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Production of positronium and muonium in oxide powders Kiefl, Robert Francis 1978

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PBOIUCTION OF POSITBONIOM AND HUONIOH IK OXIDE POWDERS by ROBERT FRANCIS KIEFL E.Sc, Carleton University, 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT 0? THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i s THE FACULTY OF GRADUATE STUDIES (Physics) He accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF'BRITISH COLUMBIA October, 197 8 (c) Robert Francis K i e f l , 1978 In presenting th i s thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r l y purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i ca t ion of th is thes is f o r f i n a n c i a l gain sha l l not be allowed without my wri t ten permission. Department of P h y s i c s The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 Date n r f n h P r 11 1Q7B ABSTBACT 1 s h o r t review c f p o s i t r o n s and mucns, and t h e i r i n t e r a c t i o n s with B a t t e r i s presented. The experimental techniques f o r s t u d y i n g these s h o r t l i v e d p a r t i c l e s are d i s c u s s e d . A t t e n t i o n i s focussed cn the f o r m a t i o n , p r o p e r t i e s , and uses of the hydrogen-like atoms, p o s i t r c i i i u m (e+e-} and muonium Cy+e -), i n gases and i n s u l a t o r s . A l s o , p o s i t r o n s have been i n j e c t e d i n t o extremely f i n e evacuated powder samples of S i 0 2 , A l ? 0 3,MgO, and ZnO. The f r a c t i o n of p o s i t r o n s forming c-Ps w i t h i n the powder g r a i n s and d i f f u s i n g o ut i n t o the vacuum r e g i o n has been measured. The l a r g e s t measurement of 2€±3,% was made f o r the 35A r a d i u s S i 0 2 powder. Using t h i s powder as a moderator the G 2 quenching r a t e c o e f f i c i e n t has been determined to be 1.43±.04 x I O ™ 1 2 cm 3/sec. Doppler broadening measurements of the a n n i h i l a t i o n l i n e v e r i f y t h a t the guenching i n v o l v e s c o n v e r s i o n o f o-Ps to p-Ps. In a d d i t i o n p o l a r i z e d muons have been i n j e c t e d i n t o S i 0 2 , A l 2 0 3 ,flgO, CaO, Sn0 2, Ge0 2 and SiO powders. Using the techniques of y*SB and MSB, upper and lower l i m i t s cn the mucnium f r a c t i o n have been determined. Non-zero muonium pr e c e s s i o n s i g n a l s are r e p o r t e d f o r S i 0 2 , CaC, BgC, and A l 2 0 3 . Evidence i s presented t h a t suggests t h a t the muonium i s d i f f u s i n g i n t o the i n t e r g r a n u l a r r e g i o n s f o r A l 2 0 3 and BgC* as r e p o r t e d e a r l i e r f o r Si0 2» Re s u l t s from these two experiments i n d i c a t e t h a t the fornation and behaviour of muonium and positronium are correlated i n i n s u l a t o r s , at lea s t in a q u a l i t a t i v e sense* Future experiments using oxide powders to produce positronium and muonium are discussed. i v TABLE OF CONTENTS P a ge Chapter I Introduction 1 Chapter II Positrons and Positronium i n Matter 5 Sect 1 Introduction 5 Sect 2 Properties of Positrons and Positronium 7 i Conservation of Charge Parity 7 in e +e Annihilation i i Free Positron Annihilation 8 i i i Bound State Annihilation 10 Sect 3 Experimental Technigues 13 i General 13 i i Lifetime Technigue 14 i i i Angular Correlation Technigue 16 i v Doppler Broadening Technigue 17 v 3y /2y Decay Eatio Technique 18 Sect 4 Ps Formation 19 i Slowing Down in Gases 19 i i Ore Gap i n Gases 20 i i i Low Energy Positron Beams i n Gases 22 iv Formation i n Solids 25 v Summary of Ps Formation 28 Sect 5 o-Ps in Gases, Powders and Gels 29 i Quenching i n Gases 29 v i i Quench Rate Coefficient i n Gases 30 i i i o-Ps i n Powders and Gels 31 Chapter III Positive Muons and Muonium i n Batter 33 Sect 1 Introduction 33 Sect 2 Properties and Uses of Muons 34 i Properties 34 i i Muons as Probes 37 Sect 3 The Technigues of Muom Spin Besonance 39 (y+SE) and Muonium Spin Besonance(MSR) In Transverse Magnetic Fields i General 39 i i y+SB 40 i i i MSR 41 i v Spectral Form 45 v Source of Polarized Muons 46 Sect 4 Mu Formation 47 i Gases 48 i i Insulators and Semi-Conductors 56 Chapter IV Measurements of Free o-Ps Production 58 E f f i c i e n c i e s i n Oxide Powders and an Accurate Determination of the 0 2 Quenching Rate Coefficient For o-Ps Sect 1 Introduction 58 Sect 2 Technique for Measuring 60 Free c-Ps Fraction _ V I Sect 3 Experimental Details €3 i Target Assemblies 63 i i Detectors 64 i i i Electronics For Lifetime Measurements 65 i v Electronics For Measuring 2-y 69 Annihilation Bate and the Doppler Broadening cf the 511 KeV Annihilation Line v Computer Link 71 v i Procedure For o-Ps Production 72 Measurements v i i Procedure For the 0 2 Quenching Bate 73 C o e f f i c i e n t Determination v i i i Procedure For Doppler Broadening 74 Measurements i x Analysis of the Annihilation Spectra 75 x Analysis of the Lifetime Spectra 78 Sect 4 Results and Discussion 80 i o-Ps Production Measurements 80 i i Quenching Bate C o e f f i c i e n t for 0 2 83 i i i Doppler Broadening Measurements on 87 Si0 2(35A) i n Vacuum,in 0 2 and in C l 2 Sect 5 Conclusions 93 Chapter V Measurements of y + and Mu 94 Fractions in Oxide Powders Sect 1 Introduction 94 - v i i -Sect 2 Technigue 96 Sect 3 Experimental Details S8 i The Polarized Beam 98 i i The Experimental Setup 99 i i i E lectronics 101 iv Procedure 103 v Target Preparation 104 v i Analysis 105 a ) High F i e l d Buns 105 b ) Low F i e l d Buns 1C8 Sect 4 Results and Discussion 111 Sect 5 Future Muonium Experiments 120 Chapter VI Concluding Remarks 122 Bibliography 123 Appendix I The Charge Conjugation Parity f o r an 126 e +e~ State and an n Photon State Appendix II a ) Quenching Cross Section for 129 Thermalized o-Ps i n a Powder B ) Quenching Cross Section for 131 Thermalized o-Ps in a Gas Appendix I I I The Muon Pol a r i z a t i o n Vector for a 132 Free Muon in a Static Magnetic F i e l d Appendix IV L i s t of the Fine Powders 133 Appendix V The o-Ps Fraction i n Vacuum 134 v m -Appendix VI Oxygen Impurities ix LIST OF FIGURES Chapter Figure T i t l e Page II 1 Feynman Diagrams for Positron 11 Annihilation 2 The 3y Annihilation Spectrum 12 3 Na 2 2 Decay Scheme 15 4 Positron Annihilation i n a Gas 21 5 Total e + Cross Sections 23 in Noble Gases 6 Angular Correlation i n 27 Single C r y s t a l Ice III 1 Asymmetric Muon Decay 36 2 Brett, fiabi Diagram for Mu 42 3 a) o 1 0 f o r Protons in H 2 and He 49 h) oio for Protons in Ar and Ne 50 c) a i 0 for Protons in Kr and Xe 51 d) o 0 i for Protons in H 2» He and Ne 52 e) a 0 i for Protons in Kr, Ar and Xe 53 I? 1 Electronics for Ps Lifetime 66 Determination 2 Na 2 2 Spectrum from Nal Detector 67 3 Electronics for 2y Annihilation Bate 70 - x -and Doppler Broadening Measurements 4 Na 2 2 Spectrum frcm GeLi Detector 76 (exp an d€ d) 5 Na 2 2 Spectrum from GeLi Detector 77 6 o-Ps Lifetime Spectrum i n AI2O3 79 7 a) o-Ps Lifetime Spectrum i n Si0 2 €4 b) o-Ps Lifetime Spectrum i n SiC2 + C.2 84 8 o-Ps Decay Hate versus 0 2 Pressure 85 9 Energy Resolution Curve at 567 KeV 88 10 a) 511 KeV Line Shape in S i C 2 89 b) 511 KeV Line Shape in Si0 2 + 0 2 89 11 o-Ps Lifetime Spectrum i n S i 0 2 • C l 2 90 12 511 KeV Line Shape i n Si0 2 • C l 2 91 V 1 The Experimental Setup 100 2 Logic Diagram for the MSB 102 Measurements 3 Free Mucniui! Precession i n Aluminum 106 4 Mu Precession in Si0 2 109 5 Mu Precession i n Al 203 113 6 Mu Precession i n A l 2 0 3 • 02 114 7 a) Mu Precession i n MgO 116 b) Mu Precession i n MgO «• 0 2 116 8 a) Mu Precession i n CaO 117 b) Mu Precession in CaO + 0 2 117 9 a) v+ Precession i n Al 118 b) y + Precession i n Ge02 118 x i L I S T OF T A B L E S T a b l e P a g e I L i s t o f Mu F r a c t i o n s i n N o b l e G a s e s 54 I I R e s u l t s o f T h e P o s i t r o n i u m E x p e r i m e n t 81 I I I R e s u l t s o f T h e M u o n i u m E x p e r i m e n t 112 - x i i -ACKNOWLEDGEMENTS I would e s p e c i a l l y l i k e to thank Dr. J.B- Barren for his guidance and h e l p f u l discussions throughout t h i s research project, and Glen M. Marshall and Dr. C. J. Oram for t h e i r constant assistance throughout a l l phases of the experiment and analysis. I would also l i k e to express my gratitude to Dr. B. Bergersen for his helpful discussions and to Dr. J. H. Brewer and the entire MSB group since they made t h i s research possible. I wish to thank Dr. D. J. Judd and Larry Spires for the i r generous pa r t i c i p a t i o n - In addition I would l i k e to thank George Clarke f o r h i s most e f f e c t i v e data transfer system and computer programs and Dr. R. Albrecht for the use of his lifetime f i t t i n g program. F i n a l l y , I would l i k e to thank the technicians of the OBC nuclear physics laboratory for th e i r co-operation and assistance. 1 -CHAPTER I INTRODUCTION -The fundamental dynamical p o s t u l a t e of quantum mechanics s t a t e s t h a t the time dependence of a p h y s i c a l s t a t e i s determined by the f u l l Hamiltonian according t o ih8_| i|i (t) > = H | ij) (t) > 9t where H = H 0 * H±nt a n < i H i n t ^ s t a e f u l l i n t e r a c t i o n Hamiltonian which i s composed of weak , e l e c t r o m a g n e t i c , and st r o n g i n t e r a c t i o n terms, and accounts f o r both e l a s t i c and i n e l a s t i c processes., Experiments i n n u c l e a r , and p a r t i c l e p h y s i c s i n v a r i a b l y i n v o l v e the 'preparation of an i n i t i a l s t a t e f o l l o w e d by the det e r m i n a t i o n of a f i n a l s t a t e . The i n i t i a l s t a t e , |i>, can be determined p r e c i s e l y by measuring a complete s e t of compatible o b s e r v a b l e s . The f i n a l s t a t e , Jf>, cannot be determined p r e c i s e l y with one s e t of measurements because the a c t of measuring i s e g u i v a l e n t to p r o j e c t i n g Jf> onto the e i g e s s t a t e c o r r e s p o n d i n g t o the measured q u a n t i t i e s . The p r o b a b i l i t y f o r making a s e t of measurements, which p r o j e c t s |f> onto Jm> i s |<mif>i2. Expanding Jf> i n terms o f Jm> s g i v e s |'f > = Z | m><m| f > m The p r o b a b i l i t i e s , J<m|f>|2, are determined e x p e r i m e n t a l l y , to w i t h i n a s t a t i s t i c a l e r r o r , by performing many s e t s of measurements. 2 -These e f f o r t s are d i r e c t e d at s t u d y i n g the time dependence of a p h y s i c a l s t a t e i n order to o b t a i n knowledge about the i n t e r a c t i o n Hamiltonian, 411 c o n s e r v a t i o n laws i n p a r t i c l e p h y s i c s are the r e s u l t of these types of experiments. The confidence i n any c o n c l u s i o n reached o b v i o u s l y depends on the s t a t i s t i c s of the experiment. The s i m p l e s t i n i t i a l s t a t e to prepare i s , of course, a one body s t a t e . The decay o f s i n g l e p a r t i c l e s p r o v i d e s v a l u a b l e i n s i g h t i n t o the fundamental i n t e r a c t i o n s and p r o p e r t i e s of p a r t i c l e s , , E x a m p l e s are (weak) (electromagnetic) (strong) The next s i m p l e s t i n i t a l s t a t e t o prepare i s , n a t u r a l l y , the two body s t a t e . A very u s e f u l subset of these two body s t a t e s are those bound together by the Coulomb f o r c e which are sometimes r e f e r r e d to as " o n i u i " s t a t e s . These Coulomb bound s t a t e s are w e l l d e f i n e d e i g e n s t a t e s of o r t i t a l angular momentum,,Also , the wave f u n c t i o n s , <Elx>, are e a s i l y c a l c u l a t e d . These p r o p e r t i e s make "onium n systems i n v a l u a b l e i n the study of the fundamental i n t e r a c t i o n s . The vast m a j o r i t y o f these "cniums" have not been observed because both pa r t n e r s are s h o r t l i v e d and must be produced a r t i f i c i a l l y . The production problem s i m p l i f i e s i f one + + • u -> e + v + v e u 2 Y »•++ , + A'' -»• p + TT partner i s stable and naturally occurring, "Oniums" such as e+e-, PTT~, y +e~, p y ~# and p p , have already been observed. At the present time the search i s on for the more elusive pi-muonium, TT + y - , The i n t e r e s t in the d i f f u s i o n and chemistry of hydrogen atoms extends naturally tc mucnium and positronium because they provide an opportunity to study the chemical interactions and motion of hydrogen-like atoms on a time scale as small as 10— 9 sec, Muonium and positronium are also of sp e c i a l i n t e r e s t i n p a r t i c l e physics. For example, the decay of the pcsitxctium ground state with spin=1, written o-Ps 3 y i s of great i n t e r e s t because the li f e t i m e i n vacuum provides a test f o r the theory of quantum electrodynamics, A na-jor d i f f i c u l t y in the experiment i s to i s o l a t e the e*e~ atom from other electrons which tend to shorten the observed l i f e t i m e . The conversion rate of muonium to anti-muonium has important consequences i n weak inte r a c t i o n theory. Such a conversion i s possible only i f the weak int e r a c t i o n conserves muon number in a m u l t i p l i c a t i v e or p a r i t y - l i k e fashion. Again, a major d i f f i c u l t y i n measuring the true vacuum conversion rate i s to i s o l a t e the y + € _ atom,, An experiment at TBIOMF has been planned f o r early 1979 that w i l l produce and detect fionium, i T * e - , The purpose of t h i s work was primarily to explore the s i m i l a r i t y i n formation and behaviour between positrcBium and muonium i n materials, p a r t i c u l a r l y powdered oxides, where copious amounts of positronium had already been observed. Such comparisons are essential to a broader understanding of the behaviour of these "onium" systems and w i l l inevitably help to r e a l i z e t h e i r f u l l potential i n physics. 5 II POSITRONS A HP POSITRONIUM IN M A 1 I 1 S Section II t1 Introduction Dirac (1930) postulated that vacancies i n a f i l l e d sea of negative energy electron states would manifest themselves physically as anti-electrons or positrons. Anderson(1933) was the f i r s t to observe positrons i n cloud chamber photographs of cosmic ray showers. The production of positron-electron pairs frcm high energy gamma rays was observed shortly afterwards (Blackett, 1933). These experimental results sparked a large e f f o r t to develop a theory for positrons i n matter. Mahorovicii (1934) was the f i r s t to suggest the existence of a bound e +e~ state, earned positronium or Ps. Pirenne (1946) was one of the f i r s t to perform c a l c u l a t i o n s on the positronium energy levels, fiheeler (1946) and Ore and Powell (1949) calculated annihilation rates frcm the S=0 and S=1 ground states respectively. In the meantime the experimental studies on positronium were just becoming possible as positron sources such as Na 2 2 and Cu 6 t + became available. The work of Deutsch (1951) firmly established the existence of positronium. Despite the great amount of experimentation since those early days, i t was not u n t i l 1974 that the f i r s t excited state of positronium, Ps*, was observed (Canter, 1975). This and many other experiments have been made possible by the development of mono.energetic teams of low energy positrons (Canter,1S72) . Sections II.2 and II.3 of t h i s chapter review the basic interactions cf positrons and positronium with matter and the experimental technigues for observing these interactions. Sections II.4 and II.5 discuss Ps formation i n matter and some previous positronium experiments in gases, powders, and gels which are relevant to t h i s study. 7 -Sect 11.2 Properties of Positrons and Positronium in Matter 1 Conservation of Charqe Conjugation Parity in- e £ A n n i h i l a t i o n Although positrons and electrons are i n d i v i d u a l l y stable spin 1/2 states, the positron-electron state i s unstable to an n i h i l a t i o n into gamma rays through electromagnetic i n t e r a c t i o n . The charge conjugation cr C L+S parity for an e +e~ state i s (-1) (see Appendix 1(a)) where L i s the o r b i t a l angular momentum and S i s the t o t a l spin. The C parity f o r a state containing n gamma rays i s (-1) n (see Appendix 1(b)). Electromagnetic interactions conserve C parity which implies (-1) L + S = (-1)n . Since i n many cases one need only consider the L=0 states, t h i s r e s t r i c t s the annihilation from spin 0 and spin 1 states to an even and odd number of y s respectively. Annihilation into a single y frcm a two body i n i t a l state cannot conserve both momentum and energy so that a spin 1 state must decay into (2m+1) Y s where m i s a positive non-zero integer. The annihilation rate into my s decreases rapi d l y l i k e am where a i s the fine structure constant (=e/tic= 1/137) so that the spin 0 and spin 1 states decay primarily into 2 y s and 3ys respectively. A i - F r e e - Postfe-ron--- A n n i h i l a t i o n - - • I n low e n e r g y e * e - s c a t t e r i n g o n l y t h e L=0 s t a t e c o n t r i b u t e s and t h u s r e s t r i c t s t h e f i n a l s t a t e t o 2y s and 3Y s f o r the S=0 and S=1 s t a t e s r e s p e c t i v e l y - D i r a c ( 1930 ) c a l c u l a t e d t h e s p i n a v e r a g e d 2 y c r o s s s e c t i o n f o r e + e -s c a t t e r i n g t o be °2Y ^ T r r e 2 c / v v<<c eqn I I . 1 where r e i s t h e c l a s s i c a l e l e c t r o n r a d i u s , e 2/mc , Ore and P o w e l l ( 1949 ) c a l c u l a t e d t h e s p i n a v e r a g e d c r o s s s e c t i o n f o r a n n i h i l a t i o n i n t o 3y s t o be a 2 y = 4 ( ^ 2 - 9 ) r e C c t / 3 v = 1 / 3 7 1 a 2 y v < < c The s i n g l e y a n n i h i l a t i o n r e q u i r e s a t J i i r d body i n t h e i n i t i a l s t a t e t o c o n s e r v e b o t h e n e r g y and momentum ,such a s an e l e c t r o n o r a n u c l e u s . I n t h e c a s e o f an e l e c t r o n t h e decay r a t e i n v o l v e s an >e _e— c o r r e l a t i o n c o e f f i c i e n t . West (1973) e s t i m a t e s t h a t t h e a n n i h i l a t i o n r a t e i n t o a s i n g l e y i n t h i s manner t o be s m a l l e r t h a n t h e 3y a n n i h i l a t i o n r a t e by a f a c t o r A 3 p where X i s t h e compton w a v e l e n g t h f o r an e l e c t r o n and p i s t h e s e c o n d e l e c t r o n d e n s i t y . On t h i s b a s i s t h e most o p t i m i s t i c p l e a d s t o a b r a n c h i n g r a t i o a / a = a 3 Y 3y A t t e m p t s t o o b s e r v e t h i s r a r e a n n i h i l a t i o n mode have been u n s u c c e s s f u l (Seddy,1 9 7 0 ) The s i n g l e gamma a n n i h i l a t i o n i n v o l v i n g a n u c l e u s i s much more l i k e l y and has been o b s e r v e d ( S o d i c k s o n , 1961) . The c r o s s s e c t i o n i s a p p r o x i m a t e l y a l + Z 5 r 2 . annihilation i n t o 0 gamma rays has also been observed (Shimizu,1968). In t h i s process the positron annihilates with a core electron and imparts the the r e s u l t i n g energy to another core electron. The Feynman diagrams for a l l . t h e s e annihilation modes are shown in f i g I I . 1.^/Free positrons are useful probes into the many electron state of the host substance since that state characterizes the subseguent an n i h i l a t i o n . For a thermalized free positron a n n i h i l a t i n g with an electron, where the t o t a l spin =0# the angle between the r e s u l t i n g 2Y S provides a measure of the e+e - pair momentum which depends primarily on the electron momentum di s t r i b u t i o n of the host. This has proven to be p a r t i c u l a r l y useful in studying metals., - 10 -(e) F i g II.1 Feynman diagrams f o r (a) 2 gamma a n n i h i l a t i o n ,(b) 3 gamma a n n i h i l a t i o n , (c) 1 gamma a n n i h i l a t i o n i n v o l v -i n g a nucleus , (d) 0 gamma a n n i h i l a t i o n i n v o l v i n g a nucleus and a second e l e c t r o n , (e) 1 gamma a n n i h i l a t i o n i n v o l v i n g a second e l e c t r o n . - 11 -I i i Bound State Anniailations-The factors that e f f e c t Ps formation i n a substance w i l l be discussed in Sect II..3- Given that i t does form, the si n g l e t <S=0 or para-positronium or p-^Ps) state and the t r i p l e t (S=1 or ortho-positronium or o-Ps) state form i n the s t a t i s t i c a l r a t i o 1:3. p-Ps decays into two 511 KeVY*s whereas o-Ps decays in t o 3 Y s . The energy spectrum i s continuous and i s shown i n f i g II.2. The mean decay rate {= 1/lifetime) in vacuum f o r p-Ps and o-Ps from theory and experiment are 1 % = p-Ps .7985 xlO 1 0 s e c _ 1 * CKolbig, 1969 ) ,exp Ap-Ps -799 ± .011 xlO 1°sec~ 1 (Theriot, 1967 ) . th o-Ps ~ 7.0379 ± .0012 x l O 6 s e c - 1 (Caswell, 1977 ) ,exp _ o-Ps " 7.056 + . 007 x l O 6 s e c - 1 (Sidley, 1978 ) The difference i n a n n i h i l a t i o n rates f o r o-Ps and p-Ps i s of order a and can be understood i n terms of the additional vertex f o r the Feyroan diagram f o r the o-Ps decay (see f i g II.1). no e r r o r given - 12 -Energy (mc^) F i g II.2 . The photon energy spectrum from the a n n i h i l a t i o n of o-Ps. (Ore,1949) - 13 -'• Sect 11-3 - . fixvec imenta 1 Tecfoai€rues~ i Genera1 The study of positrons in matter i s based on the detection of the ann i h i l a t i o n quanta. The relevant observables are the time before a n n i h i l a t i o n , the angle between the a n n i h i l a t i o n quanta, the energy of the anni h i l a t i o n quanta, and the number of annihilation quanta. - 14 -i i Lifetime Technique Na 2 2 sources are commonly used for measuring positron l i f e t i m e s because the emission of a positron i s followed, i n most decays ,by the emission cf a nuclear y of energy 1274 Ke? within 1 0 - 1 1 sec (see f i g II.3) and thus provides a convenient method of signaling a positron emission. One counter i s used to s t a r t the clock on an e+ emission and up to three y counters in coincidence can be used to stop the clock. Small p l a s t i c s c i n t i l l a t o r s provide excellent timing resolution (.3 x 10 - 9 sec), but have poor energy resolution and are very i n e f f i c i e n t . For studying short l i f e t i m e s i n s o l i d s and l i g u i d s , p l a s t i c s c i n t i l l a t o r s are e s s e n t i a l . , Larger Mai detectors are often preferred for measuring the long l i f e t i m e of o-Ps where sometimes a t r i p l e coincidence stop i s reguired (Bird, 1973). The eff i c i e n c y and energy resolution are increased substantially using t h i s type of detector although the timing resolution (3 or 4 nsec) i s not as good as may be achieved with p l a s t i c s c i n t i l l a t o r s . - 15 -F i g II.3 . N a 2 2 decay scheme. The maximum enegy f o r a p o s i t r o n r e s u l t i n g from the decay i n t o N e 2 2 * i s .544 MeV. The l i f e t i m e s f o r N a 2 2 and N e 2 2 * are 2.6 years and 1 0 - 1 1 sec r e s p e c t i v e l y . - 16 -i i i angular Correlation Technique If an S=0 e+e- state has a pair momentum component, p x , perpendicular to one of the photon emission directions then the two photons w i l l be emitted at an angle, 180°+ e where 6 * Px/m QC PJ. << m c' (West, 1972) If the positron i s thermalized then the pair momentum i s approximately egual to the electron momentum. Thus i f p_L of the electron i s 0.5 KeV/c, corresponding to an energy pf/2m o=0.25 eV, then the two photons w i l l be emitted at an angle of 1 mrad or .057°. The angular d i s t r i b u t i o n between the annihilation quanta i s measured using a long s l i t angular c o r r e l a t i o n apparatus. This apparatus measures the coincidence counting rate between two detectors as a function of the angle defined by detector 1, the source and detector 2. A t y p i c a l angular resolution would be .5 mrad.. - 17 -i v Pop pier Br o a d en in g lTtee&«4que.~ Information on-the pair momentum d i s t r i b u t i o n can also be obtained by using a high resolution Ge or GeLi detector to measure the Doppler broadening of the anni h i l a t i o n l i n e at 511 KeV. To f i r s t order, the s h i f t i n energy produced by a longitudinal pair momentum component, p„ , i s given by A E =hv-mc2^p„c/2 (Hotz, 1968) where hv i s the energy of the detected photon. Thus, i f p =0.5 KeV/c then AE =0.25 KeV. In cases where the sampled e - momentum d i s t r i b u t i o n i s i s o t r o p i c , the technigues of Doppler broadening and angular correlation ,applied to annihilation guanta i n a given d i r e c t i o n , y i e l d the same information. Charalambois £1976) has reported a system resolution of 1.08 KeV at 514 KeV using an i n t r i n s i c Ge detector, which i s eguivalent to an angular c o r r e l a t i o n apparatus with an angular resolution of 4 mr ad. The Doppler broadening technigue analyzes a l l momentum channels simultaneously and i s therefore much faster. Also, i t does not require high e + stopping densities nor strong sources as does the angular correlation technigue. The obvious disadvantage i s the poorer resolution which i s limited by the i n t r i n s i c properties of semi-cooductors such as GeLi. - 18 -v 2j£3y Decay Ratio Technique 3 y decays r e s u l t i n g from o-Ps formation can be detected using a 3y coincidence technique {Celitans, 1964a), but normalizinq the detection rate to that of 2y decays i s d i f f i c u l t because 3 y decays result i n a continuous energy spectrum. This w i l l be discussed further i n Sect IV. 1. Chanqes i n the 3 Y / 2 Y r a t i o are however, d i r e c t l y observable in the annihilation spectra. An increase i n the 3 y / 2 y r a t i o i s characterized by a reduction i n the 511 KeV phOtopeaJc and an increase in the countinq rate below 511 KeV. Nal detectors previously and GeLi detectors more recently (Sen and Patro, 1969) have been used to study the 3 y / 2 y r a t i o i n th i s manner. - 19 Sect I I , 4 Ps Formation i Slowing Dfiwn i n Gases High energy positrons lose energy through i n e l a s t i c c o l l i s i o n s leading to ionization or the emission of Bremsstrahlung radi a t i o n . The r a t i o between the energy loss rates for the two processes i s given as dE dx = EZ/800 (Segre, 1964a) dE dx. ion where E i s the positron energy i n MeV and Z i s the atomic number of the atomic species. Below energies of a few MeV, ionization dominates whereby the fas t positron loses approximately 30 eV per ion formed (Segre, 1964b), /The loss to free a n n i h i l a t i o n i s small because 1/(slowing down time) i s large in comparison to the free annihilation rate given by A 2 = nZvcr2 = nZiTr^c using eqn II. 1 where n i s the number density for the gas and Z i s the atomic number for the gas., - 20 -i i Ore-'Gaj>' i n Gases Fig. II.4 shows the d i f f e r e n t channels that a positron can take before i t annihilates. For the energy i n t e r v a l (E . ,E ) the processes of atomic or molecular ex c i t a t i o n ion exc and Ps formation are i n competition. The Ore gap i s defined as the energy i n t e r v a l (E ,E. -6.8 ev) . I t i s generally exc ion believed that Ps forming c o l l i s i o n s dominate the dE/dX i n this energy range. The Ps atom has a k i n e t i c energy less than that of the incident positron by E. -6.8 ev. A ion positron with an energy below the threshold for Ps formation |E . -6,8 eV) w i l l c o l l i d e e l a s t i c a l l y u n t i l i t annihilates ion f r e e l y . The positron usually thermalizes before ann i h i l a t i n g . The Ore l i m i t s on Ps formation are arrived at by assuming that the l a s t i o n i z i n g c o l l i s i o n above E. leads ion to a uniform population density i n the energy i n t e r v a l (0,E. ) . I t i s further assumed that a positron i n the Ore ion gap <E , E . -6.8 eV) forms Ps 100$ of the time. The lower exc ion l i m i t on f i s then { E -( E . -6.8 eV ) ) / E. . I f Ps exc ion ion the positron finds i t s e l f in the energy i n t e r v a l (E , • exc E . ) i t may or may not form Ps since e x c i t a t i o n i s a ion competing process. Thus the upper l i m i t on f i s Ps 6.8 eV/E. ion As an example, the Ore l i m i t s for argon and helium are (16r:43}% and (9^-28)1 respectively, whereas the observed fractions are 27±3% (Gittleman, 1956) and 32±3% (Pond, 1952) respectively. - 21 -Dominant f r e e e c r o s s s e c t i o n ( s > / | 2 MeV i o n i z a t i o n , energy l o s s ^ 3 0 e V / i o n > 500 KeV F i g 11.4 . Flow diagram f o r f r e e p o s i t r o n s i n a gas w i t h i o n i z a t i o n e n e r g y 1 E. and e x c i t a t i o n energy E . - 22 -i i i Low Energy Positron Beams i n Gases Unfortunately, the Ore predictions have had only limited success, one case being argon . I t has been suggested low energy resonances just above E ^ o n could re s u l t i n an non-uniform population density below E^on (Lee, 1 §67) • This would explain the f a i l u r e of the Ore l i m i t s . Since 1970,sources of thermal positrons from the back scattering of high energy positrons off various surfaces have become available. The highest e f f i c i e n c y thus f a r (3 x 10"~35J) was obtained by using a gold surface coated with HgO (Canter,1974). These thermal positrons have been used to generate monoenergtic beams of low energy positrons. Such beams have been used to measure t o t a l cross sections i n noble gases (Harris,1976 & Canter, 1974). The technigue involves passing a positron beam through a gas c e l l of length d, i n which the number density f o r the gas i s n. The pressure i s chosen so that only s i n g l e scattering i s l i k e l y . The transmission c o e f f i c i e n t through the gas i s measured at the end of the c e l l using a Nal counter to detect annihilation radiation with and without the gas. The t o t a l cross section f o r the gas,ignoring small angle s c a t t e r i n g , i s then given by °tot = C ^ v a c " ^ g a s ] / t n d ^ v a c ] and represents the sum of a l l possible cross sections, e l a s t i c and i n e l a s t i c . Although sharp resonances are not present (see f i g 11.5) the t o t a l cross section does drop o f f - 23 -loo! 50 20 10 "rf V * 2 o | ' -o I/) OC o £ 02 o 0-1 009-002 001 S £ Ne * » « * o Hi He j i i i_ 0 2 4 6 8 10 12 U 16 18 20 25 30 50 70 100 400 POSITRON ENERGY(eV ) -Fig II.5 . Total cross section measurements i n noble gases for low energy positrons.(Canter,1974) rapidly below 50 eV in some cases. This could be responsible for a non-uniform population density below E^ o n and would therefore help to explain the f a i l u r e of the Ore l i m i t s i n cases such as Kr and He. In p r i n c i p l e i t should be possible to monitor the three gamma coincidence rate as a function of positron energy and thus determine e x p l i c i t l y the energy dependence of the Ps forming cross section. This would be a firm test of the Ore gap theory. - 2 5 -i v F o r m a t i o n i n S p l i d s -T h e O r e g a p a n a l y s i s c a n n o t b e e x t e n d e d i n a s t r a i g h t f o r w a r d m a n n e r t o i n c l u d e s o l i d s - P o s i t r o n i u m h a s b e e n o b s e r v e d i n i n s u l a t o r s ( e * g . g u a r t z a n d i c e ) b u t h a s n o t b e e n o b s e r v e d i n c o v a l e n t s e m i - c o n d u c t o r s s u c h a s G e a n d S i - , T h e e n e r g y o f t h e p o s i t r o n i u m s t a t e i s m o d i f i e d b y t h e d i e l e c t r i c p r o p e r t i e s o f t h e m e d i u m a n d i s o n l y s e l l d e f i n e d i f t h e e l e c t r o n i c e n e r g y l i e s i n a f o r b i d d e n g a p - H i g h y i e l d s o f p o s i t r o n i u m f o r m a t i o n C e . g . 30%) h a v e b e e n o b s e r v e d i n o x i d e p o w d e r s ( p a u l i n a n d A m b r o s i n o , 1 9 6 9 ) . , T h e p o s i t r o n s a r e s l o w e d d o w n w i t h i n the g r a i n s a n d e v e n t u a l l y r e a c h t h e i n t e r g r a n u l a r r e g i o n a s p o s i t r o n i u m . ; P a u l i n a n d A m b r o s i n o ( 1 9 6 9 ) h a v e r e p o r t e d a n i n c r e a s e d P s f r a c t i o n f o r a m o r p h o u s S i 0 2 p o w d e r c o m p a r e d ^ w i t h t h e c r y s t a l i n e f o r m -I t s h o u l d be s t r e s s e d t h a t a P s s t a t e i n a s o l i d c a n n o t b e t r e a t e d i n d e p e n d e n t l y o f t h e e l e c t r o n s i n t h e s o l i d - I n a n u n r e a c t i v e g a s a t l o w p r e s s u r e t h e p e r t u r b i n g e f f e c t s o f t h e n e i g h b o u r i n g e l e c t r o n s o n a P s s t a t e a r e s m a l l , w h e r e a s i n a s o l i d t h i s i s n o t t r u e - F o r e x a m p l e , a n g u l a r c o r r e l a t i o n m e a s u r e m e n t s i n s i n g l e c r y s t a l i c e ( s e e f i g I I . 6 ) r e v e a l a d e l o c a l i z e d p - P s s t a t e w h e r e b y t h e p a i r m o m e n t u m d i s t r i b u t i o n h a s s i d e p e a k s r e f l e c t i n g t h e - 26 -p e r i o d i c i t y of the p-Ps centre of mass position save function. - 27 -~i i — i — i — i — i — i — i — i — i — i — i — r r - i r SINGLE CRYSTAL OF ICE 5 0 ANGLE IN MILL! RADIANS F i g II.6 . Angular c o r r e l a t i o n measurements i n s i n g l e c r y s t a l i c e f o r the d i f f e r e n t c r y s t a l , o r i e n t a t i o n s . The arrows i n d i c a t e the t h e o r e t i c a l p o s i t i o n of the peaks assuming a p e r i o d i c wave f u n c t i o n f o r p-Ps.The broad Gaussian background i s due to f r e e p o s i t r o n a n n i h i l a t i o n . (Mogensen,1971) - 28 -X . Summary-of f s roriatiaa-. In summary, the Ore gap i s a useful conceit i s gases where the formation process i s thought t o be represented well by charge exchange c o l l i s i o n s with i n d i v i d u a l atoms. Now that monoenergetic beams of low energy positrons are available i t should be possible to firmly test the v a l i d i t y of t h i s approach. In s o l i d s the si t u a t i o n i s more complex so that a more sophisticated approach i s required. - 29 -Sect t II.5 o-Ps in Gases, Powders and Gels A Quenching i n Gases Positronium gas chemistry makes use of the r e l a t i v e l y small mean decay rate cf free o-Ps of 7.056±.007 y s e c - 1 <Gidley,1977)• In gases t h i s mean decay rate i s increased i n two ways, pickoff a n n i h i l a t i o n and o-Ps to p-Ps conversion. Both processes are sai d to quench the o-Ps. Pickoff annihilation i s when the bound positron i n o-Ps annihilates with an electron from the surrounding medium. In gases t h i s can happen to a small degree during e l a s t i c c o l l i s i o n s or to a much greater degree i f a chemical compound i s formed. The resulting pair momentum i s of order 3 KeV/c corresponding to the momentum d i s t r i b u t i o n cf the valence electrons of the gas molecules. I f a gas has an unpaired electron, a spin f l i p process may occur during a c o l l i s i o n so that the c-Ps i s converted to p-Ps. The pair momentum f o r thermal p-Ps i s order 0.1 KeV/c and thus makes quenching due to a conversion process easily distinguishable from pickoff quenching associated with a chemical bond formation. - 30 -i i Quench fiate-Coefficient i a Gases-The mean guenching rate for o-Ps atoms with velocity v i n a gas with number density n and guenching cross section ° i s q x = a vn * s e e ftPPeildix ID--.. q q I f the Ps thermalizes f a s t , v iy;- the mean thermal ve l o c i t y . The mean guenching rate i s proportional t o n where the constant, of proportionality, a q w » i s referred to as the guench rate c o e f f i c i e n t . For gases which possess a guench rate c o e f f i c i e n t that i s much larger than that f o r argon (2«.51±. 05 x -10* sec-* /atm. # Cetitans, 1964b) 4 argon + gas mixtures can be used to study the reaction. The argon acts as a moderator producing 21% Ps, but has very l i t t l e guenching e f f e c t . The guench rate c o e f f i c i e n t f o r a par t i c u l a r gas i s then the slope of the guench rate versus gas concentration tin argon • gas mixtures. - 31 ; -i i i Ps i l Powders andGels Paulin and Ambrosino {1969} have studied positron l i f e t i m e s in fi n e MgO# SiG2'-, and A1 ?0 3 powders. The l i f e t i m e spectra exhibited three components at <. 4 nsecj 2 nsec and 140 nsec. They attributed the <.4 nsec component to free positron a n n i h i l a t i o n and p-Ps ann i h i l a t i o n , the 2 nsec component t o pick o f f of o-Ps within the grains, and the 140 nsec component to o-Ps i a the intergranular regions. Brandt and Paulin (1969) interpreted these r e s u l t s i n terms of a di f f u s i o n model whereby the o-Ps forms within the grains and then dif f u s e s out int o the intergranular region., Since that time many experiments have been done with fine powders., StedIt and Varlashkin (1972) have performed angular co r r e l a t i o n measurements on compressed Si0 2 powders. , They investigated the e f f e c t of powder size, powder density, baking, and temperature on the narrow component associated with p-Ps . They interpreted the res u l t s i n terms of the dif f u s i o n model suggested by Brandt and Paulin (1969). Gidley and Marko (1976) have measured the l i n e a r dependence of the o-Ps mean decay rate i n fin e SiO ? on powder density. They extrapolated back to zero powder density and obtained a value of 7.09±.02 ysec -* f o r the mean decay rate of o-Ps i n vacuum. Systematic errors were l a t e r discovered (Gidley,1978) which lower t h i s value to 7. 067±.021 |;sec-i. Positrons have also been injected into s i l i c a gels with o. a mean poire s i z e of 22 A (Chuang, 1974) . A f t e r evacuating the - 32 -gel they observed a long component in: the l i f e t i m e spectrum with a mean decay rate of 31 ysec— 1 which they attributed to o-Ps i n the pores. After adsorbing different amounts of B r ? , NO, * 2 ' °2 * a a < i H 0 2 * they measured quenching rate c o e f f i c i e n t s for these gases. They also performed angular co r r e l a t i o n measurements to determine the quenching mechanisms. - 33 -£MAPTJE III POSITIVE MOONS AJD MDONIUM IN MAT^lfi Sect I I I x l Introduction In 1935 Yukawa postulated that the nucleus was held together by an exchange force whereby heavy quanta are exchanged between the nucleons within the nucleus. He estimated on the basis of the strength and ranqe of the nuclear force that the heavy quanta should possess a mass between 50 and 100 Mev/c*. Cosmic ray experiments performed by Anderson and Neddermeyer (1937,1938) and Street and Stevenson (1937) showed the existence of a pair of oppositely charqed p a r t i c l e s with a mass ^ 100 Mev/c 2. However, further experiments (Conversi, 1947) revealed that the nuclear absorption l i f e t i m e i n carbon of the negatively charged partner was of order 10-* sec. instead of 10~ 1 8 sec. as expected i f the p a r t i c l e s were strcnqly int e r a c t i n q . These two p a r t i c l e s are now c a l l e d muons. The Yukawa meson , which i s now referred to as the pion, was discovered l a t e r that year (Lattes, 1947) i n an experiment which showed that pions decayed i n t o a neutral p a r t i c l e plus a mucn. ,. Section III.2 of t h i s chapter discusses the properties of muons and muon decay, and points out some of t h e i r uses as probes. Section III.3 reviews the basic features of y+SB and MSB. Section III.4 discusses muonium formation with s p e c i f i c reference to the analogous s i t u a t i o n i n hydrogen formation. - 34 . -Sect I I I . 2 • Properties•• •-:^^jd--q:ses--o£~<Bm$®&--- . . i P r o p e r t i e s The ... -. , p r o p e r t i e s . '"• o f muons'-i - have.- - p r o v i d -ed v a l u a b l e i n s i g h t i n t o elementary t h e o r i e s f o r •weak i n t e r a c t i o n s and e l e c t r o m a g n e t i c i n t e r a c t i o n s . . For example, the gyromagnetic r a t i o o f the muon which i s d e f i n e d as g = y 4 m c / eh (where y i s t i e , M O B . E a f l i e t i a i i o i e a t a a l : in i s the muon aass) ; i s very c l o s e t o 2 as p r e d i c t e d by the D i r a c eguation f o r a s p i n 1/2 p a r t i c l e , The:, d i f f e r e n c e a-. = fg y-2) /2 has provided one of the b e s t t e s t s f o r the theory of quantum e l e c t r o d y n a m i c s s i n c e i t has been; measured and c a l c u l a t e d to 1 part i n 10 s. /The r e s u l t s as of 1977 are = 1,165,910(9) x 10~9 (Bailey,1977) a^ 1 = 1,165,915(10)x 10 - 9 (Calmet,1977) Huons decay weakly with a l i f e t i m e o f 2 199.4 nsec i n t o an e l e c t r o n and two n e u t r i n o s i n the f o l l o w i n g way; y + -> e+ + v e + v y y r + e- + v e + v y I t was di s c o v e r e d i n 1956 from the 6 -decay of C o 6 0 (Wu, 1957) t h a t weak i n t e r a c t i o n s do not conserve p a r i t y . Hon co n s e r v a t i o n of p a r i t y i n rauoa decay a l l o w s the weak interaction Hamiltonian to contain a pseudoscalar term °y«Pe where a y i s the mucn spin operator and p e i s the electron momentum operator. The obvious consequence of such a term i s that the d i s t r i b u t i o n of decay electrons depends cn cose where e i s the angle between the muon pola r i z a t i o n vector and the electron momentum. The simplest i n t e r a c t i o n Hamiltonian containing such a term leads to the following energy-anqular d i s t r i b u t i o n dN = , > dfidw [ 1 ± |P|D(W) cose ] (eg. W i l l i a m s ^ ,1971) + f o r p o s i t r o n s - f o r e l e c t r o n s where p i s the pola r i z a t i o n vector, 0 the anqle between and the electron momentum, and w = E / J _ . v i s the enerqy of the electron expressed i n units of E i r t a x ~ % / 2 , 1 shows the parameters C(w) and D(w) as a function of «• I t should be noted that D(w) chanqes siqn qoinq from small electron enerqies to larqe electron energies, also, the di s t r i b u t i o n of enerqies, C <w), i s weiqhted towards E . max The value of D (w) averaged over a l l energies i s ,324±.004 <Cronin,1968) - 36 -T 1 1 - j ' 1 ' r W = E/ Emax Fig I I I . l . Muon decay parameters for dN(w,fi)/dwdft \ i r (e.g. Brewer,1975) - 37 -i i Muons as Probes Muons are also proving to be very useful probes into atomic and nuclear structure. When negative muons stop in matter they are captured into weakly bound atomic orbits and then proceed to cascade through the lower o r b i t s u n t i l they reach the ground state. The muon life t i m e i s shortened i n th i s ground state due to the process whereby the muon i s captured by the nucleus. Since the r a d i i of atomic o r b i t a l s vary inversely with the reduced mass i n a hydrogen-like atom, the mucnic orbits are approximately 2 00 times smaller than the corresponding ele c t r o n i c o r b i t s . In the upper part of the cascade, where there i s substantial overlap between muonic orb i t s and the K and L elec t r o n i c o r b i t s , Auger tr a n s i t i o n s dominate,, In such a t r a n s i t i o n the t r a n s i t i o n energy i s imparted to a K or L electron. Transitions between the lower o r b i t s are electromagnetic in nature whereby the tr a n s i t i o n energy i s released i n the form of an X ray. The lower orb i t s are often i n s i d e the nucleus so that the X ray energies are s h i f t e d from those calculated by an ordinary Coulomb potential because of the perturbing e f f e c t s of the nuclear charge d i s t r i b u t i o n . The present study i s directed towards positive muons. Polarized positive muons can be used as magnetic probes into the many electron states i n matter. The time dependence of the muon polarization vector i s determined by the magnetic environment i n which i t e x i s t s . The muon polarization vector i s e a s i l y observable because of the asymmetric muon decay. - 3 8 -In addition, the bouad state (Mu) provides a unique opportunity to study the chemistry and motion of hydrogen-? l i k e atoms. Moreover, macroscopic quantities of muonium are not required to obtain information on the system as i s the case f o r hydroqen studies. Each muonium atom i s detected separately so that a m i l l i o n muons are s u f f i c i e n t to determine the time dependence of the muon pol a r i z a t i o n vector. Such experiments s i l l i nevitably help to c l a r i f y our understanding of the macroscopic properties of hydroqen in matter. - 39 -Sect i l l . 3 The Techniques of u + Spin*Besonance { -y +SR) an d Mu Spin Resonance jMSR)in Transverse Magnet i c Fields i General The techniques of y +SR and MSB hoth involve measuring the time evolution of the muon polarization vector i n the presence of an externally applied magnetic f i e l d . The difference i s that i n y+SR the muon exists i n a diamagnetic environment whereas i n MSR the muon i s strongly coupled to the large magnetic moment of an electron. The time dependence of the muon po l a r i z a t i o n vector y i e l d s information on the magnetic environment of the free muon or muonium atom. This time dependence for muonium i s r a d i c a l l y different from that for free ttuons. - 40 -i i y +SR The spin Hamiltonian for a free muon i n the presence of an external magnetic f i e l d of magnitude |B| applied along the z d i r e c t i c n i s H y = h uT.ay = hwa 2 2 Z where a> = g y e B/2m yc and the components of are the Pauli spin matrices. I t follows that the energy eigenstates are |a> = | a z/2 =l/2> and |g> = |c z/2=-l/2> "-th energy eigenvalues T i g ^ e j B l and -tig e | i | » respectively. , 2m yc 2m yc The technigue of y+SR involves preparing an i n i t i a l free muon state polarized i n a di r e c t i o n perpendicular to the f i e l d d i r e c t i o n , say the x directi o n . The i n i t i a l state can then be written l , f ' ( 0 ) > = \°z ^  T/2>* The muon 2 polarization vector i s the expectation value of a.y and therefore can be written i H ^ t - i H y t , P(t) = <iJ,(0)|eB a y e * |i|)(0)'> =cosco vt x + sinw^t y see Appendix I I I where c o ^ = 2irx 13.55 KHz/G x | i | - 41 -i i i MSB The corresponding problem f o r muonium i s more d i f f i c u l t to s o l v e because i t i n v o l v e s two s p i n 1/2 p a r t i c l e s i n t e r a c t i n g with one another as w e l l as with an e x t e r n a l f i e l d . The spin Hamiltonian f o r Mu i n an e x t e r n a l f i e l d , B, i s given as H M u = tmQoV:oe + fcw^.aU + t i w e . a e 4 2 2 where Tiw o=1.84 x 1 0 _ s eV i s the h y p e r f i n e s p l i t t i n g o f Mu, ha y/2 and t i a e / 2 are muon and e l e c t r o n s p i n o p e r a t o r s , and wy and we are -g yeB / 2m yc and g eeB / 2m ec , r e s p e c t i v e l y . , The procedure f o r e v a l u a t i n g the time dependent muon p o l a r i z a t i o n vector i s the same as for the f r e e muon case. It i n v o l v e s the d i a g o n a l i z a t i o n of H 1^ which i s a 4 x 4 matrix i n order to evaluate i t s e i g e n v a l u e s and ei g e n v e c t o r s . The d e t a i l s can be found i n many sources <eg:Brewer, 1975 ). F i g II I . 2 shows the f a m i l i a r B r e i t - S a b i diagram f o r the muonium energy eigenvalues i n u n i t s of h f o r L=0 as a f u n c t i o n of the dimensionless q u a n t i t y x=B/BQ where B 0 = 1*>yi g e y e - g yy y] = 1585 G i s the e f f e c t i v e magnetic f i e l d experienced by the muon due to the e l e c t r o n . - 42 -F i g I I I . 2 . Muonium energy eigenvalues as f u n c t i o n s of x=B/1585G.The v^j are the allowed, t r a n s i t i o n energies i n u n i t s of h. v •;-i; = ,„ •: . - 43 ; -I f the external f i e l d i s applied along the z di r e c t i o n , transverse to the i n i t i a l muon polarization vector then the i n i t i a l muonium state can be written |*(0)> = K | £ h = l +l£x=l , £ x = ~ ^ > /?;•. 2 2 2 2 '2 2 2 2 where i t i s assumed that half the Hu forms with the muon and electron spins aligned and half with them anti-aligned. The x component of the muon polarization yector as a function of time i s defined as Mu . Mu iH t - i H t P x ( t ) = <^(0)|e h a j e h | ^(0)> I f B<<B0 t h i s may be approximated P (t)'v 1_ cosdi_t [cosflt + cos (6J 0+^) t] (e.g.Brewer 2 1975) where 0)_ = 1 (uii 2+^2 3 ) 2 Q =1_ (to 2 3 —11)12) 2 : .=hv. . = E.-E. ID ID 1 D The o s c i l l a t i o n s corresponding to the angular v e l o c i t y a ) Q + fi are too fa s t to resolve experimentally since they correspond to a period of -.225 nsec- Thus the observed x component of the pol a r i z a t i o n vector i s P e x p ( t ) = 1 COSU t cosfit 2 whose maximum value (1/2) i s exactly half that of the actual maximum of P (t) . For intermediate f i e l d s ^70 G , P e x p ( t ) displays^ a f a s t o s c i l l a t i o n w_ = l > i 2 + w 2 3 ) enveloped by a beat, frequency fi=i ( u _ u 1 ) . In very low f i e l d s |B<10G) fi^O so tkat only a single precession frequency i s oberservable corresponding to w-^w | 2 % C J 2 3 ^ 1 . 4 MHz 'per Gauss. The observable quantity .in y+SR and MSB i s the number of positrons emitted i n a d i r e c t i o n in the plane of precession as a function of time after the y + stop. For a low transverse f i e l d the usual spectral form i s dN = N . e - t / T ^ [ l + Asy ( t ) c o s ( u u t + * ) + Asy (t) dt 0 y + Mu cos (ai_t+e ) ] + B where f y i s the muon lifetime,, Asy + (t) i s time dependent asymmetry of the free muons, and As y M u ( t ) i s the time dependent asymmetry of the muonium. In many, cases the asymmetry relaxes exponentially so that A s^Mu ( t ) = A s W 0 ) e X p [ ~ X M u t ] and A s y y + ( t ) = A s y y + ( 0 ) e x p [ - A * + t ] Such i s the case for muons or muonium propagating f r e e l y throuqh matter where the probability f o r depolarization per unit distance i s a constant - The i n i t a l asymmetries depend on the s o l i d anqle subtended by the positron detectors, the energy selection of the positron counters, the i n i t i a l p o l a r i z a t i o n , and the f r a c t i o n of muons precessinq i n a free state or muonium state. The B term allows f o r a f l a t backqround. - 46 -v Source of- P o l a r i z e d Muons-The source of p o l a r i z e d muons o r i g i n a t e s from pion decay + + , TT ->- y + V y The n e u t r i n o s t a t e obeys a two component Key 1 equation i -5=.P V >'= I P I C I V > 1 y 1 1 1 y with an h e l i c i t y e i q e n v a l u e -1. Cons e r v a t i o n o f angular momentum and l i o e a r momentum r e q u i r e t h a t the y + i s a l s o an h e l i c i t y :0l;g.«l.t'State i n the r e s t frame of the pion. The f i r s t s t o pping muontchannels were designed t o c o l l e c t backward decaying muons from pions i n f l i g h t . These types of channels are c h a r a c t e r i z e d by a r e l a t i v e l y high energy of ^50 MeV and a p o l a r i z a t i o n <• .8 . The pions u s u a l l y O r i g i n a t e from e n e r g e t i c protons i n c i d e n t on a p r o d u c t i o n target., Recently i t was di s c o v e r e d t P i f e r , 1976) t h a t there e x i s t s a s i z e a b l e f l u x of y * s r e s u l t i n g from pions s t o p p i n g on or near the s u r f a c e of the production t a r g e t . The r e s u l t i n g " s u r f a c e muons" are monenerqetic at 4.2 MeV and momentum 29 MeV/c and are almost completely p o l a r i z e d because the pions a r e a t r e s t i n the l a b . - 47 -Segtjj. I I I M u F o r m a t i o n i G a s e s 50 MeV p o s i t i v e l y c h a r g e d muons l o s e e n e r g y i n :gases p r i m a r i l y t h r o u g h i o n i z a t i o n c o l l i s i o n s , l c s i n g ^ 30 eV p e r i o n f o r m e d ( S e g r e , 1 9 6 4 b ) , Hhen t h e muons r e a c h an e n e r g y o f s e v e r a l KeV t h e i r v e l o c i t y i s c o m p a r a b l e w i t h t h e v e l o c i t y c f t h e v a l e n c e e l e c t r o n s i n t h e gas m o l e c u l e s s o t h a t t h e y b e g i n t o c a p t u r e a n d l o s e e l e c t r o n s i n r a p i d s u c c e s s i o n . The f i n a l c h a r g e s t a t e o f t h e muon s y s t e m as i t a p p r o a c h e s t h e r m a l e n e r g i e s i s p r i m a r i l y a f u n c t i o n o f t h e c r o s s s e c t i o n s f o r e l e c t r o n c a p t u r e b y a m u o n , a 1 Q + » a n d e l e c t r o n l o s s by a muonium a t o m - a„, , T h e c r o s s s e c t i o n s a a n d •* 01 1-1 a Q _ 1 i n n o b l e g a s e s a r e a few o r d e r s o f m a g n i t u d e s m a l l e r t h a n a s o t h a t t h e s i m p l i f i c a t i o n i s v a l i d i n t o b l e -1 o g a s e s . As y e t no m e a s u r e m e n t s o n t h e y + e _ e - s y s t e m , b o n e d by . 7 5 e V , h a v e b e e n p e r f o r m e d a l t h o u g h i t s u r e l y m u s t e x i s t . P r o d u c t i o n o f M u - i o n s i n a n o n - d e p o l a r i z i n g e n v i r o n m e n t must be c o n s i d e r e d a n e x t r e m e l y d i f f i c u l t t a s k . V e r y l i t t l e i n f o r m a t i o n e x i s t s o n t h e c h a r g e e x c h a n g i n g c r o s s s e c t i o n s f o r m u o n s , b u t a l a r g e amount o f d a t a e x i s t s f o r p r o t o n c h a r g e c h a n g i n g c r o s s s e c t i o n s i n t h e e n e r g y r a n g e 2 K e V - 1 MeV, T h e s e c r o s s s e c t i o n s a r e t h o u g h t t c b e v e l o c i t y d e p e n d e n t , c o t mass d e p e n d e n t , s o t h a t much c a n be i n f e r r e d a b o u t t h e muon c h a r g e s t a t e i n g a s e s a t n e a r t h e r m a l " e n e r g i e s b y c o n s i d e r i n g t h e c o r r e s p o n d i n g s i t u a t i o n t The i j i n a±j r e f e r to the i n i t i a l and f i n a l charge s t a t e s . - 48 -f o r p r o t o n s . F i g s I I I . 3 la.), ( b ) , (c) r |d> and (e) show a 1 Q-aad oQ1 f o r p r o t o n s i n H 2 , fle# A r , He, K r , and A r . The b e h a v i o u r o f o1Q f o r He and Ne i s n o t i c e a b l y d i f f e r e n t i n t h a t i t d r o p s o f f r a p i d l y below 10 KeV. F o r He olQ/oQl .15 a t 2 KeV i m p l y i n g t h a t t h e n e u t r a l f r a c t i o n i s d e c r e a s i n g , whereas f o r X e a 1 0 / a Q 1 ^ 3 0 , s u g g e s t i n g t h a t t h e p r o t o n s a r e q u i c k l y n e u t r a l i z i n g . T a b l e I g i v e s t h e muonium f r a c t i o n s , t h e i o n i z a t i o n e n e r g i e s , a n d t h e e x p e c t e d muon c h a r g e exchange c r o s s s e c t i o n s a t 220 eV on t h e b a s i s o f the p r o t o n d a t a f o r s e v e r a l n o b l e g a s e s . The h i g h - . ' p r o b a b i l i t y f o r , f o r m a t i o n i n Xe i s e a s i l y u n d e r s t o o d a f t e r c o n s i d e r i n g t h e e x p e c t e d r a t i o between t h e c a p t u r e c r o s s s e c t i o n and t h e s t r i p p i n g c r o s s s e c t i o n a t muon e n e r g i e s o f 220 eV a s s u g g e s t e d by t h e p r o t o n d a t a . M o r e o v e r , t h e r e i s no t h r e s h o l d e n e r g y f o r Mu f o r m a t i o n i n Xe b e c a u s e t h e i o n i z a t i o n e n e r g y {12.127 eV) i s e x c e e d e d by t h e Mu b i n d i n g e n e r g y (13.6 e V ) . The p r o t o n d a t a f o r A r s u g g e s t s t h a t t h e muons a r e a l s o g u i k l y n e u t r a l i z i n g a t n e a r t h e r m a l e n e r g i e s a s i n the c a s e f o r Xe. However, i n Ar a must go t o z e r o below 1 0 2.15 eV where Mu f o m a t i o n i s e n e r g e t i c a l l y f o r b i d d e n . The f r e e muon f r a c t i o n i n Argon may r e s u l t i n p a r t f r o m Hu i n t h e e n e r g y gap (E . ,13.6 eV) b e i n g ion s t r i p p e d o f i t s e l e c t r o n . T h e c o m p e t i n g p r o c e s s e s f o r e n e r g y l o s s i n t h i s gap a r e Mu e x c i t a t i o n A r e x c i t a t i o n a n d e l a s t i c - 49 -11 E y ( K e V ) 1.1 11.1 111. - >3 •0 t F ° * t 0 ( c m ) H 2 -16 to i ' i—i i i i 111 •—r~~* i—i i i i 111 • T r r—rn o° o - | 9 trio -17 10 H 2 •4. - 1 6 tr io He - 1 7 tno H e - * • • • ' • - ' I I M i l l 10 »oo I • I L. p, E ( k e V ) F i g 1 1 1 . 3 ( a ) . The e l e c t r o n c a p t u r e c r o s s s e c t i o n f o r p r o t o n s i n h y d r o g e n and h e l i u m . ( T a w a r a , 1 9 7 3 ) - 50 -^ r~^i I I I I I I |—n—r~<~\—I I I I I I | • r—r-i 1—|-f ^ . o ( c m 2 ) 10 $ I" Ar 4 ft Am A * t - i s | . « 1 6 • N e T * * M t| Ne. • A - I S 10 t 4 V OO • n 1 7 I • • • • • I I I I • I | I • I I I I I I I I 1 L_l_l L | 10 100 E ( k e V ) F i g 1 1 1 . 3 ( b ) . The e l e c t r o n c a p t u r e c r o s s s e c t i o n f o r p r o t o n s i n a r g o n and n e o n . (Tawara,197 3) - 51 --I 4 10 C ' I r — l I 1 i ' ' i i : ^ , o ( c m 2 ) - r - ' - i— i | 1—r T - i—i~-rq -16 10 K r 10 I 6 -14 • * K r X X * o X , - , 5 h- to h X e Xe -I 6 trio ' • ' i i i i 1 1 1 • I i I I I i i 1 • I I i L 10 100 E I k e V ) F i g 111.3(c) . The e l e c t r o n capture c r o s s s e c t i o n f o r protons i n krypton and xenon. (Tawara, 1973) - 52 --16 10 H e E cro.Ccm2) •J7 10 -18 10 -16 10 Ne -I 7 10 L ' I „ ' 1 i i 111 1 — i — » — i — i i i i 11 * t - . * • . * ~ r~] I i i i 111 • — r — r - i — i i i i i II -16 no h - f o ' 7 H 2 i 4 * i 4 i » . „ - I" He 3 » V 1 » J • N e -18 (0 ' '"I • I I 1 I I 1 I • I I I I I I I 10 IOO IOOO E ( k eV) 10000 F i g 1 1 1 . 3 ( d ) . The e l e c t r o n l o s s c r o s s s e c t i o n f o r h y d r o g e n a t o m s m h y d r o g e n , h e l i u m , a n d n e o n . ( T a w a r a , 197 3) - 53 -- • | • i i i i i 111 • i 1 i — • i i ' i' | •—I ' i i i i i 111 • i • > • i °\).(cm 2 ) -IS. 10 c > K r L : • Kr • • fo'61 I !* . "' ''* Ar A M Xe X e - 1 6 * ~ ' 7 10. » , , . . . . • i l • I . I ' i i i I i I . i , I I I I I I ll , — I . 1 I I I I I I 1 1 0 10 100 W , I O O O IOOOO E(k eV) F i g 111.3(e) . The e l e c t r o n l o s s c r o s s s e c t i o n f o r hydrogen atoms i n krypton , argon , and xenon.(Tawara,1973) TABLE I. Mu F r a c t i o n i n Noble Gases. (Stambaugh,1974) Gas P r e s s u r e atm Mu F r a c t i o n * I o n i z a t i o n Energy eV E l e c t r o n c a p t c r o s s s e c t i o n f o r 220 eV muons 2 cm E l e c t r o n l o s s c r o s s s e c t i o n f o r 220 eV muon i um 2 cm He 50 1+5 24.48 9 x l 0 ' 1 8 5 x l 0 ~ 1 7 Ne 26 0±2 21 .56 9 x l 0 ~ ' 7 4 x 1 0 ' 1 8 Ar 30 65±5 15.75 -1 5 1.7x10 5 x l 0 - 1 7 Xe 44 100+(not gi ven) 12.13 3XI0" 1 5 I O " 1 6 - 55 -sc a t t e r i n g . ; I f s t r i p p i n g occurs the re s u l t i n g muon can have as mucli as 13-6 eV of k i n e t i c energy l e s s than that of the incident Mu atom and thus may get trapped below the threshold f o r Mu formation. The proton data for He and Ne indicate that muons approach thermal energies as free muons so that the absence of Mu precession i n these gases i s consistent with the proton data- The i o n i z a t i o n energies for He and Ne are much larger than for Xe or Ar. I t appears that the capture and loss cross sections are strongly correlated with either the ionization energy or possibly-..the irout-ere electron velocity d i s t r i b u t i o n . Theoretical attempts to explain the behaviour of a 1 Q and oQl for protons, even i n noble gases, are inadeguate at present. - 56 -i i Insulators an d Se m i-Go c ductors The formation process of Mu i n matter i s a complex many body problem. Measurements of the Mu f r a c t i o n i n noble qases have been made but no theory has emerged that successfully explains the results. In s o l i d s , even less experimental information i s available. I t should be stressed that the Mu states may be strongly perturbed i n s o l i d s and should be treated as Mu-(many electron s t a t e s ) , denoted |Mu (n-1)e-> In insulators i t i s believed that Mu exists i n the large i n t e r s t i t i a l s i t e s and behaves s i m i l a r l y to free Mu. Mu precession has been observed in guartz, ice and s o l i d c o 2 . Mu-like states have also been observed i n semi-conductors such as Ge and S i . The observed precession freguency i s approximately half that of free Mu (Brewer, 1915). It i s believed that Mu ex i s t s i n the i n t e r s t i t i a l s i t e s and i s highly perturbed. The reduced precession freguency in d i c a t e s that the binding energy i s reduced by several electron volts. In insulators and semi-conductors both free muon and Mu states e x i s t simultaneously. This suggests one of two things (Brewer,1975). 1 Thermal formation of Mu does not occur. 2 A f r a c t i o n of the Mu reacts epithernally and e x i s t s i n a diamagnetic environment producing what appears t o be f r e e muon p r e c e s s i o n . The absence c f thermal Mu formation i s d i f f i c u l t t o understand i n the case of i n s u l a t o r s where the b i n d i n g energy of the Mu atom i s 13 .6 eV. I t i s d i f f i c u l t t o comprehend how the |Mu (n-1)er-> s t a t e c o u l d have an energy greater than t h a t of the | y + ne~> s t a t e . . However, a j y + :;ne-> s t a t e may be meta-stable t o a t r a n s i t i o n i n t o a lower energy s t a t e , |Mu (n-1)e~> , i f the thermal muon i s trapped ah a diamagnetic state. £MM1M II M E A S U R E M E N T S O F F R E E O - P s P R O D U C T I O N E F F I C I E N C I E S I N O X I D E P 0 » D E 8 S AND AN A C C U R A T E D E T E R M I N A T I O N O F T H E 0 2 Q U E N C H I N G R A T E C O E F F I C I E N T F O B O H ? S S e c t I V . . 1 I n t r o d u c t i o n T h e p u r p o s e o f t h i s e x p e r i m e n t w a s : 1 . T o d e t e r m i n e t h e f r a c t i o n o f i n j e c t e d p o s i t r o n s f o r m i n g o - P s a n d r e a c h i n g t h e i n t e r g r a n u l a r r e g i o n s f o r v a r i o u s o x i d e p o w d e r s . 2. T o t e s t t h e f e a s a b i l i t y o f u s i n g f i n e o x i d e p o w d e r s a s h i g h y i e l d s o u r c e s c f f r e e o - P s t o s t u d y t h e i n t e r a c t i o n s c f o - P s w i t h g a s m o l e c u l e s . T h e p r e s e n c e o f f r e e o - P s i n a s a m p l e i s r e l a t i v e l y e a s y t o e s t a b l i s h b e c a u s e o f i t s c h a r a c t e r i s t i c 140 n s e c l i f e t i m e a n d c o n t i n u o u s 3 Y a n n i h i l a t i o n e n e r g y s p e c t r u m . H o w e v e r , m e a s u r i n g t h e f r a c t i o n o f p o s i t r o n s i n a f r e e c - P s s t a t e i s m o r e d i f f i c u l t . T h e 1 4 0 n s e c c o m p o n e n t i n t h e l i f e t i m e s p e c t r u m i s d i f f i c u l t t o n o r m a l i z e t o t h e p r o m p t c o m p o n e n t s b e c a u s e t h e y r e s u l t f r o m 2 y d e c a y s w h i c h y i e l d m o n o e n e r g e t i c gamma r a y s . S i m i l a r l y , n o r m a l i z i n g 3Y c o i n c i d e n c e r a t e s t o 2Y c o i n c i d e n c e r a t e s i s d i f f i c u l t b e c a u s e i t i n v o l v e s k n o w i n g t h e d e t e c t o r e f f i c i e n c y a s a - 59 -function of energy and the e f f e c t i v e s o l i d angle subtended by the detectors. This technigue also suffers from low counting rates ( t y p i c a l l y 3 or 4 counts/1000 sec.) ., even »ith a 2 0 0 i W C i source (Celitans, 1964) -. V. nose .subtle\techlii;%u'es''JoE'..-aeastt'ring. the o-Ps f r a c t i o n ibvolve quenching the o-Ps by a known amount using magnetic or chemical means. The application of a large (20 KG) magnetic f i e l d mixes the o-Ps (m=0) substate with p-Ps and causes 1/3 of the o-Ps to decay into 2y s. Chemical quenching i s the introduction of some o-Ps reactant; sfhich either induces an o-Ps+p-Ps conversion through a spin f l i p mechanism or r e s u l t s i n an o-PsX compound which i s followed by pickoff annihilation within a few nanoseconds. o In t h i s experiment samples of Si0 2 (35 A radius), S i 0 2 (70 A radius), A l ? 0 3 (150 A radius) , ZnO (560 1 radius) and MqO (fine) (see Appendix IV) were investigated.. Usinq the technique described i n Sect IV.2 the o-Ps f r a c t i o n s were determined f o r each powder. The l a r g e s t producer was found to be the.35A radius Si0 2 powder where approximately 25% of the injected positrons emerged from the powder grains as o-Ps. This powder was then used to measure the mean decay rate of o-Ps as a function of 0 2 p r e s s u r e . The rel a t i o n s h i p was found to be l i n e a r , qivinq a quenchinq rate c o e f f i c i e n t of 35.5±1.0 usec _ 1/atmos. The reaction mechanism was determined to be spin chanqinq i n nature by using a hiqh resolution GeLi detector to monitor the pair momentum d i s t r i b u t i o n -- 60 -§ § . £ £ * . 1 1 x 2 fechnigue Fjgr Measuring Free fi-Ps F r a c t j.pn The production e f f i c i e n c y of o-Ps i n the i n t e r q r a c u l a r r e g i o n cf a powder sample can he determined by measuring the 2 y counting r a t e and the o-Ps mean decay r a t e ( = 1 / l i f e t i m e ) i n the powder under vacuum and a g a i n with a gas quencher i n the i n t e r g r a n u l a r r e g i o n . In the s p e c i a l case where the gas guencher e l i m i n a t e s a l l 3 y decays and the powder s u r f a c e s produce no guenching a f f e c t , the f r e e o-Ps f r a c t i o n may be w r i t t e n dN _ dN dt Q dt v "o-Ps dN = { 1 + dt Q dN f = J. ri , Qt V , - i dN _ dN 5 d t Q d t v where dN/dt v and dN/dt Q are the 2 y counting r a t e s i n the evacuated powder sample and i n the powder sample plus gas guencher r e s p e c t i v e l y . In a more r e a l i s t i c s i t u a t i o n where the powder s u r f a c e s have a guenching e f f e c t on the o-Ps and the gas guencher dees not completely guench the o-Ps , f may be w r i t t e n o-Ps (see Appendix 27i) dN f _ • .. , , dt v r A_ _ X X — X , - . — I o _ P s = { 1 _ + [ ^ _ _ 0 - _X__oJ > X dtQ dt v 0 v v eqn IV.1 where A v , X 0 and XQ are the mean decay r a t e s i n the evacuated powder sample,in t r u e vacuum and i n the presence of the gas guencher r e s p e c t i v e l y . - 6 1 -Eqn I V - 2 i s based on the assumption that the gas guencher serves only to guench the o-Ps i n the intergranular region and does not a l t e r the fr a c t i o n of o-Ps i n the intergranular region. In t h i s experiment 0 2 at 1 atmosphere was used because of i t s effectiveness as a quencher...$80%) and i t s non toxic nature. However, 0 2 may; indeed a l t e r the fr a c t i o n of o-Ps reaching the intergranular region i n two possible ways. 1- The powder surfaces are known to adsorb gases (Steldt and Varlashkin, 1972) - A layer of 0 2 on the powder surfaces might a l t e r the transmission properties of o-Ps through the surfaces. 2. Small concentrations of 0 2 are known to increase Ps formation i n gases. I t i s conceivable that t h i s could also happen for very f i n e powders However, i f the quenching i s nearly complete as i s the case with 0 at 1 atm then the r e s u l t from eqn IV.1 i s 2 i n s e n s i t i v e to the f r a c t i o n of o-Ps i n the interqranular reqion i n the presence of the quencher. In order to estimate the error due to t h i s e f f e c t , one o quenchinq run in the 35 A radius SiO ? powder was repeated usinq 750 tor r of Cl^ f o r which A n - A /\:n ^ 1.00 . The - 62 -r e s u l t s were as follows: fo-Ps = 2 6 - 4 ± - 8 % u s i n 9 7 5 0 t o r r of 0 2 f „ = 24.8±.3 % u s i n g 750 t o r r o f C l ? o-Ps z This difference was taken into account i n the f i n a l error estimate on the o-Ps fr a c t i o n s . Sect. I I v3 Experimental Details i Target Assemblies Two 15 yCi Na 2 2 sources were prepared i n the following manner. Several drops of NaCl solution were deposited cn 1.9 ym nic k e l f o i l and allowed to dry./ A very thin coat of lacguer was applied to hold the NaCl i n place There were b a s i c a l l y two types of target assemblies. For the low density SiO^ powders the source was suspended i n the centre of a 17 cm diameter flask f i l l e d with Sio . I t 2 was calculated that 7 cm of SiC>2 { p=.035 <j/cm3) was s u f f i c i e n t to stop even the most energetic (544 KeV) positrons from Na 2 2 decays. For the high density powders { p >.13 g/cm3) a second Na 2 2 source was suspended 2 cm from the bottom of a large 4 cm diameter test tube f i l l e d with powder to a height of 5 cm. I t i s estimated that >95% of the positrons were stopped i n the powder for both types of target. A l l runs i n vacuum were performed after outgassicg at less than 10 - 3 t o r r for a period of six hours. A Wallace and Tiernan precision vacuum guage, accurate to ±2 t o r r , was used to monitor the 02 pressure when reguired. Lifetime measurements were made using two 8,9 cm dia x 8.9 cm long Nal c r y s t a l s mounted on RCA XP1140 photomultiplier tubes. f They were arranged at 70° to one another approximately 15 cm from the source (see f i g IV, 1 ) . Measurements of the Doppler broadening of the 511 KeV annihilation l i n e and the 2 y counting rate were made using an lithium d r i f t e d germanium (GeLi) detector with an active volume of 104 cc measuring 5.2cm diax5,6cm long and possessing a resolution of 1.32 KeV at 567 KeV, The detector was placed 25 cm from the source. - 65 -i i i •. • Electronics - £ or- Lifetime-;H^agureffiett^~ Fig IV.1 contains a schematic diagram of the electronics used i n the l i f e t i m e measurements.,; JCh'e el e c t r o n i c s were set up to measure the decay rate of o-Ps as a function of time a f t e r a positron stop. A Na ? ? source was chosen because the emission of a positron i s followed i n 10 - l l s e c by the emission of a nuclear gamma at 1.28 MeV (see f i g II.3). The method of constant f r a c t i o n discrimination was used to time the fast anode pulses from detectors 1 S 2. The spectrum of time delays was accumulated by using a time to amplitude converter and a pulse height analyzer. Pileup gates on each discriminator were used to r e j e c t leveats that came within 4 usee of one another. Single channel pulse height analysis was performed on the slow dynode pulses from detectors 1 & 2 to sele c t decays of o-Ps. Fig IV.2 shows the Na 2 2 energy spectrum from one of the Nal detectors showing, the single channel analyzer windows for the s t a r t and stop. The important feature i n f i g IV.2 i s that the stops reguired a gamma ray just below 511 KeV. This maximized the r a t i o stops from 3y a n n i h i l a t i o n long l i f e t i m e component stops from 2y a n n i h i l a t i o n prompt l i f e t i m e component n • This r a t i o was unity for the 35 % radius S i 0 2 i n vacuum which implies that half the events i n the l i f e t i m e spectrum were from o-Ps decays. The timing resolution was measured to be 4 nsec using a O r t e c 473A O r t e c 473A c o n s t f r a c c o n s t , f r a c d i s c . d i s c . 130 nsec d e l a y EG&G GPI00/N p i l e u p g a te EG&G GP 100/r|l p i l e u p g a te O r t e c 471 s p e c t . amp. O r t e c 471 s p e c t . amp. ConucI e a r CI26 T.A.C. EG&G Or 102/N dual OR/NOF O r t e c 420A S.C.A. I O r t e c 455 S.C.A. c o i n , c o i n O r t e c 416A gate& de I av) g e n e r a t o r a n t i - c o i r) O r t e c 418 un i v e r s a I c o i n c i d e n c e N o r t h e r n NS-700 P.H.A. gate T e k t r o n i x s w i t c h box IBM 370 TX40I0 computer v i sua 1 di sp 1 ay t e r m i na 1 F i g IV.I . E l e c t r o n i c s used t o measure o-Ps l i f e t i m e i n powders. - 67 -511 KeV 1274 KeV 13 3 2 0 0 0 0 2 8 0 0 0 0 2 4 0 0 0 0 2 0 0 0 0 0 1 6 0 0 0 0 1 2 0 0 0 0 8 0 0 0 0 h 4 0 0 0 0 0 100 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1000 1100 CHRNNEL NO 22 F i g IV.2. Na"" spectrum from one of the Nal d e t e c t o r s , showing the s i n g l e channel a n a l y z e r window s e t t i n g s f o r the s t a r t s and stops i n the l i f e t i m e determinat-' i o n s . .i;.channe 1= "1.46 KeV - 68 -Co 6° source which emits two, v i r t u a l l y simultaneous, gamma rays. An OBTEC time c a l i b r a t o r was used to c a l i b r a t e the TAC output and to check the d i f f e r e n t i a l l i n e a r i t y of the system. No non-linearity was observed using 20 nsec i n t e r v a l s over a range of 600 nsec. The average time per channel was .942 nsec. The pulse height analyzer was operated i n the 1024 channel mode. The stop was delayed so that time zero occurred i n channel 130. This was done so that negative time could be used to evaluate the random coincidence rate (see Sect IV. 3. x). - 6S . -IS Electronics For Measuring The 2 v I S l i M i l M j S J i Hate and T,he Doppler Bicadejing of t h j 5VL KeJ Line Fig IV,3 shows the elec t r o n i c s for the energy spectrum analysis used i n the determination of the 2y counting rate. The time constant on the amplifier was set at 3 ysec. The pulse height analyzer was operated in the 1024 channel mode. The energy per channel was 580 eV. The electronics for the Doppler broadening measurements were v i r t u a l l y the same as that for the 2 y counting rate measurements., A biased amplifier was inserted as indicated in f i g IV,3. Additional gain, heavy biasing and 2048 channels on the PHA were used to lower the energy per channel to 73.3 eV, This was necessary f o r an accurate determination of Doppler broadening of the a n n i h i l a t i o n l i n e at 511 KeV. - 70 -O r t e c 459 5 K v o l t power s u p p l y O r t e c I 19 H.V. f i I t e T e k t r o n i x TX40I0 v i s u a l d i s p t e r m i na I I04cc Ge-Li c r y s t a I — O r t e c 472 s e c t . amp. O r t e c 408A b i a s e d amp. N o r t h e r n NS-700 P.H.A. sw i t c h box U . B . C IBM 370 computer F i g IV.3 . E l e c t r o n i c s used t o measure t o t a l 2y a n n i h i l a t i o n r a t e s and D o p p l e r b r o a d e n i n g o f t h e 511 KeV l i n e . The b i a s e d a m p l i f i e r was o n l y used i n t h e D o p p l e r b r o a d e n i n g measurements. - 71 -v com Eater Li,nk 1 novel technigue (Clarke, 1978) was used to transfer the data from the pulse height analyzer d i r e c t l y into the IBM 370 computer where the data analysis and plotting were performed. & switch box (see f i g s IV.1 and IV.3) between the computer terminal and the pulse height analyzer made such a transfer possible. a s l i g h t modification to the PHA was necessary to synchronise the transfer of data to the computer, - 72 -v i Procedure f o r o-Ps g-r-o&uctlon- Measureme^ts-Each sample was evacuated to a pressure of 10 - 3 torr f o r a period of three .hours prior to running. Four runs were reguired to evaluate the o-Ps production e f f i c i e n c y i n the intergranular regions as described i n S e c t ' I V . 2 . F i r s t a l i f e t i m e spectrum was accumulated for approximately 2 x 1 0 * sec (333 min-) c o l l e c t i n g 5 x 10 s events. The count rates i n the Nal counters were t y p i c a l l y 2 x 10*/sec Then an energy spectrum using the GeLi detector was accumulated f o r 5 x TO3 sec. 750 t o r r of (see Appendix V) was bled into the target chamber. Then another l i f e t i m e spectrum and energy spectrum were accumulated i n . the manner described above. Care was taken not to disturb the position of the GeLi detector i n r e l a t i o n to source because the nuclear gamma ray from Na 2 2 was used to normalize the energy spectrum i n vacuum to that in 750 t o r r , o f 0 Isee Sect- IV-3-ix)-In the case of S i 0 2 (35 £) two addi t i o n a l spectra were taken using C l 2 as a quencher. - 73 -v i i Procedure for the 0^ Quenching Hate C o e f f i c i e n t Determination 35 i. radius S i 0 2 moderator sas used to determine the the dependence of the o-Ps mean decay rate on 0 2 pressure. The system was pumped down to-10- 3 t o r r , a f t e r which 750 to r r of 0 2 was bled i n . Lifetime runs of duration 2 x 10* sec, c o l l e c t i n g 5x10* events, were taken at oxygen pressures of 750, 600, 450, 300, 200, 100, 50 and 10-3 t o r r . - 74 -v i i i Procedure f o r Doppler Broadening fteasur;ejefts-Doppler broadening measurements were performed on the 35 A SiO powder sample at 10- 3 t o r r , at 750 torr of 02 , and at 750 t o r r of C l 2 . These runs were 5 x 10 3 sec i n duration c o l l e c t i n g roughly 5 x 10* events in the annihilation photopeak. A B i 2 0 7 source with a nuclear gamma ray at 567 KeV was placed nearby in order to monitor the system resolution. - 7 5 -ix Analysis of the Annihilation Spectra The purpose of t h i s part of the analysis was to evaluate the 2y counting rate i n vacuum and i n 750 t o r i of 0 2 to within a constant of proportionality. This constant of proportionality cancels out i n c a l u l a t i n q f which o-Ps contains only the r a t i o of counting rates (see egn IV.1). This task was accomplished for each annihilation spectrum by evaluating the t o t a l number of counts i n the 511 KeV photopeak (see f i g IV.4) and dividing by the number of Ccirptcn events from the 1.274 MeV nuclear gamma ray i n the f l a t region above 511 KeV. This choice of energy range (see f i g IV.5) desensitises the normalization to small changes i n gain (Sen and Patro, 1872). The 2y counting rates can then be written dN = k(P-B1-B2) d t N where k=N/t and t i s the counting time. - 76 -F i g IV.4. A n n i h i l a t i o n spectrum from the Ge-Li d e t e c t o r , expanded about 511 KeV. 1 channel = 580 eV 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 100 J L 511 KeV 1 0 0 0 0 0 0 FT \ | T N 2d L 1274 MeV J L 1 101 2 0 1 301 401 501 601 701 801 901 1001 CHANNEL NO F i g IV.5. The Na spectrum i n S i 0 2 ( 3 5 A) a t 10 t o r r . The a n n i h i l a t i o n s p e c t r a i n vacuum and 0 2 were normalized over the range i n d i c a t e d . The gai n has been lowered to show the n u c l e a r y a t 12 74 KeV, which was o f f s c a l e f o r the a c t u a l runs. 78 x Analysis of the Lifetime Spectra The l i f e t i m e spectra were f i t t e d to the function N e - A t + B t>0 dN d t B t<0 over the two regions indicated i n f i g IV.6. The st a r t i n g time for region 2 was always 48 nsec. The f i n i s h i n g time was extended to where the count rate was twice the background or to 95 nsec whichever was largest. A maximum li k e l i h o o d program (Albrecht, 1978) assuming Poisson s t a t i s t i c s was used to determine the best f i t . The x 2 was calculated by binning the data appropriately so that Gaussian s t a t i s t i c s could be applied. Although reasonable x 2 s were obtained in a l l cases, the decay rates did show some dependence on the f i t t i n g region. For the long l i f e t i m e s t h i s dependence was less than ^% whereas decay rates i n the highly guenched runs varied as much as 556 after s h i f t i n g region 2 inwards by 15 nsec. This deviation from a single exponential behaviour i s not well understood, A systematic error of 5% was attached to a l l decay rates obtained frcm these highly guenched runs. - 79 -time=0 47 nsec 100000 E 10000 1000 100 10 I r e g i o n 1 tf r e g i o n 2 1070 1120 1170 1220 1270 1320 1370 1420 1470 1520 157i CHRNNEL NO F i g IV.6. Decay r a t e versus time a f t e r the p o s i t r o n emission, i n AI2O3 (150A), showing the f i t t i n g r e g i o n s . 1 channel = .942 nsec. - 80 -Sect. sils-H Results and Discussion -i - o~Ps-Production Measurements~ Columns 2, 3 S 4 of table i give some physical properties of the: powders l i s t e d in column 1- Columns 5 S 6 give the mean decay rates i n vacuum and at 750 t o r r of 0 ?, respectively. The errors guoted for the Q2 mean decay rates originate primarily from the estimated 5% systematic error associated with the dependence of the answer on the f i t t i n g region (see Sect IV.3.x).Column f7 contains the f r a c t i o n of positrons reaching the intergranular regions i n the form o-Ps as calculated from eguation IV.1. Column 8 contains ca l c u l a t i o n s of the r a t i o o q p / n R2 where xr-qp i s the mean guenching cross section at room temperature of the powder grains (see Appendix III (a) ) and ITR 2 i s the physical cross section of the grains. These guenching cross sections are consistent with calculations assuminq that the o-Ps i s moving f r e e l y between the grains but decays at a pickoff o annihilation rate while i t i s within a few A of a powder grain. It i s clear from column 8 that the guenching probability during a c o l l i s i o n i s of order 10~ s - 10— 6. I t i s i n t e r e s t i n g to compare th i s with the corresponding probability in gases. In C l 2 , I 2» Br 2 and N02 gases, the guenching cross sections are of the order •10-** - 10- 1 3 cm 2 and are due to chemical reactions CTao, 1974). For these gases the quenching iprobability i n a c o l l i s i o n i s o f t h e TABLE I I . R e s u l t s of t h e P o s i t r o n i u m Experiment Samp 1e 1 n t r i ns i c Bu1k Dens i t y Mean Radius Mean Decay Mean Decay 1 n t e r g r a n u 1 a r Quench C r o s s Powder D e n s i t y Rate i n Vac. Rate i n 0 o-Ps F r a c t i o n S e c t i o n ( p o w d . ) P h y s i c a l C r o s s S e c t i o n 1 p • B p R X X f D a /TTR2 V q o-Ps qp g/cm^ g/cm"' I0" 8cm -1 usee -1 psec % -6 S i 0 2 .035 2.2 35 7.22±.08 40.1±2.0 • 26.4±2.6 . 8 +.3x10 -6 S i 0 2 .035 2.2 70 7.23±.12 40.0±2.0 21.5+2.0 1.6,±.8xl0 -6 Al„0, .56 3.7 150 8.39+.14 37.5+1.9 . 24.6+2.4 2.9±.4xl0 2 3 ZnO .65 5.6 560 7.30±.09 44.5±2.1 19.2+1 .9 2 . 6 ± l . x l 0 ~ 6 MgO .13 3.6' 7.43±.09 39.0±2.0 14.3+1.4 order unity since the physical cross section are t y p i c a l l y 7 x 10~ 1 6 cm2, there spin exchange i s the dominant process, such as i a 0 2 or NO, t h i s guenching p r o b a b i l i t y decreases to 10 - 2 or 10~ 3 (Tao, 1972). For argon and the other i n e r t gases the p r o b a b i l i t y f o r guenching drops to 10^ -* or 10 - s {Celitans, 1964b). I t appears there i s no large surface i n t e r a c t i o n for any of the posders.... The noticeably larger decay rate for & i 2 0 3 i s primarily a density and p a r t i c l e size effect., - 83 -i i ; '•' Qaenchiag Sate Coeffici-eat foc 0-Fig IV-.7 shows e x p l i c i t l y the guenching e f f e c t of 0 2 at 1 atmosphere on o-Ps using the 35 1 SiO ? powder as a moderator- Fig IV-8 shows graphically the dependence of the o-Ps decay rate on pressure . A reasonable f i t was obtained by assuming a l i n e a r r e l a t i o n s h i p . The best f i t gives a guenching rate c o e f f i c i e n t of 35-6±.8 y s e c - l a t i _ 1 , which at 22°C corresponds to a v - 3;..ft3±-03 x lO-" a ? s e r 1 where a i s the guehc&ing cross section and v i s the o-Ps v e l o c i t y . Osing an argon moderator iwith d 2 p a r t i a l pressures greater than 1 atmos Tao ; (1964) measured the oxygen guenching rate c o e f f i c i e n t , a v , to be .94 ± . 12 x 10-* 2 cm* sec -*. More recently the guenching rate c o e f f i c i e n t was measured using porous s i l i c a gel with a large surface area (800 m2/g) as a moderator (Chuang and Tao, 197,4b) .They reported a long l i v e d component i n t h e l i f e t i m e spectrum ,attributed to o-Ps within the pores, possessing a mean decay rate of 31-3 ysec-*. By adsorbing d i f f e r e n t amounts of 02 onto the gel they calculated a guenching rate c o e f f i c i e n t a v = 1.75 x 10- 1 2 cm?sec-» .f The 0 adsorbed samples showed an increased low momentum component i n the angular c o r r e l a t i o n data which establishes that the guenching process i s spin f l i p i n nature-no error given - 84 -100000 ZD 10000 b-1000 100 10 tinje=0 47 .nsec 1 ^ I "i r J L J L J L ZD 2100 2350 2200 2250 2300 2350 2400 2450 2500 2550 2600 CHRNNEL NO ( a ) 100000 10000 b-1000 r 100 =-10 1070 1120 1170 1220 1270 1320 1370 1420 1470 1520 1570 CHRNNEL NO (b) Fig IV. 7 (a) .Lifetime spectrum in 35A radius SiC>2 powder at 10~3 torr. (b) Same at 750 torr 02 . 1 channel=.942 nsec. - 85 -0 . 0 1.0 2 .0 3 .0 4 . 0 5 .0 6 . 0 7 .0 8 . 0 0 2 PRESSURE(TORR X l O ' F i g IV.8. The o-Ps mean decay r a t e versus the 0 2 p r e s s u r e . The b e s t f i t g i v e s a r e a c t i o n r a t e c o e f f i c i e n t of a v' = 1.43 ± .04 x l O - - ^ cm^ s e c ~ l q - 86 -The fact that a l l three moderators give approximately the same answer indicates that no large systematic errors are introduced by the moderators. - 87 -i i i Doppler Broadening Me as ure roents-i n o SiO 2 135 A 1 i n Vacuum^ 0 2 and CI• In t h i s part of the experiment a GeLi detector with a resolution of 1.32 KeV at 567 KeV (see f i g IV.9) was used to determine the o-Ps guenching mechanism i n 0 2 and Cl^ . o Fig IV.10 shows the l i n e shape in 35 A S i 0 2 with and without 0 2 present.,The counting time was adjusted so that the peak heights were the same. The l i n e shape corresponds to the d i s t r i b u t i o n of the p a r a l l e l component of the pair momentum (see Sect 1:1.3. iv)... The enhancement of a narrow component which i s c h a r a c t e r i s t i c of thermalized p-Ps i s c l e a r l y v i s i b l e when 0 2 i s added. This indicates that the quenching process i s spin exchange i n nature., o The l i f e t i m e spectrum in S i 0 2 ( 35 A ) with 750 torr of C l 2 (see f i g IV. 11 ) shows nc long component, i n d i c a t i n g that the guenchinq i s complete. In contrast to 0 2, the l i n e width with C l 2 shows a slight'broadening (see f i g IV.12). The absence of a narrow component rules out a spin f l i p quenching process. The s l i g h t broadening can be understood i f i t i s assumed there i s a certain f r a c t i o n of the positrons which form p-Ps d i r e c t l y and produce a small narrow component. The narrow component f r a c t i o n of the 511 KeV l i n e w i l l then decrease as pickoff guenchinq of o-Ps i s increased. The broad l i n e width i n C l 2 i s not surprising since C l 2 has no unpaired electrons. This result i s i n agreement with angular c o r r e l a t i o n studies on the PsCl system (Tao, 1574). - 88 -56 7 KeV 3 2 8 0 3 3 0 0 3 3 2 0 3 3 4 0 3 3 6 0 3 3 8 0 3 4 0 0 CHRNNEL NO F i g IV.9. The d e t e c t o r r e s o l u t i o n curve a t 567 KeV, measured with a Bi2 0 7 source. - 89 -511 KeV 20000 17500 15000 12500 m t— z ZD 10000 o (_) 7500 5000 2500 2490 2510 2530 2550 2570 CHANNEL NO (a) 2590 2610 tn 20000 17500 15000 12500 10000 h 7500 5000 2500 •- FWHM =1.90 KeV 0 2490 2510 2530 2550 2570 CHANNEL NO (b) 2590 2610 F i g IV.10(a) . A n n i h i l a t i o n r a d i a t i o n i n 35A r a d i u s S i 0 2 powder at 10~ 3 t o r r . (b). Same at 750 t o r r of C>2.1channel = 73 eV. - 90 -in time=0 1 0 0 0 0 P 1 0 0 0 1 0 0 \=-10 47 nsec "^ • • • * *a»* • _* k ' • • * u i a • a a* _L _L 10 7 0 130 1 9 0 2 5 0 3 1 0 3 7 0 4 3 0 4 9 0 5 5 0 CHANNEL NO F i g IV.11. L i f e t i m e spectrum i n 35A Si02 a t 750 t o r r C l 2 . 1 channel = .942 nsec. - 91 -511 KeV C O a <_) 2490 2510 2530 2550 2570 CHRNNEL NO 2590 2610 0 F i g IV. 12. A n n i h i l a t i o n r a d i a t i o n i n 35A SiO£= at,:•-750 t o r r C l 2 - 1 channel = 73 eV. - 9 2 -The chemical reaction o-Ps + Cl 2-+ o-PsCl + C l i s believed to be responsible for the large quenching cross section. The o-PsCl compound i s very short l i v e d because the positron picks o f f a valence electron from the C l atom. - 93 -Sect Il.j.5 Conclusions In conclusion of t h i s chapter we state 1. Fine grain oxide powders are high y i e l d sources of thermalized, v i r t u a l l y free, o-Ps, i d e a l for studying o-Ps int e r a c t i o n s with gases. 2. The present state of GeLi detectors i s such that they are able to distinguish guenching due to bond formation from guenching due to a spin exchange process, by the technigue of Doppler broadening. Considering the s i m p l i c i t y ,speed and f e a s a b i l i t y for a l l density targets cf such a technigue, compared with the technigue of angular c o r r e l a t i o n , GeLi detectors could prove to be very useful t o o l s in physical gas chemistry. - 9i) -CHfiPTEB V HEASQgEMENTS €F u + AND Mu FRACTIONS II OXIDE POWDEES Sect VjtJ, i P t r o d u c t i p n The purpose of this experiment was 1. To search for Mu i n powdered insulators using a transverse f i e l d MSfi apparatus. 2. To measure both the free muon and Mu i n i t i a l asymmetries and thus determine upper and lower l i m i t s on the Mu f r a c t i o n in these powders. , 3. To look for evidence that the Mu i s d i f f u s i n g out of the powder grains and into vacuum. Powdered samples of S i 0 2 (35 A), GeC2 (coarse), SnG2 (coarse), CaO (coarse), MgO ( f i n e ) , SiO(coarse) and A1 20 3 (150 A) were investigated. The ZnO (56o£) that was examined i n the positronium experiment (Chapter IV) was investigated i n a previous Mu experiment (Spires, 1977) . The r e s u l t was negative on the basis of a large muon asymmetry and the lack of Mu precession. That experiment also locked o at A l 2 0 3 (150 A ) which showed what appeared to be a large flu asymmetry relaxing very f a s t . It was f e l t that further evidence was reguired in order to make a positive i d e n t i f i c a t i o n . - 96 -Sect V.2 Technique A standard two telescope MSH apparatus f o r transverse f i e l d s {see Sect III.3) was used to measure the time evolution of the muon pol a r i z a t i o n . In low f i e l d s ' (B<10.G) there are two resolvable precession frequencies, one due to free muons i n a |a> spin state at 13.6 KHz/G and the other due to Mu i n a la a>„ * spin state at 1.4 MHz/G (see Sect i l l . 3 . i i i ) . Each precession frequency i s characterized b y an amplitude or asymmetry which relaxes with time. The asymmetries at time=0 are i n d i r e c t proportion to the f r a c t i o n of the muon ensemble i n i t i a l l y i n , a |a> state and |a a >„ state- respectively. The ' 1 Mu proportionality constant was determined experimentally by measuring the i n i t i a l free muon asymmetry in Al for which i t i s assumed that a l l muons are i n i t i a l l y i n a free muon state. f = k A s y ( t = 0 ) w h e r e k = [ A s y ^ + ( t = 0 ) ] ~ 1 f o r A l I f a l l the muons stop in the powder then the free muon fr a c t i o n and the Mu f r a c t i o n i n the powders are f u + = Asy-, ( p o w d e r ) / A s y ' , ( A l ) e q n V . l ( a ) r y + y + f M u = 2 A s y M u ( P ° w d e r ) /Asy -+(A1) e q n V . l ( b ) where Asy(powd) i s the measured i n i t i a l Mu asymmetry f o r the powder, and N o t a t i o n : a £ _ 1. 3 £ 2 ~ 2 2 where A s Y y + (powder) , and Asy y + <&1) are the measured i n i t i a l free muon asymmetries for the powder and aluminum, respectively. The factor of 2 in the expression for f • Mu arises because half of the Mu ensemble i s i n a |a g> spin state which i s not observable. In a rea l s i t u a t i o n the muons do not a l l stop i n the powder, as intended, so that the effect of muons stopping elsewhere must be subtracted. The contribution to Asy .(powder) and Asy (Al) due to muons stoppinq in the y + y + - . . vacuum vessel,tarqet holder,etc. was determined by measurinq the free muon asymmetry f o r F e 2 0 3 i n which there i s no coherent free muon precession at 13.6 KHz/G. Sutractinq t h i s asymmetry from the free muon asymmetries i n eqn v . l yields f + = A s y + ( p o w d e r ) - A s y + ( F e 2 0 3 ) e q n V . 2 A s y ^ + ( A 1 ) - A s y ^ + ( F e 2 0 3 ) f M u = 2 A s y M u ( p o w d e r ) A s y y + ( A 1 ) - A s y ^ + ( F e 2 0 3 ) e q n V . 3 - 98 -Sect £-_3_ . Expeci me at a 1 De t a i I s i The P o l a r i z e d Beam-The experiment was performed oa M20, a s t o p p i n g muon channel a t TBIUH?^The chanael was tuned to accept muons o f momentum 29 Mev/c r e s u l t i n g from the decay of pions which had stopped on the s u r f a c e o f a Be pr o d u c t i o n t a r g e t . The p o l a r i z a t i o n o f such muons i s c l o s e t o 10031 (see Sect I I I . 3 . v ) . T h e i r range i n carbon i s 14 0 i g / c i 2 so t h a t i t was p o s s i b l e to stop a l l the muons i n the t a r g e t . - 99 -i i I k s Experimental Setup Fig V,1 shows the counter arrangement used f o r the experiment. A thin (40 mg/cm2) beam defining counter functioned as a 35% e f f i c i e n t muon counter, able to discriminate cleanly against positrons of 29 MeV/c because the dE/dX for muons i s much greater than that f o r positrons at 29 He?/c. The 5 cm of carbon degrader between E1 and B2 and between L1 and 12 discriminated against low energy positrons and thus served to increase the maximum experimental asymmetry (see Sect III.2.i). Osing an aluminum target t h i s maximum experimental asymmetry was measured to be .347±.Q04 and .336±.003 for the l e f t and r i g h t telescopes respectively. The muon stop rates were t y p i c a l l y 40 K/sec with 15 yA of primary proton beam incident on a 10 cm Be production target. - 100 -y + e+ i n c i d e n t beam 1.25" D i a . l e a d c o l l i m a t o r vacuum s c a l e : 1/10 v e s s e l F i g V .1 Experimental setup f o r o b s e r v i n g f r e e muon and Mu p r e c e s s i o n i n powders. - 101 -i i i Electronics The l o g i c was designed to measure the time delay between the muon stop and a high energy positron passing through one of the telescopes (see f i g V,2) . The d e t a i l s of the electronics are written up elsewhere (Garner, 1S78) but the main features are: 1 Timing resolution = 5 nsec 2 Time/channel = 2 nsec 3 Total range = 4 ysec 4 Second muon rejector : I f a second muon entered the target within 4 ysec of the f i r s t muon, the event was rejected. 5 Second electron rejector: If a second electron was observed i n either the l e f t or right telescope within 4 ysec after the mon stop, the event was rejected. The time delay between the v+ stop and the e + event was di g i t i z e d with an EG&G TDC100 clock connected to a CAMAC interface. A microprogrammable branch driver (MBD) was used to transfer data from CAMAC to a PBP-11/40 computer. Events where the second y+ or e* arrived within 4 ysec of the f i r s t y + step, but after the f i r s t e + were rejected by the HBD. The MBD also routed the event to the appropriate l e f t or right spectrum. \ - 102 -90°/270° or "Arizona" data acquisition mode logic diagram Ll L2 L3 RI R2 R3 Ban 91 DEL] NIM MM! f • --JT II 1 ! q D 1 II I  1 R3R2 RI i 1 I Ll L2L3 Counter configuration le+left |"ui route Comae coincidence word mask T D C 1 0 0 I start pulse height « 8001100 mV KEY 6 • logical 'not' inverted pulse • bridged output ] = gate generators 0"= discriminator with output pulse shape U« logical 'or' fan in/out logical 'and' coincidence unit delay dotted . lines " denote optional units 1 [stop start] 9 2 iNlM NIMl 6 e+ right route Comae coincidence wordqS bit mosK Camoc coincidence strobe word d> level . Cgmacl coincidence | word I bit 12,13,14 or 15 e+- level Stop / Trx IOO stop pulse height = 6001100 mV F i g V.2 . The l o g i c used to c o l l e c t the l e f t and r i g h t s p e c t r a of time delays between a y + stop ( s i g n a l e d by D) and a f a s t p o s i t r o n event ( s i g n a l e d by L1.L2.L3 or R1.R2.R3). The o p t i o n a l u n i t s denoted by the dot t e d l i n e s were not used. - 103 -iv-Procedure A four sided multiple target attached to a mechanical feedthrough allowed four targets to be run in succession without disturbing the vacuum vessel. Another dual target consisting of aluminum ( for normalization) on one side and a powder target on the other was used alternately with the guad target. Powder samples were contained by using .0013 cm aluminized mylar windows. The target areas were a l l 50 cm2 i n area whereas the collimated beam was 8 cm 2 upon entering the vacuum vessel. During the runs the vacuum vessel was maintained at 10~5 t o r r . At le a s t two runs were made for each powder, one at 69G and one at 7.8G . I f the higher freguency muonium precession was v i s i b l e at 7.8G, the run was repeated l a t e r on a f t e r bleeding i n 5 t o r r of 0-2, This was the case for A1 20 3, MgO and CaO. The exception to t h i s was f o r Si0 2 where the behaviour of Mu i n powder * 0 2 had already been investigated (Marshall, 1S78). - 104 -v Target Preparation The f i r s t four powders, S i 0 2 , Ge02 , SnOg , and A l 2 0 3 , were pumped down to 10 -s tor r for a period of 24 hours i n advance of the run. They were i n s t a l l e d within the MSB apparatus without disturbing the vacuum. The f i f t h and sixth samples to be run, al and SiO (coarse) were not pumped i n advance since surface e f f e c t s were not expected tc be important. The next three targets, Fe2 03 , MgO, and CaO were pumped down to 10— 1 t o r r for a period of 3 hours i n advance of t h e i r running. In addition, the CaO, which i s commonly found as CaC0 3, was baked for 24 hours at 600 C°to ensure the reaction CaC0 3 r> CaO + C0 2 had taken place. - 105 -v i analysis a l jliak l i e l d Buns Since the position telescopes, i n i t i a l nuon polarization ( the beam d i r e c t i o n ) , and magnetic f i e l d of 69G were a l l at 90° to one another the positron counts versus time after the v* stop were f i t t e d to the following 6 parameter function. S h l g h ( t ) = N[l + A ( 0 ) e ~ A R t cos(ojt+<t>) ] e " t / T y + B eqn V.4 where N= the normalization A(0) = i n i t i a l asymmetry A R = relaxation rate for the asymmetry w = angular velocity of the free muon p o l a r i z a t i o n v e c t o r <j) = phase of t h i s precession B = f l a t background term T y = 2199.4 nsec ( the y+ lifetime) The spectra were f i t t e d over a 3.6 ysec range using 20 nsec bins s t a r t i n g at approximately 20 nsec. The function X 2 = M S h i g h ( n ) - S(n) ] 2 / S h i g h ( n ) eqn V.5 n was minimized using the computer program MINOTT where S(n) i s the number of events i n bin n and s h l g h ( n ) i s the number of events in the time i n t e r v a l corresponding to bin n as calculated from egn V.4. - 106. -Fig V.3(a) shows the raw time spectra for aluminum at 69 G along with the best f i t . Fig V.3(b) shows the data afte r subtracting the f l a t background term and folding out the exponential. More e x p l i c i t l y i t i s a plot of C h l g h ( t ) = S(n) - (E(n)+B(n)) eqn V.6 E(n) where E (n) and B(n) are the number of events in the time i n t e r v a l corresponding to bin n as calculated from E(t) = N e ~ t / x y B(t) = B 6 q n V - 7 The amplitude of the o s c i l l a t i n g function, c h i g h ( t ) # i s defined as the experimental asymmetry &sy (t) . , The s o l i d • v l i n e i n f i g V. 3(b) represents the best f i t to c h l g h ( t ) defined as C ^ g h ( t ) = A(0) e ~ A R t cosUt+ r j O - 107 -OD CO ZD o 20000 15000 .10000 5000 h 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 T I M E I N LLSEC (60 N S E C / B I N ) ( A ) 0.50 0.25 ~ 0.00 Xi Cn o -0.25 -0.50 0.0 4.0 TIME-IN uSEC (60 NSEC/BIN) ( b ) F i g V.3(a) . Number of p o s i t r o n events versus time a f t e r the muon stop i n aluminum. The t r a n s v e r s e f i e l d was 69 G .The so l -i d l i n e r e p r e s e n t s the b e s t f i t . (b) Same as (a) except the e x p o n e n t i a l has been f o l d e d out.The amplitude o f the o s c i l l -a t i o n i s the asymmetry due t o f r e e muon p r e c e s s i o n . - 108 -Jb Lew F i e l d Runs For the runs at 7.8G the number of positron events versus time after the y+ stop was f i t t e d tc the following 8 parameter function using 8 nsec bins S l 0 W ( t ) = N [ l + A M u ( 0 ) e " X M u t c o s ( 1 0 3 ( 1 J i j + t _ ( f r M u ) + A , (0)cos ( i D +t+f+) i e _ t / / T y + B y + 17 y T where N = the normalization A,. (0)= the i n i t i a l MUW. asymmetry Mu tXMu = relaxation rate of the Mu asymmetry 103io + - angular velocity of the muon polarization i n muonium M^u " t h e c o r r e s P o n < 3 i n g phase A y +(0) = the i n i t i a l free muon asymmetry angular velocity of the muon pola r i z a t i o n for free muons v y + (j, + = corresponding phase B = f l a t background term again t h i s done by using the computer program MINUIT to minimize the x z according to egn V.5 . F i g V,4(a) i s the o raw time spectrum for Si0 2 (35A) at 7.8G at 10 - 5 t o r r . Fig V.4(b) i s a plot of C l o W(n) - S(n) - [E(n)-B(n)] E(n) where E(n) and Bin) are defined as in egn 7.6 . , The s o l i d - 109 -0 . 0 0 . 5 1 . 0 1.5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 TIME IN uSEC ( 2 0 NSEC/BIN) ( a ) 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 TIME IN pSEC ( 2 0 NSEC/BIN) ( b) F i g V.4(a).Number of p o s i t r o n events versus time a f t e r the muon stop i n SiC>2 (35A) .The t r a n s v e r s e magnetic f i e l d was 7.8 G.The pres s u r e i n s i d e the vacuum v e s s e l was 10~5 t o r r . T h e s o l i d l i n e -i s the bes t f i t . (b) The same as (a) except the e x p o n e n t i a l has been f o l d e d out.The f a s t o s c i l l a t i o n i s due to muonium precess-" don whereas the slow one i s due to f r e e muon p r e c e s s i o n . - 110 -l i n e i n f i g v.4(b) i s the f u n c t i o n c i ? J ( t ) = A(0)e" AMu t [ COS(103OJ + t - <f.Mu) ] y + A . (O)cos'(u) + t + <j> , ) ' y - y y T p r o p e r l y normalized to 20 nsec b i n s . The amplitude of the f a s t o s c i l l a t i o n i n f i g V. 4(b) i s defined as the muonium asymmetry , AsYjy{a('t) . The base l i n e f o r the Mu asymmetry o s c i l l a t e s i n time at a freguency reduced by a f a c t o r 103 (see Sect I I I . 3 ) . The amplitude of t h i s p r e c e s s i o n i s d e f i n e d as the f r e e muon asymmetry , Asy u +(t) , - 111 -Sect Vj.4 Res a l t s and Discussion Table I I I summarizes the results of a l l runs i n vacuum. The free muon and Mu f r a c t i o n s were calculated according to egns V.2 and V.3 respectively. The l e f t and r i g h t telescopes were analyzed seperately. In some cases the values calculated f o r the l e f t and right hand sides d i f f e r e d by several standard deviations. The errors l i s t e d i n Table I I I are either the MINUIT errors or half the difference between the l e f t and r i g h t hand telescopes, whichever was largest. The Mu asymmetry i n A^ 0-3 relaxes very rapidly and i s only marginally i n d e n t i f i a b l e (see f i g V.5). There are three factors which strongly support the claim the observed o s c i l l a t i o n i s actually Mu precession 1. The freguency corresponds to Mu to within a r e l a t i v e l y large f i t t i n g error. 2. The precession s i g n a l for the l e f t side i s 180° out of phase i n r e l a t i o n to the r i g h t side (see f i g V.5) 3. The addition of 5 torr or 0 2 destroys the s i g n a l (see f i g V. 6) ., The cause of t h i s fast depolarization i s not clear. I f the precession signal i s due to muonium within the grains then the random l o c a l magnetic f i e l d (RLMF) of A l 2 0 3 i s responsible. The BLMF due to the nuclear magnetic moment cf the A 1 2 T nucleus d e f i n i t e l y contributes to the TABLE I I I . R e s u l t s of t h e Muonium Experiment Sample p + Asymmetry u + R e l a x a t i o n Mu Asymmetry Mu Re 1axat i on P o l a r i z e d u + P o l a r i z e d Mu M i s s i n g a t Time=0 Rate a t TirneO Rate F r a c t i o n F r a c t i o n F r a c t i o n -1 usee -1 psec % t % A1umi num .342±.006 .03l±.009 100 by assump-t i o n F e 2 0 3 .070±.006 .009±.009 sio2 .17 ±.02 .03 ±.02 .083±.004 . I8±.04 35±5 61 ±3 4±6 CaO . 185+.010 .07±.02 .047±.005 2.5±.6 43±3 35+4 22±5 MgO .262±.0I6 .05±.04 .020±.004 1.9±.5 71 ±6 I5±3 I4±7 A l 2 0 3 . .267±.0I3 .08±.02 .047+.018 11.3±4.4 72±4 35±I4 -7±I5 G e 0 2 .18 ±.03 .044±,0I6 no s i gna1 40±7 0 60±7 S n 0 2 .336±.0I9 .056±.025 no s i g n a l 98±5 0 2±5 SiO .24 ±.01 .0491.009 no s i g n a l 63.5±l 0 36+1 - 113 -.0 0.2 0.4 0.6 0.8 1.0 TIME IN LISEC (20 NSEC/BIN) 1 .2 (a) 1 .4 -0.15 h -0.25 0.0 0.2 0.4 TIME IN M.SEC (20 NSEC/BIN) 1 .4 (b) F i g V . 5 ( a ) . Number of p o s i t r o n events versus time a f t e r the muon stop, with the e x p o n e n t i a l f o l d e d out, i n A12C>3 (150A) f o r the l e f t t e l e s c o p e . The t r a n s v e r s e f i e l d was 7.8 Gauss. The pressure i n the vacuum v e s s e l was 10~ 5 t o r r . . (b). Same as (a) except f o r the r i g h t t e l e s c o p e . - 114 -0.0 0.2 0.4 0.6 0.8 1.0 1.2 TIME IN LISEC (20 NSEC/BIN) . (a) 1 .4 0.00 0.0 0.2 0.4 0.6 0.8 1.0 1.2 TIME IN pSEC (20 NSEC/BIN) (b) 1 .4 F i g V.6 (a). Number o f p o s i t r o n events versus time a f t e r the muon stop, w i t h the e x p o n e n t i a l f o l d e d out, i n A I 2 O 3 (150A). The pressure i n the vacuum v e s s e l was 10~5-torr. The t r a n s v e r s e f i e l d was 7.8 Gauss. (b). Same as (a) except w i t h 5 t o r r of 0^ i n the vacuum v e s s e l . - 115 -d e p o l a r i z a t i o n b u t i t i s p r o b a b l y n o t t h e o n l y c a u s e s i n c e t h i s f a s t d e p o l a r i z a t i o n i s n o t p r e s e n t i n i c e where t h e p r o t o n n u c l e a r m a g n e t i c moment i s p r e s e n t . P h y s i c a l i n p u r i t i e s may a l s o c o n t r i b u t e t o t h i s BLMF, I f t h e muonium i s i n t h e i n t e r g r a n u l a r r e g i o n s t h e n t h e a f f e c t o f a d s o r b e d g a s e s on t h e s u r f a c e must a l s o be c o n s i d e r e d . F i g s V.7 (a) and V.7(b) show t h e e f f e c t c f 5 t o r r o f 0 2 on t h e Mu p r e c e s s i o n s i g n a l i n MgO. A g a i n t h e p r e c e s s i o n s i g n a l i s d e s t r o y e d . S u c h i s n o t t h e c a s e f o r c o a r s e CaO ( s e e f i g s V . 8 ( a ) 6 V . 8 ( b ) ) , w h i c h i s c l e a r l y a p a r t i c l e s i z e 0 e f f e c t . T h e S i 0 2 (35A) i n an 0 2 e n v i r o n m e n t h a s t e e n i n v e s t i g a t e d by M a r s h a l l ( 1 9 7 7 ) . The g u e n c h i n g r a t e c o e f f i c i e n t was m e a s u r e d a n d f o u n d t o be c o n s i s t e n t w i t h m e a s u r e m e n t s u s i n g an a r g o n m o d e r a t o r ( G a r n e r , 1 9 7 8 ) . T h i s i s s t r o n g e v i d e n c e t h a t t h e Mu was i n t h e i n t e r g r a n u l a r r e g i o n s . G e 0 2 s h o w e d t h e l a r g e s t m i s s i n g f r a c t i o n . T h e r e was n o muonium p r e c e s s i o n o b s e r v e d d e s p i t e t h e f a c t t h a t t h e f r e e muon p r e c e s s i o n a c c o u n t e d f o r o n l y 4 0 ± 7 % o f t h e muons (see f i g s V . 9 ( a ) and V . 9 ( b ) ) . I t i s v e r y p r o b a b l e t h a t t h e m i s s i n g f r a c t i o n i s due t o f a s t d e p o l a r i z a t i o n o f Mu s i n c e 1 . , G e 0 2 and S i 0 2 a r e c h e m i c a l l y v e r y s i m i l a r s o o n e w o u l d e x p e c t t h a t Mu f o r m a t i o n i n S i 0 2 w o u l d i m p l y Mu f o r m a t i o n i n G e 0 2 , 2 . Mu p r e c e s s i o n i s 100 t i m e s more s e n s i t i v e t o BLMF t h a n u+ p r e c e s s i o n . T h e f a c t t h a t a l o n g - 116 --0.30 0.4 0.6 0.8 1.0 TIME IN uSEC (20 NSEC/BIN) 1 .2 (a) 1.4 0.4 0.6 0.8 1.0 TIME IN uSEC (20 NSEC/BIN) 1 .2 (b) 1 .4 F i g V.7 (a). Number of p o s i t r o n events versus time a f t e r the muon stop, with the e x p o n e n t i a l f o l d e d out, i n f i n e MgO. The pr e s s u r e i n the vacuum v e s s e l was 10~5 t o r r . The t r a n s v e r s e f i e l d was 7.8 Gauss. .(b) Same as (a) except with 5 t o r r o f 0 2 i n the vacuum v e s s e l . - 117 -0 . 3 0 0 . 0 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 .0 1 .2 TIME IN LISEC (20 NSEC/BIN) . (a) 1 . 4 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 .0 TIME IN LISEC (20 NSEC/BIN) 1 .2 (b) 1 .4 F i g V.8 (a). Number of p o s i t r o n events versus time a f t e r the muon stop, with the e x p o n e n t i a l f o l d e d out, i n coarse CaO. The pressure i n the vacuum v e s s e l / was 10~5 t o r r . The t r a n s v e r s e f i e l d was 7.8 Gauss. (b) Same as (a) except w i t h 5 t o r r o f i n the vacuum v e s s e l . 0 . 5 0 - 0 . 2 5 - 0 . 5 0 - 118 i ~ r 0 . 0 0 . 5 1 .0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 TIME IN uSEC (60 NSEC/BIN) (a) 4 . 0 0 .50 0.25 h X tn -H X U 0 . 0 0 -0.25 -0.50 0.0 0.5 1.0 1 . 5 2.0 2.5 3.0 3.5 TIME IN LISEC (60 NSEC/BIN) (b) 4 . 0 F i g V.9 (a). Number of p o s i t r o n events versus time a f t e r the muon stop, w i t h the e x p o n e n t i a l f o l d e d out, i n aluminum. The pressure i n the vacuum v e s s e l was 10~5 t o r r . The t r a n s v e r s e f i e l d was 69 Gauss. (b) Same as (a) except i n GeO„. - 119 -l i v e d y+ p r e c e s s i o n was o b s e r v e d i n G e 0 2 s u g g e s t s t h a t t h e m i s s i n g component i s Mu. The m i s s i n g f r a c t i o n i n MgO (14±7%) c o u l d be due t o Mu w i t h i n t h e g r a i n s and t h e o b s e r v e d f r a c t i o n due t o Mu i n t h e i n t e r g r a n u l a r r e g i o n . T h i s would be p o s s i b l e i f t h e v a r i a n c e on t h e p a r t i c l e s i z e i s l a r g e a s e x p e c t e d . On t h i s a s s u m p t i o n t h e o b s e r v e d Mu r e l a x a t i o n r a t e i s a r e s u l t c f s u r f a c e d e p o l a r i z a t i o n . The m i s s i n g f r a c t i o n i n CaO (22±7%) c a n n o t be e x p l a i n e d t h i s way b e c a u s e t h e a d d i t i o n o f 0 2 had no a f f e c t on t h e Mu p r e c e s s i o n . T h i s i m p l i e s t h e p a r t i c l e s i z e i s much l a r g e r t h a n t h e mean d i f f u s i o n l e n g t h b e f o r e d e c a y . However i t i s p o s s i b l e t h a t t h e o b s e r v e d p r e c e s s i o n s i g n a l i s due t o Mu t r a p p e d i n p o r e s w i t h i n t h e g r a i n s . The m i s s i n g f r a c t i o n would t h e n c o r r e s p o n d t o Mu d e p o l a r i z i n g f a s t w i t h i n t h e s o l i d CaO r e g i o n s . - 120 -Sect Future flugnium Experiments The results of t h i s experiment leave many questions unanswered which should be re-examined in the future. The o r i g i n of the missing f r a c t i o n , e s p e c i a l l y i n Ge0 2, should be investigated. I s o t o p i c a l l y pure samples of Ge02 are now available. I f the nuclear magnetic moment of Ge 7 3, which composes 7.76% of the natural Ge , i s responsible for the f a s t depolarization of Mu then an i s o t o p i c a l l y pureGe02 sample w i l l show Mu precession. Fine Ge02 powder should also be examined since i t i s expected that muonium w i l l diffuse into the intergranular regions before i t has a chance to depolarize. A s i n g l e run with oxygen i s not the best technigue in order to determine whether Mu has reached the intergranular regions because the oxygen w i l l also depolarize Mu which i s cn the surface. I t i s then neccessary to examine the relaxation rate as a function of 0 2 pressure i n order to establish that the Mu i s in the intergranular regions (Marshall, 1S78). One f a i r l y simple way to establish that the Mu i s i n between the grains i s t c show a l i n e a r dependence between powder density and relaxation rate. Such a dependence i s only possible i f the Mu i s moving f r e e l y between grains. The d i f f u s i o n model should be tested thoroughly by doing studies of the vacuum fr a c t i o n of Mu versus temperature and p a r t i c l e size for a l l powders which form Mu. In t h i s regard i t would be very i n t e r e s t i n g tc compare the - 121 -d i f f u s i o n constants for muonium and positronium in the various oxides . F i n a l l y , the p o s s i b i l i t y of depositing chemicals on the surface of these powders c l e a r l y suggests a series of experiments i n surface chemistry. - 122 -• CHAPTEB VI CQMCL03>I#G: BBM-A££-S~ I t has been shows that f i n e powdered oxides can be used to e f f i c i e n t l y produce muonium and positronium- Furthermore, the r e s u l t s indicate that i f these oxides are i n a f i n e powdered form Hu l i k e Ps reaches the intergranular regions-Tie applications i n gas chemistry; surface chemistry,diffusion studies and the study of fundamental properties of flu and Ps are numerous-Careful measurements have revealed Mu precession i n Ca<G, MgO, and A1 20 3 where they: had hot be en= seen be fore . These r e s u l t s indicate that the fdrmatioa processes f o r Mu and Ps are c l o s e l y linked at l e a s t i n a q u a l i t a t i v e sense despite the,;larger:mass difference. 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B e v - , ; 1 413-- 126 -APPENDIX J J i l CHARGE CG^JJJ GA TI G N PARITY FQ1 AN e + e~ STATE The charge c o n j u g a t i o n operator a c t s on a s t a t e v e c t o r by r e v e r s i n g the s i g n cn a l l the i n t e r n a l guantum numbers of the p a r i c l e s i n v o l v e d such as the charge, strangeness, fcarycn number, lepton number, e t c . Consider a s p i n 1/2 fermion - a n t i f e r m i o n s t a t e vector 1 2 3 4 5 6 | F F > = | a, - a , L ( L * 1 ) , , S<S+1), S z > where guantum number 1 = i n t e r n a l guantum numbers of fermion # 1 2 = i n t e r n a l guantum numbers o f fermion # 2 3 = ( o r b i t a l angular momentum) 2 U = z component of o r b i t a l a ngular momentum 5 = ( t o t a l spin)« 6 = z component of s p i n Now expanding | F F > i n terms of the ke t s 1 2 3 4 5 6 | a, -a, 0 , <j>, SLz , s ;2 z > where guantum number 1 5 2 = as d e f i n e d before 3 & 4 = s p h e r i c a l angles between fermion 1 6 2 5 = t h i r d component of s p i n f o r fermion 1 6 = t h i r d component of s p i n f o r fermion 2 - 127 Gives F> = E E l / d f i Y L M ( 0 / ' } » ) x s ( S l z , S 2 z ) |a,-a,0,<j),Slz,S2z> Sl„ S2 Applying the operators which exchange space variables (E ), spin variables (E ), and i n t e r n a l guantum ' space ' r s p i n numbers ( C ) gives E E . C|F F > space sp i n ' = E E /df2Y L M(e,<j,)x s(Sl z,S2 z) |-a,a,-0,-<j>,S2z,Slz> SI S2 z z = E E /•d«Y L M ( ' - e ; -$ ) x s(S2 z fSl z) |-a,a,e,(j),Sl z,S2 z> S1 S 2 z z = ( - 1 ) L ( - 1 ) S + 1 ( - 1 ) T 1 | FF > where C|F F> = (-l) ; n|F F> Since the state vector for two i d e n t i c a l fermions must be antisymmetric under such an exchange < - 1 ) L + s = (-1/1 Thus the C parity ( - 1 ) n for positronium obeys t h i s rule. - 128 -JPJPJJLQIX j IB) CHARGE COMJOGAflON PARITY FOR AJ n PJOTjQN-STATE C l a s s i c a l l y , the vector potential f o r the e l e c t r o -magnetic f i e l d s must change sign when a l l charges are reversed i n sign since the f i e l d s B = Curl A E = -3A - Gradtfi are observed to reverse t h e i r signs. The photon f i e l d operator in Fock space i s defined as 2 A(x) = 1 / d k E ' { A, . e . e ~ l k > x + A * . e . e l k ' x } (2T T ) ^ 2 ( I k o ) V 2 j = l where Aj-ij creates a photon of momentum k and polarization j and A, .annihilates one of the same. Since the f i e l d theoretic vector potential must have the same symmetry as the c l a s s i c a l vector potential, t h i s implies „ + + m t C AgjC* = -A K j n Thus an n photon state has C parity ( -1) since C A* . A,+ . . . . A,+ . I 0 > k m k 2 : 2 k n : n ' = CA* .CtCA.+ . ... CA.+ . C +C|0> k i D l k 2 : 2 k n 3 n 1 = ( ~ D nA^ • A.+ A,+ . |0> k i D i k 2 j 2 k n 3 n ' - 129 -APPENDIX • II; :f A>; - M^ AN/^ O.UENCflIN-^ :Ca€i;SS S^£om>0*r A PQlDEa 121 o^Ps Let n be the number density for a pbMer with i n t r i n s i c ty P 1 , bulk density P B , and mean radius R 1 = 4 T T R 3 P B / P I e q n A I I . l n Assume there exists a o-Ps atom at time=0 . Let P|t) be the probability, that i t s t i l l e x i s t s at time t. Define a as r\V> — = - [ a n v + X 0 ] e q n A l l . 2 dt where v i s i t s v e l o c i t y and \ 0 i s the mean decay rate of free o-Ps. From egn AII.2 i t follows,: P(t) = e x p [ - ( a n v + X ) t ] e q n A l l . 3 ;From egn A l l . 3 the observable mean decay rate i n an evacuated powder i s X, = a v n + X v q p o Using egn A l l . 1 i t follows ° q p = 1 A v " A o 7rR3pB/pI v I f i t i s assumed that the o varies as 1/v so that the Mir A v i s independent of v then the mean cross section ° q p ( v ) = ( X y - X 0 ) ( A ) n For a Maxwellian speed d i s t r i b u t i o n - 130 -= 2m - 1 = [5.92 x 10 6cm/sec] where m = 1.02 MeV k = 1.38 x 1 0 ~ 1 6 erg/deg 6 = 295° K APPENDIX II (BV QUENCHING RATE COEFFICIENT Q-F- A- GAS-FOR 0--P-S-Eguation A l l . 3 can be rewritten f o r a gas P ( t ) = e x p [ - ( o v n +\ ) t ] A l l . 4 q o where a i s the cross section at ve l o c i t y v, n i s the q number density for the guenching gas and A q i s the mean decay rate i n the absence of the guenching gas. I t follows from ego"•Ail.4 that A q = Xo + CTqvn where i s the observed decay rate i n the presence of the guencher. The guenching rate c o e f f i c i e n t f o r the gas i s defined as a^v and i s independent of v provided a g goes as 1/v. - 132 -APPENDIX I I I THE MOON POLARIZATION VECTOR FOB A FBEE MUON IN A STATIC IlMkM The task i s to ev a l u a t e i H y t - i H v t P(t) = < f (0) | e*1 e 7 1 | * ( 0 ) > U(t)>= e " i a ° z U ( 0 ) > = e " i a a z 1{|S Z=1> + Is =-l>> /2 2 z 2 where a = g ue|B| 4cm a r i{';e"ia|s =1> + e i a|s =-!>} ' /7 Z 2 Z 2 t h e r e f o r e P z ( t ) = <i|» ( t j | a z | * (t) > = l { e i a e i a - e ~ i a 2 e } = 0 In order to e v a l u a t e p (t) and p (t) i t i s advantaqeous to x y d e f i n e a complex p o l a r i z a t i o n P c ( t ) = P x ( t ) + i P y ( t ) = l [ e i a < S z = l | + e~ i a<S =-l| ] 2S+ 2 2 2 :[e~ i a|S z=l>+e l a|S z=-l>] 2 2 where S +=S X+ is y i s t h e S z r a i s i n g o perator t h e r e f o r e P C (t) = [ e l a « S = l | + e~ i a<^S=-l | ] e i a | S = l > Z 2 Z 2 2 2 i a T e = c o s ( 2 a t ) + i s i n ( 2 a t ) t h e r e f o r e P(t) = cos g ve|B|t x + s i n g pe|B|t y 2m yc 2 m y c - 133 -APPENDIX IV LIST OF THE FINE POWDERS SAMPLE MANUFACTURERS LISTED MANUFACTURER MEAN BADIUS ( A ) S i 0 2 S i 0 2 A 1 2 0 3 ZnO MgO 35 70 150 560 l i g h t powder (radius not available) Cabot Corp.1 Cabot Corp. Davidson Chemical Division W. R. Grace S Co. , New Jersey Zinc Matheson Coleman 6 E e l l Cabot Corp Cabot-Sil Division 125 High Street Boston Mass. 02110 U.S.A. - 134 MEliSH I THE O-Ps F8ACTIQN 1^ ? VACUUM Consider a large number of o-Ps atoms , N{0) , at time=0. Let H|t) be the number of atoms a f t e r time t. Then d N ( t ) = - X N ( t ) d t e q n A V . l o where *o i s the free o-Ps decay rate. I f a guenchinq agent i s present then eqn AV.1 must be rewritten d N ( t ) = - X Q N ( t ) d t ^ Q = X 0 + X q e q n A V . 2 N ( t ) = N ( 0 ) e x p [ - X Q t ] where i s the mean quenchinq rate. The t o t a l number of 2y decays r e s u l t i n g from the quenching process i s ^ X n N ( t ) d t = 5 ( X n - X n ) N ( 0 ) e x p ( - X n t ) d t ° Q o C A f * Q ( X Q - X Q ) / X Q N ( 0 ) [ e x p ( - X Q t ) ] ° ( X Q - X o ) / X Q N ( 0 ) It follows that i f the o-Ps i s being produced at a constant rate , d X / d t , then the 2Y decays w i l l occur a rate d t " U Q A o ' / A Q d t e q n A V . 3 Define ( d N / d t ) v •= 2 Y counting rate i n the evacuated powder ( d N / d t ) = 2 Y counting rate i a the powder+quencher ( d N / d t ) ^ = 2 Y countinq rate due e+ s that do not reach the interqranular reqions as o-Ps ( d N / d t ) C Q = the 2> cbunting rate i f the guenchinq were complete and there, were no 3 y decays - 135 -A O = the true vacuum mean decay rate of o-Ps AQ ==. the mean decay rate i n the powder sample • guencher A V = the mean decay rate i n the evacuated powder Then i t follows that o-Ps f r a c t i o n i n vacuum i s f 0 _ P s = [ ( d N / d t ) C Q - ( d N / d t ) o ] / ( d N / d t ) C Q = { 1 + ( d N / d t ) q / [ ( d N / d t ) C Q - ( d N / d t ) Q ] } _ 1 eqn AV.4 Since (dN/dt) and (dN/dt) are not observable the problem i s to express f i a terms of the o-Ps observables A Q # A?V# (dN/dt) v » ( d N / d t ) Q a n d t h e "known Xo = 7.05 Psec-». By d e f i n i t i o n of ( d N / d t ) ^ and (dN/dt ) 0 the rate of o-Ps production i s dX/dt = 1 [ (dN/dt) p f T(dN/dt) ] eqn AV. 5 k CQ o wbere k i s the e f f i c i e n c y f o r detection. In the powder+guencher the rate of 2.y decays r e s u l t i n g from the guenching of o-Ps i s ( d X / d t ) 2 y = 1 [ (dN/dt) Q-.(dN/dt) Q ] eqn AV.6 Substituting egns AV.5 and AV.6 into egn AV.3 y i e l d s (dN/dt) - ( d N / d t ) Q = ( A Q - A O ) [ ( d N / d t ) C Q - ( d N / d t ) Q ] AQ eqn AV.7 Similarly (dN/dt) v - ( dN/dt ) j o =. f-Xv-X0) [ (dN/dt) C Q - (dN/dt ) Q ] eqn AV.8 - 136 -Subtracting egn IV-7 from egn AV-8 yields ( d N / d t ) - ( d N / d t ) = [ ( d N / d t ) - ( d N / d t ) ] Q V CQ o R e w r i t n g t h i s g i v e s A - A - A - A Q o v o v ( d N / d t ) ( d N / d t ) „ = [ ( d N / d t ) - ( d N / d t ) 1 \ \ - \ A - A CQ Q v Q o - v o v -1 Bewriting egn A V - 8 e q n A V . 9 ( d N / d t ) ( d N / d t ) - ( d N / d t ) q A - A v o A V + ( d N / d t ) v ( d N / d t ) r n - ( d N / d t ) CQ 0 e q n AV.10 Using e p AV.9 L • H • S • = A - A - v o v + ( d N / d t ) v ( d N / d t ) Q - ( d N / d t ) v A _ - A A - A Q v - v o Q v e q n A V . l l Substituting egn AV-11 in t o egn AV- 4 f o - P s = ^ ~ * v A ° + ( d N / d t ) v A - A A - A Q o - V o « 1 X v ( d N / d t ) - ( d N / d t ) v I AQ v e q n AV.12 q e d - 137 -H E M D I X VI OXYGEN IMPURITIES The following i s the manufactures l i s t of impurities for the 99.6555 oxygen used i n t h i s experinent. ,3% argon .05% nitrogen 2ppm carbon dioxide 20ppm hydrocarbons ) 

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