i v e s o u r c e , i s o f t e n u s e d t o c h e c k t h e a d e q u a c y o f s u c h a m o d e l . I n t e r n a l C o n v e r s i o n a n d C o n v e r s i o n C o e f f i c i e n t s S p i n a n d p a r i t y c h a n g e s o f a t r a n s i t i o n c a n b e d e d u c e d f r o m t h e 15 Table II C l a s s i f i c a t i o n of Gamma Tra n s i t i o n s P a r i t y Favored Case Approx. Relative J 0 P a r i t y Change Class Value of 10% 0 (0-T~>.0) No Ml + (E2) (k R ) 2 1 Yes E l 1 2 2 No E2 (k R) 3 Yes E3 P a r i t y Unfavored Case 0 (0 -/> 0) Yes E l 1 1 No Ml + (E2) (k R ) 2 2 Yes M2 + (E3) (k R ) 4 3 No M3 + (E4) (k R ) 6 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 ( I . C . C . ) . T h e I . C . C . o f a t r a n s i t i o n i s d e f i n e d a s J -* = "Iu7" w h e r e iOz. i s t h e t r a n s i t i o n p r o b a b i l i t y f o r i n t e r n a l c o n v e r s i o n . I t s h o u l d be n o t e d t h a t . . N - ( E . - B . ) U e . c . e . 1 w h e r e N ( E . - B-;) a n d N y ( E p ) r e f e r t o t h e number c o n v e r s i o n e l e c t r o n s c . e . * a n d gamma r a y s w i t h e n e r g y E a - B^ a n d E 0 r e s p e c t i v e l y , e m i t t e d p e r u n i t t i m e ; a n d t h a t fjJt= uv+ u. + u, + w h e r e K , L j , L J J , . . . d e n o t e t h e d i f f e r e n t a t o m i c o r b i t a l s . T h e e n e r g y t r a n s f e r b e t w e e n t h e n u c l e u s a n d t h e a t o m i c e l e c t r o n i n i n t e r n a l c o n v e r s i o n i s a d i r e c t i n t e r a c t i o n b e t w e e n t h e b o u n d e l e c t r o n a n d t h e same m u l t i p o l e f i e l d w h i c h o t h e r w i s e w o u l d h a v e r e s u l t e d i n t h e e m i s s i o n o f a gamma r a y ^ . T h e t r a n s i t i o n p r o b a b i l i t y f o r i n t e r n a l c o n -v e r s i o n t h e r e f o r e c o n t a i n s t h e same n u c l e a r w a v e f u n c t i o n s a s t h e t r a n s -i t i o n p r o b a b i l i t y f o r gamma r a d i a t i o n . 1 2 I t h a s b e e n s h o w n t h a t ' , t o a c l o s e a p p r o x i m a t i o n , t h e n u c l e a r w a v e f u n c t i o n s c a n c e l i n t h e c a l c u l a t i o n o f 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 . T h e I . C . C . ' s t h e n d e p e n d o n l y o n t h e e n e r g y d i f f e r e n c e b e t w e e n t h e i n i t i a l a n d f i n a l s t a t e s , o n t h e s p i n a n d p a r i t y c h a n g e o f t h e t r a n s i t i o n , a n d o n t h e a n g u l a r momentum, p a r i t y a n d b i n d i n g e n e r g y o f t h e e l e c t r o n b e i n g c o n v e r t e d . T h e i n t e r n a l c o e f f i c i e n t s c a n b e w r i t t e n a s 17 where etc. These i n d i v i d u a l c o e f f i c i e n t s can be calculated and t h e i r values compared to those obtained experimentally to deduce the spin and p a r i t y change of a t r a n s i t i o n . T h e o r e t i c a l i n t e r n a l conversion c o e f f i c i e n t s have been calculated by S l i v and Band^. They have calculated f o r n u c l e i with atomic K number between 33 and 98 and o( T > ck-, a n d (AT r o r n u c l e i with L I L I I L I I I atomic numbers between 41 and 98. In both cases c a l c u l a t i o n s were done f o r m u l t i p o l a r i t i e s up to J , = 5 for both p a r i t y favored and p a r i t y g unfavored t r a n s i t i o n s . Similar c a l c u l a t i o n s have been done by Rose . Investigations of i n t e r n a l conversion c o e f f i c i e n t s therefore lead to knowledge of the spin and p a r i t y changes involved i n the ra d i o a c t i v e decay of' a nucleus. Such in v e s t i g a t i o n s require a s u i t a b l e spectrometer capable of measuring energies and i n t e n s i t i e s of electrons and gamma rays. A spectrometer with these features was constructed using a s i l i c o n l i t h u m - d r i f t e d semiconductor detector. The development and c h a r a c t e r i s t i c s of t h i s spectrometer are the main topic of Chapters I I , I I I and IV. 18 CHAPTER I I SEMICONDUCTOR DETECTORS 1 . The P - N J u n c t i o n A s i s w e l l k n o w n , e l e c t r i c a l c o n d u c t i o n i n s e m i c o n d u c t o r s i s due t o m o b i l e c a r r i e r s , s u c h a s e l e c t r o n s i n t h e u n f i l l e d c o n d u c t i o n b a n d , o r v a c a n c i e s o r " h o l e s " i n t h e v a l e n c e b a n d , w h i c h move u n d e r t h e i n f l u e n c e o f a n e x t e r n a l e l e c t r i c f i e l d . I n a p u r e s e m i c o n d u c t o r c r y s t a l , t h e n u m b e r o f c a r r i e r e l e c t r o n s ( n ) a n d t h e number o f c a r r i e r h o l e s ( p ) a r e e q u a l a n d d e p e n d o n l y o n t h e e n e r g y gap b e t w e e n t h e c o n d u c t i o n a n d v a l e n c e b a n d s , a n d o n t h e c r y s t a l t e m p e r a t u r e . H o w e v e r , i m p u r i t i e s i n t h e c r y s t a l c a n c a u s e a n i n e q u a l i t y b e t w e e n n a n d p . When t h i s i s s o we h a v e a n N - t y p e o r a P - t y p e s e m i c o n d u c t o r , d e p e n d i n g u p o n w h e t h e r t h e e l e c t r o n s (n) o r h o l e s ( p ) a r e m o r e n u m e r o u s . T h e s e i n e q u a l i t i e s a r i s e b e c a u s e , f o r e x a m p l e , t h e i m p u r i t i e s may i n t r o -d u c e l e v e l s h i g h i n t h e f o r b i d d e n z o n e b e t w e e n t h e c o n d u c t i o n a n d v a l e n c e b a n d s . A n e l e c t r o n f r o m s u c h a l e v e l , w h e n e x c i t e d i n t o t h e c o n d u c t i o n b a n d , b e c o m e s a c a r r i e r , w h i l e t h e h o l e l e f t b e h i n d i s t r a p p e d i n p o s i -t i o n . H e n c e i m p u r i t i e s o f t h i s t y p e l e a d t o N - t y p e s e m i c o n d u c t o r s . T h e s e i m p u r i t i e s a r e c a l l e d d o n o r i m p u r i t i e s a s t h e y " d o n a t e " e l e c t r o n s t o t h e c o n d u c t i o n b a n d . O t h e r i m p u r i t i e s l e a d t o l e v e l s l y i n g l o w i n t h e f o r b i d d e n z o n e , n e a r t h e t o p o f t h e v a l e n c e b a n d . V a l e n c e e l e c t r o n s c a n e a s i l y b e e x c i t e d i n t o t h e s e l e v e l s l e a v i n g m o b i l e h o l e s b e h i n d , w h i l e t h e e l e c t r o n s a r e t r a p p e d . T h e s e i m p u r i t i e s a r e c a l l e d a c c e p t o r i m p u r i t i e s a s t h e y a c c e p t e l e c t r o n s f r o m t h e v a l e n c e b a n d , l e a d i n g t o t h e f o r m a t i o n o f a P - t y p e s e m i c o n d u c t o r . T h e e n e r g y l e v e l s t r u c t u r e s 19 FIG. 3 . - -Impurity Levels Conduction ? E l e c t r o n i n j e c t e d into Band conduction band  ^L&y Impurity l e v e l Valence Band Donor Impurity Conduction I Band E l e c t r o n Energy — Impurity l e v e l (for accepting electrons) Valence Band Acceptor Impurity 20 f o r b o t h t y p e s o f i m p u r i t i e s a r e s h o w n i n F i g . 3 . I t i s p o s s i b l e t o c o n v e r t P - t y p e m a t e r i a l t o N - t y p e m a t e r i a l b y d i f f u s i n g a d o n o r i m p u r i t y i n t o t h e c r y s t a l , a n d c o n v e r s e l y , N - t y p e m a t e r i a l c a n b e c o n v e r t e d t o P - t y p e b y a c c e p t o r d i f f u s i o n . I f t h e d i f f u s i o n p r o c e s s e x t e n d s o n l y p a r t w a y , t h e c r y s t a l w i l l h a v e two d i f f e r e n t r e g i o n s . T h e j u n c t i o n b e t w e e n t h e s e r e g i o n s i s c a l l e d a P - N j u n c t i o n . T h e r e w i l l t h e n b e a d i f f u s i o n o f f r e e e l e c t r o n s f r o m t h e N-t y p e r e g i o n i n t o t h e P - t y p e r e g i o n w h i c h w i l l c o n t i n u e u n t i l t h e C o u l o m b r e p u l s i o n f r o m t h e c h a r g e b u i l d u p b a l a n c e s t h e d i f f u s i o n f o r c e s . The e f f e c t i s t o c r e a t e , a t t h e j u n c t i o n , ' a r e g i o n f r e e o f c h a r g e c a r r i e r s , c a l l e d t h e d e p l e t i o n l a y e r . T h e s e l a y e r s a r e v e r y n a r r o w , b e i n g - 6 9 t y p i c a l l y 10 cm H o w e v e r , t h e a p p l i c a t i o n o f a r e v e r s e b i a s t o t h e j u n c t i o n ( n e g a t i v e v o l t a g e o n t h e P - t y p e s i d e ) c a u s e s a g r e a t i n c r e a s e i n t h e w i d t h o f t h e d e p l e t i o n l a y e r , t h e i n c r e a s e d e p e n d i n g o n t h e v o l t a g e a p p l i e d . D e p l e t i o n l a y e r s > 3 m m h a v e b e e n a c h i e v e d . T h e s e d e p l e t i o n l a y e r s h a v e e x t r e m e l y h i g h r e s i s t i v i t y . T h e o n l y c o n t r i b u t i o n t o t h e c o n d u c t i o n c u r r e n t , i n t h e a b s e n c e o f e x t e r n a l i o n i z i n g e v e n t s , a r e t h o s e e l e c t r o n - h o l e p a i r s g e n e r a t e d b y t h e r m a l a g i t a t i o n , a p r o c e s s t h a t c a n b e r e d u c e d b y c o o l i n g t h e c r y s t a l . 2. T h e P - I - N C r y s t a l A P - I - N c r y s t a l i s made b y d i f f u s i n g a d o n o r i m p u r i t y i n t o a P - t y p e c r y s t a l , o r a n a c c e p t o r i m p u r i t y i n t o a n N - t y p e c r y s t a l . T h e i m p u r i t y t o b e d i f f u s e d i n t o t h e c r y s t a l ( s a y P - t y p e ) m u s t b e c h o s e n s o t h a t t h e a d d e d d o n o r e l e c t r o n s c o m p e n s a t e f o r t h e a c c e p t o r l e v e l s w h i c h e x i s t e d i n t h e P - t y p e m a t e r i a l , l e a v i n g a r e g i o n w i t h no f r e e c h a r g e c a r r i e r s o t h e r •21 t h a n t h o s e d u e t o t h e r m a l a g i t a t i o n . I f p r o p e r d i f f u s i n g t e c h n i q u e s a r e u s e d , o n l y a t h i n l a y e r o f P - t y p e m a t e r i a l o n o n e s i d e o f t h e c r y s t a l a n d a t h i n l a y e r o f N - t y p e m a t e r i a l o n t h e o t h e r s i d e w i l l r e m a i n u n c o m p e n s a t e d . T h e s e l a y e r s h a v e a l o w r e s i s t i v i t y c o m p a r e d t o t h e c o m p e n s a t e d r e g i o n a n d a c t a s e l e c t r i c a l c o n -t a c t s f o r a p p l y i n g a r e v e r s e b i a s . T h e c o m p e n s a t e d r e g i o n h a s a h i g h r e s i s t i v i t y . I n a d d i t i o n , t h e j u n c t i o n s b e t w e e n t h e P - t y p e a n d c o m p e n s a t e d r e g i o n , a n d t h e c o m p e n s a t e d a n d N - t y p e r e g i o n s , a c t l i k e P - N j u n c t i o n s . T h e r e f o r e a P - I - N c r y s t a l w i l l a c t l i k e a P - N j u n c t i o n u n d e r r e v e r s e b i a s , t h e o n l y d i f f e r e n c e b e i n g t h a t t h e c o m p e n s a t e d r e g i o n , o f a P - I - N c r y s t a l c a n b e made m u c h l a r g e r ( > 2 cm) t h a n t h e d e p l e t e d r e g i o n o f a P - N j u n c t i o n . A l s o t h e w i d t h o f t h e c a r r i e r f r e e r e g i o n o f a P - I - N c r y s t a l i s o n l y s l i g h t l y d e p e n d e n t o n t h e a p p l i e d r e v e r s e b i a s . T h e c o m p e n s a t e d r e g i o n o f a P - I - N c r y s t a l h a s i n c o r r e c t l y b e e n c a l l e d i n t r i n s i c i n t h e p a s t . H e n c e t h e name P - I - N c r y s t a l s . 3 . S e m i c o n d u c t o r C r y s t a l s a s P a r t i c l e D e t e c t o r s A n e n e r g e t i c c h a r g e d p a r t i c l e t h a t p e n e t r a t e s a s e m i c o n d u c t o r c r y s t a l w i l l i n t e r a c t w i t h t h e c r y s t a l a n d l o s e e n e r g y i n o n e o f t h e 9 f o l l o w i n g t h r e e w a y s . a ) The c h a r g e d p a r t i c l e may i m p a r t s u f f i c i e n t e n e r g y t o a n e l e c t r o n t o r a i s e i t t o t h e c o n d u c t i o n b a n d , l e a v i n g a h o l e i n t h e v a l e n c e b a n d . T h e e n e r g y o f t h e p r i m a r y p a r t i c l e i s r e d u c e d b y a n amount e q u a l t o t h e w i d t h o f t h e e n e r g y g a p b e t w e e n t h e two b a n d s . T h e r e m a i n i n g e n e r g y i s s h a r e d r a n d o m l y b e t w e e n t h e p r i m a r y p a r t i c l e , t h e s e c o n d a r y e l e c t r o n , a n d t h e s e c o n d a r y h o l e . E a c h o f t h e s e w i l l t h e n l o s e t h e i r e n e r g i e s b y p r o c e s s e s a ) , b ) o r c ) . b ) T h e p r i m a r y p a r t i c l e may l o s e e n e r g y b y i n t e r a c t i n g w i t h t h e c r y s t a l l a t t i c e i t s e l f . T h e s e i n t e r a c t i o n s e x c i t e t h e l a t t i c e i n o p t i c a l a n d a c o u s t i c a l modes o f v i b r a t i o n . T h e p r i m a r y p a r t i c l e , a f t e r t h i s l o s s o f e n e r g y , w i l l c o n t i n u e t o l o s e e n e r g y b y p r o c e s s a ) , b ) , o r c ) . c ) When a p a r t i c l e h a s i n s u f f i c i e n t e n e r g y f o r e i t h e r o f t h e a b o v e p r o c e s s e s , i t m u s t l o s e i t s r e m a i n i n g e n e r g y b y t h e r m a l l o s s e s t o t h e l a t t i c e m a t e r i a l . T h e o v e r a l l e n e r g y l o s s p r o c e s s i s s h o w n s c h e m a t i c a l l y i n F i g . 4. When a r e v e r s e b i a s i s a p p l i e d t o a c r y s t a l , t h e e l e c t r o n s a n d h o l e s p r o d u c e d b y p r o c e s s a ) a b o v e c a u s e t h e c u r r e n t a c r o s s t h e c r y s t a l t o i n c r e a s e . I t i s p o s s i b l e , b y m e a s u r i n g t h i s c u r r e n t i n c r e a s e , t o d e d u c e t h e e n e r g y l o s t b y t h e p r i m a r y p a r t i c l e . T h i s w i l l b e d e s c r i b e d i n m o r e d e t a i l i n l a t e r s e c t i o n s . T h e n u m b e r o f e l e c t r o n - h o l e p a i r s t h a t c o n t r i b u t e t o t h e c u r r e n t i s g i v e n b y n = E / £ w h e r e E i s t h e e n e r g y l o s t i n t h e c a r r i e r f r e e r e g i o n o f t h e c r y s t a l a n d £ i s t h e a v e r a g e e n e r g y r e q u i r e d t o p r o d u c e a n e l e c t r o n - h o l e p a i r . The v a l u e o f £ d e p e n d s o n t h e s e m i c o n d u c t o r m a t e r i a l ( u s u a l l y g e r m a n i u m o r s i l i c o n ) , o n t h e t y p e o f p r i m a r y p a r t i c l e , a n d o n t h e t e m p e r a t u r e o f t h e c r y s t a l . 9 T h e f l u c t u a t i o n i n t h e number o f e l e c t r o n - h o l e p a i r s i s g i v e n b y 23 F I G . 4.--E n e r g y L o s s i n S e m i c o n d u c t o r C r y s t a l s P r i m a r y P a r t i c l e E n e r g y = E E x c i t a t i o n o f e l e c t r o n O p t i c a l o r a c c o u s t i c a l t o c o n d u c t i o n b a n d . e x c i t a t i o n E n e r g y L o s s = E „ E n e r g y L o s s = E r P r i m a r y P a r t . E n e r g y = ( E - E 3 ) ( l - p ) H o l e E n e r g y = p ( E - E , ) / 2 E l e c t r o n E n e r g y = P ( E - E 3 ) / 2 P r i m a r y P a r t . E n e r g y = E - E , T h e s e n o w b e c o m e p r i m a r i e s f o r f u t u r e g e n e r a t i o n i f t h e i r e n e r g y i s l a r g e e n o u g h . p i s t h e f r a c t i o n o f e n e r g y l o s t b y t h e p r i m a r y p a r t i c l e . 24 < A n > = ( E / 6 )h F w h e r e n_> i s t h e RMS f l u c t u a t i o n s i n n a n d F i s t h e s o - c a l l e d F a n o f a c t o r ; a s t a t i s t i c a l f a c t o r i n t r o d u c e d b y U . F a n o ^ i n 1 9 4 6 . A v a l u e o f F = 0 w o u l d i m p l y t h a t no e n e r g y was l o s t b y p r o c e s s e s b ) o r c ) g i v e n p r e v i o u s l y , w h i l e a v a l u e o f F = 1 w o u l d i m p l y t h a t t h e p r o b a b i l i t y o f p r o d u c i n g a n e l e c t r o n - h o l e p a i r a p p r o a c h e s z e r o . S i n c e t h e t r u e p i c t u r e i s s o m e w h e r e b e t w e e n t h e s e two e x t r e m e s , t h e v a l u e o f F m u s t b e b e t w e e n 0 a n d 1 . CHAPTER I I I LITHIUM ION DRIFTED SILICON DETECTORS 1. S i ( L i ) Detectors f o r Photons and Electrons A l i t h i u m ion d r i f t e d s i l i c o n detector ( S i ( L i ) ) i s a P-I-N c r y s t a l operated under reverse bias. These c r y s t a l s are made by d i f f u s i n g l i t h i u m ions (a donor impurity) i n t o a c r y s t a l of P-type s i l i c o n at a high temperature. The l i t h i u m compensates f o r the acceptor impurity i n the P-type s i l i c o n as described e a r l i e r , creating a c a r r i e r free region. The N- and P-type regions are h i g h l y doped and supply good e l e c t r i c a l contacts. F i g . 5 schedmatically shows some features of a S i ( L i ) detector. The average energy required to produce an electron-hole pair i n s i l i c o n by electrons depends only on the temperature of the c r y s t a l 1 1 . This dependence i s shown i n F i g . 6. The number of electron-hole p a i r s produced i n the c a r r i e r free region i s l i n e a r with e l e c t r o n energy pro-vided the e l e c t r o n loses a l l i t s energy i n t h i s region. This sets a minimum thickness f o r the compensated region and also requires a dead layer (window) t h i n enough that no appreciable amount of energy i s l o s t as the e l e c t r o n passes through i t . F i g . 7 shows the range of electrons 12 i n s i l i c o n as a fu n c t i o n of energy . F i g . 8 shows the loss i n el e c t r o n energy i n s i l i c o n per micron of dead layer as a function of e l e c t r o n 12 energy . An in c i d e n t e l e c t r o n may be scattered out of the compensated region of the detector, as shown i n F i g . 9. The "backscattered" e l e c t r o n w i l l 2,1: have l o s t only part of i t s energy i n the detector. I t has been shown ' -25-FIG. 5.— S i ( L i ) Crystals 26 P-layer (grounded) Incident p a r t i c l e s Dead layer (window) N layer (+ voltage applied) a) Physical b) Concentration of c a r r i e r s c) E l e c t r i c f i e l d due to applied bias FIG. 6.--£ vs. Temperature 27 T i n °K FIG. 7.--Range of Electrons i n S i Range i n S i l i c o n (microns) 28 FIG. 8.--Energy Loss i n Dead Layer  10 t E l e c t r o n Energy Loss (Kev/micror 1 ) 10 100 1000 E l e c t r o n Energy (Kev) 10,000 FIG. 9.--P a r t i a l Energy Loss Processes Backscattered E l e c t r o n Incident Electrons 'Backscattered" E l e c t r o n Compensated region of detector > E l e c t r o n too energetic to be stopped by this thickness of c r y s t a l 29 that the f r a c t i o n of electrons scattered out of a S i ( L i ) detector does not depend on e l e c t r o n energy. I t depends only on the source-detector geometry used. The detection of photons (gamma rays or x-rays) with a S i ( L i ) detector requires that the photon's energy be transferred to an e l e c t r o n (or e l e c t r o n s ) , and that the e l e c t r o n be detected. This tran s f e r of energy can be accomplished by three processes; they are a) P h o t o - e l e c t r i c e f f e c t . The photon, with energy , i s absorbed by an atomic e l e c t r o n with binding energy E„. The electron i s ejected from the atom with energy Eg - Eg. The x-ray or auger e l e c t r o n emitted due to the vacancy i n the atomic s h e l l w i l l i n t e r a c t also. b) Compton s c a t t e r i n g . The photon su f f e r s an i n e l a s t i c c o l l i s i o n with an atomic electron, l o s i n g energy E £ to the electron. I f E^ i s greater than the binding energy of the elec t r o n , i t w i l l be ejected from the atom. The photon i s l e f t with reduced energy and may undergo further i n t e r a c t i o n s . c) P a i r production. 2 • I f the photon energy i s greater than 2 m0 c , where m0 i s the e l e c t r o n r e s t mass, the photon may i n t e r a c t with the coulomb f i e l d of the nucleus, creating an e l e c t r o n - p o s i t r o n p a i r . The photon i s completely absorbed and the excess energy i s shared by the e l e c t r o n and positron. 2 The excess energy i s E = E j - 2 m, c , The cross-sections as functions of photon energy for these three processes i s shown i n F i g . 10. The measurement of the energy of a photon with a S i ( L i ) detector FIG. 10.— Photon Cross Section for S i l i c o n Photon Energy i n Kev 31 requires that a known f r a c t i o n of i t s energy be transferred to the electrons, and that the electrons be completely stopped i n the compensated region. In Compton s c a t t e r i n g the photon i s u s u a l l y scattered out of the detector a f t e r t r a n s f e r r i n g an unknown f r a c t i o n of i t s energy to the elect r o n . For this reason the Compton process i s not a useful means of measuring the photon's energy. The p h o t o - e l e c t r i c e f f e c t and pair production, on the other hand, transfer a l l of the photon's energy to electrons. In the case of the p h o t o - e l e c t r i c process, the f u l l energy of the photon can be determined by measuring the energy of the photo-electron produced, provided that i t i s stopped i n the compensated region. The p r o b a b i l i t y that the x-ray caused by the vacancy i n the atomic s h e l l w i l l escape without undergoing a p h o t o - e l e c t r i c i n t e r a c t i o n i n the compensated region i s n e g l i g i b l e as the p h o t o - e l e c t r i c cross-section f o r t h i s energy ( < 2 Kev for s i l i c o n ) i s very large. The po s i t r o n and el e c t r o n produced i n the p a i r process lose t h e i r energy i n the usual way. The positron, once i t has l o s t i t s energy, w i l l i n t e r a c t with an atomic e l e c t r o n to form two photons, each with energy 2 m„ c . These photons may i n t e r a c t i n the compensated region by eit h e r the p h o t o - e l e c t r i c or the Compton s c a t t e r i n g processes, or they may escape. A known f r a c t i o n of the incident photon's energy w i l l be deposited i n the detector provided neither of these two secondary photons undergo Compton s c a t t e r i n g . Ey i s deposited i f both photons produce 2 photo-electrons, E^ - m0 c i s deposited i f one photon escapes and . 2 the other produces a photo-electron, and E^ -. 2 mb c i s deposited i f 32 both escape. The c o l l e c t i o n , a m p l i f i c a t i o n and analysis of these charge-carriers produced by the energy loss i n S i ( L i ) detectors may be used to produce an energy spectrum of the incident r a d i a t i o n . 2. Associated E l e c t r o n i c s The e l e c t r o n i c s required to c o l l e c t , amplify and analyze the free charge c a r r i e r s produced i n the compensated region of a S i ( L i ) detector are shown diagrammatically i n F i g . 11. The e l e c t r o n i c s described are those used i n this report and are of " s t a t e - o f - t h e - a r t " q u a l i t y . The preamplifier i s a high gain, low noise, charge s e n s i t i v e a m p l i f i e r (Tennelec, model 135 M) that u t i l i z e s the inherent high input impedance and low noise of a f i e l d - e f f e c t t r a n s i s t o r (FET). The equi-valent c u r c u i t for a S i ( L i ) detector coupled to an FET preamplifier i s shown i n F i g . 12. and represent the c r y s t a l capacitance and res i s t a n c e r e s p e c t i v e l y . Rg and C g are the resistance and capacitance i n the connections between the c r y s t a l and the preamplifier. R^ i s the 9 load resistance of the bias voltage supply ( t y p i c a l l y 10 ohms). The p a r a l l e l combination of and R^, i s the feedback impedance of the charge s e n s i t i v e stage of the preamplifier. I f Rg i s small and R^ and R^ are large, the output voltage V„ i s given by _Q_A_ • ' C, + C + CL. (A+l) d s F where A i s the open loop gain of the preamplifier and Q i s the charge deposited on C^; that i s , Q i s the free charge c a r r i e r s produced i n the FIG. 11.— Schematic of E l e c t r o n i c s ? High voltage supply (0-» - 1000 V) Pulse Shaper Main Amp. Base-l i n e Restorer Biased Amp. Pulse Stretcher C r y s t a l To M.C.A. <-FIG. 12.— Equivalent C i r c u i t for Detector-Preamp. A\* = R6i : C s = 1 FE.T. Cf -/wi-•p-compensated region of the detector. I f A i s large, the output voltage reduces to v JL The pulse shaper i s the i n t e g r a t i n g d i f f e r e n t i a t i n g network shown i n F i g . 13. I t s c h a r a c t e r i s t i c s are given i n Table I I I . The pulse from the preamplifier i s shaped to give the best s i g n a l to noise gain i n the main a m p l i f i e r . The main a m p l i f i e r i s a Nuclear Chicago, Model 27001. I t s gain i s continuously v a r i a b l e from 6 to 400. The baseline r e s t o r e r i s an Ortec, Model 438. I t s function i s to insure that a pulse i s not superimposed on the t a i l of a preceding pulse; that i s , i t prevents pile-up of the i n d i v i d u a l s i g n a l s . The biased a m p l i f i e r (Ortec, Model 408) discriminates against pulses below a given voltage. This discriminator voltage i s adjustable. A l l pulses above t h i s voltage are amplified l i n e a r l y and t h e i r baseline restored to zero. The pulse stretcher (Ortec, Model 411) insures that the pulses are compatible with the input to the multi-channel analyser (MCA), a Nuclear Data, Model 110. The MCA consists of a a n a l o g - t o - d i g i t a l converter, and a 128 word memory (128 channels). I t s readout i s v i s u a l (Nuclear Data 410 Display), or by a teletype p r i n t e r and paper tape puncher. A t y p i c a l output of th i s system i s shown i n F i g . 14. The radio-a c t i v e source used was "^Co, which decays by e l e c t r o n capture to "^Fe. F I G . 1 3 . - -P u l s e S h a p e r N e t w o r k 0«.-v ( ?oS> T 1 T 3 T 4 a r e 2N4124 T 0 T r a r e 2N4126 37 Table I I I Ch a r a c t e r i s t i c s of the Pulse Shaper Integration D i f f e r e n t i a t i o n Time Const. C l Time Const. C2 (Msec.) (pf) (A sec.) (,*f) 0.2 20 0.2 .002 0.47 47 0.5 .005 1.0 100 l.o .01 2.0 200 2.0 .02 4.7 47 5.0 .05 10.0 1000 10.0 .1 A m p l i f i c a t i o n R 3 (ohms) Gain 22 2 47 4 100 8 T y p i c a l Low Energy Spectrum Source: ~^Co Detector: S^ Kev/chan: .378 K 121.4 r /\ FWHM 3.3-/ « / L+M+ •121.9 Y-121.9 I • ,»-o L-2.7-jJ FWHM K 136.3 © / \ / \ I \ / / \ L+M+ •136.3 K-136.3 30 40 50 60 70 80 Channel Number 90 100 110 120 39 The four peaks are due to the gamma rays and conversion electrons from the 136.3 and 121.9 Kev t r a n s i t i o n s i n "^Fe. The f i r s t peak i s due to the K conversion electrons from the 121.9 Kev t r a n s i t i o n . The second i s due to gamma rays from this t r a n s i t i o n , as well as the L+ M+ con-ver s i o n electrons whose energy i s only s l i g h t l y lower than the gamma ray's energy. The t h i r d and fourth are due to the K conversion electrons and gamma rays plus L+M+ conversion electrons from the 136.3 Kev t r a n s i t i o n . 3. Inherent Resolution of the Detector-Analyser System The peaks i n F i g . 14 represent t o t a l energy loss by mono-energetic p a r t i c l e s i n the compensated region of the detector. The width of these peaks at h a l f maximum (FWHM-full-width-half maximum) i s c a l l e d the r e s o l u t i o n LO , and i s due to f l u c t u a t i o n s i n the response of the detector-analyser system to these mono-energetic p a r t i c l e s . The f l u c t u a t i o n s i n the response have two independent causes. They are a) S t a t i s t i c a l f l u c t u a t i o n s i n the number of electron-hole pairs produced i n the detector. The r e l a t i o n s h i p between the FWHM and the 9 fl u c t u a t i o n s i n the number of pairs ^ A n > i s U>c = 2.35 £ <An> assuming that the peak i s gaussian shaped. From equation I I - 1 the FWHM becomes L^c = 2.35 ( E £ ) ^ F b) Fluctuations due to noise generated i n the detector and associated 9 e l e c t r o n i c s . A d e t a i l e d analysis of noise has been done by Goulding . 40 He shows that there are three main sources of noise, which may be sum-marized as follows. The f i r s t , shot noise, r e s u l t s from electron-hole p a i r s generated by thermal e x c i t a t i o n i n the detector. I t s co n t r i b u t i o n to LO i s given by 2 J-lO = ( K C T R S ) 2 s s T eq s The second, f l i c k e r noise, i s generated by f l u c t u a t i o n s i n the current flowing into the input stage of the preamplifier, and i t s c o n t r i b u t i o n i s W F = ( K F C T S F ) X " F i n a l l y , leakage noise i s caused by currents over the surface of the detector and i t s contribution i s W L " ( K L i S L ) 1 " In the above equations, the K's are constants, i s the t o t a l capacitance of c r y s t a l and input stage, T i s the c r y s t a l temperature ( i n °K), R i s the equivalent noise resistance of the preamplifier input, the S's are factors that depend upon the shape of the pulses, and i i s the leakage current. Since these noise sources are independent of each other, and indepen-dent of the number of electron-hole p a i r s , the t o t a l r e s o l u t i o n i s given by = ( K s CT T R e q S s + ^ °T S F + \ 1 S L + £ ^  (2.35 f ) V For good r e s o l u t i o n , each term i n th i s equation must be made as small as pos s i b l e . R i s set by the type of input to the preamplifier used. I t cannot be changed without redesigning the preamplifier. The factors S can be lowered by the proper choice of time constants i n the pulse shaper. The usual procedure for f i n d i n g the best time con-stants i s to minimize the r e s o l u t i o n by changing and i n the pulse shaper a f t e r a l l other parameters have been f i x e d . C can be lowered by using low capacitance connectors between the c r y s t a l and preamplifier, and by the proper choice of detector. The capacitance of a S i ( L i ) detector, assuming i t can be treated as a p a r a l l p l ate capacitor, i s C d = i A/W where £ i s the p e r m i t t i v i t y of s i l i c o n . Therefore C d = 1.05 A/W picofarads Here A i s the area of the detector i n square centimeters and W i s the thickness of the compensated region i n centrimeters. The r e l a t i o n s h i p between noise and t o t a l input capacitance f o r the 135 M preamplifier i s ^ U) = 1.5 Kev + .018 Kev/pf ( i n s i l i c o n ) The Fano f a c t o r (F) i n the equation for L*J c depends on the c r y s t a l m a t e r i a l . I t i s very d i f f i c u l t to measure accurately, but most reports 9 17 give values f o r s i l i c o n ranging from .2 to .4 ' The temperature of the c r y s t a l e f f e c t s three terms, i n the equation f o r U)^. Decreasing the temperature decreases the c o n t r i b u t i o n to the r e s o l u t i o n due to shot noise by decreasing the number of thermally, pro-duced electron-hole p a i r s . I t also decreases the c o n t r i b u t i o n due to leakage current by decreasing i , but increases the c o n t r i b u t i o n due to f l u c t u a t i o n s i n the number of electron-hole pairs produced by increasing £ (see F i g . 6 ) . The leakage current also varies with the reverse bias applied to the c r y s t a l . The bias voltage must be high enough to accelerate the electrons and holes away from each other before they are able to reunite. Unless great care i s taken i n the preparation of the c r y s t a l and.in keep-ing the^ surface of the c r y s t a l free from contaminates, the term involv-ing the leakage current w i l l dominate over a l l the others and w i l l e f f e c t -i v e l y set the minimum r e s o l u t i o n obtainable. Since the c r y s t a l i s u s u a l l y cooled much below room temperature, i t must be placed i n a vacuum chamber to insure that no condensation occurs on the c r y s t a l surface, as t h i s w i l l add to the surface leakage current. F i g . 15 shows the vacuum chamber used for cooling the c r y s t a l . In summary, once the detector-analyser system has been chosen, there are only three adjustments that can be made to improve the r e s o l u t i o n . They are i Temperature of the c r y s t a l i i Bias voltage i i i Time constants of the pulse shaper. In order to determine the best r e s o l u t i o n obtainable with the detector-analyser system described i n Section I I I - 2, the c r y s t a l temperature was varied by changing the length of the c o l d - f i n g e r . At each s e t t i n g , the temperature was measured by copper-constantin thermo-couples, and the r e s o l u t i o n optimized by adjusting the bias voltage and the time constants. The r e s u l t s of t h i s procedure for the two c r y s t a l s FIG; 15.— Crystal Chamber to vacuum pump Liquid Nitrogen Chamber Cold Finger Crystal c -O FIG. 16.--P l o t of Temperature vs. Optimized Resolution f o r Two Detectors 45 used are shown i n F i g . 16. The c h a r a c t e r i s t i c s of these c r y s t a l s are given i n Table IV. The optimum r e s o l u t i o n f or the detector was reached at T = 190°C V = 400 v o l t s , and time constants of 2 /(sees. The optimum r e s o l u t i o n for the detector was reached at T = -100°C, V = 350 v o l t s and time constants of 2 X s e c s . The peak used was the 121.9 Kev gamma peak of ~^Co. 4. Other Contributions to the Resolution Peaks due to monoenergetic p a r t i c l e s may be broadened by e f f e c t s other than the f l u c t u a t i o n s i n the response of the detector analyser system. These e f f e c t s are source charging, source absorption, s c a t t e r i n g from surrounding materials, and dead layer absorption. Sources that emit electrons w i l l quickly charge themselves to high (and sometimes f l u c t u a t i n g ) p o t e n t i a l s , thus a l t e r i n g the energy of the emitted electrons. The source must therefore be well grounded. The e f f e c t of too thick a source i s to degrade the energy of electrons coming from below the surface by c o l l i s i o n losses (source absorption). This adds a low energy component, or t a i l , to the peak, r e s u l t i n g i n a greater width. To keep this peak broadening to a minimum, the source must be kept t h i n , the maximum thickness depending on the source material and the el e c t r o n energy. An example of peak broading due to source absorption i s shown i n F i g . 17. The peak i s the 114 Kev K con-v e r s i o n peak of "^Co. The S^ detector was used to obtain both spectra. Thin sources may be made i n a number of d i f f e r e n t ways^, but those used i n th i s experiment were prepared by subliming the source material onto a thi n aluminum backing, as explained below.. The sublimation chamber i s shown i n F i g . 18. A drop of a s o l u t i o n of the source material F I G . 1 7 . -E f f e c t o f S o u r c e T h i c k n e s s o n R e s o l u t i o n T h i c k S o u r c e T h i n S o u r c e 1000 f A P e a k i s a t 1 1 4 . 8 K e v 3 . 3 K e v k M 2 . 5 K e v 0 • » • r, ° _ » k tt 9 o 30 4 0 50 60 3 0 4 0 50 6 0 Table IV Ch a r a c t e r i s t i c s of the Two Detectors Detector S\ Simtec type KQ2 Obtained from Simtec Ltd. i n October, 1968 Recommended reverse bias 400-800 v o l t s Thickness (W) 2 mm 2 Area (A) 50 mm Window (Dead Layer) .2 microns Detector Kj Kevex type A80-5 Obtained from Kevex Corporation i n February, 1968 Recommended reverse bias 300-700 v o l t s Thickness (W) 5 mm 2 Area (A) 80 mm Window (Dead Layer) 5 microns FIG. 18.--Sublimation Chamber Glass viewer Source backing Source Material z Tungsten ribbon Copper' To vacuum pump ^ Ceramic feed through To pulser •9-Tungsten Ribbon FIG. 19.— Pulser C i r c u i t 49 2.N SSS no v//j.d To Variac 60 VAC) o_ - - w — 0 — SooJl To Tungsten Ribbon I hi S" i s deposited on the tungsten ribbon. The material i s then dried with an i n f r a - r e d lamp and the chamber evacuated. A large current (-10 Amps) i s pulsed through the ribbon, and as a r e s u l t a l o c a l hot-spot develops i n the region of the droplet where the ribbon width has been reduced. The source material i s sublimed o f f the ribbon and onto the aluminum backing. The thickness of the source can be varied by the number of current pulses used, the length of the pulses, or by the amount of source material deposited on the ribbon. The current pulse generator i s shown i n F i g 0 19. Scattering of electrons or photons from the chamber walls, source backing, source holder, etc. does not normally broaden a peak. Compton s c a t t e r i n g through small angles can, on occasion, produce a peak that looks l i k e a f u l l energy peak. In most cases, however, the energy l o s t i n the s c a t t e r i n g processes leaves a residue that appears at considerably lower energies than the undistorted peak and i s u s u a l l y smeared over the lower energy background as a continuum. The exception to t h i s i s the case of low-energy photons, which may be scattered at large angles with only a s l i g h t loss i n energy. From the Compton process one can deduce that F i _ 1 * ^ ( 1 " C o S e ) where E'^ and E^ are the energies of the scattered and i n c i d e n t gamma rays r e s p e c t i v e l y and Q i s the s c a t t e r i n g angle. The c r o s s - s e c t i o n for t h i s process i s very large for E$ <£. 100 Kev and 20°< © < 100°. Hence large mass concentrations should be kept as f a r away from the source and detector as p o s s i b l e . F i g . 20(a) shows two types of source holders and F i g . 20(b) shows t h e i r e f f e c t on the 41 Kev x-ray peak of europium. FIG. 20.-Two Types of Source Holders and Their E f f e c t on Low Energy Photon Resolution Detector Ring holder a) 'Thin Afi. with source sublimed onto i t Ae or l u c i t e r i n g E l e c t r i c a l contact y Thin Ai Cardboard Cardboard holder b ) 70 : SO 90 Too 110 120 Channel No. *• E f f e c t s of Backscattering from Source Holder on 41 Kev X-Rays FIG. 21 a ) . — E f f e c t s of Dead Layer on Low Energy Electrons 53 F i g . 8 showed the energy loss of electrons passing through the dead layer of a S i ( L i ) detector. F i g s . 21 shows the e f f e c t of the dead layers 153 of the Ki and S-^  detectors on a portion of the Gd el e c t r o n spectrum. The spectrum taken with the K-^  detector (21(a)) shows the two gamma peaks at 97.4 and 103.2 Kev and a degraded e l e c t r o n peak at lower energy. The spectrum taken with the detector (21(b)) has three e l e c t r o n peaks, two of which are superimposed on the gamma peaks. The gamma spectrum by i t s e l f , taken with the electrons absorbed by a t h i n aluminium absorber, i s included f o r comparison of the two spectra. CHAPTER IV ANALYSIS OF SPECTRA 1. Computer Analyses A computer program was w r i t t e n to s i m p l i f y the analysis of spectra obtained with the detector-analyser system described above. I t i s 2 explained i n d e t a i l i n Appendix A. As stated there, a value of X /(n-m) = 1 i s i n d i c a t i v e of a good f i t , although i t was found experimentally 2 that f i t s with valves of 'X /(n-m) between 0 and 3 s t i l l f i t the function _ 2 G[ to the data very w e l l . I f "X /(n-m) was greater than 3, the f i t was rerun using d i f f e r e n t portions of the t o t a l spectrum, as the goodness of f i t i s very s e n s i t i v e to any n o n - l i n e a r i t y i n the background. I t was found that a l l the spectra analysed with t h i s program could be f i t t e d 2 with a goodness of f i t parameter, /\. /(n-m), less than 3. The program i s capable of separating peaks that overlap; that i s , peaks whose energy difference i s less than the r e s o l u t i o n of the system. F i g . 22 shows two such peaks. They are the and x-ray peaks of 109 s i l v e r that r e s u l t from the e l e c t r o n capture decay of Cd. Their energies are 22.1 and 25.0 Kev r e s p e c t i v e l y . The s o l i d curve i s a p l o t of the f u n c t i o n f i t t e d to t h i s data. F i g s . 23(a) and 23(b) are the com-ponents of t h i s composite peak given by the computer program. To check the accuracy of the separation of these peaks, the r a t i o of t h e i r i n t e n s i t i e s was found and compared with the accepted value of 4.64 given i n reference 18. This r a t i o i s F T = <5-5 - 3 ) R -54-FIG. 22.--Charmel No. FIG. 23.--Components of Peak i n F i g . 22 3000 Counts 2000 1000 10 a) component 20 ' 500 400 300 200 100 30 40 Channel No. i « « 10 /\ 20 b) component 30 to" R i s the c o r r e c t i o n factor f o r the d i f f e r e n c e i n e f f i c i e n c y of the S\ . detector for the two d i f f e r e n t energies. This c o r r e c t i o n f a c t o r i s .9 + .05 (see F i g . 26). The r a t i o of t h e i r i n t e n s i t i e s i s therefore 4.9 + which i s i n agreement with the value quoted above. D i f f e r e n t values of gain of the a m p l i f i e r system were used to determine the e f f e c t of gain on the uncertainty i n the p o s i t i o n of the peaks and on the r e l i a b i l i t y of the i n t e n s i t y estimates given by the f i t t i n g routine. The peak used was the 114.9 Kev K-conversion e l e c t r o n peak r e s u l t i n g from the e l e c t r o n capture decay of ~*^Co. The spectra of t h i s peak were taken for the same length of time f o r each gain s e t t i n g so the i n t e n s i t i e s would be the same. The r e s u l t s f o r the error i n p o s i t i o n and i n t e n s i t y are given i n Table V. Gain (Kev/Channel) 2.0 1.0 0.5 0.3 0.1 Table V Change of Error with System Gain Peak Uncertainty (Channel) (Kev) t.2 +.2 + + .1 + .1 .05 ±.03 I n t e n s i t y Error (Percent.) +5.6 +4.0 +3.0 + .03 +2.0 +2.0 From Table V i t can be seen that a gain s e t t i n g of .3 Kev/Channel w i l l minimize the error i n the i n t e n s i t y and p o s i t i o n of a peak. Since the MCA has 128 channels the best r e s u l t s are obtained i f the biased a m p l i f i e r i s set.so that a range of 35 —> 45 Kev i s covered by the MCA. 58 2. Energy C a l i b r a t i o n This work i s mainly concerned with low energy electrons and photons; that i s , with energies up to approximately 120 Kev. Three d i f f e r e n t biased a m p l i f i e r settings are needed to cover this range of energies i f the minimum error possible i n peak p o s i t i o n and i n t e n s i t y i s to be obtained. Each of these three settings was c a l i b r a t e d using as many photon sources of known energy as were a v a i l a b l e . The energy range of each s e t t i n g , and the sources along with the energies of t h e i r photon peaks are l i s t e d i n Table VI. The r e s u l t s of these c a l i b r a t i o n s are p l o t t e d i n F i g s . 24(a), (b), and ( c ) . 2 A l e a s t square f i t using a function of the form LJ = a + bx + cx was done on the c a l i b r a t i o n data. The values of a and b found for each s e t t i n g are given on the c a l i b r a t i o n curves (Figs. 24). The value of c 4 was found to be at l e a s t a f a c t o r of 10 smaller than the value of b for 2 each s e t t i n g . Since the maximum error i n ignoring the x term i s then approximately .04 Kev (which i s less than the error i n the energies of most c a l i b r a t i o n sources) the c a l i b r a t i o n curves were assumed l i n e a r . I t should be noted that the errors associated with the values of a and b given on the c a l i b r a t i o n curves are only the s t a t i s t i c a l errors of the f i t t i n g procedure, and do not contain the possible errors i n the quoted c a l i b r a t i o n energies. The energy of conversion e l e c t r o n peaks can be obtained from these c a l i b r a t i o n curves i f the energy l o s t by an e l e c t r o n i n the dead layer of the detector i s known. Simtec quotes a value for the dead layer of the Si detector of .2 microns. This value was checked using the conversion Table VI Energy C a l i b r a t i o n Sources Source Energy (Kev) Reference Sett i n g 1. Energy Range 6 -•50 Kev 5 7 C o 14.35 + .05 18 1 0 9 C d (K* ) 22.1 + .1 Ag x-rays ( K ^ ) 25.0 t ' . l 1 3 3 B a (K« ) 30.9 - .1 Cs x-rays (K* ) 35.1 ± .1 1 5 3 G d (K* ) 41.3 - .1 Eu x-rays ( K , ) 47.3 ± .1 Setting 2 Energy Range 38 -* 85 Kev 1 5 3 G d (K„ ) 41.3 + .1 Eu x-rays (K^ ) 47.3 + .1 2 4 1 A r a 59.54 * .02 18 1 3 3 B a 81.0 - .2 22 Settin g 3 Energy Range 75 -* 128 Kev 1 3 3 B a 81.0 * .2 22 154 + Eu 86.9 . - .2 22 105.3 - .2 122.9 * .2 ' 5 7 C o 121,91 - .05 18 FIG. 24 a).--Setting #1 FIG. 2.4 b).--Setting #2 80 a = 38.33 Kev + 01 + b = .3631 Kev/Ch. - .0005 133T 70 Energy (Kev) Energy (Kev) = .3631 (Channel No.) + 38.33 "141 Am 60 50 Gd 40 Gd K* 10 20 30 40 50 60 Channel No. 70 80 90 100 110 FIG. 24 c ) . — Setting #3 63 e l e c t r o n standards l i s t e d i n Table VII. The apparent energies of th e i r peaks were found from Figs.24, and the d i f f e r e n c e between these energies and those given by Reference 18 was used to deduce the thickness of the dead layer (see F i g . 8). Table VII Energy Lost i n Dead Layer of S\ Detector E Dead Layer (Kev) (microns) .3 - .3 .3 + .3 .1 + .3 .1 + .3 .3 + .3 .3 + .3 0. + .3 0. + .3 Averaging these values gives a dead layer of .175 + .3 microns, which i s i n agreement with the value of .2 microns quoted by Simtec. Since better e l e c t r o n standards were not a v a i l a b l e , i t was impossible to f i n d the thickness more accurately. The value of .2 microns was therefore used to f i n d the c o r r e c t i o n to the e l e c t r o n energies. I t was found that the p o s i t i o n of the c a l i b r a t i o n peaks could change by as much as one channel due to changes i n e l e c t r o n i c gain. To guard against t h i s happening while a spectrum was being taken, c a l i b r a t i o n runs were performed before and a f t e r each spectrum containing peaks of unknown energies was taken. If the s h i f t i n the c a l i b r a t i o n peaks was greater than .2 channels, the data was discarded and the spectrum taken again. For each spectrum used, new values of a and b were calculated f o r the Energy (Kev) Energy (Kev) Source from Ref. 18 from F i g . 24 1 0 9 C d (K Q_ .,) 62.2 ± .2 61.9 ± .1 1 0 9 C d ( L Q .,) 84.2 ± .2 84.1 + .1 5 7 C o ( K 1 2 2 Q) 114.9 + .2 114.6 + .1 5 7 C o ( K 1 0 , 0 ) 129.2 + .2 129.2 + .1 64 c a l i b r a t i o n curves. The maximum possible error i n the energy of unknown peaks was estimated by summing the d i f f e r e n t errors involved. The error i n peak p o s i t i o n from the f i t t i n g procedure ranged from .03 Kev f o r intense peaks to .2 Kev f o r weak peaks. The error i n the c a l i b r a t i o n curves was estimated to be a maximum of .2 Kev (.15 Kev for the error due to energy uncertainty of the c a l i b r a t i o n peaks and .05 Kev f o r t h e i r p o s i t i o n u n c e r t a i n t y ) . The maximum error i n el e c t r o n energy due to an error i n the value used f o r the thickness of the dead layer of the detector was .24 Kev f o r 100 Kev electrons and .5 Kev for 20 Kev electrons (assuming a maximum error i n the thickness of .3 microns). The maximum error i n the energies of unknown peaks i s therefore .4 Kev f o r photons and .6 and .9 Kev for 100 and 20 Kev electrons r e s p e c t i v e l y . The actual error i n measured energies i s probably much less than these values f o r a l l but very low i n t e n s i t y peaks. 3. Separation of Ele c t r o n and Photon Spectra Quite often e l e c t r o n and photon peaks overlap i n a spectrum. I t i s convenient therefore to be able to separate the e l e c t r o n and photon spectra. The procedure used was as follows: F i r s t a t o t a l spectrum con-t a i n i n g both e l e c t r o n and photon peaks was taken. An aluminum absorber 19 thick enough to stop a l l electrons was then placed between the source and detector and a spectrum containing only photon peaks was taken. The i n t e n s i t i e s of the photon peaks was corrected f o r the absorber and sub-tracted from the t o t a l spectrum, leaving only peaks due to electrons. The photon peaks were corrected f o r the absorber by an empirical equation of the form I = J-o exp (A/(E - E ) ) IV - 1 Here A, B, and E are constants that are var i e d to f i t experimental absorption data, I and I a are the reduced and i n i t i a l i n t e n s i t i e s r e s p e c t i v e l y , and E i s the photon energy. F i g . 25 i s a p l o t of th i s f u nction along with the experimental absorption data. The values A = 5, E = 7, and B = 1.5 give a s a t i s f a c t o r y f i t to the experimental data. I t should be noted that t h i s c o r r e c t i o n function cannot be used to correc t the t o t a l photon spectrum f o r the absorber. That i s , one cannot m u l t i p l y the counts found i n each channel by the value of I/l0 at the energy corresponding to that channel and get the same spectrum as one would f i n d without the absorber. The reason i s that the monoenergetic photons that pass through the absorber without l o s i n g any energy ( f r a c t i o n I/Io ) w i l l have a spread i n energy due to r e s o l u t i o n and a low energy continuum r e s u l t i n g from Compton s c a t t e r i n g . Therefore i f one applied t h i s c o r r e c t i o n continuously the peaks would be d i s t o r t e d as the c o r r e c t i o n on the lower energy side would be too large and the c o r r e c t i o n on the higher energy side would be too small. The lower energy continuum would also be much too large. Therefore the value of l / l 0 corresponding to the energy of each peak was found and th i s value was used to correct the data over that peak region a f t e r the background from higher energy photons was subtracted. Only the peaks without background were subtracted from the t o t a l spectrum. The r e s u l t i s that the e l e c t r o n spectrum con-tains the background from photons as well as the background from electrons. 4 . E f f i c i e n c y C a l i b r a t i o n s The e f f i c i e n c y of the Si detector f o r photons as a f u n c t i o n of photon energy was found using standard sources obtained from I.A.E.A., 66 FIG. 25.--Absorption Curve for Photons i n Aluminum Absorber 10 20 • 30 40 50 60 70 80 Energy (Kev) * Vienna. The relevant c h a r a c t e r i s t i c s of these sources are l i s t e d i n Table IX. The sources are heat sealed between two thi n p l a s t i c discs and cold-welded between two thi n aluminum d i s c s . The f r a c t i o n of the inten-s i t y of the photon peaks absorbed by t h i s i n c a p s u l a t i o n was found by measuring the decrease i n i n t e n s i t y when one side of a dummy (no source) capsule was placed between the source and the detector. These f r a c t i o n s were used to corre c t the number of photons radiated into the s o l i d angle -3 of the detector (8.2 x 10 Std) per u n i t time f o r each c a l i b r a t i o n peak. These i n t e n s i t i e s are included i n Table IX. The r a t i o of the actual i n t e n s i t y per u n i t time of a given photon peak as measured with the S-^  detector to the calculated i n t e n s i t y for that peak i s the i n t r i n s i c e f f i c i e n c y of th i s detector f o r that photon peaks energy. This r a t i o i s pl o t t e d i n F i g . 26 for the f i v e energies l i s t e d i n Table IX. The low energy portion of th i s curve ( <30 Kev) i s extra-polated to match curves given i n reference 12. The e f f i c i e n c y of the S\ detector f o r electrons was assumed constant (see Chapter I I I - 1 ) . I t has not been measured f o r th i s detector. A value of 80 * 57o i s assumed, which i s i n agreement with measurements made 23 25 by various groups ' ' . Low energy e l e c t r o n standards have only r e c e n t l y become a v a i l a b l e to th i s laboratory and t h i s e f f i c i e n c y w i l l be measured i n the near future. The er r o r i n the photon e f f i c i e n c y curve i s estimated to be 2? 5°L. This value i s the sum of the errors i n the source strength, i n the f r a c t i o n of t o t a l r a d i a t i o n represented by a peak, and i n the measured i n t e n s i t y of that peak. The t o t a l error may be larger than 5"L as any error i n the ca l c u l a t e d s o l i d angle subtended by the detector has not been included. 68 Table VTII Photon E f f i c i e n c y C a l i b r a t i o n Data Source Strength* Energy of Percent of (Mc) t % Cal. peak (Kev) d i s i n t e g r a t i o n 1 3 7 C s 10.4 + .2 30. 5 years 32. , l + . l 5. ,7 ± .2 Am 10.4 + .1 432. 9 years 59. ,54 + .02 35. ,9 ± .6 203 u Hg 20.3 + .2 46. 8 days 72. ,873 + .001 9. ,7 ± .5 279, ,191 * .008 81. ,55 + .15 Co 11.4 + .1 271. 6 days 121. ,97 ± .03 85. ,0 ± 1.7 at January 1,1970; 00:00 Universal time Absorption (%) Intensity"' Source Energy (Kev) by capsule (photons/sec) 1 3 7 C s 32.1 + .1 6.5 1300 2 4 1Am 59.54 + .02 3.8 8974 2 0 3 H g 72.873 - .001 2.8 28188 5 7 C o 121.97 + .03 2.1 23918 2 0 3 H g 279.19 + .008 1.4 21059 I n t e n s i t y calculated to be radiated into the s o l i d angle subtended by the detector, a f t e r corrections have been made for the l i f e - t i m e of the source and absorption by the capsule. CHAPTER V DECAY OF 1 5 3GADOLINIUM 1. Introduction The e l e c t r o n capture decay of 153 Gd to 153 Eu has been investigated previously by a v a r i e t y of techniques 26-30 The decay scheme deduced by 18 Lederer et a l . from these measurements i s given i n F i g . 27. There i s a disagreement between the values given by d i f f e r e n t authors for the capture branching r a t i o s , e s p e c i a l l y to the ground state. I t was there-fore decided that a r e - i n v e s t i g a t i o n of this decay using the S i ( L i ) spectrometer described i n the previous chapters would be informative. 2. Source Preparation 153 The Gd source material was obtained from Union Carbide Corp. I t s chemical form was GdCC ^ disso l v e d i n 1 N. HCt . The s p e c i f i c a c t i v i t y 153 of Gd i n the m a t e r i a l was 5.46 m i l l i c u r i e s / m i l l i g r a m . 2 Source material was sublimed onto a t h i n aluminum backing (.8 mg/cm ) i n the manner described e a r l i e r . The maximum thickness of source material that would not degrade the low energy e l e c t r o n peaks by source absorption was found experimentally by preparing successively thinner sources u n t i l no improvement i n peak shape was noted. This thickness was estimated to 2 be cs10 M. gm/cm from the s p e c i f i c a c t i v i t y (5.46 m Ci/mgm), the source 2 strength ( ^ 50 x C i ) , and the source area ( ^ 1.5 cm ) . The aluminum backing was mounted on cardboard (see F i g . 20) to reduce backscatter. Since GdC& ^ i s hygroscopic, sources must be kept i n a vacuum, i n 22 a desiccator, or covered with c o l l o d i o n so that they do not absorb -70-71 F I G . 2 7 . — 153 M a i n T r a n s i t i o n s i n t h e D e c a y o f Gd = 5 . 8 E , = 70 K e v = 6 . 5 E „ = 139.8 Kev = 6 . 6 E „ = 145.6 Ke/ = 8 . 4 E „ = 1 5 9 . 6 K e v = 7 . 8 E,, = 243 K e v 72 moisture from the atmosphere and therefore become thicker. The sources could not be covered with c o l l o d i o n as this would absorb energy as the electrons passed through i t . They were therefore stored i n a desiccator when not i n the c r y s t a l chamber. 153 3. Gd Spectra 153 The t o t a l spectrum and the photon spectrum of Gd f o r each of the three biased a m p l i f i e r s e t t i n g s , along with the energy c a l i b r a t i o n data, were taken with the Si detector. The i n t e n s i t y of the peaks i n the photon spectra were corrected for the absorber (see Chapter IV) and subtracted from the t o t a l spectra to get the three e l e c t r o n spectra. These three spectra were normalized to the same time (the less intense regions were taken over longer periods of time), matched i n energy using the overlap between the set t i n g s , and then p l o t t e d as one composite spectrum i n F i g . 28. The same matching procedure was used to obtain the composite photon spectrum (Fig. 29). The energies of the peaks i n these two spectra were found using the energy c a l i b r a t i o n data and the channel p o s i t i o n of the peaks as given by the computer f i t t i n g program. The energies of the el e c t r o n peaks were corrected for the absorption i n the dead layer of the Si detector. These energies are included i n F i g s . 28 and 29. The o r i g i n s of the ele c t r o n peaks were deduced by subtracting the binding energies of the K-, L-, or M+N- s h e l l atomic electrons of europium from the energies of the gamma peaks and comparing these values with the energies of the ele c t r o n peaks. The o r i g i n s of the gamma peaks were deduced by comparing t h e i r energies with the t r a n s i t i o n energies given on the decay scheme ( F i g . 27). Both the el e c t r o n and photon peaks, along F I G . 2 8 . — 153 C o n v e r s i o n E l e c t r o n S p e c t r u m o f Gd 2 L 20 S e t t i n g 1 S e t t i n g 2 5 4 . 6 , ' 2 1 . 1 x 4 4 8 . 9 ., 3 6 . 5 r 6 1 . 9 S e t t i n g 3 r 9 5 . 4 8 9 . 5 i 1 0 1 . 5 6 8 . 1 -tor "10T5 1213 WT~ C h a n n e l N o , 180 2 0 0 220 240 260 LO FIG. 29.--153 Photon Spectrum of Gd 112 10 Setting 1 K-41.3 Setting 2 x 20 64.8 Setting 3 97.4 103.2 r 4 r 47.3 40 60 80 100 120 140 Channel No. 160 180 200 220 240 Table IX Peak I d e n t i f i c a t i o n and I n t e n s i t i e s 75 Peak Energy (Kev) 21.1 36.5 48.9 54.6 61.9 68.1 89.5 95.4 101.5 41.3 47.3 69.8 97.4 103.2 Peak O r i g i n K69.7 Auger1 K, K 97.4 103.2 L69.7 M+N 69.7 L97.4 J 1 0 3 . 2 + M f N 9 7 . 4 ^ 1 0 3 . 2 K x-rays K x-rays 172.9 103.2 97.4 0 103.2 0 Intensity (Counts) 13107 - 7.3% 10516 * 5.3% 80 T 5 37702 * 2.3% 80 * 5 1866 * 12.3% 80 * 5 200 * 40% 298 * 15% 1810 - 3.6% 1056 * 4.1% S-^  Detector E f f . (%) 8 0 - 5 +80 + 1894 - 4.8% 8 0 - 5 7789 * 3.1% 80 * 5 1886 * 4 . 8 % 80 t 5 7943 * 3% . 18.6* .9 5.8* .3 2.0- .1 1.75* . 09 Corrected Intensity 16384 * 12% 13145 - 10% 47127 - 7.3% 2333 * 17% , 250 * 45% + 2336 - 10% *8768 * 8.1% 2357'- 10% 51230* 1.5% 30.6*1.5 166000 ± 6.5% 42200 * 8% 3892 * 20% 65990 - 8.6% 46200 * 9.17= a f t e r the M„_, , conversion electrons were subtracted. 97.4 76 with t h e i r deduced o r i g i n s , are l i s t e d i n Table X. The peak i n t e n s i t i e s found by the f i t t i n g program, and t h e i r i n t e n s i t i e s corrected for the detector e f f i c i e n c y , are included i n Table X. The contribution to the i n t e n s i t y of the 95.4 Kev e l e c t r o n peak due to the M conversion electrons from the 97 . 4 Kev t r a n s i t i o n was c a l -g culated using the M conversion c o e f f i c i e n t s of Rose and assuming that the t r a n s i t i o n was E l . This contribution was substracted to give the i n t e n s i t y of L-^Q-J ^ conversion electrons. I n t e n s i t i e s of peaks r e s u l t i n g from other t r a n s i t i o n s were too weak to be observed above the background. 4 . Conversion C o e f f i c i e n t s The K-conversion c o e f f i c i e n t s and the L-conversion c o e f f i c i e n t s (Table XI) were calculated and compared to the t h e o r e t i c a l c o e f f i c i e n t s given by S l i v and Band^. 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 can be assigned from these comparisons. Comparison of the K-conversion c o e f f i c i e n t s require that the 69.7 Kev t r a n s i t i o n be a mixture of Ml and E2, the 97 . 4 Kev t r a n s i t i o n be E l , and the 103.2 Kev t r a n s i t i o n be a mixture of Ml and E2. The L-conversion c o e f f i c i e n t s are i n agreement with these assignments. The K- and L-conversion c o e f f i c i e n t s contain the rather large u n c e r t a i n t i e s i n the e f f i c i e n c y of the S;[ detector f o r photons and electrons. The r a t i o of these c o e f f i c i e n t s should be more exact as these e f f i c i e n c i e s cancel out. That i s , the r a t i o °^K/ ^ L i s equal to the number of K-conversion electrons from a t r a n s i t i o n divided by the number of L-conversion electrons from that t r a n s i t i o n , as measured by the detector. These r a t i o s are given i n Table XII along with the t h e o r e t i c a l values of °^K/ °^L. The percentage E2 admixture i n the 69 . 4 Kev and 103.2 Kev t r a n s i t i o n s was calculated from these r a t i o s to be 07, — * 207, and 167> — * 327, 77 Table X K-Conversion C o e f f i c i e n t s ( p O K T r a n s i t i o n Measured Energy (Kev) Values 69.7 97.4 103.2 4.2 + 1.3 .2 + .04 1.02 + .17 E l .64 .26 .24 Th e o r e t i c a l Values Ml E2 4 . 6 1 . 6 1 . 4 3 2.85 1.2 1.07 M2 50.0 13.0 11.0 L-Conversion C o e f f i c i e n t s ( o( ) 1~J 69.7 97.4 103.2 .60 + 035 - .007 18 + .22 .03 .09 .039 .034 ,65 .25 .209 5.34 .830 .860 64.0 3.4 3.2 Table XI T r a n s i t i o n Energy (Kev) 69.7 97.4 103.2 Measured Values 7.0 + 1.2 5 . 6 t 1.1 Th e o r e t i c a l Values E l Ml 6.67 5 . 3 + 7.07 6 . 8 4 E2 1.55 1.24 78 r e s p e c t i v e l y . The admixture of E2 i n the 103.2 Kev t r a n s i t i o n i s consider-ably higher than the value of 1.7% given by reference 18. The 97.4 Kev t r a n s i t i o n i s assumed to be pure E l as the next allowed multipole has a 4 t r a n s i t i o n p r o b a b i l i t y that i s reduced by a fac t o r of (kR) (see Table I I ) . 5. Capture Branching Ratios The f r a c t i o n of t o t a l capture t r a n s i t i o n s that go to a given l e v e l i n the daughter n u c l e i i n ele c t r o n capture decay i s c a l l e d the capture branch-ing r a t i o to that l e v e l . Defining the terms N = Number of capture t r a n s i t i o n s to the excited state at energy E 153 E above the ground state i n Eu I e ( E 0 ) = Inte n s i t y of the e = K, L, M+N+ conversion electrons from 153 the E 0 t r a n s i t i o n i n Eu 153 1^ (E c) = Inte n s i t y of the gammas from the E 0 t r a n s i t i o n i n Eu. Then from the i n t e n s i t i e s given i n Table X the number of capture 153 t r a n s i t i o n s to the excited l e v e l s of Eu are N172.9 = X * ( 6 9 - 7 ) + XK ( 6 9 ' 7 ) + \ ( 6 9 - 7 ) + IM+N+ ( 6 9 ' 7 ) = (2.33 - .32) x 10 4 N103.2 = T& ( 1 0 3 - 2 ) + \ ( 1 0 3 - 2 ) + h ( 1 ° 3 - 2 ) + V N f ( 1 0 3 ' 2 ) - N 1 7 2 > 9 = (8.1 - 1.2) x 10 4 N, 9 7.4 = ' 1t ( 9 7' 4> + I K ( 9 7 ' 4 ) + h ( 9 7 ' 4 ) + W ( 9 7 ' 4 ) = (8.15 - .71) x 10 4 ^172 9 W a S S U D t r a c t e c ^ from the t o t a l r a d i a t i o n from the 103.2 Kev t r a n s i t i o n to get N^^^ 2 a s t^ i e 172.9 Kev l e v e l feeds the 103.2 l e v e l v i a the 69.4 Kev t r a n s i t i o n . 153 The number of capture t r a n s i t i o n s to the ground state of Eu can be deduced from the i n t e n s i t y of the K x-rays. This c a l c u l a t i o n requires that the f r a c t i o n of K-capture to L+M+N+ -capture t r a n s i t i o n s i s known, that the number of K x-rays r e s u l t i n g from t r a n s i t i o n s other than K-153 capture to the ground state of Eu i s known, and that the K-fluorescent y i e l d (W ) of europium i s known. K The K-fluorescent y i e l d i s the f r a c t i o n of vacancies i n the K-atomic s h e l l that r e s u l t i n K x-rays (the r e s t give r i s e to Auger e l e c t r o n s 1 ) . 18 The K-fluorescent y i e l d of europium i s .92 The i n t e n s i t y of K x-rays r e s u l t i n g from t r a n s i t i o n s other than K-capture to the ground state i s the sum of the K-conversion electrons from a l l t r a n s i t i o n s and the K-capture t r a n s i t i o n s to a l l other l e v e l s , m u l t i p l i e d by the K-fluorescent y i e l d . I f a l l the capture t r a n s i t i o n s are assumed to be allowed or f i r s t forbidden non-unique ( A J = 0, +1; = *1) , then the f r a c t i o n of the t o t a l capture t r a n s i t i o n s that are K-captures can be calculated from p r o b a b i l i t y r a t i o s given by Brysk and 33 21 Rose and by Zyryanova . These r a t i o s are. Ui-Lj. Q - E - B L 1x2 = .128 (• U K Q - E - B R' • (ignoring the di f f e r e n c e i n the L s h e l l II ,041 ( J ^ binding energy) l^M+N = 229 ( Q " E " ^ N ) ? ' U) T + u) T Q - E - B L L I L I I L^.^ - capture i s not allowed. 80 In these equations (jJe i s the p r o b a b i l i t y of an ele c t r o n i n the e atomic s h e l l being captured, Q i s the energy difference between the ground 153 153 18 states of Gd and Eu (= 243 Kev ), E i s the energy of the excited state the capture t r a n s i t i o n s i s going to, and i s the binding energy of the e atomic s h e l l i n Eu. 153 The number of K-capture t r a n s i t i o n s to any l e v e l i n Eu i s W L T ^ N % N N E(K) = N E / ( l + ^ ( l + T ^ ) ( l + - 7 ^ ) ) The number of K x-rays that do not r e s u l t from the K-capture to the ground state i s N(K x-ray) = ( N 1 7 2 < 9 ( K ) + N 1 0 3 > 2 ( K ) + N 9 ? < 4 ( K ) + I R(69.7) + I R(97.4) + I K(103.2))W R 4 = (19.2 + 2.1) x 10 The number of K x-rays r e s u l t i n g from the K-capture t r a n s i t i o n s to the ground state i s N u + N - N(K x-ray) = (1.6 * 1.6) x 10 4 The number of K-capture t r a n s i t i o n s to the ground state i s N 0(K) = 1 f 2 ^ = ( 1 . 8 * 1.8) x 10 4 . K and the number of capture t r a n s i t i o n s to the ground state i s ^ L T ^ L T T ^ M + N K J-iJ Li = (2.3 + 2.3) ± 10 4 153 The t o t a l number of capture t r a n s i t i o n s to a l l l e v e l s i n Eu i s therefore 81 N = N + N + N + N 172.9 103.2 97.4 o = (2.09 * .25) x 10 5 The capture branching r a t i o s are therefore given by f = N / N . E E These values, expressed as percentages, are given i n Table XIII, along with those found by other i n v e s t i g a t o r s . Table XII Capture Branching Ratios Measured y (log f t values Leutz (1960) i n brackets) Ref. 26 from Ref. 26 Ref. 30 172.9 11 * 3 (5.8) 17 11 12 103.2 39 * 10 (6.6) 32 50 32 97.4 39 * 8 (6.6) 40 35 30 0 11 * i i ( 7 . 3 ) 9 4 24 The reduced l i f e t i m e s ( f t values) of the capture t r a n s i t i o n s can be c a l c u l a t e d using these capture branching r a t i o s and the e l e c t r o n capture 21 p r o b a b i l i t i e s given by Zyryanova . They are f t = (1.683 (Q - E - B K ) 2 + .2196 (Q - E - B ^ ) 2 + .0092 2^ in 2 ( Q - E - BLlI)')42 E 2 where the energies are i n units of tr\0c , "/\ = N X / N i s i n sec \ and E E 7\ i s defined by t\ = Q,n 2/-^ = 242 days. The logarithm of these values are given i n Table XIII. These log f t values i n d i c a t e that the 82 e l e c t r o n capture t r a n s i t i o n s are allowed or f i r s t forbidden. 6. Spin and P a r i t y Assignments 153 153 The ground states of Eu and Gd have been assigned the values of J 7 7 " = 5/2+ and 3/2+ re s p e c t i v e l y by atomic beam experiments 153 The 103.2 and the 69.7 Kev t r a n s i t i o n s i n Eu, as they are Ml + (E2) i n character, require that A J = 0, *1; ATT = 1. The 97.4 Kev t r a n s i t i o n , being E l i n character requires that AJ = 0, *1; ATT = -1. These requirements give the p a r i t y of the 103.2 and 172.9 Kev l e v e l s of 153 Eu as p o s i t i v e and the p a r i t y of the 97.4 Kev l e v e l as negative. 153 Therefore there i s no p a r i t y change between the ground state of Gd 153 and the 172.9, 103.2 and 0 Kev l e v e l s of Eu. The capture t r a n s i t i o n s to these l e v e l s i s therefore assumed to be allowed ( A J = 0, *1; A T f = 1) as the next type of t r a n s i t i o n s that does not have a p a r i t y change i s second forbidden with a log f t > 10. The capture t r a n s i t i o n to the 97.4 153 Kev l e v e l of Eu involves a p a r i t y change and i s therefore assumed to be f i r s t forbidden ( A J = 0, *1, *2; A TT = -1), which i s i n agreement with the log f t value of 6.6. 153 The possible J 1* values of the excited states of Eu are therefore 97.4 Kev J * = 3/2", 5/2", 7/2" 103.2 Kev = 3/2+ 5 / 2 + 172.9 Kev j " " = 3 / 2 + 5 / 2 + These values of j " - are i n agreement with those given on F i g . 27. CHAPTER VI CONCLUSIONS The spectrometer described i n previous chapters has proved success-f u l i n i n v e s t i g a t i n g low energy t r a n s i t i o n s r e s u l t i n g from electron capture decays. Although i t s r e s o l u t i o n does not compare favourably with that 2 obtained by large magnetic spectrometers f o r electrons , or bent c r y s t a l 28 spectrometers f o r low energy gamma rays , i t i s s u f f i c i e n t to separate the K-, L-, and M+N conversion electron peaks and the gamma ray peaks r e s u l t i n g from the excited state t r a n s i t i o n s associated with these decays. I t has, however, three advantages over these spectrometers. Namely, that large portions of the energy spectrum can be taken at one time, that the ele c t r o n and gamma ray spectra can be taken using the same source and the same geometry, and that the e f f i c i e n c y i s considerably greater. I t should be noted that much better r e s o l u t i o n (<.4 Kev compared 34 to 2 Kev) f o r low energy x-rays has been obtained using S i ( L i ) detectors To achieve t h i s r e s o l u t i o n the input stage of the preamplifier must be cooled with l i q u i d nitrogen to reduce the e l e c t r o n i c noise of the input stage. The c r y s t a l must have a small surface area and a large compensated region to reduce the input capacitance of the preamplifier. And the chamber must be evacuated to at l e a s t 10 7 Torr. to reduce condensation on the surfaces of the c r y s t a l to a minimum. I t i s f e l t that the pro-blems involved with t h i s type of system when sources or absorbers are changed (since they must be placed i n s i d e the chamber) would n u l l i f y the advantages of achieving better r e s o l u t i o n . The r e s o l u t i o n of the type of spectrometer used can be improved by using germanium c r y s t a l s instead of s i l i c o n as the average energy required -83-84 to produce an electron-hole p a i r i n germanium (2.9G\/) i s less than i n s i l i c o n ( 3 . 7 e v ) . Germanium i s not used, however, as these c r y s t a l s must be kept at a temperature less than - 3 0 ° C or the l i t h i u m ions w i l l d r i f t out of the compensated region. I t i s therefore very d i f f i c u l t to keep these c r y s t a l s free of surface condensation when sources or absorbers are being changed. The uncertainty i n the i n t e n s i t y of photon peaks can be reduced by a better c a l i b r a t i o n of the e f f i c i e n c y of the detector. This has not been done yet as the c a l i b r a t i o n sources were not received u n t i l December 1 9 6 9 , and the e l e c t r o n i c equipment has been i n almost constant use i n other experiments since that time. The uncertainty i n the i n t e n s i t y of e l e c t r o n peaks can be reduced by measuring the e f f i c i e n c y of the detector rather than using a value deduced from backscatter experiments done by other workers. The e f f i c i e n c y can be measured by detecting the K-conversion electrons that are i n coin-cidence with the K x-rays of an e l e c t r o n capture decay that only involves one excited state. The e l e c t r o n spectrum w i l l contain a peak due to f u l l energy loss K-conversion electrons and a lower energy continuum due to the backscattered K-conversion electrons. The r a t i o of the i n t e n s i t y of the peak to the t o t a l i n t e n s i t y i s the e f f i c i e n c y of the detector. Once the backscatter f r a c t i o n of the S i ( L i ) detector i s known, i t w i l l be possible to obtain spectra with this spectrometer and to 23 correct these spectra for backscattering . I t w i l l also be possible to separate the d i f f e r e n t j£ groups involved i n a decay by detecting those J& p a r t i c l e s that are i n coincidence with the r a d i a t i o n from t r a n s i t i o n s that de-excite d i f f e r e n t l e v e l s of the daughter nucleus. 85 A new c r y s t a l chamber has been b u i l t with f a c i l i t i e s for mounting two S i ( l i ) detectors. This chamber w i l l be used to measure the back-sc a t t e r f r a c t i o n of electrons using, the coincidence method described above. I t w i l l also be used to determine the sequence of t r a n s i t i o n s involved i n a given decay by measuring coincidences between r a d i a t i o n r e s u l t i n g from the d i f f e r e n t t r a n s i t i o n s . This chamber has a l i q u i d nitrogen capacity of 15 l i t r e s , and can keep the S i ( L i ) detectors cooled f o r approximately three days (compared to ~3 hours f o r the chamber described i n Chapter III) without r e f i l l i n g . This w i l l allow longer runs to be taken without the constant a t t e n t i o n needed previously. The chamber also has f a c i l i t i e s f o r i n s e r t i n g absorbers between the source and detectors without opening the chamber, which would require warming the c r y s t a l s to room temperature. I t w i l l therefore be much more s u i t a b l e f o r i n v e s t i g a t i n g r a d i o a c t i v e n u c l e i than the chamber described i n this t h e s i s . 86 APPENDIX A F i t t i n g Routine The purpose of a l e a s t square f i t i s to f i n d values of the parameters P , which minimize the function R 2 = (y± - y. ( P ^ P 2, . .., P J ) 2 (A - 1) In t h i s equation the summation i s over a l l data points. The y^'s are the experimental data, the a ^ ' s a r e t n e weights associated with the y^'s> a n& the y^'s are the values of the function that i s used to represent the data. 2 A necessary and s u f f i c i e n t condition for R to be a minimum, as a function of the P,'s, i s k 4 ~ = 0 f o r a l l k. These equations can be solved exactly i f y ( P p P 2 > ••••> P ) i s a l i n e a r f u n c t i o n of the P 's. I f not, no e x p l i c i t s o l u t i o n e x i s t s . In this case, K. 31 a method of l i n e a r i z a t i o n can be used. One such method i s that of Gause This method consists of l i n e a r i z i n g the function y with respect to a set of parameters SP, by using a truncated Taylor's s e r i e s . That i s , i f P, = P° + SP, , where P° i s the i n i t i a l estimate of the parameter P, , then k k k k k m \ — ^ (~^P~^ ^ P k + k * § n e r d e r i v i t i v e s Here y = y ( P ^ P 2 > P^) y° = r (p;, p°, . . . p*) 1 2 m 87 and the der i v a t i v e s are evaluated at the i n i t i a l estimates of the para-meters. The function i s a l i n e a r function of the S P, ' s. and k *'2 - Z^-yr - ^ K , ' i 1 . k U P k j o (A - 2) i s a minimum when ,.2 d R = 0 f o r a l l k. (A - 3) d ( o \ ) These equations can be solved f o r exactly and a new estimate for P^ ( P 1 s P° + o P^ .) used i n equation ( A - 2) . This i t e r a t i o n process can be continued u n t i l SP^. ^  ^ f ° r A H ^ simultaneously. A ^ i s u s u a l l y chosen so that y. <PJ, P*. .... P ^ . y . (Pj P ^ + A 2 P ^ + A ^ f o r a l l i . Equations A - 3 can be written as a matrix equation. Writing B = ( B ^ B 2, , B^) = £ . . l ( 7 l . T i , ( ^ \ C = n x n matrix — r £k v ~ i v ^ P t j o y P K SP = ( SP., £ P 9 , S P ) 1 2 a m 88 Then equations A - 3 become c £P = B which has solutions P = A B where A i s the inverse of the matrix C. The "sample standard deviation" i n the f i n a l estimate of the para-32 meter P. xs k n-m 2 2 where ^ i s the value of R for the f i n a l parameters, n i s the number of data points, m i s the number of parameters, and A^ i s the diagonal element of the matrix A. 2 _ i -The "goodness of f i t " can be estimated by the quantity . If (a^) 2 i s a good estimate of the standard deviation i n y^, and the experimental _ 2 points are a c t u a l l y represented by the function y, ~)C w i l l have an approximately chi-squared d i s t r i b u t i o n with n-m degrees of freedom and 2 31 '"X /n-m should then be approximately unity . Then i f one puts a^ 2 = J- 2 (y/)2 (the standard d e v i a t i o n i n y^) , ~)C /n-m w i l l be approximately unity i f y. —> y. f o r a l l i . i i The function used to represent portions of spectra containing peaks was the sum of Gaussian peaks superimposed on a l i n e a r background. That i s 2 \ = exp ( 41n 2 ( ) ) j = 1 j + a + ib In t h i s equation J = number of peaks i n the portion of spectrum 89 th H.. = height of the j — peak i = channel number j = p o s i t i o n of the peak i n channels = FWHM of the peak i n channels a + ib = l i n e a r background. A computer program was written to f i t t h i s function to the experi-mental data using the method described above. The input requirements of the program are the number of channels, the counts i n each channel, the number of peaks, the convergence c r i t e r i a , and the i n i t i a l estimates of /i^ and lu y The program estimates i n i t i a l values f o r Ry a and b. The output of the program contains the f i n a l estimates of the para-me ters U., u)., H., a and b, along with th e i r standard deviations, 0"", . J J J K I t also contains the value of y. at each channel, the value of y.. = H. exp (4 In 2 ( =*) ) (the f i t t e d peak minus background) f o r each U). J channel, the i n t e n s i t y of each peak ( I . = (• Y 0)h H. VO.) J 4 In 2 j j 2 with i t s standard deviation, and the goodness of f i t parameter, "% /n-m. 90 REFERENCES 1 Siegbahn, K. (Ed.); Beta- and Gamma-Ray Spectroscopy, North-Holland Publishing Co. (1955). 2 Siegbahn, K. (Ed.); Alpha-, Beta-, and Gamma Ray Spectroscopy, North-Holland Publishing Co. (1965) 3 Feenberg, E., and Trigg, G.; Rev. Mod. Phys. _22 399 (1950). 4 Fermi, E.; Nuclear Physics, U n i v e r s i t y of Chicago Press (1949). 5 De Benedetti, S.; Nuclear Interactions, John Wiley and Sons (1964). 6 Evans, R. D.; The Atomic Nucleus, McGraw-Hill (1950). 7 S l i v , L. A. and Band, I. M.; C o e f f i c i e n t s of Internal Conversion of Gamma Radiation, Academy of Sciences, U. S. S. R. 8 Rose, M. E. : Internal Conversion C o e f f i c i e n t s , North-Holland Publishing Co. (1958). 9 Goulding, F. S.; Nucl. I n s t r . and Meth. 43 1 (1966). 10 Fano, U.; Phys. Rev. 70 44 (1946), and Phys. Rev. 72 26 (1947). 11 Pehl, R. H. , Goulding, F. S., Landis, D. A., and Lenzlinger, M.; Nucl. Instr. and Meth. 54 45 (1968). 12 A P r a c t i c a l Guide to Semiconductor Detectors; Technical Measurements Corp. 13 Bothe, W.; Z. Naturf., 4a 542 (1949). 14 Planskoy, B.; Nucl. I n s t r . and Meth. 61 285 (1968). 15 Kevex Technical Report, November 1967. 16 Tennelec Sale Sheet. 17 Dalby, D. A.; M.Sc. Thesis, U n i v e r s i t y of B r i t i s h Columbia. 18 Lederer, C. M., Hollander, J. M. and Perlman, I.; Table of Isotopes Sixth E d i t i o n , John Wiley & Sons. 19 Wapstra, A. H., Nijgh, G. J . , and Van Lieshout, R.; Nuclear Spectroscopy Tables, North-Holland Publishing Co. 91 20 Handbook of Chemistry and Physics, Chemical Rubber Publishing Co. 21 Zyryanova, L. N.; Once Forbidden Beta-Transitions, I n t e r n a t i o n a l Series of Monographs on Nuclear Energy, Pergamon Press (1963). 22 Ng, L. K. ; Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia. 23 Charoenkwan, P.; Nucl. I n s t r . and Meth. 34 93 (1965). 24 Bosch, H., Krmpotic, F., and P l a s t i n o , A.; Nucl. I n s t r . and Meth. 23 79 (1963). 25 Rester, D. H. and Rainwater, W. J.; Nucl. Instr. and Meth. _41 51 (1966). 26 Blok, L., Goedbloed, W., Mastenbroek, E., and Blok, J.; Physica 28 993 (1962). 27 Cretzu, T., Holmuth, K., and Winter, G.; Nucl. Phys. _56 415 (1964). 28 Alexander, P.; Phys. Rev. 134 B499 (1964). 29 Graham, R. L. and Geiger, J. S.; B u l l . Am. Phys. Soc. JJ. 369 (1966). 30 Boyer, P. Chedin, P. and Oms, J.; Nucl. Phys. A99 213 (1967). 31 Helmer, R. G., Heath, R. L., Putnam, M. and Gipson, D. H.; Nucl. I n s t r . and Meth. J57 46 (1967). 32 Freund, J. E.; Mathematical S t a t i s t i c s , P r e n t i c e - H a l l (1962). 33 Brysk, H. and Rose, M. E.; Rev. Mod. Phys. 30 1169 (1958). 34 Nuclear Equipment Corp.; Technical Report. 

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