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A positron spectrometer Brown, Charles Grant 1970

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A POSITRON SPECTROMETER by CHARLES GRANT BROWN B . A . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1 9 6 7 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of PHYSICS We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard from candidates f o r the degree of MASTER OF APPLIED SCIENCE THE UNIVERSITY OF BRITISH COLUMBIA September, 1 9 7 0 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Charles Grant Brown Depar tment o f PHYSICS The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8 , Canada Date 2Q September 1970 ABSTRACT The e x i s t i n g i n t e r m e d i a t e image n u c l e a r spectrometer has been m o d i f i e d t o count e i t h e r p o s i t r o n s or negatrons by the a d d i t i o n of a h e l i c a l b a f f l e . Design c o n s i d e r a t i o n s of the h e l i c a l b a f f l e and source requirements f o r the present i n v e s t i g a t i o n have been d i s c u s s e d . An i n v e s t i g a t i o n of the p o s i t r o n spectrum of ^"^Eu has been completed. K u r i e - p l o t a n a l y s i s of the data has confirmed the presence of two primary p o s i t r o n groups with end p o i n t e n e r g i e s 7 1 3 - 5 ^ 2KeV and 4 7 1 ± 5KeV, and i n t e n s i t i e s ( 1 . 0 ± ' 0 . 1 ) x 1 0 ~ ^ per decay and ( 0 . 6 ^ 0 . 2 ) x 1 0 ~ ^ per decay r e s p e c t i v e l y . I t has been p o s s i b l e t o a s s i g n e r r o r l i m i t s t o these i n t e n s i t i e s f o r the f i r s t time. The presence of an i n t e r n a l p a i r f o r m a t i o n p o s i t r o n d i s t r i b u t i o n has a l s o been confirmed. The i n t e n s i t y of the p a i r f o r m a t i o n p o s i t r o n s was deduced from the data f o r the f i r s t time as ( 0 . 4 ^ 0 . 0 5 ) x 10~^ per decay, i n good agreement with t h e o r e t i c a l p r e d i c t i o n s . The r e s u l t s are i n good agreement with p r e v i o u s i n v e s t i g a t i o n s , e x c e p t i n g the i n t e n s i t y of the 7 1 3 « 5 K e V primary p o s i t r o n group. The d i s p a r i t y may be caused by e f f e c t s due to source and backing t h i c k n e s s i n p r e v i o u s work. i i TABLE OF CONTENTS Page ABSTRACT.... i i LIST OF DIAGRAMS i v LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i i CHAPTER 1 - BETA DECAY (a) I n t r o d u c t i o n - N u c l e i and N u c l e a r S t a t e s 1 (b) B e t a Decay 2 ( c ) E x c i t e d S t a t e Decay...... 1 6 CHAPTER 2 - THE POSITRON SPECTROMETER (a) The I n t e r m e d i a t e Image M a g n e t i c S p e c t r o m e t e r 1 9 (b) M o d i f i c a t i o n s t o t h e S p e c t r o m e t e r . . . . 24 (c) O p t i m i z a t i o n 27 (d) The B e t a D e t e c t i o n C i r c u i t 30 CHAPTER 3 - SOURCE PREPARATION (a) R a d i o a c t i v e Source Requirements 38 (b) Source P r e p a r a t i o n f o r the C u r r e n t I n v e s t i g a t i o n 4 0 CHAPTER 4 - THE POSITRON DECAY OF J £u (a) P r e v i o u s I n v e s t i g a t i o n 4 4 (b) The C u r r e n t I n v e s t i g a t i o n 4 7 CHAPTER 5 " CONCLUSIONS' 58 REFERENCES 6 1 i i i LIST OF DIAGRAMS Page 14-1 A P a r t i a l Energy L e v e l Diagram Of N. 2 2 A T y p i c a l Energy L e v e l Diagram Of Negatron E m i s s i o n . 3 3 A T y p i c a l Energy L e v e l Diagram Of P o s i t r o n E m i s s i o n . 4 h A T y p i c a l Energy L e v e l Diagram Of E l e c t r o n Capture. 5 5 Dimensions and Angles Of The H e l i c a l B a f f l e . 2 9 i v LIST OF TABLES Page I The Gamow-Teller S e l e c t i o n Rules. 11 I I Spectrometer Performance. 24 I I I A Summary Of R e s u l t s . 5 6 v LIST OP FIGURES Page 1 A T y p i c a l Energy D i s t r i b u t i o n Of (3" P a r t i c l e s . 1 0 2 A T y p i c a l Energy D i s t r i b u t i o n Of p + P a r t i c l e s . 1 0 3 A Composite Primary D i s t r i b u t i o n . . 1 5 4 A K u r i e - p l o t Of A Composite Primary D i s t r i b u t i o n . 1 5 5 The I n t e r n a l P a i r Formation P o s i t r o n Energy D i s t r i b u t i o n . 1 8 6 The Spectrometer. 2 0 7 The A x i a l Magnetic F i e l d Of The Spectrometer. 2 1 8 A T y p i c a l Beta Spectrum. 2 3 9 Spectrometer R e s o l u t i o n . 2 3 10 The H e l i c a l B a f f l e . 2 8 1 1 The H e l i c a l B a f f l e - T r a n s m i s s i o n vs B a f f l e Angle. 3 1 1 2 The E f f e c t Of B a f f l e P l a t e Angle. 3 1 1 3 B l o c k Diagram - Tire Beta D e t e c t i o n C i r c u i t . 3 3 14 The Charge S e n s i t i v e Stage Of The D e t e c t o r And P r e a m p l i f i e r . 3 4 1 5 C i r c u i t Diagram - The Pulse Shaper. 3 7 1 6 The Source Holder And Source B a c k i n g . • 4 2 17 The Source D e p o s i t i o n Apparatus. 4 2 18 P a r t i a l Decay Scheme Of 1 5 2 E u . 4 5 1 9 The I n t e r n a l C o n v e r s i o n Peak At 1 9 7 - 8 K e V . 48 2 0 The I n t e r n a l C o n v e r s i o n Peak At 2 9 4 . 0 3 K e V . 49 .'• v i LIST OP FIGURES (cont'd) Page 2 1 The P o s i t r o n Data. 5 1 2 2 K u r i e - p l o t Of The Primary P o s i t r o n Groups. 5 3 2 3 The P o s i t r o n Data And F i t t e d D i s t r i b u t i o n s . 5 5 v i i ACKNOWLEDGEMENTS I would l i k e t o express my g r a t i t u d e t o Dr. K. C. Mann f o r h i s patience and guidance throughout the course of t h i s work. I am indebted to Mr. P. Taminga f o r the t e c h n i c a l a s s i s t a n c e provided i n p r e p a r i n g s o u r c e s , and to Mr. A. F r a s e r f o r the c o n s t r u c t i o n of the h e l i c a l b a f f l e . T h i s p r o j e c t was supported by a G r a n t - i n - A i d - o f - R e s e a r c h t o - D r . K. C. Mann by the N a t i o n a l Research C o u n c i l of Canada. v i i i 1 Chapter 1 - Beta Decay (a) I n t r o d u c t i o n - N u c l e i and Nuclear S t a t e s The n u c l e i of atoms are composed of heavy, s p i n I = \ p a r t i c l e s i n motion. These p a r t i c l e s , c a l l e d n ucleons, form a quantum-mechanical system and are of two k i n d s : p r o t o n s , with charge + e, s p i n I = §, and r e s t mass 9 3 8 . 2 5 6 ± 0 . 0 0 5 M e V 1 • neutrons, with no charge, s p i n 1 = |, and r e s t mass 9 3 9 . 5 5 0 ^ 0 . 0 0 5 MeV^. T h i s quantum-mechanical system can e x i s t o n l y i n d i s c r e t e energy s t a t e s , each of which may be u n i q u e l y c l a s s i f i e d by the p r o p e r t i e s of th a t s t a t e . A nucleus i s d e s c r i b e d , i n g e n e r a l , by the t o t a l number of nucleons, A,(the Mass Number) and by the number of protons, Z, (the Atomic Number). The p r o p e r t i e s commonly used to d e s c r i b e a s t a t e of the system a r e : the energy, W, the angular momentum (or s p i n ) , J , and the p a r i t y , T T . Other p r o p e r t i e s of some n u c l e a r s t a t e s are known. These i n c l u d e the e l e c t r i c a l and the magnetic moments and the l i f e t i m e s of the s t a t e s . The s t a t e s of a nucleus are i l l u s t r a t e d by an e n e r g y - l e v e l diagram. The s t a t e of lowest energy i s c a l l e d the ground s t a t e , and s t a t e s of hi g h e r energy are c a l l e d e x c i t e d s t a t e s . Diagram 1 shows part of the simple e n e r g y - l e v e l diagram of N i t r o g e n 14. The angular momentum (or s p i n ) , J , of a s t a t e i s the t o t a l a n gular momentum of the s t a t e i n u n i t s of t i . I t i s the v e c t o r sum of the s p i n s , I , of the nucleons. S p i n i s i n t e g r a l f o r even-A n u c l e i and h a l f - i n t e g r a l f o r odd-A n u c l e i , as r e q u i r e d by quantum mechanics. 2 W 2 5 . 1 0 MeV 0 — ^ 4 . 9 1 MeV 1 + 3 . 9 4 MeV 2 . 3 1 MeV 0 + Ground S t a t e 1 + Diagram 1 - A P a r t i a l Energy L e v e l Diagram 2 of 1 % . The p a r i t y , i f , of a s t a t e i s the symmetry of the wave f u n c t i o n of a s t a t e under r e f l e c t i o n of the c o - o r d i n a t e system. The p a r i t y operator has the eigenvalue plus or minus one ( u s u a l l y denoted simply +or - ) . Nuclear s t a t e s may decay to s t a t e s of lower t o t a l energy through the emission; of p a r t i c l e s from the n u c l e u s , the capture of atomic e l e c t r o n s , the emission of e l e c t r o m a g n e t i c r a d i a t i o n ( H r a y s ) , or the " I n t e r n a l - C o n v e r s i o n " process where an atomic e l e c t r o n i s e j e c t e d . In a l l cases the energy of the system i s conserved, (b) Beta Decay One of the processes of decay t o a s t a t e of lower energy i s Beta Decay. T h i s may take one of t h r e e forms: i ) Negatron E m i s s i o n - The simultaneous e m i s s i o n by the nucleus (Z,A) of an e l e c t r o n e~ , (negatron), and an a n t i n e u t r i n o , V , i s accompanied by a change of n u c l e a r s t a t e t o a s t a t e of the element (Z+1,A). The negatron ( p~ p a r t i c l e ) has a charge 3 r e s t mass 0 , 5 1 1 0 0 6 ± 0 . 0 0 0 0 0 2 M e V , and s p i n I = |. The a n t i n e u t r i n o , y, has no charge, r e s t mass l e s s than 0.2KeV (2xlO"VieV)1, and s p i n 1 = |. Diagram 2 i s a t y p i c a l energy-l e v e l diagram of e l e c t r o n e m i s s i o n . (Z,A) (Z+1,A) Diagram 2 - A T y p i c a l Energy L e v e l Diagram Of Negatron Emission. The energy, E Q , r e l e a s e d i n negatron e m i s s i o n i s g i v e n by the e q u a t i o n ^ : = Mn (Z,A) - M^CZ+ljA-) - m. - B ( Z ) + B ( Z + 1 ) * = M a(Z,A) - M«(Z+1,A) + B(Z+1)» - B ( Z + 1 ) Eqn. 1-1 where: M Z , A ) = the n u c l e a r mass of a nucleus of Atomic Number Z and Mass Number A. Ma(Z,A)= the atomic mass of an atom of Atomic Number Z and Mass Number A. me = the r e s t mass of a negatron or p o s i t r o n . B(Z) = the b i n d i n g energy of the Z atomic e l e c t r o n s of an atom of Atomic Number Z. B ( Z + l ) * = the b i n d i n g energy of the Z atomic e l e c t r o n s of the s i n g l y i o n i z e d atom of Atomic Number (Z+l).. 4 The q u a n t i t y B ( Z + 1 ) * - B(Z-HL) , the energy of s i n g l e i o n i z a t i o n of the (Z-KL,A) atom, i s u s u a l l y extremely s m a l l and i s n e g l e c t e d i i ) P o s i t r o n E m i s s i o n - The simultaneous e m i s s i o n by the nucleus (Z,A) of a p o s i t r o n e** and a n e u t r i n o y i s accompanied by a change of n u c l e a r s t a t e t o a s t a t e of the element ( Z - 1 , A ) . The p o s i t r o n ( ( 3 + p a r t i c l e ) has charge + e, r e s t mass 0 . 5 1 1 0 0 6 ± 0 .000002MeV 1 (the same as the ( i " p a r t i c l e ) , and s p i n I = \. The n e u t r i n o y has no charge, r e s t mass l a s s than 0.2KeV, and spin- I = §. Diagram 3 i s a t y p i c a l e n e r g y - l e v e l diagram of p o s i t r o n e m i s s i o n . (Z,A) (Z-1,A) Diagram 3 - A T y p i c a l Energy L e v e l Diagram Of P o s i t r o n Emission. The energy, r e l e a s e d i n p o s i t r o n e m i s s i o n i s g i v e n by the e q u a t i o n : E 0 = M„(Z,A) - M„ ( z - 1,A) - me - B ( Z ) + B ( Z - l ) * = M a(Z,A) - Ma. ( z - 1,.A) - 2mc + B ( Z - l ) * - B ( Z - l ) Eqn. 1-2 5 where: B ( Z - l ) * = the b i n d i n g energy of the Z atomic .electrons of the s i n g l y i o n i z e d atom of Atomic Number ( Z - l ) . i i i ) E l e c t r o n Capture - E l e c t r o n Capture (EC) i s the capture by the nucleus (Z,A) of an o r b i t a l atomic K - s h e l l e l e c t r o n e~, the simultaneous e m i s s i o n by the nucleus of a monoenergetic n e u t r i n o V, and an accompanying change of n u c l e a r s t a t e t o a s t a t e of the element (Z - 1,A). Negatron capture from other atomic s h e l l s (L,M,N) i s p o s s i b l e but l e s s l i k e l y . The energy r e l e a s e d i s gi v e n t o the n e u t r i n o , the onl y emitted p a r t i c l e . Diagram 4 i s an e n e r g y - l e v e l diagram of e l e c t r o n c a p t u r e . / (Z,A) /-EC ( Z - l , A ) Diagram 4 - A T y p i c a l Energy L e v e l Diagram Of E l e c t r o n Capture. The energy, E Q , r e l e a s e d i n e l e c t r o n capture i s g i v e n by the equation-^: E 0 = M n(Z,A) - M n(Z-l , A ) - h me - B (Z) - B(Z) +• B ( Z - l ) * = M a(Z,A) - M a(Z- 1,A) - B K ( Z ) +• B*(Z - 1 ) - B ( Z - l ) Eqn. 1-3 6 where: * B (Z) = t h e b i n d i n g energy of the captured atomic e l e c t r o n i n the (Z,A) atomic s t r u c t u r e . B * ( Z - l ) = t h e b i n d i n g energy of the Z - l atomic e l e c t r o n s of the e x c i t e d aton of Atomic Number(Z-l). P a r t i c l e s are emitt e d and/or absorbed i n each of the three beta decay p r o c e s s e s . In both negatron and p o s i t r o n e m i s s i o n , the energy r e l e a s e d i s shared between the negatron ( p o s i t r o n ) and the a n t i n e u t r i n o ( n e u t r i n o ) . In e l e c t r o n c a p t u r e , the energy r e l e a s e d i s c a r r i e d away by a monoenergetic n e u t r i n o , the only emitted p a r t i c l e . The c o n s e r v a t i o n laws demand t h a t n e u t r i n o s or a n t i -n e u t r i n o s be emitted i n these r e a c t i o n s . E x p e r i m e n t a l r e s u l t s show t h a t the e n e r g i e s of the emitt e d e l e c t r o n s form a continuum with end p o i n t energy E 0 . The "missing energy", c o r r e s p o n d i n g t o the d i f f e r e n c e between the e l e c t r o n energy and the end p o i n t energy, i s c a r r i e d away by the emitt e d n e u t r i n o . Energy i s thereby conserved. Furthermore, the phenomena of beta decay are those of n u c l e i making i s o b a r i c t r a n s i t i o n s ( Mass Number A remains c o n s t a n t ) . T h i s means t h a t the t o t a l a ngular momentum, J , of the nucleus must remain h a l f - i n t e g r a l ( f o r odd-A n u c l e i ) or i n t e g r a l (even-A n u c l e i ) . I t would not be p o s s i b l e f o r the nucleus t o emit a s i n g l e p a r t i c l e of s p i n §, such as the e l e c t r o n , because the nucleus i s composed of protons ( s p i n |) and neutrons ( s p i n § ) . Another s p i n | p a r t i c l e i s r e q u i r e d t o conserve angular momentum. C o n s e r v a t i o n of charge r e q u i r e s the second e m i t t e d p a r t i c l e t o have no charge. 4 P a u l i f i r s t p o s t u l a t e d the n e u t r i n o t o s a t i s f y these 7 requirements. C o n s e r v a t i o n of momentum due t o n e u t r i n o momentum was v e r i f i e d when i t became p o s s i b l e t o measure i n d i v i d u a l n u c l e a r r e c o i l s from beta e m i s s i o n . The e x i s t e n c e of the n e u t r i n o was confirmed-' by d e t e c t i n g the n e u t r i n o capture r e a c t i o n : The a n t i n e u t r i n o , V , i n negatron e m i s s i o n i s r e q u i r e d t o be an a n t i p a r t i o l e by the now e s t a b l i s h e d law of l e p t o n c o n s e r v a t i o n . That i s , the number of leptons minus the number of a n t i l e p t o n s i s a conserved q u a n t i t y . In t h i s case the nucleus (Z,A) co n t a i n s no leptons or a n t i l e p t o n s . Thus, i f a |3~ p a r t i c l e ( l e p t o n ) i s e m i t t e d , than the other p a r t i c l e e mitted must be an a n t i l e p t o n , nance an a n t i n e u t r i n o , ~V, S i m i l a r l y , i n p o s i t r o n e m i s s i o n the second p a r t i c l e i s r e q u i r e d to be a n e u t r i n o , ~p, while i n e l e c t r o n capture the em i t t e d p a r t i c l e i s r e q u i r e d t o be a n e u t r i n o , ^ . The energy d i s t r i b u t i o n of the emitt e d e l e c t r o n s (or p o s i t r o n s ) was f i r s t g i v e n by Fermi and i s : 2/+ P *>n + /3+ n(E)dE 2TT Eqn. 1 - 4 where: n(E)dE the p r o b a b i l i t y of e m i s s i o n of a |3* the energy i n t e r v a l [ E , E - d E j . the t o t a l energy of the (3 p a r t i c l e . p a r t i c l e i n E g the c o u p l i n g constant f o r the r e a c t i o n . the energy r e l e a s e d i n the decay. P the momentum of the e l e c t r o n ( p o s i t r o n ) . 8 F ( E , Z) = the c o r r e c t i o n t o the p r o b a b i l i t y d i s t r i b u t i o n due t o the i n t e r a c t i o n between the outgoing p a r t i c l e and the e l e c t r c s t a t i c f i e l d of the n u c l e a r charge Z. M = the n u c l e a r matrix element i n v o l v e d i n the t r a n s i t i o n . The f o l l o w i n g assumptions are made i n co n n e c t i o n with t h i s e q u a t i o n : t h a t the n e u t r i n o ( a n t i n e u t r i n o ) has zer o r e s t mass; and t h a t t h e . r e c o i l energy of the daughter nucleus i s n e g l i g i b l e . The n e u t r i n o r e s t mass has been shown t o be l e s s than 2KeV by y g Q 1 Q s e v e r a l experiments'' , y ' a n c j i s compatible with z e r o r e s t -mass.* R e c o i l energy of the nucleus i n the most s i g n i f i c a n t cases ( f o r example 1 2 B decay) i s at l e a s t t h r e e orders o f magnitude s m a l l e r than the end p o i n t energy. Thus, the assumptions made are v a l i d . The f a c t o r F(E,TZ) of eq u a t i o n 1-4 i s a Coulomb f i e l d f a c t o r (commonly c a l l e d the Fermi f a c t o r ) , a measure of the Coulomb a t t r a c t i o n ( f o r negatrons) or r e p u l s i o n ( f o r p o s i t r o n s ) due t o the n u c l e a r charge. T h i s f a c t o r i s important f o r a l l elements but those of low-Z. At high beta e n e r g i e s the f a c t o r has l i t t l e e f f e c t on the shape of the d i s t r i b u t i o n . As a consequence, f o r high-Z elements, the number of low energy, p o s i t r o n s i s reduced while the number of low energy negatrons i s i n c r e a s e d . The Coulomb f i e l d f a c t o r i s known t o be ( i n c l u d i n g r e l a t i v i s t i c e f f e c t s ) ^ : * A c c o r d i n g to the two component n e u t r i n o t h e o r y , the n e u t r i n o r e s t mass i s r e q u i r e d t o be z e r o . 9 F(E,=FZ) = 2 ( 1 - * ) (2pR) e M R H - i y ) 2 [ r t 2 « - i ) - 2 Eqn. 1 - 5 where: -Z Is used f o r p o s i t r o n s . +Z i s used f o r negatrons. * = (l-(«:z) 2)^ 0 0 = the f i n e s t r u c t u r e c o n s t a n t , y = otzE/p R = the n u c l e a r r a d i u s OCA . Values of F(E,:pZ) have been t a b u l a t e d f o r a l l p r a c t i c a l 12 13 14 cases. "* ' i f more accurate v a l u e s are necessary, W i l k i n s o n has summarized the methods of c a l c u l a t i n g these values and shown when approximations may be made. 1 5 F i g u r e s 1 and 2 show >+ the e f f e c t of the Coulomb shape f a c t o r on (3 and (3 d i s t r i b u t i o n s . E q u a t i o n 1-4 i s i n t e g r a t e d t o get the t o t a l p r o b a b i l i t y of decay P: P = n(E)dE = I g 2 E p ( E 0 - E ) 2 F ( E , : f Z ) l M l 2 d E J J Eqn. 1 - 6 The magnitude of the n u c l e a r matrix e l e m e n t , |M | , i s a measure of the o v e r l a p of the n u c l e a r wave f u n c t i o n s of the i n i t i a l and f i n a l s t a t e s . For the m a j o r i t y of cases i t may be shown t h a t I M I 2 i s energy independent, and of the form: Eqn. 1-7 where: C_ and C._ = the c o u p l i n g constants f o r the i n t e r a c t i o n , r GT 10 n(E) (9~Coulomb shape c o r r e c t i o n f a c t o r a p p l i e d .The two curves c o i n c i d e at h i g h e n e r g i e s E F i g u r e 1 - A T y p i c a l Energy D i s t r i b u t i o n Of (S~ P a r t i c l e s Showing The E f f e c t Of The Shape C o r r e c t i o n F a c t o r For |3~ P a r t i c l e s . n(E) shape c o r r e c t i o n f a c t o r The two curves o i n c i d e at high e n e r g i e s 'igure 2 - A T y p i c a l Energy D i s t r i b u t i o n Of /3 P a r t i c l e s Showing The E f f e c t Of The Shape C o r r e c t i o n F a c t o r For/3 + P a r t i c l e s . 11' Uf. and *U/ = the wave f u n c t i o n s of the I n i t i a l and f i n a l ' L If n u c l e i . Q + = the operator which changes a neutron i n t o a proton ( f o r negatron emission) but does not f l i p the s p i n . O M = the P a u l ! s p i n m a t r i c e s . The square of the magnitude of the n u c l e a r matrix element depends, then, upon the s p i n and p a r i t y of the i n i t i a l and f i n a l n u c l e a r s t a t e s . Thus f o r some t r a n s i t i o n s , t h a t i s f o r some A J andATr, we have c o n s i d e r a b l y reduced t o t a l p r o b a b i l i t y , P, of the decay. Those cases are d e s c r i b e d by the Gamow-T e l l e r s e l e c t i o n r u l e s , presented i n Table I . Each s u c c e s s i v e case i n the t a b l e has a lower p r o b a b i l i t y of decay than, the preceding case. Table I - The Gamow-Teller S e l e c t i o n R u l e s . 6 , 1 1 , 1 6 C l a s s Of The T r a n s i t i o n P a r i t y Change, A f f Angular Momentum Change, A T Allowed NO 0 , ± 1 F i r s t Forbidden Non-unique YES 0 , ± 1 (no 0 — 0 ) F i r s t F orbidden Unique YES ± 2 Second Forb i d d e n NO ± 2 Nuclear wave f u n c t i o n are not- w e l l known i n g e n e r a l , although n u c l e a r models give approximations t o them. Because 12 of t h i s l a c k of knowledge, n u c l e a r matrix elements f o r t r a n s i t i o n s may only be approximated themselves. T h e o r e t i c a l i n v e s t i g a t i o n s are able t o gi v e g e n e r a l forms f o r the square of the n u c l e a r matrix element, known as the shape c o r r e c t i o n f a c t o r . The form of the shape c o r r e c t i o n depends upon the type of the t r a n s i t i o n , t h a t i s upon the s p i n s and p a r i t i e s of i n i t i a l and f i n a l s t a t e s . E q u a t i o n 1-4 i s w r i t t e n i n the f o l l o w i n g form i n c l u d i n g the shape c o r r e c t i o n f a c t o r C : n(E)dE = CEpF(E,TZ) ( E D - E ) 2 d E Eqn. 1-8 For allowed decay ( A J = 0, ^1 ;Arr= NO ), the shape c o r r e c t i o n f a c t o r C<, i s a c o n s t a n t . The shape c o r r e c t i o n f a c t o r C, f o r f i r s t f o r b i d d e n t r a n s i t i o n s ( A J = 0 , ± l , i 2 ; A.Tf=YES J has the g e n e r a l form : where: E = the t o t a l ( 3 - p a r t i c l e energy. p = the ( 3 - p a r t i c l e momentum. q = the n e u t r i n o ( a n t i n e u t r i n o ) momentum. "X = a constant which depends upon Z and upon the end p o i n t energy.. k,a,b,c = constants which are f u n c t i o n s of the n u c l e a r wave f u n c t i o n . Of i n t e r e s t t o the c u r r e n t i n v e s t i g a t i o n i s the shape c o r r e c t i o n f a c t o r f o r the f i r s t f o r b i d d e n non-unique t r a n s i t i o n s . 1 3 In g e n e r a l , the shape c o r r e c t i o n f a c t o r f o r non-unique decay i s i n d i s t i n g u i s h a b l e from the allowed case because k i s v e r y l a r g e , and a,b,c are s m a l l . 1 1 > ^ K o t a n i and R o s s 1 ? and o t h e r s ^ , 1 9 have shown t h a t i n some cases t h i s i s not the case and t h a t the f i r s t forbicJden non-unique shape c o r r e c t i o n f a c t o r may be approximated as: C = ' X p ^ - f q ^ + D Eqn. 1-10 where: D = a constant t o be determined f o r each i s o t o p e . The shape c o r r e c t i o n f a c t o r , C, p r o v i d e s a u s e f u l t o o l f o r a n a l y s i s of experimental beta decay data. The square of nu c l e a r matrix element, | M | , i s not known e x a c t l y because of the l a c k of knowledge of the n u c l e a r wave f u n c t i o n s of most n u c l e i . However, the g e n e r a l form of C i s known f o r the cases above and f o r other t r a n s i t i o n s . The a p p l i c a t i o n of the shape c o r r e c t i o n f a c t o r w i l l be d i s c u s s e d below. A parent nucleus may decay through ( 3 - p a r t i c l e e m i s s i o n (among other processes) t o one or more s t a t e s of the daughter nucleus or n u c l e i . Each t r a n s i t i o n w i l l g i ve r i s e t o a (3-particle energy d i s t r i b u t i o n with a unique end p o i n t energy and shape. These d i s t i n c t , independent energy d i s t r i b u t i o n s are c a l l e d primary beta groups. When the energy d i s t r i b u t i o n n(E)dE (Eqn. 1-4) of a primary beta group i s p l o t t e d , the d i s t r i b u t i o n i s g e n e r a l l y b e l l - s h a p e d ( F i g u r e s 1 and 2 ) . I f an i s o t o p e decays through two or more primary |3 groups (or through two or more primary j3 groups), then the e x p e r i m e n t a l 14 d i s t r i b u t i o n w i l l be a composite |3 d i s t r i b u t i o n ( F i g u r e 3)« Primary beta groups are ana l y s e d by the K u r i e - p l o t method. I f we w r i t e e q u a t i o n 1-8 i n the f o l l o w i n g form: / n(E) = E n - E V CpEF Eqn. 1-11 i t i s c l e a r t h a t a p l o t of the LHS versus E should be a s t r a i g h t l i n e . Thus i f . the shape c o r r e c t i o n f a c t o r , C, i s known, the end p o i n t energy E 0may be a c c u r a t e l y found. A l s o , i f the end p o i n t energy i s known, the shape c o r r e c t i o n f a c t o r may be a c c u r a t e l y f i t t e d . In f a c t , both E 0 and C may be f i t t e d t o experimental d a t a . In a d d i t i o n , K u r i e - p l o t a n a l y s i s p r o v i d e s a method of s e p a r a t i n g one primaty beta group from a composite of two or more groups. For example, the K u r i e - p l o t of a composite d i s t r i b u t i o n of two (3 groups, n, (E) - n2(E), E Q | ) Eoz , w i l l have the mathematical form: /n, (E) + n 2 ( E ) V CpEF —1 = ( n o n l i n e a r f u n c t i o n of E) f o r E <E o £ Eot " E f o r 2o2.<£<E o l v/CpEP V Eqn. 1-12 C l e a r l y , the K u r i e - p l o t i n the r e g i o n E C 2 ( E ( E o i w i l l be a s t r a i g h t l i n e ( F i g u r e 4 ) , while the p l o t f o r E^EQJ, w i l l d i v e r g e n o t i c e a b l y from the s t r a i g h t l i n e . T h i s allows a s t r a i g h t l i n e t o be f i t t e d t o the r e g i o n E 0 2 ( E < E 0 , of the K u r i e - p l o t . The d i s t r i b u t i o n n,(E) over the e n t i r e energy range O ( E ( E 0 1 may then be s u b t r a c t e d from the composite d i s t r i b u t i o n n , ( E ) + n^(E) l e a v i n g the second group n ^ E ) . T h i s procedure may be repeated. 1 5 n(E) Figure 4 - A Kurie-plot Of A Composite Primary (3 D i s t r i b u t i o n . 16 s u c c e s s i v e l y s u b t r a c t i n g the beta group of h i g h e s t end p o i n t energy from the remaining composite group, t o decompose m u l t i -group d i s t r i b u t i o n s . The success o f the K u r i e - p l o t method i s due t o the f a c t t h a t each beta group has an independent p r o b a b i l i t y d i s t r i b u t i o n , (c) E x c i t e d S t a t e Decay A nucleus (Z,A) which i s i n an e x c i t e d s t a t e may decay t o a s t a t e of lower t o t a l energy of the same nucleus i n s e v e r a l ways. Among these a r e : the e m i s s i o n of e l e c t r o m a g n e t i c quanta (gamma r a y s ) ; the e j e c t i o n of atomic e l e c t r o n s ( " i n t e r n a l c o n v e r s i o n " ) * ; or the e m i s s i o n of a p o s i t r o n - e l e c t r o n p a i r ( i n t e r n a l p a i r f o r m a t i o n ) * * . Only i n t e r n a l p a i r f o r m a t i o n i s of i n t e r e s t t o the c u r r e n t i n v e s t i g a t i o n . The t r a n s i t i o n energy must be g r e a t e r than twice the e l e c t r o n r e s t mass (t h a t i s , g r e a t e r than 1.022MeV) i n order f o r i n t e r n a l p a i r f o r m a t i o n t o occur . In a d d i t i o n , the s p i n and p a r i t y changes of the t r a n s i t i o n must be f a v o u r a b l e t o i n t e r n a l p a i r f o r m a t i o n . T h e o r e t i c a l c a l c u l a t i o n s of the I n t e r n a l P a i r Formation C o e f f i c i e n t * * have been made u s i n g the Born approx-i m a t i o n , ^ the exact Coulomb wave f u n c t i o n s o l u t i o n s of the 01 22 Di r a c e q u a t i o n , and the Sch r o d i n g e r approximation . These * We d e f i n e the I n t e r n a l C o n v e r s i o n C o e f f i c i e n t oc f o r a p a r t i c u l a r s h e l l as the r a t i o of the p r o b a b i l i t y of e j e c t i o n of an e l e c t r o n from t h a t p a r t i c u l a r s h e l l t o the p r o b a b i l i t y of gamma e m i s s i o n . **We d e f i n e the I n t e r n a l P a i r Formation C o e f f i c i e n t as the r a t i o of the p r o b a b i l i t y of i n t e r n a l p a i r f o r m a t i o n t o the p r o b a b i l i t y of gamma e m i s s i o n . 17 c a l c u l a t i o n s have been c a r r i e d out f o r both low and hig h Z n u c l e i and f o r both e l e c t r i c and magnetic m u l t i p o l e s of m u l t o p o l a r i t y J L 1 1 The T h e o r e t i c a l c a l c u l a t i o n s have been 11 23 shown t o f i t e x p e r i m e n t a l data v e r y w e l l . ' T h e o r e t i c a l c a l c u l a t i o n s of the p o s i t r o n energy d i s t r i b u t i o n , [~~'(Ejg^dEp+, f o r i n t e r n a l p a i r f o r m a t i o n have a l s o been made. The energy d i s t r i b u t i o n a l s o depends upon the m u l t i p o l a r i t y of the t r a n s i t i o n i n v o l v e d . A gain, the t h e o r e t i c a l 11 21 22 23 20 c a l c u l a t i o n s f i t the experimental data v e r y w e l l . 3 ' ' ' Of i n t e r e s t t o the present i n v e s t i g a t i o n i s the p o s i t r o n energy d i s t r i b u t i o n f o r an e l e c t r i c d i p o l e (1=1) or E l t r a n s i t i o n . F o r an E l t r a n s i t i o n the s e l e c t i o n r u l e s governing the change of s p i n and p a r i t y from i n i t i a l t o f i n a l s t a t e a r e : A J = 0, ^ =1; Alt =YES. The p o s i t r o n energy d i s t r i b u t i o n , a c c o r d i n g t o the Schro d i n g e r approximation t o the D i r a c e q u a t i o n , i s g i v e n by the e q u a t i o n : H E W - ) d E / y = 46Tr^3Eflf E^3- dE f o r E l t r a n s i t i o n s Eqn. 1 - 1 3 where: EA+ and En- = the e n e r g i e s of the p o s i t r o n and the ' negatron r e s p e c t i v e l y . pfi+ and p _ = the momenta of the p o s i t r o n and the ' r negatron r e s p e c t i v e l y . k = the t r a n s i t i o n energy. T h i s energy d i s t r i b u t i o n i s shown g r a p h i c a l l y i n F i g u r e 19 Chapter 2 - The P o s i t r o n Spectrometer T h i s chapter d e s c r i b e s the m o d i f i c a t i o n s t o the inte r m e d i a t e image spectrometer i n t h i s l a b o r a t o r y t o enable measurements t o be made of the p o s i t r o n component i n the b e t a -152 decay of J Eu. (a) The Intermediate Image Magnetic Spectrometer The spectrometer i n use i n t h i s l a b o r a t o r y i s the twin lens 24 intermediate image type developed by S l a t i s and Siegbahn and developed here i n 1 9 6 6 - 1 9 6 7 25 F i g u r e 6 giv e s an a x i a l c r o s s -s e c t i o n of the spectrometer. The p r i n c i p a l elements of the spectrometer are the two t h i n e l e c t r o m a g n e t i c l e n s e s , s eparated t o give the c h a r a c t e r i s t i c a x i a l magnatic f i e l d (shown i n F i g u r e 7 ) . The f i e l d i s a minimum a t the geometric c e n t e r of the spectrometer. T h i s f i e l d c o n f i g u r a t i o n b r i n g s the beta p a r t i c l e envelope t o an ' i n t e r m e d i a t e ' r i n g focus at the p o s i t i o n of minimum f i e l d . The advantage of t h i s i s t h a t the c o n c e n t r a t i o n of the e l e c t r o n beam a t the r i n g focus makes i t p o s s i b l e t o use a narrow b a f f l e at t h i s p o s i t i o n t o absorb non-focussed beta p a r t i c l e s . A f t e r p a s s i n g through the r i n g f o c u s , the beta p a r t i c l e envelope d i v e r g e s a g a i n and then r e f o c u s s e s on the a x i s . A f u r t h e r advantage i s t h a t the i v - , s p h e r i c a l a b e r r a t i o n at the second focus i s reduced, r e s u l t i n g i n a s m a l l e r image s i z e and a l l o w i n g the use of a s m a l l e r d e t e c t o r . The d e t e c t o r , however, i s s t i l l about f i f t y percent l a r g e r than the so u r c e . The r a d i o a c t i v e source and the s u r f a c e b a r r i e r type s i l i c o n d e t e c t o r are p o s i t i o n e d at opposite ends of the 150 cm 20 . 8 c m 33cm 21cm A - Source B - D e t e c t o r C - Ring b a f f l e D -. H e l i c a l b a f f l e E - Pb cone F - D e t e c t o r b a f f l e G - D e t e c t o r b i a s t r a n s f e r box _ 3cm 2 . 2 5 c m lcm 3 1 . 9 c m 3 7 . 5 c m 4 1 . 7 c m 6 9 . 3 c m 100 . 2 c m F i g u r e 6 - The Spectrometer ( A x i a l Cross S e c t i o n ) . Magnetic F i e l d (Gauss) 4 5 0 400 3 5 0 3 0 0 . 2 5 0 2 0 0 1 5 0 . Length of b a f f l e p l a t e s 4cm 9Gauss T o 2 ( 5 3 o " zTo" 5 t T " T O " F i g u r e 7 - The A x i a l Magnetic F i e l d Of The Spectrometer. JL V a r i a t i o n i n magnetic f i e l d over the l e n g t h of the b a f f l e p l a t e s — 7 7 J fe" $0" A x i a l Length (cm) 2 2 evacuated chamber, near the maxima of the f i e l d . Both source and e.etector may be moved a x i a l l y by e x t e r n a l c o n t r o l s . In a d d i t i o n , the source may be moved by e x t e r n a l c o n t r o l s i n a plane p e r p e n d i c u l a r t o the spectrometer a x i s . The l a t t e r a l l o w s 'extremely a c c u r a t e c e n t e r i n g of the source on the spectrometer a x i s . The magnetic f i e l d f o c u sses an envelope of beta p a r t i c l e s of a s p e c i f i c momentum, p, onto the d e t e c t o r . Aluminum b a f f l e s are p l a c e d near the sour c e , at the f i e l d minimum, and near the d e t e c t o r . The b a f f l e s determine the s i z e of the beta p a r t i c l e envelope by a b s o r b i n g non-focussed p a r t i c l e s . The source b a f f l e prevents other envelopes from p a s s i n g through the r i n g b a f f l e ( a t the f i e l d minimum) a f t e r m u l t i p l e r o t a t i o n s i n the f i e l d . The r i n g b a f f l e absorbs p a r t i c l e s of the wrong momentum. The d e t e c t o r b a f f l e prevents the d e f l e c t i o n of s c a t t e r e d e l e c t r o n s or ph o t o - e l e c t r o n s onto the d e t e c t o r . Beta s p e c t r a w i l l o f t e n e x h i b i t the i n t e r n a l c o n v e r s i o n peaks mentioned i n Chapter 1 ( a ) , e i t h e r superimposed upon the primary beta continuum, or beyond the primary beta end p o i n t . These peaks (or l i n e s ) p r ovide a convenient means of determ i n i n g the spectrometer r e s o l u t i o n . The r e s o l u t i o n , R , of a spectrometer i s d e f i n e d as:, ^ p ~lp0 , expressed as a percentage, Where; p e i s the e l e c t r o n momentum at the maximum of an i n t e r n a l c o n v e r s i o n l i n e , and Ap i s the f u l l width of the l i n e at h a l f -siaxiEHiaD (see F i g u r e 9 ) . The t r a n s m i s s i o n , v T , of a spectrometer i s the f r a c t i o n of beta p a r t i c l e s of momentum p;l@aving the ;-source and r e a c h i n g the d e t e c t o r . 23 F i g u r e 9 - Spectrometer R e s o l u t i o n R From An I n t e r n a l C o n v e r s i o n Peak. 2 4 With the present spectrometer, the e x i s t e n c e of the int e r m e d i a t e image and the s m a l l image s i z e permits a hig h r e s o l u t i o n (low percentage) while a l l o w i n g a high t r a n s m i s s i o n . P r e v i o u s work i n t h i s l a b o r a t o r y has shown t h i s spectrometer t o 2 5 , 2 6 be v e r y f l e x i b l e . Table I I g i v e s r e s o l u t i o n s and t r a n s m i s s i o n s o b t a i n e d w i t h sources of v a r i o u s diameters and a p p r o p r i a t e b a f f l e s . 2 5 T a b l e I I - Spectrometer Performance . Source Diameter (mm) R e s o l u t i o n R {%) T r a n s m i s s i o n T (*) 0 . 6 0 . 5 1 0 . 4 9 0 . 9 0 . 7 0 O . 9 6 1 . 2 0 . 9 4 1 . 2 6 2 . 5 2 . 2 5 . 9 6 E l e c t r o n s of a p a r t i c u l a r momentum, p, are fo c u s s e d by the spectrometer. The momentum, p, i s d i r e c t l y p r o p o r t i o n a l t o the c u r r e n t i n the e l e c t r o m a g n e t i c l e n s e s , s i n c e no i r o n i s used. In the present i n v e s t i g a t i o n , the c u r r e n t i s s e t by a d i a l p o tentiometer i n the c u r r e n t r e g u l a t o r c i r c u i t . Thus, the momentum of the focussed bate p a r t i c l e s i s d i r e c t l y p r o p o r t i o n a l t o the potentiometer s e t t i n g . Momenta w i l l be expressed i n terms of d i a l potentiometer s e t t i n g (or j u s t POT) f o r the remainder.of t h i s t h e s i s , (b) M o d i f i c a t i o n s t o the Spectrometer Charged p a r t i c l e s moving i n e x t e r n a l e l e c t r i c and magnetic 2 5 f i e l d s a r e . s u b j e c t to the Lorentz F o r c e * . We have an a x i a l magnetic f i e l d and no e l e c t r i c f i e l d i n the present case.. E l e c t r o n s emerging from the source are r e s t r i c t e d to a s m a l l envelope by the source b a f f l e . As a consequence of the Lor e n t z F o r c e , the emergent e l e c t r o n s w i l l d e s c r i b e a h e l i c a l t r a j e c t o r y of v a r y i n g r a d i u s as they t r a v e l from source t o d e t e c t o r . P o s i t r o n s and ncgatrons t r a v e l i d e n t i c a l paths except t h a t the sense of h e l i c i t y i s : r e v e r s e d . A c o r r e c t l y designed b a f f l e w i t h vanes, or p l a t e s , p a r a l l e l t o one of the h e l i c a l t r a j e c t o r i e s w i l l a llow e i t h e r p o s i t r o n s or negatrons (but not both) t o pass through (see F i g u r e 10). T h i s ' h e l i c a l ' b a f f l e then permits the s e p a r a t i o n of the p o s i t r o n and the negatron s p e c t r a . 2 7 A l b e r g e r et a l made use of two h e l i c a l b a f f l e s , one on e i t h e r s i d e of the ce n t e r annular b a f f l e ( r i n g b a f f l e ) i n a s i m i l a r t h i n lerts i n t e r m e d i a t e image spectrometer. The b a f f l e s c o n s i s t e d of 48 f l a t p l a t e s of 6 .5cm a x i a l l e n g t h and one s i x t e e n t h inch t h i c k n e s s each. The two h e l i c a l b a f f l e s were : a l i g n e d o p t i c a l l y i n an e f f o r t t o reduce the l o s s of t r a n s m i s s i o n due t o non - a l i g n e d b a f f l e s . A c o n s i d e r a t i o n i n the de s i g n of the h e l i c a l b a f f l e i s the a x i a l l e n g t h of the b a f f l e p l a t e s . The e l e c t r o n t r a j e c t o r i e s are not, i n f a c t , s t r a i g h t l i n e s , but are curved. I t i s not p r a c t i c a l t o make curved b a f f l e p l a t e s , so' f l a t p l a t e s are used. In u s i n g f l a t b a f f l e p l a t e s , one must choose the r e g i o n of the * L o r e n t z Force "F = q (E~ + "vxB), where: E*""= the e l e c t r i c f i e l d ; B = the magnetic f i e l d ; q = the charge of the p a r t i c l e ; v*"= the v e l o c i t y of the p a r t i c l e . 26 e l e c t r o n t r a j e c t o r y t h a t best approximates a s t r a i g h t l i n e . T h i s i s the r e g i o n where t h e r e i s the l e a s t change of the magnetic f i e l d s t r e n g t h over the a x i a l l e n g t h of the b a f f l e p l a t e s . I f the p l a t e s are e x c e s s i v e l y l o n g , a s t r a i g h t l i n e w i l l be a poor approximation t o the t r a j e c t o r y . The r e s u l t i s a s i g n i f i c a n t l o s s of t r a n s m i s s i o n as e l e c t r o n s curve i n t o the b a f f l e p l a t e s . I t was found i n the c u r r e n t work t h a t the l o s s e s of t r a n s m i s s i o n due t o two separate h e l i c a l b a f f l e s (as used by A l b e r g e t a l ) exceeded the gains p e r m i t t e d by s h o r t e r ( a x i a l l y ) p l a t e s . The l o s s e s were due t o i n a c c u r a c y In alignment of the two b a f f l e s which caused an i n c r e a s e i n b a f f l e c r o s s - s e c t i o n a l a r e a . (The gains were due t o (shorter a x i a l l e n g t h of p l a t e s . because the magnetic f i e l d v a r i e s l e a s t about the minimum of the f i e l d . That i s , on e i t h e r s i d e of the annular b a f f l e . ) Consequently, a h e l i c a l b a f f l e with 6 0 f l a t p l a t e s o n l y 4 c m l ong ( a x i a l l y ) was c o n s t r u c t e d . I t was p o s s i b l e t o v a r y the angle of the p l a t e s r e l a t i v e t o the spectrometer a x i s . The 4 c m l e n g t h corresponded t o a v a r i a t i o n of l e s s than 5 $ i n magnetic f i e l d s t r e n g t h over the a x i a l l e n g t h of the b a f f l e (see F i g u r e 7 ) and made a reasonable approximation t o the s l i g h t l y curved t r a j e c t o r y . Because of the extremely- low i n t e n s i t y of p o s i t r o n decay i n the c u r r e n t i n v e s t i g a t i o n , i t was found ne c e s s a r y t o lower the background count r a t e . The background count r a t e ©as composed of e l e c t r o n i c noise i n h e r e n t i n the d e t e c t i o n c i r c u i t ( d e t e c t o r , p r e a m p l i f i e r , e t c . ) and of t r u e background counts due to gamma rays from the s o u r c e . I t was e s t a b l i s h e d t h a t t r u e 2 7 background counts due t o cosmic r a d i a t i o n , and t o r a d i o a c t i v e i m p u r i t i e s i n the spectrometer and surroundings were n e g l i g i b l e . The e l e c t r o n i c n o i s e was measured as one q u a r t e r of the t o t a l background count r a t e by removing the source from the spectrometer. To reduce the background count r a t e , a c o n i c a l p i e c e of Lead (covered w i t h approximately one s i x t e e n t h i n c h of Aluminum on a l l s u r f a c e s ) was p l a c e d on the spectrometer a x i s between the source and the h e l i c a l b a f f l e (see F i g u r e 6 ) . The a x i a l , l e n g t h of, the Lead was 3 i n , or about e i g h t h a l f - t h i c k n e s s e s of Lead f o r the a b s o r p t i o n of the most e n e r g t i c gamma ra y s expected from the s o u r c e . F o l l o w i n g the placement of the Lead cone, the background count r a t e dropped t o , e s s e n t i a l l y , the e l e c t r o n i c noise count r a t e . By r e v e r s i n g the c u r r e n t through the magnetic c o i l s , i t was p o s s i b l e t o focus e i t h e r p o s i t r o n s or negatrons as d e s i r e d , (c) O p t i m i z a t i o n The f i r s t s t e p i n the o p t i m i z a t i o n procedure was the s e t t i n g of the angle of the h e l i c a l b a f f l e p l a t e s . I t was found i n p r e l i m i n a r y work wi t h the two h e l i c a l b a f f l e s mentioned e a r l i e r , t h a t an angle of approximately 15° between the b a f f l e p l a t e s and the spectrometer a x i s gave maximum t r a n s m i s s i o n . The c u r r e n t through the magnetic c o i l s was such t h a t negatrons would pass through the h e l i c a l b a f f l e and p o s i t r o n s would h i t the b a f f l e „ 1 5 2 p l a t e s and be absorbed. A v e r y t h i c k source of Eu of about 1 . 5 m m diameter was used f o r the angle o p t i m i z a t i o n procedure. Thus, very high negatron count r a t e s were a v a i l a b l e and s t a t i s t i c s b e t t e r than .1% s t a n d a r d d e v i a t i o n were o b t a i n e d . 2 9 I t was expected t h a t the t r a n s m i s s i o n would show a d e f i n i t e maximum as the c o r r e c t b a f f l e p l a t e angle was approached. The t r a n s m i s s i o n of the h e l i c a l b a f f l e may be w r i t t e n : T r a n s m i s s i o n = _d. = 1 - Sino£ - S i n Qf P P i Eqn. 2 - 1 assuming a s t r a i g h t l i n e t r a j e c t o r y , where: 1 = the l e n g t h of the b a f f l e p l a t e s . p = the p i t c h , or d i s t a n c e between b a f f l e p l a t e s p e r p e n d i c u l a r t o the spectrometer a x i s . oc = the angle of the b a f f l e p l a t e s . & = the angle between the e l e c t r o n beam and the spectrometer a x i s . d = the width of the e l e c t r o n beam allowed t o pass through two adjacent b a f f l e p l a t e s . The t r a n s m i s s i o n of the h e l i c a l b a f f l e reaches a maximum of 1 . 0 (or 1 0 0 $ ) when cC= (y. Diagram 5 shows the above dimensions and a n g l e s . spectrometer a x i s e l e c t r o n beam b a f f l e p l a t e s Diagram 5 . - Dimensions And Angles Of The H e l i c a l B a f f l e . 30 The t r a n s m i s s i o n of the h e l i c a l b a f f l e behaved as expected when the b a f f l e angle was v a r i e d . F i g u r e 11 shows the v a r i a t i o n of t r a n s m i s s i o n with b a f f l e a n g l e . F i g u r e 12 shows the e f f e c t of b a f f l e angle upon the 294.03KeV K - I n t e r n a l C o n v e r s i o n peak of 1 5 2 E u (the 344.27KeV 1 5 2 G d t r a n s i t i o n ) . The optimum b a f f l e angle was 15.5°, which gave a b a f f l e t r a n s m i s s i o n of 76$. Of the 2k% l o s s of t r a n s m i s s i o n due t o the b a f f l e , 15$ was due t o the c r o s s - s e c t i o n of the b a f f l e caused by the t h i c k n e s s of each b a f f l e p l a t e . The remaining 9$ l o s s was due t o cur v a t u r e of the e l e c t r o n t r a j e c t o r y and to u n c e r t a i n t y of the b a f f l e p l a t e a n g l e . The spectrometer was used i n the high t r a n s m i s s i o n c o n f i g u r a t i o n f o r the low energy range, 25KeV t o 1.5MeV 2S developed by Walton i n t h i s l a b o r a t o r y . . (See T a b l e I I ) T h i s c o n f i g u r a t i o n allows a r e s o l u t i o n of 2.1% at the 197.84KeV K - I n t e r n a l C o n v e r s i o n peak u s i n g a source diameter of 2.8mm. The width of the annular s l i t at the in t e r m e d i a t e focus i s 2.5mm., which i s the optimum s l i t width f o r the source b a f f l e s used. (d) The Beta D e t e c t i o n C i r c u i t The beta p a r t i c l e s were d e t e c t e d by a s u r f a c e b a r r i e r type s i l i c o n c r y s t a l with 20 v o l t s b i a s . A block diagram of the d e t e c t i o n c i r c u i t i s gi v e n i n F i g u r e 6. The s i l i c o n d e t e c t o r has a very high r e s i s t a n c e ( s e v e r a l Megohms). When the b i a s v o l t a g e i s a p p l i e d t o the c r y s t a l a s m a l l c u r r e n t flows through the c r y s t a l ( a few microamps). Beta p a r t i c l e s h i t t i n g the s u r f a c e b a r r i e r s i l i c o n d e t e c t o r cause a change i n the c u r r e n t f l o w i n g through the d e t e c t o r . 3 1 B a f f l e T r a n s -m i s s i o n d V 1 . 0 Y ( 1 - 4 c m \ 1 c m |sin « c - Si n : 15.5°J ) 0 . 5 -»•— • 0 - ' i • i • i — 1 4 . 5 ° 1 5 ° 1 5 . 5 ° 1 6 * 1 6 . 5 * B a f f l e Angle F i g u r e 1 1 - The H e l i c a l B a f f l e - T r a n s m i s s i o n vs B a f f l e Angle. r CPM 3 x 1 0 6 0 -10 h ' . 3 5 .40 POT F i g u r e 1 2 - The E f f e c t Of B a f f l e P l a t a Angle On The 2 9 4 . 0 3 K e V I n t e r n a l C o n v e r s i o n Peak. 3 2 T h i s change i s caused by the charged p a r t i c l e l o s i n g i t s energy i n the d e t e c t o r . The l o s s of energy may take three forms: e x c i t a t i o n of atomic e l e c t r o n s to the c o n d u c t i o n band of the c r y s t a l l a t t i c e , l e a v i n g h o l e s i n the atomic l e v e l s ; e x c i t a t i o n of the c r y s t a l l a t t i c e ; thermal l o s s e s to the c r y s t a l s t r u c t u r e . The e l e c t r o n s and h o l e s produced i n the f i r s t of the above processes cause a s i g n i f i c a n t change i n the s m a l l b i a s c u r r e n t through the c r y s t a l . T h i s change of c u r r e n t can be d e t e c t e d with low noise e l e c t r o n i c s , through a charge c o l l e c t i o n p r o c e s s . The F.E.T. p r e a m p l i f i e r i s a ' s t a t e of the a r t ' product; a P - l l F i e l d E f f e c t T r a n s i s t o r p r e a m p l i f i e r obtained from Simtec I n d u s t r i e s L t d . The p r e a m p l i f i e r d e t e c t s the change i n c u r r e n t through the c r y s t a l d e t e c t o r and a m p l i f i e s the change. The e q u i v a l e n t c i r c u i t f o r s m a l l s i g n a l s ( i . e . - s m a l l changes i n c u r r e n t ) i s shown i n F i g u r e 14. and C i are the r e s i s t a n c e and c a p a c i t a n c e of the c r y s t a l d e t e c t o r . R^ i s the output r e s i s t a n c e of the d e t e c t o r b i a s power s u p p l y . R s and Cs are the s t r a y r e s i s t a n c e and c a p a c i t a n c e of the e l e c t r i c a l connections (R s i S n e g l i g i b l e ) , and Rf and Cf are the feedback impedance of the c h a r g e - s e n s i t i v e a m p l i f i e r s t a g e s . I f Q i s the f r e e charge produced i n the d e t e c t o r by an i n c i d e n t beta p a r t i c l e , thus the charge c o l l e c t e d on C±, then the r e s u l t i n g output s i g n a l v o l t a g e , V 0 , i s : V 0 = QA Ci+C2+(A+l)Cf , Eqn. 2-2 where A i s the open c i r c u i t g a i n of the c h a r g e - s e n s i t i v e stages of the p r e a m p l i f i e r . 33 S i l i c o n C r y s t a l B i a s T r a n s f e r Box Broken l i n e i n d i c a t e s the part of the d e t e c t i o n c i r c u i t i n s i d e the spectrometer B i a s Power Supply F.E.T. P r e a m p l i f i e r Pulse Shaper A m p l i f i e r Time Gate Timer S c a l e r F i g u r e 1 3 - B l o c k Diagram - The Beta D e t e c t i o n C i r c u i t . I •» R£ A/V ~0 . rz F.E.T. R f ~10 9.ft. (• l p f -o v c B r o k e n l i n e e n c l o s e s the e l e c t r i c a l e q u i v a l e n t o f t h e S i l i c o n d e t e c t o r F i g u r e 14 - S m a l l S i g n a l E q u i v a l e n t C i r c u i t Of The Charge S e n s i t i v e Stage Of The D e t e c t o r And P r e a m p l i f i e r . 3 5 Because F i e l d E f f e c t T r a n s i s t o r s have a v e r y h i g h input impedance and a low output impedance when used i n the common-d r a i n c o n f i g u r a t i o n , high g a i n i s r e a d i l y o b tained i n the F.E.T. s t a g e s . Furthermore, the h i g h F.E.T. input impedance i s i d e a l f o r the measurement of the s m a l l changes i n c u r r e n t i n v o l v e d . For l a r g e g a i n A, the output v o l t a g e , V 0 , becomes: T h i s output from the c h a r g e - s e n s i t i v e stage of the p r e a m p l i f i e r i s then f e d t o two e m i t t e r f o l l o w e r type a m p l i f i e r stages to provide low output impedance f o r the s i g n a l p u l s e . The s i g n a l pulse from the p r e a m p l i f i e r has a v e r y s h o r t r i s e time ( ~ 5 0 nsec) and i s of v e r y s h o r t d u r a t i o n . Because of t h i s , the pulse must be shaped to enable the f o l l o w i n g stages t o a m p l i f y i t more e a s i l y and to give a b e t t e r s i g n a l -t o - n o i s e r a t i o . The pulse shaper used i s of the i n t e g r a t o r -29 d i f f e r e n t i a t i o n type and was developed by P. Taminga ^ t and used v 25 by Walton i n t h i s l a b o r a t o r y . F i g u r e 1 5 i s a c i r c u i t diagram of t h i s pulse shaper. The main a m p l i f i e r i s an Atomic Instrument Co. Model 2 1 5 with g a i n c o n t i n u o u s l y v a r i a b l e from 0.4 to 64 and with an input d i s c r i m i n a t o r to determine the minimum v o l t a g e of pulse accepted f o r a m p l i f i c a t i o n . In the present i n v e s t i g a t i o n , the d i s c r i m i n a t o r was s e t to accept o n l y p u l s e s due t o 5 0 K e V or more e n e r g e t i c beta p a r t i c l e s . 36 The time gate was a simple b a s e - v o l t a g e - g a t e d e m i t t e r f o l l o w e r c i r c u i t of g a i n one u s i n g the output gate of an O r t e c Model 225 timer a c c u r a t e t o 0.1 s e c . The s c a l e r was a Tennelec T C 5 6 2 v i s u a l d i s p l a y . To decrease gain, increase R 3 O +. 24vdc °° Time constant-d i f f e r e n t i a t o r = R^ C-^  Time constant-integrator = R 2 C 2 9 O out (neg.) (pos .) Figure 15 - C i r c u i t Diagram - The Pulse Shaper. 3 8 . Chapter 3 - Source P r e p a r a t i o n (a) R a d i o a c t i v e Source Requirements As p o i n t e d out by Walton^5, the r e s o l u t i o n of the magnetic spectrometer i n t h i s l a b o r a t o r y i s c r i t i c a l l y dependent upon source diameter. (See T a b l e I I ) However, d e c r e a s i n g source diameter leads r a p i d l y t o low t r a n s m i s s i o n . The p o s i t r o n component of '^^Eu has been e s t i m a t e d by 27 ?0 ^1 previous workers > J > t o be approximately 0.02$ of the t o t a l decay. The requirements of the present i n v e s t i g a t i o n were f o r a source of s u f f i c i e n t a c t i v i t y t o enable c o u n t i n g of the v e r y 1 low i n t e n s i t y p o s i t r o n s . At the same time, the source diameter isnust be s m a l l enough t o ensure a r e s o l u t i o n of the order of 2$ and s t i l l be t h i n enough t h a t the source a b s o r p t i o n above 200KeY be n e g l i g i b l e . In a d d i t i o n t o these requirements, the b a c k i n g on which the source i s t o be p l a c e d must be t h i n enough not t o c o n t r i b u t e s i g n i f i c a n t l y t o back s c a t t e r i n g e f f e c t s above 200KeV p o s i t r o n e n e r g i e s . . Source a b s o r p t i o n i s the l o s s of e l e c t r o n energy as the charged p a r t i c l e passes through the source m a t e r i a l . The energy i s l o s t through the i n t e r a c t i o n of the p a r t i c l e w i t h the atomic e l e c t r o n s of the source m a t e r i a l and with the c r y s t a l l a t t i c e of the source m a t e r i a l . The ammou'nt of energy l o s t i s p r o p o r t i o n a l t o the d i s t a n c e the p a r t i c l e t r a v e l s through the source before emerging. Thus, p o s i t r o n s or negatrons e m i t t e d from a t h i c k source w i l l l o s e more energy than those from a t h i n source on the average. Because t h i s energy l o s s must be kept t o 3 9 a minimum i f a c c u r a t e p a r t i c l e e n e r g i e s are d e s i r e d , sources must be made as t h i n as p o s s i b l e . Back s c a t t e r i n g i s the s c a t t e r i n g of e l e c t r o n s by the Coulomb f i e l d s of the n u c l e i of the source m a t e r i a l and the source backing m a t e r i a l . The amount of b a c k s c a t t e r i n g depends both upon the atomic number of the b a c k i n g m a t e r i a l ( s t r e n g t h of the Coulomb f i e l d ) and upon i t s t h i c k n e s s ( i n c r e a s e d p r o b a b i l i t y of b a c k s c a t t e r i n g ) . Because there i s a l o s s of energy of the b a c k s c a t t e r e d p a r t i c l e , the presence of b a c k s c a t t e r i n g w i l l cause a s u r p l u s of low energy p a r t i c l e s t o be focussed by the spectrometer. I t i s c l e a r t h a t t o a v o i d b a c k s c a t t e r i n g e f f e c t s the source b a c k i n g must be as t h i n as p o s s i b l e and i t must be made of a m a t e r i a l whose atomic number (or numbers) i s as low as p o s s i b l e . Van Wijngaarten and Connor3 2 showed the e f f e c t s of source 1 ^ 4 t h i c k n e s s on the shape of the beta spectrum of Cs. They were ab l e t o show t h a t spectrum d i s t o r t i o n due t o source t h i c k n e s s was c l e a r l y v i s i b l e i n sources of a c t i v i t y 1 0 0 C i (prepared f o r a S i e g b a h n - S l a t i s t h i n l e n s spectrometer) at beta ener g i e s below 5 0 0 K e V , and t h a t spectrum d i s t o r t i o n due t o backing t h i c k n e s s was c l e a r l y v i s i b l e a t beta e n e r g i e s below 400KeV u s i n g 1.6mg/cm2 Aluminum b a c k i n g . To a v o i d these e f f e c t s , Van Wijngaarten and Connor developed source backings of t h i n v i n y l V.Y.N.S. r e s i n f i l m . V.Y.N.S. r e s i n i s an organic m a t e r i a l and i s thus composed of only very l i g h t elements (Carbon, Hydrogen, Oxygen). T h e r e f o r e , the requirement f o r low Atomic Number i s met. In a d d i t i o n , 4 0 P 3 2 , 3 3 the f i l m s prepared were extremely t h i n (5 t o 10 gm/cm ) To a v o i d charge b u i l d - u p w i t h i n the source m a t e r i a l (to a v o i d a r e t a r d i n g Coulomb f i e l d ) the v i n y l f i l m s were "rendered 2 conducting by the vacuum d e p o s i t i o n of a t h i n (5 t o 10 gm/cm ) 3 2 l a y e r of G o l d " . A f u r t h e r advance made by Van Wijngaarten and Connor was the vacuum s u b l i m a t i o n of source m a t e r i a l onto the v i n y l source b a c k i n g . T h i s enabled them t o prepare sources of uniform t h i c k n e s s and of c o n s i s t e n t s i z e ( d i a m e t e r ) , (b) Source P r e p a r a t i o n f o r the Current I n v e s t i g a t i o n 25 An attempt was made i n t h i s l a b o r a t o r y by Walton s Johnson-* , and the present i n v e s t i g a t o r t o d u p l i c a t e the vacuum s u b l i m a t i o n of s o u r c e s . I t was not s u c c e s s f u l , a p p a r e n t l y 152 1 3 4 because Eu r e q u i r e s a much high e r temperature than ~> Cs to i n t i a t e s u b l i m a t i o n . When the h i g h e r temperatures were a c h i e v e d , the Tungsten or Molybdenum cup h o l d i n g the source m a t e r i a l would a l s o s u b l i m a t e , r e s u l t i n g i n sources of u n d e s i r e a b l e t h i c k n e s s . The source m a t e r i a l f o r the c u r r e n t i n v e s t i g a t i o n was a s o l u t i o n of EUCI3 i n IN HC1. I t was decided t o f i r s t attempt t o a v a i l a b l e 0.175mg/cm^ Aluminum f o i l as a source b a c k i n g m a t e r i a l because of the ease of p r e p a r a t i o n of backings with t h i s m a t e r i a l Van Wijngaarten and Connor demonstrated t h a t t h i s b a c k i n g was the next most d e s i r e a b l e t o the v i n y l - G o l d b a c k i n g s , and t h a t i t would cause spectrum d i s t o r t i o n o n l y below 200KeV. S l a t i s ^ p o i n t e d t h a t t h i s f o i l i s " . . . q u i t e r e s i s t a n t t o a c i d s , and sources may be prepared from ... ve r y s l i g h t l y a c i d s o l u t i o n s of HC1 ...". To i n c r e a s e the pH of the source s o l u t i o n , i t was 4 1 evaporated t o dryness, then r e d i s s o l v e d i n g l a s s - d i s t i l l e d HgO s e v e r a l t i m es. T h i s procedure d i d indeed reduce .the a c i d i t y ( i n c r e a s e the pH) of the source m a t e r i a l s o l u t i o n . However, enough a c i d i t y remained t o r e a c t with the Aluminum backing and sources prepared i n t h i s manner had l i f e - t i m e s r a n g i n g from s e v e r a l months f o r s m a l l t h i n sources t o s e v e r a l days f o r sources u s e f u l f o r p o s i t r o n measurements. These source l i f e -times were not a c c e p t a b l e f o r the present i n v e s t i g a t i o n . V i n y l - G o l d backings were prepared u s i n g V.Y.N.S. v i n y l r e s i n and the method of p r e p a r a t i o n of Ng 2^ of t h i s l a b o r a t o r y . Source m a t e r i a l was reduced i n a c i d i t y by the method d e s c r i b e d above and was d e p o s i t e d on the backing by drop d e p o s i t i o n . See F i g u r e 17- T h i s method was extremely f l e x i b l e as the source diameter c o u l d be v a r i e d by v a r y i n g the s i z e of the drop p l a c e d on the backing and the source t h i c k n e s s c o u l d be v a r i e d by v a r y i n g the c o n c e n t r a t i o n (or d i l u t i o n ) of the source m a t e r i a l s o l u t i o n . A l l sources prepared were kept i n evacuated chambers a t a l l times except when necessary t o move them from one chamber t o another. T h i s was t o prevent the a b s o r p t i o n of H 20 by the sources as the Europium compounds tend t o be h y g r o s c o p i c . In a d d i t i o n , sources were p r o t e c t e d from l o s s of source m a t e r i a l by c o a t i n g each source with an extremely t h i n l a y e r of c o l l o d i o n . T h i s was accomplished by d i s s o l v i n g c o l l o d i o n compound i n e t h e r i n a very d i l u t e s o l u t i o n . The s o l u t i o n was then a p p l i e d t o source and backing by l e t t i n g a drop f a l l on the backing from a h e i g h t of about 1 cm. The s o l u t i o n would spread r a p i d l y over 4 2 Aluminum source "bolder V i n y l - G o l d backing Source m a t e r i a l F i g u r e 1 6 - The Source Holder And Source B a c k i n g . Gla s s dropper Source h o l d e r and b a c k i n g Ta b l e Rubber t u b i n j h^z^C-clamp F i g u r e 1 7 - The Source D e p o s i t i o n Apparatus 43 the e n t i r e backing and source as the e t h e r evaporated, l e a v i n g a l a y e r of c o l l o d i o n as p r o t e c t i o n . 44 Chapter 4 - The P o s i t r o n Decay Of 1 ^ 2 E u (a) P r e v i o u s I n v e s t i g a t i o n 27 A l b e r g e r , O f e r , and Goldhaber 1 f i r s t found p o s i t r o n decay . 1 5 2 i n 1 3 year Eu u s i n g an in t e r m e d i a t e image magnetic spectrometer with a h e l i c a l b a f f l e . T h e i r o b j e c t was to e s t a b l i s h an independent measurement of the energy, s e p a r a t i o n between 9 . 3 hour 1 5 2 E u ( 1 ; > 2 m E u ) and 1 2 year 1 5 2 E u ( 1 5 2 E u ground s t a t e ) from a knowledge of the end p o i n t e n e r g i e s of the primary beta groups of both 1 ^ 2 E u and 1 ^ 2 m E u . The- source used was prepared from an aged sample of "^-^Eu obtained from the i r r a d i a t i o n of E U 2 O 3 e n r i c h e d i n ^ -^Eu. The s t r e n t h of the source was approximately 0 . 2 mCi ("a few mg/cm^") and the source b a c k i n g was 0 . 0 0 1 i nch Aluminum ( 6 . 9 rng/cm^). The r e s o l u t i o n of the spectrometer was 4$. They were able to d e t e c t the presence . of two d i s t i n c t primary p o s i t r o n groups with end p o i n t s of 715KeV and 470KeV. I n t e n s i t i e s were a s s i g n e d t o these groups ' a f t e r s u b t r a c t i n g the i n t e n s i t y of p a i r p r o d u c t i o n p o s i t r o n s (from the l4o8KeV E l t r a n s i t i o n of 1^l2Sm) u s i n g a t h e o r e t i c a l c a l c u l a t i o n . They were not able t o d e t e c t the p a i r p r o d u c t i o n p o s i t r o n d i s t i b u t i o n i n t h e i r d a t a . Assigned i n t e n s i t i e s were: 1 . 6 x 1 0 " ^ p e r v d i s i n t e g r a t i o n f o r the 7 1 5 K e v primary beta group, 0 . 8 x l 0 - i * f o r the 470KeV primary beta group, and 0 . 5 x 1 0 " ^ f o r the p a i r p r o d u c t i o n p o s i t r o n s . Antonova, V a s i l e n k o , K a m i n s k i i and K a g a n s k i i ^ l c o n t i n u e d a previous . i n v e s t i g a t i o n of K a m i n s k i i and K a g a n s k i i - ^ u s i n g a type magnetic spectrometer with double focussing and a co i n c i d e n c e d e t e c t i o n c i r c u i t t o measure the p o s i t r o n spectrum of ^ 2 E u and ^ 2 m E u . T h e i r sources were approximately 1 t o on rH rH ^ > t— oo m © > OJ co W (D >R \R ^ >R >R o o t— oo vo m i> D— OJ -=t- m s 1578KeV e-> CD LT -3-cu > « roj co o t*3 OJ •\l530KeV 'L > OJ O C > > > m ^ <s GO OJ o O! w o, OJ w 1235KeV 1*2 I.O > co o 0J ON 0 a i « K 1087KeV OJ i c - > u l a i 3 6 6 . 5 K e V 1 — v OJ 121.8KeV 0 (0") 5 0 KeV 9 - 3 h 1 5 2 E u . \JEC 1.7$ 2 6 $ 1.4$ •EC 17$ •EC 2 3 $ •EC 2 $ • EC 1$ 0 . 0 0 6 $ + 0 . 0 1 0 $ l642KeV 1123KeV 7 5 5 . 6 K e V 3 4 4 . 2 K e V ^ G d F i g u r e l 8 - P a r t i a l Decay Scheme Of 1 5 2 £ u , From'A Table Of The I s o t o p e s ' 2 . 46 2 mg/cm2 t h i c k w i t h u n s p e c i f i e d s o u r c e b a c k i n g . The s o u r c e s .... were p r e p a r e d from E u 2 0 3 o f a n a t u r a l i s o t o p e compound i r r a d i a t e d w i t h slow n e u t r o n s . The r e s o l u t i o n o f the s p e c t r o -meter was a p p r o x i m a t e l y 1%. P r i m a r y p o s i t r o n end p o i n t s o f 713KeV and 470KeV were o b s e r v e d . I n t e n s i t i e s were a s s i g n e d t o the groups by com p a r i s o n w i t h t h e o b s e r v e d p a i r p r o d u c t i o n p o s i t r o n i n t e n s i t y , w hich was assumed t o agree w e l l w i t h t h e o r e t i c a l p r e d i c t i o n s . T h e i r r e s u l t s were c o n t a m i n a t e d by the presence o f p a i r p r o d u c t i o n p o s i t r o n s from the decay o f ^ ^ 4 E u . • P e r d r i s a t e t a l 3 ^ w h i l e s e a r c h i n g f o r monoenergetic K - p o s i t r o n s * due t o the l409KeV t r a n s i t i o n measured p r i m a r y p o s i t r o n end p o i n t s o f 740KeV and 490KeV. The s o u r c e used was one of 6mg/crn2 t h i c k n e s s . The r e s u l t s of A l b e r g e r e t a l and Antonova e t a l a r e i n good agreement. The r e s u l t s o f P e r d r i s a t e t a l do not a g r e e , but t h e s e r e s u l t s were not the o b j e c t o f the P e r d r i s a t e t a l exp e r i m e n t and t h i s must be t a k e n i n t h a t l i g h t . They do not agree i n the order, of magnitude. The s o u r c e s used i n a l l t h r e e p r e v i o u s i n v e s t i g a t i o n s were e x t r e m e l y t h i c k . I t i s r e a d i l y c o n c e i v a b l e t h a t the r e s u l t s of the p r e v i o u s -i n v e s t i g a t i o n s have been a f f e c t e d by so u r c e and b a c k i n g t h i c k n e s s . A l l p r e v i o u s i n v e s t i g a t i o n s quote s o u r c e and/or b a c k i n g t h i c k n e s s e s l a r g e r t h a n t h o s e which Van W i j n g a a r t e n and * These monoenergetic p o s i t r o n s a r i s e from the c a p t u r e o f t h e p a i r p r o d u c t i o n e l e c t r o n s i n the K atomic s h e l l . The b i n d i n g energy of t h i s s h e l l thus enhances the energy a v a i l a b l e t o the p o s i t r o n and g i v e s i t an energy g r e a t e r t h a n the maximum p a i r p r o d u c t i o n energy a l l o w e d ( g r e a t e r by the K s h e l l e l e c t r o n b i n d i n g e n e r g y ) . Connor showed l e a d t o d i s t o r t i o n . T h i s .is almost c e r t a i n i n the work of A l b e r g e r et a l who were not able to observe the d i s t i n c t i v e p a i r p r o d u c t i o n energy d i s t r i b u t i o n i n t h e i r d a t a . Antonova e t a l p o i n t out the e f f e c t s of source t h i c k n e s s i n t h e i r d a t a . (b) The Current I n v e s t i g a t i o n The p o s i t r o n decay spectrum of ^ - 5 2 g u ^ a s been measured wit h .a maximum count r a t e of 3 2 counts per minute above a background of 7 counts per minute. A previous chapter has d i s c u s s e d source requirements and techniques used t o achieve t h e i r source backings and t h e i r s o u r c e s . A source of approximately 1 C i a c t i v i t y and of 2.8mm diameter was used a t a spectrometer r e s o l t u i o n of 2 . 1 $ . The source b a c k i n g was the V.Y.N.S. f i l m with a t h i n l a y e r of Gold evaporated onto i t . Source m a t e r i a l was o b t a i n e d from Union Carbide C o r p o r a t i o n as a s o l u t i o n of EUCI3 i n IN HC1. The s p e c i f i c a c t i v i t y of the source m a t e r i a l was 1 0 . 0 mCi/mg and the source m a t e r i a l c o n t a i n e d no s i g n i f i c a n t amounts of Eu. No ^ Eu i n t e r n a l c o n v e r s i o n negatron peaks were measured at a spectrometer r e s o l u t i o n of 0 . 7 $ . The e f f e c t s of source b a c k i n g and t h i c k n e s s were checked by t a k i n g the i n t e r n a l c o n v e r s i o n e l e c t r o n peak at 1 9 7 . 8 4 K e V ^ 7 and checking i t s r e s o l u t i o n and shape (See F i g u r e 1 9 ) . I t was noted t h a t the peak was s l i g h t l y asymmetric, with an excess of e l e c t r o n s on the low energy s i d e , i n d i c a t i n g t h a t below t h i s energy the e f f e c t s of source a b s o r p t i o n would change the shape of the energy d i s t r i b u t i o n of p o s i t r o n s . The i n t e r n a l c o n v e r s i o n 50 3 7 e l e c t r o n peak a t 294.03KeV showed no such asymmetry. See F i g u r e 20. I t was c o n c l u d e d t h a t the energy d i s t r i b u t i o n o f p o s i t r o n s above 300KeV would show no d i s t o r t i o n due t o sou r c e a b s o r p t i o n , and i n the r e g i o n , 200KeV t o 300KeV, the d i s t o r t i o n would be o n l y s l i g h t . So f a r as b a c k - s c a t t e r i n g i s c o n c e r n e d , our e x p e r i e n c e has been t h a t d i s t o r t i o n e f f e c t i s g r e a t e r on be t a c o n t i n u a t h a n on I n t e r n a l C o n v e r s i o n peak s h a p e s . Thus, we cannot e n t i r e l y r u l e out the p o s s i b i l i t y of some d i s t o r t i o n of t h e spectrum due t o b a c k - s c a t t e r i n g . B a c k - s c a t t e r i n g i s not so energy-dependent as t o e f f e c t a peak ( s m a l l energy i n t e r v a l ) but over a l a r g e e n e rgy range i t w i l l a f f e c t the shape o f t h e continuum. The p o s i t r o n momentum d i s t r i b u t i o n was t a k e n from p o s i t r o n e n e r g i e s o f 8 5 K e V t o 7 5 0 K e V . No p o s i t r o n s were cou n t e d above 713KeV w i t h i n the s t a t i s t i c s o f the co u n t s t a k e n . Data p o i n t s from 8 5 K e V t o 3 0 0 K e V were t a k e n w i t h s t a n d a r d d e v i a t i o n s o f 5$ t o 3$;.-"Dsfca p o i n t s above 3 0 0 K e V were t a k e n w i t h s t a n d a r d d e v i a t i o n s of b e t t e r t h a n 3 $ • The s p e c t r o m e t e r was c a l i b r a t e d . 3 7 in momentum on the 197.84KeV K - I n t e r n a l C o n v e r s i o n peak ( t r a n s i t i o n energy 244.68Kev37). The momenta and e n e r g i e s of a l l data p o i n t s were c a l c u l a t e d from the c a l i b r a t e d momentum. By comparison w i t h gamma r a y measurement done i n t h i s l a b o r a t o r y t h i s method of c a l i b r a t i o n has proved t o be a c c u r a t e t o b e t t e r t h a n 0 . 0 5 K e V over an energy range o f 2 0 0 K e V from the c a l i b r a t i o n p o i n t . The data ( F i g u r e 21) c l e a r l y shows the d i s t i n c t i v e p a i r p r o d u c t i o n p o s i t r o n energy d i s t r i b u t i o n superimposed upon a 51 p o s i t r o n continuum. The f i r s t s t e p i n the da t a a n a l y s i s was t o d e c i d e upon the form of the shape c o r r e c t i o n f a c t o r t o be used. ? 1S2 The T a b l e of the I s o t o p e s g i v e s the ground s t a t e o f J Eu w i t h JV o f 3 " and the two e x c i t e d s t a t e s o f ^^Sm t o which p o s i t r o n decay o c c u r s w i t h of 2^ and 4"^  (see F i g u r e 1 8 ) . F o r p o s i t r o n decay t h e n , A J = 1 , ATT = YES f o r b o t h p r e v i o u s l y o b s e r v e d c a s e s , and the decays are f i r s t f o r b i d d e n non-unique. The form of the shape c o r r e c t i o n f a c t o r f o r f i r s t f o r b i d d e n non-unique t r a n s i t i o n s i s (from C h a p t e r 1 ( b ) ): C. = ' X p 2 + q 2 + D Eqn. 4-1 where : p = the momentum of the p o s i t r o n . q = the momentum of the n e u t r i n o . *X = a c o n s t a n t which depends upon Z and upon the end p o i n t e n e r g y . D = a c o n s t a n t t o be d e t e r m i n e d e x p e r i m e n t a l l y . Langer and S m i t h 1 9 d i d e x t e n s i v e e x p e r i m e n t a l f i t t i n g of 152 f i r s t f o r b i d d e n shape f a c t o r s t o Eu data ( i n a d d i t i o n t o s e v e r a l o t h e r i s o t o p e s ) . T h e i r r e s u l t s (which a re used i n the c u r r e n t i n v e s t i g a t i o n ) were: C, = 0 . 7 9 P 2 + q 2 + (5 ± 2) Eqn. 4-2 where D = ( 5 ^ 2 ) was the parameter d e t e r m i n e d by Langer and Sm i t h and the f a c t o r < X = 0 . 7 9 i s a t h e o r e t i c a l l y c a l c u l a t e d 17 v a l u e 1 . K u r i e - p l o t a n a l y s i s (see F i g u r e 2 2 ) , u s i n g a l e a s t s q u a r e s f i t computor r o u t i n e on t h a t p a r t of the data above the p a i r p r o d u c t i o n p o s i t r o n end p o i n t energy of 3 8 6 . 3 K @ V ( p l u s an F i g u r e 22 - K u r i e - p l o t Of The Primary P o s i t r o n Groups. 5 4 a l l o w a n c e . f o r the f i n i t e r e s o l u t i o n o f the s p e c t r o m e t e r ) * , c l e a r l y showed the presence o f two p r i m a r y p o s i t r o n groups w i t h end p o i n t e n e r g i e s of 7 1 3 - 5 ^ 2 K e V and 4 7 1 ^ 5 K e V . No a d d i t i o n a l p o s i t r o n groups i n the energy range 3 8 6 . 3 K e V t o 7 5 0 K e V were f o u n d . The energy s e p a r a t i o n o f the two p o s i t r o n g r o u p s , 242 . 5 6 K e V , i s i n g e n e r a l agreement w i t h the gamma r a y r e s u l t s , 244.6oKeV, of Walton i n t h i s l a b o r a t o r y . From the f i t t e d s t r a i g h t l i n e s of the K u r i e - p l o t , the momentum d i s t r i b u t i o n , n ( p ) , of t h e two p o s i t r o n groups c o u l d be deduced. These d i s t r i b u t i o n s were t h e n s u b t r a c t e d from the data and the p a i r p r o d u c t i o n p o s i t r o n d i s t r i b u t i o n was f i t t e d t o the s u b t r a c t e d d a t a . Care was t a k e n i n t h i s l a s t f i t t i n g t o f i t o n l y the r e g i o n above 3 0 0 K e V (below which s o u r c e a b s o r p t i o n might a f f e c t t he shape o f the d i s t r i b u t i o n ) and below 3 8 6 . 3 K e V p l u s an a l l o w a n c e f o r f i n i t e s p e c t r o m e t e r r e s o l u t i o n . The f i t t e d d i s t r i b t u i o n s a r e shown i n F i g u r e 23* a l o n g w i t h the sum of the t h r e e f i t t e d d i s t r i b u t i o n s and the d a t a . I t was no t e d t h a t t h e r e was an ex c e s s o f p o s i t r o n s above the sum of the t h r e e d i s t r i b u t i o n s i n t h e ^ r e g i o n below 2 0 0 K e V as e x p e c t e d from the p r e v i o u s s o u r c e t h i c k n e s s measurements. To a r r i v e a t the i n t e n s i t y (the f r a c t i o n o f the t o t a l 1 ^ 2 E u decays) of the two p r i m a r y p o s i t r o n groups and o f the p a i r p r o d u c t i o n p o s i t r o n s , t h e i n t e n s i t y o f the 244.68KeV t r a n s i t i o n 2 - 2 was deduced from p r e v i o u s measurements as 8.19 x 10 . The * The p a i r p r o d u c t i o n p o s i t r o n end p o i n t energy was deduced from the p a i r p r o d u c t i o n c r e a t i o n e n e r g y , 1022.0012KeV, and from the E l t r a n s i t i o n e n e r g y , l4o8.3KeV 3 9 . CPM 56 p K - 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 , cC, f o r t h i s t r a n s i t i o n i s 8 . 3 x 1 0 ~ 2 , g i v i n g an o v e r a l l i n t e n s i t y of K - s h e l l C o n v e r s i o n e l e c t r o n s f o r t h i s t r a n s i t i o n of 0 . 6 8 x 1 0 " . The area under the momentum d i s t r i b u t i o n of t h i s C o n v e r s i o n e l e c t r o n peak: was then measured and compared t o the areas under the momenta d i s t r i b u t i o n s of the primary p o s i t r o n , groups and of the p a i r p r o d u c t i o n p o s i t r o n s . I n t e n s i t i e s were found t o be: ( 1 . 0 ^ 0 . 1 ) x 1 0 ~ 4 f o r the 7 1 3 - 5 K e V primary p o s i t r o n group; ( 0 . 6 ^ 0 . 2 ) x 1 0 f o r the 4 7 1 K e V primary p o s i t r o n . g r o u p ; and ( 0 . 4 ± 0 . 0 5 ) x 1 0 ~ 4 f o r the p a i r p r o d u c t i o n p o s i t r o n s . These r e s u l t s are summarized i n Table I I I with the r e s u l t s of pre v i o u s i n v e s t i g a t i o n s . T able I I I - A Summary Of R e s u l t s . 713-5KeV Primary R Group 4 7 1 K e V Primary A ' Group P a i r P r o d u c t i o n 3 I n t e n s i t y per decay E 0 (KeV-) I n t e n s i t y per decay E 0 (KeV) Intens i t y per decay A l b e r g e r et a l . 7 1 5 =k 1 0 -4 1 . 6 x 10* 4 7 0 ± 3 0 0 . 8 x 1 0 4 ~ 4 0 . 5 x 1 0 assumed Antonova et a l . 7 1 3 3 1 . 4 x 1 0 4 4 7 0 ± 1 0 0 . 5 x i d 4 0 . 4 x 10 4 assumed P e r d r i s a t et a l . 740 ± 1 0 4 9 3 A 1 3 C u r r e n t . I n v e s t i g a -t i o n 7 1 3 . 5 = 2 (l.OffO.l) x 1 0 4 4 7 1 ± 5 ( 0 . 6 ± p . 2 ) x 1 0 4 ( 0 . 4 ± 0 . 0 5 ) x 1 0 57 I t may be seen t h a t the c u r r e n t i n v e s t i g a t i o n i s i n g e n e r a l .agreement with previous work, e x c e p t i n g the i n t e n s i t y of the more e n e r g e t i c ( 7 1 3 . 5 K e V ) primary p o s i t r o n group. T h i s may be due to source t h i c k n e s s e f f e c t s and to back s c a t t e r i n g from the source backings i n the previous works, although no e r r o r l i m i t s are quoted f o r the i n t e n s i t y r e s u l t s of previous i n v e s t i g a t i o n s . 5 8 Chapter 5 - Conclusions The existing beta spectrometer has been modified to count either positrons or negatrons by the addition of a he l ica l baff le . Design considerations of the he l i ca l baffle have been reviewed in a previous chapter. The transmission of the he l ica l baffle was found to be 7 6 $ , and the rejection of electrons of the undesired charge was complete within the l imits of the measurements (2 x 10"^). The spectrometer has been used to take the positron 152 'spectrum of ^ Eu. Spectrometer resolution attained in this investigation was a considerable improvement over the ear l ier work of Alberger et a l . with a spectrometer of this type. The thinner source and source backings used in this investigation resulted in data with less spectrum shape distortion at low positron energies than the'data from 2 7 3 1 earl ier investigations ' . In the current investigation, source absorption,effects were expected and found only below 200KeV positron energies (see Figure 23)- This represents a considerable improvement over the data of Alberger et a l . who were not able to observe the dist inctive pair production positron shape. It is also an improvement on the data of Antonova et a l . who found source absorption effects up to 300KeV positron energies. The use of the v inyl Gold source backing may also contribute to the improved spectrum shape, for Alberger et a l . quote 0.001 inch Aluminum as a backing. Antonova et a l . do not specify their source backing. 5 9 The positron spectrum of Euhas been analysed and the existence of two primary positron groups has been confirmed. End point energies are 7 1 3 . 5 ^ 2KeV and 4 7 1 ± 5KeV, in excellent agreement with the previous investigations. The accuracy of these end point energies has been improved (see Table I I I ) . The existence of a pair production positron component has also been confirmed. The end point energy of the pair production positrons, 3 8 6 ^  2KeV, is i n good agreement with the gamma ray r e s u l t s , 3 8 6 . 3 K e V . I n t e n s i t i e s of the primary positron groups have been deduced as ( 1 . 0 ^ 0 . 1 ) -h ' 4 . - 4 x 10 per decay for the 7 1 3 - 5 K e V group and ( 0 . 6 ^ 0 . 2 ) x 1 0 per decay for the 471KeV group. The i n t e n s i t y of the pair production positrons has been deduced for the f i r s t time from the data as ( 0 . 4 = * = 0 . 0 5 ) x 1 0 ^ per decay. This i s in good agreement with the t h e o r e t i c a l op p r e d i c t i o n s " . It has been possible to assign error l i m i t s to the i n t e n s i t i e s for the f i r s t time. The 471KeV primary positron i n t e n s i t y agrees well with previous work. The i n t e n s i t y of the 7 1 3 ' 5 K e V primary positron group seems to be considerably smaller than the published r e s u l t s , although error estimates of these i n t e n s i t i e s are not included in previous investigations. The d i s p a r i t y may be caused by e f f e c t s due to source and backing thickness i n t h e i r work. It should be noted that measurement of the primary positron end point energies is the best method of obtaining 60 15? 152 the ^ Sm ground state enersy separation from Eu. The 152 primary positron decays are to known levels of ^ 5m, thus a simple addition of the end point energy, 2mQ, and the energy 15? of the excited state of J Sm gives the energy separation of 1857.3 ^ 2KeV. The alternative i s to use electron capture intensit ies which, in this case, may only be deduced Indirectly through gamma ray intensity measurements and are thus inaccurate. 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' 2 0 M.E.Rose; Phys.Rev. 7 6 ( 1 9 4 9 ) 6 7 8 . 2 1 S.A .S.Brimberg; Phys.Rev. 8 7 _ ( 1 9 5 2 ) 1 5 0 . 2 2 M.E.Rose, G.E.Uhlenbeck; Phys.Rev. 4 8 ( 1 9 3 5 ) 2 1 1 . 2 3 S.D.Bloom; Phys.Rev. 8 8 ( 1 9 5 2 ) 3 1 2 . 6 2 24 H .S la t i s , K.Siegbahn; Arkiv fur Fys'ik _ l ( 1 9 4 9 ) 3 2 9 -2 5 T.Walton; M.Sc. Investigation, U.B.C. ( 1 9 6 7 ) . 2 6 L.K.Ng; Ph.D. Investigation, U.B.C. ( 1 9 6 7 ) . 2 7 D.E.Alberger et a l . ; P h y s . R e v . 1 1 2 ( 1 9 5 8 ) 1 9 9 8 . 2 8 F.Ajzenberg-Selove (Ed.); Nuclear Spectroscopy; Acedemic Press ( i 9 6 0 ) . 2 9 P.Tarainga; U.B .C. Positron Physics Group; unpublished. 3 0 D.L.Kaminskii , M.G.Kaganskii; Sov.Phys.J .E.P.T. 3 5 ( 8 ) ( 1 9 5 9 ) 6 4 6 . 3 1 S.F.Antonova et a l . ; S o v . P h y s . J . E . P . T .37(10 ) ( I 9 6 0 )477 -3 2 W.VanWijngaarten, R.D.Connor; C . J . P . 4 2 ( 1 9 6 4 ) 5 0 4 . 3 3 B.O.Pate, L.Yaffe; C . J . C h e m . 2 l ( l 9 5 5 ) l 5 • 3 4 J.Johnson; M.Sc. Investigation, U .B . C . ( 1 9 7 0 ) . 3 5 H .S la t i s ; from K.Siegbahn, Beta and Gamma Spectroscopy, 1 s t edit ion, page 2 6 3 . 3 6 C.F .Perdrisat et a l . ; Nuclear Physics 3 1 ( 1 9 6 2 ) 1 6 0 . 3 7 Malmstem et a l . ; Arkiv fur Fysik 3 3 ( 2 6 ) ( 1 9 6 6 ) 3 6 1 . 3 8 T.Walton; Ph.D. Investigation, U . B . C , unpublished. 

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