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Relaxation and formation processes of the muon and muonium in the gas phase Mikula, Randall John 1981

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RELAXATION AND FORMATION PROCESSES OF THE MUON AND MUONIUM IN THE GAS PHASE by RANDALL JOHN MIKULA B.Sc., U n i v e r s i t y of Saskatchewan 1975 Honours C e r t i f i c a t e , U n i v e r s i t y of Saskatchewan 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (C h e m i s t r y ) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA August, 1981 (c) R a n d a l l John M i k u l a , 1981 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It i s understood that copying or pu b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of British^Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date DF-fi (2/79. i i ABSTRACT The p o s i t i v e muon i s an u n s t a b l e (T£ =2.2jjsec) p a r t i c l e but one w i t h p r o p e r t i e s v e r y s i m i l a r t o the p r o t o n from a c h e m i c a l and atomic p h y s i c s p o i n t of view. I t has, however, a mass o n l y 1/9 t h a t of the p r o t o n , a f a c t which makes i t i d e a l f o r s t u d y i n g any mass dependence i n c h e m i c a l and p h y s i c a l phenomena. The ^uSR and MSR t e c h n i q u e s have been u t i l i z e d t o study v a r i o u s r e l a x a t i o n phenomena t h a t occur i n the gas phase when the muon or muonium (the muon and e l e c t r o n bound s t a t e analogous t o the hydrogen atom) i n t e r a c t s w i t h i t s environment. The f r a c t i o n of muons t h a t t h e r m a l i z e as muonium has a l s o been measured. I t was found t h a t 83% of the muons s t o p p i n g i n formed muonium, the remainder s t a y i n g i n the charge d s t a t e . Other gases i n v e s t i g a t e d were Hj. (61 %) , 0 ^ ( 8 6 % ) , N H 3 ( 9 0 % ) , H e ( 0 % ) , N e ( 4 % ) , A r ( 7 4 % ) , Kr(lOO%) and X e O 0 0 % ) . The a m p l i t u d e of the s i g n a l was found t o be s t r o n g l y p r e s s u r e dependent and t h i s has been e x p l a i n e d i n terms of the t h e r m a l i z a t i o n time of the muons i n t h e s e gas t a r g e t s . V a r i o u s gas m i x t u r e s were a l s o s t u d i e d where i t was found t h a t r e l a x a t i o n s of t h e ^iSR s i g n a l o c c u r e d as a f u n c t i o n of added reagent gas c o n c e n t r a t i o n . T h i s phenomena has been a t t r i b u t e d t o r e a c t i o n s of muon m o l e c u l a r i o n s w i t h t h e reagent gas, f o r m i n g muonium t h e r m a l l y . T h i s r e p r e s e n t s t he f i r s t r e l i a b l e measurements of muon r e l a x a t i o n i n the gas phase. E v i d e n c e i s p r e s e n t e d i n d i c a t i n g t h a t such r e a c t i o n s o ccur from the f i r s t v i b r a t i o n a l s t a t e of these muon m o l e c u l a r i o n s . The systems s t u d i e d and t h e i r room temperature r a t e c o n s t a n t s ( c m 3 - m o l e c u l e s ~ 1 - s e c " 1 ) a r e : Neyj + +Xe U | = 1 .9±.3X10- 1 1 ) , N e L i + +NH3 (k ( J=0.5±.2xlO- 1 1 ') , Neju'+CHy (^=0. 54±. 24x10' 1 1 ) , Ne^u + +Ar (^=0), Heyj + +Xe (k^ = 0±0.2x1 0" 1 1 ) , and He^J + +NH3 ( k^ =0 . 22. 1 x 1 0" 1 1 ) The s p i n exchange i n t e r a c t i o n s of muonium w i t h NO and 0-^  were a l s o s t u d i e d as a f u n c t i o n of temperature i n the range 295K t o 478K. The measured r a t e c o n s t a n t s e x h i b i t a temperature dependence c o n s i s t e n t w i t h TV/* and hence a c o n s t a n t s p i n exchange c r o s s s e c t i o n . The temperature averaged s p i n exchange c r o s s s e c t i o n s found a r e : f o r Mu+O^, 6~SE=9.0±1x1 0" 1 6 c m 2 and f o r Mu+NO, e i e = 1 0 . 5+1 x 1 0 - 1 6 c m 2 . These v a l u e s a r e e s s e n t i a l l y t he same as the c r o s s s e c t i o n s found f o r hydrogen atom s p i n exchange w i t h the same m o l e c u l e s , i n q u a l i t a t i v e agreement w i t h c u r r e n t t h e o r e t i c a l p r e d i c t i o n s . i v TABLE OF CONTENTS 1. INTRODUCTION 1 1.1. The P o l a r i z e d P o s i t i v e Muon 3 1.2. The y^SR Technique 7 1.3. Muonium And The MSR Technique 13 1.4. H i s t o r i c a l P e r s p e c t i v e And S u b j e c t M a t t e r Of The T h e s i s 17 2. EXPERIMENTAL 28 2.1. Muon Beams And Beam L i n e s 28 2.2. Gas T a r g e t And Mag n e t i c F i e l d 33 2.3. Muon S t o p p i n g D i s t r i b u t i o n And W a l l E f f e c t s . .' 38 2.4. The Counter System, Data A c q u i s i t i o n And A n a l y s i s 42 3. MUONIUM FORMATION IN THE GAS PHASE 47 3.1. I n t r o d u c t i o n 47 3.2. T h e o r e t i c a l Background For Charge Exchange ... 63 3.3. Muonium F o r m a t i o n In The Rare Gases 69 3.4. P r e s s u r e Dependence Of The Asymmetry 80 3.5. Muonium F o r m a t i o n In Pure P o l y a t o m i c Gases ... 94 3.6. Muonium F o r m a t i o n In Doped Rare Gases 105 4. MUON MOLECULAR ION FORMATION AND RELAXATION PROCESSES 121 4.1. R e l a x a t i o n In Pure Gases 121 4.2. Muon R e l a x a t i o n In Gas M i x t u r e s 126 5. MUONIUM SPIN EXCHANGE WITH OXYGEN AND NITRIC OXIDE 148 5.1. I n t r o d u c t o r y Remarks 148 V 5.2. R e l a x a t i o n Of The MSR S i g n a l 150 5.3. The C r o s s S e c t i o n For S p i n Exchange 155 5.4. E x p e r i m e n t a l R e s u l t s 158 5.4a. Room Temperature R e s u l t s 159 5.4b. Temperature Dependent R e s u l t s 167 5.5. Comparison W i t h The R e s u l t s Of Mobley 177 5.6. Comparison W i t h Theory And W i t h Hydrogen Atom R e s u l t s 183 APPENDICES 191 APPENDIX 1. THE TIME EVOLUTION OF THE MUON SPIN IN A TRANVERSE MAGNETIC FIELD 191 APPENDIX 2. THE MONTE CARLO SIMULATION AND EXPERIMENTAL TESTS OF THE STOPPING DISTRIBUTION ON THE OBSERVED ASYMMETRY 201 APPENDIX 3. THE SPIN EXCHANGE F FACTORS 212 v i LIST OF FIGURES F i g u r e 1.1. Counter and gas t a r g e t c o n f i g u r a t i o n . ... 8 F i g u r e 1.2. Time h i s t o g r a m of muon p r e c e s s i o n i n 3 6 p s i argon i n a t r a n s v e r s e magnetic f i e l d of 70 gauss. . 10 F i g u r e 1.3. Muon s i g n a l S ( t ) i n argon c o r r e s p o n d i n g t o the time h i s t o g r a m of f i g u r e 1.2 12 F i g u r e 1.4. Time h i s t o g r a m of muonium i n 3 6 p s i argon i n a t r a n s v e r s e magnetic f i e l d of 8 gauss 15 F i g u r e 1.5. Muonium s i g n a l S ( t ) i n 3 6 p s i argon c o r r e s p o n d i n g t o the time h i s t o g r a m of f i g u r e 1.4. 16 F i g u r e 1.6. The s i g n a l s S ( t ) i n n i t r o g e n a t 3t>psi showing muonium p r e c e s s i o n i n a f i e l d of 8G ( t o p ) and muon p r e c e s s i o n i n a f i e l d of 75G (b o t t o m ) . ... 20 F i g u r e 1.7. Time h i s t o g r a m N ( t ) f o r yu* i n aluminum i n a f i e l d of 75G ( t o p ) ; the c o r r e s p o n d i n g ^JSR s i g n a l i s g i v e n a t the bottom 23 F i g u r e 1.8. Muon S i t ) i n pure neon ( t o p ) and neon w i t h xenon i m p u r i t y (bottom) 24 F i g u r e 1.9. Muonium S ( t ) showing r e l a x a t i o n s due t o c h e m i c a l r e a c t i o n 25 F i g u r e 2.1. Layout of the M8, M9 and M20 beam l i n e s o f f the p i o n p r o d u c t i o n t a r g e t (T2) a t TRIUMF '30 F i g u r e 2.2. S u r f a c e muon range c u r v e o b t a i n e d i n mylar and t a k e n from M a r s h a l l ( 1 978) 32 F i g u r e 2.3. Gas cans and gas h a n d l i n g system 34 v i i F i g u r e 2.4. F i e l d map of h e l m h o l t z c o i l s a l o n g beam d i r e c t i o n . The l i n e i s meant t o guide the eye o n l y . 37 F i g u r e 2.5. E l e c t r o n i c s c o n f i g u r a t i o n 45 F i g u r e 3.1. The charge exchange c r o s s s e c t i o n s glo and &oi f o r p r o t o n s i n argon from A l l i s o n ( 1 9 5 8 ) and T a w a r a d 973) 51 F i g u r e 3.2. The n e u t r a l f r a c t i o n f o r p r o t o n s i n argon c a l c u l a t e d from the d a t a of f i g u r e 3.1 52 F i g u r e 3.3. The number of charge changing c y c l e s N c f o r h e l i u m e v a l u a t e d from e q u a t i o n 3.6 56 F i g u r e 3.4. N c f o r p r o t o n charge exchange i n v a r i o u s gases 58 F i g u r e 3.5. V e c t o r diagram of v e l o c i t i e s f o r the charge exchange c o l l i s i o n s 65 F i g u r e 3.6. Helium n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1958) and T a w a r a ( l 973) 71 F i g u r e 3.7. Neon n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1958) and T a w a r a d 973) 72 F i g u r e 3.8. The n e u t r a l f r a c t i o n f o r p r o t o n s i n argon c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). ... 73 F i g u r e 3.9. K r y p t o n n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 958) and T a w a r a d 973) 74 F i g u r e 3.10. Xenon n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 958) and T a w a r a d 973) 75 F i g u r e 3.11. Asymmetry i n k r y p t o n as a f u n c t i o n of p r e s s u r e 8 1 v i i i F i g u r e 3.12. Asymmetry i n xenon as a f u n c t i o n of p r e s s u r e 82 F i g u r e 3.13. Hydrogen n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). 96 F i g u r e 3.14. N i t r o g e n n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1958) and Tawara ( 1 973 ) 97 F i g u r e 3.15. Ammonia n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1958) and T a w a r a d 973) 98 F i g u r e 3.16. Methane n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 958) and Tawara ( 1 973) 99 F i g u r e 3.17. NH^ S ( t ) f o r muon and muonium 100 F i g u r e 3.18. Neon w i t h xenon i m p u r i t y showing the e f f e c t on the muon and muonium S ( t ) 107 F i g u r e 3 . 1 9 . Neon w i t h argon i m p u r i t y showing the e f f e c t on the muon and muonium S ( t ) 108 F i g u r e 3.20. Mu and muon asymmetries f o r neon ( l 8 p s i ) and xenon m i x t u r e s 115 F i g u r e 3.21. Mu and muon asymmetries f o r neon ( l 8 p s i ) and ammonia m i x t u r e s 117 F i g u r e 3.22. Mu and muon asymmetries f o r neon ( l 8 p s i ) and argon m i x t u r e s 1 1 8 F i g u r e 3.23. Mu and muon asymmetries f o r neon ( I 8 p s i ) and methane m i x t u r e s 1 1 9 F i g u r e 4.1. Muon r e l a x a t i o n f o r xenon i n neon ( I 8 p s i ) . 131 F i g u r e 4.2. Muon r e l a x a t i o n f o r xenon, methane and argon i n neon ( 1 8 p s i ) 132 F i g u r e 4.3. Muon r e l a x a t i o n f o r ammonia i n neon ( I 8 p s i ) . The r a t e =5. 01:2 . Ox 1 0" 1 2 c m 3 / m o l e c u l e -sec 133 F i g u r e 4.4. Muon r e l a x a t i o n f o r xenon i n h e l i u m ( 4 5 p s i ) . The r a t e kj=0.Ot2.Ox 10~n cm 3/atom-sec. .134 F i g u r e 4.5. Muon r e l a x a t i o n f o r ammonia i n h e l i u m ( 4 5 p s i ) . The r a t e k«i = 2 . 5±1 . Ox 1 0" 1 2 c m 3 / m o l e c u l e -sec 135 F i g u r e 4.6. Temperature dependence of the Neu*+Xe r e a c t i o n . The r a t e kj[ = 5. 3± 1 .Ox 1 0" 1 1 cm 3/atoms-sec a t 333K which g i v e s E a = 3 . 7±1 k c a l / m o l e 146 F i g u r e 5.1. N i t r o g e n muonium s i g n a l a t I 5 p s i and 38p s i 151 F i g u r e 5.2. R e l a x a t i o n r a t e A as a f u n c t i o n of O z c o n c e n t r a t i o n f o r the r e a c t i o n Mu+Oj i n n i t r o g e n moderator a t 15psi and 38 p s i p r e s s u r e 161 F i g u r e 5.3. R e l a x a t i o n r a t e X as a f u n c t i o n of NO c o n c e n t r a t i o n f o r the r e a c t i o n Mu+NO i n n i t r o g e n moderator a t 15psi and 38 p s i p r e s s u r e 162 F i g u r e 5.4. R e l a x a t i o n r a t e X as a f u n c t i o n of 0 2 c o n c e n t r a t i o n f o r the r e a c t i o n Mu+O^ ^ i n argon moderator a t 15psi p r e s s u r e 163 F i g u r e 5.5. R e l a x a t i o n of MSR s i g n a l due t o s p i n exchange w i t h 02 a t 438K 169 F i g u r e 5.6. R e l a x a t i o n r a t e A v s . c o n c e n t r a t i o n of 0 a t 478K and 295K 1 72 F i g u r e 5.7. R e l a x a t i o n r a t e A v s . c o n c e n t r a t i o n of NO a t 388K and 438K 173 F i g u r e 5.8. Log k v s . l o g T f o r Mu + 0 a . The s l o p e of the l i n e i s n=.9±.5 175 F i g u r e 5.9. Log k v s . l o g T f o r Mu + NO. The s l o p e of the l i n e i s n=.6±.4. 176 F i g u r e 5.10. A r r h e n i u s p l o t of l o g k v s . 1/T f o r Mu + O a. The a c t i v a t i o n energy o b t a i n e d from the s l o p e i s .7±.5kcal/mole 178 F i g u r e 5.11. A r r h e n i u s p l o t of l o g k v s . 1/T f o r Mu + NO. The a c t i v a t i o n energy o b t a i n e d from the s l o p e i s .4±.3kcal/mole 179 F i g u r e 5.12. T h e o r e t i c a l s p i n exchange c r o s s s e c t i o n s from A q u i l a n t i (1 980) 188 F i g u r e A1.1. B r i e t - R a b i diagram showing the energy l e v e l s of muonium i n a t r a n s v e r s e magnetic f i e l d . .196 F i g u r e A1.2. Muonium S ( t ) i n s o l i d Ar (77K) a t 66.5G showing two freq u e n c y p r e c e s s i o n of the muon s p i n (from K i e f 1( 1981 )) 199 F i g u r e A1.3. MSR spectrum w i t h p e r f e c t time r e s o l u t i o n 200 F i g u r e A2.1. R e l a t i o n s h i p of c o u n t e r s i z e and s t o p p i n g d i s t r i b u t i o n 202 F i g u r e A2.2. Monte C a r l o d a t a S ( t ) and f i t 209 x i LIST OF TABLES T a b l e 1.1. Some p r o p e r t i e s of the p o s i t i v e muon 4 T a b l e 1.2. Some p r o p e r t i e s of the muonium and hydrogen atoms. 18 Ta b l e 2.1. Comparison of p r e s e n t r e s u l t s w i t h t h o s e of Stambaugh f o r muonium and muon f o r m a t i o n f r a c t i o n s i n v a r i o u s gases 40 Ta b l e 3.1. Massey c r i t e r i a p r e d i c t i o n s of Mu f o r m a t i o n peaks 55 Tab l e 3.2. Range of i n t e g r a t i o n and number of charge exchange c y c l e s f o r v a r i o u s gases 60 Tab l e 3.3. The time spent i n the t h r e e s t a g e s of t h e r m a l i z a t i o n f o r the r a r e gases 61 Tab l e 3.4. N e u t r a l f r a c t i o n s o b s e r v e d f o r muons i n the r a r e gases and compared t o p r o t o n e x t r a p o l a t i o n s . . 76 Ta b l e 3.5. Asymmetry v s . p r e s s u r e f o r t h e r a r e gases. ; 78 Ta b l e 3.6. A b s o l u t e asymmetry v s . p r e s s u r e f o r v a r i o u s gases 79 Ta b l e 3.7. \ 0 and phase a n g l e as a f u n c t i o n of gas p r e s s u r e 85 Ta b l e 3.8. R e s u l t s of a Monte C a r l o c a l c u l a t i o n and the e f f e c t of a change i n e x p e r i m e n t a l s o l i d a n g l e on the muon asymmetry 89 Ta b l e 3.9. D e p o l a r i z a t i o n e s t i m a t e d from t o t a l asymmetry as a f u n c t i o n of p r e s s u r e 91 Ta b l e 3.10. N e u t r a l f r a c t i o n s o b s e r v e d f o r muons i n the p o l y a t o m i c gases and compared t o p r o t o n e x t r a p o l a t i o n s 101 T a b l e 3.11. A b s o l u t e asymmetry of p o l y a t o m i c gases and e q u i v a l e n t d e n s i t y r a r e gases 103 Tab l e 3.12. M i x t u r e asymmetries f o r doped gases 110 Ta b l e 3.12. C o n t i n u e d 111 T a b l e 3.12. C o n t i n u e d 112 Ta b l e 3.12. C o n t i n u e d 113 Ta b l e 3.12. Co n t i n u e d 114 T a b l e 4.1. \ 0 i n v a r i o u s pure gases 125 Tab l e 4.2. R e l a x a t i o n s as a f u n c t i o n of added gas c o n c e n t r a t i o n f o r the gas m i x t u r e s s t u d i e d . 128 Ta b l e 4.2. C o n t i n u e d 129 Ta b l e 4.2. C o n t i n u e d 1 ™ Ta b l e 4.3. P o s s i b l e r e a c t i o n p a t h s f o r t h e muon m o l e c u l a r i o n T a b l e 4.3. C o n t i n u e d T a b l e 4.4. D i s s o c i a t i o n e n e r g i e s f o r Ne/U+and He//" from v=0 and V=1 s t a t e s , 140 Ta b l e 4.5. Langevin r a t e c o n s t a n t s f o r the m o l e c u l a r i o n r e a c t i o n s 145 T a b l e 5.1. A v s . C o n c e n t r a t i o n of O a and NO a t I 5 p s i and 3 8 p s i moderator p r e s s u r e 160 Ta b l e 5.2. Room temperature r e l a x a t i o n r a t e s 164 Ta b l e 5.3. Comparison of the p r e s e n t room temperature x i i i - '> CTse f o r Mu+NO and Mu+O a w i t h those of Mobley and w i t h c o r r e s p o n d i n g H atom results 166 Ta b l e 5.4. C o n c e n t r a t i o n dependent r e l a x a t i o n r a t e s as a f u n c t i o n of temperature f o r Mu+0 2 170 Tab l e 5.5. C o n c e n t r a t i o n dependent r e l a x a t i o n r a t e s as a f u n c t i o n of temp e r a t u r e f o r Mu+NO 171 Tab l e 5.6. B i m o l e c u l a r r a t e c o n s t a n t s as a f u n c t i o n of temp e r a t u r e f o r Mu+O^ and Mu+NO s p i n exchange 174 Ta b l e 5.7. Comparison of Mu and H s p i n exchange c r o s s s e c t i o n s f o r r e a c t i o n s w i t h NO and 0 2 180 Tab l e 5.8. 6^SE f ° r Mu+O^; comparison of t h e o r y and experiment 187 Ta b l e A2.1. T o t a l asymmetry as a f u n c t i o n of p r e s s u r e . 204 Ta b l e A2.2. Monte C a r l o program l i s t i n g ..206 Tab l e A2.2. C o n t i n u e d 207 Ta b l e A2.2. C o n t i n u e d 208 Ta b l e A2.3. E x p e r i m e n t a l and Monte C a r l o asymmetry t e s t s 211 Ta b l e A3.1. The s o l u t i o n s t o e q u a t i o n A3.14 showing t h e time r a t e of change of the. muonium s p i n s t a t e s i n t e r a c t i n g w i t h oxygen m o l e c u l e s 217 x i v ACKNOWLEDGEMENT I t i s a p l e a s u r e t o thank my r e s e a r c h s u p e r v i s o r , Dr. Don F l e m i n g , f o r h i s su p p o r t i n t h i s work. He has always been a v a i l a b l e w i t h h e l p f u l s u g g e s t i o n s ; t o o f f e r encouragement when t h i n g s were g o i n g b a d l y ; and always t h e r e t o c e l e b r a t e when the e x p e r i m e n t s were go i n g w e l l . The s u p p o r t of many pe o p l e was n e c e s s a r y f o r the s u c c e s s f u l c o m p l e t i o n of t h i s t h e s i s but u n f o r t u n a t e l y i t i s o n l y p o s s i b l e t o mention a few. I would l i k e t o thank Dr. Dave Garner f o r showing me the " r o p e s " , as i t were, of the TRIUMF c y c l o t r o n and the MSR t e c h n i q u e s . I am a l s o i n d e b t e d f o r h i s i m p l e m e n t a t i o n and su p p o r t of the v a r i o u s f i t t i n g and p l o t t i n g programs used i n the d a t a a n a l y s i s . I would a l s o l i k e t o thank Dr. J e s s Brewer f o r many h e l p f u l d i s c u s s i o n s and f o r h i s p a r t i n s u p p o r t i n g the da t a a r c h i v i n g system. I must a l s o thank B r i n P o w e l l and the men i n the m e c h a n i c a l shop who b u i l t the h i g h temperature gas t a r g e t and who on more than one o c c a s i o n were c a l l e d upon t o make l a s t minute m o d i f i c a t i o n s t o save t h e e x p e r i m e n t . F i n a l l y , and most i m p o r t a n t l y , I would l i k e t o thank my p a r e n t s ; who have p r o v i d e d encouragement and support t h r o u g h o u t my e d u c a t i o n ; and t o d e d i c a t e t h i s t h e s i s t o them. 1 1. INTRODUCTION The p o s i t i v e muon i s i n many ways s i m p l y a l i g h t i s o t o p e of the p r o t o n . S i m i l a r l y , muonium (t h e p*-e~ bound s t a t e ; Mu) can be thought of i n ana l o g y t o . the hydrogen atom. The major d i f f e r e n c e between the muon and p r o t o n , from a c h e m i c a l and atomic p h y s i c s v i e w p o i n t , i s t h e i r d i f f e r e n c e i n mass (iry=l/9mp). T h e r e f o r e , by s t u d y i n g the i n t e r a c t i o n s of muons w i t h m a t t e r , one can t e s t the mass dependence of many of the t h e o r i e s d e v e l o p e d f o r p r o t o n i n t e r a c t i o n s . In analogous muon and p r o t o n (or muonium and hydrogen atom) systems the f a c t o r of 9 change i n mass i s unprecedented. For example, by comparing hydrogen and t r i t i u m t h e r e i s o n l y a f a c t o r of t h r e e change i n mass whereas Mu and T d i f f e r by a f a c t o r of 27 i n mass. The two major s e c t i o n s of t h i s t h e s i s a r e devo t e d t o charge c h a n g i n g p r o c e s s e s ( i . e . e l e c t r o n c a p t u r e and l o s s as t h e p o s i t i v e muon t h e r m a l i z e s i n m a t t e r ) and t o e l e c t r o n s p i n exchange (where t h e e l e c t r o n i n muonium can s p i n exchange w i t h the e l e c t r o n s of a paramagnetic s p e c i e s ) . The study of charge exchange p r o c e s s e s i s i m p o r t a n t i n the u n d e r s t a n d i n g of many phenomena, i n c l u d i n g r a d i a t i o n damage, the d e s i g n of r a d i a t i o n d e t e c t o r s and t h e b e h a v i o r of plasmas i n t h e r m o n u c l e a r f u s i o n e x p e r i m e n t s . In 2 p a r t i c u l a r , w i t h the muon one can probe charge exchange near t h e r m a l e n e r g i e s , a r e g i o n o f t e n i n a c c e s s i b l e t o p r o t o n e x p e r i m e n t s . The phenomenon of e l e c t r o n s p i n exchange i s one of the most fundamental of atomic c o l l i s i o n p r o c e s s e s , w i t h a p p l i c a t i o n s i n a s t r o p h y s i c s and i n the o p e r a t i o n of the hydrogen maser. Muonium s p i n exchange s t u d i e s p r o v i d e a v a l u a b l e t e s t of any mass dependence i n the t h e o r y of s p i n exchange and t h i s has r e c e n t l y g e n e r a t e d a l o t of i n t e r e s t ( S h i z g a l ( 1 9 7 9 ) , A q u i l a n t i ( 1 9 8 0 ) ) . The u t i l i z a t i o n of the p o s i t i v e muon t o stu d y problems of i n t e r e s t i n c h e m i s t r y and atomic p h y s i c s i s r e l a t i v e l y new. I t i s not so new, however, t h a t t h i s t h e s i s w i l l a ttempt t o cov e r a l l of the background n e c e s s a r y f o r a complete u n d e r s t a n d i n g of the e x p e r i m e n t a l s t r e n g t h s and s h o r t c o m i n g s . For t h i s t h e r e a r e many good r e v i e w s of the s u b j e c t , a few of which a r e mentioned a t the b e g i n n i n g of Appendix 1. An attempt has been made, however, t o p r o v i d e an o v e r v i e w of the experiment which s h o u l d e n a b l e a newcomer t o u n d e r s t a n d the r e s u l t s w i t h o u t h a v i n g t o r e s o r t t o the d e t a i l e d d e s c r i p t i o n s g i v e n i n the r e f e r e n c e s of Appendix 1. 3 1.1. The P o l a r i z e d P o s i t i v e Muon The muon i s an u n s t a b l e p a r t i c l e t h a t was f i r s t i d e n t i f i e d i n cosmic r a y s (Anderson(1 9 3 7), S t r e e t ( 1 9 3 7 ) ) and i s now r o u t i n e l y produced f o r r e s e a r c h purposes i n meson " f a c t o r i e s " such as TRIUMF ( T R I - U n i v e r s i t y Meson F a c i l i t y ) , SIN ( S c h w e i z e r i s c h e s I n s t i t u t f u r N u k l e a r f o r s c h u n g ) and LAMPF (Los Alamos Meson and P r o t o n F a c i l i t y ) . The exp e r i m e n t s f o r t h i s t h e s i s were a l l done a t TRIUMF. The muon decays i n t o a p o s i t r o n and two n e u t r i n o s w i t h a mean l i f e of about 2.2 yusec. The p o s i t i v e muon i s i n many r e s p e c t s s i m i l a r t o a p r o t o n (charge +1 , s p i n 1/2) except f o r i t s mass s i n c e myu=l/9ny. Some p r o p e r t i e s of the muon are summarized i n t a b l e 1 . 1 . A l t h o u g h b o t h p o s i t i v e and n e g a t i v e muons a re found i n n a t u r e , and a r e b e i n g e x t e n s i v e l y s t u d i e d (yjSR1 (1 977 ) , yuSR2 (1 980 ) , t h i s t h e s i s w i l l be e x c l u s i v e l y concerned w i t h the p o s i t i v e muon. Muons are produced at the TRIUMF c y c l o t r o n w i t h a h i g h energy p r o t o n beam ( t y p i c a l l y 500 MeV), which i s d i r e c t e d a t a b e r y l l i u m t a r g e t p r o d u c i n g p o s i t i v e p i o n s . The p o s i t i v e p i o n can then decay i n the p a r i t y v i o l a t i n g p r o c e s s ( w i t h a mean l i f e of about 2 6 n s e c ) , 1 .1 The P o s i t i v e Muon Charge: +1 S p i n : 1/2 Mass: 105.66 MeV/c 2 206.8 me 0. 1 1 26 m,, Mag n e t i c Moment: 4 . 4 9 x 1 0 ~ 2 3 e r g / g a u s s 3. 18334 jj,f 0.00484ywt g - f a c t o r : 2.0023318=1.000006 g € Mean L i f e t i m e : 2 . 1 9 9 yjs Gyromagnetic R a t i o : 13.5544 kHz/gauss 3. 18334 «"„ T a b l e 1 . 1 . Some p r o p e r t i e s of the p o s i t i v e muon. 5 p r o d u c i n g a 4.1MeV i n the r e s t frame of t h e p i o n . The muon n e u t r i n o Ojx has n e g a t i v e h e l i c i t y which means t h a t i t s s p i n (1/2) i s d i r e c t e d o p p o s i t e t o i t s momentum. In o r d e r t o c o n s e r v e momentum ( l i n e a r and a n g u l a r ) i n the s p i n z e r o p i o n system, the muon must a l s o have i t s s p i n d i r e c t e d o p p o s i t e t o i t s momentum. Hence n a t u r e p r o v i d e s a 100% l o n g i t u d i n a l l y s p i n p o l a r i z e d muon beam. Not o n l y i s each muon 100% l o n g i t u d i n a l l y p o l a r i z e d , i t remains p o l a r i z e d down t o keV e n e r g i e s as the muon s t o p s i n m a t t e r . I t s subsequent d e p o l a r i z a t i o n forms a l a r g e p a r t of t h i s t h e s i s . S i n c e the muon i s s p i n p o l a r i z e d , i t w i l l p r e c e s s i n a t r a n s v e r s e magnetic f i e l d w i t h a c h a r a c t e r i s t i c Larmor f r e q u e n c y , \) =13.55 kHz/gauss. Because of i t s p o l a r i z a t i o n , every muon s t a r t s t h i s p r e c e s s i o n w i t h the same i n i t i a l phase. The muon e v e n t u a l l y d e cays, a l s o v i a the p a r i t y v i o l a t i n g weak i n t e r a c t i o n , i n t o a p o s i t r o n and two n e u t r i n o s , w i t h a mean l i f e of 2.2 usee. 1 .2 T h i s decay i s a n i s o t r o p i c w i t h most of the p o s i t r o n s b e i n g emmitted a l o n g the muon s p i n d i r e c t i o n . T h i s f a c t can be most e a s i l y u n d e r s t o o d from the decay scheme of e q u a t i o n 1.2. In t h i s c a s e , the decay p o s i t r o n e x i t s w i t h maximum energy (52.8MeV), l e a v i n g the two n e u t r i n o s t o c a r r y o f f the same momentum i n the o p p o s i t e d i r e c t i o n . I n f a c t , i s an 6 a n t i n e u t r i n o which has the o p p o s i t e h e l i c i t y t o 0 e« Hence, as i n the o r i g i n a l p i o n decay, momentum c o n s e r v a t i o n f o r c e s the e* (which i s known t o have p o s i t i v e h e l i c i t y ) t o e x i t a l o n g the o r i g i n a l yj* s p i n d i r e c t i o n . In p r a c t i c e , the experiment averages over the spectrum of p o s i t r o n e n e r g i e s ( ( B r e w e r ( 1 9 7 5 ) ) w i t h the r e s u l t t h a t the number of p o s i t r o n s o b s e r v e d a t a n g l e 0- w i t h r e s p e c t t o the muon s p i n i s g i v e n by Ne(e-)= 1 + A^cosO- 1 .3 where Ne(0-) i s the number of p o s i t r o n s and Ayw. i s the asymmetry or s t r e n g t h of the c o r r e l a t i o n between muon s p i n d i r e c t i o n and p o s i t r o n e m i s s i o n . The form of e q u a t i o n 1.3 can be d e r i v e d from weak i n t e r a c t i o n t h e o r y ( S a c h s ( 1 9 7 5 ) ) , where i t i s shown t h a t the energy averaged asymmetry i s 1/3. In p r a c t i c e , A^ , i s g e n e r a l l y t r e a t e d e m p i r i c a l l y and can be a f f e c t e d by such t h i n g s as p o s i t r o n d e t e c t i o n e f f i c i e n c y , beam p o l a r i z a t i o n and s o l i d a n g l e subtended by the p o s i t r o n t e l e s c o p e s . 7 1.2. The uSR Technique The p o l a r i z a t i o n of the muon beam, c o u p l e d w i t h , the f a c t t h a t the p o s i t r o n decay o c c u r s p r e f e r e n t i a l l y a l o n g the muon s p i n d i r e c t i o n , a l l o w s one t o mon i t o r the muon and observe i t s i n t e r a c t i o n s w i t h m a t t e r . In a t r a n s v e r s e magnetic f i e l d , the d e t e c t i o n of decay p o s i t r o n s from p r e c e s s i n g muons r e f l e c t s the i n s t a n t a n e o u s p o s i t i o n of the muon s p i n v e c t o r . T h i s i s the b a s i s of the yuSR or muon s p i n r o t a t i o n t e c h n i q u e . The decay p o s i t r o n s a r e d e t e c t e d by p o s i t r o n t e l e s c o p e s which c o n s i s t of two or t h r e e c o u n t e r s i n a row such t h a t a p u l s e o b s e r v e d i n a l l t h r e e c o u n t e r s i s an i n d i c a t i o n of a decay p o s i t r o n (which has enough energy t o t r i g g e r a l l t h r e e ) r a t h e r than s i m p l y n o i s e or a c o n t a m i n a t i n g beam p o s i t r o n (which, when degraded, g e n e r a l l y does not have enough energy t o t r i g g e r a l l t h r e e c o u n t e r s ) . The b a s i s of the t e c h n i q u e i n v o l v e s s t a r t i n g a c l o c k when a muon e n t e r s the t a r g e t and measuring the time u n t i l a decay p o s i t r o n i s ob s e r v e d . Then the c l o c k i s r e s e t and the p r o c e s s r e p e a t e d u n t i l 1 0 6 t o 1 0 7 e v e n t s a re c o l l e c t e d . In g e n e r a l t h e r e a re two p o s i t r o n t e l e s c o p e s , one on e i t h e r s i d e of the t a r g e t (see f i g u r e 1.1) which g i v e a c o n s i s t e n c y check of the e x p e r i m e n t , as w e l l as p r o v i d i n g i n c r e a s e d d a t a c o l l e c t i o n e f f i c i e n c y . As can be seen from f i g u r e 1.1 the p o s i t r o n t e l e s c o p e s o n l y "see" a s m a l l s e c t i o n of the 8 F i g u r e 1 . 1 . Counter and gas t a r g e t c o n f i g u r a t i o n . An incoming muon s t o p s i n the t a r g e t p r o v i d i n g a s t a r t p u l s e t o a c l o c k , which i s stopped by the d e t e c t i o n . o f a decay p o s i t r o n , g i v i n g r i s e t o the c h a r a c t e r i s t i c w i g g l e s of a uSR spectrum i n a t r a n s v e r s e f i e l d . 9 p o s s i b l e decay d i r e c t i o n s . T h i s means t h a t most of the p o s i t r o n decays a r e not o b s e r v e d and t h e r e f o r e a f t e r a s u i t a b l e l e n g t h of time ( t y p i c a l l y two muon l i f e t i m e s ) the c l o c k i s r e s e t anyway. Every event i s b i n n e d i n a time h i s t o g r a m which i s incremented by one a t the a p p r o p r i a t e time b i n a f t e r each e v e n t . S i n c e •©• = Wy* t , from e q u a t i o n 1.3, the h i s t o g r a m w i l l e x h i b i t a maximum c o r r e s p o n d i n g t o those t i m e s when the muon's s p i n was p o i n t i n g d i r e c t l y a t the p o s i t r o n t e l e s c o p e and a minimum c o r r e s p o n d i n g t o t i m e s when i t was p o i n t i n g d i r e c t l y away. T h i s l e a d s t o the w i g g l e s t y p i c a l of a yuSR experiment as shown i n f i g u r e 1.2 o b t a i n e d i n pure argon i n a t r a n s v e r s e f i e l d of 70 gauss. Such a h i s t o g r a m has the form N(0,t)=No e -^V ( 1+A^(t)cos(wp t + ^ ) )+BG 1.4 where N ( ^ , t ) i s the number of c o u n t s i n a g i v e n time b i n of the h i s t o g r a m , N 0 i s a n o r m a l i z a t i o n f a c t o r , e"^'^* r e p r e s e n t s the e x p o n e n t i a l decay of the muons (where i s the muon l i f e t i m e , 2.2usec), Ayu(t) i s the time dependence of the muon asymmetry, Wy* i s the p r e c e s s i o n f r e q u e n c y (w/U=27T^u) of the JJ* which depends on the f i e l d , (j) i s the i n i t i a l phase a n g l e of the stopped muon and BG i s a time independent background term due t o a c c i d e n t a l e v e n t s . The asymmetry Ajx(t) can have a c o m p l i c a t e d time dependence and i n t r a n s v e r s e f i e l d gas phase s t u d i e s t h i s time dependence l e a d s t o a l o s s of a m p l i t u d e due t o s p i n d e p h a s i n g , which i s 10 o o o o o o o o o o o o o o o o o o o o o '—1 C D L O C \ J C D C D O O C \ J SlNflOD JO d39N(1N F i g u r e 1.2. argon i n a Time h i s t o g r a m of t r a n s v e r s e magneti muon p r e c e s s i o n i n 3 6 p s i c f i e l d of 70 gauss. 11 assumed t o be an e x p o n e n t i a l decay analogous t o r e l a x a t i o n i n NMR. I t i s u s u a l l y w r i t t e n as A ^ ( t ) = A ^ e " ^ 1.5 where X = 1 / T a a n c * Ay* i s t n e i n i t i a l a m p l i t u d e of the s i g n a l ( f i g u r e 1.3). An example of such dephasing would be muon p r e c e s s i o n i n an inhomogeneous magnetic f i e l d . The b a s i c i n f o r m a t i o n c o n t e n t i n h e r e n t i n the experiment i s shown more c l e a r l y by d e f i n i n g the yuSR s i g n a l as S(t)=Ayi.(t)cos(w Mt + $) 1.6 which has the e x p o n e n t i a l muon decay and background removed. T h i s has a form analogous t o e q u a t i o n 1.3, which i s the t h e o r e t i c a l d e s c r i p t i o n of the p o s i t r o n decay d i r e c t i o n . F i g u r e 1.3 shows the S(t) c o r r e s p o n d i n g t o f i g u r e 1.2. The s l o w l y d e c r e a s i n g asymmetry ( i . e . r e l a x a t i o n ) i s due t o f i e l d i n h o m o g e n i e t i e s . In both f i g u r e s 1.2 and 1.3 (and i n a l l subsequent f i g u r e s ) the c u r v e s a re X 2 f i t s t o the d a t a , as e x p l a i n e d i n more d e t a i l l a t e r . 12 ID o o o o o cn C \ J o ( \ J o o o o o o I I F i g u r e 1.3. Muon s i g n a l S ( t ) i n argon c o r r e s p o n d i n g t o the time h i s t o g r a m of f i g u r e 1.2. 13 1.3. Muonium And The MSR Technique As the muon t h e r m a l i z e s i n m a t t e r i t goes t h r o u g h t h r e e g e n e r a l energy regimes. The f i r s t i s a t h i g h e n e r g i e s of about 4.1 MeV down t o 30keV where the muon l o s e s energy t h r o u g h i o n i z a t i o n of the media i n the u s u a l B e t h e - B l o c h type of p r o c e s s . The second i s from about 30keV down t o the eV range (depending upon the m a t e r i a l ) where e l e c t r o n c a p t u r e and l o s s i s i m p o r t a n t . F i n a l l y i t emerges from t h i s regime e i t h e r as a muon or as t h e n u c l e u s of a muonium atom (Mu=yu*e~ i n a n a l o g y w i t h H f o r the hydrogen atom) w i t h s e v e r a l eV of energy. In the l a s t energy regime the muon (or i t s Mu atom) i s t h e r m a l i z e d by e l a s t i c ( i n the case of r a r e gas t a r g e t s ) or i n e l a s t i c c o l l i s i o n p r o c e s s e s . S i n c e the incoming muons a r e p o l a r i z e d and the e l e c t r o n s of the s t o p p i n g media a r e n o t , muonium may form i n one of two s t a t e s : " t r i p l e t " loi^fXf or the a n t i p a r a l l e l s t a t e |tf^,>. L a t e r i n the t h e s i s t h i s w i l l sometimes be l o o s e l y r e f e r r e d t o as the " s i n g l e t " s t a t e . Only the t r i p l e t s t a t e i s e x p e r i m e n t a l l y o b s e r v a b l e and i t p r e c e s s e s i n a t r a n s v e r s e magnetic f i e l d as does the bare muon e x c e p t much f a s t e r ( 103 t i m e s f a s t e r , e s s e n t i a l l y w i t h a Larmor f r e q u e n c y due t o the magnetic moment of the e l e c t r o n ) . The e x p l i c i t t i me dependence of the p o l a r i z a t i o n i n muonium i s g i v e n i n Appendix 1. For the p r e s e n t time i t i s o n l y n e c e s s a r y t o note t h a t i n a 1 4 h y p e r f i n e f r e q u e n c y of 4.463GHz and i s e x p e r i m e n t a l l y u n r e s o l v a b l e . T h i s e x p e r i m e n t a l u n o b s e r v a b i l i t y of the s i n g l e t s t a t e can be thought of c l a s s i c a l l y i n t h a t the s i n g l e t s t a t e has z e r o magnetic moment and hence cannot p r e c e s s . The t r i p l e t s t a t e p r e c e s s e s a t 1.395MHz/gauss (which i s e a s i l y o b s e r v a b l e w i t h the p r e s e n t a p p a r a t u s ) and l e a d s t o the t y p i c a l time h i s t o g r a m shown i n f i g u r e 1.4, o b t a i n e d i n 3 6 p s i argon (as i n f i g u r e 1.2) but i n a f i e l d of 8 gauss. T h i s h i s t o g r a m has the form N ( ^ , t ) = N 0 e - t / > [ l+A m Jt )cos(w^t+^J+AaCOs(w„t+fL) +BG 1.7 where t h e r e a re now two terms s i m i l a r t o thos e i n e q u a t i o n 1.4, c o r r e s p o n d i n g t o both muonium and muon p r e c e s s i o n . The n o t a b l e e x c e p t i o n i s t h a t t h e r e i s no l o n g e r any r e l a x a t i o n a s s o c i a t e d w i t h Ayu. because a t the low f i e l d s n e c e s s a r y t o observe muonium p r e c e s s i o n , Ajx appears e s s e n t i a l l y o n l y as a time dependent background. T h i s can best be i l l u s t r a t e d by d e f i n i n g the muonium s p i n r o t a t i o n (MSR) s i g n a l analogous t o equat i o n 1.6. S ( t ) = A^ ( t ) c o s ( w^ t + ^rnu)+Vcos(w/'t+(^ ) 1 .8 F i g u r e 1.5 shows S ( t ) f o r the h i s t o g r a m of f i g u r e 1.4. The muonium p r e c e s s i o n i s q u i t e pronounced but d i s t o r t e d i n t o an ar c by the background muon asymmetry which at t h i s low f i e l d 15 LO O O O O O O O LO O LO r - LO c\j 91NHQ3 JO cJ3gNi1N F i g u r e 1.4. Time h i s t o g r a m of muonium i n 3 6 p s i argon i n a t r a n s v e r s e magnetic f i e l d of 8 gauss. 16 JLdl3NNASb F i g u r e 1.5. Muonium s i g n a l S ( t ) i n 3 6 p s i argon c o r r e s p o n d i n g t o the time h i s t o g r a m of f i g u r e 1.4. 1 7 shows o n l y a f r a c t i o n of a p e r i o d . I t s h o u l d be noted t h a t f i g u r e s 1.2 and 1.4 r e p r e s e n t e x a c t l y the same t a r g e t , w i t h o n l y a change of magnetic f i e l d i n v o l v e d . S i n c e i t s mass i s o n l y 1/9 t h a t of the H atom, muonium i s c o n s i d e r e d t o be the u l t i m a t e l i g h t i s o t o p e of hydrogen. Some of the p r o p e r t i e s of Mu and H are compared i n t a b l e 1.2. In p a r t i c u l a r , note t h a t the e l e c t r o n reduced mass i n Mu and H a r e v i r t u a l l y i d e n t i c a l and hence they a r e e x p e c t e d t o have the same s i z e and i o n i z a t i o n p o t e n t i a l . In t h i s r e s p e c t i t s h o u l d be noted t h a t p o s i t r o n i u m i s e x c l u d e d as a l i g h t i s o t o p e of hydrogen because i t s Bohr r a d i u s i s much s m a l l e r and i t does not have a t r u e n u c l e u s . Moreover, i t i s i n t e r e s t i n g t o note t h a t the vacuum h y p e r f i n e s p l i t t i n g i n Mu (>X=4463MHz) can be o b t a i n e d from the v a l u e f o r H (\>0=1420MHz) s i m p l y by r a t i o i n g the magnetic moments of the muon and p r o t o n ; t h i s i s not the case f o r p o s i t r o n i u m . 1.4. H i s t o r i c a l P e r s p e c t i v e And S u b j e c t M a t t e r Of The T h e s i s One of the t o p i c s t o be d i s c u s s e d i n t h i s t h e s i s i s the amount of muonium formed i n v a r i o u s gases. T h i s i s de t e r m i n e d by d e f i n i n g f Q , the f r a c t i o n of muonium formed Muonium 18 Mass: 0.1131 mp 207.8 m t Reduced Mass: 0.9956yUp Bohr R a d i u s : 0 . 5315x10' 8cm 1.0044 ( a 0 ) H F i r s t I o n i z a t i o n P o t e n t i a l : 13.54 eV 0.9956 H(I.P.) H y p e r f i n e Frequency: 2.8044xl0 1° rad/s Mean Thermal V e l o c i t y (300K): 0.75xl0 6cm/s 2.97 v(H) Ta b l e 1.2. Some p r o p e r t i e s of the muonium and hydrogen atoms. 19 i n a p a r t i c u l a r substance and f the f r a c t i o n of the t o t a l asymmetry t h a t i s due t o d i a m a g n e t i c as f 0 = 2 A ( n u / ( 2 A n u + A / x ) and 1 .9 where the f a c t o r of two i n f 0 a c c o u n t s f o r unobserved s i n g l e t muonium ( i t i s assumed t h a t muonium forms w i t h e q u a l p r o b a b i l i t y i n both the s i n g l e t and t r i p l e t s t a t e s ) . F i g u r e 1.6 shows S ( t ) f o r the same n i t r o g e n t a r g e t a t low f i e l d (8 gauss) f o r the A h w measurement and a t h i g h f i e l d (75 gauss) f o r the Admeasurements. As noted a l r e a d y , the apparent d i s t o r t i o n i n the MSR s i g n a l i n f i g u r e 1.6 and 1.5 i s due t o slow muon p r e c e s s i o n . The i n i t i a l a m p l i t u d e s and i n f i g u r e 1.6 a r e . 1 7 and .065 r e s p e c t i v e l y and t h e r e f o r e f 0 =83% and f4.= 17%. T h i s can be compared t o a s i m i l a r experiment on argon ( f i g u r e s 1.3 and 1.5) where f 0 =74%. Thus one can see t h a t n i t r o g e n i s b e t t e r a t f o r m i n g muonium than a r g o n , an i m p o r t a n t r e s u l t f o r muonium c h e m i s t r y s t u d i e s ( G a r n e r ( 1 9 7 8 ) ) . The a b s o l u t e asymmetries c o r r e s p o n d i n g t o measured muon and muonium asymmetries i n v a r i o u s m a t e r i a l s a re of p a r t i c u l a r i n t e r e s t . To det e r m i n e t h e s e , aluminum i s chosen as an a r b i t r a r y s t a n d a r d ( s i n c e no m a t e r i a l g i v e s a h i g h e r hjx a l t h o u g h many a r e the same) f o r measuring the t o t a l asymmetry. S i n c e t h e r e i s no muonium f o r m a t i o n i n a metal (Brewer(1975) ) , the h i g h f i e l d or a m p l i t u d e i n aluminum i s taken t o e x h i b i t 100% asymmetry f o r a g i v e n e x p e r i m e n t a l NITROGEN MSR SIGNAL 36 PSI i— L U •z. >-CO cr -0.20 0.15 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 NITROGEN MUON SIGNAL 36 PSI r 0.10 h £ 0.05 1 — L U ^ 0.00 CO CE -0.05 h -0.10 0.0 0.5 1.0 1.5 2.0 TIME IN MICROSECONDS 2.5 3.0 3.5 F i g u r e 1.6. The s i g n a l s S ( t ) i n n i t r o g e n a t 3 6 p s i showing muonium p r e c e s s i o n i n a f i e l d of 8G (top) and muon p r e c e s s i o n i n a f i e l d of 75G (bo t t o m ) . 21 s e t up. T h i s s t a n d a r d i s always checked e m p i r i c a l l y s i n c e the asymmetry i s a f u n c t i o n of the beam p o l a r i z a t i o n , degrader t h i c k n e s s , c o u n t e r s i z e and c o u n t e r e f f i c i e n c y . The t o t a l asymmetry i s d e f i n e d by e q u a t i o n 1.10 i n gases and i s o f t e n not as l a r g e as i n an aluminum t a r g e t . Thus one d e f i n e s the t o t a l asymmetry and the f o r m a t i o n f r a c t i o n s as A t o r = 2 A n u + > a n d f o + f + = 1 1 - 1 0 and the a b s o l u t e asymmetry as the p e r c e n t a g e of the t o t a l asymmetry i n a gas v e r s u s the t o t a l asymmetry i n aluminum f o r a g i v e n e x p e r i m e n t a l s e t up. As noted e a r l i e r the asymmetry i s a f u n c t i o n of the e x p e r i m e n t a l c o n f i g u r a t i o n and f o r t h i s reason the d a t a from any d i f f e r e n t e x p e r i m e n t a l p e r i o d s are not e a s i l y comparable. The d a t a p r e s e n t e d i n t h i s t h e s i s have been c a r e f u l l y t a b u l a t e d t o ensure t h a t comparisons a r e made f o r gas t a r g e t s w i t h the same e x p e r i m e n t a l c o n s t r a i n t s . I t i s t h e r e f o r e o f t e n not p o s s i b l e t o d i r e c t l y compare d a t a between the p r e s e n t e d t a b l e s . F i g u r e 1.7 shows the JJ* s i g n a l i n aluminum o b t a i n e d under the same c o n d i t i o n s as i n f i g u r e 1.6. From t h i s we can d e t e r m i n e t h a t A a^ =700% i n n i t r o g e n a t 36>psi and A a^ s =92% i n argon a t 3 6 p s i . In th e s e n i t r o g e n and argon t a r g e t s , t h e n , t h e r e i s a " m i s s i n g f r a c t i o n " of p o l a r i z a t i o n . T h i s i s a g e n e r a l phenomenon i n both gases and condensed m a t t e r , the u n d e r s t a n d i n g of which i s i m p o r t a n t t o p r o v i d e the p r o p e r i n t e r p r e t a t i o n of the 22 mechanism of muonium (H atom) f o r m a t i o n . Recent c o n t r o v e r s y i n l i q u i d s f o r example, has f o c u s e d on hot atom v e r s u s spur models of Mu f o r m a t i o n (^JSR2 ( 1 980 ) ) . Another i n t e r e s t i n g phenomenon t h a t i s e a s i l y measured by the ^ JSR and MSR t e c h n i q u e s i s the r e l a x a t i o n of the asymmetries due t o i n t e r a c t i o n s of the muon s p i n w i t h i t s environment. Examples a r e g i v e n i n f i g u r e s 1.8 and 1.9. F i g u r e 1.8 shows the | i + s i g n a l i n neon s l o w l y r e l a x i n g due t o the a d d i t i o n of some xenon i m p u r i t y . The mechanism f o r t h i s muon r e l a x a t i o n p r o b a b l y i n v o l v e s the t h e r m a l f o r m a t i o n of muonium and w i l l be d i s c u s s e d l a t e r i n the t h e s i s . F i g u r e 1.9a shows the muonium s i g n a l r e l a x i n g due t o the c h e m i c a l r e a c t i o n ( p r o b a b l y Mu+HI f o r m i n g MuH) which p l a c e s the muon i n a d i a m a g n e t i c s t a t e . S i n c e the JJ* p r e c e s s e s i n the f i e l d 103 tim e s s l o w e r than Mu i t s e l f , i t i s r a p i d l y dephased c a u s i n g the Mu asymmetry t o d i s a p p e a r . . In f i g u r e 1.9b the r e l a x a t i o n i s due t o s p i n exchange w i t h the paramagnetic i m p u r i t y 0 2 , where t r i p l e t muonium i s c o n v e r t e d i n t o the u n o b s e r v a b l e s i n g l e t s t a t e . In bo t h c a s e s , r e l a x a t i o n s a r e due t o th e r m a l p r o c e s s e s s i n c e the s l o w i n g down time of the yu'/Mu i s on a ns time s c a l e whereas these r e l a x a t i o n s a r e measured on a ^jsec time s c a l e . The d i f f e r e n c e i n time z e r o a m p l i t u d e s i n f i g u r e 1 .8 s h o u l d a l s o be not e d ; the i n i t i a l a m p l i t u d e Ayu i n the Ne/Xe m i x t u r e i s 0.12 compared t o 0.18 i n pure neon. T h i s d i f f e r e n c e i s due t o e p i t h e r m a l ( e a r l y time) charge' c h a n g i n g p r o c e s s e s . With the pSR and MSR t e c h n i q u e s 23 ALUMINUM PLATE MUON HISTOGRAM 30450.0 £ 26100.0 g 21750.0 ° 17400.0 LU §E 13050.0 ZD -z. 8700.0 4350.0 0.0 0 . 5 5 0.0 0.5 1.0 1.5 2.0 2.5 ALUMINUM PLATE MUON SIGNAL T cr. i — UJ C O cr 0 .30 0 .05 -0 .20 -0 .45 0.0 0.5 1.0 1.5 2.0 TIME IN MICROSECONDS 2.5 3.0 3.0 3.5 3.5 F i g u r e 1 . 7 . Time h i s t o g r a m N ( t ) f o r p* i n aluminum i n a f i e l d of 7 5 G ( t o p ) ; the c o r r e s p o n d i n g uSR s i g n a l i s g i v e n at the bottom. 24 or: ex >-or >-CO ex 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 F i g u r e 1.8. Muon -S(t) i n pure neon (top) and neon w i t h xenon i m p u r i t y (bottom). In the t o p , the r e l a x a t i o n A=.083us- 1 w h i l e i n the bottom i t i s . 2 5 U S ' 1 . The i n i t i a l 'amplitudes a re 0.18 and 0.12, r e s p e c t i v e l y . 25 T i 1 r ti2 RT 6.9 GRU55 -0.15 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 . 3 1.14 *1016 molecules/cc NO N 2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 TIME ipS) F i g u r e 1.9. Muonium S ( t ) showing r e l a x a t i o n s due t o c h e m i c a l r e a c t i o n . The t o p f i g u r e s show r e l a x a t i o n due t o c h e m i c a l r e a c t i o n w i t h HI i n a f i e l d of 6.9G ( t a k e n from G a r n e r ( 1 9 7 9 ) ) . The bottom f i g u r e s show r e l a x a t i o n due to s p i n exchange w i t h NO i n a f i e l d of BG. In both c a s e s the moderator was pure N 4 a t 300K and l 5 p s i p r e s s u r e . 26 o n l y the f i n a l muonium and muon asymmetries can be o b s e r v e d , a f t e r the muon has stopped i n the t a r g e t . As noted p r e v i o u s l y , t h i s t h e s i s i s c o n c e r n e d w i t h the study of muonium f o r m a t i o n and r e l a x a t i o n p r o c e s s e s of both the JJ* and Mu atom due t o s p e c i f i c i n t e r a c t i o n s w i t h t h e i r e n v i r o n m e n t s . By the t e c h n i q u e s d e s c r i b e d above, the f r a c t i o n s f 0 and f v have been measured i n the r a r e gases, as w e l l as i n H^N^NH^ and C H ^ and i n a v a r i e t y of gas m i x t u r e s a t d i f f e r e n t p r e s s u r e s and i n some c a s e s d i f f e r e n t t e m p e r a t u r e s . The r e l a x a t i o n of the jp* s i g n a l i n these gases (or i t s l a c k t h e r e o f ) i s i n t e r p r e t e d i n terms of the f o r m a t i o n of | i + m o l e c u l a r i o n s . The s p i n exchange r e a c t i o n s of Mu w i t h NO and 0;^  have been s t u d i e d i n the t e m p e r a t u r e range 295 t o 478K. The e a r l i e s t s t u d i e s of t h i s n a t u r e i n gases were c a r r i e d out by Mobley et a l (Mobley(1967)) u s i n g a v e r y d i f f e r e n t l o n g i t u d i n a l f i e l d t e c h n i q u e . A l t h o u g h w e l l m o t i v a t e d , t h i s e a r l y d a t a i s c h a r a c t e r i z e d by poor s t a t i s t i c s and i n some cas e s q u e s t i o n a b l e i n t e r p r e t a t i o n ( t h i s w i l l be d i s c u s s e d i n d e t a i l i n the c h a p t e r on s p i n exchange). More r e c e n t work by Stambaugh (Stambaugh(1972)) i n v e s t i g a t e d t h e r e l a t i v e f r a c t i o n s of Mu f o r m a t i o n i n r a r e gases and gas m i x t u r e s a t m o d e r a t e l y h i g h gas p r e s s u r e s ( 6 0 0 p s i ) . T h i s d a t a , a l t h o u g h somewhat l i m i t e d i n scope p r o v i d e s an i n t e r e s t i n g b a s i s f o r comparison w i t h the p r e s e n t low p r e s s u r e d a t a . T h i s t h e s i s d e t a i l s the f i r s t measurements of Mu 27 f o r m a t i o n and r e l a x a t i o n p r o c e s s e s i n low p r e s s u r e gases as w e l l as p r o v i d i n g the f i r s t measurement of the temperature dependence of the Mu s p i n exchange ( w i t h NO and 0 - ) . 28 2. EXPERIMENTAL 2.1. Muon Beams And Beam L i n e s Muons are t r a n s p o r t e d from the b e r y l l i u m p r o d u c t i o n t a r g e t t o the e x p e r i m e n t a l a r e a by a beam l i n e which c o n s i s t s of a s e r i e s of qu a d r u p o l e and d i p o l e magnets. These q u a d r u p o l e s and d i p o l e s a c t on ch a r g e d p a r t i c l e s ( i n t h i s case muons) i n much the same way t h a t l e n s e s and p r i s m s a c t upon l i g h t . Quadrupoles f o c u s the muon beam w h i l e the d i p o l e s , or bending magnets, g i v e a spectrum of e n e r g i e s ; by c h o o s i n g the a n g l e t h a t the next q u a d r u p o l e i s a t , one can s e l e c t the momentum of the p a r t i c l e coming out of the bending magnet. In p r a c t i c e , of c o u r s e , the beam l i n e i s f i x e d and the momentum of the beam i s s e l e c t e d by v a r y i n g the s t r e n g t h of the magnetic f i e l d . The beam l i n e s coming o f f the T2 p r o d u c t i o n t a r g e t at TRIUMF are shown i n f i g u r e 2.1. In c o n v e n t i o n a l muon beams, muons a r i s e from the decay of p i o n s i n f l i g h t . However, by "imaging" the t a r g e t , one 29 can t r a n s p o r t muons from p i o n s d e c a y i n g on the s u r f a c e of the b e r y l l i u m t a r g e t . These are c a l l e d s u r f a c e muons. In c o n v e n t i o n a l muon beams a c e r t a i n amount of k i n e m a t i c d e p o l a r i z a t i o n i s i n e v i t a b l e ( W e i s s e n b e r g ( 1 9 6 7 ) ) . However, s u r f a c e muons o r i g i n a t e from a unique p i o n momentum ( z e r o ) and hence t r a v e l towards the f i r s t l e n s of the beamline w i t h a l l t h e i r s p i n s i n the same d i r e c t i o n ; thus the p o l a r i z a t i o n of a s u r f a c e muon beam i s e s s e n t i a l l y 100% ( P i f e r ( 1 9 7 6 ) ) . In t h i s t h e s i s , e x c l u s i v e use has been made of s u r f a c e muons. With t h e i r low energy (4.2MeV), they can be stopped e a s i l y i n one atmosphere p r e s s u r e of most gases. E a r l i e r muon e x p e r i m e n t s , on the o t h e r hand, d i d not have s u r f a c e muons a v a i l a b l e and hence made use of a c o n v e n t i o n a l muon beam, n e c e s s i t a t i n g the use of h i g h p r e s s u r e s t o p p i n g t a r g e t s (Stambaugh(1972), M o b l e y ( 1 9 6 7 ) ) . As i n d i c a t e d e a r l i e r , a c o n v e n t i o n a l muon beam a r i s e s from a p i o n beam t h a t i s imaged from the t a r g e t a t some i n t e r m e d i a t e f o c u s a f t e r the f i r s t b ending magnet. These p i o n s then ' decay i n the s t r a i g h t s e c t i o n of q u a d r u p o l e magnets between the two bending magnets, shown i n f i g u r e 2.1 f o r the M20 beam l i n e . The o n l y muons t h a t w i l l be r e t a i n e d i n the beam l i n e a r e those d e c a y i n g e i t h e r p a r a l l e l or a n t i - p a r a l l e l t o the p i o n momentum. S i n c e the p i o n momentum i s t y p i c a l l y 150-200 MeV/c, even the muons t h a t decay backwards i n the p i o n frame a r e s t i l l moving f o r w a r d down the beam p i p e . For example, w i t h a 170 MeV/c p i o n beam passed t h r o u g h the f i r s t bending magnet one has the p o s s i b i l i t y of f o r w a r d muons a t 181'MeV/c F i g u r e 2.1. Layout of the M 8 , M9 and M20 beam l i n e s o f f the p i o n p r o d u c t i o n t a r g e t (T2) a t TRIUMF. 31 or backward muons a t 86.7 MeV/c. In o r d e r t o choose between these beams a t t h e i r d i s t i n c t momenta, the second bending magnet can be tuned ( f i g u r e 2.1) t o d i r e c t e i t h e r the f o r w a r d or backward muons down the beam l i n e t o the e x p e r i m e n t a l t a r g e t . In p r a c t i c e , the bending magnets have a f i n i t e r e s o l u t i o n and i t i s p r e f e r a b l e t o tune f o r the backward muons s i n c e t h e i r momentum i s v e r y d i f f e r e n t from the i n i t i a l p i o n momentum and hence most of the u n d e s i r e a b l e c o n t a m i n a t i n g p i o n s and beam p o s i t r o n s w i l l not be s e l e c t e d t h r ough the second bending magnet. In a t y p i c a l e x p e r i m e n t a l c o n f i g u r a t i o n , backward muons have momenta about 80-100 MeV/c, which c o r r e s p o n d s t o a range of 7000mg/cm 2 or about 39 meters of argon a t 15psi p r e s s u r e ! C o n s e q u e n t l y , h i g h p r e s s u r e t a r g e t s (about 6 0 0 p s i ) a re r e q u i r e d i n o r d e r t o s t o p a s u f f i c i e n t number of the i n c i d e n t muons. T h i s s i t u a t i o n i s i n marked c o n t r a s t t o t h a t f o r s u r f a c e muons. A t y p i c a l range c u r v e f o r s u r f a c e muons i s shown i n f i g u r e 2.2 where the maximum i n range i s about 145 mg/cm2, w i t h a range s p r e a d of o n l y about ±15%. T h i s c o r r e s p o n d s t o a range of about 80cm i n argon gas a t I 5 p s i . In p r a c t i c e , i n c i d e n t muons f i r s t pass t h r o u g h s e v e r a l vacuum windows and a t i m i n g c o u n t e r , thus r e d u c i n g t h e i r a c t u a l range i n the gas t o about 30cm. The a v a i l a b i l i t y of such a beam g r e a t l y f a c i l i t a t e s s t u d i e s of the i n t e r a c t i o n s of muons w i t h m a t t e r near the i d e a l gas regime. T h i s t h e s i s p r e s e n t s the f i r s t study of 32 F i g u r e 2.2. S u r f a c e muon range c u r v e o b t a i n e d taken from M a r s h a l l ( 1 9 7 8 ) . i n mylar and 33 JU" charge exchange and muonium f o r m a t i o n i n low p r e s s u r e gases. A l l of the e x p e r i m e n t s d e s c r i b e d i n t h i s t h e s i s were done on the M20 beamline a t the TRIUMF c y c l o t r o n ( T r i u m f ( 1 9 8 0 ) ) shown i n f i g u r e 2.1. The d e t a i l s r e g a r d i n g t h i s beamline w i l l not be d i s c u s s e d here s i n c e they can be found i n many r e f e r e n c e s ( T r i u m f ( 1 9 8 0 ) , G a r n e r ( 1 9 7 9 ) ) . I t may be n o t e d , however, t h a t the M20 c h a n n e l t y p i c a l l y produces 100 s u r f a c e muons-s" 1-cm" 2 per microampere of 500 MeV p r o t o n c u r r e n t . 2.2. Gas T a r g e t And Magnetic F i e l d Two d i f f e r e n t gas t a r g e t s were used, one f o r the asymmetry measurements w i t h a 25cm i n s i d e d i ameter ( t o m i n i m i z e the number of muons t h a t r e a c h the w a l l s ) and one w i t h a 17.5cm di a m e t e r which was w e l l i n s u l a t e d f o r the h i g h t e m p e r a t u r e s p i n exchange measurements. A schematic diagram of t h e i r c o n s t r u c t i o n and a s s o c i a t e d gas h a n d l i n g system i s found i n f i g u r e 2.3. Kapton (Kapton(1980)) windows were used (,012cm t h i c k n e s s ) i n o r d e r t o w i t h s t a n d the p r e s s u r e •and temperature changes i n v o l v e d i n c h a n g i n g t a r g e t s and s t i l l a l l o w the low energy muons (range about 145mg/cm2) t o 34 0- SeoAs, h\ pipe- (*v\o-cl\iAecJL ewdsj Sto-x*\e.<i=> stetl yt& reamed <\««> supf.\ to cans and gas h a n d l i n g system. 35 p e n e t r a t e the t a r g e t . I t was found t o be s u p e r i o r t o the f i r s t g e n e r a t i o n mylar windows e x c e p t as r e g a r d s a t t a c k by c e r t a i n r e a c t i v e gases, n o t a b l y ammonia. The h i g h temperature gas can has s t a i n l e s s s t e e l ends which a r e s e p a r a b l e from the aluminum p i p e t h a t makes up the body. T h i s a l l o w s one t o e a s i l y v a r y the l e n g t h of the can merely by i n s e r t i n g a s h o r t e r aluminum p i p e w i t h machined ends. The temperature of the gas can was m o n i t o r e d w i t h a c o p p e r - c o n s t a n t a n thermocouple mounted i n s i d e the can and o u t p u t t e d t o a c h a r t r e c o r d e r and d i g i t a l v o l t meter. The t e m p e r a t u r e g r a d i e n t a l o n g the l e n g t h of the can o b s e r v a b l e by the c o u n t e r s was o n l y ±2K i n s p i t e of the water c o o l i n g of t h e end window. H e a t i n g of t h e t a r g e t was a c c o m p l i s h e d w i t h f o u r s e c t i o n s of 750K h e a t i n g t a p e . Roughly one hour i s needed t o e q u i l i b r a t e the can a t any t e m p e r a t u r e a f t e r which i t remains r e l a t i v e l y c o n s t a n t (±2K). As w i l l be seen l a t e r , even s m a l l i m p u r i t i e s can d r a s t i c a l l y a f f e c t the observed muonium f o r m a t i o n . For t h i s r e a s o n , t h e gas can was c o n d i t i o n e d f o r each run by h e a t i n g t o about 400K under vacuum. The base p r e s s u r e of the system was t y p i c a l l y 1(3~ 7psi a f t e r bake out a t 400K f o r 5-10 h o u r s . A l l of the r a r e gases used were p u r i f i e d by p a s s i n g them over hot (1000-1200K) T i sponge t o e l i m i n a t e N x and O x i m p u r i t i e s . A c t i v a t e d c h a r c o a l a t l i q u i d n i t r o g e n t e m p e r a t u r e was a l s o used and -found t o be s a t i s f a c t o r y f o r He and Ne but the hot t i t a n i u m was the e a s i e s t and most 36 e f f i c i e n t p u r i f i e r t o use. The p o l y a t o m i c gases were not p u r i f i e d but i n a l l c a s e s they were " u l t r a h i g h p u r i t y " grade w i t h l e s s than 1Oppm O a i m p u r i t y . P r e s s u r e s were measured w i t h H e l i c o i d gauges a c c u r a t e t o about ±.04psi. The reagent gases were i n t r o d u c e d by measuring t h e i r p r e s s u r e s i n a c a l i b r a t e d volume of about 30cm 3 and then r e l e a s i n g them i n t o the gas can. The volumes of the two gas t a r g e t cans used were 36.65 i . 3 4 X and 27.96 ± . 2 8 ^ f o r the 25.0cm and 17.5cm di a m e t e r cans, r e s p e c t i v e l y . The gas h a n d l i n g system was s t a i n l e s s s t e e l t u b i n g w i t h b r a s s b e l l o w s type v a l v e s . I t was found t h a t copper t u b i n g , a l t h o u g h e a s i e r t o work w i t h , tended t o be ' d i r t i e r ' and q u i t e troublesome u n l e s s p r e - t r e a t e d by h e a t i n g t o r e l a t i v e l y h i g h t e m p e r a t u r e s under vacuum. The gas t a r g e t assembly i s p o s i t i o n e d i n the c e n t e r of a d o u b l e h e l m h o l t z c o i l arrangement which produced a magnetic f i e l d v a r i a b l e i n the range from about 1 t o 75 gauss. The f i e l d homogeniety i s about .1% over a 1000cm 3 volume i n the c e n t r e of -the c o i l s but drops o f f r a p i d l y a f t e r t h a t and i s i l l u s t r a t e d i n the f i e l d map of f i g u r e 2.4. F i e l d i n h o m o g e n i e t i e s cause a r e l a x a t i o n i n the uSR or MSR s i g n a l . As can be seen i n f i g u r e s 1.3 and 1.5, the asymmetry i s s l o w l y d e c r e a s i n g . In pure gases t h i s r e l a x a t i o n ( A 0) i s always p r e s e n t t o some s m a l l e x t e n t , and i s thought t o be p r i m a r i l y due t o f i e l d i n h o m o g e n i e t i e s . A t y p i c a l \ t f o r Mu i s about .45 ^ J S " 1 which c o u l d be caused by a f i e l d v a r i a t i o n 37 6 GAUSS FIELD MRP OF HELMHOLTZ COILS DISPLACEMENT FROM CENTER (INCHES) F i g u r e 2.4. F i e l d map of h e l m h o l t z c o i l s a l o n g beam d i r e c t i o n . The l i n e i s meant t o guide the eye o n l y . 38 of about 0.6 gauss. T h i s i s det e r m i n e d by the use of e q u a t i o n 2.1 which can be found i n any b a s i c NMR t e x t ( P o o l e ( 1 9 7 1 ) ) and where AB i s the FWHM of the magnetic f i e l d . l/\=T a=2 / 0 U B ) 2.1 As can be seen i n f i g u r e 2.4, t h e f i e l d i n h o m o g e n i e t i e s a r e q u i t e l a r g e over the o b s e r v a t i o n r e g i o n of the p o s i t r o n t e l e s c o p e s . T h i s can e a s i l y a ccount f o r the l a r g e r e l a x a t i o n s observed at low p r e s s u r e s where the muons have a much l a r g e r s t o p p i n g r e g i o n . The f i e l d homogeniety i n the d i r e c t i o n p e r p e n d i c u l a r t o the beam d i r e c t i o n i s s i m i l a r t o t h a t i n f i g u r e 2.4, whereas the homogeniety p e r p e n d i c u l a r t o the p l a n e of the c o i l s i s somewhat b e t t e r . 2.3. Muon S t o p p i n g D i s t r i b u t i o n And W a l l E f f e c t s I f any muons are i n i t i a l l y s c a t t e r e d i n t o the w a l l s of the gas t a r g e t , they can a f f e c t the c a l c u l a t i o n of the f o r m a t i o n f r a c t i o n of muonium (such muons p r e c e s s w i t h 100% of t h e i r i n i t i a l p o l a r i z a t i o n ) . I t i s i m p o r t a n t t h a t these e f f e c t s a re known and c o r r e c t e d f o r . In t h i s t h e s i s the 39 w a l l e f f e c t s were e s t i m a t e d f o r ev e r y run by f i r s t d o i n g a pure n i t r o g e n r u n. The asymmetries thus o b t a i n e d can then be compared t o runs where the number of w a l l s t o p s were known. T h i s was a c c o m p l i s h e d by r u n n i n g an e q u a l d e n s i t y of a i r ( t o n i t r o g e n ) i n the t a r g e t , s i n c e a i r has no muon or muonium s i g n a l . One can g e n e r a l l y o n l y e x t r a p o l a t e t h e s e r e s u l t s i n o t h e r gases because of t h e i r d i f f e r e n t d e n s i t i e s and number of e l e c t r o n s . The A^i found w i t h a i r i n the t a r g e t can then be s u b t r a c t e d from the obse r v e d hjx t o g i v e the c o r r e c t muon and muonium f r a c t i o n s i n a g i v e n gas t a r g e t . As f a r as p o s s i b l e , the need f o r such c o r r e c t i o n s was a v o i d e d i n t h i s t h e s i s by o n l y making use of d a t a where the w a l l e f f e c t was z e r o . In those cases where the o n l y d a t a a v a i l a b l e had t o be c o r r e c t e d f o r w a l l s i g n a l s , i t i s c l e a r l y l a b e l l e d . The d a t a where w a l l s i g n a l s o ccur i s s t i l l v a l i d but u s u a l l y i n v o l v e s a g r e a t e r u n c e r t a i n t y because of the c o r r e c t i o n s t h a t must be made. I t was found i n t h i s work a t TRIUMF and by Stambaugh a t LAMPF (StambaugM1972)) t h a t almost a l l of the s c a t t e r i n g i s due t o the f r o n t d e f i n i n g c o u n t e r and window, w i t h m u l t i p l e s c a t t e r i n g from the gas b e i n g n e g l i g i b l e . W i t h no gas i n the t a r g e t , a l l the muons s c a t t e r e d t h r o u g h l a r g e a n g l e s a r e f r e e t o t r a v e l t o the w a l l s and g i v e a w a l l s i g n a l . At low muon e n e r g i e s , as i n the p r e s e n t e x p e r i m e n t , the a d d i t i o n of the t a r g e t gas i s enough to s t o p t h e s e muons from r e a c h i n g the w a l l s , s i n c e they would have t o have been s c a t t e r e d t h r o u g h l a r g e a n g l e s and a l r e a d y have l o s t a s i g n i f i c a n t Target Gas Press u r e ( p s i ) Reference He 735 99*5 115 1 Ne 382 10012 0*2 1 Ar ' 441 35*5 65i5 1 Xe 64.7 1015 100 . 1 He 18 100±1 OH 2 Ne 18 96±5 415 2 Ar 18 26*4 7414 2 Xe 10 013 100*3 2 Reference 1 i s Stambaugh(1967) and reference 2 i s t h i s t h e s i s . Note that no e r r o r estimate was given for the xenon of reference 1. T a b l e 2 . 1 . Comparison of p r e s e n t r e s u l t s w i t h those of Stambaugh f o r muonium and muon f o r m a t i o n f r a c t i o n s i n v a r i o u s gases. 41 f r a c t i o n of t h e i r energy. At the h i g h e r p r e s s u r e s of Stambaugh, n e c e s s i t a t e d by t h e i r use of c o n v e n t i o n a l muon beams, much t h i c k e r windows (.6cm A l ) were used than i n the p r e s e n t experiment (.012cm mylar or k a p t o n ) . T h i s causes severe s c a t t e r i n g problems, which b e s i d e s n e c e s s i t a t i n g c o r r e c t i o n s t o t h e d a t a , reduces the u s e f u l s i g n a l , t h u s l e a d i n g t o f u r t h e r i n a c c u r a c i e s because of backgrounds and poor s t a t i s t i c s . A l t h o u g h c o r r e c t i o n s were attem p t e d i n h i s d a t a , a JJ* s i g n a l due t o w a l l s t o p s c o u l d e x p l a i n the d i s c r e p a n c i e s between the p r e s e n t r e s u l t s and tho s e of Stambaugh(1972). R e p r e s e n t a t i v e d a t a i s g i v e n i n t a b l e 2.1. Because of the momentum r e s o l u t i o n of the beam l i n e and the d e g r a d i n g of the muon beam t h r o u g h v a r i o u s c o u n t e r s and windows, the f i n a l range of the beam has q u i t e a v a r i a t i o n . One can r e a s o n a b l y expect the stopped muon t o be anywhere from the f r o n t t o the r e a r of the gas can. An extended s t o p p i n g d i s t r i b u t i o n w i l l m a n i f e s t i t s e l f i n an i n c r e a s e d r e l a x a t i o n due to f i e l d i n h o m o g e n i e t i e s . T h i s d i s t r i b u t i o n i s peaked a t some energy near 4.1 MeV and the gas p r e s s u r e s were a d j u s t e d t o b r i n g t h i s peak i n the stopped muon d i s t r i b u t i o n between the p o s i t r o n t e l e s c o p e s . T h i s was a c c o m p l i s h e d by v a r y i n g the p r e s s u r e t o maximize t h e decay p o s i t r o n r a t e i n the t e l e s c o p e s . These p r e s s u r e s were then used f o r the r a t e e x p e r i m e n t s o b s e r v i n g the muon or muonium r e l a x a t i o n where t h e a d d i t i o n of a s m a l l i m p u r i t y does not change the s t o p p i n g d i s t r i b u t i o n . In some c a s e s , when p r e s s u r e e f f e c t s were b e i n g s t u d i e d , a lower r a t e had t o be 42 a c c e p t e d when the s t o p p i n g d i s t r i b u t i o n moved from i t s optimum p o s i t i o n . 2.4. The Counter System, Data A c q u i s i t i o n And A n a l y s i s The c o u n t e r s c o n s i s t e d of a t h i n (.035cm) muon d e f i n i n g c o u n t e r and s i x (.6cm) decay p o s i t r o n c o u n t e r s (used t o form two p o s i t r o n t e l e s c o p e s ) . A t h i n muon d e f i n i n g c o u n t e r was n e c e s s a r y s i n c e low energy s u r f a c e muons have a ve r y s h o r t range (-^l 45mg/cm2 from f i g u r e 2.2). A muon s t o p i s d e f i n e d by t h i s c o u n t e r a l o n e s i n c e the range i n the t a r g e t gas i t s e l f i s o n l y ~60mg/cm 2 and a f t e r h a v i n g p a s s e d t h r o u g h the beam p i p e window (.005cm m y l a r ) , 8cm of a i r , the t h i n c o u n t e r and f i n a l l y the gas can window, i t w i l l s u r e l y s t o p i n t he t a r g e t . The muon s t o p p r o v i d e s the s t a r t s i g n a l t o a h i g h f r e q u e n c y time t o d i g i t a l c o n v e r t e r or " c l o c k " . The p o s i t r o n t e l e s c o p e s a re then s e t up such t h a t decay p o s i t r o n s from the muons s t o p p i n g i n the ends of the can are u n d e t e c t e d . Each c o u n t e r of the p o s i t r o n t e l e s c o p e i s 20x20x.6cm and i s 99% e f f i c i e n t f o r p o s i t r o n d e t e c t i o n . T h e i r c o n f i g u r a t i o n as shown i n f i g u r e 1 .1 g i v e s about 1-2% s o l i d a n g l e . S i g n a l s from t h e s e decay p o s i t r o n s p r o v i d e the c l o c k s t o p s i g n a l . The two i n c h e s of carbon s h i e l d i n g the 43 l a s t two c o u n t e r s of each t e l e s c o p e s e r v e s t o e l i m i n a t e the c o n t a m i n a t i n g beam p o s i t r o n s (P=30MeV/c) from t h e c l o c k s t o p s i g n a l . They are e l i m i n a t e d from the c l o c k s t a r t s i g n a l by p u l s e h e i g h t d i s c r i m i n a t i o n a t the t h i n c o u n t e r . A slower moving, h e a v i e r muon d e p o s i t s more energy than an e l e c t r o n i n the c o u n t e r and hence g i v e s a b i g g e r p u l s e . By i g n o r i n g a l l of the p u l s e s below a c e r t a i n l e v e l , one can e f f e c t i v e l y remove i n t e r f e r e n c e from the beam p o s i t r o n s . The b a s i s of the experiment i s the m o n i t o r i n g of the decay of the muon as i t p r e c e s s e s i n a t r a n s v e r s e magnetic f i e l d . To do t h i s one must f i r s t d e c i d e when a muon i s i n the t a r g e t and c o n s e q u e n t l y s t a r t the c l o c k . As mentioned e a r l i e r , t h i s i s done when t h e r e i s a p u l s e of s u f f i c i e n t v o l t a g e from the t h i n c o u n t e r . The c l o c k i s sto p p e d when a p u l s e i s r e c e i v e d i n a l l t h r e e of the c o u n t e r s i n a p o s i t r o n t e l e s c o p e i n d i c a t i n g the decay of the muon i n the t a r g e t . S i n c e the t e l e s c o p e s o n l y "see" about 1-2% of the decay e v e n t s , one must s t o p w a i t i n g and s t a r t over a f t e r some f i n i t e t i m e . I t i s o b v i o u s t h a t i f a second muon a r r i v e s b e f o r e the f i r s t has decayed, then v a r i o u s d i s t o r t i o n s w i l l o c c u r ( G a r n e r ( 1 9 7 9 ) ) . The e l e c t r o n "good e v e n t " l o g i c i s then d e s i g n e d t o r e j e c t such bad e v e n t s , a l l o w i n g the a c c u m u l a t i o n of a time h i s t o g r a m of the muons' p r e c e s s i o n c o r r e s p o n d i n g t o i n t e r f e r e n c e f r e e c l o c k s t a r t s and s t o p s . A good event i s d e f i n e d as one i n which t h e r e i s a muon t h a t e n t e r s the t a r g e t and decays d e t e c t a b l y w i t h i n time t ( c o r r e s p o n d i n g i n t h i s case t o about two muon l i f e t i m e s ) 44 w i t h no i n t e r f e r i n g muon s t o p s i n between. The e l e c t r o n i c s a r e then w i r e d such t h a t o n l y t h e s e e v e n t s a r e c o u n t e d . An e x c e l l e n t d i s c u s s i o n of the d i s t o r t i o n s t h a t can oc c u r i s found i n D.M. Garner' s Ph.D. T h e s i s ( G a r n e r ( 1 9 7 9 ) ) . A d e t a i l e d diagram of the e l e c t r o n i c s used i s g i v e n i n f i g u r e 2.5. I t has been found t h a t a p p r o x i m a t e l y one m i l l i o n e v e n t s i n a h i s t o g r a m c o n s t i t u t e a r e l i a b l e s e t of d a t a t o a n a l y z e . Sometimes, however, as i n the case of a r a p i d l y r e l a x i n g s i g n a l , more events a re accumulated t o d e c r e a s e the s t a t i s t i c a l e r r o r i n the a n a l y s i s . T y p i c a l l y i t t a k e s two to t h r e e hours f o r each e x p e r i m e n t . The d a t a i s f i t t o e q u a t i o n 1.4 or 1.7, u s i n g the c h i - s q u a r e d m i n i m i z a t i o n r o u t i n e MINUIT ( C e r n ( 1 9 7 8 ) ) . Most of the d a t a was f i t on the U n i v e r s i t y of B r i t i s h Columbia computer system but w i t h the l a t e r i m p l e m e n t a t i o n of MINUIT on our PDP 11/40, the more r e c e n t runs were f i t a t TRIUMF i m m e d i a t e l y a f t e r the da t a was t a k e n . S e v e r a l examples of fX2 f i t s t o the d a t a have a l r e a d y been g i v e n i n the f i g u r e s showing argon and n i t r o g e n h i s t o g r a m s and S ( t ) ' s . As a check a g a i n s t time dependent c o n t a m i n a t i o n of the gas t a r g e t s e v e r a l s e n s i t i v e runs were stopped h a l f way th r o u g h and then r e s t a r t e d w i t h o u t changing a n y t h i n g . These two runs a r e then a n a l y z e d s e p a r a t e l y t o g i v e an i n d i c a t i o n of any changes (e.g. an i n c r e a s e of muonium f o r m a t i o n or r e l a x a t i o n due t o o u t g a s s i n g or magnetic f i e l d d r i f t s ) . I n v a r i a b l y , the two runs gave i d e n t i c a l r e s u l t s , a l l o w i n g F i g u r e 2.5. E l e c t r o n i c s conf i g u r a t i o n . 46 one t o have c o n f i d e n c e i n the accumulated d a t a . The major problem i n f a c t was i n i n i t i a l l y i n t r o d u c i n g pure gases i n t o the t a r g e t and o u t g a s s i n g from the can was g e n e r a l l y not s i g n i f i c a n t . 47 3 . MUONIUM FORMATION IN THE GAS PHASE 3 . 1 . I n t r o d u c t i o n Charge exchange i s an i m p o r t a n t atomic c o l l i s i o n p r o c e s s w i t h a p p l i c a t i o n s t o u n d e r s t a n d i n g the b e h a v i o r of plasmas, the d e s i g n of r a d i a t i o n d e t e c t o r s , and s t u d i e s of r a d i a t i o n damage. A l t h o u g h the f o c u s i n r e c e n t y e a r s has s h i f t e d t o the study of m u l t i p l y c h a r g e d i o n s ( I C P E A C ( 1 9 7 9 ) ) i t i s s t i l l i m p o r t a n t t o study the s i m p l e r p r o c e s s e s . With the p r e s e n t s t a t e of the t h e o r y i t i s thought t h a t the charge exchange p r o c e s s i s s i m p l y v e l o c i t y dependent and t h e r e f o r e muon, p r o t o n , d e u t e r o n and t r i t o n d a t a a r e e a s i l y comparable. The e l e c t r o n c a p t u r e and l o s s d a t a f o r the p r o t o n g e n e r a l l y does not e x t e n d t o t h e r m a l e n e r g i e s ( a l t h o u g h merged beam t e c h n i q u e s a r e a v a i l a b l e which go t o even lower r e l a t i v e v e l o c i t y ( G e n t r y ( 1 9 7 5 ) ) because the n a t u r e of the u s u a l t r a n s m i s s i o n type experiment demands an e n e r g e t i c p r o t o n (or H atom) l e a v i n g the i n t e r a c t i o n r e g i o n 48 t o be a n a l y z e d . The p r o t o n (or H atom) i s passed through a d e n s i t y of gas s u f f i c i e n t t o i n s u r e charge e q u i l i b r a t i o n ( ~ l 0 " 5 p s i ) but not so dense t h a t the p a r t i c l e l o s e s a s i g n i f i c a n t amount of energy. C o n v e r s e l y , the muon and muonium f r a c t i o n s can o n l y be measured a f t e r t h e r m a l i z a t i o n where the i n i t i a l jx* beam of about 2MeV i s stopped i n the moderator gas. Thus the muon and p r o t o n d a t a , a l t h o u g h not d i r e c t l y comparable, s h o u l d be complementary. As a muon slows down i n a gas i t goes t h r o u g h t h r e e g e n e r a l regimes of energy l o s s . The f i r s t i s a t h i g h e n e r g i e s where the muon l o s e s most of i t s energy t h r o u g h B e t h e - B l o c h type i o n i z a t i o n of the m a t e r i a l i t i s s l o w i n g down i n . D u r i n g t h i s p r o c e s s no a p p r e c i a b l e amount of muonium forms. I t i s t h e dominant p r o c e s s u n t i l JJ" e n e r g i e s of about 30keV are reached. At t h i s p o i n t the second regime b e g i n s d u r i n g which e l e c t r o n c a p t u r e and l o s s c y c l e s o c c u r w i t h the moderator gas. I t i s the s e charge c h a n g i n g c y c l e s t h a t d e t e r m i n e the f i n a l s t a t e of the muon ( i . e . whether i t t h e r m a l i z e s as muonium or as a d i a m a g n e t i c muon). In t h i s regime from about 30keV t o 50eV the muon undergoes many e l e c t r o n c a p t u r e and l o s s c y c l e s and spends an a p p r e c i a b l e amount of i t s time as muonium. F i n a l l y the muon i s at a low enough energy ( £50eV) t h a t charge exchange i s no l o n g e r o c c u r i n g and the muon or muonium e n t e r s the t h i r d regime where t h e r m a l i z a t i o n o c c u r s v i a e l a s t i c and i n e l a s t i c c o l l i s i o n s . To b e t t e r u n d e r s t a n d t h e s e p r o c e s s e s i t i s u s e f u l t o 49 c o n s i d e r them as f o l l o w s . One can assume t h a t the f o r m a t i o n of Mu" i s n e g l i g i b l e ( A l l i s o n ( 1 9 5 4 ) and w r i t e the e q u a t i o n s f o r t h i s two component system ( i . e . a n ^ Mu). F o l l o w i n g A l l i s o n one has d f 0 / d n = - f o e o i + f + s - , 0 ; at+/aTT=-t+6,0 + f 0 ^ o > 3.1 where f 0 and f + a r e the n e u t r a l and charge d f r a c t i o n s , r e s p e c t i v e l y , and S*ot i s the c r o s s s e c t i o n f o r e l e c t r o n l o s s and 6",0 i s the c r o s s s e c t i o n f o r e l e c t r o n c a p t u r e . The symbol TT r e p r e s e n t s the number of atoms of t a r g e t gas per cm 3 which t h e beam has t r a v e r s e d . The s o l u t i o n s t o these e q u a t i o n s f o r an i n i t i a l beam of JJ* a r e ; f + = 60,/(So, + + +G,0)e^[6^Go^ f 0 = + 6,e)- + 6lo)e-*ie,'*€^ 3 .2 In a t y p i c a l p r o t o n t r a n s m i s s i o n e x p e r i m e n t , 7T i s i n c r e a s e d u n t i l df/dTT becomes z e r o . I n t h i s so c a l l e d e q u i l i b r i u m s i t u a t i o n one has f + = 601/(<S"o«+ 6 i» ) and f Q = &el + 6" l o) 3 . 3 which f o l l o w s i m m e d i a t e l y from e q u a t i o n 3 . 1 . I t s h o u l d be emphasized t h a t the f r a c t i o n s f 0 and f + are i n h e r e n t l y f u n c t i o n s of energy. Measured p r o t o n c r o s s s e c t i o n d a t a i n 50 argon as a f u n c t i o n of energy i s shown i n f i g u r e 3.1 w i t h c o r r e s p o n d i n g n e u t r a l f r a c t i o n s f 0 p l o t t e d i n f i g u r e 3.2. The shapes of t h e s e c u r v e s a r e q u a l i t a t i v e l y s i m i l a r i n a l l gases as w i l l be d i s c u s s e d l a t e r . The p r o t o n energy s c a l e i n f i g u r e 3.1 extends t o lOOOkeV, but w i t h an ever d i m i n i s h i n g c r o s s s e c t i o n f o r H atom f o r m a t i o n . The c r o s s s e c t i o n s drop o f f r a p i d l y a t low e n e r g i e s as w e l l . The g e n e r a l f e a t u r e s of f i g u r e 3.1 a r e d u p l i c a t e d i n a l l of the gase s , w i t h some s h i f t s t o h i g h e r or lower e n e r g i e s depending upon the i o n i z a t i o n p o t e n t i a l of t h e gas i n v o l v e d . One would q u a l i t a t i v e l y expect Mu(H) atom f o r m a t i o n t o b e g i n t o be i m p o r t a n t when the i n c i d e n t v e l o c i t y v p i s comparable t o t h a t of the o r b i t a l e l e c t r o n . In a s i m p l e Bohr atom p i c t u r e : Vp =ve =occZe« /n 3.4 where od= 1/137 i s the f i n e s t r u c t u r e c o n s t a n t and Z C f f i s the s c r e e n e d n u c l e a r c h a r g e . For example, f o r the o u t e r e l e c t r o n s i n Ar (n=3), one c o u l d expect t h a t Mu f o r m a t i o n b e g i n s t o become i m p o r t a n t a t -300 keV p r o t o n energy and c o r r e s p o n d i n g l y a t ~-30keV muon energy. T h i s s i m p l e s c a l i n g of muon and p r o t o n e n e r g i e s by t h e i r r e s p e c t i v e masses can be j u s t i f i e d t h e o r e t i c a l l y , as d i s c u s s e d l a t e r . For i n n e r s h e l l charge exchange, the e n e r g i e s w i l l be c o r r e s p o n d i n g l y h i g h e r . I t s h o u l d be noted t h a t the p r o t o n d a t a i n f i g u r e s 3.1 and 3.2 (and f o l l o w i n g ) do not d i s t i n g u i s h d i f f e r e n t 51 O LD CE mini i i |iiiiu i j£ pin111 i—[IIIIII i i—pin111 i ^ffin i O O O + + + + + + + x + X •tx >•-x+ x + X + X + X + X + X + + + -+ 0 X X + + o o CO t— _J O > >-LU O I— o """I I I limn i i limit i i L u n , |llim • • Imn., O O O — i — . ^ O O — i . o o o o 10 F i g u r e 3 .1 . The charge exchange c r o s s s e c t i o n s <5?0 and fo r p ro tons in argon from A l l i son ( 1 958 ) and Tawara (1 973 ) F i g u r e 3.2. The n e u t r a l f r a c t i o n f o r p r o t o n s i n argon c a l c u l a t e d from the d a t a of f i g u r e 3.1. 53 s h e l l s (nor does the p r e s e n t muon d a t a ) but t h a t o u t e r s h e l l charge exchange i s e x p e c t e d t o be the dominant p r o c e s s a t the e n e r g i e s of i n t e r e s t . I t s h o u l d a l s o be noted t h a t p o s s i b l e c a p t u r e i n t o e x c i t e d e l e c t r o n i c s t a t e s of muonium cannot be d i s t i n g u i s h e d from ground s t a t e c a p t u r e but i n g e n e r a l t h i s i s e x p e c t e d t o be a s m a l l e f f e c t s c a l i n g by about 1/n 3 (Doughty(1978), S h a h ( l 9 8 0 ) ) . The q u e s t i o n of at what energy the c r o s s s e c t i o n f o r charge exchange w i l l peak can most e a s i l y be answered i n terms of the a d i a b a t i c c r i t e r i o n f i r s t i n t r o d u c e d by Massey ( M a s s e y ( 1 9 5 4 ) ) , f o r the charge exchange p r o c e s s jj*(p)+X >Mu(H)+X + 3.5 which has s i n c e found wide a p p l i c a b i l i t y ( H a s t e d ( 1 9 6 4 ) ) . The charge c a p t u r e c r o s s s e c t i o n 6)a i s e x p e c t e d t o peak when aAE/fiv=1 (a r e s u l t of the u n c e r t a i n t y p r i n c i p l e 4EAt=fi; At i s s i m p l y the v e l o c i t y of the incoming p a r t i c l e d i v i d e d i n t o the d i s t a n c e of the i n t e r a c t i o n ) where a i s an i n t e r a c t i o n d i s t a n c e c h a r a c t e r i s i n g the c o l l i s i o n , AE i s the t h r e s h o l d energy ( i o n i z a t i o n p o t e n t i a l of the gas minus the i o n i z a t i o n p o t e n t i a l of muonium) and v i s the muon v e l o c i t y . T h i s s i m p l e but u s e f u l concept has the p h y s i c a l i n t e r p r e t a t i o n t h a t i f the i n t e r a c t i o n time i s l o n g enough then t h e r e i s a h i g h p r o b a b i l i t y of re s o n a n t e l e c t r o n t r a n s f e r . The p r e d i c t e d peak e n e r g i e s f o r o u t e r s h e l l e l e c t r o n c a p t u r e f o r the gases s t u d i e d i n t h i s t h e s i s a re 54 g i v e n i n t a b l e 3.1. Another parameter of i n t e r e s t i n the case of muonium i s the number of charge c h a n g i n g c y c l e s . F o l l o w i n g A l l i s o n ( 1 9 5 4 ) t h i s i s d e f i n e d as c N C=L €£(E)dE/( dE/dx) 3.6 where £ T C i s the c r o s s s e c t i o n f o r a charge c h a n g i n g c y c l e 6^= 6, D 6' 0,/(<s, 0+s 6 l) 3.7 and dE/dx i s the s t o p p i n g power of the gas, L i s the number of atoms of gas per cm 3 and E;_ i s the i n i t i a l energy of the p a r t i c l e . S i n c e <£]„ and <s~ol have been measured f o r p r o t o n s (Tawara(1973)) over a range of e n e r g i e s and i n d i f f e r e n t g a s e s , <S~C(E) can r e a d i l y be e v a l u a t e d and hence one can c a l c u l a t e N c from the i n t e g r a l i n e q u a t i o n 3.6. Above some energy ( E ^ ^ 3 0 k e V f o r the muon) the €T / 0 and c r o s s s e c t i o n s a r e too s m a l l t o l e a d t o any a p p r e c i a b l e number of charge c h a n g i n g c y c l e s . Below a c e r t a i n energy E^ ( t e n s of eV) t h e same t h i n g i s a g a i n t r u e , t o g i v e almost z e r o c o n t r i b u t i o n t o the i n t e g r a l . Thus one has the number of charge changing c y c l e s r i s i n g r a p i d l y as the p r o t o n (muon) slows from h i g h e n e r g i e s and then a s y m t o t i c a l l y l e v e l l i n g o f f a t lower e n e r g i e s . The N c can be e v a l u a t e d n u m e r i c a l l y u s i n g dE/dx data f o r p r o t o n s (Whaling(1958)) and the r e s u l t s a r e shown f o r p r o t o n s i n h e l i u m i n f i g u r e 3.3. The c r o s s AE (ev) E p E^ the energy where f e peaks (KeV) (KeV) H e l i u m 10.94 720 80 Neon 8.02 390 43 Argon 2.22 30 3.3 K r y p t o n ~.H 5 4 ~.S" Xenon -N i t r o g e n 2.06 25 2.8 Hydrogen 1.86 21 2.3 Methane — Ammonia — Following Hasted(l980) a. has been taken to be 7x10"*cm* for a l l the gases for comparative purposes. T h i s i s probably too large i n the case of helium and neon where i t should perhaps be a f a c t o r of two or three lower. The energy peaks s c a l e simply as the a. f a c t o r (aAE/vp afi) and i t i s l e f t open whether or not these c o r r e c t i o n s should be a p p l i e d . Tab le 3 . 1 . Massey c r i t e r i a p r e d i c t i o n s of Mu fo rmat ion peaks . 56 o o LO OsJ C\J o o o in o o o o o o o o o o o LO o LO o LO r- o C\J LO CO r- LO CO « — 1 o CD O CO I— _ l o > >-or UJ o I— o cr Q _ S 3 1 G A 3 9 N I 9 N U H 3 3 9 d b H 3 JO d39NnN F i g u r e 3.3. The number of charge c h a n g i n g c y c l e s N c f o r h e l i u m e v a l u a t e d from e q u a t i o n 3.6. 57 s e c t i o n d a t a i s taken from s e v e r a l s o u r c e s but m a i n l y from r e v i e w s by T a w a r a d 9 7 3 ) and A l l i s o n ( 19 5 8 ). Note t h a t i n f i g u r e 3.3 t h e dE/dx d a t a has been e x t r a p o l a t e d t o the lower e n e r g i e s where c r o s s s e c t i o n d a t a i s s t i l l a v a i l a b l e t o i l l u s t r a t e t h a t the number of charge c h a n g i n g c y c l e s e v e n t u a l l y reaches a maximum. T h i s i s j u s t a n o t h e r way of s a y i n g t h a t e v e n t u a l l y the p r o t o n (muon) i s a t such a low energy t h a t charge exchange i s no l o n g e r e n e r g e t i c a l l y p o s s i b l e . A g a i n t h i s i s a f u n c t i o n of the energy d i f f e r e n c e between the i o n i z a t i o n p o t e n t i a l of the t a r g e t medium and of muonium. F i g u r e 3.4 shows the i n t e g r a l N c u s i n g the e x i s t i n g dE/dx p r o t o n d a t a w i t h o u t e x t r a p o l a t i o n (except f o r helium) and i t c l e a r l y shows the d i f f e r e n c e s i n v a r i o u s gases. As p r e v i o u s l y n o t e d , i t i s g e n e r a l l y assumed t h a t the charge c a p t u r e and l o s s p r o c e s s e s are s i m p l y v e l o c i t y dependent ( A l l i s o n ( 1 9 5 8 ) , Tawara(1973), G r y s i n s k i ( 1 9 6 5 ) ) and i t i s t h e r e f o r e p o s s i b l e t o s i m p l y s c a l e the p r o t o n r e s u l t s t o the case of the muon. Because of t h i s s i m p l e v e l o c i t y dependence of the c r o s s s e c t i o n s , a l l of the p r e c e e d i n g d a t a f o r p r o t o n s may be e x t r a p o l a t e d t o the case of muons s t o p p i n g i n the same m a t e r i a l . The number of charge c h a n g i n g c y c l e s f o r a muon i s s i m p l y ( 1 / 9 ) N C ( p r o t o n ) over a s i m i l a r l y s c a l e d energy range. T a k i n g the example of A l l i s o n , i f N t ( p r o t o n )= 9 8 0 f o r H + i n h e l i u m from 300keV t o 9keV, then N c(muon)=115 f o r the energy range 35keV t o 1keV. The same s c a l i n g f a c t o r a p p l i e s t o the time spent as a n e u t r a l , t h , as d i s c u s s e d l a t e r . The number of e x p e c t e d 58 CO LU CO CE CD CO ZD O i — i cn CE o O O o o o O o O O o o o o LO O LO o LO o LO CM LO o C\J LO C\J O oo r - LO CO 1—1 o o co i— i o > o >-CD cn LU o I— o cn o_ S313A3 3NI9NtlH3 39cldH3 30 d39Nf1N F i g u r e 3 . 4 . N c f o r p ro ton charge exchange in v a r i o u s gases, 59 charge exchange c y c l e s and the ranges of i n t e g r a t i o n used are g i v e n i n t a b l e 3.2 f o r both the muon and p r o t o n . Another v e r y i m p o r t a n t q u e s t i o n f o r t h e muonium experiment i s the time spent as a n e u t r a l s p e c i e s . S i n c e s i n g l e t muonium i s u n o b s e r v a b l e (as d i s c u s s e d e a r l i e r and i n Appendix 1 ) , i f the charge c h a n g i n g c y c l e produced muonium i n the s i n g l e t s t a t e f o r a time l o n g e r than the h y p e r f i n e p e r i o d (1 / \ ) e = . 22ns) , then the p o l a r i z a t i o n of t h a t muon i s l o s t and A ^ i s s u b s e q u e n t l y reduced. The time spent as a n e u t r a l can be e x p r e s s e d as where p c i s I 5 p s i , T 0 i s 273K, v(E) i s the speed of the p a r t i c l e and the o t h e r terms have been d e f i n e d i n e q u a t i o n 3.6. T h i s time depends s i m p l y upon the p r e s s u r e and temperature of the t a r g e t gas and has an a s y m t o t i c b e h a v i o r dependent upon the lower energy l i m i t E+. The time t h a t a muon spends i n the v a r i o u s energy s t a g e s i n the r a r e gases i s shown i n t a b l e 3.3. In p a r t i c u l a r note t h a t the t o t a l time spent as a n e u t r a l i s l e s s than about ,1ns i n the charge exchange regime and s i n c e t h e r e a r e r o u g h l y 100 charge c h a n g i n g c y c l e s f o r the muon, ( t a b l e 3.2) the time per c y c l e i s l e s s than .OOJns which i s an o r d e r of magnitude s m a l l e r than the h y p e r f i n e i n t e r a c t i o n time of .22ns. The importance of t h i s w i l l be d i s c u s s e d l a t e r . F i n a l l y the p* or muonium reaches an energy where no r t n=p 0T/pT 0 <si dE/(e- 0, v(E) (dE/dx) ) 3.8 60 N C H + from 600KeV to 9KeV N C J J + from 67Kev to 1KeV Hel ium 997 c y c l e s 111 c y c l e s Neon 478 c y c l e s 53 c y c l e s Argon 681 c y c l e s 76 c y c l e s Krypton 854 c y c l e s Hydrogen 642 c y c l e s N i t rogen 694 c y c l e s 95 c y c l e s 71 c y c l e s 77 c y c l e s The range of i n t e g r a t i o n for neon i s only from 600KeV to 40Kev for protons and therefore only from 67KeV to 4.4Kev for muons. Tab le 3 .2 . Range of i n t e g r a t i o n and number of charge exchange c y c l e s fo r v a r i o u s gases . H + from 27MeV to 300KeV Bethe-Bloch time 600Kev to 9Kev t„ time as a ne u t r a l He 45psi 267ns .7ns Ne 17p$i 163ns data not a v a i l a b l e Ar 15pii 124ns ,14ns Kr 12psi 92ns .14ns Xe 9psi 96ns data not a v a i l a b l e Equivalent times y* from 3MeV to 35KeV JJ* 35KeV tolKeV Mu 200eV to .025eV Bethe-Bloch time t n time as a n e u t r a l e l a s t i c c o l l i s i o n s He 45ps Ne 17ps Ar 15ps Kr 12ps Xe 9ps i 30ns 18ns Uns 10ns 1 1ns .077ns no data •014ns .014ns no data 2.2ns 1 ins 22ns 55ns 1 16ns The e l a s t i c c o l l i s i o n times are c a l c u l a t e d using an e f f e c t i v e cross s e c t i o n of lO'^cm"*-. As noted in the text these c a l c u l a t e d times that th*e muon spends in the neut r a l state are ge n e r a l l y too small to cause s i g n i f i c a n t d e p o l a r i z a t i o n and i t must be in the region from iKeV to thermal energies (where there i s no experimental information) that must be important i n causing the large observed d e p o l a r i z a t i o n . Tab le 3 .3 . The time spent in the th ree s tages of t h e r m a l i z a t i o n fo r the ra re gases . 62 more charge changing c y c l e s can oc c u r and ( f o r the r a r e gases) the r e m a i n i n g energy l o s s i s by e l a s t i c c o l l i s i o n s o n l y . Assuming an average s c a t t e r i n g a n g l e of 90 degrees, the average energy l o s s per c o l l i s i o n i s AE=-p2/M=-2mE/M 3.9 where p i s the muon (muonium) momentum and m and M are the masses of the muon and moderator r e s p e c t i v e l y . T h i s can be r e w r i t t e n as an energy l o s s per u n i t time r a t h e r than per c o l l i s i o n s i n c e the number of c o l l i s i o n s per second i s s i m p l y nGv where n i s the number of atoms/cm 3, 6~ i s some e f f e c t i v e c r o s s s e c t i o n "and v i s the r e l a t i v e v e l o c i t y . One then o b t a i n s dE/dt = -n 6" v2mE/M; t =M £ 1 /E^ 1 - 1 /Ej^ j /p.VA n6* mH) 3.10 Thus i t i s apparent t h a t the h e a v i e r the moderator gas, the l e s s e f f i c i e n t i t i s i n t h e r m a l i z i n g the muons- by e l a s t i c c o l l i s i o n s . These t i m e s a r e a l s o compared f o r the r a r e gases i n t a b l e 3 .3 . I t must be emphasized t h a t t h e r e are no c l e a r c u t energy regimes i n the s l o w i n g down p r o c e s s and t h a t the o v e r l a p , e s p e c i a l l y of the charge c h a n g i n g and e l a s t i c c o l l i s i o n t h e r m a l i z a t i o n p r o c e s s e s i s v i t a l t o the u n d e r s t a n d i n g of the f i n a l muonium f o r m a t i o n f r a c t i o n s and asymmetries i n v a r i o u s gases. In p a r t i c u l a r , t h e gap i n the p r o t o n dE/dx and c r o s s s e c t i o n d a t a from 9KeV t o e n e r g i e s 63 where charge exchange i s u n i m p o r t a n t p r o b a b l y i s t h e key t o the u n d e r s t a n d i n g of the a b s o l u t e asymmetries and m i s s i n g f r a c t i o n s i n the MSR e x p e r i m e n t s . The MSR e x p e r i m e n t s i n d i c a t e t h a t charge exchange i s s t i l l i m p o r t a n t at these low e n e r g i e s . T h i s p o i n t w i l l be d i s c u s s e d l a t e r i n t h i s c h a p t e r . In p o l y a t o m i c gases low energy i n e l a s t i c c o l l i s i o n s e x c i t i n g r o t a t i o n a l and v i b r a t i o n a l s t a t e s can be i m p o r t a n t c o n t r i b u t o r s i n q u i c k l y t h e r m a l i z i n g the muon. For t h i s reason i t i s d i f f i c u l t t o e s t i m a t e the time f o r t h e r m a l i z a t i o n i n t h e s e systems. 3 ' 2 . T h e o r e t i c a l Background For Charge Exchange As t h e muon slows down, i t undergoes many c o l l i s i o n s w i t h the moderator gas and w i t h each c o l l i s i o n t h e r e i s a chance t h a t i t w i l l c a p t u r e an e l e c t r o n t o form muonium. One of the f i r s t (and most e a s i l y u n d e r s t o o d ) t h e o r e t i c a l t r e a t m e n t s of t h i s p r o c e s s was g i v e n by Thomas(l927) and w i l l be o u t l i n e d h e r e . The Thomas model i s a c l a s s i c a l t r e a t m e n t and can be e a s i l y u n d e r s t o o d i n p h y s i c a l terms. I t i s a l s o i n t e r e s t i n g because of i t s c l o s e agreement w i t h t h r e e quantum c a l c u l a t i o n s : a) second Born a p p r o x i m a t i o n ( D r i s k o ( 1 9 5 5 ) ) , b) i m p u l s e a p r o x i m a t i o n ( B r a n s d e n (1 9 6 3 ) ) and 64 c) continuum d i s t o r t e d wave approach ( C h e s h i r e ! 1 9 6 4 ) ) . The model t h a t w i l l be d i s c u s s e d f o r i l l u s t r a t i v e p urposes here i s f o r e l e c t r o n c a p t u r e from l i g h t atoms a t h i g h impact v e l o c i t i e s . The s i m p l e s t system which comes t o mind i s of c o u r s e e l e c t r o n c a p t u r e from a hydrogen atom by a p r o t o n . The f o l l o w i n g d i s c u s s i o n of the a p p r o x i m a t i o n s and c a l c u l a t i o n s i n t h i s t h e o r y can be found i n a more complete form i n Thomas(l927) and M a p l e t o n ( 1 9 7 2 ) . The b a s i s of the t h e o r y i s t o d e s c r i b e the c a p t u r e p r o c e s s i n t h i s t h r e e body system as two s e p a r a t e two body c o l l i s i o n s . The f i r s t i s the incoming p r o t o n c o l l i d i n g w i t h the o r b i t a l e l e c t r o n and the second i s the e l e c t r o n c o l l i d i n g w i t h i t s o r i g i n a l p r o t o n . T h i s i s i l l u s t r a t e d i n f i g u r e 3 . 5 where the number i n b r a c k e t s i n d i c a t e s the p o s i t i o n of t h e p a r t i c l e s a t one of t h r e e t i m e s . The d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n f o r the f i r s t c o l l i s i o n i s s i m p l y t h e R u t h e r f o r d c r o s s s e c t i o n <Ae =2TTbdb=(TTeV2m2V« ) c s c * (S-/2 ) sinSdS- 3 .11 where b i s the impact parameter, e i s the e l e c t r o n i c c h a r g e , V i s the impact v e l o c i t y and i s the c e n t r e of mass s c a t t e r i n g a n g l e . I t s h o u l d be noted t h a t m, the e l e c t r o n mass, i s a p p r o x i m a t e l y the same as the reduced mass and t h i s a p p r o x i m a t i o n i s a l s o v a l i d f o r an incoming muon. U s i n g U as the e l e c t r o n v e l o c i t y a f t e r t h i s f i r s t impact and from the v e c t o r diagram of v e l o c i t i e s i n f i g u r e 3 . 5 e q u a t i o n 3 .11 65 F i gu re 3 .5 . Vec to r d iagram of v e l o c i t i e s fo r the charge exchange c o l l i s i o n s . 66 can be r e w r i t t e n as d6* = ( T r e V m 2 V 5 ) c s c 3 ( V 2 ) d U 3.12 The p r o b a b i l i t y t h a t the s c a t t e r e d e l e c t r o n ( i n i t i a l l y at a d i s t a n c e r from the n u c l e u s ; p o s i t i o n e(1) i n f i g u r e 3.5) w i l l i n t e r a c t i n such a way w i t h i t s n u c l e u s t h a t i t w i l l be c a p t u r e d by the incoming p a r t i c l e i s g i v e n by P = ( t a r g e t a r e a / a r e a of sphere) =b' db' dtf' /4TTr 2 3.13 The R u t h e r f o r d s c a t t e r i n g c r o s s s e c t i o n i s a g a i n used t o g i v e P = ( e V l 6 m 2 U a r 2 77)cscw(0/2)sin£' d$-' d<£' 3.14 In o r d e r f o r c a p t u r e t o o c c u r , the f i n a l r e l a t i v e v e l o c i t y w of the e l e c t r o n w i t h r e s p e c t t o the incoming p a r t i c l e p must be l e s s than the escape v e l o c i t y f o r the e l e c t r o n at d i s t a n c e x from p or (1/2)mw 2^e 2/x. In o t h e r words, the end of the v e l o c i t y v e c t o r u' (the i n i t i a l and f i n a l speeds of the s c a t t e r e d e l e c t r o n i n the second c o l l i s i o n a r e a p p r o x i m a t e l y the same) must l i e i n the sphere whose volume i s 4TTw3/3 i n v e l o c i t y space. In s p h e r i c a l c o o r d i n a t e s t h i s means 67 (U') 2du' sin^'dS-' d$' =(4TT/3)w3 3.15 The s m a l l e r w i s compared t o u', the g r e a t e r i s the v a l i d i t y of e q u a t i o n 3.15 where the t i p of the u' v e c t o r f a l l s i n the sphere of volume 47Tw3/3. Now w i t h the assumption t h a t du'=w and £ = <O'=60° (so t h a t V=U=u', dU=du', r = x) one has from e q u a t i o n s 3.11 and 3.14 ds = (8TTeVm 2V 5) (2e2/mr)/'L and P=8 e 6 / 3 m 3 V 6 r 3 3.16 So the charge exchange c r o s s s e c t i o n i s s i m p l y the c r o s s s e c t i o n f o r the i n i t i a l p a r t i c l e - e l e c t r o n impact t i m e s the p r o b a b i l i t y t h a t t h i s l e a d s t o an e l e c t r o n v e l o c i t y t h a t w i l l s c a t t e r the e l e c t r o n o f f of the o r i g i n a l n u c l e u s i n such a way as t o be c a p t u r e d by the incoming p a r t i c l e ; hence de (charge exchange ) = ( 6477e 11 /3m5 r 3 V 1 1 )( 2/mr ) / % 3.17 A l t h o u g h t h i s t h e o r y i s o n l y v a l i d i n t h i s h i g h energy range, i t does e x p l i c i t l y i d e n t i f y the v e l o c i t y dependence of the charge exchange c r o s s s e c t i o n ; i n p a r t i c u l a r t h e r e i s no s p e c i f i c dependence on the p a r t i c l e mass. Hence, the s i m p l e ( V " 1 1 ) v e l o c i t y dependence a l l o w s one t o e a s i l y compare the muon and p r o t o n charge exchange p r o c e s s e s . I t s h o u l d be emphasized t h a t t h i s same V " 1 1 v e l o c i t y dependence i s found f o r the t h r e e q u a n t a l c a l c u l a t i o n s mentioned 68 e a r l i e r . Thus, s i n c e ny=l/9mp the charge exchange c r o s s s e c t i o n f o r a 9keV p r o t o n i n c i d e n t on a t a r g e t s h o u l d be the same as f o r a 1keV muon on the same t a r g e t . T h i s concept of s c a l i n g c r o s s s e c t i o n s by t h e p a r t i c l e mass ( i . e . f o r the same v e l o c i t y ) i s w e l l e s t a b l i s h e d , a t l e a s t a t r e l a t i v e l y h i g h e n e r g i e s (Tawara(1979)). I t has been c o r r o b o r a t e d r e c e n t l y i n t h e o r e t i c a l s t u d i e s of ji* and p* charge exchange w i t h hydrogen ( B e l k i c ( 1 9 7 3 ) , Banyard(1978) ) . For the v e r y s i m p l e systems, the charge exchange t h e o r y seems t o be w e l l u n d e r s t o o d p a r t i c u l a r l y a t h i g h e n e r g i e s but i t i s c l e a r t h a t f o r m o l e c u l e s and l a r g e atoms and w i t h low impact v e l o c i t i e s , none of the t h e o r i e s a r e t o t a l l y adequate a l t h o u g h much p r o g r e s s has been made i n t h i s a rea ( M a p l e t o n ( 1 9 7 2 ) ) . At low e n e r g i e s , m o l e c u l a r o r b i t a l models ar e u s u a l l y invoked w i t h charge exchange t a k i n g p l a c e a t the c r o s s i n g p o i n t s of d i a b a t i c p o t e n t i a l energy s u r f a c e s (Johnson(1978) , S i d i s ( l 9 7 2 ) , K u bach(1976)). A g a i n t h e r e i s a s i m p l e v e l o c i t y dependence ( a l t h o u g h i t i s no l o n g e r V- 1 1 ) . In g e n e r a l t h e n , one e x p e c t s t o be a b l e t o make use of measured p r o t o n c r o s s s e c t i o n s t o p r e d i c t the b e h a v i o r of muons at s i m i l a r v e l o c i t i e s . S i m i l a r l y , one may use the muon r e s u l t s t o p r e d i c t the b e h a v i o r of p r o t o n s i n analogous systems. The p r o t o n d a t a i s g e n e r a l l y i n the form of c r o s s s e c t i o n s a t d i s c r e e t e n e r g i e s , whereas the muon i s o n l y o b s e r v a b l e a f t e r i t has t h e r m a l i z e d from about 2MeV, 69 u n d e r g o i n g charge exchange i n low energy r e g i o n s (<1keV) where p r o t o n d a t a i s o f t e n not a v a i l a b l e f o r comparison. The p r o t o n and muon da t a can s t i l l be compared, however, i f the parameter of i n t e r e s t i s t a k e n t o be the n e u t r a l f r a c t i o n f Q ( e q u a t i o n 3.3). These comparisons s h o u l d be v a l i d f o r a l l the r a r e gases and s h o u l d o n l y break down a t e n e r g i e s when the e q u i l i b r i u m a p p r o x i m a t i o n b r e a k s down or when c h e m i c a l p r o c e s s e s (hot atom r e a c t i o n s f o r example), which depend on the mass of the p a r t i c l e v i a t u n n e l l i n g and z e r o p o i n t e n e r g i e s , become i m p o r t a n t . T h i s e x p e c t a t i o n i s c o n s i s t e n t w i t h the e x p e r i m e n t a l d a t a o b t a i n e d f o r t h i s t h e s i s : the muonium f o r m a t i o n f r a c t i o n s i n t h e r a r e gases are c o n s i s t e n t w i t h the known p r o t o n c r o s s s e c t i o n s but tend t o be i n c o n s i s t e n t i n methane, hydrogen and ammonia where hot c h e m i c a l p r o c e s s e s might be ex p e c t e d t o oc c u r a t low e n e r g i e s . 3.3. Muonium Fo r m a t i o n In The Rare Gases By s c a l i n g the known 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 s f o r the p r o t o n <S]Q (Tawara(1979)) t o e q u i v a l e n t muon v e l o c i t i e s , the f r a c t i o n of muonium ex p e c t e d t o form i n the r a r e gases can be p r e d i c t e d . The graphs of f 0 f o r p r o t o n s 70 i n the r a r e gases a r e shown i n f i g u r e s 3.6 t o 3.10. T h i s d a t a c l e a r l y demonstrates the a p p l i c a b i l i t y of the Massey c r i t e r i a d i s c u s s e d e a r l i e r . W i t h d e c r e a s i n g i o n i z a t i o n p o t e n t i a l , the peak i n p r o t o n charge exchange c r o s s s e c t i o n moves t o p r o g r e s s i v l e y lower e n e r g i e s ( t h e r e i s , i n f a c t , no o b v i o u s peak i n Kr and X e ) . The c o r r e s p o n d i n g peak f o r the muon system i s e x p e c t e d a t 1/9 the p r o t o n energy. S i m i l a r l y , the lower the i o n i z a t i o n p o t e n t i a l , the h i g h e r the f 0 . In the case of He and Ne, the f r a c t i o n s f Q show an i n c r e a s e a t the l o w e s t e n e r g i e s but i t i s u n l i k e l y t h a t t h i s i s a r e a l e f f e c t . At the s e low e n e r g i e s , the e q u i l i b r i u m a p p r o x i m a t i o n f o r the n e u t r a l f r a c t i o n s may not be a p p l i c a b l e so some disagreement between the e x t r a p o l a t e d p r o t o n d a t a and the t h e r m a l muonium f r a c t i o n s may be e x p e c t e d . The t r e n d s , however, a r e repr o d u c e d q u i t e w e l l and one can expect t h a t as the muon ( p r o t o n ) t h e r m a l i z e s i n the gas, the n e u t r a l f r a c t i o n s w i l l be a s y m p t o t i c t o v a l u e s <.1 i n He and Ne, t o —.8 i n Ar and t o 1.0 i n Kr and Xe. Charge exchange i s e x o t h e r m i c f o r xenon r i g h t down t o t h e r m a l e n e r g i e s . T h i s d a t a f o r the r a r e gases i s summarized i n t a b l e 3.4. T y p i c a l e x p e r i m e n t a l JJSR (muon) and MSR (muonium) s i g n a l s f o r argon a t 3 6 p s i have been g i v e n e a r l i e r ( f i g u r e s 1.3 and 1.5) from which the r e l a t i v e f r a c t i o n s f 0 and f + can e a s i l y be found from the measured a m p l i t u d e s A^ h and A^ ,, as d e s c r i b e d e a r l i e r . There i s e s s e n t i a l y no Mu formed i n e i t h e r He or Ne ( c a r e must be taken t o i n s u r e sample 71 F i g u r e 3.6. Helium n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). 72 .1111 1 1 1 1 1 i i 111 -e -a — — — -CJ a -— — a Q - a -a - a -a a a B a -a _ a -a -a -a a — a -a -1 a 1 1 1 1 1 o o H o o o i n o L O o L O o L O o ° o C O r - C D r o o —. o o o o o o o • CO I— I o > >-C D rr UJ -ZL UJ o v— o cn Q_ •3znuyin3N N o u a o y j F i g u r e 3.7. Neon n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). 73 •3zn«ain3N Noiiotiyj F i g u r e 3.8. The n e u t r a l f r a c t i o n f o r p r o t o n s i n argon c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). 74 O t Q_ >— id LO o LO o LO O CO CD .—i o o o o CO > o >-CD cn LU LU O Q_ 0 LO O CO O 0 O O i g u r e 3.9. K r y p t o n n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). 75 O L LU X LO o LO O LO O O CD CD ro — O O O O o LO O O CO I— I o > CD cn LU •z. o V— o Q_ F i g u r e 3.10. Xenon n e u t r a l f r a c t i o n c a l c u l a t e d A l l i s o n ( 1 9 5 8 ) and Tawara(1973). from 76 Target Gas f 0 f + E r r o r f^ ( H ) Helium 0% 1.00% 0 10% Neon 4% 96% 6 10% Argon 74% 26% 4 80% K r y p t o n 100% 0% 6 100% Xenon 100% 0% 3 * 100% The e r r o r for krypton i s high because of an i n t e r f e r i n g wall s i g n a l . The values given are averages of s e v e r a l runs with the exception of the neon value where i t i s from a s i n g l e run with u l t r a high p u r i t y neon p u r i f i e d with a double charcoal t r a p at l i q u i d nitrogen temperature. The e r r o r for the helium run i s zero because a b s o l u t e l y no muonium s i g n a l was observed. T a b l e 3.4. N e u t r a l f r a c t i o n s o b s e r v e d f o r muons i n the r a r e gases and compared t o p r o t o n e x t r a p o l a t i o n s . 77 p u r i t y ) . The a m p l i t u d e s A r v ^ a n ( 3 hjA are d r a m a t i c a l l y dependent on the moderator p r e s s u r e as shown i n f i g u r e 3.11 f o r k r y p t o n and 3.12 f o r xenon. T a b l e 3.5 g i v e s the muon and muonium asymmetries f o r the r a r e gases a t s e v e r a l p r e s s u r e s . I t i s c l e a r from t a b l e 3.5 t h a t the asymmetry i s v e r y p r e s s u r e dependent. I t must be no t e d , however, t h a t the c a l c u l a t e d r e l a t i v e f c and f + are c o n s t a n t . T h i s i s shown more d r a m a t i c a l l y i n t a b l e 3.6 f o r argon, methane and n i t r o g e n where t h e r e a r e no w a l l e f f e c t s t h a t must be c o r r e c t e d f o r and the a b s o l u t e asymmetry (A+ 0 + /A^.(aluminum) ) was a l s o d e t e r m i n e d . The m i s s i n g f r a c t i o n ( A ^ j i s o f t e n l e s s than 100%) w i l l be d i s c u s s e d i n the next s e c t i o n . The r e l a t i v e muonium and muon f r a c t i o n s a r e independent of gas p r e s s u r e , a l t h o u g h the a b s o l u t e asymmetry i s h i g h e r at h i g h e r gas p r e s s u r e s . T h i s i n d i c a t e s t h a t t h e charge exchange p r o c e s s i s dependent o n l y upon the number of c o l l i s i o n s , which i s i n t u i t i v e l y r e a s o n a b l e s i n c e r e g a r d l e s s of the time e l a p s e d between c o l l i s i o n s , the 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 or e l e c t r o n l o s s do not change. The t o t a l asymmetry i n k r y p t o n and xenon a r e anomalously s m a l l d e s p i t e t h e i r l a r g e d e n s i t i e s . S i m i l a r , r e s u l t s i n k r y p t o n have been r e p o r t e d by o t h e r workers ( B o l t o n ( 1 9 7 9 ) ) . T h i s i s due t o the f a c t t h a t t h e r m a l i z a t i o n t h r o u g h e l a s t i c c o l l i s i o n s i s v e r y i n e f f i c i e n t ( t a b l e 3.3). Co n s e q u e n t l y , the muonium remains a t r e l a t i v e l y h i g h e n e r g i e s f o r g r e a t e r l e n g t h s of t i m e , thus i n c r e a s i n g the p r o b a b i l i t y of subsequent charge c h a n g i n g c y c l e s ( t h i s i s of Target and Pressure r •in* He 18psi .154*.004 .0351.005 0 .12 He 40psi .2101.003 .071.01 0 .14 He 43psi .2221.002 .0871.01 0 .14 Ne 6psi .0901.005 '.04 .0101.006 .07 Ne 1 2psi .1001.002 ~.03 .0221.001 . 1 1 Ne 18psi .1701.002 -0 .0051.005 .18 Ne 24psi .2551.003 -.015 -0 .24 Ne 30psi .3001.002 -.009 .0271.002 .35 Ar-^ 8psi .0791.003 .071.002 .0381.003 .09 Ar 1 5psi .0741.002 .0221.002 .0781.003 .21 Ar 1 5psi .0701.002 .0091.002 .1001.002 .26 Ar 30psi .0921.003 .0151.002 . 11 It.004 .30 Ar 36psi .1001.003 -0 .1301.004 .36 Kr 6psi .0651.004 .065 .0401.004 .08 Kr 1 Opsi .0201.003 .02 .0861.004 .17 Kr 1 4psi ~0 ~0 . 1 201.006 .24 Xe 6psi .0461.003 .046 .0501.003 .10 Xe 9psi -0 ~0 .0701.010 .14 Xe 1 Opsi .0401.010 .040 .0891.006 .18 6psi a i r has Au=.07±.0l I5psi a i r + lOpsi He has Au=.024t.01 These r e s u l t s i n d i c a t e that the Au in the Xenon and Krypton are due only to muons stopping i n the walls of the t a r g e t . Thus one can conclude that there i s 100% muonium formation in these gases. Tab le 3 . 5 . Asymmetry v s . p r e s su re fo r the r a re gases . 79 Target R e l a t i v e F r a c t i o n s Absolute Asymmetry Ni 15psi A^=0. 1210.007 f 0-84% A ^ -95% A^.«0.04510.003 £ +-16% 36psi A*-0. 17110.004 £ 0=82% A ^ - 1 0 0 % A^«0.07610.002 f + = 18% Ar 15psi A„-0. 1110.005 fo =76% A a t < -80% A^-0.07110.004 f +=24% Ar 36psi A„-0.13310.004 f. =73% A ^ =92% A^-0.1010.003 £*=27% CH H I6psi Aa-0.1 110.004 f,=86% A a f e s=65% A^ =0. 03710 . 002 f^ . = 1 4% CH 4 44psi Afl = 0. 1810.005 f e =86% A ^ j - 1 0 0 % A r-0.05810.002 f + = 14% He 45psi A ^ =63% Ne 30psi A a t l =83% Kr 6psi A a^ s -41 % Kr lOpsi A f c^ s=55% Kr 14psi Xe 6psi A»Wi =7 1% A ^ - 4 2 % X e 1 ° P s i A a b j=63% The p o s s i b i l i t y of an i n t e r f e r i n g w a l l s i g n a l i n t h e He, and Xe c o u l d o n l y c a u s e t h e A a b s t o be h i g h e r than i t r e a l l y i s Ne, Kr Tab le 3 . 6 . Abso lu te asymmetry v s . p r e s su re fo r v a r i o u s gases . 80 c o u r s e enhanced by the l a r g e even a t low e n e r g i e s ) which l e a d s t o lower asymmetry. As w i l l be d i s c u s s e d i n s e c t i o n 3.4 ( w i t h the h e l i u m example) the l a s t few charge exchange c y c l e s a r e v e r y i m p o r t a n t i n d e t e r m i n i n g the t o t a l asymmetry because of the l o n g e r times spent as a n e u t r a l (and t h e r e f o r e l o n g e r times i n the d e p o l a r i z a b l e s i n g l e t s t a t e ) compared t o t h e h i g h e r energy c y c l e s t h a t occur t o o q u i c k l y to. cause any d e p o l a r i z a t i o n . 3.4. P r e s s u r e Dependence Of The Asymmetry The muon e n t e r s the t a r g e t a t about 2 MeV a f t e r b e i n g slowed down by the d e f i n i n g c o u n t e r and beam p i p e and t a r g e t windows. As the muon slo w s down i n the gas, i t has a c e r t a i n p r o b a b i l i t y of c a p t u r i n g an e l e c t r o n from the medium t o form muonium, d i r e c t l y r e l a t e d t o the c r o s s s e c t i o n f o r t h i s p r o c e s s ( S " / 0 ) . S i m i l a r l y , once muonium i s formed i t has a c r o s s s e c t i o n 6"0, f o r the l o s s of t h i s e l e c t r o n and subsequent r e t u r n t o the p* s t a t e . These charge changing c y c l e s c o n t i n u e u n t i l the muon or muonium i s t h e r m a l i z e d and they a r e no l o n g e r e n e r g e t i c a l l y a l l o w e d (an e x c e p t i o n i s ju + +Xe—>Mu+Xe +, where the e l e c t r o n c a p t u r e i s e n e r g e t i c a l l y a l l o w e d even at t h e r m a l e n e r g i e s ) . As shown i n t a b l e 3.2, 8 1 s: z: or 0.10 0.05 H 0.00 -0.05 KRYPTON 8 GAUSS iHps ; in cc 0.10 0.05 0.00 -0.05 l I I I I i KRYPTON 8 GRUSS I Dps; o.io h t— U J 31 0.05 h 0.00 -0.05 r-F i g u r e 3 . 1 1 . Asymmetry i n k r y p t o n as a f u n c t i o n of p r e s s u r e . 82 0.20 010 h a 0.00 F -0.10 0.20 0.00 h 5 000 -0.10 F i g u r e 3.12. Asymmetry in xenon as a f u n c t i o n of p r e s s u r e . 83 t h e r e a r e i n the o r d e r of 100 charge c h a n g i n g c y c l e s f o r t h e muon (depending on the n a t u r e of the t a r g e t ) and t h e r e f o r e the t h e r m a l i z a t i o n time (and e s p e c i a l l y the time spent as a n e u t r a l ) i s v e r y i m p o r t a n t . I f the time between charge c h a n g i n g c y c l e s i s l a r g e compared t o the h y p e r f i n e i n t e r a c t i o n time (.22ns), then any s i n g l e t muonium formed w i l l be u n o b s e r v a b l e and any t r i p l e t muonium w i l l s u b s e q u e n t l y c y c l e back t o y j + ( t h e d e p o l a r i z e d s i n g l e t muonium i s e q u a l l y l i k e l y t o l o s e an e l e c t r o n t o g i v e a ji* but i t w i l l be out of phase w i t h t h e r e s t of the ensemble and s t i l l be u n o b s e r v a b l e ) whereupon i t w i l l have a 50% chance of c o n v e r t i n g t o s i n g l e t muonium on i t s next charge c a p t u r e and thus b e i n g rendered u n o b s e r v a b l e . I t i s easy t o see then t h a t i f the time f o r each charge c h a n g i n g c y c l e were >.22ns, over 100 c y c l e s a l l of the asymmetry would be l o s t . Such e f f e c t s a re e x p e c t e d t o be i n v e r s e l y p r o p o r t i o n a l t o the moderator p r e s s u r e . I t has been found, i n g e n e r a l , t h a t the a m p l i t u d e s ( a b s o l u t e asymmetries) f o r Mu f o r m a t i o n a r e indeed r e l a t e d t o the moderator p r e s s u r e , as shown i n t a b l e 3.5 f o r the r a r e gases. The same e f f e c t i s found i n p o l y a t o m i c gases ( t a b l e 3.6). There can be another e x p l a n a t i o n f o r t h i s l o s s of asymmetry a t low p r e s s u r e s ( b e s i d e s the p o l a r i z a t i o n l o s s due t o l o n g s l o w i n g down t i m e s ) : due t o the extended s t o p p i n g d i s t r i b u t i o n of the muons i n the gas t a r g e t a g e n e r a l r u l e of thumb i s t h a t £R/R £-10% ( H a r v e y ( 1 9 7 4 ) , 84 ' P i f e r ( 1 9 7 6 ) , Burcham(1976) ) and i n a t y p i c a l gas t a r g e t w i t h s u r f a c e muons t h i s g i v e s A,R=i0cm. Coupled w i t h the momentum r e s o l u t i o n of the beam l i n e ( P i f e r ( 1 9 7 6 ) , Oram ( l 98 l ) ) t h i s can l e a d t o a p p r e c i a b l e s t o p p i n g d i s t r i b u t i o n s (on the or d e r of 20 t o 45 cm, depending on the p r e s s u r e of the mode r a t i n g g a s ) . Such l a r g e s t o p p i n g d i s t r i b u t i o n s can be e x p e r i m e n t a l l y v e r i f i e d s i n c e they s h o u l d be accompanied by l a r g e i n c r e a s e s i n the r e l a x a t i o n X , as a f u n c t i o n of p r e s s u r e (due t o the d e c r e a s e i n f i e l d homogeniety over the l a r g e r s t o p p i n g d i s t r i b u t i o n ) . That an i n c r e a s e d s t o p p i n g d i s t r i b u t i o n can a f f e c t the r e l a x a t i o n can e a s i l y be seen from e q u a t i o n 2.1 shown e a r l i e r . The d a t a o b t a i n e d w i t h the same geometry f o r both argon and neon i s shown i n t a b l e 3 .7 . The X 0 goes through a minimum ( c o r r e s p o n d i n g t o a s t o p p i n g r e g i o n i n t h e c e n t r e of the c o i l s ) and then i n c r e a s e s as the s t o p p i n g r e g i o n g e t s s m a l l e r but moves toward the f r o n t of the gas can where f i e l d i n h o m o g e n i e t i e s a r e a g a i n l a r g e ( f i g u r e 2 . 3 ) . There i s a l s o e v i d e n c e f o r t h i s extended s t o p p i n g r e g i o n i n the phase d a t a of the muon p r e c e s s i o n . I f t he muons a r e s t o p p i n g i n the c e n t r e of the c o i l s (and c o n s e q u e n t l y i n the c e n t r e of the p o s i t r o n t e l e s c o p e s ) the phase a n g l e w i l l be 90 d e g r e e s . As the muon d i s t r i b u t i o n moves toward the f r o n t of the gas can ( i . e . toward the beam l i n e ) , the phase a n g l e (of the backward p o i n t i n g muons) w i l l become l a r g e r . I t w i l l get s m a l l e r f o r lower p r e s s u r e s when the d i s t r i b u t i o n moves t o the back of the of the gas can. T h i s i s a l s o i l l u s t r a t e d i n t a b l e 3 .7 . Target and Pressure Argon 8psi Argon I5psi Argon 30psi Neon 6psi Neon 12psi Neon iBpsi Neon 24psi Neon 30psi Neon 40psi Muonium r e l a x a t i o n (usee _') .78+.05 .521.02 1 .821.07 Muon Relaxation (usee" 1) .161.01 .081.01 .211.01 .361.04 .171.02 .091.01 .0571.006 .035t.004 .0831.010 Phase angle f 163 219 264 320 434 An a d d i t i o n a l run with 4 l p s i argon but with the target moved back (so that the stopping d i s t r i b u t i o n would remain in the center of the helmholtz c o i l s ) , showed a muonium r e l a x a t i o n of .461.01 usee -' and a muon r e l a x a t i o n of .021.01 usee" 1 . This i n d i c a t e s that the change of r e l a x a t i o n i s not a pressure dependent phenomena but i s due to the f i e l d • inhomogenieties of the helmholtz c o i l s . Tab le 3 .7 . \ Q and phase ang le as a f u n c t i o n of gas p r e s s u r e . 86 At lower p r e s s u r e s , t he AR w i l l be l a r g e s t and i t i s c l e a r t h a t a l a r g e /\R has the same e f f e c t as i n c r e a s i n g the p o s i t r o n t e l e s c o p e c o u n t e r s i z e (see f i g u r e A2.1). The obs e r v e d asymmetry can be e x p r e s s e d q u i t e s i m p l y as a f u n c t i o n of c o u n t e r s i z e (or number of co u n t s ) i f one uses e q u a t i o n s 1.4 and 1.7 and assumes e q u a l r e l a x a t i o n s and n o r m a l i z a t i o n s . The e x p r e s s i o n i s A=(N^-N L)/(N R+N L) where N L and ar e the cou n t s i n the l e f t and r i g h t t e l e s c o p e s r e s p e c t i v e l y . T h i s can a l s o be w r i t t e n i n anal o g y t o e q u a t i o n 1.3 as NL=1+Acos0- where A i s the asymmetry f o r an i n f i n i t e l y s m a l l c o u n t e r and 0 i s the (2D) s o l i d a n g l e subtended by the p o s i t r o n t e l e s c o p e . I n t e g r a t i n g t h i s e x p r e s s i o n over the 2D s o l i d a n g l e subtended by the c o u n t e r s , one o b t a i n s A(0-)=Acos 2 (0/2) 3.18 For l a r g e s o l i d a n g l e s (or s i m i l a r l y l a r g e s t o p p i n g d i s t r i b u t i o n s ) , the observed asymmetry (compared t o the u n d i s t r i b u t e d muons s t o p p i n g i n an aluminum p l a t e ) s h o u l d be de c r e a s e d . T h i s f o r m u l a i s o n l y v a l i d f o r a muon ensemble s t o p p i n g d i r e c t l y between the p o s i t r o n t e l e s c o p e s and i t i s ex p e c t e d t h a t muons s t o p p i n g upstream or downstream would have an even g r e a t e r e f f e c t i n r e d u c i n g the asymmetry. These s o l i d a n g l e e f f e c t s must be un d e r s t o o d b e f o r e one can comment on the p o s s i b l e e f f e c t s of the t h e r m a l i z a t i o n time 87 on the obser v e d asymmetries i n t a b l e 3.5. The magnitude of the s e e f f e c t s were t e s t e d by v a r y i n g the p o s i t r o n t e l e s c o p e s i z e and by s i m u l a t i n g the e x p e r i m e n t a l c o n d i t i o n s w i t h a Monte C a r l o c a l c u l a t i o n (where the e f f e c t s of s t o p p i n g d i s t r i b u t i o n can be s i m u l a t e d ) . Appendix 2 has a l i s t i n g of t h e program and some e x p l a n a t i o n of how i t works. T a b l e 3.8 shows the Monte C a r l o r e s u l t s and the d a t a from the e x p e r i m e n t a l l y changed c o u n t e r s i z e . The f a c t t h a t the t o t a l asymmetry i s the same w i t h an aluminum p l a t e i n the gas can a l o n e and w i t h the mylar l i n i n g i n d i c a t e s t h a t no muons a r e s t o p p i n g i n the w a l l s of the gas can s i n c e A+o^. f o r mylar i s o n l y 17% of A ^ i n aluminum. With the t h i n f o i l s r e p l a c i n g the aluminum p l a t e (about 30 f o i l s w i t h *-l20mg/cm2 t o t a l ; more than enough t o s t o p the muons a f t e r they have e n t e r e d the evac u a t e d gas can) the a b s o l u t e asymmetry i s e s s e n t i a l l y the same as f o r the aluminum p l a t e . The l o s s of asymmetry o b s e r v e d when the f o i l s a r e spread throughout the gas can i s a measure of the e f f e c t of the s t o p p i n g d i s t r i b u t i o n on the t o t a l asymmetry. The i n c r e a s e i n X as the d i s t a n c e between the f o i l s i s i n c r e a s e d shows t h a t the s t o p p i n g r e g i o n i s becoming l a r g e r . The e f f e c t of cha n g i n g the c o u n t e r s i z e i s seen t o be n e g l i g i b l e i n a f f e c t i n g the obser v e d asymmetry. These e x p e r i m e n t a l r e s u l t s a r e c o n f i r m e d by the Monte C a r l o c a l c u l a t i o n which shows t h a t the e f f e c t s of s t o p p i n g d i s t r i b u t i o n and c o u n t e r s i z e on the t o t a l asummetry i s o n l y 88 about 10% whereas the obser v e d changes a r e an o r d e r of magnitude l a r g e r ( t a b l e 3.5). The p r e s s u r e dependence of the a b s o l u t e asymmetry must t h e r e f o r e be due t o the r e p e a t e d charge c h a n g i n g c y c l e s t h a t occur d u r i n g the s l o w i n g down p r o c e s s . The s l o w i n g down time and the time spent as a n e u t r a l d u r i n g t h e r m a l i z a t i o n a r e t h e r e f o r e v e r y i m p o r t a n t i n d e t e r m i n i n g the f i n a l o bserved asymmetry i n gas t a r g e t s . T h i s i n f o r m a t i o n r e g a r d i n g i n t e r a c t i o n s i n the c r i t i c a l r e g i o n from where the p r o t o n d a t a s t o p s , down i n energy t o where charge exchange i s no l o n g e r i m p o r t a n t i s not a v a i l a b l e i n the p r o t o n d a t a . From Appendix 1 the time dependence of the muon p o l a r i z a t i o n i n s i n g l e t muonium i s P^u(t) ( s i n g l e t ) =cos(w_t) cos (we +jOt 3.19 where the cos (wQ t="cos (wQ t ) term (W 0>>JL) i s the cause of the r a p i d p r e c e s s i o n which makes the s i n g l e t h a l f of the muonium ensemble u n o b s e r v a b l e due t o the e x p e r i m e n t a l time r e s o l u t i o n . The c o s ( w _ t ) term can be i d e n t i f i e d w i t h c o h e r e n t Mu Larmor p r e c e s s i o n ( t a b l e 1.2). U s i n g the c o s ( w 0 t ) term the l o s s - of p o l a r i z a t i o n due t o s i n g l e t muonium f o r m a t i o n d u r i n g t h e r m a l i z a t i o n can be e s t i m a t e d . For example, as noted e a r l i e r , i f the time between charge exchange c y c l e s (time as s i n g l e t muonium) i s >.22ns then the p o l a r i z a t i o n of t h a t muon i s l o s t . I f the muon spends a Target T o t a l Asymmetry Lambda Al Plate .35 A l Plate and mylar l i n i n g .35 A l f o i l s .04 .04 5" spread .34 .04 A l f o i l s 25" spread .32 .06 Argon small s o l i d angle .313 .14 Argon large s o l i d angle .305 Monte Carlo with small stopping d i s t r i b u t i o n .20 Monte Carlo with large stopping d i s t r i b u t i o n .18 .21 .01 The large s o l i d angle ref ewed to in the tab l e corresponds to-0-of 34 degrees and the small s o l i d angle r e f e r s to of 18 degrees. Table 3.8. R e s u l t s of a Monte C a r l o c a l c u l a t i o n and the e f f e c t of a change i n e x p e r i m e n t a l s o l i d a n g l e on the muon asymmetry. 90 s i g n i f i c a n t amount of time as muonium d u r i n g i t s s l o w i n g down p r o c e s s , then the observed asymmetry can become reduced due t o the d e p o l a r i z a t i o n e f f e c t of s i n g l e t s t a t e f o r m a t i o n t h a t a l l muons go th r o u g h as they t h e r m a l i z e . T h e r e f o r e the obs e r v e d f r a c t i o n depends upon cos(•©•) =cos(w.+jv)t and as l o n g as the time i n the s i n g l e t s t a t e i s s m a l l , cosC9)-1.0. For t = 10" 1 1 seconds, cos(-©-) = .96 and almost a l l of the p o l a r i z a t i o n i s r e t a i n e d . T h i s i s a p p r o x i m a t e l y the case f o r 4 1 p s i argon where A a\> s i s 97% and one can e s t i m a t e t = 8 . 4 x l 0 " 1 2 seconds. S i n c e t h i s time i s i n v e r s e l y p r o p o r t i o n a l t o p r e s s u r e , i t can be e s t i m a t e d t h a t a t I 5 p s i one can expect t ( s i n g l e t ) t o be 2.3x10" 1 1 seconds. U s i n g t h i s t i me A a k s a t I 5 p s i i s e s t i m a t e d t o be 80%. In f a c t 'A*y>6 (argon 15psi)=80% which i s i n good agreement w i t h the p r e d i c t e d v a l u e (one must r e c o g n i z e t h a t the e r r o r s i n the observ e d v a l u e s have been i g n o r e d ) . T a b l e 3.9 shows t h e s e e s t i m a t e d t i m e s and p r e d i c t e d Aab$ f o r the runs where t h e r e a re no w a l l e f f e c t s and the agreement i s q u i t e s a t i s f a c t o r y . The e r r o r i n A«.V>s i s g e n e r a l l y about 4 t o 8% and, due to the p r e c i p i t o u s b e h a v i o u r of the c o s i n e f u n c t i o n , t h e s e e r r o r s can l e a d t o l a r g e v a r i a t i o n s i n the p r e d i c t e d a b s o l u t e asymmetries. N e v e r t h e l e s s , t h i s t y pe of rough e s t i m a t e s h o u l d be u s e f u l i n q u a l i t a t i v e p r e d i c t i o n s as w i l l be seen l a t e r . In g e n e r a l one can c o n c l u d e t h a t the time spent as a n e u t r a l a t gas p r e s s u r e s from I 5 p s i t o 4 8 p s i v a r i e s from 10" 1 0 t o 10" 1 1 seconds r e s p e c t i v e l y . T h i s e s t i m a t e i s i n 91 Target Gas Observed Predicted P r e d i c t e d Observed Pressure Asymmetry Time Asymmetry Asymmetry CH^ I8psi CH H 44psi 65% .0308ns .0126ns 95% 100% N x 15psi N x 36psi 95% .0110ns .0047ns 99% 100% Ar 15psi Ar 36psi Ar 4 l p s i 80% .0230ns .0096ns .0084ns 96% 97% 92% 96% T h i s t a b l e uses the observed asymmetry and equation ( c o s ( w B t ) = A ^ v ) to obtain an estimate of the time spent as a neu t r a l i n the s i n g l e t s t a t e . With t h i s estimate and the f a c t that t h i s time i s i n v e r s e l y r e l a t e d to the pressure of the ta r g e t , the asymmetry at a d i f f e r e n t pressure can be p r e d i c t e d . As can be seen above, the agreement i s q u i t e s a t i s f a c t o r y . T a b l e 3.9. D e p o l a r i z a t i o n e s t i m a t e d from t o t a l asymmetry as a f u n c t i o n of p r e s s u r e . The. lower p r e s s u r e Aft\>5 i s used t o e s t i m a t e t h e time the muonium i s i n a s i n g l e t s t a t e ( d u r i n g t h e r m a l i z a t i o n ) from e q u a t i o n 3.19. T h i s time i s then s c a l e d t o the h i g h e r p r e s s u r e t a r g e t where the A^Vs can be p r e d i c t e d and compared t o the e x p e r i m e n t a l l y o b s e r v e d v a l u e . 92 r e a s o n a b l e agreement w i t h some c a l c u l a t i o n s r e f e r r e d t o e a r l i e r ( c a l c u l a t e d from e q u a t i o n 3.7 and shown i n t a b l e s 3.2 and 3.3) f o r N c and t ^ u s i n g known p r o t o n c r o s s s e c t i o n s . These times a r e a f u n c t i o n of the 6*,0 and Gaf of t h e p a r t i c u l a r gas i n v o l v e d . I t i s c l e a r from the reduced t o t a l asymmetries i n t a b l e 3.5 and t a b l e 3.6 t h a t the s l o w i n g down ti m e s a r e of s u f f i c i e n t magnitude t o s i g n i f i c a n t l y d e p o l a r i z e the muon, p a r t i c u l a r l y a t p r e s s u r e s lower than 1 5 p s i . T h i s c o n c l u s i o n i s i n c o n t r a s t t o i n i t i a l s p e c u l a t i o n t h a t the t h e r m a l i z a t i o n t i m e s were f a r too s h o r t ( B r e w e r ( 1 9 7 5 ) , Hughes(1966)) t o cause l o s s of p o l a r i z a t i o n . S i n c e the muon undergoes about 100 charge c h a n g i n g c y c l e s b e f o r e t h e r m a l i z a t i o n , i t must be o n l y the l a s t c o u p l e of c y c l e s where d e p o l a r i z a t i o n o c c u r s . At lower e n e r g i e s , d u r i n g the l a t t e r s t a g e of t h e r m a l i z a t i o n , the or Mu p r o b a b l y undergoes s e v e r a l e l a s t i c c o l l i s i o n s which do not i n v o l v e charge exchange and the time between s u c c e s s i v e charge exchange c o l l i s i o n s i s i n c r e a s i n g . As noted p r e v i o u s l y , the a c c u mulated number of c h a rge c h a n g i n g c y c l e s N c f o r p r o t o n s and hence f o r muons has an a s y m t o t i c b e h a v i o r as a f u n c t i o n of energy ( f i g u r e 3.4). A f t e r about 9keV f o r p r o t o n s or 1keV f o r muons the charge c h a n g i n g c y c l e s a r e few and f a r between, as i s v e r i f i e d by the d r o p i n c r o s s s e c t i o n s a t lower e n e r g i e s (see f i g u r e 3.1). The i mportance of the l a s t few c o l l i s i o n s i s s u p p o r t e d by the c a l c u l a t i o n s of s l o w i n g down time as f o l l o w s ; the e s t i m a t e of the time spent as a n e u t r a l p a r t i c l e , "^H, d u r i n g 93 m o d e r a t i o n i n 4 5 p s i h e l i u m from 35keV (any h i g h e r energy i s s i m p l y d e s c r i b e d by the s l o w i n g of a charged p a r t i c l e muonium f o r m a t i o n i s i n s i g n i f i c a n t ) t o 1keV t o be 55x 1 0" 1' seconds. S i n c e t h e r e a r e r o u g h l y 110 charge changing c y c l e s and o n l y h a l f of the c y c l e s w i l l r e s u l t i n s i n g l e t muonium the time as s i n g l e t muonium i s o n l y 3 . 5x 1 0" 1 3 seconds . So cos (wt) =/. 0 . Thus one might expect 100% of t h e . t o t a l asymmetry t o be r e t a i n e d i n a 4 5 p s i h e l i u m t a r g e t . I n s t e a d we f i n d <70% ( t a b l e 3.6). C o n s e q u e n t l y , the l a s t few c y c l e s must be v e r y i m p o r t a n t i n the r e g i o n from 1keV t o t h e r m a l e n e r g i e s . T h i s c o n t e n t i o n i s born out by the o b s e r v e d asymmetries i n the r a r e gases where He has a low t o t a l asymmetry and a l s o has the l a r g e s t number of charge c h a n g i n g c y c l e s . S i m i l a r l y Xe and Kr have low asymmetries i n s p i t e of the r e l a t i v e l y l a r g e s t o p p i n g d e n s i t i e s because of the h i g h p r o b a b i l i t y of charge exchange even a t low e n e r g i e s i n these gases. F i n a l l y , i t s h o u l d be emphasized t h a t the p r e s s u r e dependent l o s s of asymmetry does not a f f e c t the o b s e r v e d r a t i o s of muonium t o muon asymmetries and thus the n e u t r a l and c h a r g e d f r a c t i o n s p r e v i o u s l y d e f i n e d f o r comparison w i t h s i m i l a r p r o t o n s t u d i e s can be i n v e s t i g a t e d w i t h o u t i n t e r f e r e n c e due t o the n a t u r e of the d e t e c t i o n t e c h n i q u e and any a s s o c i a t e d problems. T h i s i s i l l u s t r a t e d i n t a b l e 3.6 showing the p r e s s u r e dependence of A a^ s and the p r e s s u r e independence of the f 0 and f + . S i n c e the yjSR experiment o n l y g i v e s the f i n a l f r a c t i o n s a t t h e r m a l e n e r g i e s , (which 94 a r e not s i m p l y r e l a t e d t o the c r o s s s e c t i o n s ) comparisons w i t h p r o t o n d a t a may not be s t r a i g h t f o r w a r d . T h i s can be seen i n the f o l l o w i n g way. The p r o t o n f 0 and f + a r i s e from a 100% H* beam a t a g i v e n energy whereas the j j * beam slows from r o u g h l y 2MeV to..025 eV and the " i n i t i a l " beam a t a g i v e n energy w i l l be a m i x t u r e of n e u t r a l s and charged p a r t i c l e s . N e v e r t h e l e s s , e q u a t i o n 3.3 i s s t i l l e x p e c t e d t o be v a l i d so t h a t the p r o t o n d a t a can s t i l l be used f o r q u a l i t a t i v e p r e d i c t i o n s of e x p e c t e d r e s u l t s f o r muons and s i m i l a r l y t he muon experiment s h o u l d s t i l l be a b l e t o p r e d i c t the b e h a v i o r of p r o t o n s i n gases. 3.5. Muonium Formation In Pure P o l y a t o m i c Gases As w i t h the r a r e gases p r e v i o u s l y d i s c u s s e d , p r o t o n charge exchange c r o s s s e c t i o n s a re a v a i l a b l e i n many p o l y a t o m i c gases (Tawara(1973), A l l i s o n ( 1 9 5 4 ) ) ; n o t a b l y H 2, N^, CHq. and NHj, which have been s t u d i e d i n t h i s t h e s i s . The energy dependence of the n e u t r a l f r a c t i o n s f 0 from p r o t o n charge exchange a r e shown i n f i g u r e s 3.13 t o 3.16. C l e a r l y , they r e f l e c t -the t r e n d s d i s c u s s e d e a r l i e r ( t a b l e 3.1, M a s s e y ( 1 9 5 4 ) ) . Based on thes e d a t a , the low energy 95 asymptote s h o u l d y i e l d o b s e r v a b l e Mu f r a c t i o n s of 0.9. i n H x, 0.80 i n N zand 1 .0 i n both CH^ and NH 3 (both of which a r e e x o t h e r m i c f o r Mu f o r m a t i o n r i g h t down t o t h e r m a l e n e r g i e s ) . T y p i c a l e x p e r i m e n t a l s p e c t r a f o r N 7 have been r e f e r r e d t o e a r l i e r ( f i g u r e 1.6); a sample s p e c t r a f o r NH^ i s shown i n f i g u r e 3.17. T a b l e 3.10 compares the r e l a t i v e f r a c t i o n s f 0 and f + a t each p r e s s u r e s t u d i e d , w i t h the e x p e c t e d n e u t r a l f r a c t i o n s based on the p r o t o n charge exchange d a t a ( f i g u r e s 3.13 t o 3.16). As w i t h the r a r e gases p r e v i o u s l y d i s c u s s e d , one c o u l d say t h a t the t r e n d s are r e a s o n a b l y reproduced i n the case of n i t r o g e n g i v e n the e x t r a p o l a t i o n s i n v o l v e d . The n o t a b l e e x c e p t i o n s , however, a r e the f 0 and f + f o r NH^ and CH^ where the i o n i z a t i o n p o t e n t i a l i n d i c a t e s t h a t t h e r e s h o u l d be 100% muonium f o r m a t i o n . I n s t e a d i t i s found t h a t a s i g n i f i c a n t f + remains ( t a b l e 3.10). A s i m i l a r a l t h o u g h not so s t r i k i n g d i s c r e p a n c y e x i s t s i n the case of H^ as w e l l . These d i s c r e p a n c i e s can be u n d e r s t o o d i n terms of hot atom r e a c t i o n s of -the Mu atom. A f t e r emerging from the charge exchange regime, and p r i o r t o i t s e v e n t u a l t h e r m a l i z a t i o n , Mu i s s t i l l h i g h l y e p i t h e r m a l (-^20eV) r e l a t i v e t o t y p i c a l c h e m i c a l bond e n e r g i e s . Chemical r e a c t i o n s , p a r t i c u l a r l y h i g h l y endothermic H atom a b s t r a c t i o n and s u b s t i t u t i o n r e a c t i o n s , a r e then p o s s i b l e ; Mu+NH3 >NHj_Mu+H 3.20 96 UJ CD O Cn Q >— CO I— I Q > >— CD cn UJ o v— o cn LO o LO o LO o LO o O CD CD CO o •—i O o o o o o o •3ZI~ltiyin3N NOIiDHcJJ F i g u r e 3.13. Hydrogen n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). 97 i r 11 o o o E E B S-O O B B 3 CO I— I o > L U CD : o a B B B a a >— CD CH U J -z. LU •z. o I— o ct: •_ in o LO o LO o LO o o CD CO CO —< o o o o o o o o o Q3ZIlHyin3N N0I13Ud3 F i g u r e 3.14. N i t r o g e n n e u t r a l f r a c t i o n c a l c u l a t e d from A l l i s o n ( 1 9 5 8 ) and Tawara(1973). 98 c n o 2: z: CE LO O LO 0 LO O CD r- CD «—« O 0 O 0 0 CO LO .—« o ° 0 0 O 0 03ZPbain3N NOIlGHclJ F i g u r e 3.15. A l Ammonia n e u t r a l f r a c t i o n c a l c u l a t e d l i s o n d 958) and Tawara (1 973). from o o o X x x < — X o cn LO o CD LO o ro i n o ° o o o O o o o o . Methane n e u t r a l f r a c t i o n c a l c u l a t e d A l l i s o n ( 1 9 5 8 ) and Tawara(1973) . AMMONIR MUONIUM 5.IGNRL 7 GRUSS -U .20 0 . 0 0 . 5 1 . 0 1 . 5 2.0 2 RMMONIR MUON 5IGNRL 7 0 GRUSS 0.0 3 . 0 A sec F i g u r e 3.17. NH S ( t ) f o r muon and muonium. 101 Tar g e t Gas f e f + E r r o r f D ( H ) N i t r o g e n 83% 17% 4 80% Hydrogen 61% 39% 4 90% Methane 86% 14% 4 100% Ammonia 90% 10% 4 100% The gases were a l l unpurif jei with the exception of the hydrogen which was p u r i f i e d through an a c t i v a t e d charcoal trap at l i q u i d nitrogen temperature. T a b l e 3.10. N e u t r a l f r a c t i o n s observed f o r muons i n the p o l y a t o m i c gases and compared to p r o t o n e x t r a p o l a t i o n s . 1 02 Mu+CH4 >MuH+CH^ 3 # 2 T Mu+CH^ >CH3Mu+H 3.22 Si n c e such r e a c t i o n s o ccur a t time z e r o , they a re not a f f e c t e d by the a p p l i e d magnetic f i e l d and hence a r e ex p e c t e d t o c o n t r i b u t e t o an i n c r e a s e d d i a m a g n e t i c f r a c t i o n f + . T h i s concept was i n f a c t the b a s i s f o r e a r l y Mu c h e m i s t r y s t u d i e s i n l i q u i d s ( B r e w e r ( 1 9 7 5 ) ) . S i m i l a r l y , i n the gas phase, such hot atom r e a c t i o n s c o u l d p r o v i d e an e x p l a n a t i o n f o r the anomalously h i g h f + f o r H l f NH 3 and CHjj v a l u e s i n t a b l e 3.10. T h i s i n t e r p r e t a t i o n i s not d e f i n i t i v e but s u g g e s t s an i n t e r e s t i n g a r e a f o r f u t u r e s t u d y . Not o n l y a r e hot atom r e a c t i o n s i n t e r e s t i n g i n t h e i r own r i g h t ( S h i z g a l ( 1 9 8 0 ) , Wolfgang(1965)) but t h e i r s tudy c o u l d shed some l i g h t on a c u r r e n t c o n t r o v e r s y s u r r o u n d i n g muonium f o r m a t i o n i n l i q u i d s ( P e r c i v a l ( 1 9 8 1 ) , W a l k e r ( 1 9 8 1 ) ) . The d a t a i n t a b l e 3.11 shows the a b s o l u t e asymmetry i n the p o l y a t o m i c gases compared t o s i m i l a r (or lo w e r ) d e n s i t y r a r e gases. In a l l c a s e s , the r a r e gases have a lower a b s o l u t e asymmetry. T h i s e f f e c t i s a s c r i b e d t o the more e f f i c i e n t t h e r m a l i z a t i o n of t h e muon or muonium i n a p o l y a t o m i c moderator. In the r a r e gases, e l a s t i c c o l l i s i o n s ( f o r e n e r g i e s below e l e c t r o n i c e x c i t a t i o n s ) a r e the o n l y means f o r energy l o s s (and a r e q u i t e i n e f f i c i e n t ) whereas i n 1 03 Target Gas and I .P . Re l a t ive A, P ressure (eV) Charge Dens i t y Argon 15psi 15.8 270 80% N i t r o g e n 15psi 15.6 210 95% Argon 36psi 15.8 648 92% N i t r ogen 36psi 15.6 504 1 00% Ammonia 40psi 10.2 400 1 00% Methane 44psi 12.6 400 1 00% He 4 5ps i 24.5 90 63% Ne 30ps i 21.6 300 83% Kr 14psi 14.0 504 71% Xe 10psi 12.2 540 63% The p o s s i b i l i t y of an i n t e r f e r i n g w a l l s i g n a l i n t h e He, Ne , Xe c o u l d o n l y c a u s e t h e Aafc,«, t o be h i g h e r t h a n i t r e a l l y i s . Tab le 3 .11 . Abso lu t e asymmetry of po l ya tomic gases and e q u i v a l e n t d e n s i t y r a re gases . 1 04 p o l y a t o m i c systems v a r i o u s v i b r a t i o n a l and r o t a t i o n a l modes se r v e t o t h e r m a l i z e the muon or muonium r e l a t i v e l y q u i c k l y . T h i s l e s s e n s the importance of the l a s t few charge changing c o l l i s i o n s because of the s h o r t e r time spent i n t h i s c r i t i c a l low energy regime. E l a s t i c c o l l i s i o n s can l e a v e the muonium e p i t h e r m a l f o r many nanoseconds (because so l i t t l e energy i s l o s t per c o l l i s i o n as noted from e q u a t i o n 3 . 8 ) where the p o s s i b i l i t y of more charge changing c o l l i s i o n s can l e a d t o l o s s of asymmetry. T h i s e x p l a i n s the h i g h e r i n n i t r o g e n v e r s u s argon where the i o n i z a t i o n p o t e n t i a l and d e n s i t y a r e comparable and the o n l y s i g n i f i c a n t d i f f e r e n c e i s the p o s s i b i l t y of f a s t e r t h e r m a l i z a t i o n time i n n i t r o g e n . Note a l s o the ammonia and xenon t a r g e t s where i n both cases the i o n i z a t i o n p o t e n t i a l s are b oth s m a l l e r than t h a t of muonium and the t o t a l t a r g e t d e n s i t i e s were comparable, yet the ammonia has the h i g h e r a b s o l u t e asymmetry. In g e n e r a l t h e n , i t can be s t a t e d t h a t the i n c r e a s e d e f f i c i e n c y f o r t h e r m a l i z a t i o n ( h i g h e r energy l o s s per c o l l i s i o n due t o p o s s i b l e v i b r a t i o n a l and r o t a t i o n a l e x c i t a t i o n s ) l e a d s t o h i g h e r f i n a l asymmetries i n p o l y a t o m i c gas t a r g e t s . F i n a l l y i t s h o u l d be noted t h a t the f Q and f+ f o r the p o l y a t o m i c gases may be somewhat q u e s t i o n a b l e s i n c e these gases were not p u r i f i e d i n any way ( w i t h the e x c e p t i o n of the hydrogen which was p u r i f i e d u s i n g an a c t i v a t e d - c h a r c o a l t r a p a t l i q u i d n i t r o g e n t e m p e r a t u r e ) . A l l of the c o n c l u s i o n s i n t h i s s e c t i o n , however, a r e u n a f f e c t e d by 1 05 whatever s m a l l i m p u r i t i e s may have been p r e s e n t . As shown i n s e c t i o n 3.6, the t o t a l asymmetry i s not changed by i m p u r i t i e s and i t i s u n l i k e l y t h a t an i m p u r i t y a t the ppm l e v e l can cause an i n c r e a s e i n the f + . I f a n y t h i n g , the e f f e c t s a s c r i b e d t o hot atom p r o c e s s e s are even g r e a t e r than d e s c r i b e d s i n c e any i m p u r i t y would te n d t o g i v e a l a r g e r than normal f 0 r a t h e r than the l a r g e r than e x p e c t e d f + t h a t i s t a k e n as e v i d e n c e f o r hot atom p r o c e s s e s . 3.6. Muonium Formation In Doped Rare Gases The study of muonium f o r m a t i o n i n gas m i x t u r e s i s i n t e r e s t i n g i n t h a t i t p r o v i d e s a d d i t i o n a l i n f o r m a t i o n on the mechanisms of charge exchange and, i n one c a s e , on hot atom r e a c t i o n s as w e l l . P r e v i o u s s t u d i e s of t h i s n a t u r e have been c a r r i e d out by Stambaugh(1972) a t r e l a t i v e l y h i g h moderator p r e s s u r e s i n He and Ne but o n l y a t two d i f f e r e n t p a r t i a l p r e s s u r e s of added Xe. In t h i s t h e s i s Ne was chosen p r e f e r e n t i a l l y as an i n e r t moderator s i n c e t h e r e i s r e l a t i v e l y l i t t l e muonium f o r m a t i o n and, u n l i k e h e l i u m , i t i s dense enough t o p r o v i d e a good s i g n a l a t low p r e s s u r e s . Complete s t u d i e s (up t o 5 d i f f e r e n t p a r t i a l p r e s s u r e s ) were c a r r i e d out f o r Ne doped w i t h A r , Xe, CH^, and NH^. Some 106 r e s u l t s were a l s o o b t a i n e d f o r Xe and NH^ i n He. F i g u r e 3.18 ( t o p ) shows the jiSR s i g n a l f o r pure Ne a t I 8 p s i . The mid d l e p a r t of the same f i g u r e shows the e f f e c t of adding 200ppm Xe (--0 . 6x 1 0 1 6atoms/cm 3) on the jiSR s i g n a l w h i l e the bottom p a r t shows the c o r r e s p o n d i n g MSR s i g n a l . Very s i m i l a r c o n c e n t r a t i o n dependent s i g n a l s were o b t a i n e d f o r CHJJ, and NHj. The a d d i t i o n of A r , on the o t h e r hand, r e s u l t s i n a v e r y d i f f e r e n t c o n c e n t r a t i o n dependence. F i g u r e 3.19 (top) shows the e f f e c t of a d d i n g 1930ppm argon t o the juSR s i g n a l w h i l e the bottom of t h a t f i g u r e shows the e f f e c t on the MSR s i g n a l . I t i s i n t e r e s t i n g t o compare f i g u r e s 3.18 and 3.19 from two p o i n t s of view; the i n i t i a l a m p l i t u d e and the r e l a x a t i o n . In f i g u r e 3.18 the a d d i t i o n of the s m a l l amount of xenon causes a l a r g e l o s s i n ^ JSR a m p l i t u d e and a l s o a s m a l l r e l a x a t i o n of the r e m a i n i n g muon s i g n a l (but a l a r g e i n c r e a s e i n MSR a m p l i t u d e ) . I n f i g u r e 3.19, however, the l o s s of asymmetry f o r a much l a r g e r amount of added argon i s s i m i l a r but no r e l a x a t i o n of the r e m a i n i n g muon s i g n a l i s ob s e r v e d . The e f f e c t s of add i n g NH^ or CH^ a r e s i m i l a r t o t h a t of xenon i n t h a t t h e r e i s a l a r g e l o s s of a m p l i t u d e but t h e r e i s l i t t l e i f any r e l a x a t i o n of the r e m a i n i n g muon s i g n a l . Note t h a t muonium f o r m a t i o n i s e x o t h e r m i c f o r xenon, ammonia and methane but not f o r argon. The r e l a x a t i o n of the muon s i g n a l i s a t t r i b u t e d t o muon m o l e c u l a r i o n s as d i s c u s s e d i n the next c h a p t e r . The l o s s of a m p l i t u d e of the muon s i g n a l i s a t t r i b u t e d t o e p i t h e r m a l T 1 1 r 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 TIME l u S ) -0.10 \-0.0 0.5 1.0 1.5 2.0 2.5 3.0 TIME IN iiSEC £ 0 NSEC/Blh) F i g u r e 3.18. Neon w i t h xenon i m p u r i t y showing the e f f e c t o the muon and muonium S ( t ) . The t o p f i g u r e shows the pSR s i g n a l i n pure neon a t I 8 p s i . The mi d d l e f i g u r e shows^the e f f e c t of add i n g 200ppm Xe. The bottom f i g u r e shows the e f f e c t of t h i s Xe on the MSR s i g n a l . 108 0 0.5 1 0 1 5 2.0 2.5 3.0 3.5 4.0 0.10 0.05 h o.oo H -0.05 -0.10 0.0 0.5 1.0 1.5 2.0 2.5 T I M E IN u S E C (20 N S E C / B I N ) F i g u r e 3.19. Neon w i t h argon i m p u r i t y showing the e f f e c t on the muon and muonium S ( t ) . The t o p f i g u r e shows the e f f e c t of a d d i n g I930ppm of argon t o the muon s i g n a l w h i l e the bottom f i g u r e shows the e f f e c t on the c o r r e s p o n d i n g muonium s i g n a l . 109 muonium f o r m a t i o n . From such s i g n a l s , the a m p l i t u d e s A ^ u and hp are found as a f u n c t i o n of c o n c e n t r a t i o n of added r e a g e n t . The da t a o b t a i n e d f o r the v a r i o u s m i x t u r e s s t u d i e d i s found i n t a b l e 3.12. F i g u r e s 3.20 t o 3.23 i l l u s t r a t e some of the t a b u l a t e d d a t a i n g r a p h i c a l form. I t can be seen t h a t , w i t h i n the e r r o r s , the t o t a l asymmetry i s c o n s t a n t . T h i s i s c o n f i r m a t i o n t h a t muonium f o r m a t i o n i n these systems i s an e p i t h e r m a l p r o c e s s , even though i t i s e n e r g e t i c a l l y a l l o w e d a t t h e r m a l e n e r g i e s ( f o r Xe, CH^. and NH^). I f i t were t h e r m a l , then the muonium f o r m a t i o n would oc c u r a t random t i m e s , l e a d i n g t o no coheren c e , and hence no o b s e r v a b i I t y , of the muonium p r e c e s s i o n . In r a r e gas m i x t u r e s such as Ne p l u s ppm i m p u r i t i e s of Xe one sees muonium f o r m a t i o n t y p i c a l of the Xe, even though i t i s p r e s e n t i n such s m a l l amounts (see t a b l e 3.12 and f i g u r e 3.20). E s s e n t i a l l y the same t r e n d i s observed w i t h He: t h e r e f o r e i t i s independent of moderator gas. Stambaugh(1972) a l s o measured the r e l a t i v e f r a c t i o n s i n v a r i o u s gas m i x t u r e s of xenon w i t h h e l i u m and neon. The agreement between the p r e s e n t r e s u l t s and those of Stambaugh i s w i t h i n the e r r o r s but as noted f o r the pure gases, the p o s s i b i l t y of i n t e r f e r i n g w a l l s i g n a l s can d r a s t i c a l l y reduce the f 0 and i n c r e a s e the f + . As noted p r e v i o u s l y , the r e l a t i v e f r a c t i o n s a r e e x p e c t e d t o be independent of p r e s s u r e and hence can be compared d i r e c t l y by q u o t i n g the i m p u r i t y l e v e l s i n ppm. In neon and ammonia m i x t u r e s , because of the low i o n i z a t i o n p o t e n t i a l of NH^, the muonium 1 10 Muonium Asymmetry (x2) in Xenon doped Neon; 7gauss C o n c e n t r a t i o n ^ 1 6 ) Asymmetry atoms/cc e r r o r e r r o r 0.00 0. 1 63 0.34 0.854 1 .35 0.00 0.02 0.03 0.09 0.15 0.048 0.11 0. 1 32 0.16 0.210 0.014 0.014 0.014 0.014 0.014 Muon Asymmetry in Xenon doped Neon;70gauss C o n c e n t r a t i o n ( 1 0 1 6 ) Asymmetry atoms/cc e r r o r V e r r o r 0.00 0. 1 63 0.34 0.67 0.854 1 .35 0.00 0.02 0.03 0.07 0.09 0 . 1 5 0.24 0.12 0.095 0.049 0.048 0.007 0.014 0.014 0.014 0.014 0.014 0.014 Tab le 3 .12. M ix tu re asymmetr ies fo r doped gases . 111 Muonium Asymmetry (x2) i n Xenon doped Helium;7gauss C o n c e n t r a t i o n d O 1 6 ) Asymmetry atoms/cc e r r o r ^Mw, e r r o r 0.0 0.0 0.014 0.0140 0.85 0.10 0.092 0.0140 1.66 0.199 0.096 0.0080 3.8 0.456 0.102 0.0030 Muon Asymmetry Xenon doped Helium;70gauss C o n c e n t r a t i o n ( 1 0 1 6 ) Asymmetry atoms/cc e r r o r A^A e r r o r 0.0 0.0 0.154 0.004 0.85 0.10 0.083 0.004 1.66 0.199 0.053 0.004 3.8 0.456 0.039 0.005 T a b l e 3.12. C o n t i n u e d Muonium Asymmetry (x2) C o n c e n t r a t i o n ( 1 0 1 6 ) atoms/cc e r r o r in Ammonia doped Neon;7gauss Asymmetry A ^ t t o , e r r o r 0.0 0.00 0.048 0.004 0.18 0.02 0.124 0.006 0.66 0.07 0.176 0.007 0.33 0.04 0.166 0.007 1.36 0.13 0.194 0.009 Muon Asymmetry in Ammonia doped Neon*, 70gauss C o n c e n t r a t i o n ( 1 0 1 6 ) Asymmetry atoms/cc e r r o r (\ ^  e r r o r 0.0 0.00 0.22 0.01 0.18 0.02 0.11 0.010 0.33 0.04 0.09 0.009 0.66 0.07 0.036 0.006 1.36 0.13 0.028 0.004 Tab le 3 .12. Cont inued 1 1 3 Muonium Asymmetry (x2) in Argon doped Neon;7gauss C o n c e n t r a t i o n ( 1 0 1 6 ) Asymmetry atoms/cc e r r o r ^ e r r o r 0.0 0.00 0.048 0.010 1.6 0.16 0.074 0.008. 3.42 0.376 0.114 0.012 5.76 0.749 0.140 0.014 Muon Asymmetry in Argon doped Neon;70gauss C o n c e n t r a t i o n ( 1 0 1 6 ) Asymmetry atoms/cc e r r o r A^A. e r r o r 0.0 0.0 0.194 0.006 1.6 0.16 0.157 0.004 3.42 0.376 0.135 0.005 5.76 0.749 0.080 0.007 Tab le 3 .12. Cont inued 1 1 4 Muonium Asymmetry (x2) i n Methane doped Neon;7gauss C o n c e n t r a t i o n ( 1 0 1 6 ) Asymmetry atoms/cc e r r o r e r r o r 0.0 0.00 0.048 0.010 0.425 0.0595 0.176 0.010 0.85 0. 1 02 0. 1 92 0.010 1 .7 0. 187 0.24 0.010 Muon Asymmetry i n Methane doped Neon;70ga C o n c e n t r a t i o n ( 1 0 1 6 ) Asymmetry atoms/cc e r r o r A u. p r r n r 0.0 0.0 0. 194 0.006 0.425 0.0595 0.050 0.006 0.85 0. 102 0.037 0.006 1 .7 0. 187 0. 020 0.006 Tab l e 3.12. C o n t i n u e d 1 15 I O 2 1 (_) I 2 1 o I— cr c_> o c_> o LU X 0 0 0 JlcJ13NNASb o F i g u r e 3.20. Mu and muon asymmetries f o r neon ( l 8 p s i ) and xenon m i x t u r e s . 1 1 6 f o r m a t i o n c r o s s s e c t i o n s a r e e x p e c t e d t o be l a r g e even a t low e n e r g i e s . When the i m p u r i t y gas has a h i g h e r i o n i z a t i o n p o t e n t i a l than muonium, the r i s e of f 0 as a f u n c t i o n of c o n c e n t r a t i o n i s more g r a d u a l . T h i s i s d r a m a t i c a l l y i l l u s t r a t e d i n the case of argon i n neon where complete muonium f o r m a t i o n r e q u i r e s much l a r g e r c o n c e n t r a t i o n s than i n the case of xenon. T h i s i s a r e f l e c t i o n of the f a c t t h a t 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 s a t low e n e r g i e s a re much s m a l l e r than f o r xenon or ammonia (see f i g u r e s 3.23 and 3.22 of neon and argon and neon and methane) and a r e comparable t o neon i t s e l f . At h i g h e r e n e r g i e s 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 s f o r neon and h e l i u m a r e q u i t e l a r g e and can o f f s e t the l a r g e r muonium f o r m a t i o n or 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 s of the argon. These c r o s s s e c t i o n s drop o f f r a p i d l y a t lower e n e r g i e s where the much l a r g e r 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 something l i k e xenon can dominate t o l e a d t o u n u s u a l l y l a r g e n e u t r a l f r a c t i o n s i n the s e ppm m i x t u r e s . These e f f e c t s a r e a g a i n i n d i c a t i o n s of the importance of the l a s t few c o l l i s i o n s where an i m p u r i t y gas can be v e r y i m p o r t a n t i n d e t e r m i n i n g the f i n a l muonium or n e u t r a l f r a c t i o n ; i . e . j u s t p r i o r t o b e i n g t h e r m a l i z e d a ppm i m p u r i t y w i t h a s i g n i f i c a n t l y d i f f e r e n t €" / 0 and &rol c r o s s s e c t i o n than the moderator i t s e l f can p l a y an i m p o r t a n t r o l e . S i m i l a r l y one would expect i m p u r i t i e s w i t h s i m i l a r c r o s s s e c t i o n b e h a v i o r (as the moderator) t o have a much s m a l l e r e f f e c t -- e x a c t l y as obser v e d e x p e r i m e n t a l l y i n the 1 1 7 II + X II X LU CO <_> I 2 1 O t— CL CJ •z. o (_) CO LO O LO o (XI <\J O o o o LO O O O O F i g u r e 3.21. Mu and muon asymmetries f o r ammonia m i x t u r e s . neon ( I 8 p s i ) and 1 18 i z: o t— CE C J z. o C J o CD LY. CE F i g u r e 3.22. Mu and muon asymmetries f o r neon d 8 p s i ) and argon m i x t u r e s . 1 19 x 21 CJ I O I— cx CJ z o CJ L U z CL t— L U LO o in o LO (\J oo O O o o o O o o AcJ13WWASd F i g u r e 3.23. Mu and muon asymmetries methane m i x t u r e s . f o r neon ( I 8 p s i ) and 120 case of argon (see f i g u r e 3.22). T h i s i s why o n l y a s m a l l amount of xenon (or methane or ammonia) i m p u r i t y can have such a d r a m a t i c e f f e c t upon the muonium f r a c t i o n i n a neon moderator. The muon a t low e n e r g i e s t h a t has a s m a l l p r o b a b i l i t y of e l e c t r o n c a p t u r e from neon or h e l i u m , may c o l l i d e w i t h a xenon where i t s t i l l would have a l a r g e p r o b a b i l i t y of e l e c t r o n c a p t u r e t o form muonium. Such a l e v e l of s e n s i t i v i t y i s the reason why i t was n e c e s s a r y t o take s p e c i a l c a r e i n p u r i f y i n g the He and Ne; f o r example, even the u l t r a h i g h p u r i t y h e l i u m ( 9 9 . 9 9 9 % pure) s t i l l p roduced a muonium s i g n a l u n l e s s f i r s t passed through the hot t i t a n i u m p u r i f i e r . 121 4. MUON MOLECULAR ION FORMATION AND RELAXATION PROCESSES 4.1. R e l a x a t i o n In Pure Gases In t h i s s e c t i o n v a r i o u s r e l a x a t i o n phenomena observed f o r b o t h the muon and muonium w i l l be d i s c u s s e d , b e g i n n i n g w i t h pure i n e r t gases and then g o i n g on t o the r a r e gas m i x t u r e s where e v i d e n c e f o r t h e r m a l muonium f o r m a t i o n has been o b t a i n e d . The e f f e c t of an extended s t o p p i n g d i s t r i b u t i o n a t lower moderator p r e s s u r e s on the r e l a x a t i o n of the muon and muonium s i g n a l s has been r e f e r r e d t o e a r l i e r ( t a b l e 3.7). There i t was suggested t h a t these i n c r e a s e d r e l a x a t i o n s were due t o f i e l d inhomogeniety e f f e c t s . R e p r e s e n t a t i v e d a t a of i n t e r e s t i s shown i n t a b l e 4.1. I t can be seen t h a t , r o u g h l y s p e a k i n g , the X (Mu) i s t y p i c a l l y 10 t i m e s the muon v a l u e and, moreover, both change d r a m a t i c a l l y w i t h p r e s s u r e . T h i s type of b e h a v i o r i s what one would expect from f i e l d i n h o m o g e n i e t i e s . As noted i n e q u a t i o n 2.1, the f i e l d 122 inhomogeniety AB i s r e l a t e d t o t h e \ by X=1/^%~#AB/2. The inhomogeniety a l o n g the beam d i r e c t i o n i s most i m p o r t a n t and, as can be seen from f i g u r e 2.4, i s e a s i l y l a r g e enough t o account f o r the o bserved X v a l u e s . S i n c e ^=1.39x10* w h i l e Xfll(= 1 . 35x 1 0 6 , a t any f i e l d t h i s f a c t o r of r o u g h l y 100 s h o u l d l e a d t o a 100 t imes l a r g e r X f o r the muonium s i g n a l compared t o the muon s i g n a l . From t a b l e 4.1 i t i s c l e a r t h a t t h e r e i s g e n e r a l l y o n l y a f a c t o r of 10 d i f f e r e n c e . T h i s i s due t o the f a c t t h a t the muon s i g n a l i s o b s e r v e d at 10 t i m e s the magnetic f i e l d as the muonium s i g n a l , hence AB i s t en t i m e s l a r g e r i n the muon c a s e . The net e f f e c t then i s t o d e c r e a s e XtyT) by o n l y a f a c t o r of 10 compared t o X(Mu). A l t h o u g h the f i e l d i n h o m o g e n i e t i e s appear t o account f o r the o b s e r v e d pure gas r e l a x a t i o n s , t h e r e a r e o t h e r more i n t e r e s t i n g d e p o l a r i z a t i o n mechanisms, which a r e s m a l l e r e f f e c t s but i n t e r e s t i n g c a s e s f o r f u t u r e s t u d y . One i s a d i p o l e i n t e r a c t i o n between the e l e c t r o n s p i n i n muonium and the n u c l e a r s p i n of v a r i o u s g a s e s , n o t a b l y xenon, which c o u l d be c o n t r i b u t i n g t o the o b s e r v e d Mu r e l a x a t i o n r a t e . Another i s a s p i n - i n t e r m o l e c u l a r r o t a t i o n mechanism which i n v o l v e s an a n g u l a r momentum c o u p l i n g . I f the c o l l i d i n g s p e c i e s ( i n t h i s case muonium and xenon) form a d i a t o m i c m o l e c u l e f o r a s h o r t time the r o t a t i o n a l motion can c o u p l e t o the s p i n a n g u l a r momentum t o d e p o l a r i z e the muon. These e f f e c t s have been s t u d i e d w i t h the r e l a x a t i o n of r u b i d i u m vapour i n t e r a c t i n g w i t h v a r i o u s gases and i t was shown 123 ( T o r r e y ( 1 9 6 3 ) , F r a n z e n ( 1 9 5 9 ) , C h e n ( l 9 6 7 ) , V o l k ( l 9 B 0 ) ) t h a t by f a r the major c o n t r i b u t i o n t o r e l a x a t i o n was the r o t a t i o n a l a n g u l a r momentum c o u p l i n g . T h i s depends upon the t r a n s i e n t f o r m a t i o n of a d i a t o m i c s p e c i e s which i n t u r n depends upon the r e l a t i v e v e l o c i t y of the c o l l i d i n g s p e c i e s . I f we s c a l e the Rb-Xe c r o s s s e c t i o n v i a r e l a t i v e v e l o c i t y t o the Mu-Xe system we f i n d a \ <10" 3 ^ i s ~ 1 which i s not o b s e r v a b l e w i t h the p r e s e n t a p p a r a t u s . R o t a t i o n a l c o u p l i n g s of a n g u l a r momenta may p l a y an i m p o r t a n t r o l e i n the d e p o l a r i z a t i o n and hence the observed r e l a x a t i o n s i n m o l e c u l a r i o n systems such as He^j* and Nejj* . In t h e s e c a s e s i t i s an i n t r a m o l e c u l a r d i p o l e - d i p o l e or s p i n - r o t a t i o n a l c o u p l i n g as opposed t o t h e s p i n i n t e r m o l e c u l a r r o t a t i o n a l mechanism d i s c u s s e d p r e v i o u s l y . In o r d e r t o a p p r e c i a t e t h e s e p r o c e s s e s , i t i s u s e f u l t o c o n s i d e r the p r o t o n s t u d i e s of Hardy (Hardy(1966) where 1/T^ (or f o r comparison X ) was measured i n hydrogen gas as a f u n c t i o n of d e n s i t y . The analogous muon system can be imagined t o be He^j* or more d i r e c t l y MuH. I t was found t h a t a t a d e n s i t y of 1.0 amagat;, 1 /T a = . 006^us" 1 . S i n c e i t i s w e l l known t h a t these r e l a x a t i o n s have a tf2 dependence and are i n v e r s e l y p r o p o r t i o n a l t o d e n s i t y (Bloom(1967), C h e n ( l 9 6 7 ) ) one c o u l d expect t o observe X = 1 /T7 =. 06yus ~ 1 i n the c o r r e s p o n d i n g muon system ( s i n c e ^ = 1 / 3 ^ ) . Note t h a t t h e r e are two c o n t r i b u t i o n s t o t h i s r e l a x a t i o n : a d i p o l a r term w i t h ^ * dependence and the s p i n r o t a t i o n term w i t h 2 dependence ( C h e n ( l 9 6 7 ) . As shown by H a r d y d 9 6 6 ) , the 124 d i p o l a r term i s n e g l i g i b l e and can be i g n o r e d even i n the muon systems. T h i s p r e d i c t e d muon r e l a x a t i o n of ,06^s~ 1 i s e s s e n t i a l l y b u r i e d i n the a m p l i t u d e of the magnetic f i e l d i n h omogeniety. These e f f e c t s a r e e x p e c t e d t o be g r e a t e s t i n MuH or Heyu* systems but u n f o r t u n a t e l y the low d e n s i t i e s of these t a r g e t s f o r c e s one t o use h i g h e r p r e s s u r e s where -the r e l a x a t i o n s become s m a l l e r and s m a l l e r compared t o the f i e l d e f f e c t s . For example a t a t y p i c a l t a r g e t p r e s s u r e of 40 p s i 1/T2 =. 003^JS" 1 (H a) which l e a d s t o a X f o r the muon experiment of o n l y .OSjjsec" 1. T h i s i s i n c o n t r a s t t o an e a r l i e r p r e d i c t i o n t h a t the muon s i g n a l i n gases would be g r e a t l y d e p o l a r i z e d i n m o l e c u l a r i o n s such as He^i + due t o a s p i n r o t a t i o n a l t ype of c o u p l i n g (Hughes(1957)). The f a c t t h a t the A 0 f o r the muon i s so s i m i l a r i n NH^, N z and Ar i s a l s o e v i d e n c e t h a t i t i s p r o b a b l y not due t o a s p i n r o t a t i o n i n t e r a c t i o n as suggested by Hughes ( t a b l e 4.1). T h i s i s not t o say t h a t these e f f e c t s a r e not p r e s e n t but t h a t they a re s m a l l compared t o the f i e l d inhomogeniety e f f e c t s . I t i s c l e a r , however t h a t t h i s c o u l d become an i n t e r e s t i n g area f o r f u t u r e study when improvements a r e made t o the magnetic f i e l d homogeniety. 125 Ta r g e t Gas and P r e s s u r e ^ Aluminum P l a t e N i t r o g e n I 5 p s i 0.43±.05 0.051.03 Hydrogen 4 5 p s i 0.811.06 0.071.02 Methane 15 p s i 0.411.04 0.101.03 Ammonia 4 0 p s i 0.301.02 0.04±.02 Heli u m 3 0 p s i 0.051.01 Neon 17psi 0.051.01 Argon 15psi 0.511.05 0.071.01 Kr y p t o n 6 p s i 0.761.12 Xenon 6 p s i 0.731.08 .0141.002 T a b l e ' 4 . 1 . o i n v a r i o u s pure gases. 126 4 . 2 . Muon R e l a x a t i o n In Gas M i x t u r e s D u r i n g the study of muonium f o r m a t i o n i n the r a r e gases and gas m i x t u r e s an i n t e r e s t i n g phenomenon was obser v e d f o r the f i r s t t i m e : the t h e r m a l r e l a x a t i o n of the ji* s i g n a l due to the a d d i t i o n of an i m p u r i t y gas. T h i s e f f e c t was i n f e r r e d i n e a r l y e x p e r i m e n t s u s i n g s u r f a c e muons at B e r k e l e y (Brewer 1 ( 1 9 7 5 ) ) but was not observed i n the gas m i x t u r e e x p e r i m e n t s a t h i g h moderator p r e s s u r e s by Stambaugh ( 1 972 ) . E q u a t i o n 4.1 g i v e s the JJSR s i g n a l a g a i n , where A i s the r e l a x a t i o n ( s p i n d ephasing) r a t e , A^ . i s the i n i t i a l a m p l i t u d e and w^  the p r e c e s s i o n f r e q u e n c y . S(t)=A |A.e" X*cos(yt+<^) 4.1 As i n muonium c h e m i s t r y s t u d i e s ( G a r n e r ( 1 9 7 9 ) ) , \ i s r e l a t e d t o a s i m p l e b i m o l e c u l a r r a t e c o n s t a n t k by the (pseudo) f i r s t o r d e r e x p r e s s i o n X=k [ x]+A 0 4 . 2 where [x] i s the c o n c e n t r a t i o n of i m p u r i t y gas and X i s the r e l a x a t i o n o bserved i n the pure moderator gas. Thus a p l o t of the obser v e d r e l a x a t i o n A v s . the c o n c e n t r a t i o n of the i m p u r i t y g i v e s the r a t e c o n s t a n t k. The da t a has been 127 t a b u l a t e d a l o n g w i t h the f i t t e d s l o p e s which c o r r e s p o n d t o the b i m o l e c u l a r r a t e c o n s t a n t s k i n t a b l e 4.2. The most complete s e t of data was o b t a i n e d f o r xenon i n neon and t h i s i s p l o t t e d i n f i g u r e 4.1. Some r e p r e s e n t a t i v e p o i n t s of the Xe d a t a a r e compared w i t h the c o n c e n t r a t i o n dependence of \ f o r Ar and CH^ i n Ne i n f i g u r e 4.2. S i m i l a r p l o t s f o r NH^ i n Ne, Xe i n He and NH 5 i n He a r e shown i n f i g u r e s 4.3 t o 4.5. Note the d r a m a t i c d i f f e r e n c e s i n s l o p e s (and hence r e a c t i o n r a t e s ) . The p h y s i c a l o r i g i n s of the o b s e r v e d t h e r m a l r e l a x a t i o n of the JJ* s i g n a l w i l l now be d i s c u s s e d , w i t h r e f e r e n c e t o the p o s s i b l e mechanisms l i s t e d i n t a b l e 4.3. R e a c t i o n 1, i n which a bare | T c o l l i d e s w i t h i m p u r i t y X f o r m i n g Mu was d i s c o u n t e d as a p o s s i b i l i t y because the o b s e r v e d r e a c t i o n i s not c o l l i s i o n c o n t r o l l e d as would be e x p e c t e d and a l s o because one would e x p e c t the same r a t e r e g a r d l e s s of moderator. In h e l i u m no r e l a x a t i o n i s o b s e r v e d whereas i n neon i t i s . Moreover, the r e a c t i o n w i t h NH^ i s v e r y slow a l t h o u g h i t i s i n f a c t t h e most e x o t h e r m i c . Note t h a t t h e r e i s no r e l a x a t i o n w i t h ( e n d o t h e r m i c ) argon. The e n e r g e t i c s suggest t h a t the JJ* must be bound i n some k i n d of m o l e c u l a r complex ( i . e . as a JU* m o l e c u l a r i o n ) , a s u g g e s t i o n f i r s t made some y e a r s ago (Brewer 1( 1975). The p o s s i b l e JJ" m o l e c u l a r i o n s formed a r e Ne^Li* (or HejJ + ) w i t h the moderator i t s e l f or p o s s i b l y Xyu* w i t h the i m p u r i t y gas X. However, s i n c e t h e r e a r e f a r more c o l l i s i o n s w i t h the moderator than w i t h the i m p u r i t y , the Muon R e l a x a t i o n i n Xenon doped Neon (Ifcpsi) A l l r e l a x a t i o n e r r o r s are one standard d e v i a t i o n . Concentration*10'«) R e l a x a t i o n ( j i s e c " 1 ) atoms/cc e r r o r e r r o r 0.0 0.0 0.083 0.009 0.0 0.01 0.083 0.014 0.163 0.025 0. 105 0.03 0.30 0.02 0.117 0.02 0.326 0.045 0.270 0.06 0.335 0.05 0.15 0.028 0.61 0.05 0.12 0.02 0.652 0.08 0.30 0.10 0.67 0.094 0.255 0.05 0.85 0.09 0.32 0.04 1 .34 0. 174 0.27 0.10 2.67 0.32 0.54 0.10 The r e l a x a t i o n r a t e k 4 i s 1.91.3x10" 1 1 cm'/atoms-sec. Table 4.2. R e l a x a t i o n s as a f u n c t i o n of added gas c o n c e n t r a t i o n f o r the gas m i x t u r e s s t u d i e d . Muon R e l a x a t i o n i n Argon doped Neon (l»psi) Concentration(10' *) Relaxation(jisec 1) atoms/cc e r r o r e r r o r 0.0 0.0 0.054 0.012 1.6 0.16 0.0565 0.011 3.42 0.376 0.061 0.0125 5.76 0.749 0.041 0.017 The r e l a x a t i o n r a t e kj_ i s -.0011.01x10"" cm 3/atoms-sec. Muon R e l a x a t i o n i n Methane doped Neon ( I 8 p s i ) ConcentrationOO'*) R e l a x a t i o n ( ^ s e c " ' ) atoms/cc e r r o r e r r o r 0.0 0.0 .054 .012 0.425 0.0595 .0845 .027 0.85 0. 102 .080 .034 1.7 0. 187 .1575 .043 The r e l a x a t i o n r a t e k^ i s 0.51.2X10"" cmVmolecules-sec Muon R e l a x a t i o n i n Ammonia doped Neon <18psi) Concentration(10' *) R e l a x a t i o n f j j s e c " ' ) atoms/cc e r r o r e r r o r 0.0 0.00 0.097 0.009 0.0 0.00 0.090 0.009 0.33 0.04 0.128 0.02 0.66 0.07 0.161 0.044 0.68 0.07 0.129 0.02 1.00 0.1 0.133 0.02 The r e l a x a t i o n r a t e k A i s 0.51.2X10-'' cm'/molecules-sec Table 4.2. Continued Muon R e l a x a t i o n i n Ammonia doped Helium (45psi) Concentration (10 1«) R e l a x a t i o n (jjsec -') atoms/cc e r r o r e r r o r 0.0 0.0 0. 11 0.01 0.36 0.04 0. 11 0.01 0.81 0.08 0. 136 0.01 1.08 0.11 0. 133 0.01 e r e l a x a t i o n r a t e *<l i s 0.25J.1X10 -1 ' Muon R e l a x a t i o n i n Xenon doped Helium (45psi) C o n c e n t r a t i o n ^ 1 ' ! atoms/cc e r r o r n c e n t r a t i o n * 10 1«) Relaxation(yjsec-1) e r r o r 0.0 0 .0 0 . 1 1 0.01 0.72 0 .07 0 .085 0.01 1 .02 0 .10 0 .12 0.01 The r e l a x a t ion r a t e k«l i s 0.0*.2X10" " cm Muon R e l a x a t i o n i n Xenon doped Neon (24psi and 333K) C o n c e n t r a t i o n d O " ) R e l a x a t i o n (usee - 1) atoms/cc e r r o r e r r o r 0.0 0.0 0.073 0.005 0.29 0.03 0.27 0.02 0.575 0.06 0.38 0.02 The r e l a x a t i o n r a t e k 4 i s 5.7*.7X10-'" cm 1/atoms-sec, Tab le 4 . 2 . Cont inued 131 MOLECULAR ION XENON IN NEON 0 . 6 0 0 . 5 0 -co 0 . 4 0 ZL L U t — cr cn z. o cr x cr _ i L U cn 0 . 3 0 -0 . 2 0 h 0 . 1 0 0 . 0 0 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 I M P . IN M O L E C U L E S - C M " 3 X 10" 1 6 3 . 0 F i g u r e 4 . 1 . Muon r e l a x a t i o n fo r xenon in neon ( I8ps i ) The ra te k^  = 1 . 9±. 3x 1 0" 1 1 cm 3 /atoms-sec . 1 32 Impurity in atom-crrr3x IO - 1 6 F i g u r e 4.2. Muon r e l a x a t i o n f o r xenon, methane and argon i n neon ( 1 8 p s i ) . The r a t e s a r e 1.9±. 3x10" 1 1, 5.4t2.4x10 - 1 2 and -0 cm 3/atom-sec f o r the xenon, methane and arg o n , r e s p e c t i v e l y . 133 MOLECULRR ION NHv IN NEON cn -< LU I— CE LY 0 . 5 0 0 . 4 0 h 0.30 h o 0 . 2 0 h CE X CE _ l LxJ LY 0 . 1 0 0 . 0 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 I M P . IN M O L E C U L E S - C M " 3 X 10" 1 6 1 . 2 i gu re 4 . 3 . Muon r e l a x a t i o n fo r ammonia in neon ( I 8ps i ) The ra te k d =5.0±2.Ox 1 0 " 1 2 cm 3 /mo l e cu l e- sec . 0.50 0.40 CO 0.30 CE LY o 0.20 CE X CE _J LU LY 0.10 F 0.00 1 1 1 1 I i °-° 0.2 0.4 0.6 0.8 1.0 1.2 IMP. IN MOLECULES-CM"3 X 10"16 F i g u r e 4.4. Muon r e l a x a t i o n f o r xenon i n h e l i u m (45ps The r a t e k A = 0.0±2.Ox 1 0 " 1 2 cm 3/atom-sec. 135 0 . 5 0 CO 3. L U I— cr cr 0 . 4 0 h 0 . 3 0 o 0 . 2 0 h CE X cr _ J L U cr. 0.10 7-0 . 0 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 I M P . IN M O L E C U L E S - C M " 3 X 10"3 6 1 . 2 F i g u r e 4.5. Muon r e l a x a t i o n f o r ammonia i n h e l i u m ( 4 5 p s i ) The r a t e k^ = 2.5±1.Ox 1 0 " 1 2 c m 3 / m o l e c u l e - s e c . 136 1 ) X >Mu + X* 2a) 2b) X=Xe AE=-l.4eV X-CH, A E — l . O e V X-NH3 AE=-3.4eV X-Ar AE-+2.2eV Neji* + X >Mu + X* + Ne X=Xe AE=+.33eV X-CHH AE-=+.73eV X«NHj AE=-1.63eV X=Ar AE=+3.93eV Heu*+ X >Mu + X* + He X=Xe AE=+.29eV X=NH3 AE=-1.7leV Neji 4 + X >Mu + X* + Ne f i r s t e x c i t e d s t a t e of Neyj* X=Xe AE—.77eV X=CHH AE=-.37eV X=NHj AE=-2.77eV X=Ar AE«+2.83eV Tab le 4 . 3 . P o s s i b l e r e a c t i o n paths f o r the muon mo lecu la r i o n . 1 37 3b) Heu*+ X >Mu + X* + He f i r s t e x c i t e d state of Heu X=Xe AE=-.30eV X=NH, AE»-2.3eV 4a) Neu*+ X 4b) He 5) —>Xu* + Ne X=Xe AE="2.8eV X=CH4, AE=-2.8eV X=NH3 AE=-6.9eV X=Ar AE=-l.8eV U*+ X >Xu* + He X=Xe AE=-3.leV X=NB> AE=-7.2eV X^ u*+ X >Mu + X* + X A - . O y i - i n pure NH 3 \ = . 1 0 / 4 S-. i n p u r e C H | | Summary of r e s u l t s Relaxation of muon s i g n a l i s observed in the Ne+Xe system and to a small extent in the Ne+CH,^  and Ne+NH^ systems. E s s e n t i a l l y no r e l a x a t i o n i s observed i n the He+Xe, Ne+Ar, and He+NHj systems. Table 4.3. C o n t i n u e d 138 f o r m a t i o n of s i g n i f i c a n t amounts of X.p* seems u n l i k e l y . Hence, r e a c t i o n 5 i s d i s c o u n t e d , a l s o on the grounds t h a t ^ i n the pure doping gases would be l a r g e r than o b s e r v e d i n t a b l e 4.1. T h i s l e a v e s t h r e e p o s s i b i l i t i e s f o r r e a c t i o n s of the Ne^j* (or He^J+) m o l e c u l a r i o n . R e a c t i o n . 4 i s almost c e r t a i n l y g o i n g on but i t l e a d s t o no o b s e r v a b l e r e l a x a t i o n . T h i s r e a c t i o n p r o v i d e s a ready e x p l a n a t i o n of the f a c t t h a t t h e r e i s a r e l a x a t i o n i n the xenon doped neon but not i n the ammonia doped neon. The l a c k of any s i g n i f i c a n t r e l a x a t i o n i n the ammonia systems can be e x p l a i n e d i n view of i t s l a r g e p r o t o n a f f i n i t y (9eV f o r NH 3 vs 4.9eV f o r Xe) (Walder(1980)) which would p r o b a b l y make r e a c t i o n 4 dominate i n the ammonia doped neon and h e l i u m . Thus one i s l e d t o c o n c l u d e t h a t r e a c t i o n s 2 or 3 must be r e s p o n s i b l e f o r t h e observ e d r e l a x a t i o n s . From the ground s t a t e v i b r a t i o n a l l e v e l s of Ne^j* or Hep*, however, the f o r m a t i o n of Mu i n r e a c t i o n 2 i s endothermic f o r a l l the systems o b s e r v e d except the neon and h e l i u m moderators doped w i t h ammonia, where no r e l a x a t i o n was observed anyway. From the f i r s t e x c i t e d s t a t e s of these i o n s , however, r e l a x a t i o n w i t h xenon and methane (and ammonia, a l t h o u g h i t i s u n u s u a l l y s m a l l ) i m p u r i t i e s s h o u l d be o b s e r v a b l e . T h i s i s in d e e d the case w i t h the Hep* i o n , but v e r y l i t t l e , i f any, r e l a x a t i o n i s seen w i t h the Heju* i o n . The b i n d i n g e n e r g i e s ( p r o t o n a f f i n i t i e s ) of the r a r e gas h y d r i d e i o n s a r e w e l l known (Walder(1980)) and by u s i n g a harmonic p o t e n t i a l w e l l , a s i m p l e z e r o p o i n t energy c o r r e c t i o n can be made f o r the c o r r e s p o n d i n g p* m o l e c u l a r \ 139 i o n e n e r g i e s . These v a l u e s a r e g i v e n i n t a b l e 4.4, which i n c l u d e s t h e e x p e r i m e n t a l and t h e o r e t i c a l p r o t o n d a t a . There s t i l l appears t o be an i n c o n s i s t e n c y , however, i n ' t h a t the c o r r e s p o n d i n g r e a c t i o n s w i t h h e l i u m moderators s h o u l d a l s o be o b s e r v a b l e . T h i s i n c o n s i s t e n c y can be r e s o l v e d when f o r m a t i o n and p o s s i b l e l i f e t i m e s of these e x c i t e d s t a t e s a re c o n s i d e r e d . F o r m a t i o n of the m o l e c u l a r i o n can occur i n two ways: a t e r m o l e c u l a r r e a c t i o n such a s : jj*+Ne+Ne > Ne^j*+Ne 4.3 or an e p i t h e r m a l two body c o l l i s i o n of the t y p e : Mu+Ne >NejLT+e" 4.4 Both p r o c e s s e s a r e l i k e l y t o produce the m o l e c u l a r i o n i n an e x c i t e d s t a t e . These same r e a c t i o n s a r e p o s t u l a t e d t o occur i n the He moderator, but i n t h i s case t h e r e must be an e f f e c t i v e mechanism f o r quenc h i n g the e x c i t e d s t a t e . I t s h o u l d be noted t h a t the r a d i a t i v e l i f e t i m e s of these m o l e c u l a r i o n s are e x p e c t e d t o be many t i m e s the muon l i f e t i m e of 2.2ps ( P a r k e r ( 1 9 6 4 ) ) . S i n c e t y p i c a l r a d i a t i v e l i f e t i m e s f o r s i m p l e d i a t o m i c s a re on the or d e r of m i l l i s e c o n d s (33ms f o r the v=1 s t a t e of CO (Massey(1971)) and a r e f u n c t i o n s of the square of the d i p o l e moment, one can e s t i m a t e the r a d i a t i v e l i f e t i m e of the v=V v i b r a t i o n a l 1 40 Molecular Ion De D 0 D , AE v-1—>v-0 ( a l l i n ev) HeH* 2.01.1 1.88 1.65 .23 from T o l l i v e r ( 1 9 7 9 ) NeH* 2.28*.1 2.1 1.7 .37 from Bondybey(1972) and Chupka(1968) Now us i n g the f a c t that bond s t r e n g t h and v i b r a t i o n a l e nergies vary i n v e r s e l y as the square root of the reduced mass of the v i b r a t i n g system, one can c a l c u l a t e the corresponding d i s s o c i a t i o n c o n s t a n t s f o r the muon molecular i o n s . Thus one has: Heu* 2.0 1.69 1.1 .62 Ne^T 2.3 1.73 0.63 1.1 Tab le 4 .4 . D i s s o c i a t i o n ene rg i e s fo r Ne and v = i s t a t e s . and He from v=0 141 s t a t e of the He^i + t o be about 33jusec ( i f the d i p o l e moment of the Hep* i s -10 times t h a t of CO) In o r d e r t o have a s m a l l p r o b a b i l i t y of d e - e x c i t a t i o n of any e x c i t e d v i b r a t i o n a l s t a t e s by c o l l i s i o n s w i t h moderator gas atoms ( i . e . v i b r a t i o n a l t r a n s l a t i o n a l energy t r a n s f e r ) , the c o n d i t i o n (a/d) (fi\>M, /TTkTM)»1 4.5 (Massey(1971), Hasted(1964)) must be s a t i s f i e d , where M, i s the mass of the moderator gas, M i s the mass of the m o l e c u l a r i o n , a i s the range of the i n t e r a c t i o n , d i s the a m p l i t u d e of the v i b r a t i o n , 0 i s the t r a n s i t i o n f r e q u e n c y and kT i s boltzmann's c o n s t a n t t i m e s t e m p e r a t u r e . Thus one can see t h a t the l i g h t e r i n e r t gases are most e f f i c i e n t i n c o l l i s i o n a l d e - e x c i t a t i o n of d i a t o m i c m o l e c u l e s (Massey(1971)) and t h a t the l a r g e r the t r a n s i t i o n energy (between v i b r a t i o n a l energy l e v e l s ) , the l o n g e r i s the l i f e t i m e of the e x c i t e d s t a t e . T h i s concept i s w e l l e s t a b l i s h e d i n the c o l l i s i o n s of d i a t o m i c m o l e c u l e s i n r a r e gas e n v i r o n m e n t s . For example i n CO i n He and Ar a t 15psi and room t e m p e r a t u r e , one f i n d s X = . 1 j j s e c " 1 , and .0001jjsec" 1 r e s p e c t i v e l y ( M a s s e y ( 1 9 7 1 ) ) . I f one can compare s i m p l e d i a t o m i c m o l e c u l e s w i t h the Ne^T and He^j* m o l e c u l a r i o n s , then i t i s r e a s o n a b l e t h a t the helium-muon m o l e c u l a r i o n r e l a x e s t o the ground s t a t e t h r o u g h c o l l i s i o n s w i t h the h e l i u m moderator b e f o r e b e i n g a b l e t o r e a c t w i t h any reagent 142 gas and t h a t the neon-muon m o l e c u l a r i o n i s i n i t s f i r s t e x c i t e d s t a t e l o n g enough t o r e a c t v i a r e a c t i o n 3 and show some d e p o l a r i z a t i o n . The t r a n s i t i o n energy i n CO i s a p p r o x i m a t e l y .27eV (Barrow(1962)) compared t o ,62eV f o r Hep* ( T o l l i v e r (1 979) ) and 1 . 1 eV f o r Ne^u+ (Bondybey (1 972 ) , Chupka(1968)). Thus i t i s q u i t e p o s s i b l e t h a t the f i r s t e x c i t e d s t a t e i s l o n g l i v e d enough i n the neon t o l e a d t o a r e l a x a t i o n but not i n a h e l i u m moderator. In a d d i t i o n the h e l i u m moderator must be run a t 4 3 p s i compared t o o n l y I 8 p s i f o r neon and t h i s a l s o c o n t r i b u t e s t o the r e l a x a t i o n of the v=1 s t a t e i n the h e l i u m more so than i n the neon. G i v e n the low r a t e of the measured m o l e c u l a r i o n r e a c t i o n s i n neon (1.9± 0.3x10" 1 1 cm 3/atom-sec f o r xenon and — 5 x 1 0 " 1 2 f o r methane and ammonia), i t i s l i k e l y t h a t r e a c t i o n 3 (which l e a d s t o d e p o l a r i z a t i o n of the muon) i s competing w i t h r e a c t i o n 4 (from t a b l e 4.3) and w i t h c o l l i s i o n s which put the m o l e c u l a r i o n i n the u n r e a c t i v e ground s t a t e , l e a d i n g t o a background J J * s i g n a l t h a t does not r e l a x . The e f f e c t of t h i s c o n s t a n t background i s t o reduce the observed r e l a x a t i o n s and indeed the r e l a x a t i o n s measured a r e a l r e a d y a t the edge of the s e n s i t i v i t y of the exper iment. I t may be noted t h a t i n e a r l i e r e x p e r i m e n t s by Stambaugh e t a l (Stambaugh(1972)), the p o s s i b l e f o r m a t i o n of JJ* m o l e c u l a r i o n s was commented upon but no r e l a x a t i o n was ob s e r v e d . Under the c o n d i t i o n s of t h a t experiment ( 3 8 2 p s i neon and 920ppm xenon) t h e r e s h o u l d have been a A = 1 8U S " 1 143 (based on the r a t e i n t a b l e 4.2) which would have wiped out the muon s i g n a l e n t i r e l y . In the Stambaugh e x p e r i m e n t s , de-e x c i t a t i o n c o l l i s i o n s which put the m o l e c u l a r i o n s i n t o the ground s t a t e must be the reason t h a t no r e l a x a t i o n was ob s e r v e d . S i n c e the p r e s s u r e s used t h e r e were 20x l a r g e r than those used i n t h i s work, the 20x s h o r t e r e x c i t e d s t a t e l i f e t i m e c o u l d e a s i l y render the muon r e l a x a t i o n u n o b s e r v a b l e g i v e n the p r e s e n t e x p e r i m e n t a l c a p a b i l i t i e s . A l t e r n a t i v e l y , an a p p r e c i a b l e w a l l s i g n a l due t o s c a t t e r e d muons from the t h i c k e n t r a n c e window i n Stambaugh's experiment would a l s o g i v e r i s e t o a z e r o r e l a x a t i o n . In a d d i t i o n t o the s h o r t e n e d l i f e t i m e of the muon m o l e c u l a r i o n s ' e x c i t e d s t a t e , the h e l i u m m o l e c u l a r i o n r e a c t i o n s c o u l d c o n c i e v a b l y be ren d e r e d u n o b s e r v a b l e due t o i n s t a b i l i t y of Hep* e x c i t e d s t a t e s , a l t h o u g h t h i s seems u n l i k e l y i n view of the e x i s t e n c e of the p r o t o n h e l i u m e x c i t e d s t a t e s ( T o l l i v e r ( 1 979)) . In any case i t • i s c l e a r t h a t the d e p o l a r i z a t i o n r e a c t i o n must i n v o l v e the f i r s t e x c i t e d s t a t e of the Nep +m o l e c u l a r i o n . The t h e o r e t i c a l r a t e c o n s t a n t s f o r t h e s e t y p e s of r e a c t i o n s a re g i v e n by the r e l a t i o n ( G ioumousis(1958)) k L = 2 r t e ( ^ ) ' / l 4.6 where k L i s the L a n g e v i n r a t e c o n s t a n t , e i s the e l e c t r o n i c c h a r g e , c< i s the p o l a r i z a b i l i t y of the t a r g e t atom and p i s 1 44 the reduced mass of the system. These c a l c u l a t e d r a t e c o n s t a n t s f o r the v a r i o u s gas m i x t u r e s s t u d i e d a r e summarized i n t a b l e 4.5. From t a b l e 4.5 i t can be seen t h a t the L a n g e v i n r a t e c o n s t a n t s f o r t h e s e i o n m o l e c u l e r e a c t i o n s a r e two o r d e r s of magnitude f a s t e r than the observed d e p o l a r i z a t i o n s . T h i s may suggest t h a t the model i s t o t a l l y i n a p p r o p r i a t e , as d i s c u s s e d e l s e w h e r e ( G e n t r y ( 1 9 7 8 ) ) . A more l i k e l y e x p l a n a t i o n of t h i s i n t e r f e r e n c e i s the f o r m a t i o n of X^i + ( i . e . i n t e r f e r e n c e from r e a c t i o n 4 where X i s xenon, methane, ammonia or ground s t a t e Hep*) l e a d i n g t o s m a l l o b s e r v e d r e l a x a t i o n r a t e s . I t must be noted t h a t the e x p e r i m e n t a l r a t e c o n s t a n t s i n t a b l e 4.2 can o n l y be lower l i m i t s of the t r u e r a t e of t h e s e r e a c t i o n s , because of the d i f f i c u l t i e s i n d i s t i n g u i s h i n g between v a r i o u s r e a c t i o n pathways i n these e x p e r i m e n t s . The t emperature dependence of the r e l a x a t i o n r a t e s h o u l d p r o v i d e some guidance and such measurements were a t t e m p t e d but met w i t h l i t t l e s u c c e s s . The major problem was m a i n t a i n i n g the p u r i t y of t h e t a r g e t gas a t e l e v a t e d t e m p e r a t u r e s . The r e s u l t s f o r xenon i n neon ar e summarized i n f i g u r e 4.6. There appears to.be e v i d e n c e f o r an a c t i v a t i o n energy f o r the p r o c e s s which i n i t s e l f i s f u r t h e r e v i d e n c e d i s c a r d i n g r e a c t i o n 1, but not much more can be s a i d i n view of the q u a l i t y of the d a t a . C l e a r l y , much more can be l e a r n e d from such systems, but p r o b a b l y not b e f o r e many e x p e r i m e n t a l problems a r e s o l v e d . For example, i t would be u s e f u l t o run lower p r e s s u r e s t o t r y t o l e n g t h e n the l i f e t i m e of the Neju + 145 Reaction P o l a r i z a b i l i t y Reduced mass ( A 3 ) (amu) Heu*+Xe 4.05 3.99 Neu*+Xe 4.05 17.4 Heu*+NHS 2.3 3.23 Neu*+NHj 2.3 8.63 Neu*+Ar 1.64 13.5 Neu*+CHM 2.6 8.95 T h e o r e t i c a l r a t e (10"'molec/cm 3-sec) 2.4 1.13 1 .98 1.21 0.82 1 .26 Tab le 4 . 5 . Langev in r a t e cons t an t s fo r the mo lecu l a r ion r e a c t i o n s . 1 46 MOLECULAR ION XE IN NEON 3 3 3 K 0 . 0 0 1 1 1 1 1 I I 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 I M P . IN M O L E C U L E S - C M " 3 X IO"1 6 F i g u r e 4 . 6 . Temperature dependence of the Neu++Xe r e a c t i o n . The r a te k A = 5.3+1.Ox 10 " 1 1 cm 3 /a toms-sec at 333K which g i ves E f l ^ . T S i l k c a l / m o l e . 1 47 e x c i t e d s t a t e . U n f o r t u n a t e l y t h i s would produce more s t o p s i n the w a l l s of the t a r g e t , which g i v e s the same e f f e c t as a l a r g e s i g n a l from ground s t a t e m o l e c u l a r i o n s . A h i g h e r f i e l d t o g i v e a g r e a t e r number of o s c i l l a t i o n s c o u l d p o s s i b l y d i s t i n g u i s h the f a s t r e l a x i n g and s t a t i o n a r y p a r t s of the y,* s i g n a l . T h i s would have t o be accompanied by the c o n s t r u c t i o n of new c o i l s because o t h e r w i s e a h i g h e r f i e l d means a h i g h e r A B and the r e l a x a t i o n s a re l i k e l y t o be l o s t i n a l a r g e r X0' The number of moderators t h a t a re a v a i l a b l e i s a l s o l i m i t e d s i n c e i t i s r e q u i r e d t h a t t h e r e be a l a r g e muon f r a c t i o n t o the s i g n a l . T h e r e f o r e , a l t h o u g h i t would be i n t e r e s t i n g t o lo o k a t a l l of the r a r e gas m o l e c u l a r i o n s , t h e r e i s too much muonium f o r m a t i o n i n ar g o n , k r y p t o n and xenon t o make t h i s p o s s i b l e . T h i s l e a d s t o a n o t h e r drawback which i s t h a t even a t t h e low xenon c o n c e n t r a t i o n s used, the muon f r a c t i o n i s r a p i d l y reduced t o too s m a l l a s i g n a l from which t o o b t a i n u s e f u l r e s u l t s . Overcoming these drawbacks w i l l be the next s t e p i n s t u d y i n g t h e s e muon m o l e c u l a r i o n p r o c e s s e s . 148 5. MUONIUM SPIN EXCHANGE WITH OXYGEN AND NITRIC OXIDE 5.1 . I n t r o d u c t o r y Remarks The phenomenon of e l e c t r o n s p i n exchange appears i n many NMR and r a d i o f r e q u e n c y s p e c t r o s c o p y e x p e r i m e n t s (Happer (1977 ), B a l l i n g ( 1 9 6 3 ) ) . H + H s p i n exchange i n p a r t i c u l a r i s an i m p o r t a n t p r o c e s s i n the o p e r a t i o n of the hydrogen maser and i n r e l a t e d EPR s t u d i e s as w e l l as i n the u n d e r s t a n d i n g of the 21cm l i n e i n a s t r o p h y s i c s ( P u r c e l l ( 1 9 5 4 ) , Dalgarno ( 1 9 6 1 ) ). The t h e o r y of H + H s p i n exchange has been c o n s i d e r e d i n some d e t a i l and S h i z g a l ( 1 9 7 9 ) has compared the s p i n exchange c r o s s s e c t i o n s £^ Efor H + H w i t h those of Mu + H. More r e c e n t l y A q u i l a n t i ( 1 9 8 0 ) has compared the c r o s s s e c t i o n s f o r H + 0 2 and Mu + 0 2 . There are a l s o s e v e r a l e x p e r i m e n t a l d e t e r m i n a t i o n s of <&~SE f o r H w i t h O z and w i t h NO w i t h which t o compare the p r e s e n t v a l u e s f o r muonium ( A n d e r l e ( 1 9 8 1 ) , Gordon(1973 ), B e r g ( l 9 6 5 ) , Brown ( l 972 ) . Such a comparison 1 4 9 can p r o v i d e a v a l u a b l e t e s t of the importance of i s o t o p e e f f e c t s i n e l e c t r o n s p i n exchange. The o n l y p r e v i o u s s t u d i e s of muonium s p i n exchange i n gases i s the work of M o b l e y ( l 9 6 7 ) c a r r i e d out a t h i g h moderator p r e s s u r e s , n e c e s s i t a t e d by the use of h i g h momentum c o n v e n t i o n a l muon beams. These workers have o b t a i n e d <5~S£ f o r Mu + 0^ and Mu + NO i n argon gas a t 600psi by measuring the JL\* p o l a r i z a t i o n i n a s t r o n g l o n g i t u d i n a l magnetic f i e l d . At such moderator p r e s s u r e s , the r a t e s of t e r m o l e c u l a r c h e m i c a l r e a c t i o n s between Mu and 0 2 or NO are ex p e c t e d t o be comparable t o the s p i n exchange r a t e s . Mobley i g n o r e d any such c o n t r i b u t i o n and t h i s , c o u p l e d w i t h the g e n e r a l l y poor q u a l i t y of the low s t a t i s t i c s d a t a was the m o t i v a t i o n t o re p e a t these e x p e r i m e n t s w i t h a low p r e s s u r e moderator. In a d d i t i o n , no temperature dependent s t u d i e s have p r e v i o u s l y been r e p o r t e d . The a v a i l a b i l i t y a t TRIUMF of a beam of low momentum s u r f a c e ja* has made i t p o s s i b l e t o r e i n v e s t i g a t e the s p i n exchange c r o s s s e c t i o n s f o r muonium w i t h oxygen and n i t r i c o x i d e a t moderator p r e s s u r e s near 15psi where t e r m o l e c u l a r c h e m i c a l r e a c t i o n s s h o u l d be u n i m p o r t a n t . The p r e s e n t e x p e r i m e n t s employed a t r a n s v e r s e magnetic f i e l d w h i ch, u n l i k e the l o n g i t u d i n a l f i e l d e x p e r i m e n t s of Mobley, i n v o l v e the d i r e c t o b s e r v a t i o n of muonium. 150 5.2. R e l a x a t i o n Of The MSR S i g n a l The MSR s i g n a l from e q u a t i o n 1.6 i s S ( t ) = A n a e A t cos(w n^t + ( } m J+A^cos(w^t^) 5.1 where the r e l a x a t i o n of the s i g n a l , X , i s due t o the i n t e r a c t i o n s of the Mu atom w i t h i t s environment. As noted p r e v i o u s l y , one of the i m p o r t a n t f e a t u r e s of these e x p e r i m e n t s , and of muonium c h e m i s t r y i n g e n e r a l , i s t h a t t h e r e can never be more than one Mu atom a t a time u n d e r g o i n g r e a c t i o n . Hence, u n l i k e the c o r r e s p o n d i n g H atom r e a c t i o n s , t h e r e can be no second o r d e r e f f e c t s and X can o n l y be a pseudo f i r s t o r d e r r a t e c o n s t a n t . In g e n e r a l t h e r e can be t h r e e c o n t r i b u t i o n s t o i t s magnitude: X = \0+\e+\x= V +k W 5.2 where \ 0 i s the background r e l a x a t i o n due t o magnetic f i e l d i n h o m o g e n i e t i e s ; \ c i s due t o the l o s s of p o l a r i z e d Mu v i a c h e m i c a l r e a c t i o n s ; . X i i s due t o the d e p o l a r i z i n g e f f e c t s of s p i n exchange between Mu and paramagnetic r e a g e n t s ; and k i s the c o r r e s p o n d i n g b i m o l e c u l a r r a t e c o n s t a n t . The e f f e c t of magnetic f i e l d inhomogeniety can be seen i n f i g u r e 5.1 which shows X =0.45jusec" 1 a t I 5 p s i and X =0 .2 l^usec" 1 a t 3 8 p s i . As 151 F i g u r e 5.1. N i t r o g e n muonium s i g n a l a t 15psi and 3 8 p s i . 1 52 noted p r e v i o u s l y , t h i s p r e s s u r e dependence i s a r e f l e c t i o n of the g r e a t e r f i e l d homogeniety at h i g h e r p r e s s u r e s w i t h a s m a l l e r s t o p p i n g d i s t r i b u t i o n (see t a b l e 3.7). When a Mu atom undergoes a c h e m i c a l r e a c t i o n t h a t p l a c e s the ji* i n a d i a m a g n e t i c environment, the p*-e~ h y p e r f i n e i n t e r a c t i o n i n muonium i s broken, and the muon p r e c e s s e s 103 times s l o w e r , c a u s i n g i t t o l o s e i t s phase coherence w i t h the u n r e a c t e d muonium ensemble. C o n s e q u e n t l y , the MSR s i g n a l r e l a x e s w i t h r a t e c o n s t a n t X j u s t as an NMR or ESR s i g n a l d i s a p p e a r s due t o c h e m i c a l r e a c t i o n s (Ambidge(1976)). The Mu atom may a l s o undergo an a d d i t i o n r e a c t i o n i n which a muonic r a d i c a l i s formed. Such r a d i c a l s have been i d e n t i f i e d i n l i q u i d s a t h i g h t r a n s v e r s e magnetic f i e l d s (Roduner(1978), (1981)) but i t i s not o b v i o u s whether or not these r e a c t i o n s would l e a d t o r e l a x a t i o n of the MSR s i g n a l i n weak f i e l d s , p a r t i c u l a r l y i f the r a d i c a l s formed have no n u c l e a r moments o t h e r than t h a t of t h e p* ( B u c c i ( 1 9 7 8 ) ) . T h i s c h a p t e r i s c o n c e r n e d w i t h the d e p o l a r i z a t i o n of i n muonium due t o s p i n exchange w i t h paramagnetic m o l e c u l e s , r e p r e s e n t e d by Mu(f)+X (J)-->Mu(|)+X(T). T h i s p r o c e s s can be thought of i n a n a l o g y w i t h hydrogen atom maser and r e l a t e d ESR s t u d i e s ( B e r g ( l 9 6 5 ) , Crampton (1 979), B r o w n d 972), Westenburgt1969), Gordon(1973)) as w e l l as w i t h r e c e n t atomic beam s t u d i e s ( A n d e r l e ( 1 9 8 1 ) ) , i n which the h y p e r f i n e s t a t e of the c o u p l e d p r o t o n and e l e c t r o n i s changed as a r e s u l t of the s c a t t e r i n g p r o c e s s ( e . g . |F=1,m=1> —y 153 -> |F=0,m=0>). In p r i n c i p l e , t he f i e l d dependence of the p o l a r i z a t i o n can be used t o d i s t i n g u i s h c h e m i c a l r e l a x a t i o n (Ac.) from d e p o l a r i z a t i o n ( \^ ) r e l a x a t i o n i n l o n g i t u d i n a l (and t r a n s v e r s e ) magnetic f i e l d s (Mobley (1 967) , Brewer (1 975).) .• In both the l o n g i t u d i n a l f i e l d e x p e r i m e n t s of Mobley and the p r e s e n t t r a n s v e r s e f i e l d e x p e r i m e n t , i t has been assumed t h a t the c h e m i c a l r e l a x a t i o n ( Ac) i s n e g l i g i b l e . The po.ssible c h e m i c a l r e l a x a t i o n s of i n t e r e s t a r e the b i m o l e c u l a r r e a c t i o n Mu + 0X > MuO + 0 5.3a and the t e r m o l e c u l a r r e a c t i o n s Mu + 0 2 - — > MuC\ 5.3b Mu + NO -^-> MuNO 5 > 3 c where i t i s noted t h a t MuO and MuOz a r e r a d i c a l s , whereas MuNO i s n o t . The n e g l e c t of any c h e m i c a l c o n t r i b u t i o n t o the r e l a x a t i o n i s j u s t i f i e d based on the measured r a t e c o n s t a n t s f o r the H atom a n a l o g r e a c t i o n s : k H(300K)=1.0±0.5x10 3cm 3mol- 1sec 1 f o r r e a c t i o n 5.3a (Wolfrum(1975)) and k H ( 3 0 0 K ) = 1.0±0.6x10 1 6cm 6mol" 2sec- 1 i n 1 54 d i f f e r e n t moderators f o r both t e r m o l e c u l a r r e a c t i o n s 5.3b and 5.3c over a p r e s s u r e range from .02 t o 15psi ( O k a ( l 9 7 7 ) , Wolfrum(1975), H i k i d a ( 1 9 7 0 ) ) . Assuming t h a t t he Mu atom r e a c t i o n r a t e s s c a l e as the mean r e l a t i v e v e l o c i t y , and u s i n g the maximum r e a c t a n t c o n c e n t r a t i o n s i n the p r e s e n t experiment ( 3 x 1 0 ' 6 m o l e c u l e s / c m 3 ) one o b t a i n s Xc=10"1°psec"1 f o r r e a c t i o n 5.3a, \c<0.07psec"1 f o r r e a c t i o n s 5.3b and 5.3c i n 15psi moderator p r e s s u r e and \L<0.17psec"1 f o r 5.3b and 5.3c a t 3 8 p s i moderator p r e s s u r e . These v a l u e s may be compared w i t h the measured background r e l a x a t i o n s i n t h i s t h e s i s of 0.45psec" 1 and 0.21^usec~ 1 f o r 15 and 38ps i m o d e r a t o r s , r e s p e c t i v e l y , and w i t h the t o t a l measured r e l a x a t i o n of \=9jjsec~'* a t the h i g h e s t Oz and NO c o n c e n t a t i o n s used. I t i s c o n c l u d e d , t h e r e f o r e , t h a t any r e l a x a t i o n i n the MSR s i g n a l from 0^ and NO r e a g e n t s i n <40psi moderator must be due t o d e p o l a r i z a t i o n ( A^) by e l e c t r o n s p i n exchange. The same statement can not be made w i t h c o n f i d e n c e f o r the 600psi moderator e x p e r i m e n t s of Mobley (1967 )•, a p o i n t c o n s i d e r e d l a t e r i n t h i s c h a p t e r . 155 5.3. The Cros s Sect i o n For S p i n Exchange I f the time between muonium c o l l i s i o n s w i t h p aramagnetic m o l e c u l e s ( >100 ns i n the p r e s e n t e x p e r i m e n t ) i s much l o n g e r than the h y p e r f i n e m i x i n g p e r i o d ( 0 . 2 2 n s ) , then e l e c t r o n s p i n exchange l e a d s e s s e n t i a l l y t o the same r e s u l t as r e p e a t e d i o n i z a t i o n and muonium f o r m a t i o n : each exchange c o l l i s i o n has a 50% chance of l e a v i n g t h e muon w i t h an e l e c t r o n of d i f f e r e n t s p i n . Thus, each exchange c o l l i s i o n e f f e c t i v e l y d e p o l a r i z e s muonium by 50% s i n c e s p i n " f l i p " l e a d s t o d e p o l a r i z a t i o n w h i l e the exchange of l i k e s p i n s does n o t . The s p i n exchange c r o s s s e c t i o n , ^ ~ s E , i s then p r o p o r t i o n a l t o 2 S J L > where Gl\ i s the e x p e r i m e n t a l l y d e t e r m i n e d d e p o l a r i z a t i o n c r o s s s e c t i o n o b t a i n e d from the c o r r e s p o n d i n g r a t e c o n s t a n t k w h i c h , i n t u r n , i s r e l a t e d t o the measured r e l a x a t i o n r a t e Ai v i a the u s u a l e x p r e s s i o n ; X j f n x < v r Q . > = n * 5.4 where n x i s the number d e n s i t y of paramagnetic X m o l e c u l e s and v r i s the r e l a t i v e c o l l i s i o n v e l o c i t y and <vr s - ^ r e p r e s e n t s a s u i t a b l e a verage. In a b u l k k i n e t i c experiment such as the p r e s e n t one,-which assumes t h e r m a l e q u i l i b r i u m among the r e a c t a n t s , the ma c r o s c o p i c b i m o l e c u l a r ( d e p o l a r i z a t i o n ) r a t e c o n s t a n t k^ i s 156 r e l a t e d t o the v e l o c i t y dependent c r o s s s e c t i o n ( £ r.(v)) by kd=4TT(yu/27rkbT)"^ jGA(v)e~%^ v,3 dv 5.5 where k b i s Boltzmann's c o n s t a n t , u i s the reduced mass of the system, and T i s the a b s o l u t e t e m p e r a t u r e . I f the r e a c t i o n r a t e i s c o l l i s i o n c o n t r o l l e d v i a some e f f e c t i v e ( v e l o c i t y independent) hard sphere c r o s s s e c t i o n 6*^, then e q u a t i o n 5.5 i s t r i v i a l l y i n t e g r a t e d , y i e l d i n g *a 6 i = ( Bk b T/ty i ) V * 6 4 5.6 where v r i s the average r e l a t i v e c o l l i s i o n v e l o c i t y and 6^ i s the obser v e d d e p o l a r i z a t i o n c r o s s s e c t i o n . In t h i s case the t e m p e r a t u r e dependence of the r e a c t i o n r a t e s h o u l d j u s t be t h a t of Vr i t s e l f , namely TV%. In g e n e r a l , the v e l o c i t y dependence of £>dl(v) must be known from some model. In any e v e n t , i t i s common t o a s s o c i a t e e q u a t i o n 5.5 w i t h the u s u a l A r r h e n i u s e x p r e s s i o n f o r the r a t e c o n s t a n t , k A ( T ) = A e " % f 5.7 where the frequ e n c y f a c t o r A has the same form as e q u a t i o n 5.6. The e x p l i c i t assumption i n w r i t i n g e q u a t i o n 5.7 i s t h a t the T^- dependence i n the mean v e l o c i t y i s s m a l l compared t o the e x p o n e n t i a l dependence, but t h i s may not 157 always be the c a s e . Sometimes i t may be more a p p r o p r i a t e t o i n t e r p r e t e q u a t i o n 5.6 i n the f orm . k^ =A' T A, where A' i s indeed t e m p e r a t u r e independent. I t can be noted t h a t e q u a t i o n 5.6 f o l l o w s i m m e d i a t e l y from e q u a t i o n 5.7 when E<>=0. The a c t u a l r e l a t i o n s h i p between 6"^ and S" 5 6depends upon a n g u l a r momentum c o u p l i n g of the c o l l i s i o n p a r t n e r s v i a an I • S i n t e r a c t i o n , where I i s the s p i n of Mu and !§ i s the s p i n of the paramagnetic i m p u r i t y s p e c i e s X. The net e f f e c t of t h i s c o u p l i n g i n t h e c o l l i s i o n t h e o r y a n a l y s i s i s t o i n t r o d u c e an a d d i t i o n a l f a c t o r , f , such t h a t \j[= (1 / 2 ) f \ s £ . T h i s f a c t o r i s d i f f e r e n t f o r T, and T a r e l a x a t i o n s . I t can be d e r i v e d i g n o r i n g the s t r u c t u r e of the oxygen and n i t r i c o x i d e m o l e c u l e s and t r e a t i n g them s i m p l y as s p i n 1 and s p i n 1/2 p a r t i c l e s i n the s t a n d a r d c o l l i s i o n t h e o r y framework. T h i s i s o u t l i n e d i n Appendix 3 f o l l o w i n g the f o r m a l i s m s e t up by B a l l i n g ( 1 9 6 3 ) . The r e s u l t s agree w i t h s i m i l a r c a l c u l a t i o n s by B e r g ( l 9 6 5 ) and M o b l e y ( 1 9 6 7 ) . In l o n g i t u d i n a l magnetic f i e l d s ( i . e . when one i s measuring a T, r e l a x a t i o n ) , -f=1 f o r s p i n 1/2 (NO) and f=32/27 f o r s p i n 1 (0X) w h i l e i n t r a n s v e r s e magnetic f i e l d s , ( a Tx r e l a x a t i o n ) f=3/4 f o r s p i n 1/2 and f=8/9 f o r s p i n 1. Thus i n the p r e s e n t t r a n s v e r s e f i e l d s tudy G~$e = 8/3 <£"^ f o r Mu+NO and 6;£=9/4G4 f o r Mu+Oa. 158 5.4. E x p e r i m e n t a l R e s u l t s Measured c o n c e n t r a t i o n s of r e a c t a n t gas were added t o the gas t a r g e t v e s s e l by f i l l i n g a s m a l l b u l b of known volume t o a measured p r e s s u r e and then f l u s h i n g i t i n t o the evac u a t e d t a r g e t can w i t h the moderator gas. . No p u r i f i c a t i o n was c a r r i e d out on the gases used ( o b t a i n e d from the Matheson company) and t y p i c a l i m p u r i t y l e v e l s were <0.4% i n the oxygen ( m o s t l y a r g o n ) ; <0.1% NO^ and <0.03% N 20 i n t he n i t r i c o x i d e ; and <lOppm 0 a i n the n i t r o g e n moderator. I t i s c o n c i e v a b l e t h a t the e f f e c t i v e H0X i n the NO c o u l d be r a i s e d t o 0.2% by the r e a c t i o n of the oxygen i n the moderator w i t h the n i t r i c o x i d e and t h e r e b y cause i n t e r f e r e n c e due t o the r e a c t i o n Mu+NOx-->MuO+NO 5.8 However, by s c a l i n g t he b i m o l e c u l a r r a t e c o n s t a n t f o r the H an a l o g r e a c t i o n ( k H ( 3 0 0 K ) = 8 x 1 0 1 3 c m 3 m o l ' 1 s e c " 1 ) (Wagner(1977) by t h e mean r e l a t i v e c o l l i s i o n v e l o c i t y f o r Mu, i t i s e s t i m a t e d t h a t , a t the h i g h e s t NO c o n c e n t r a t i o n s used, r e a c t i o n 5.8 would g i v e \ =0.02usec~ 1. The p o s s i b l e a d d i t i o n r e a c t i o n f o r m i n g MuNO (which has plagued p o s i t r o n i u m s t u d i e s ) (Chuang(1974)), i s not r e p o r t e d f o r H atoms and i s not exp e c t e d t o be im p o r t a n t h e r e . 1 59 5.4a. Room Temperature R e s u l t s S i n c e i t has been shown t h a t Xc =0 i n the p r e s e n t e x p e r i m e n t , then e q u a t i o n 5.2 f o r A may be w r i t t e n as > = \0+h=\ + h M 5.9 where i s a b i m o l e c u l a r r a t e c o n s t a n t and [x] i s the reagent c o n c e n t r a t i o n . The v a r i a t i o n of X w i t h O x and NO c o n c e n t r a t i o n a t 15psi and 3 8 p s i moderator p r e s s u r e i s r e c o r d e d i n t a b l e 5.1. The d e p o l a r i z a t i o n r a t e c o n s t a n t s (k<j[) can be det e r m i n e d by f i t t i n g the v a r i o u s A 's measured at d i f f e r e n t v a l u e s of [x] t o the s i m p l e l i n e a r dependence r e q u i r e d by e q u a t i o n 5.9 and i l l u s t r a t e d i n f i g u r e s 5.2 t o 5.4. The measured v a l u e s of k± a r e summarized i n t a b l e 5.2. From the r e s u l t s i n t a b l e 5.2, t h r e e c o n c l u s i o n s can be drawn; i ) kj[ i s independent of the n a t u r e of the moderator, i i ) k^  i s independent of the moderator p r e s s u r e and i i i ) ki (Mu+O^ )^ =kji (Mu+NO) w i t h i n e r r o r s . The independence of kJL on the moderator p r e s s u r e s u p p o r t s the e x p e c t a t i o n t h a t the r a t e s of r e a c t i o n s 5.3b and 5.3c a r e i n s i g n i f i c a n t , as does the f a c t t h a t t h e r e i s no l a r g e t emperature dependence, as w i l l be seen l a t e r . The p r e s s u r e dependence of A0 has a l r e a d y been d i s c u s s e d and i t may be noted t h a t the s m a l l v a l u e of A0 f o r S i O a powder (Mar s h a l l (1978)) i s a l s o c o n s i s t e n t w i t h a s m a l l e r s t o p p i n g r e g i o n . 160 NO Spin Exchange with Mu at 1 5psi Concentrat ion(1 0 ' * ) Relaxation(usee atoms/cc e r r o r X e r r o r 0.0 0.0 0.507 0.023 0.291 0.03 1 .054 0.110 0.572 0.06 2.17 0.284 1 .135 0.12 4.215 0.35 1 .54 0.16 4.88 1.19 2.15 0.22 8.08 1 .36 °X Spin Exchange with Mu at 1 5psi Concentration ( 1 0 " ) Relaxation (yjsec atoms/cc e r r o r X e r r o r 0.0 0.0 0.508 0.023 0.467 0.048 1.807 0.32 1 .36 0.14 4.00 0.65 NO Spin Exchange with Mu at 38psi Concentration(1 0 ' ' ) Relaxation(jisec" atoms/cc e r r o r X error 0.0 0.0 0.209 0.03 1.15 0.15 5.5 0.93 2.29 0.24 6.67 1.3 Spin Exchange with Mu at 38psi Concentration( 10 1 *) Relaxation (^jsec atoms/cc e r r o r X e r r o r 0.0 0.0 0.209 0.03 1 .09 0.11 3.30 0.29 1 .97 0.21 5.68 2.0 Tab le 5 .1 . \ v s . C o n c e n t r a t i o n of O-j, and NO at I5ps i and 38psi moderator p r e s s u r e . 161 IO.O I- Mu +O2, N2 moderator 9 .O - A 3 S P s i N 2 • ISpsi N 2 8 . 0 I-0 . 0 * 1 1 I I 0-0 0 . 5 1 .0 1 . 5 2 . 0 2 . 5 0 2 IN MOLECULES-CM" 3 X I O " 6 F i g u r e 5.2. R e l a x a t i o n .rate X as a f u n c t i o n of 0, c o n c e n t r a t i o n f o r the r e a c t i o n Mu+Oa i n n i t r o g e n moderator at I 5 p s i and 38 p s i p r e s s u r e . 162 F i g u r e 5.3. R e l a x a t i o n r a t e A as a f u n c t i o n of NO c o n c e n t r a t i o n f o r the r e a c t i o n Mu+NO i n n i t r o g e n moderator at I 5 p s i and 3 8 p s i p r e s s u r e . F i g u r e 5.4. R e l a x a t i o n r a te X as a f u n c t i o n of 0 a c o n c e n t r a t i o n fo r the r e a c t i o n Mu+Oa in argon moderator 15psi p r e s s u r e . 164 Reaction Moderator A 0(jisec-' ) kj (10"1 "cm'/sec) S^dO'^cm 2) 15psi Ar 0.41t0.05 2.510.2 3.310.2 Mu+C^ 15psi 0.5110.02 2.610.4 3.510.5 38psi N x 0.2110.03 2.810.3 3.710.3 PowAe o.osso.oi l.&to.H 3.5-±o.r Mu+NO 15psi N x 0.5010.02 2.810.2 3.810.3 38psi N x 0.2110.03 3.410.5 4.510.6 T a b l e 5.2. Room temperature r e l a x a t i o n r a t e s i n pure moderator (\a) and the b i m o l e c u l a r d e p o l a r i z a t i o n r a t e c o n s t a n t s (k^) w i t h c o r r e s p o n d i n g h a r d sphere c r o s s s e c t i o n s (<SoO f o r Mu+C\ and Mu+NO. 1 65 The s p i n exchange p r o c e s s i s not e x p e c t e d t o e x h i b i t an a c t i v a t i o n energy as the l a t e r d i s c u s s i o n w i l l show. T h e r e f o r e the <S*^  s h o u l d be t emperature independent and t h u s r e l a t e d t o the b i m o l e c u l a r r a t e c o n s t a n t by the u s u a l e x p r e s s i o n kj^S'jvv ( r e c a l l e q u a t i o n 5.6), where v"r i s the mean r e l a t i v e v e l o c i t y of the c o l l i d i n g s p e c i e s . As d i s c u s s e d e a r l i e r , i n a weak t r a n s v e r s e magnetic f i e l d , the s p i n exchange c r o s s s e c t i o n s of i n t e r e s t are r e l a t e d t o the e x p e r i m e n t a l l y d e t e r m i n e d d e p o l a r i z a t i o n c r o s s s e c t i o n s ( i n t a b l e 5.2) a c c o r d i n g t o ^ £ = 8 / 3 S ^ f o r Mu + NO and £ ^ = 9 / 4 ^ f o r Mu + 0 a . T a b l e 5.3 compares the p r e s e n t room temp e r a t u r e v a l u e s of S ^ e w i t h the e a r l i e r h i g h moderator p r e s s u r e r e s u l t s of Mobley(!967) and w i t h the c o r r e s p o n d i n g H atom r e s u l t s (Brown(1 972) , B e r g ( l 9 6 5 ) , A n d e r l e ( 1 9 8 1 ) , Gordon(1973)) . U n f o r t u n a t e l y , the r e p o r t e d H atom s p i n exchange c r o s s s e c t i o n s v a r y c o n s i d e r a b l y . B a s i c a l l y t h e r e a r e two s e t s of d a t a : the e a r l i e r v a l u e s of Brown(l972) and B e r g ( l 9 6 5 ) , and the more r e c e n t r e s u l t s of Gordon(!973) and A n d e r l e ( 1 9 7 9 ) . S i n c e t h e s e l a t e r r e s u l t s were o b t a i n e d by v e r y d i f f e r e n t e x p e r i m e n t a l t e c h n i q u e s , the c o n s i s t e n c y between them i s t a k e n as e v i d e n c e t h a t they are more r e l i a b l e than the d a t a of Brown and Berg (as d i s c u s s e d by A n d e r l e and Gordon). Thus the p r e s s u r e averaged room temperature v a l u e s f o r 6^(Mu+ 0 a )=8. Oi-1 .2x10' 1 6cm 2 and 6 ^ - (Mu+NO) = 1 1 . O i l .2x10" 1 6 c m 2 a r e q u i t e s i m i l a r t o the c o r r e s p o n d i n g H atom c r o s s s e c t i o n s 166 M o l e c u l e "*( 1 5 p s i ) C\ 7 . 9*1 . 2 NO 10.1.7 a) R e s u l t s from t h i s t h e s i s . An average of the I 5 p s i Ar and Kx moderator r e s u l t s f o r Mu+O^ has been used. b) From Mobley (1 967) . c) H atom r e s u l t s (averaged) of Brown(l972) and B e r g ( 1 9 6 5 ) . d) H atom r e s u l t s from A n d e r l e ( 1 9 8 1 ) and Gordon(1973). a ( 3 8 p s i ) b ( 6 0 0 p s i ) 8.41.8 5.91.6 22+2 1011 12.11.7 7.1±1.0 2512 1311 T a b l e 5.3. Comparison of the p r e s e n t room temperature • . £ $ E f o r Mu+NO and Mu+Oz w i t h those of Mobley and w i t h c o r r e s p o n d i n g H atom result*. 167 of I0±1 and 1 3 * 1 x 1 0 " 1 6 c m 2 f o r the 0 X and NO r e s u l t of An d e r l e ( 1 9 8 1 ) and a l s o t o the 10+1 and 14+1x10" 1 6cm 2 o b t a i n e d by Gordon( 1 9.73) f o r the O^and NO systems. 5.4b. Temperature Dependent R e s u l t s U s i n g the a p p a r a t u s d e s c r i b e d e a r l i e r , the s p i n exchange r e a c t i o n r a t e s f o r Mu+O^ and Mu+NO were i n v e s t i g a t e d i n the temperature range 300K t o 478K. The thermocouple used t o mo n i t o r the temperature r e g i s t e r e d a g r a d i e n t a l o n g the l e n g t h of the p* s t o p p i n g d i s t r i b u t i o n of ^5K and t h i s was t a k e n t o be t h e e r r o r . S i n c e the p r e v i o u s room temperature s t u d i e s had shown no dependence on moderator p r e s s u r e , the temperature dependence was examined at I 5 p s i p r e s s u r e o n l y . A t y p i c a l MSR spectrum f o r the r e a c t i o n Mu+NO o b t a i n e d a t 478K i s shown i n f i g u r e 5.5. Note t h a t the time dependent muon background i s l a r g e r here than i n f i g u r e 5.1 because the s m a l l e r s i z e of the temperature s t u d i e s t a r g e t ( c o u p l e d w i t h the lower d e n s i t y of t h e moderator a t h i g h e r t e m p e r a t u r e s ) a l l o w s more muons to r e a c h the w a l l s of the t a r g e t v e s s e l . C o n c e n t r a t i o n dependent r e l a x a t i o n r a t e s a r e g i v e n i n t a b l e 5.4 f o r Mu+O^ and i n t a b l e 5.5 f o r Mu+NO as a f u n c t i o n of t e m p e r a t u r e . T y p i c a l p l o t s of t h i s d a t a a r e shown i n f i g u r e s 5.6 and 5.7 f o r the Mu+0 2 d a t a at' 478K and 295K and the Mu+NO da t a a t 168 438K and 388K, from which the b i m o l e c u l a r r a t e c o n s t a n t s k (T) a r e o b t a i n e d from the s l o p e s . These s l o p e s (k (T)) a r e t a b u l a t e d i n t a b l e 5.6. I t can be seen from the data t h a t t h e r e i s o n l y a v e r y weak dependence on t e m p e r a t u r e , c o n s i s t e n t w i t h T^-1-, as d i s c u s s e d e a r l i e r . A c c o r d i n g l y , i t i s assumed t h a t k(T)=AT n ; hence a p l o t of l o g k vs l o g T w i l l g i v e the power n. Such p l o t s a re shown i n f i g u r e 5.8 and 5.9 where the s l o p e s a r e found t o be . 6 i . 4 and 0.9±.5 f o r Mu+NO and Mu+O-j. r e s p e c t i v e l y . These v a l u e s are c o n s i s t e n t w i t h n=1/2 but i n view of the r e l a t i v e l y l a r g e e r r o r s cannot be o f f e r e d as p r o o f of a s i m p l e TX/* temperature dependence. However, as argued i n the p r e v i o u s d i s c u s s i o n c h e m i c a l r e a c t i o n i s u n l i k e l y and moreover the s p i n exchange p r o c e s s i s l i k e l y t o be c o l l i s i o n c o n t r o l l e d a t t e m p e r a t u r e s >300K. Of c o u r s e , the data can always be f i t t o an A r r h e n i u s type of e x p r e s s i o n ( i . e . e q u a t i o n 5.7 where l o g k^ v s . 1/T g i v e s an a c t i v a t i o n energy from the s l o p e ) . T h i s i s shown i n f i g u r e s 5.10 and 5.11 g i v i n g E a=0.7±.5 and 0.4±.2 kc a l / m o l e f o r the 0^ and NO r e a c t i o n s r e s p e c t i v e l y . The s m a l l e s t a c t i v a t i o n e n e r g i e s measured t o date f o r the c h e m i c a l r e a c t i o n s of muonium a r e £1 k c a l / m o l e ( G a r n e r ( 1 9 7 9 ) , F l e m i n g ( 1 9 8 1 ) ) , r e i n f o r c i n g the c l a i m t h a t e s s e n t i a l l y what i s observed i n the p r e s e n t case i s a s i m p l e Vi V T* dependence. W h i l e i n p r i n c i p l e the T* and E f c dependence can be s e p a r a t e d , t h i s i s not p r a c t i c a l f o r the p r e s e n t d a t a g i v e n t h e i r r e l a t i v e l y l a r g e e r r o r s . Moreover, i t s h o u l d be 1 6 9 I5fst 'NITROGEN 478 K cr t— LU CO CL - 0 . 2 0 0 . 3 0 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 NITROGEN AND NITRIC OXIDE 478 K 1 1 0 . 2 0 - 0 . 2 0 T _L _L 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 TIME (VS) F i g u r e 5 .5 . R e l a x a t i o n of MSR s i g n a l due t o s p i n exchange w i t h NO a t 438K. 1 70 Oj_ Spin Exchange w i t h Mu at I5p s i and 400K Concent r a t ion( 1 0 1 6 ) R e l a x a t i o n (ysec -1) atoms/cc e r r o r X e r r o r 0.0 0.376 1.14 1 .89 2.65 0.1 0.075 0.21 0.32 0.42 0.84 1 .93 4.15 8.0 10.8 0.09 0.26 0.66 2.7 1.3 Oj_ Spin Exchange w i t h Mu at I5p s i and 438K Concentrat i o n ( 1 0 ' 6 ) Relaxat ion(usee"') atoms/cc e r r o r X e r r o r 0.0 0.67 2.04 0.1 0.15 0.36 0.81 3.35 8.63 0.05 0.30 0.86 Spin Exchange w i t h Mu at 15psi and 478K C o n c e n t r a t i o n ( 1 0 1 ( ) R e l a x a t i o n ( u s e e " ' ) atoms/cc e r r o r X e r r o r 0.0 0.1 0.661 0.11 0.452 0.08 1.9 0.56 1 .66 0.285 7.5 2.9 2.73 0.44 13.2 2.9 Tab le 5 . 4 . C o n c e n t r a t i o n dependent r e l a x a t i o n r a t e s as a f u n c t i o n of temperature fo r Mu+O, . 171 NO Spin Exchange w i t h Mu at I5p s i and 388K Concentration ( 1 0 " ) Relaxat ion (usee* 1) atoms/cc e r r o r X e r r o r 0.0 0.67 1.15 1 .88 0.1 0.15 0.21 0.32 0.737 2.85 4.70 6.86 0.044 0.27 0.46 0.59 NO Spin Exchange w i t h Mu at I5p s i and 438K Concent r a t ion ( 1 0 " ) Relaxat ion (jisec"') atoms/cc e r r o r X e r r o r 0.0 0.68 1 .22 1 .90 0.1 0.15 0.22 0.33 0.81 3.08 5.25 7.80 0.05 0.36 0.41 0.743 NO Spin Exchange w i t h Mu at 15psi and 478K Concentration ( 1 0 " ) Relaxat ion (^isec" 1) atoms/cc e r r o r X e r r o r 0.0 0.1 0.661 0.11 0.478 0.091 2.0 0.41 0.926 0. 167 3.9 1 .08 2.37 0.38 12.1 3.4 Tab le 5 .5 . C o n c e n t r a t i o n dependent r e l a x a t i o n r a t e s as a f u n c t i o n of temperature fo r Mu+NO. F i g u r e 5.6. R e l a x a t i o n r a t e A v L v s . c o n c e n t r a t i o n of Cs 478K and 295K. 0 0.5 1.0 1.5 2.0 2.5 NO concentration in molecules-cm-3x 10"1 F i g u r e 5 .7 . R e l a x a t i o n r a t e A : " X 0 v s . c o n c e n t r a t i o n of NO a t 388K and 4 3 8 K . System Mu + NO Mu + NO Mu + NO Mu + NO Temperature 295t5 38515 43815 478*5 k A (lCT'cm* molecr'sec"') 2.84+-0.2 3.3010.23 3.6210.25 4.010.7 Mu + Ox Mu + Ox Mu + Ot Mu + t \ 29515 40015 438*5 478t5 2.64*0.4 3.45*0.4 3.95*0.3 4.1510.7 Ta b l e 5.6. B i m o l e c u l a r r a t e c o n s t a n t s as a f u n c t i o n t e mperature f o r Mu+Q^ and Mu+NO s p i n exchange 175 F i g u r e 5 .8 . Log k v s . l og T fo r Mu + 0 a . The s lope of the l i n e i s n = . 9 ± . 5 . 176 F i g u r e 5 . 9 . Log k v s . l og T fo r Mu + NO. The s lope of the l i n e i s n=.6±.4. 1 77 noted t h a t a l t h o u g h the a c t i v a t i o n e n e r g i e s f o r the known t e r m o l e c u l a r H atom r e a c t i o n s ( e q u a t i o n 5.3) a r e comparable t o t h e s e v a l u e s ( O k a ( l 9 7 7 ) , W o l f r u m ( 1 9 7 5 ) ) , they have o p p o s i t e s i g n s . Based on t h e i r t e mperature independence, the s p i n exchange c r o s s s e c t i o n s can be d e t e r m i n e d as shown i n e q u a t i o n 5.6 and w r i t t e n as In c o r r e s p o n d i n g s t u d i e s of H atom p r o c e s s e s by A n d e r l e and Gordon, i t has been assumed t h a t the H atom c r o s s s e c t i o n s can be o b t a i n e d from an e q u a t i o n of the form of e q u a t i o n 5.10. The Mu c r o s s s e c t i o n s so o b t a i n e d a r e compared w i t h the H atom ones i n t a b l e 5.7. Temperature averaged v a l u e s a r e a l s o shown. 5.5. Comparison With The R e s u l t s Of Mobley A l t h o u g h the agreement between the p r e s e n t (room t e m p e r a t u r e ) r e s u l t s and those of Mobley, o b t a i n e d i n a l o n g i t u d i n a l magnetic f i e l d , a r e r e a s o n a b l y good ( t a b l e 5.3), the l a t t e r v a l u e s a r e n e v e r t h e l e s s about 40% l o w e r . 5. 10 RATE CONSTANT VS 1/T MU + 02 1 0 i 1 1 1 1 1 1— o r— o L U I — CE LY 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4. 1/T U0~3) F i g u r e 5.10. A r r h e n i u s p l o t of l o g k v s . 1/T f o r Mu + 0. The a c t i v a t i o n energy o b t a i n e d from the s l o p e i s . I t . 5 k c a l / m o l e . 179 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1/T (10~3) F i g u r e 5 .11. A r r h e n i u s p l o t of l og k v s . 1/T f o r Mu + NO. The a c t i v a t i o n energy ob t a i ned from the s lope i s . 4 ± . 3 k c a l / m o l e . 180 System Temperature • 6^e(10*'cm) Mu + NO 29515 10.0±0.7 Mu + NO 38515 10.2±0.7 Mu + NO 43815 10.610.7 Mu + NO 47815 11.212.0 * H + NO 310 10.6*0.9 a H + NO 373 9.910.9 Mu + OZ 29515 • 7.9H.2 Mu + O,. 40015 8.9H.0 Mu + Ox 438-15 9.710.7 Mu + OX 47815 9.8H.7 " H + OX 310 8.810.7 *• H + Oj 315 9.811.0 *H + Ot 350 8.310.7 a H + O x 388 8.010.7 °- -fror* Gordon i\\T>>) T a b l e 5.7. Comparison of Mu and H s p i n exchange c r o s s s e c t i o n s f o r r e a c t i o n s w i t h NO and 0-. 181 The c e n t r a l problem w i t h the i n t e r p r e t a t i o n of Mobley's r e s u l t s l i e s i n e v a l u a t i n g t h e r o l e p l a y e d by the t e r m o l e c u l a r r e a c t i o n s 5.3b and 5.3c a t 6 0 0 p s i . An e s t i m a t e of X t can be o b t a i n e d by r e p e a t i n g t h e c a l c u l a t i o n of th e s e r e a c t i o n s u s i n g the h i g h e s t c o n c e n t r a t i o n of NO and 0 a used i n Mobley's experiment ( ~ 1 0 1 7 m o l e c u l e s / c m 3 ) t o g i v e X =1Vpsec"1. T h i s e s t i m a t e s u g g e s t s t h a t the c h e m i c a l e f f e c t s c o u l d be g r e a t e r than the s p i n exchange ones by as much as a f a c t o r of t h r e e . How might t h i s a f f e c t the i n t e r p r e t a t i o n of Mobley's data? In a t r a n s v e r s e f i e l d e x p e r i m e n t , (such as thes e t h e s i s e x p e r i m e n t s ) both c h e m i c a l r e a c t i o n and s p i n exchange l e a d t o a " s p i n - s p i n " r e l a x a t i o n of the MSR s i g n a l by c a u s i n g the l o s s of phase coherence of the muon s p i n p r e c e s s i o n . In a l o n g i t u d i n a l f i e l d experiment (such as M o b l e y ' s ) , muon s p i n p r e c e s s i o n i s not o b s e r v e d . I n s t e a d , the time dependent muon p o l a r i z a t i o n i s s i m p l y m o n i t o r e d d i r e c t l y from the d i f f e r e n c e between f o r w a r d (or muon s p i n "up" s t a t e s ) and backward (muon s p i n "down" s t a t e s ) p o s i t r o n c o u n t i n g r a t e s . In g e n e r a l , the s p i n u p - s p i n down p o p u l a t i o n d i f f e r e n c e (or forward-backward asymmetry) decays w i t h time due t o " s p i n -l a t t i c e " r e l a x a t i o n . E l e c t r o n s p i n exchange i n a l o n g i t u d i n a l f i e l d l e a d s t o a d i r e c t l o s s i n the muon s p i n p o l a r i z a t i o n , t h e r e b y c a u s i n g a r e l a x a t i o n on the time s c a l e of the s p i n exchange i t s e l f . T h i s t ime s c a l e i s a d j u s t a b l e by v a r y i n g t h e c o n c e n t r a t i o n of t h e paramagnetic r e a c t a n t so t h a t the s p i n exchange may be o b s e r v e d d u r i n g the l i f e t i m e 182 of t he muon. On the o t h e r hand, any c h e m i c a l r e a c t i o n i n a l o n g i t u d i n a l f i e l d t h a t p l a c e s t h e muon i n a d i a m a g n e t i c e n v i r o n m e n t , such as MuNO, merely b r e a k s the y*-e~ h y p e r f i n e i n t e r a c t i o n w i t h o u t c h a n g i n g t h e muon s p i n p o l a r i z a t i o n . F u r t h e r m o r e , the s p i n l a t t i c e r e l a x a t i o n t i m e , , f o r d i a m a g n e t i c muons i s s i m i l a r t o t h a t f o r d i a m a g n e t i c p r o t o n s , on the o r d e r of m i l l i s e c o n d s , i n gases, which i s immeasurably slow on t h e m i c r o s e c o n d time s c a l e of the muon l i f e t i m e . C o n s e q u e n t l y , when c h e m i c a l r e a c t i o n s compete w i t h s p i n exchange i n a l o n g i t u d i n a l f i e l d e x p e r i m e n t , t h o s e r e a c t i o n s t h a t r e s u l t i n d i a m a g n e t i c p r o d u c t s not o n l y cause no s p i n l a t t i c e r e l a x a t i o n , they p r e v e n t f u r t h e r r e l a x a t i o n i n the d i a m a g n e t i c muon p r o d u c t s . , Such r e a c t i o n s cannot be i g n o r e d , however, s i n c e t he ensemble p o l a r i z a t i o n i s we i g h t e d by the o v e r a l l r e a c t i v i t y of muonium. The r e s u l t i n g e x p r e s s i o n f o r the time dependent forward-backward muon asymmetry i n a l o n g i t u d i n a l f i e l d ( B rewer(1975)) c o n t a i n s b o t h a r e l a x i n g and a n o n - r e l a x i n g component and i s g i v e n by A ( t ) = XtA0/(Xt+Xl>) + ( X D A 0 / ( X £ + A D ) ) e - U t ^ ' t 5.11 where A 0 i s the i n i t i a l f i e l d dependent l o n g i t u d i n a l asymmetry and A 0 i s the d e p o l a r i z a t i o n r a t e . The magnetic f i e l d dependence of X„ i s such t h a t as B — O O , AD -->0. The s p i n exchange r e l a x a t i o n r a t e , Xi , (where XD = \j/( 1 +x 2 x=B/B 0 and B e i s the muonium h y p e r f i n e f i e l d of 1585 gauss) 183 i s o b t a i n e d by measuring X D as a f u n c t i o n of magnetic f i e l d and e x t r a p o l a t i n g t o z e r o f i e l d . Under the assumption t h a t Xc=0, e q u a t i o n 5.11 reduces t o the e x p r e s s i o n used by Mobley: A(t)=k0e-^ 5.12 I t can be shown t h a t Mobley's model w i l l g i v e X 's s m a l l e r than those o b t a i n e d i f e q u a t i o n 5.11 were a c t u a l l y used. Indeed, Mobley's r e p o r t e d s p i n exchange c r o s s s e c t i o n s a r e about 40% s m a l l e r than those g i v e n h e r e . T h i s i s perhaps an i n d i c a t i o n of the e x p e c t e d i n t e r f e r e n c e by c h e m i c a l r e a c t i o n s which are n e g l e c t e d i n e q u a t i o n 5.12. An a l t e r n a t e e x p l a n a t i o n i s t h a t the poor s t a t i s t i c a l q u a l i t y of Mobley's d a t a has l e a d t o t h i s d i s c r e p a n c y ( B r e w e r ( 1 9 7 5 ) ) . 5.6. Comparison With Theory And W i t h Hydrogen Atom R e s u l t s S i n c e i t seems c l e a r t h a t the e a r l i e r H atom s p i n exchange c r o s s s e c t i o n s measured by Berg and Brown a r e too l a r g e by a f a c t o r of about two, the f o l l o w i n g d i s c u s s i o n 184 w i l l c o n c e n t r a t e on a comparison of the p r e s e n t Mu atom r e s u l t s w i t h the c o r r e s p o n d i n g H atom r e s u l t s of A n d e r l e and of Gordon. Three c o n c l u s i o n s can be drawn from the data p r e s e n t e d i n t a b l e s 5 .3 and 5 . 7 : i ) w i t h i n the e r r o r s t h e r e i s no i s o t o p e e f f e c t i n e l e c t r o n s p i n exchange i n the temperature range 300K t o 478K i i ) <S^ efor NO i s about 30% l a r g e r than t h a t f o r C\ and i i i ) a l t h o u g h somewhat model dependent, t h e r e i s , w i t h i n e r r o r s , no temperature dependence seen i n £~ s e. I t i s of i n t e r e s t then t o compare the s e r e s u l t s w i t h t h e o r e t i c a l c a l c u l a t i o n s . In the u s u a l c o l l i s i o n t h e o r y framework, the c r o s s s e c t i o n a p p r o p r i a t e f o r s c a t t e r i n g of d i s t i n g u i s h a b l e p a r t i c l e s i s the f o l l o w i n g p a r t i a l wave sum, £~SE = ( T T / k 2 ) ^ ( 2 i + 1 ) s i n 2 A , 5.13 where A^ i s the d i f f e r e n c e between s i n g l e t and t r i p l e t phase s h i f t s f o r the s c a t t e r i n g of two s p i n 1/2 p a r t i c l e s (Mu+NO) or the d i f f e r e n c e between q u a r t e t and d o u b l e t phase s h i f t s f o r the s c a t t e r i n g of s p i n 1/2 and s p i n 1 p a r t i c l e s (Mu+0 2) ( A q u i l a n t i ( 1 9 8 0 ) ) . In the case of Mu(H)+H s p i n exchange, the i n t e r a c t i o n p o t e n t i a l s a r e v e r y w e l l known ( B e r l i n s k y ( 1 9 8 0 ) , S h i z g a l ( 1 9 7 9 ) ) . S h i z g a l has c a l c u l a t e d < T s e f o r t h i s case and f i n d s t h a t a t t e m p e r a t u r e s > 3 0 0 K , the r a t i o £^ E(H)/£^ E(Mu)=1 .0, t e n d i n g a s y m p t o t i c a l l y t o 0 . 8 at v e r y h i g h t e m p e r a t u r e s . At low T, p a r t i c u l a r l y <50K , pronounced resonance s t r u c t u r e i s p r e d i c t e d which s t r o n g l y 185 f a v o u r s <S 6^ f o r Mu s p i n exchange. U n f o r t u n a t e l y , a l t h o u g h the e x p e r i m e n t a l H+H s p i n exchange c r o s s s e c t i o n s a r e w e l l known over a wide t e m p e r a t u r e range (Crampton(1980), H a r d y ( 1 9 7 9 ) , D e s a i n t f u s e i e n ( 1 9 7 6 ) ) , the c o r r e s p o n d i n g ones f o r Mu+H are e x t r e m e l y d i f f i c u l t t o o b t a i n . In c o n t r a s t , the -measurements of Mu(H)+O a and NO s p i n exchange c r o s s s e c t i o n s a r e now a v a i l a b l e but i n t h i s case the i n t e r a c t i o n p o t e n t i a l s a r e not w e l l known. Recent c a l c u l a t i o n s , however, of Mu(H)+O x s p i n exchange have been c a r r i e d out which have y i e l d e d some agreement w i t h the p r e s e n t e x p e r i m e n t a l r e s u l t s ( A q u i l a n t i ( 1 9 8 0 ) ) . In the temperature range of i n t e r e s t , t h e r e a r e no open v i b r a t i o n a l or e l e c t r o n i c c h a n n e l s f o r the H(Mu)+0 2 r e a c t i o n , but r o t a t i o n a l i n t e r a c t i o n s need t o be t aken i n t o a c c o u n t . The consequent c o u p l e d c h a n n e l problem i s f o r m a l l y d i f f i c u l t t o s o l v e so t h a t c e r t a i n a p p r o x i m a t i o n s are u s u a l l y i n v o k e d . A q u i l a n t i uses two methods i n h i s c a l c u l a t i o n s ; one i s an a v e r a g i n g over the a n i s o t r o p i c s of the i n t e r a c t i o n t o g i v e a s p h e r i c a l l y symmetric i n t e r a c t i o n ( S I ) and the o t h e r i s t o average over the. s c a t t e r i n g a m p l i t u d e s o b t a i n e d at d i f f e r e n t f i x e d o r i e n t a t i o n s . I t was found t h a t the l a t t e r ' o r i e n t e d frame d e c o u p l e d ' (OFD) scheme was the most s u c e s s f u l , p a r t i c u l a r l y i n r e p r o d u c i n g the Mu d a t a ( f i g u r e 5.12). T a b l e 5.8 compares the p r e s e n t v a l u e s of 6~ S e f o r Mu+0 2 w i t h the (OFD) t h e o r e t i c a l c a l c u l a t i o n s of A q u i l a n t i over the measured temperature range. The t h e o r e t i c a l c r o s s s e c t i o n s a r e r o u g h l y two t i m e s 186 l a r g e r than the e x p e r i m e n t a l ones, f o r both Mu and H atom s p i n exchange; and show an i n c r e a s e w i t h t e m p e r a t u r e t h a t i s not seen i n t h e d a t a , a l t h o u g h the e x p e r i m e n t a l e r r o r must be kept i n mind. C o n s i d e r i n g the a p p r o x i m a t i o n s i n h e r e n t i n the. c a l c u l a t i o n s , t h e agreement between t h e o r y and experiment i s r e a s o n a b l e . I n p a r t i c u l a r , the r a t i o 6" S E-(H)/ S s e ( M u ) i s i n good agreement as shown i n f i g u r e 5.12. The dashed l i n e i s from the SI c a l c u l a t i o n w h i l e the s o l i d l i n e i s the OFD c a l c u l a t i o n . I t i s c l e a r t h a t the l a t t e r i n t e r a c t i o n g i v e s the b e s t agreement ( i . e . the r o t a t i o n a l a n i s o t r o p y i s i m p o r t a n t ) and t h i s may be a t t r i b u t a b l e t o the enhanced s e n s i t i v i t y of the Mu i n t e r a c t i o n t o r o t a t i o n a l s t a t e s of the 0^ m o l e c u l e , which c o u l d be e x p l a i n e d by the i n c r e a s e d mean r e l a t i v e v e l o c i t y w h erein the muonium i n t e r a c t i o n time i s s h o r t e n e d so t h a t i t o n l y sees one o r i e n t a t i o n of the oxygen at a t i m e , whereas the s l o w e r H atom s t a y s around l o n g enough t o have any r o t a t i o n a l a n i s o t r o p y averaged o u t . The enhanced s e n s i t i v i t y of t h e o r e t i c a l c a l c u l a t i o n s t o the r e a c t i o n s of muonium p r o v i d e s m o t i v a t i o n f o r c o n t i n u e d study of t h i s u l t r a - l i g h t i s o t o p e of hydrogen, an a s p e c t which i s p a r t i c u l a r l y c r u c i a l i n s t u d y i n g c h e m i c a l r e a c t i o n s of muonium ( G a r n e r ( 1 9 7 9 ) , F l e m i n g ( 1 9 8 1 ) ) . A l t h o u g h d e t a i l e d c a l c u l a t i o n s a r e c l e a r l y the most d e s i r a b l e , a s o l u t i o n of e q u a t i o n 5.13 based on the random phase a p p r o x i m a t i o n (RPA) p r o v i d e s a s i m p l e b a s i s f o r comparing £>W f o r H and Mu w i t h a paramagnetic m o l e c u l e 187 Reaction Temperature (K) ° g P ' Q 0 ' 1 6 c n , 2 ) ^ 0 ^ 1 6 ^ 2 ) Mu+O 2 9 5 + 5 Mu+O, 4 0 0 ± 5 Mu+0 2 4 3 8 + 5 Mu+0 2 4 7 8 ± 5 H + 0 2 9 5 H + 0 ^ 3 1 0 H + O ; 3 1 5 H + 0 , 3 5 0 H + O ^ 3 8 8 7 . 9 ± 1 . 0 B ) 1 5 2 8 . 9 + 1 . 0 2 0 . 0 9.7± 0 . 7 2 2 1 9.811.7 24.'o 1 0 ± 1 C ) d) H + O 2 9 5 2 1 + 2 . 1 E ) H + N O 2 9 5 2 5 + 2 . 5 a") AepxiLvxti (H?0) t) TI^ Js tresis c) A^Jlerle (1180 1 6 . 7 8 . 8 ± 0 . 7 ^ 1 6 . 9 9 . 8 ± 1 . 0 1 7 ! 8 . 3 + 0 . 7 1 9 ; 8 8 . 0 ± 0 . 7 2 1 . 9 T a b l e 5.8. £Tse f o r Mu+C\ ; comparison of t h e o r y and exper iment. 188 ~ 500 1000 T E M P E R A T U R E , Kelvin F i g u r e 5.12. T h e o r e t i c a l s p i n exchange c r o s s s e c t i o n s from A q u i l a n t i ( 1 9 8 0 ) . The t o p f i g u r e g i v e s the temp e r a t u r e averaged f o r b o t h H and Mu w i t h O x w h i l e the bottom g i v e s t h e i r r a t i o (R) . I n both f i g u r e s , the d o t t e d l i n e r e p r e s e n t s c a l c u l a t i o n s w i t h the SI a p p r o x i m a t i o n w h i l e the s o l i d l i n e i s from the OFD c a l c u l a t i o n . 189 ( W i t t k e ( 1 9 5 6 ) , G l a s s g o l d ( 1 9 6 4 ) , S h i z g a l ( 1 9 7 9 ) ) . I f t h e r e a r e enough p a r t i a l waves c o n t r i b u t i n g t o the s c a t t e r i n g c r o s s s e c t i o n , t h e n , i n the most s i m p l i s t i c form of t h i s a p p r o x i m a t i o n , a c u t - o f f p a r t i a l wave, Jtc , can be d e f i n e d such t h a t f o r J<lc, s i n 2 A j = l / 2 and f o r i >lc , sin 2 A j ; = 0. C o n s e q u e n t l y , e q u a t i o n 5.13 reduces t o the form £~"SE =(7T/2k 2) 2. ) 5.14 He where, w i t h the f u r t h e r a p p r o x i m a t i o n t h a t ^ ( 2 i + 1 ) = i 2 , 67r = R2TT/2 5.15 By d e f i n i n g a sharp c u t - o f f r a d i u s R c , e q u a t i o n 5.15 then p r e d i c t s an e f f e c t i v e mass and temperature independent g e o m e t r i c a l c r o s s s e c t i o n f o r s p i n exchange, c o n s i s t e n t w i t h the e x p e r i m e n t a l r e s u l t s . The p h y s i c a l i n t e r p r e t a t i o n of R t i s t h a t i t r e p r e s e n t s the i n t e r a c t i o n r a d i u s where the d i f f e r e n c e i n phase s h i f t s goes t o z e r o . These r e s u l t s i n d i c a t e t h a t the b a s i c Mu(H) atom s p i n exchange i n t e r a c t i o n i s one of s h o r t range. U s i n g an e f f e c t i v e c r o s s s e c t i o n of 1 0 x 1 0 " 1 6 c m 2 ( r o u g h l y the average of the e x p e r i m e n t a l c r o s s s e c t i o n s f o r both NO and O a) one o b t a i n s a c u t - o f f r a d i u s of R =2.5 X; ( i . e . beyond an i n t e r a c t i o n r a d i u s of 2.5A" the d i f f e r e n c e between t r i p l e t and s i n g l e t ( q u a r t e t and d o u b l e t ) s c a t t e r i n g p o t e n t i a l s r a p i d l y f a l l s t o z e r o ) . A l t h o u g h the random phase a p p r o x i m a t i o n of e q u a t i o n 190 5.15 i s a s i m p l i s t i c view of the p r o c e s s , i t i s c o n s i s t e n t w i t h S h i z g a l ' s c a l c u l a t i o n s f o r T>300K f o r Mu(H)+H and i s a l s o i n good agreement w i t h the r e c e n t Mu(H)+O a c a l c u l a t i o n s done by A q u i l a n t i ( 1 9 8 0 ) . In the c a l c u l a t i o n s of S h i z g a l , the number of p a r t i a l waves making s i g n i f i c a n t c o n t r i b u t i o n s t o the H + H c r o s s s e c t i o n i s r e l a t i v e l y s m a l l , <25 near 300K. S i n c e the muonium atom mass i s o n l y 1/9 t h a t of the hydrogen atom, the c o r r e s p o n d i n g number of p a r t i a l waves f o r Mu + H s p i n exchange i s <10 near 300 K. T h i s might seem too few f o r e q u a t i o n 5.15 t o have much v a l i d i t y but n e v e r t h e l e s s t h e s i m p l e i n t e r p r e t a t i o n f o l l o w i n g from t h a t e q u a t i o n i s c o n s i s t e n t w i t h the c a l c u l a t e d r e s u l t s . In the c a l c u l a t i o n s of both S h i z g a l and A q u i l a n t i no dominant resonance s t r u c t u r e i s p r e d i c t e d beyond -~. 05eV (~500K) and the t h e r m a l l y averaged s p i n exchange c r o s s s e c t i o n s f o r Mu and H a r e indeed p r e d i c t e d t o be e s s e n t i a l l y mass independent a t 300K. I t i s o n l y a t low e n e r g i e s and, c o n s e q u e n t l y , low t e m p e r a t u r e s , p a r t i c u l a r l y below 50K, where marked resonance e f f e c t s due t o t h e v e r y l i g h t Mu atom mass a r e l i k e l y . The t h e o r y can be more t h o r o u g h l y t e s t e d by g o i n g t o lower t e m p e r a t u r e s and t h i s i s an i m p o r t a n t next s t e p f o r the exper i m e n t a i i s t . 191 APPENDIX 1. THE TIME EVOLUTION OF THE MUON SPIN IN A TRANVERSE MAGNETIC FIELD The e x p l i c i t s o l u t i o n of the problem of the time dependence of the muon s p i n i n muonium has been d i s c u s s e d i n almost e v e r y review of the yjSR t e c h n i q u e ( G u r e v i c h ( 1 9 7 1 ) , Brewer(1975) , Schenck( 1 975) , P e r e i v a l ( 1 9 7 6 ) , Fleming(19 7 9 ) and Garner(19 7 9 ) ) and w i l l not be t r e a t e d i n d e t a i l h e r e . The t r i v i a l problem of the time dependence of the muon s p i n i n p* w i l l be s e t up t o i l l u s t r a t e the method i n v o l v e d , and the f i n a l r e s u l t f o r the yu* s p i n i n muonium w i l l be g i v e n . When the muon t h e r m a l i z e s i n matter i t s s p i n remains p o l a r i z e d so t h a t i n z e r o f i e l d i f one t a k e s the muon s p i n d i r e c t i o n as the p o l a r i z a t i o n a x i s , t h e r e i s o n l y one s t a t e |oC>. The experiment i s done i n t r a n s v e r s e f i e l d , however, so the q u a n t i z a t i o n a x i s must be r o t a t e d 90 degrees v i a the s p i n 1/2 r o t a t i o n m a t r i x \ A1 . 1 O p e r a t i n g on the s t a t e |oC> we have a new s t a t e v e c t o r 1 92 f o r the t r a n s v e r s e f i e l d e x p e r i m e n t a l s i t u a t i o n . A1 .2 The H a m i l t o n i a n f o r t h i s s i m p l e system i s T B J A1 .3 where g^ u i s the muon g f a c t o r ( ~ 2 ) , py*=eti/2mc, the muon magneton and i s the magnetic f i e l d . The m a t r i x r e p r e s e n t a t i o n of H w i t h r e s p e c t t o the | <* >, \ f> b a s i s s e t i s ( w i t h =g^ » ^ B l ) H - A1 .4 71 The e n e r g i e s of the b a s i s v e c t o r s are used t o w r i t e the time dependence of the s t a t e v e c t o r i n a t r a n s v e r s e magnetic f i e l d ( a l o n g the z d i r e c t i o n ) as In o r d e r t o f i n d the time dependence of the muon s p i n p o l a r i z a t i o n i n the x-y p l a n e , one must use the the p o l a r i z a t i o n o p e r a t o r = S^+iS"^ =6"+ where the G's are the P a u l i s p i n o p e r a t o r s : 1 9 3 6* + U>* 0 ^ \ f > - 2I<*> A1 .6 thus the p o l a r i z a t i o n i s s i m p l y A1 .7 Thus the r e a l p a r t of the muon p o l a r i z a t i o n i n the x-y plan e e x h i b i t s a Larmor p r e c e s s i o n , cos(w^it) i n ana l o g y t o e q u a t i o n 1.4 from c h a p t e r 1. The d e t e r m i n a t i o n of the muon p o l a r i z a t i o n i n muonium i s f a r more c o m p l i c a t e d , but f o l l o w s a s i m i l a r r o u t e . As the muon t h e r m a l i z e s i t can c a p t u r e e l e c t r o n s from the media. These e l e c t r o n s a r e u n p o l a r i z e d so t h a t muonium forms i n i t i a l l y i n two s t a t e s w i t h e q u a l p r o b a b i l i t y , the |oCy* cLc> " t r i p l e t " s t a t e and the 1 /^x ( l o ^ u ^ t > _ oit>) " s i n g l e t " s t a t e . I t i s c o n v e n i e n t t o change the b a s i s from the |nyme> t o the |Fsms> system where Fs r e p r e s e n t s the h y p e r f i n e a n g u l a r momentum and ,v i t s p r o j e c t i o n on the q u a n t i z a t i o n a x i s . In t h i s b a s i s one has ( i n z e r o f i e l d ) l l , l > * |<A<*> |l,0>« VaO<H> *V>) lo,o>= A1 .8 1 94 Then the q u a n t i z a t i o n a x i s can be r o t a t e d ' -t o g i v e the s t a t e s i n a weak t r a n s v e r s e magnetic f i e l d which a r e ' ft The H a m i l t o n i a n f o r the muonium system i s A1 . 1 0 where S and I are the e l e c t r o n and muon s p i n o p e r a t o r s and a i s the Fermi c o n t a c t term, ( C a r r i n g t o n ( 1 9 6 7 ) ) , d e f i n e d by A1 . 1 1 In f r e q u e n c y u n i t s f o r Mu v,0=4463MHz compared t o 1420MHz f o r the H atom. The fi m a t r i x i n the | > r e p r e s e n t a t i o n i s A1 . 1 2 u) . a % + 4 195 from which the e n e r g i e s of the s t a t e s and hence t h e i r time dependence can be c a l c u l a t e d . Note t h a t w± = l / 2 ( w < . / f i t w r / f t ) and the h y p e r f i n e f r e q u e n c y O0=a/h=we/2TT. The energy l e v e l s a r e i l l u s t r a t e d i n the f a m i l i a r B r ^ j t - R a b i diagram ( B r e i t ( 1 9 3 1 ) , Feynmann(1965)) shown i n f i g u r e A1.1. In weak f i e l d s t he t r a n s i t i o n s and a r e degenerate and i t i s f o r t h i s reason t h a t the MSR experiment i s done a t low f i e l d . As the f i e l d i s r a i s e d , the degeneracy i s l o s t and two f r e q u e n c y muonium p r e c e s s i o n can be observed as i l l u s t r a t e d i n f i g u r e A 1 . 2 , which shows muonium in solid argon a t 66.5 gauss ( K i e f 1 ( 1 9 8 1 ) ) . Now t h a t the time dependent s t a t e s can be w r i t t e n , a p p l i c a t i o n of the p o l a r i z a t i o n o p e r a t o r l e a d s t o : A1 . 1 3 VTo? * ' J where SL » (v? * n?") * " i s the beat f r e q u e n c y noted e a r l i e r and x = 2w +/w 0 . At low f i e l d x«0 and the r e a l p a r t of the p o l a r i z a t i o n can be w r i t t e n as Re< 4 5 \ [ Coo (u.t) CctoUlt) +• CaO (iJ-t) C«o po +Jl) t] A1 . 1 4 where the cos (w_t )cos (Jit) term a r i s e s from the o r i g i n a l t r i p l e t muonium f r a c t i o n w h i l e the cos(w_ t ) c o s ( w e t term 1 T i 1 1 r 1 2 3 FIELD (H/H0) F i g u r e A 1 . 1 . B r i e t - R a b i diagram showing the energy l e v e l s of muonium i n a t r a n s v e r s e magnetic f i e l d . In weak f i e l d s ( < 1 0 G ) \>a and a r e degenerate and t h i s l e a d s t o the c h a r a c t e r i s t i c muonium p r e c e s s i o n . 197 a r i s e s from the o r i g i n a l s i n g l e t muonium f r a c t i o n ; w.. , d e f i n e d e a r l i e r , e q u a l s 103VCU, which i s the c h a r a c t e r i s t i c muonium p r e c e s s i o n f r e q u e n c y . I t s h o u l d be noted t h a t the terms t r i p l e t and s i n g l e t a r e merely c o n v e n i e n t l a b e l s and have no p r e c i s e meaning i n t h i s p u r e l y quantum m e c h a n i c a l d e r i v a t i o n . C l a s s i c a l l y , a s i n g l e t or t o t a l s p i n z e r o system would not p r e c e s s i n a t r a n s v e r s e magnetic f i e l d (because of z e r o d i p o l e moment). The t r i p l e t s t a t e would p r e c e s s and f o r t h i s reason the o b s e r v a b l e component of e q u a t i o n A1.14 i s a s c r i b e d t o t r i p l e t muonium and the un o b s e r v a b l e component t o s i n g l e t muonium. Hence the l o s s of asymmetry due t o " s i n g l e t " muonium f o r m a t i o n i s due t o the l i m i t e d time r e s o l u t i o n of the e x p e r i m e n t a l a p p a r a t u s . At a t y p i c a l f i e l d of t e n gauss, the c o r r e s p o n d i n g p r e c e s s i o n f r e q u e n c i e s and p e r i o d s a r e - %l.fo\xlO\r^ / 3 . = 7 / .%s period A1 . 1 5 _TL= O.nxI0bn*Jl/s . C W , M r b B 22.^$ period S i n c e the e x p e r i m e n t a l a p p a r a t u s t y p i c a l l y has a time r e s o l u t i o n of about 5 ns, i t can be seen t h a t t h e second term of e q u a t i o n A1.14 has too s h o r t a p e r i o d t o be r e s o l v e d and hence i t averages t o z e r o . The f i r s t term i s the c h a r a c t e r i s t i c muonium p r e c e s s i o n modulated by the v e r y slow 1 98 c o s ( A t ) term. F i g u r e A1.3 shows a p l o t of e q u a t i o n A1.14 i n a f i e l d of 100 gauss assuming p e r f e c t time r e s o l u t i o n . The s i n g l e t muonium s i g n a l i s shown r a p i d l y o s c i l l a t i n g between one and z e r o , but much t o o f a s t t o be d e t e c t a b l e . Thus the net r e s u l t i s t h a t one can o n l y observe the average of the s i g n a l which i s shown by the d o t t e d l i n e . Or, s t a t e d another way, the f o r m a t i o n of s i n g l e t muonium l e a d s t o a d e p o l a r i z a t i o n ( i . e . h a l f the s i g n a l i s u n o b s e r v a b l e due t o the e x p e r i m e n t a l time r e s o l u t i o n ) . T h i s i s the reason the e x p e r i m e n t a l l y o b s e r v e d muonium asymmetry i s m u l t i p l i e d by two when the t o t a l asymmetry i s c a l c u l a t e d . T r i p l e t muonium can o n l y be obser v e d a t low f i e l d s where the and ^ r j degeneracy i s m a i n t a i n e d . At f i e l d s of 75 gauss where the muon s i g n a l i s o b s e r v e d , the w_ term becomes u n r e s o l v a b l e and the muonium s i g n a l e f f e c t i v e l y averages t o z e r o , a l l o w i n g i n t e r f e r e n c e f r e e o b s e r v a t i o n of the p* asymmetry. 199 L O O Adl3WWASU o o o LO LO C\J O O O LO CM LO O F i g u r e A 1 . 2 . Muonium S ( t ) in s o l i d Ar (77K) at 66.5G showing two f requency p r e c e s s i o n of the muon sp in (from K i e f K 1981 ) ) . F i g u r e A 1 . 3 . MSR spectrum w i t h p e r f e c t time r e s o l u t i o n . The time e v o l u t i o n of the ii* s p i n i n muonium i n a 100G t r a n s v e r s e magnetic f i e l d . E x p e r i m e n t a l l y , the f a s t o s c i l l a t i o n s a t the h y p e r f i n e f r e q u e n c y are averaged over g i v e the MSR s i g n a l r e p r e s e n t e d by the d o t t e d l i n e . 201 APPENDIX 2. THE MONTE CARLO SIMULATION AND EXPERIMENTAL  TESTS OF THE STOPPING DISTRIBUTION ON THE OBSERVED ASYMMETRY T h i s Monte C a r l o program was d e s i g n e d t o s i m u l a t e the MSR experiment t o determine the e f f e c t of c o u n t e r s i z e and muon s t o p p i n g d i s t r i b u t i o n on the measured asymmetry. As d i s c u s s e d i n c h a p t e r 3, t h e r e a r e two main c o n t r i b u t i o n s t o the change i n t o t a l asymmetry as a f u n c t i o n of t a r g e t p r e s s u r e . One i s the i n c r e a s e d time spent as a n e u t r a l at lower p r e s s u r e s ( i . e . muonium i n the s i n g l e t s t a t e w i l l become u n o b s e r v a b l e ) , which causes a l o s s of asymmetry due to d e p o l a r i z a t i o n v i a the h y p e r f i n e i n t e r a c t i o n . T h i s e f f e c t has been d i s c u s s e d i n Appendix 1. At lower p r e s s u r e s the muon s t o p p i n g d i s t r i b u t i o n i s a l s o i n c r e a s e d and t h i s c o u l d a l s o l e a d t o a reduced asymmetry s i n c e a l a r g e muon s t o p p i n g r e g i o n i s e q u i v a l e n t t o a l a r g e c o u n t e r s i z e , as i l l u s t r a t e d i n f i g u r e A 2 . 1 . The asymmetry can be w r i t t e n as A= Mf-Ni =Ae- y t cos(wu t + i )=Acos*> A2.1 where N L and Ne. a r e the number of c o u n t s i n the l e f t and r i g h t p o s i t r o n t e l e s c o p e s , r e s p e c t i v e l y . T h i s e q u a t i o n h o l d s f o r p o i n t d e t e c t o r s , as l o n g as the n o r m a l i z a t i o n s a re 202 F i g u r e A2.1. R e l a t i o n s h i p of c o u n t e r s i z e and s t o p p i n g d i s t r i b u t i o n . Case I w i t h muons s t o p p i n g a l o n g the l e n g t h of the gas t a r g e t l e a d s t o p o s i t r o n d e t e c t i o n as e a r l y as t ^ ( p o i n t C) and as l a t e a.s t, ( p o i n t A). T h i s l e a d s t o a l o s s of asymmetry compared t o the case where a l l of the muons s t o p at p o i n t B. T h i s can be seen by comparing case I I and case I where the times a re the same ( i . e . a l a r g e s t o p p i n g d i s t r i b u t i o n i s e q u i v a l e n t t o a l a r g e s o l i d a n g l e , or l a r g e c o u n t e r s i z e . E q u a t i o n A2.2 shows how t h i s l a r g e c o u n t e r s i z e can l e a d t o a l o s s of asymmetry. 203 the same f o r r i g h t and l e f t , r e l a x a t i o n s a r e t h e same and taken t o be z e r o , and the c o u n t e r s a r e 180 degrees a p a r t . However, the c o u n t e r s have a s i z e and a f t e r i n t e g r a t i n g over t h i s s o l i d a n g l e one has <A>=Acos 2 (-e/2) A2.2 where O* i s the h a l f a n g l e subtended by t h e p o s i t r o n t e l e s c o p e (as shown i n f i g u r e A2.1), A i s t h e asymmetry assuming i n f i n i t e l y s m a l l c o u n t e r s and <A> i s t h e obser v e d average asymmetry. Even i n g o i n g from i n f i n i t e l y s m a l l t e l e s c o p e s t o i n f i n i t l y l a r g e t e l e s c o p e s , the use of t h i s f o r m u l a o n l y p r e d i c t s a f a c t o r of two change i n asymmetry. From t a b l e A2.1 i t can be seen t h a t t h e r e a r e much l a r g e r e f f e c t s than t h i s . The f o r m u l a i n e q u a t i o n A2.2 does not a l l o w f o r any r o t a t i o n of the muon s p i n d u r i n g t h e r m a l i z a t i o n f o r muons s t o p p i n g f u r t h e r down the gas can, nor does i t account f o r muons w i t h a d i s t r i b u t i o n i n the y d i r e c t i o n ( l a t e r a l l y a c r o s s the c a n ) . For t h e s e r e a s o n s , a Monte C a r l o program was w r i t t e n t o account f o r t h e s e p o s s i b i l i t i e s and d e t e r m i n e t h e i r e f f e c t on t h e asymmetry. S i n c e the muon p o l a r i z a t i o n i s p r e d o m i n a n t l y i n t h e x-y p l a n e , o n l y t h i s p l a n e has been c a l c u l a t e d , a c o n s i d e r a t i o n a l s o d i c t a t e d by the c o s t of the program. The random number g e n e r a t i o n f o r the v a r i o u s f u n c t i o n s i n v o l v e d was a c c o m p l i s h e d by f i r s t c h o o s i n g the x - a x i s number of a g i v e n f u n c t i o n and then randomly c h o o s i n g a y Target and A Pressure He l 8 p s i .I54t.004 .0351.005 0 .12 He 40psi .2101.003 .071.01 0 .14 He 43psi .2221.002 .0871.01 0 .14 Ne 6psi .0901.005 -.04 .0101.006 .07 Ne t2psi .1001.002 -.03 .0221.001 .11 Ne tBpsi . 1701.002 -0 .0051.005 .18 Ne 24psi .255t.003 -.015 "0 .24 Ne 30psi .3001.002 -.009 .0271.002 .35 Ar 8psi .0791.003 .071.002 .0381.003 .09 Ar I5psi .0741.002 .022*.002 .078i.003 .21 Ar 15psi .0701.002 .0091.002 .1001.002 .26 Ar 30psi .0921.003 .0151.002 . 111*.004 .30 Ar 36psi .1001.003 -0 .1301.004 .36 Kr 6psi .0651.004 .065 .040*.004 .08 Kr lOpsi .0201.003 .02 .0861.004 .17 Kr I4psi ~0 -0 .1201.006 .24 Ze 6psi .0461.003 .046 .0501.003 .10 Ze 9psi ~0 ~0 .0701.010 .14 Ze lOpsi .0401.010 .040 .0891.006 .18 6psi a i r has Au-.071.01 15psi a i r + lOpsi He has A^j«.0241.0l These r e s u l t s i n d i c a t e that the Au in the Zenon and are due only to muons stopping i n the walls of the t a r g e t . Thus one can conclude that there i s 100% muonium formation in these gases. Tab le A 2 . 1 . T o t a l asymmetry as a f u n c t i o n of p r e s s u r e . 205 v a l u e . I f the y v a l u e chosen i s l e s s than the y v a l u e c a l c u l a t e d u s i n g the random x v a l u e then t h a t p o i n t i s used, i f not then new x and y v a l u e s a re chosen and the p r o c e s s i s r e p e a t e d u n t i l a match i s found. T h i s can be i l l u s t r a t e d by c o n s i d e r i n g the e x p o n e n t i a l decay of the muon y = e ~ * ' ^ f - . F i r s t the f u n c t i o n i s n o r m a l i z e d t o the range 0 — M f o r the x and y a x i s , and then an x v a l u e i s p i c k e d a t random. Then a random y' v a l u e i s chosen and i f t h i s y' v a l u e i s l e s s t han or e q u a l t o the y c a l c u l a t e d g i v e n the random x v a l u e , the p o i n t i s a good one and x i s used as the time of the muon's decay. I f y'>y then the p r o c e s s i s r e p e a t e d . T h i s has the e f f e c t of r e p r o d u c i n g the f u n c t i o n i f enough e v e n t s a r e p r o c e s s e d . The program i t s e l f i s q u i t e s t r a i g h t f o r w a r d and g e n e r a l l y s e l f e x p l a n a t o r y ( l i s t i n g i n t a b l e A2.2). The r e s u l t of the program i s shown i n f i g u r e A2.2 w i t h the f i t t e d v a l u e f o r the asymmetry. The c o u n t e r s i z e s can e a s i l y be v a r i e d as can the muon s t o p p i n g d i s t r i b u t i o n and the f i e l d inhomogeniety. As can be seen from f i g u r e A2.1 and t a b l e A2.1, even w i t h the l a r g e s t s t o p p i n g d i s t r i b u t i o n , ( r e g u l a t e d by the s i z e of the a p p a r a t u s ) , the change i n asymmetry i s not n e a r l y enough t o account f o r what i s obs e r v e d as a f u n c t i o n of p r e s s u r e . In a d d i t i o n t o the Monte C a r l o s i m u l a t i o n , an e x p e r i m e n t a l change of s o l i d a n g l e ( k e e p i n g the t a r g e t p r e s s u r e c o n s t a n t ) and s t u d i e s w i t h d i s t r i b u t e d aluminum f o i l s were c a r r i e d out as d e s c r i b e d i n c h a p t e r 2. A l l had o n l y a s m a l l e f f e c t on t h e SLIST ASYTEST *PRINT* 1 DIMENSION RIGHT(500),LEFT(500) 2 INTEGER LEFT,RIGKT,C 3 DO 3 1=1,500 4 RIGKT(I)=0.0 5 3 LEFT(I)=0.0 6 REAL H,J,K,HYP 7 8 A=0.5 B=1.0 9 D=2.0 10 J = 3.0 11 K=4.0 12 YY=5.0 13 BY=6.0 14 PHI=0.0 15 PI=3.14159 16 PI2=PI/2.0 17 5 DO 100 1=1,500000 18 C 19 C. ..PICK X-STOPPING POSITION 20 c 21 10 A=FRAND(A) 22 AA=16.0*A-8.0 23 AB=AA*AA 24 F=EXP(-AB/100.) 25 B=FRAND(B) 26 IF(F.GE.B)GO TO 11 27 GO TO 10 28 11 CONTINUE 29 c 30 c. ..PICK Y-STOPPING POSITION 31 c 32 12 YY=FRAND(YY) 33 Y=YY*10.0-5.0 34 YB=Y*Y 35 YEX=EXP(-YB/4.0) 36 BY=FRAND(BY) 37 IF(YEX.GE.BY)GO TO 15 38 GO TO 12 39 15 CONTINUE 40 c 41 c. ,..PICK DECAY TIME 42 c 43 20 C=IRAND(500) 44 X=C 45 G = EXP(-X/2200. ) 46 D=FRAND(D) 47 IF (G.GE.D) GO TO 21 48 GO TO 20 49 21 CONTINUE 50 AABS=ABS(AA) 51 YABS=ABS(Y) 52 HYP=SQRT((AABS*AABS)+(YABS*YABS 53 E=(8.78336E-3)*X*(6.00-((HYP*0.i 54 c T a b l e A2.2. Monte C a r l o program l i s t i n g . 207 55 C...PICR POSITRON DIRECTION FROM CARDIOID 56 C 57 30 J"FRAND(J) 56 J=J*2.0*PI 56.5 PHI«(6.78336E-3)*AABS*5.0 59 2«E*J+PH2 60 H-1.0+0.2*COS(J) 62 K-FRAND(K) 62 K=K*1.2 63 IF (K.GE.K) GO TO 31 64 GO TO 30 65 31 CONTINUE 66 FA=Z/(2.0*PI ) 67 L-IFIX(FA) 66 Z=Z-L*2.0*PI 69 IF(AABS.GT.4.0)GO TO 50 70 IFU.LE.PI)GO TO 33 71 C 72 C...FOP. MUONS IN BETWEEN COUNTERS 73 C...FOR LEFT SIDE 74 C 75 ASTN=ATAN((4.0-AA)/(18.0+Y)) 76 APTN=ATAN<(4 .0+AA)/U8.0+Y)) 77 Ki«3.0*PI2+APTN 76 W2=3.0*PI2-ASTN 79 32 IF (Z.GT.W1) GO TO 60 80 IF (Z.GE.W2) GO TO 39 61 GO TO 60 82 C 63 C...FOR RIGHT SIDE 84 C 8 5 33 ASTNl=ATAN((4.0-AA!/(18.0-y)) 86 APTN1-ATAN((4.0+AA)/(IB.0-Y)) 67 W3=P12+ASTN1 88 W4=P12-APTN1 69 IF (2.GT.W3) GO TO 60 90 IF (Z.GE.W4) GO TO 38 91 GO TO 60 92 38 RIGHT(C)«RIGHT(C)+1 93 > GO TO 100 94 39 LEFT(C)»LEFT(C)+1 95 GO TO 100 96 C 97 C...FOR MUONS OUTSIDE COUNTERS 96 C...FOR MUONS AA POSITIVE 99 C 100 50 IF (AA.LE.0.0)GO TO 55 101 C 102 C...FOR POSITIVE LEFT SIDE 103 C 104 IF (Z.LE.PI)GO TO 51 105 ATN3=2.0*PI-ATAN((18.0+Y)/(4.0+AA)) 106 ATN4=2.0*PI-ATAN((6.0+Y)/(-4.0*AA)) 107 IF (Z.GT.ATN3)GO TO 60 10B IF (Z.GE.ATN4)GO TO 39 109 GO TO 60 110 C Tab le A 2 . 2 . Cont inued 111 C...FOR P O S I T I V E K 1UHT b l i i t " 112 C 113 51 WW1=ATAN((6.0-Y)/(-4.0+AA)) 114 WW2=ATAN((18.0-y)/(4.0+AA)) 115 IF (Z.GT.WWl)GO TO 60 116 IF (Z.GT.WW2)GO TO 36 117 GO TO 60 118 C 119 C...FOR MUONS AA NEGATIVE 120 C...FOR NEGATIVE LEFT SIDE 121 C 122 55 IF (Z.LE.PI)GO TO 56 123 WW3=PI+ATAN((6.0+Y)/(-4.0-AA)) 124 WW4=P1+ATAN((18.0+Y)/(4.0-AA)) 125 IF(Z.GT.WW3)GO TO 60 126 IF(Z.GE.WW4)G0 TO 39 127 GO TO 60 128 C 129 C...FOR NEGATIVE RIGHT SIDE 130 C 131 56 WW5=PI-ATAN((6.0-Y)/(-4.0-AA)) 132 WW6=PI-ATAN((18.0-Y)/(4.0-AA)) 133 IF(Z.GT.WW6)GO TO 60 134 IF (Z.GE.WW5)GO TO 38 135 GO TO 60 136 60 GO TO 10 137 100 CONTINUE 138 WRITE(6,999) LEFT 139 WRITE(6,999) RIGHT 140 999 FORMATU0I8) 141 STOP 142 END End of F i l e Tab le A 2 . 2 . Cont inued 209 LO LO LO LO LO O ' 1 O Q i — i C\i O Q Q O O AcJ13WWASd F i g u r e A2.2. Monte C a r l o d a t a S ( t ) and f i t . T h i s shows the r e s u l t s of a f l a t muon d i s t r i b u t i o n t h roughout the can (the worst p o s s i b l e case) which o n l y l e a d s t o a r e d u c t i o n of asymmetry of 10% from .20 t o .18. 210 obser v e d asymmetry. These r e s u l t s a r e summarized i n t a b l e A2.3. The i n e s c a p a b l e c o n c l u s i o n from these c a l c u l a t i o n s i s t h a t l a r g e changes observed i n asymmetry a r e due t o f o r m a t i o n of s i n g l e t muonium d u r i n g t h e r m a l i z a t i o n , c a u s i n g an a d d i t i o n a l l o s s of p o l a r i z a t i o n a t lower p r e s s u r e s . Target A l P l a t e A l P l a t e and mylar l i n i n g A l f o i l s 5" spread A l f o i l s 25" spread Argon small s o l i d angle Argon large s o l i d angle Monte Carlo with small stopping d i s t r i b u t i o n Monte Carlo with large stopping d i s t r i b u t i o n T o t a l Asymmetry .35 .35 .34 .32 .313 .305 .20 .18 Lambda .04 ,04 .04 .06 14 .21 .01 The large s o l i d angle refer™* to in the tab l e corressponds to 4> 34 degrees and the small s o l i d angle r e f e r s to & of 18 degrees. Tab le A 2 . 3 . Expe r imenta l and Monte C a r l o asymmetry t e s t s . 212 APPENDIX 3. THE SPIN EXCHANGE F FACTORS There w i l l be no attempt here t o g i v e a d e t a i l e d e x p l a n a t i o n of the s p i n exchange t h e o r y . T h i s s e c t i o n i s o n l y i n t e n d e d t o g i v e a b r i e f o u t l i n e of how the f f a c t o r s i n the s p i n exchange c r o s s s e c t i o n s of c h a p t e r 5 a r i s e . The approach used here f o l l o w s t h a t of B a l l i n g et a l (1963) where the t h e o r y has been worked out i n d e t a i l . For an incoming p l a n e wave g i v e n by A3 . 1 where 1/LV-1- i s a n o r m a l i z a t i o n f a c t o r and | s 0 > i s the i n i t i a l s p i n s t a t e of the system, the s c a t t e r e d wave can then be w r i t t e n a s y m p t o t i c a l l y as el*-''is.> * sil MS.(U) I S„> A3.2 where M s s(k : k„ ) i s i n g e n e r a l a m a t r i x i n s p i n space which a c c o u n t s f o r the p o s s i b i l i t y of s p i n s t a t e changes. I f one assumes t h e r e i s no s p i n - o r b i t c o u p l i n g and t h a t the s c a t t e r i n g can be d e s c r i b e d i n terms of independent phase s h i f t s ( i . e . s i n g l e t and t r i p l e t phase s h i f t s f o r the s p i n 1/2, s p i n 1/2 system of n i t r i c o x i d e and muonium and q u a r t e t 213 and d o u b l e t phase s h i f t s f o r the s p i n 1/2, s p i n 1 system of oxygen and muonium), then the M m a t r i x t a k e s the form h--i>)R, « r A 3' 3 where the f s are the s c a t t e r i n g a m p l i t u d e s and the P's are the p r o j e c t i o n o p e r a t o r s f o r the p a r t i c u l a r s p i n s t a t e s . In terms of the P a u l i s p i n m a t r i c e s , the p r o j e c t i o n o p e r a t o r s a r e d e f i n e d a s : P^  = Mb * ^ A3 . 4 P, = V4( \ - G„0 • G n v ) PH = l41H + e;.- ^ p x s ' 4 ( 2 - <s\U T h i s a l l o w s one t o w r i t e the s c a t t e r i n g m a t r i x M as and the s c a t t e r i n g a m p l i t u d e s can be expanded i n terms of the phase s h i f t s as A3. 6 214 B a l l i n g et a l have used a d e n s i t y m a t r i x f o r m a l i s m where p i s the i n i t i a l d e n s i t y m a t r i x and p' = S ^>S +is the d e n s i t y m a t r i x a t an i n f i n i t e time a f t e r the c o l l i s i o n ; w i t h S as the u s u a l s c a t t e r i n g m a t r i x r e l a t e d t o M by a f t e r some m a n i p u l a t i o n s and s u b s t i t u t i o n s i n t o the e q u a t i o n f o r p ' , ( t r e a t e d i n d e t a i l i n B a l l i n g ( 1 9 6 3 ) ) , the d e r i v a t i v e of the d e n s i t y m a t r i x w i t h r e s p e c t t o time can be taken t o g i v e the time r a t e of change of the muonium d e n s i t y m a t r i x due t o c o l l i s i o n s w i t h n i t r i c o x i d e or oxygen (depending on which problem one i s i n t e r e s t e d i n s o l v i n g ) . A f t e r i n t r o d u c i n g two more s u b s t i t u t i o n s ; the s p i n f l i p c r o s s s e c t i o n (n) (i) J and (<*) (i) OO A 3 . 9 the problem can be e x p r e s s e d i n a form which i s amenable t o s o l u t i o n ( the s p i n 1/2, s p i n 1/2 case i s g i v e n e x p l i c i t l y i n B a l l i n g et a l ) and f o r n i t r i c o x i d e and muonium one o b t a i n s : = U ^ S F t [ - 3 D * ( I ^ K K O - < W P dLt A3 . 1 0 215 where v i s the r e l a t i v e v e l o c i t y of the c o l l i d i n g s p e c i e s , N i s the number of n i t r i c o x i d e m o l e c u l e s / c m 3 and Tr i s the t r a c e over the r e l a v e n t s p i n s t a t e s . For t r a n s v e r s e r e l a x a t i o n s (T^) (the o f f - d i a g o n a l elements of the d e n s i t y m a t r i x ) the s o l u t i o n of t h e s e e q u a t i o n s l e a d s t o : The a n a l o g y of t h i s t o the normal r a t e e q u a t i o n 5.4 of c h a p t e r 5 i s o b v i o u s . T h e r e f o r e i n the t r a n s v e r s e f i e l d e x periment where one measures T z, i t i s s i m p l y r e l a t e d t o the s p i n - f l i p and spin-exchange c r o s s s e c t i o n s by the f f a c t o r s d i s c u s s e d i n c h a p t e r 5 by A3. 1 2 where 6^ e=2<s0 s i n c e the exchange of l i k e s p i n s l e a d s t o no d e p o l a r i z a t i o n . A s i m i l a r a n a l y s i s f o r the d i a g o n a l elements ( i . e . T, r e l a x a t i o n s as would be measured by a l o n g i t u d i n a l magnetic f i e l d MSR e x p e r i m e n t ) l e a d s t o : 6 > l cT S F =Ji<5- S E The d e t a i l s of t h i s s p i n 1/2, s p i n 1/2 problem have 216 been worked out c o m p l e t e l y i n the paper by B a l l i n g et a l and i n v o l v e f o u r p r o d u c t s of 8x8 m a t r i c e s and an o t h e r 5 a d d i t i o n and s u b t r a c t i o n o p e r a t i o n s and t h e r e f o r e w i l l not be reproduced h e r e . A n a l y s i s of the muonium and oxygen i n t e r a c t i o n i s even more c o m p l i c a t e d and i n v o l v e s the same p r o c e d u r e s except w i t h 16x16 m a t r i c e s . The problem can be reduced t o one i n v o l v i n g 12x12 m a t r i c e s by r e c o g n i s i n g t h a t the s i n g l e t oxygen s t a t e i s not p o p u l a t e d under the c o n d i t i o n s of the ex p e r i m e n t . The s t a r t i n g e q u a t i o n f o r the s o l u t i o n of t h i s problem i s A3. 14 The t e d i o u s but s t r a i g h t f o r w a r d c a l c u l a t i o n s f o r the Mu and OZ system have been c a r r i e d out w i t h the s o l u t i o n s t o the time r a t e of change of the d e n s i t y m a t r i x g i v e n i n t a b l e A3.1 i n an analogous manner t o the n o t a t i o n of B a l l i n g ( 1 9 6 3 ) . The X ^ r e f e r t o the oxygen s p i n s t a t e s (X,, =X 1 T = X M = 1/3; assuming no p o l a r i z a t i o n of the oxygen) and the H{.l r e f e r t o the muonium s p i n s t a t e t r a n s i t i o n s where the s u b s c r i p t s r e f e r t o the muonium s p i n s t a t e s (1=|1,1>, 2=|1,0>, 3=|1,-1> and 4=|0,0>). The m a t r i x 217 H„ -BH,, +<1+3iK)2(X u - X „ ) H l l +(1-3iK>2<X„ )H,(  + X 3 3 ) H „ + 8 ( X H + X 1 Z ) ( H n + H v v - H I 1 ( - H 4 t ) H 2 l - 8 H a i + ( i + 3 i K ) 2 ( X l l - X 3 3 ) H H 1 + (1-3iK)2(X | | -X 4 ( X „ + X 3 J ) H 4 h + 4 ( X 1 1 + X 3 3 ) H | ( + 4 ( X „ + X „ ) H I, *3j)H 2/, U ' " 3 3 Hjj - 8 H 3 J + d + 3 i K ) 2 ( X 3 J -X u )H 3j + ( ,- 3 iK) 2 (X„ -X 4(X„ + X 3 J ) H 3 j + 8 ( X 2 1 + X 3 J ) (H^+H^+H^+H,,. ) H 4 S = - 8 H ^ + ( , + 3 i K ) 2 ( X ( l - X 3 j ) H „ + ( l - 3 i K ) 2 ( Z / ; -X^ J H ^ 4(X„ + X 3 5 ) H 1 2 + 4 ( X u + X 3 3 ) H r / + 4(X„ +X 22 ) H 33 fi,a - 8 H , l * ( 1 * 3 i K ) 2 ( X , | - x J 3 ) H u + ( , - 3 i R , 2 ( X / / - X ^ H ^ H, 3=0 H, I F=-8H / ( J T + ( l + 3 i K ) 2 ( X / , - X 3 3 ) H / i + ( l - 3 i K ) 2 ( X / / - Z J J J H ^ 4 ( X ( / + X 3 3 ) H f l + 4 ( X M + Z 2 2 ) ( H , S - H ^ 3 ) H 2 3 = - 8 H i 3 + ( 1 + 3 i K ) 2 ( X „ - X 3 3 ) H V 3 + ( i - 3 i K ) 2 ( X / / " X ^ j H ^ " 4< x/, + X 3 3 ) H ^ + 4 ( X n + X 3 5 H H ( 2 + H / J f ) H 2 , - B H „ + ( l + 3 i K ) 2 U ( , - X 3 3 ) H ^ + ( l - 3 i K ) 2 ( X ; i -* 3 3>H n 4(X„ +* 3 3>H, U+8X, | H 3 J - 4 ( X n + X „ ) H „ H » - B H „ + < , + 3 i K ) 2 ( X / | - X „ ) H 3 4 + ( l - 3 i R ) 2 ( X / | - X „ >H 3 1 -4(X„ • X 3 3 ) H 3 ; L - 4 ( X M + X j j ) ( H 1 | * H J f | ) Table A3.1. The s o l u t i o n s t o e q u a t i o n A3.14 showing the time r a t e of change of the muonium s p i n s t a t e s i n t e r a c t i n g w i t h oxygen molecules:,(H=p). 218 elements not l i s t e d a r e analogous t o those shown except t h a t a l l of the s u b s c r i p t s w i l l be r e v e r s e d . And a f t e r some a p p r o x i m a t i o n s f o l l o w i n g B a l l i n g , the s o l u t i o n s a r e q u i t e s t r a i g h t f o r w a r d and one f i n d s =8/9 6lF = 4/9 6 ^ e f o r the t r a n s v e r s e f i e l d experiment ( T a r e l a x a t i o n s ) and G)> =32/27GSF = 1 6/27 ^ g f o r the l o n g i t u d i n a l (T, r e l a x a t i o n s ) f i e l d e x p e r i m e n t s . 219 BIBLIOGRAPHY A l l i s o n ( 1 9 5 8 ) S.K. A l l i s o n , Rev. Mod Phys. 30, 1137, (1958). Ambidge(1976) P.F. Ambidge, J.N. B r a d l e y And D.A. Whytock, J . Chem. Soc. Faraday J_, 7_2, 11 57, ( 1 976); N.C. Verma And R.W. Fessenden, J . Chem. Phys. 5_8, 2501, (1973); P. N e t a , R.W. Fessenden And R.H. S c h u l e r , J . Phys. Chem. 75, 1654 (1971); H. Endo And G.P. G l a s s , J . Phys. Chem. 80, 1519, (1976). A n d e r l e ( 1 9 7 9 ) M. A n d e r l e , D. B a s s i y , S. I a n n o t t a , S. M a r c h e t t i And G. S c o l e s , P r o c . Of 7 t h I n t e r n a t i o n a l Symposium On M o l e c u l a r Beams, R i v a D e l Garda, I t a l y , May (1979). A n d e r l e ( 1 9 8 1 ) M. A n d e r l e , D. B a s s i , S. I a n n o t t a , S. M a r c h e t t i And G. S c o l e s , Phys. Rev. A, 23, 34, (1981). Anderson(1937) C C . Anderson And S.H. Neddermeyer, Phys. Rev., 51, 884, (1937). A q u i l a n t i ( 1 9 8 1 ) V. A q u i l a n t i , G. G r o s s i , And A. Lagana, H y p e r f i n e I n t e r a c t i o n s , 8, 347, (1981). B a l l i n g ( 1 9 6 3 ) L.C. B a l l i n g , R.J. Hanson And F.M. P i p k i n , Phys. Rev. 133A, 607, (1963). Banyard(1978) K.E. Banyard And J.C. Moore, J . Phys. B., 11, 3899, (1978). Barrow(1962) G. M. Barrow, M o l e c u l a r S p e c t r o s c o p y , M c G r a w - h i l l , New Yor k , (1962). B e l k i c d 973) Dz.S. B e l k i c And R.K. Janev, J . Phys. B., 6, 2613, (1973). Berg(1965) H. C. Berg, Phys Rev. 137A, 1621, (1965). B e r l i n s k y ( 1 9 8 0 ) A . J . B e r l i n s k y And B. S h i z g a l , Can. J . Phys., 58, 220 8 8 1 , ( 1 9 0 8 ) . B l o o m ( 1 9 6 7 ) M. Bloom And I . Oppenheim, Advan. Chem. Phys., 1 2 , 5 4 9 , ( 1 9 6 7 ) , I . Oppenheim And M. Bloom, Can. J . Phys., 3 9 , 8 4 5 , ( 1 9 6 1 ) And M. Bloom And I . Oppenheim, Can. J . Phys., 4J_, 1 5 8 0 , ( 1 9 6 3 ) . B o l t o n ( 1 9 7 9 ) P.R. B o l t o n , W. Beer, P.O. Egan, V.W. Hughes, D.C. Lu, F.G. M a r i a n a , P.A. Souder, J . V e t t e r , M. G l a d i s c h , G.zu P u t l i t z , B u l l . Am. Phys. S o c , 2 4 , 6 7 5 , ( 1 9 7 9 ) . B o n d y b e y ( 1 9 7 2 ) V. Bondybey, P.K. Pearson And H.F. S c h a e f e r , J . Chem. Phys., 5 7 , 1 1 2 3 , ( 1 9 7 2 ) . B r a n s d e n ( 1 9 6 3 ) B. H. Bransden And I .M. C h e s h i r e , P r o c . Phys. Soc. (London), EM, 8 2 0 ( 1 9 6 3 ) . B r e w e r ( 1 9 7 5 ) J.H. Brewer, K.M. Crowe, F.N. Gygax And A. Schenck, Muon P h y s i c s , V o l . I l l , V.W. Hughes And C.S. Wu, Eds., Academic P r e s s , 1 9 7 5 ; J.H. Brewer And K.M. Crowe, Ann. Rev. N u c l . S c i . 2 8 , 2 3 9 ( 1 9 7 8 ) . Brewer 1 ( 1 9 7 5 ) J.H. Brewer, D.G. F l e m i n g , A.E. P i f e r , T. Bowen, D.A. D e l i s l e , P r o c e e d i n g s Of The 9 + h ICPEAC, S e a t t l e , J.S. R i s l e y And R. G e b a l l e Eds., 1 5 7 , ( 1 9 7 5 ) . B r i e t ( 1 9 3 1 ) G. B r i e t And I . R a b i , Phys. Rev. 3_8, 2 0 8 2 , ( 1 9 3 1 ) . B r o w n ( l 9 7 2 ) R.L. Brown, J o u r n a l Of Re s e a r c h , N.B.S., 7 6 A , 1 0 3 , ( 1 9 7 2 ) B u c c i ( 1 9 7 8 ) C. B u c c i , G. G u i d i , G.M. De'Munari, M. P o d i n i , R. T e d e s c h i , P.R. C r i p p a And A. Phys. L e t t s . 5 7 , 6 3 4 , ( 1 9 7 8 ) . B u rcham(1976) W.E. Burcham, N u c l e a r P h y s i c s : An I n t r o d u c t i o n , , Longman, New J e r s e y ^ ( 1 9 7 6 ) . C a r r i n g t o n ( 1 9 6 7 ) A. C a r r i n g t o n And A.D. McLauchlan, I n t r o d u c t i o n To  Magnetic Resonance, Harper And Row, New York, P 14, ( 1 9 6 7 ) . M a n f r e d i , P. V e c l i , Chem. 221 C e r n ( l 9 7 8 ) F. James And M. Roos, MINUIT, CERN Computer 7600 I n t e r i m Programme L i b r a r y , (1971). Chen(1967) F.M. Chen And R.F. S n i d e r , J . Chem. Phys., 48, 3185, (1967). C h e s h i r e ( 1 9 6 4 ) I.M. C h e s h i r e , P r o c . Phys. Soc. (London), 84, 89 (1964). — Chuang(1974) S.Y. Chuang, S.J. Tao, Phys. Rev. A, 9, 989, (1974). Chupka(1968) W.A. Chupka And M.E. R u s s e l l , J . Chem. Phys., 49, 5426, (1968). Crampton(1979) S.B. Crampton, T .J. G r e y t a k , D. K l e p p n e r , W.D. P h i l l i p s , D.A. Smith And A. W e i n r i b , Phys. Rev. L e t t s . 42, 1039, (1979). D a l g a r n o ( 1 9 6 1 ) A. D a l g a r n o , P r o c . Roy. S o c , A262, 132, (1961). D e s a i n t f u s e i e n ( 1 9 7 6 ) M. D e s a i n t f u s c i e n And C. Aud o i n , Phys Rev. 13A, 2070 (1976). Doughty(1978) B. M. Doughty, M.L. Goad, R.W. Cernosek, Phys. Rev. A. j_8(1), 29, (1978). D r i s k o ( 1 9 5 5 ) R.M. D r i s k o , T h e s i s , C a r n e g i e I n s t i t u t e Of Technology, (1955) . Feynmann(1965) R.P. Feynmann, R.B. L e i g h t o n And M. Sands, The  Feynmann L e c t u r e s On P h y s i c s V o l . I l l , A d d i s o n -w e s l e y l e y (1965). F l e m i n g ( 1 9 7 9 ) D.G. F l e m i n g , D.M. Gar n e r , L.C. Vaz, D.C. Walker, J.H. Brewer, And K.M. Crowe In P o s i t r o n i u m And  Muonium C h e m i s t r y , H.J. Ache, Ed., American Chemical S o c i e t y Advances In C h e m i s t r y S e r i e s , (1979). Fleming(1981) D.G. F l e m i n g , D.M. Garner And R.J. M i k u l a , H y p e r f i n e 222 I n t e r a c t i o n s , 8, 337, (1981). Franzen(1959) W. F r a n z e n , Phys. Rev., 115, 850, (1959). G a r n e r d 978) D.M. Garner, D.G. F l e m i n g And J.H. Brewer, Chem. Phys. L e t t s . , 55, 163, (1978). Garner(1978) D.M. G a r n e r , D.G. Fle m i n g And J.H. Brewer, Chem. Phys. L e t t s . , 55, 163, (1978). Garner(1979) D. M. Garner Ph.D. T h e s i s U n i v e r s i t y Of B r i t i s h Columbia (1979). Gentry(1975) W.R. G e n t r y , D.J. McClure And C H . D o u g l a s s , Rev. S c i . I n s t r u m . , 46, 367, (1975). Gentry(1978) W.R. G e n t r y , K i n e t i c s Of Ion M o l e c u l e R e a c t i o n s , P.J. A u s l o o s Ed., Plenum, New York, 6~5~i (191 BY. Gioumousi s(1958) G. Gioumousis And D.P. St e v e n s o n , J . Chem. Phys., 29, 294, (1958). G l a s s g o l d ( 1 9 6 4 ) A.E. G l a s s g o l d And S.A. L e b e d e f f , Ann. Of P h y s i c s , 28, 181, (1964). Gordon(1973) E. B. Gordon, B . I . Ivanov, A.P. Perminov, A.N. Ponomarev, V.L. T a l ' r o z e And S.G. K h i d i r o v , JETP L e t t s . J_7, 395, (1973). G r y s i n s k i ( 1 9 5 9 ) M. G r y s i n s k i , Phys. Rev., _M5, 374, (1959). G r y s i n s k i ( 1 9 6 5 ) M. G r y s i n s k i , Phys. Rev. 138, A336, (1965). G u r e v i c h ( 1 9 7 1 ) I . I . G u r e v i c h , I.G. I v a n t e r , E.A. Meleshko, B.A. N i k o l ' s k i i , V.S. Roganov, V . I . S e l i v a n o v , V.P. S m i l g a , B.V. S o k o l o v , And V.D. Shestakov, Sov. Phys. JETP 3_3, 253, ( 1971 ) . Happer(1977) W. Happer And A.C. Tarn, Phys. Rev. A5, 1877, (1977). — 223 Hardy(1966) W.N. Hardy, Can. J . Phys., 44, 265, (1966). H a r d y ( l 9 7 9 ) W.N. Hardy, A . J . B e r l i n s k y And L.A. Whitehead, Phys Rev. L e t t s . , 42, 1042, (1979). Harvey(1974) B.G. Harvey, I n t r o d u c t i o n To N u c l e a r P h y s i c s And  C h e m i s t r y P r e n t i c e - h a l l , New J e r s e y ^ (1974). H a s t e d d 964) Hast e d , P h y s i c s Of Atomic C o l l i s i o n s B u t t e r w o r t h s , London, 422, (1964T7 H i k i d a ( 1 9 7 0 ) T. H i k i d a , J.A. Eyre And L.M. Dorfman, J . Chem. Phys. 54, 3422, (1970); S.W. Benson, D.M. Golden, R.W. Lawrence, R. Shaw And R.W. W o o l f o l k , I n t . J . Chem. K i n e t i c s , V o l V I I Supplement, 1975, Pg. 439; K. Oka, D.L. S i n g l e t o n And R.J. C v e t a n o v i c , J . Chem. Phys. 67, 4681, (1977); N. Washida, H. Akimoto And M. Okuda, J . Phys. Chem. 82, 2293 (1978); W. Hack, H.C. Wagner And K. Hoyerman, Ber. Bunsenge Phys. Chem. 82, 713, (1978); W.E. Jo n e s , S.D. Macknight And L. Teng, Chem. Rev. 7_3' 407, (1973). Hughes(1957) V.W. Hughes, Phys. Rev., 108, 1106, (1957). H u g h e s d 966) V.W. Hughes, Ann. Rev. Nuc. S c i . , J_6, 445, (1966). Hughes(1966) V.W. Hughes, Ann. Rev. Nuc. S c i . , 445, (1966). ICPEAC(1979) P r o c e e d i n g s Of The 1 1 + k ICPEAC, N. Oda And K. Takayanagi Eds., Kyot o , 387, (1979). Johnson(1978) R.E. Johnson And J.W. B o r i n g , C o l l i s o n S p e c t r o s c o p y , R.G. Cooks Ed., Plenum, New Y o r F j (1978) . Kapton(1980) A Type Of P l a s t i c (DOW Chemical Trade Name) K ie f1 (1981 ) R.F. K i e f l , J.B. Warren, G.M. M a r s h a l l , C.J. Oram And CW. Clawson, J . Chem. Phys., 1±, 308, ( 1981). K l e p p n e r ( 1 9 6 2 ) D. K l e p p n e r , H.M. Goldenberg And N.F. Ramsey, Phys. 224 Rev. 126, 603, (1962); H. H e l w i g , Phys. Rev. 166, 4, ( 1 9 6 8 7 7 Kubach(1976) C. Kubach, C. B e n o i t , V. S i d i s , J . Pommier And M. B a r a t , J . Phys. B., 9, 2073, (1976). Mapleton(1972) R.A. Ma p l e t o n Theory Of Charge Exchange, ( w i l e y , New York: 1972) M a r s h a l l ( 1 9 7 8 ) G.M. M a r s h a l l , J.B. Warren, D.M. Gar n e r , G.S. C l a r k , J.H. Brewer And D.G. F l e m i n g , Phys. L e t t s . 65A, 3.51, (1978); And Ph.D T h e s i s U n i v e r s i t y Of B r i t i s h Columbia (1981). Massey(1952) E l e c t r o n i c And I o n i c Impact Phenomena, O x f o r d C l a r e n d o n P r e s s , H.S.W. Massey And E.H.S. Burhop Eds., P 441, (1952) . Massey(1971) E l e c t r o n i c And I o n i c Impact Phenomena, 2nd E d i t i o n , V o l . I l l ; H.S.W Massey, Ed., O x f o r d C l a r e n d o n P r e s s , 1465 To 1524, (1971). Mobley(1967) R.M. Mobley, Ph.D. T h e s i s , Y a l e U n i v e r s i t y , 1967; R.M. Mobley, J.M. B a i l e y , W.E. C l e l a n d , V.W. Hughes And J.E. Rot h b e r g , J . Chem. Phys., 44, 4354, (1966); R.M. Mobley, J . J . Amato, V.W. Hughes, J.E. R o t h b e r g , And P.A. Thompson, I b i d , 4_7, 3074, ( 1967). O k a d 977) K. Oka, D.L. S i n g l e t o n , R.J. C v e t a n o v i c , J . Chem. Phys., 67, 4681, (1977). Oram(1981) C.J. Oram, J.B. Warren, G.M. M a r s h a l l And J . Doornbos, N u c l . I n s t r u m . Methods, 179, 95, (1981). P a r k e r ( 1 9 6 4 ) J.G. P a r k e r , J . Chem. Phys., 4J_, 1600, (1964). P e r c i v a K 1976) P.W. P e r c i v a l And H. F i s c h e r , Chem. Phys. 16, 89, (1976). P e r c i v a l d 9 8 l ) P.W. P e r c i v a l , H y p e r f i n e I n t e r a c t i o n s , 8, 315, (1981). P i f e r d 976) A.E. P i f e r , T. Bowen And K.R. K e n d a l l , N u c l . I n s t r . 225 Methods, J_35, 39, (1976). P o o l e d 97 1 ) C P . P o o l e And H.A. F a r a c h , R e l a x a t i o n I n Magnetic  Resonance, Academic P r e s s , New York, P 10, (1971). P u r c e l l d 9 5 4 ) E.M. P u r c e l l And G.B. F i e l d A s t r o p h y s . J . , 124, 542, (1954). Roduner(1978) E. Roduner, P.W. P e r c i v a l , D.G. F l e m i n g , J . Hochmann And H. F i s c h e r , Chem. Phys. L e t t s . 57, 37, (1978); E. Roduner, Ph.D. T h e s i s , P h y s i k a l i s c h Chemiches I n s t i t u t , U n i v e r s t a t Z u r i c h , 1979. Roduner(1981) E. Roduner, H. F i s c h e r , Chem. Phys., 54, 261, (1981). Sachs(1975) A.M. Sachs And A. S i r l i n , Muon P h y s i c s , V o l . I I , C.S. Wu And V.W. Hughes, Academic P r e s s , New York, (1975). S c h e n c M 1975) A. Schenck, In N u c l e a r And P a r t i c l e P h y s i c s At  I n t e r m e d i a t e E n e r g i e s , Ed. J.B. Warren, Plenum, New York, 159, (1976). Shah(1980) M.B. Shah, J . Geddes And H.B. G i l b o d y , J . Phys. B. J_3, 4049, (1980). S h i z g a l d 979) B. S h i z g a l , J o u r n . Of P h y s i c s 12B, 3611, ( 1 9 7 9 ) . S h i z g a l d 980) B. S h i z g a l And J.M. F i t z p a t r i c k , J . Chem. Phys., 72, -3143, (1980) . S i d i s ( 1 9 7 2 ) V. S i d i s , J . Phys. B., 5, 1517, (1972). Stambaugh(1972) R.D. Stambaugh, Ph.D. T h e s i s ( Y a l e ) And R.D. Stambaugh, D.E. Ca s p e r s o n , T.W. Crane, V.W. Hughes, H.F. Kaspar, P. Souder, P.A. Thompson, H. O r t h , G. Zu P u t l i t z And A.B. Dennison, Phys. Rev. L e t t e r s 33, 568, (1974). S t r e e t ( 1 9 3 7 ) J.C. S t r e e t And E.C. S t e v e n s o n , Phys. Rev., 52, 226 1003, (1937). TRIUMF(1980) TRIUMF Annual R e p o r t s , 1975-1981. Tawara(1973) H. Tawara And A. Russek, 1973, Rev. Mod. Phys. 45, 178. ~ Tawara(1979) H. Tawara, Phys. L e t t s . , 7j_a, 208 (1979). Thomas(1927) L.H. Thomas, P r o c . Roy. Soc. (London)A, 114, 561, (1927). T o l l i v e r ( 1 9 7 9 ) D.E. T o l l i v e r , G.A. K y r a l a And W.H. Wing, Phys. Rev. L e t t s . , 43, 1719, (1979). T o r r e y ( 1 9 6 3 ) H.C. T o r r e y , Phys., Rev. J_30, 2306, (1963). uSR1(1977) P r o c e e d i n g s Of The 1 s t I n t e r n a t i o n a l T o p i c a l M e e t i n g On Muon S p i n R o t a t i o n , R o r s c h a c h , H y p e r f i n e I n t e r a c t i o n s , 6, (1978). i i S R 2 d 980) ' P r o c e e d i n g s Of The 2"<* I n t e r n a t i o n a l T o p i c a l M e e t i n g On Muon S p i n R o t a t i o n , Vancouver, H y p e r f i n e I n t e r a c t i o n s , 8, (1980). V i d a K 1976) D. V i d a l And M. L a l l e m a n d , J . Chem. Phys., 64, 4293, (1976). V o l k d 980) C H . V o l k , T.M. Kuon, J.G. Mark, Y.b. Kim And J.C. Woo, Phys. Rev. L e t t s . , 44, 136, (1980). Wagner(1976) H.Gg. Wagner, U. Welzbacker And R. Z e l l n e r , Ber. Bunsenges. P h y s i k . Chem., 80, 902, (1976). Walder(1980) R. Walder And J.L. F r a n k l i n , I n t . J . Mass. Sp e c t . And Ion Phys., 36, 85, (1980). Walker(1981) D.C. Walker, H y p e r f i n e I n t e r a c t i o n s , 8, 329, (1981). Weissenberg(1967) 227 A.O. Weissenberg, Muons, N o r t h H o l l a n d , Amsterdam, ( 1967). Westenberg( 1 969) A.A. Westenberg And N. De Haas, J . Chem. Phys. 51, 5215 (1969). Whaling(1958) W. W h a l i n g Handbuch Der P h y s i k , 34, 193, (1958). W i t t k e ( 1 9 5 6 ) E.P. W i t t k e And R.H. D i c k e , Phys Rev. 103, 620, (1956); M. P u r c e l l And G.B. F i e l d , A s t r o p h y s . J . 124, 542, (1956). Wolfgang(1965) R. Wolfgang, Prog. R e a c t . K i n e t . , 3, 97, (1965). Wolfrum(1975) J . Wolfrum, P h y s i c a l C h e m i s t r y — An Advanced T r e a t i s e , Ch. 9, H. E y r i n g , D. Hendersen And W. J o s t , Eds. Academic P r e s s , 1975; Supplementary T a b l e s Of Gas K i n e t i c D ata, Department Of C h e m i s t r y , Birmingham U n i v e r s i t y , 1973. PUBLICATIONS Y.C. Jean, J.H. Brewer, D.G. Fleming, D.M. Garner, R.J. Mikula, L.C. Vaz and D.C. Walker, Reactivity of Mu atoms in aqueous solution. Chem. Phys. Letts. _57 293-297 (1978). R.J. Mikula, D.M. Garner, D.G. Fleming, G.M. Marshall and J.H. Brewer, Proceedings of the f i r s t International Conference on Muon Spin Rotation, Rorschach, Switzer-land. Hyperfine Interactions. j> 379-383 (1979). D.G. Fleming, D.M. Garner, J.H. Brewer and R.J. Mikula, Reaction dynamics of the Mu atom using surface y + in the gas phase. Hyperfine Interactions. j> 405-408 (1979). D.P. Spencer, D.G. Fleming, J.H. Brewer and R.J. Mikula, Proceedings, Symposium on the Origins of Optical A c t i -vity in Nature, Vancouver, June 1979; Elsevier (1979). D.G. Fleming, R.J. Mikula and D.M. Garner, Muonium spin-exchange in low pressure gases: Mu + 0£ and Mu + NO. J. Chem. Phys. 73(6), 2751 (1980). T. Suzuki, R.J. Mikula, D.M. Garner, D.G. Fleming and D.F. Measday, Muon capture in oxides using the lifetime method. Phys. Letters 95B (2) 202 (1980). D.G. Fleming, R.J. Mikula and D.M. Garner, y +-e~ hyperfine interactions and muonium spin exchange in low pressure gases. Proceedings,fifth International Conf. on Hyperfine Interactions, Berlin,, Hyperfine Inter-actions, 9, 207 (1981). R.J. Mikula, D.M. Garner, D.G. Fleming, Temperature dependence of muonium reaction rates in the gas phase. Proceedings, second International Conf. on muon spin rotation, uSR2, Vancouver, Hyperfine Interactions, 8_ 337 (1981). R.J. Mikula, D.M. Gamer,and D.G. Fleming, u + ther*-malization and muonium formation in noble gases. uSR2 conference, Vancouver, Hyperfine Interactions 8 307 (1981). 

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