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UBC Theses and Dissertations

Search for munoic radicals (μ⁺) radicals in condensed media Kent, Michael 1977

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A SEARCH FOR MUONIC ( JUL+) RADICALS I N CONDENSED MEDIA by MICHAEL KENT B.Sc, University of B r i t i s h Columbia A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Chemistry) ViTe accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1977 © Michael Kent, 1977 In present ing th is thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree t h a t the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representa t ives . It is understood that copying or p u b l i c a t i o n of th is thes is for f inanc ia l gain sha l l not be allowed without my wr i t ten permission. Department of C h e m i s t r y The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date August 16, 1977 ABSTRACT The t e c h n i q u e o f muonium s p i n r o t a t i o n (MSR) has been used i n the t r a n s v e r s e f i e l d method i n an attempt at the d i r e c t d e t e c t i o n o f muonic r a d i c a l s . Carbon d i s u l f i d e , carbon d i o x i d e , and s u l f u r d i o x i d e were chosen as s u b s t r a t e s i n t o which p o s i t i v e muons were i m p l a n t e d . The p o s i t i v e muon, t h r o u g h i t s asymmetric decay, a c t s as a s e n s i t i v e d e t e c t o r of the i n t e r a c t i o n s o f i t s s p i n w i t h the medium. The t h e o r y of t h e MSR t e c h n i q u e has been d i s c u s s e d w i t h p a r t i c u l a r emphasis b e i n g p l a c e d on a method o f measure-ment o f t h e h y p e r f i n e i n t e r a c t i o n o f a p o s i t i v e muon w i t h a paramagnetic environment, such as would be e x p e c t e d i f t h e muon were p a r t o f a p o l y a t o m i c f r e e r a d i c a l . T e n t a t i v e e v i d e n c e f o r t h e e x i s t e n c e of such a . s p e c i e s has been found i n CC^ a t 77 K. M o l e c u l a r o r b i t a l c a l c u l a t i o n s were performed on assumed s t r u c t u r e s f o r t h e a d d i t i o n p r o d u c t s o f t h e muonium atom (ju +e~) w i t h the s u b s t r a t e m a t e r i a l s . The MSR e x p e r i m e n t a l system at TRIUMF i s d e s c r i b e d w i t h r e s p e c t t o the t r a n s v e r s e f i e l d t e c h n i q u e . i v TABLE OF CONTENTS Page ABSTRACT i i i LIST OF TABLES v i i i LIST OF FIGURES i x ACKNOWLEDGEMENTS x i CHAPTER I : INTRODUCTION 1 CHAPTER I I : MSR TECHNIQUE 5 -A) P a r t i c l e H e l i c i t y 5 B) T r a n s v e r s e F i e l d Method 10 C) E x p e r i m e n t a l H i s t o g r a m 12 CHAPTER I I I : BASIC MUONIUM THEORY 13 A) S l o w i n g Down P r o c e s s F o r P o s i t i v e Muons 13 B) Hot R e a c t i o n s o f Muonium 15 C) G e n e r a l R e a c t i o n Scheme 16 D) P o l a r i z a t i o n o f the Muon i n Muonic S p e c i e s 18 i ) G e n e r a l E x p r e s s i o n 18 i i ) F r e e Muon 19 V i i i ) Q u a s i - F r e e Muon 20 i v ) Free Muonium 21 v) Q u a s i - F r e e Muonium 31 v i ) Muonic R a d i c a l s 33 CHAPTER IV: INDIRECT EVIDENCE OF MUONIC RADICALS 38 CHAPTER V: DIRECT DETECTION EXPERIMENTAL SCHEME 40 A) Method o f R a d i c a l I d e n t i f i c a t i o n 40 B) Example: I d e n t i f i c a t i o n o f Muonium 41 i n Q u a r t z i ) Q u a r t z i n Low E x t e r n a l F i e l d 41 i i ) Two-Frequency P r e c e s s i o n o f 44 Muonium i n a Moderate E x t e r n a l M a g n e t i c F i e l d C) S p i n D e n s i t y P r e d i c t i o n s 46 D) S e l e c t i o n o f C h e m i c a l s 48 E) Temperature C o n s i d e r a t i o n s 48 CHAPTER V I : MOLECULAR ORBITAL CALCULATION OF SPIN DENSITIES 49 A) Computer Programs 49 B) HS0 2 51 V I C) HC0 2 D) HCS 2 53 56 CHAPTER V I I : EXPERIMENTAL A) Beam Source i ) P r o d u c t i o n Target i i ) C o n v e n t i o n a l Muons i i i ) S u r f a c e Muons B) H e l m h o l t z C o i l s C) Target Systems i ) C o n v e n t i o n a l Mode C e l l i i ) S u r f a c e Mode C e l l i i i ) C 0 2 Target i v ) Q u a r t z R e f e r e n c e Target D) C r y o s t a t E) E x p e r i m e n t a l D e t a i l s o f the C o n v e n t i o n a l Mode 66 i ) D e g r a d a t i o n and C o l l i m a t i o n o f the Beam 66 i i ) S c i n t i l l a t o r Placement 66 i i i ) L o g i c System 68 i v ) Data A q u i s i t i o n 69 F) E x p e r i m e n t a l D e t a i l s o f t h e S u r f a c e Mode 72 58 58 58 58 60 61 63 63 63 64 64 65 v i i G) P r e p a r a t i o n o f C h e m i c a l s 73 CHAPTER V I I I : DISCUSSION OF EXPERIMENTAL RESULTS 74 A) S u r f a c e Mode Experiment on Fused Q u a r t z 74 at 300 K 74 B) S u r f a c e Mode Experiment i n C S 2 at 300 K 75 C) C o n v e n t i o n a l Mode Ex p e r i m e n t s on C S 2 and S 0 2 a t Hel i u m Temperature (4.2 K) 75 D) C o n v e n t i o n a l Mode E x p e r i m e n t s on C 0 2 76 CHAPTER IX: CONCLUSIONS 84 CHAPTER X: REFERENCES 86 v i i i LIST OF TABLES Page '.'.I. Muon P r o p e r t i e s 1 I I . E i g e n v a l u e s and E i g e n s t a t e s f o r t h e B r e i t - R a b i Diagram 24 i x LIST OF FIGURES F i g u r e Page 1 Schematic R e p r e s e n t a t i o n o f H e l i c i t i e s 6 2 R e p r e s e n t a t i o n o f Imposed N e g a t i v e H e l i c i t y on Muons from P i o n Decay 7 3 R e p r e s e n t a t i o n o f Imposed P o s i t i v e H e l i c i t y on P o s i t r o n s o f Maximum Energy from Muon Decay 7 4 P l o t o f t h e (1 + cos 6 ) D i s t r i b u t i o n f o r V a r i o u s V a l u e s o f Asymmetry kp. 9 5 Muon S p i n P r e c e s s i o n i n the P l a n e P e r p e n d i c u l a r t o an E x t e r n a l M a g n e t i c F i e l d 11 6 The Muonium R e a c t i o n Scheme 17 7 The Energy E i g e n s t a t e s o f t h e Ground S t a t e (1=0) o f Muonium i n an E x t e r n a l M a g n e t i c F i e l d 23 8 E v o l u t i o n of Muonium i n 100 G T r a n s v e r s e F i e l d 26 9 Asymmetry P l o t f o r Muonium i n Fused Q u a r t z 42 10 F o u r i e r T r a n s f o r m Spectrum o f Q u a r t z Data at Low F i e l d 43 X 11 F o u r i e r T r a n s f o r m Spectrum o f Q u a r t z Data at Moderate E x t e r n a l F i e l d 45 12 S p i n D e n s i t y D i s t r i b u t i o n i n HS0 2 Isomers 51 13 S p i n D e n s i t y D i s t r i b u t i o n i n HCC>2 Isomers 53 14 S p i n D e n s i t y D i s t r i b u t i o n i n HCS 2 Isomers 56 15 M20 Muon Channel 59 16 S u r f a c e Mode Target C e l l 62 17 Apparatus Used With C o n v e n t i o n a l Muons 67 18 A p p a r a t u s Used With S u r f a c e Muons 71 19 F o u r i e r T r a n s f o r m Spectrum o f CCv, Data at 195 K i n 7.5 G E x t e r n a l F i e l d 77 20 F o u r i e r T r a n s f o r m Spectrum o f C 0 2 Data a t 77 K i n 20 G E x t e r n a l F i e l d ( i ) 79 21 F o u r i e r T r a n s f o r m Spectrum of CC>2 Data at 77 K i n 20 G E x t e r n a l F i e l d ( i i ) 80 22 F o u r i e r T r a n s f o r m Spectrum o f S i Data (Ref. 52) i n 20 G F i e l d - 81 23 F o u r i e r T r a n s f o r m Spectrum o f C 0 2 Data i n 40 G E x t e r n a l F i e l d 83 ACKNOWLEDGEMENTS I i w o u l d l i k e t o e x p r e s s my g r a t i t u d e t o Dr. D.G. F l e m i n g f o r h i s g u i d a n c e , encouragement and su p p o r t t h r o u g h o u t a l l a s p e c t s o f t h i s t h e s i s . I am a l s o g r a t e f u l t o Dr. J.H. Brewer f o r many h e l p f u l d i s c u s s i o n s on t h e t h e o r e t i c a l and i n t e r p r e t a t i o n a l a s p e c t s of t h i s t h e s i s . In a d d i t i o n I w i s h t o e x t e n d my th a n k s t o Dr. K. Nagamine f o r t h e d e s i g n and c a r e o f t h e l i q u i d h e l i u m c r y o s t a t and f o r h i s k i n d a s s i s t a n c e d u r i n g t h e e x p e r i m e n t a t i o n . I am i n d e b t e d t o Mr. R. Hayano, Dr. J.H. Brewer and Mr. D.M. Garner f o r t h e i r development o f an e f f i c i e n t and t r u l y b e a u t i f u l g r a p h i c s - o r i e n t e d s o f t w a r e system f o r p r o -c e s s c o n t r o l , d i a g n o s t i c , and a n a l y s i s t a s k s i n the e x p e r i -mental system. A s p e c i a l t h a n k s t o o t h e r members o f t h e MSR group at TRIUMF f o r many h e l p f u l hours o f i n s t r u c t i o n and a s s i s t a n c e . I a l s o g r a t e f u l l y acknowledge the r e c e i p t o f s e v e r a l a s s i s t a n t s h i p s from t h e Department o f C h e m i s t r y . - I -I . INTRODUCTION In 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 paper, p o s i t i v e muons are brought t o r e s t i n s e v e r a l s o l i d o r l i q u i d i n s u l a -t o r s . In c o n t r a s t t o n e g a t i v e muons, t h e i m p l a n t e d p o s i t i v e muons are not c a p t u r e d i n t o a tomic o r m o l e c u l a r o r b i t s , nor 1 do they undergo n u c l e a r i n t e r a c t i o n s . T a b l e I c o n t a i n s r e l e v a n t i n f o r m a t i o n about the p o s i t i v e muon wh i c h , a p a r t from i t s mass and l i f e t i m e , i s s i m i l a r t o a p r o t o n . T a b l e I . Muon p r o p e r t i e s . S p i n ( 3^ ) +i Mass (m^ ) 206.7 m = 105.6 MeV e Magn e t i c moment ( # > 5 ^ 3 . 1 8 ^ 2m^ c L i f e t i m e ( ~t ) 2.2 psec Muonium (Mu) i s formed when a p o s i t i v e muon c a p t u r e s an e l e c t r o n from the medium and thus becomes n e u t r a l i z e d : i t i s l i k e a t omic hydrogen except t h a t i t s mass i s about 1/9 o f t h e hydrogen mass. The s m a l l e r mass o f t h e muon, however, has o n l y a l i t t l e e f f e c t on t h e reduced mass o f t h e complete system which i s v e r y s i m i l a r t o t h e reduced mass - 2. -o f hydrogen: m, 'Mu 0.995 m H (1.1) T h e r e f o r e t h e b i n d i n g energy and t h e s i z e o f t h i s r a d i o a c t i v e atom a r e p r a c t i c a l l y t h e same as f o r at o m i c hydrogen. To t h e e x t e n t t h a t t h e Born-Oppenheimer a p p r o x i m a t i o n i s v a l i d , t h e two i s o t o p e s a r e e x p e c t e d t o e x h i b i t s i m i l a r c h e m i c a l b e h a v i o u r . Comparison o f c h e m i c a l r e a c t i o n r a t e s f o r Mu and H p r o v i d e s a unique o p p o r t u n i t y f o r t e s t i n g models o f dynamic i s o t o p e e f f e c t s 4-i n c h e m i c a l k i n e t i c s , but d i s c u s s i o n o f t h i s a r e a o f r e s e a r c h i s beyond the scope of t h i s paper. mine whether muonium, as a r e a c t i v e f r e e r a d i c a l , i s c a p a b l e o f p a r t i c i p a t i n g i n c h e m i c a l r e a c t i o n s i n t h e s t o p p i n g medium t o form muonic p o l y a t o m i c r a d i c a l s — s u c h s p e c i e s c o u l d be c h a r a c t e r i z e d by a . d i r e c t measurement o f t h e - e n e r g y o f h y p e r -f i n e i n t e r a c t i o n between t h e magnetic moment of t h e muon and t h a t o f t h e u n p a i r e d e l e c t r o n i n t h e r a d i c a l . The h y p e r f i n e s p l i t t i n g o f muonium can be measured w i t h c o n s i d e r a b l e a c c u r a c y by s t u d y i n g t h e p r e c e s s i o n o f t h e s p i n i n a magnetic f i e l d . T h i s p r e c e s s i o n i s r e v e a l e d by t h e d i r e c -t i o n . o f t h e p o s i t r o n e m i t t e d i n t h e decay o f t h e muon, d i s c u s s e d i n S e c t i o n . I I . From a F o u r i e r a n a l y s i s o f t h e p r e c e s s i o n s i g n a l i t i s p o s s i b l e t o o b t a i n t h e v a l u e o f t h e h y p e r f i n e s p l i t t i n g 3 The c u r r e n t s t u d y was u n d e r t a k e n i n an e f f o r t t o d e t e r -- 3 -o f t h e ground s t a t e o f the muonium atom i n t h e medium. From the o b s e r v e d h y p e r f i n e s p l i t t i n g and t h e c o n t a c t h y p e r f i n e e q u a t i o n ( i n S e c t i o n I I I - D - i v ) one f i n d s an e x p e r i m e n t a l v a l u e f o r t h e u n p a i r e d e l e c t r o n d e n s i t y at the muon. Among the f i r s t t o c a r r y out such e x p e r i m e n t s were Babaev and c o - w o r k e r s ^ . They found, f o r example, t h a t t h e h y p e r f i n e s p l i t t i n g o f muonium i m p l a n t e d i n f u s e d q u a r t z (4404 +/- 70 MHz) i s not f a r from t h e s p l i t t i n g i n vacuum (4463 MHz), s u g g e s t i n g t h a t muonium s i t s i n a s p a c i o u s i n t e r -s t i t i a l s i t e . T h i s measurement has been r e p e a t e d h e r e , and the same method has been a p p l i e d i n t h e s e a r c h f o r muonic p o l y a t o m i c r a d i c a l s . The d e t e c t i o n method i s based on t h e f a c t t h a t when a p o s i t i v e muon decays i t e m i t s a p o s i t r o n p r e f e r e n t i a l l y a l o n g i t s s p i n d i r e c t i o n , and r e q u i r e s t h a t , t h e muons i n i t i -a l l y have a : w e l l - d e f i n e d . d i r e c t i o n o f s p i n p o l a r i z a t i o n at the s t a r t o f t h e expe r i m e n t . .The b a s i c method and t h e o r y o f t h i s t e c h n i q u e a re i n t e r p r e t e d i n s e c t i o n s I I and I I I . S t u d i e s o f t h e p r e c e s s i o n and d e p o l a r i z a t i o n o f p o s i -t i v e muons and muonium i n m a t t e r share many c h a r a c t e r i s t i c s w i t h t h e a s s o c i a t e d t e c h n i q u e s o f NMR and ESR. The i m p o r t a n t d i f f e r e n c e i s t h a t the more s t a n d a r d resonance t e c h n i q u e s i n v o l v e a b s o r p t i o n o f m a c r o s c o p i c amounts o f power by macro-15 12 s c o p i c s p i n ensembles ( — 10 n u c l e i o r ^ 10 e l e c t r o n s ) , - 4- -6 w h i l e as few as 10 muons imbedded i n t h e medium can be used p a s s i v e l y t o d e t e c t coherent l o c a l f i e l d s ( t h r o u g h t h e p r e c e s -s i o n f r e q u e n c y ) and random l o c a l f i e l d s ( t h r o u g h t h e r e l a x a t i o n X t i m e ) . T h i s i s p o s s i b l e because the asymmetric muon decay e f f i c i e n t l y c o n v e r t s i n f o r m a t i o n about the muon p o l a r i z a t i o n i n t o an e a s i l y d e t e c t a b l e e x t e r n a l phenomenon ( t h e p o s i t r o n e m i s s i o n d i r e c t i o n ) . I n t e r e s t e d r e a d e r s a r e d i r e c t e d t o t h e r e v i e w a r t i c l e s o f Brewer et a l . , and Schenck , f o r i n f o r m a t i o n about t h e wide v a r i e t y o f c h e m i c a l and p h y s i c a l a p p l i c a t i o n s o f v a r i o u s MSR t e c h n i q u e s (where the acronym s t a n d s f o r Muon ( o r Muonium) S p i n R e l a x a t i o n , R o t a t i o n , Resonance, e t c . , and i s i n t e n d e d t o suggest t h e analogy w i t h NMR and ESR). - 5 -I I . MSR TECHNIQUE A) P a r t i c l e H e l i c i t y The p o s i t i v e muon ( u + ) i s produced a l o n g w i t h a neu-t r i n o (^) i n t h e decay o f t h e p o s i t i v e p i o n (TT +) a c c o r d i n g t o the p r o c e s s 4- -f TT JUL . + ( i i . i ) The mean l i f e t i m e o f t h e p i o n i s 26 nsec and the k i n e t i c energy o f t h e o u t g o i n g muon i n t h e r e s t frame o f t h e p i o n i s 4.1 MeV (29 MeV/c). The decay i s governed by t h e weak 7 i n t e r a c t i o n which l e a d s t o a v i o l a t i o n o f p a r i t y , r e s u l t i n g from t h e f a c t t h a t a l l n e u t r i n o s have n e g a t i v e h e l i c i t y ( s p i n a n t i p a r a l l e l t o momentum) w h i l e t h e i r ' m i r r o r ' p a r t i c l e , t h e a n t i n e u t r i n o ( ) 7 ) , has p o s i t i v e h e l i c i t y . Both p a r t i c l e s have e f f e c t i v e l y z e r o mass and s p i n = £, and t h e i r h e l i c i t i e s a r e s c h e m a t i c a l l y r e p r e s e n t e d i n F i g u r e 1. S i n c e t h e p i o n has z e r o s p i n , t he muon's s p i n ( s = i) must c a n c e l t h a t o f the n e u t r i n o (s = J ) ; c o n s e r v a t i o n o f a n g u l a r momentum then f o r c e s the muon t o have n e g a t i v e h e l i -c i t y . Thus t h e muon i s born w i t h 100% 'backward' l o n g i t u d i n a l p o l a r i z a t i o n i n t h e r e s t frame o f the p i o n , as r e p r e s e n t e d i n F i g u r e 2. NEUTRINO V Momentum S p i n N e g a t i v e H e l i c i t y ANTINEUTRINO V P o s i t i v e H e l i c i t y F i g u r e 1: Schematic R e p r e s e n t a t i o n o f H e l i c i t i e s Upon r e f l e c t i o n a c r o s s a p l a n e which i s p e r p e n d i c u l a r t o t h e s p i n a x i s , s p i n a n g u l a r momentum does not change d i r e c t i o n , w h i l e l i n e a r momentum does. P a r i t y i s v i o l a t e d : t he n e u t r i n o and a n t i n e u t r i n o are d i s t i n c t l y I ON 1 d i f f e r e n t p a r t i c l e s , - each w i t h d e f i n i t e h e l i c i t y , j - 7 -F i g u r e 2: R e p r e s e n t a t i o n o f Imposed N e g a t i v e H e l i c i t y  on Muons from P i o n Decay F i g u r e 3: R e p r e s e n t a t i o n o f Imposed P o s i t i v e H e l i c i t y on P o s i t r o n s o f Maximum Energy from Muon Decay - 8 -The muon l a t e r decays v i a t h e weak i n t e r a c t i o n by t h e p r o c e s s ^ e + Ve + cn-2) w i t h a mean l i f e t i m e o f 2.2 usee. Due t o t h e n o n c o n s e r v a t i o n o f p a r i t y i m p l i c i t i n the d e f i n i t e h e l i c i t y o f n e u t r i n o s , the p o s i t r o n ( e + , s = §) tends t o be e m i t t e d a l o n g t h e muon s p i n d i r e c t i o n w i t h p o s i t i v e h e l i c i t y . F o r t h e case o f maximum energy ( 52 MeV ) r e p r e s e n t e d i n F i g u r e 3, b o t h n e u t r i n o s a r e e m i t t e d at 180° t o t h e p o s i t r o n which then comes o f f l o n g i -t u d i n a l l y p o l a r i z e d i n t h e r e s t frame o f the muon. In g e n e r a l , t h e number o f p o s i t r o n s e m i t t e d a t an a n g l e 1 -8 Q w i t h r e s p e c t t o t h e muon s p i n d i r e c t i o n i s g i v e n by'' 6 ihs! ~ j + A cos 9 ("-3) The asymmetry A i s a f u n c t i o n o f t h e energy o f t h e decay p o s i t r o n , w i t h an average v a l u e of about 1/3 and a maximum v a l u e o f 1 f o r p o s i t r o n s o f maximum energy. The asymmetric decay o f s p i n p o l a r i z e d muons ( r e p r e s e n t e d i n F i g u r e 4) pro-v i d e s the b a s i s f o r MSR s p e c t r o s c o p i c e x p e r i m e n t a l methods. - 9 -- 10 -B) T r a n s v e r s e F i e l d Method In t h e t r a n s v e r s e f i e l d MSR t e c h n i q u e a beam o f p o s i -t i v e muons w i t h a h i g h degree o f s p i n p o l a r i z a t i o n i s momentum s e l e c t e d from the decay o f p i o n s and st o p p e d i n a t a r g e t w i t h no l o s s o f s p i n p o l a r i z a t i o n . A u n i f o r m magnetic f i e l d i s a p p l i e d i n a d i r e c t i o n p e r p e n d i c u l a r t o t h a t o f the i n i t i a l muon s p i n p o l a r i z a t i o n . I n t e r a c t i o n o f the muon's magnetic moment w i t h the e x t e r n a l f i e l d and/or w i t h l o c a l magnetic f i e l d s ( i f t h e muon i s i n a f e r r o m a g n e t i c environment) causes a time dependent e v o l u t i o n o f the p o l a r i z a t i o n , w i t h p r e c e s s i o n components i n the p l a n e t r a n s v e r s e t o t h e e x p e r i m e n t a l f i e l d . A s c h e m a t i c diagram'of t h e e x p e r i m e n t a l arrangement i n t r a n s -v e r s e f i e l d i s shown i n F i g u r e 5. I f a p o s i t r o n c o u n t e r w i t h a f i n i t e a n g l e o f a c c e p t a n c e i s f i x e d i n t h e p l a n e o f p r e c e s s i o n , t h e p r o b a b i l i t y o f d e t e c t i o n o f t h e decay p o s i t r o n r i s e s and f a l l s i n t i m e as the d i r e c t i o n o f muon p o l a r i z a t i o n sweeps p a s t t h e c o u n t e r . A h i g h r e s o l u t i o n c l o c k i s s t a r t e d by t h e s i g n a l i n one c o u n t e r a r r a y as t h e muon e n t e r s the t a r g e t , and i s s t o p p e d by t h e s i g n a l i n t h e p o s i t r o n c o u n t e r a r r a y , i f and when the decay p o s i t r o n i s d e t e c t e d . The measured i n t e r v a l s a c c u -mulated from many s e p a r a t e j u + s t o p / d e c a y e v e n t s a r e b i n n e d i n t o a time h i s t o g r a m . - 11 -F i g u r e 5: Muon S p i n P r e c e s s i o n i n t h e P l a n e P e r p e n d i c u l a r t o an E x t e r n a l M a g n e t i c F i e l d b e a m i ^ \ \ i / . ^ \ N 1 ' X ' Muon i s d e t e c t e d as i t e n t e r s the t a r g e t a r e a Muon s t o p s i n t a r g e t , p r e c e s s e s , and l a t e r decays e m i t t i n g a p o s i t r o n a l o n g i t s s p i n d i r e c t i o n P r o b a b i l i t y o f p o s i t r o n d e t e c t i o n r i s e s and f a l l s as p o l a r i z a t i o n sweeps p a s t the d e t e c t o r . - 12. -•}.. G) E x p e r i m e n t a l H i s t o g r a m The e x p e r i m e n t a l d i s t r i b u t i o n o f e v e n t s p e r b i n as a f u n c t i o n o f t h e measured time i n t e r v a l i s e q u i v a l e n t t o t h e p o s i t r o n d e t e c t i o n p r o b a b i l i t y as a f u n c t i o n o f t i m e s i n c e t h e muons stopped. The g e n e r a l form o f an MSR h i s t o g r a m i s N(t) = N0(S + e * P ( % ) [ l - A P(t)J) where N a and B a r e a n o r m a l i z a t i o n f a c t o r and random background r e s p e c t i v e l y , i s t h e muon l i f e t i m e (2.2 u s e e ) , w h i c h l e a d s t o an e x p o n e n t i a l decay o f t h e s i g n a l , and t h e asymmetry A c i s the ( e m p i r i c a l ) maximum asymmetry seen when t h e r e i s no depo-l a r i z a t i o n . The term P ( t ) i s t h e n o r m a l i z e d muon p o l a r i z a t i o n i n a g i v e n d i r e c t i o n , and i s t h e sum o f c o n t r i b u t i o n s from each of_.the d e t e c t a b l e muonic -.species i n the t a r g e t . In a d d i t i o n ' t o t h e o v e r a l l e x p o n e n t i a l decay o f t h e s i g n a l , each o s c i l -l a t o r y component i n P ( t ) may e x h i b i t an e x p o n e n t i a l damping w i t h a c h a r a c t e r i s t i c r e l a x a t i o n time ' ' i f t h e f r a c t i o n of t h e muon ensemble w i t h which i t i s a s s o c i a t e d i s d i s a p -p e a r i n g t h r o u g h c h e m i c a l r e a c t i o n s , o r b e i n g d e p o l a r i z e d by s p i n r e l a x a t i o n mechanisms. The time e v o l u t i o n o f t h e muon s p i n p o l a r i z a t i o n has \tO s *>•«• been t h e o r e t i c a l l y a n a l y s e d by s e v e r a l groups , f a c i l i t a t i n g the i n t e r p r e t a t i o n o f e x p e r i m e n t a l h i s t o g r a m s and t h e d e r i v -a t i o n of v a r i o u s parameters i n v o l v e d i n muonium c h e m i s t r y i n the gaseous, l i q u i d , and s o l i d phases. I I I . BASIC MUONIUM THEORY A) S l o w i n g Down P r o c e s s f o r P o s i t i v e Muons S i n c e e x p e r i m e n t a l o b s e r v a t i o n b e g i n s s i m u l t a n e o u s l y w i t h t h e a r r i v a l o f a f a s t muon i n the t a r g e t , s e v e r a l ques-t i o n s r e l a t i n g t o t h e s l o w i n g down p r o c e s s a re o f b a s i c i m p o r t a n c e : (1) What a r e t h e e s s e n t i a l s t a g e s o f t h e d e c e l e r a t i o n p r o c e s s ? (2) What i s the time s c a l e f o r each s t a g e ? (3) I s the muon s p i n p o l a r i z a t i o n a f f e c t e d ? ( 4 ) In what s t a t e o r s t a t e s does the muon f i n a l l y t h e r m a l i z e ? These q u e s t i o n s a r e q u a l i t a t i v e l y answered i n t h e f o l l o w i n g d i s c u s s i o n as p r e l i m i n a r i e s t o a t r e a t m e n t o f t h e ti m e e v o l u -t i o n of t h e muon s p i n p o l a r i z a t i o n i n d i f f e r e n t t h e r m a l muonic s p e c i e s . W h i l e l i t t l e i s known about t h e d e t a i l s o f t h e mechanism i n v o l v e d i n t h e s l o w i n g and s t o p p i n g o f e n e r g e t i c p o s i t i v e muons i n m a t t e r , t h e r e i s much e x p e r i m e n t a l e v i d e n c e t o sup-1 . p o r t t h e v a l i d i t y of a q u a l i t a t i v e d e s c r i p t i o n - i t -A p o s i t i v e muon e n t e r i n g a condensed t a r g e t w i t h a k i n e t i c energy of many MeV w i l l l o s e energy by i n t e r a c t i o n 1. w i t h bound e l e c t r o n s , c a u s i n g e x c i t a t i o n and i o n i z a t i o n down t o s e v e r a l KeV; i t then slows down by s c a t t e r i n g w i t h e l e c -.1.1. t r o n s u n t i l i t s v e l o c i t y approaches t h a t o f the v a l e n c e e l e c t r o n s of t h e t a r g e t atoms ( c o r r e s p o n d i n g t o an energy 200 eV). In t h i s energy range t h e muon c a p t u r e s and l o s e s e l e c t r o n s i n r a p i d s u c c e s s i o n , f o r m i n g u n s t a b l e muon-+ - 12. lum atoms ( ju e ) i n a s e r i e s o f charge-exchange c y c l e s . The d e c e l e r a t i o n p r o c e s s g e n e r a l l y t a k e s no more th a n l O - " ^ --9 10 sec t o muonium f o r m a t i o n , d u r i n g which time t h e r e i s n e g l i g i b l e d e p o l a r i z a t i o n o f t h e muon . In most n o n - m e t a l l i c t a r g e t s , at some s t a g e i n the s l o w i n g down p r o c e s s , e s s e n t i - . a l l y a l l t h e muons form s t a b l e muonium atoms, which subse-q u e n t l y may e i t h e r d e c e l e r a t e t o t h e r m a l e n e r g i e s (by c o l --12 l i s i o n w i t h t a r g e t m o l e c u l e s ) w i t h i n 10 sec o r t a k e p a r t 1 i n "hot atom" c h e m i c a l r e a c t i o n s . The time r e q u i r e d f o r muonium t o t h e r m a l i z e i s s h o r t e r than t h e muonium h y p e r f i n e p e r i o d ( 2 T T / W 0 - 2.24 x 1 0 ~ 1 0 s e c ) , so t h e f r a c t i o n o f i n c i -dent muons (assumed t o be 100% p o l a r i z e d a l o n g t h e beam a x i s b e f o r e e n t e r i n g t h e t a r g e t ) t h e r m a l i z i n g as muonium w i l l s t i l l be f u l l y p o l a r i z e d i m m e d i a t e l y a f t e r t h e r m a l i z a t i o n . r.B) Hot Atom R e a c t i o n s o f Muonium As n o t e d i n the p r e c e d i n g s e c t i o n , b e f o r e t h e r m a l i z a t i o n , muonium may r e a c t e p i t h e r m a l l y w i t h i n an energy range o f r o u g h l y 20 t o 1 eV by "hot atom r e a c t i o n s " . These a r e chem-i c a l r e a c t i o n s t h a t are u s u a l l y f o r b i d d e n i n t h e t h e r m a l r e g i o n due t o l a c k o f t h e energy n e c e s s a r y t o overcome p o t e n -13 t i a l b a r r i e r s . In analogy w i t h hot t r i t i u m r e a c t i o n s , the most common h o t - r e a c t i o n s o f muonium can be c l a s s i f i e d as f o l l o w s : S u b s t i t u t i o n : Mu* + RH * MuR + H (111,1) A b s t r a c t i o n : Mu* + RH >- MuH + R (111,2) A d d i t i o n : Mu* + X, MuX (111,3) The f i r s t two r e a c t i o n s p l a c e the muon i n a d i a m a g n e t i c s p e c i e s which may have s u f f i c i e n t energy t o r e a c t f u r t h e r , perhaps i n some ca s e s r e s u l t i n g i n para m a g n e t i c m o l e c u l e s i n c o r p o r a t i n g muons. In the t h i r d r e a c t i o n , muonium may . add t o an u n s a t u r a t e d m o l e c u l e t o form a muonic r a d i c a l . S i n c e t h e s e "hot atom" r e a c t i o n s o c c u r i n an i n t e r v a l w hich i s s h o r t compared t o the response time o f a t y p i c a l MSR -9 experiment ( 10 sec ) they a re c o n s i d e r e d complete a t the s t a r t o f t h e experiment ( t = 0 ). - 16 -C ) G e n e r a l R e a c t i o n Scheme IV As r e p r e s e n t e d i n t h e g e n e r a l r e a c t i o n scheme shown i n F i g u r e 6, t h e i n i t i a l muon p o l a r i z a t i o n i s d i s t r i b u t e d amongst the t h e r m a l i z e d s p e c i e s Mu, R^, and a c c o r d i n g t o t h e f o r -m ation p r o b a b i l i t i e s h R and h D , where Mu r e p r e s e n t s muonium and R^ and are t h e h o t - r e a c t i o n muonic r a d i c a l and muonic d i a m a g n e t i c p r o d u c t s , r e s p e c t i v e l y . The o t h e r r e a c t i o n p a t h s r e p r e s e n t r e a c t i o n s o f t h e r m a l i z e d muonium w i t h t h e s u b s t r a t e t o form muonic r a d i c a l R 2 and d i a m a g n e t i c p r o d u c t , and t h e r e a c t i o n s o f muonic r a d i c a l s R^ and R 2 t o form d i a m a g n e t i c p r o d u c t s D 2 and D^. The r a t e c o n s t a n t s o f t h e s e r e a c t i o n s a r e p s e u d o - f i r s t o r d e r s i n c e t h e s m a l l number o f s t o p p e d muons 8 9 * ( t y p i c a l l y 10 - 10 i n an e x p e r i m e n t ) has a n e g l i g i b l e e f f e c t on t h e s u b s t r a t e c o n c e n t r a t i o n ; f u r t h e r m o r e , the e x p e r i m e n t a l t e c h n i q u e r e q u i r e s l i t e r a l l y t h a t no more than one muon be i n the t a r g e t a t any t i m e . F i g u r e 6: The Muonium R e a c t i o n Scheme --18-D) P o l a r i z a t i o n o f t h e Muon i n Muonic S p e c i e s i ) G e n e r a l E x p r e s s i o n The muon s p i n p o l a r i z a t i o n f o r an ensemble which f o l l o w s t h e g e n e r a l r e a c t i o n scheme ( d i s c u s s e d i n s e c t i o n C) may be e x p r e s s e d as P ( t ) = 2 P X ( t ) (111,4) x where Ix are t h e d i f f e r e n t muonic s p e c i e s . C o n s i d e r t h e case of a s p e c i e s x which has been formed at time t ' ( O ^ t ' ^ t ) and s t i l l e x i s t s at time t . I t s c o n t r i b u t i o n i s g i v e n by t P X ( t ) = J p X ( t , t ' ) q ( t , t ' ) d f (111,5) o where p ( t , t ' ) i s t h e muon s p i n p o l a r i z a t i o n d e f i n e d by t h e complete h i s t o r y o f t h e s p e c i e s x formed at time t ' , and q ( t , t ' ) i s t h e p r o b a b i l i t y -that x has been formed at time t ' and s t i l l e x i s t s at time t (which may i n c l u d e terms h R and h D o f S e c t i o n I I I - C ) . The e x p r e s s i o n s f o r muon s p i n p o l a r i z a t i o n p ( t , t ' ) i n muonium and i t s r e a c t i o n p r o d u c t s can be g i v e n as p r o d u c t s of m o d i f i c a t i o n s o f t h e e x p r e s s i o n s f o r t h e i d e a l s p e c i e s ' f r e e muon' and ' f r e e muonium' by t a k i n g i n t o account i n t e r a c t i o n s w i t h the m a t e r i a l environment. - 11 -i i ) Fre^e Muon In an e x t e r n a l f i e l d B a p p l i e d p e r p e n d i c u l a r , t o t h e mutual p l a n e o f t h e muon p o l a r i z a t i o n and t h e d e t e c t o r a x i s , f r e e muon s p i n s p r e c e s s i n t h i s p l a n e at t h e i r Larmor X f r e q u e n c y U>/* = g> ^ S = g ^ 6 B = 13.55 KHz/G ( I I I , 6 ) XTT h 2 n y c The d i s t r i b u t i o n o f d e t e c t e d p o s i t r o n s from muon decay i n a g i v e n d i r e c t i o n i n t h e p l a n e t h u s become o s c i l l a t o r y i n time and t h e e v o l u t i o n o f muon s p i n p o l a r i z a t i o n i s s i m p l y the complex q u a n t i t y p^Ct) = exp (-iCO^t) . ( I H , 7 ) T h i s e x p r e s s i o n may be f a c t o r e d t o g i v e t h e two t r a n s v e r s e components o f the muon s p i n p o l a r i z a t i o n p * ( t ) = cos o ^ t P£(t) = s i n t J ^ t ( 1 1 1 , 9 ) ' x y ( H I , 8 ) where the r e a l p a r t p / 4 < ( t ) i s the muon p o l a r i z a t i o n a l o n g t h e i n i t i a l d i r e c t i o n x and t h e i m a g i n a r y p a r t p£(t) i s the muon p o l a r i z a t i o n a l o n g t h e d i r e c t i o n y p e r p e n d i c u l a r t o b o t h x and z, the f i e l d d i r e c t i o n . - 20 -i i i ) Q u a s i - F r e e Muon In g e n e r a l i f t h e muon i s i n a d i a m a g n e t i c e n v i r o n -ment (as p a r t o f a m o l e c u l e w i t h s a t u r a t e d b o n d i n g ) i t can be c o n s i d e r e d t o be ' q u a s i - f r e e ' . We n e g l e c t the sl o w depo-l a r i z a t i o n mechanisms f o r muons i n a d i a m a g n e t i c environment. These mechanisms c o r r e s p o n d t o r e l a x a t i o n s o b s e r v e d i n p r o t o n s p i n resonance and may have r e l a x a t i o n t i m e s o f t h e o r d e r o f m i l l i s e c o n d s , but o n l y i n paramagnetic l i q u i d s : muon r e l a x -lb a t i o n s o f t h i s o r d e r have been seen i n M n C l 2 s o l u t i o n s In g e n e r a l , E q u a t i o n ( i l l , 7 ) may be used t o d e s c r i b e muon p r e c e s s i o n i n p r o d u c t s D^, D 2, D^, and o f F i g u r e 6 a l t h o u g h i n t h e l a t t e r t h r e e , t h e s i g n a l i s o b s e r v a b l e o n l y i f t h e muonic p r e c u r s o r s r e a c t t o form t h e s e p r o d u c t s i n a ve r y s h o r t time ( 7 J <<^ 10~^~® s e c ) i n o r d e r t o p r e v e n t des-t r u c t i o n o f t h e phase coherence o f the muon ensemble. I f such were t h e case, o n l y one d i a m a g n e t i c ' q u a s i - f r e e ' s i g n a l , a s s o c i a t e d w i t h the e p i t h e r m a l f r a c t i o n h^, would be d e t e c t -a b l e . - 2 1 -i v ) F ree Muonium The h y p e r f i n e i n t e r a c t i o n between muon and e l e c t r o n m agnetic moments i n g r o u n d - s t a t e ( I s ) f r e e muonium i n an 1 e x t e r n a l magnetic f i e l d B has been d e s c r i b e d i n an a l o g y t o the hydrogen atom by the s p i n H a m i l t o n i a n HMU= i - C J ^ - O e ) + + i.6Je-<V (111,10) where t h e h y p e r f i n e s p l i t t i n g h6J Q (U) Q = 2rr x 4463 MHz) i s the z e r o - f i e l d energy d i f f e r e n c e between s i n g l e t ( J = 0 ) and t r i p l e t ( J = 1 ) t o t a l a n g u l a r momentum s t a t e s . T h i s s p l i t t i n g may be thought o f as the i n t e r a c t i o n o f t h e e l e c -t r o n ' s magnetic moment w i t h t h e c o n t a c t f i e l d due t o t h e muon, B Q = 1593 G. In e q u a t i o n ( 1 1 1 , 1 0 ) , and <3e a r e the muon and e l e c t r o n P a u l i s p i n o p e r a t o r s , U)^ and 60 e a r e the muon and e l e c t r o n Larmor f r e q u e n c i e s , t h e l a t t e r g i v e n by ^ = S^Mt B - 2 . * M H * / G ( i n , i i ) - 17. -The free-muonium Hamiltonian leads to a field-dependence of energy l e v e l s as shown in the Bre i t -Rab i diagram in Figure 7. The energy eigenstates and eigenvalues are given i n Table 2, i n terms of the basis l^00*/^ where the axis of quant izat ion i s along the magnetic f i e l d , and as a function of the dimen-s ionles s s p e c i f i c f i e l d X - l£J = U & * U ^ (111,12) In the case of free muonium in a transverse f i e l d (per-pendicular to the i n i t i a l muon p o l a r i z a t i o n ) , the muonium precess ion and hyperfine frequencies correspond to a super-p o s i t i o n of Am = t r a n s i t i o n s between Zeeman e igenstates . In the notat ion O J ^ - W ^ , these are the t r a n s i t i o n frequen-c ie s u 1 2 , <^>23' C J 1 4 ' a n d ^34 i n F i S u r e 7 -In the formation of muonium, the muon i s assumed to be i n i t i a l l y completely p o l a r i z e d , while the e lec t ron i t captures i s genera l ly unpolar ized . Using the i n i t i a l d i r e c t i o n of muon p o l a r i z a t i o n as the quant izat ion ax i s , the i n i t i a l condi t ions can be expressed as fo l lows : h a l f of the muonium ensemble i s formed in the z e r o - f i e l d eigenstate | aQ^ = jm = h , mQ= , and ha l f in the s tate | b Q ^ =|m = £ , m e = In t h i s representat ion, the two halves of the muonium ensemble in states | a ) and jb) represent r e s p e c t i v e l y , a spin-1 system in which muon and e lec t ron spins are locked - 23 -Figure 7: The Energy Eigenstates of the Ground State (1=0)  of Muonium in an External Magnetic F i e l d as a function of the dimensionless s p e c i f i c f i e l d , defined in Equation (111,12) . The four allowed t r a n s i t i o n s ( A m = * 1) between the ground state energy l e v e l s are shown at a p a r t i c u l a r f i e l d value. - -T a b l e II. E i g e n v a l u e s and E i g e n s t a t e s f o r the  B r e i t - R a b i Diagram from Ref. 1 E"UgfJirATE:s m t iu. t«<v ( /7je^> U") = f ^ ) ( ( = / F«l ; ' ^ > a C l + - > ( 1 - ^ | F = o, ™ F = o> - 25 -t o g e t h e r by t h e h y p e r f i n e i n t e r a c t i o n , and a s p i n - 0 m i x t u r e o f s t a t e s , i n which the muon p o l a r i z a t i o n o s c i l l a t e s about z e r o a t a h i g h f r e q u e n c y ; t h e net e f f e c t o f t h i s o s c i l l a t i o n ( which a t 28 rad / n s e c i s t o o r a p i d t o be r e s o l v e d ) i s t o d e p o l a r i z e h a l f o f the muon ensemble. The t r i p l e t s t a t e , w i t h a magnetic moment dominated by the e l e c t r o n , w i l l p r e c e s s i n t h e e x t e r n a l f i e l d a t i t s Larmor f r e q u e n c y i n a sense o p p o s i t e t o t h a t o f t h e f r e e muon i n the same f i e l d : . ( . I l l , -Lo ) S i n c e t h e muon and e l e c t r o n s p i n s a re ' l o c k e d ' t o g e t h e r t h i s muonium p r e c e s s i o n f r e q u e n c y can be o b s e r v e d i n t h e muon's lo t decay p a t t e r n . A t h e o r e t i c a l p l o t o f t h e e v o l u t i o n o f muon p o l a r i z a t i o n i n f r e e muonium i n 100 G t r a n s v e r s e f i e l d i s shown i n f i g u r e 8. The e x a c t time dependence o f the muon s p i n p o l a r i z a t i o n i n f r e e muonium i n a t r a n s v e r s e magnetic f i e l d can be d e s c r i b e d u s i n g t h e S c h r o d i n g e r approach: the i n i t i a l s t a t e s | a ( 0 ) ^ and |b(0)^. a r e expanded i n energy e i g e n s t a t e s , the s t a t i o n a r y s t a t e s a re a l l o w e d t o e v o l v e i n time as exp ( i C J . t ) , and the r e s u l t s | a ( t ) ) and | b ( t ) ^ a r e reexpanded i n t h e b a s i s lm m \ i n which t h e muon p o l a r i z a t i o n can e a s i l y be e x p r e s s e d , i r- e/|( F i g u r e 8: E v o l u t i o n of Muonium i n 100 G T r a n s v e r s e F i e l d - 27 -The e x p l i c i t e x p r e s s i o n f o r t h e time dependence o f the muon s p i n p o l a r i z a t i o n i n muonium i s j y t ) : = i [ c * ( e l ^ + rt • ( e 1 ^ + e t U w t ) ] ( i " i i , 14, where c and s have been p r e v i o u s l y d e f i n e d (see T a b l e 1 ) and the f o u r t r a n s i t i o n f r e q u e n c i e s (see f i g u r e 5 ) are UJ | Z = CJ_ - J T (III, 15) U)^ = -60. + -O. 4- CJ 0 (111,16) UZ3 = UL + -n- (111,17) = 6J_ +• -JT- + t J e (111,18) w i t h 6 J _ = z ( d J e - ^ U * ) ( i n , i 9 ) JTL = ^ ° [ ( i ^ - x 2 ) ^ - l ] ( i n , 2 0 ) The e q u a t i o n (III,l*r) can be r e w r i t t e n v i a t r i g o n o m e t r i c i d e n t i t i e s and p r e v i o u s d e f i n i t i o n s as f o l l o w s : (111,21) where j = C X - 5 Z = — (111,22) In weak f i e l d s ( X « l ) , E q u a t i o n (111,21) can be a p p r o x i m a t e d by * e tU . t [cos Jit +• CCs(uo+Jl)t ] (111,23) E x p e r i m e n t a l l y , w i t h p o s i t r o n d e t e c t o r s f i x e d i n t h e p l a n e o f p r e c e s s i o n , t h e r e a l p a r t o f the muon p o l a r i z a t i o n i s o b s e r v e d a l o n g the x - a x i s , and the i m a g i n a r y p a r t i s ob s e r v e d a l o n g t h e y - a x i s . The f r e q u e n c y (6J 0 + J~>-) i s t o o h i g h t o observe e x p e r i m e n t a l l y s i n c e Ub i s beyond t h e time r e s o l u t i o n o f the e x p e r i m e n t a l a p p a r a t u s ( F i g u r e 8 ) . The ob s e r v e d muonium p r e c e s s i o n a t f r e q u e n c y 6J_ i s modulated a t the "beat f r e q u e n c y " _TL, w i t h h a l f t h e i n i t i a l p o l a r i z a t i o n a m p l i t u d e . T h i s " t w o - f r e q u e n c y " p r e c e s s i o n p a t t e r n then has the form f ^ J t ) ~ ^ £ - L U ^ COSJLXZ (III, 24) The m o d u l a t i o n f r e q u e n c y JX i s r e l a t i v e l y slow: i n m o d e r a t e l y low f i e l d s i t can be approx i m a t e d by £ J - n ~ (III, 25) - 1°i -Thus, from t h e 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 o f t h e p r e c e s s i o n f r e q u e n c y U_ and t h e s p l i t t i n g f r e q u e n c y , t h e h y p e r -f i n e f r e q u e n c y lJ0 may be d e t e r m i n e d . At e a r l y t i m e s o r i n a v e r y weak f i e l d (a few gauss) the c o n d i t i o n JlLt« ^— i s e s t a b l i s h e d . E q u a t i o n ( I I I , 23) can then be f u r t h e r a p p r o x i m a t e d as fiwft) - " a ^ P ( t U - t ) ( I I I , 26) In t h i s l i m i t t h e " s p l i t t i n g " and h y p e r f i n e m o d u l a t i o n s can ( i n p r a c t i c e ) be n e g l e c t e d and muonium p r e c e s s i o n s i m p l y t r e a t e d as a f a s t e r v e r s i o n ( r e c a l l i n g E q u a t i o n I I I , 7) o f the muon p r e c e s s i o n a l r e a d y mentioned. - 3 © -The MSR time h i s t o g r a m f o r muonium p r e c e s s i o n , a n a l o -gous t o E q u a t i o n ( I I , 4) f o r f r e e j i +, can be w r i t t e n Hit) =• f j ( B + e x p ( - ^ ) [ | l A P j t ) ] ) ( i n , 27) where, i n the absence o f r e l a x a t i o n ( d i s c u s s e d n e x t ) , P j ^ C t ) can be w r i t t e n from E q u a t i o n (111-26) as P x ( t ) c= l£ Cos L)jt ( I I I , 28) and P1 It) \ 5 i n ( J . t ( H I ; 29) f o r t h e r e a l and i m a g i n a r y components r e s p e c t i v e l y . - 3> -v) Quasi-Free Muonium When a muonium atom i s stopped in matter i t s behaviour may d i f f e r from that of free muonium due to perturbat ion by the mater ia l environment. In the time scale of the MSR experiment, d i r e c t re l ax-at ion of the muon magnetic moment in muonium by the surround-ings i n diamagnetic media can be neglected, s ince even in paramagnetic so lut ions , the for muon re laxa t ion i s only of order ~1 jjsec. However, the p o l a r i z a t i o n of the muon i s s t rongly af fected by the perturbat ion of the e lec t ron through the muonium hyperfine i n t e r a c t i o n . The quantity )} i s introduced to represent the re l ax-at ion rate of the muonium e lectron which, for muonium in the absence of other paramagnetic species , i s dominated by e l ec -t r o n - l a t t i c e re laxa t ion mechanisms. ESR data on hydrogen atoms i n so lu t ion support the contention that i ^ ^ i n l i q u i d s i s too slow to not iceably af fect the muon p o l a r i z a t i o n on the time sca le of the experiment: t y p i c a l re l axa t ion rates for the e lec t ron of atomic hydrogen i n l i q u i d s are le s s than -5 -1 10 sec . In add i t ion , muonium has recent ly been success-l«? f u l l y observed i n u l t ra-pure water In the s o l i d phase (with r e s t r i c t i o n to sp in le s s in su-l a t o r s ) , i t i s reasonable to assume that l/A i s n e g l i g i b l y - -s m a l l compared to the h y p e r f i n e frequency u)0 , and a l s o s m a l l compared to the p r e c e s s i o n frequency £J, of t r i p l e t muonium. T h i s assumption has been e x p e r i m e n t a l l y v a l i d a t e d i n p r e v i o u s d i r e c t o b s e r v a t i o n of muonium p r e c e s s i o n i n s e v e r a l pure s o l i d s . In fuse d q u a r t z the 'two-frequency p r e c e s s i o n ' d e s c r i b e d by equation ( I I I - 2 3 ) has been observed i n moderate f i e l d s , and the value of CJC e x t r a c t e d from the 'beat frequency' i s c o n s i s t e n t with the h y p e r f i n e frequency of muonium i n vacuum. When muonium p r e c e s s i o n has been observed, a f a i r l y 1 r a p i d damping of the s i g n a l has u s u a l l y been noted. In a d d i -t i o n to the d e p o l a r i z a t i o n of the muonium e l e c t r o n , t h i s r e l a x a t i o n may be due to random l o c a l magnetic f i e l d s , or chemical r e a c t i o n s of muonium. The e f f e c t of r e l a x a t i o n can be d e s c r i b e d by i n t r o -d ucing the parameter 'Tg' which corresponds to a s p i n d e p o l a r -i z i n g time of the ensemble of p o s i t i v e muons i n muonium, and i s d e f i n e d i n analogy to the s p i n - s p i n r e l a x a t i o n time a s s o c i -a t e d w i t h the NMR technique. Hence P M u ( t ) i n Equation ( I I I , 27) i s r e w r i t t e n as ( H I , 3 0 ) 3 1 ) In the t r a n s v e r s e f i e l d MSR method chemical r e l a x a t i o n cannot be d i s t i n g u i s h e d from non-chemical r e l a x a t i o n . Measurements of the r e l a x a t i o n time Tg i n a p a r t i c u l a r medium -5 -7 are r e l i a b l e i n the range from about 1 0 to 1 0 sec. - 33 -v i ) Muonic R a d i c a l s When muonium has gone i n t o a c o v a l e n t bond as p a r t o f a f r e e r a d i c a l t h e r e may be h y p e r f i n e c o u p l i n g between t h e muon and e l e c t r o n m agnetic moments'. The i s o t r o p i c component i s a c o n t a c t i n t e r a c t i o n which r e q u i r e s n o n - v a n i s h i n g s p i n d e n s i t y o f t h e u n p a i r e d e l e c t r o n a t the muon i n a muonic r a d i c a l . F o r a f r e e muonium atom i n the ground s t a t e the e l e c t r o n has 100% s c h a r a c t e r , and t h e wave f u n c t i o n i s e x a c t l y 5U known: \ - '/ " if/ (o) = (iraj) 1 ( i n , 32) where a Q = 0 . 5 3 A . The h y p e r f i n e s p l i t t i n g AE = h\/o , where ]) may be e v a l u a t e d from t h e Fermi e x p r e s s i o n 6 ( I I I , 33) t o be 4463 MHz. F o r m o l e c u l e s t h i s e q u a t i o n can be r e w r i t t e n as V? = f f " > A > / v V < I I ] C ' 3 4 > where yO^ i s t h e d i m e n s i o n l e s s s p i n d e n s i t y a t t h e muon e v a l -u a t e d from t h e t o t a l e l e c t r o n wave f u n c t i o n : i t r e p r e s e n t s - 34- -the f r a c t i o n o f u n p a i r e d e l e c t r o n on the muon and i s g i v e n . by />r - z. ( mc«r- i^wr) a " , s s y where n i s the p r i n c i p a l quantum number and s denotes an s f u n c t i o n . The s p i n d e n s i t y may be p o s i t i v e o r n e g a t i v e at a p a r t i c u l a r n u c l e u s but t h e summation o v e r a l l n u c l e i e q u a l s u n i t y f o r a m o l e c u l e w i t h one u n p a i r e d e l e c t r o n . The i s o t r o p i c h y p e r f i n e i n t e r a c t i o n i n a muonic p o l y -a t o m i c r a d i c a l i s e x p e c t e d t o be weaker than the i n t e r a c t i o n i n muonium s i n c e the u n p a i r e d e l e c t r o n w a v e f u n c t i o n i s not e n t i r e l y l o c a l i z e d i n t h e I s o r b i t a l o f t h e muon i n a r a d i c a l . P r e d i c t i o n s o f t h e i s o t r o p i c c o u p l i n g e x p e c t e d i n s e v e r a l muonic r a d i c a l s a r e g i v e n l a t e r i n t h i s paper. P r o v i d i n g t h a t c o n t a c t i n t e r a c t i o n o f t h e muon magnetic moment w i t h the magnetic moment o f a s i n g l e u n p a i r e d e l e c t r o n i s dominant i n a p a r t i c u l a r r a d i c a l ( i e . w i t h n e g l i g i b l e s p i n - o r b i t i n t e r a c t i o n ) , t h e s p i n h a m i l t o n i a n o f f r e e muonium (see e q u a t i o n I I I - 1 0 ) i s an adequate a p p r o x i m a t i o n f o r use w i t h such a muonic r a d i c a l i f (J0 i s r e p l a c e d w i t h u ( t h e h y p e r f i n e f r e q u e n c y i n the r a d i c a l ) . Thus t h e e x p r e s s i o n f o r the muon p o l a r i z a t i o n i n s u i t a b l e r a d i c a l s , F^/t) s h o u l d be c o m p l e t e l y analogous t o t h a t o f muonium ( e q u a t i o n I I I - Z I ). - 35 -I f t h e h y p e r f i n e i n t e r a c t i o n i n the r a d i c a l i s a n i s o t r o p i c ( a r i s i n g from r e l a t i v e a n g u l a r momentum between the u n p a i r e d e l e c t r o n and the muon), the m o d i f i e d muonium d e s c r i p t i o n would s t i l l be a p p r o p r i a t e i f the a n i s o t r o p i c components were a v e r -aged t o z e r o by r a p i d m o l e c u l a r t u m b l i n g i n a p e r i o d s h o r t e r than t h a t o f t h e h y p e r f i n e i n t e r a c t i o n . S i n c e t h i s p e r i o d i s not u s u a l l y l e s s than 10 sec and p e r i o d s o f m o l e c u l a r r o t --12 a t i o n s i n l i q u i d s are of t h e o r d e r o f 10 s e c , the a n i s o -23 t r o p i c i n t e r a c t i o n v a n i s h e s i n most l i q u i d s In s o l i d o r v i s c o u s phases, however, th e a n i s o t r o p i c s p i n i n t e r a c t i o n may be c o n s i d e r a b l e and, even i f smeared out by a random o r i e n t a t i o n o f t h e m o l e c u l e s , i t may v e r y appre-c i a b l y widen th e i s o t r o p i c h y p e r f i n e s i g n a l s . A n i s o t r o p y c o u l d be c o n s i d e r a b l y reduced by m o t i o n a l n a r r o w i n g : i t i s known t h a t t h e range of o b s e r v e d r o t a t i o n a l b e h a v i o u r f o r m o l e c u l e s i n dense phases i s e x t r e m e l y wide, v a r y i n g from n e a r l y complete h i n d r a n c e t o r e o r i e n t a t i o n t o almost f r e e motion . The problem o f a n i s o t r o p i c i n t e r a c t i o n between a muonic r a d i c a l and i t s s u r r o u n d i n g m a t e r i a l can be m i n i -mized by s e l e c t i n g s u b s t r a t e s w i t h no n u c l e a r s p i n s . S i n c e t h e e l e c t r o n 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 s (T^) -6 o f p r o t o n i c r a d i c a l s are seldom s h o r t e r than 10 s e c , i t i s r e a s o n a b l e t o assume t h a t r e l a x a t i o n by t h i s mechanism i n muonic r a d i c a l s i s n e g l i g i b l e on the time s c a l e o f t h e e x p e r -- 36 -i m e n t — e x c e p t i o n s are s m a l l r a d i c a l s w i t h o r b i t a l l y degenerate ground s t a t e s ( i n which s p i n - o r b i t c o u p l i n g i s not quenched) and r a d i c a l s whose u n p a i r e d e l e c t r o n has h y p e r f i n e c o u p l i n g \0c w i t h s e v e r a l n u c l e i . In the l a t t e r case the muonium d e s c r i p -t i o n ( i n which o n l y two s p i n - f p a r t i c l e s are c o u p l e d ) becomes i n a p p r o p r i a t e . D e l o c a l i z a t i o n o f t h e u n p a i r e d e l e c t r o n o y e r s e v e r a l p a r a m a g n e t i c n u c l e i l e a d s t o a system of s p i n - s p i n i n t e r a c t i o n s t h a t i s independent o f t h e r o t a t i o n o f the m o l e c u l e . F o r t h i s r e a s o n carbon d i o x i d e , carbon d i s u l f i d e , and s u l f u r d i -o x i d e were chosen as p a r t i c u l a r l y s u i t a b l e s u b s t r a t e s f o r t h e g e n e r a t i o n o f muonic r a d i c a l s i n s i t u , s i n c e t h e most n a t u -r a l l y abundant i s o t o p e s o f c a r b o n , oxygen, and s u l f u r atoms have z e r o s p i n . In muonic r a d i c a l s i n c o r p o r a t i n g t h e s e i s o t o p e s the problem o f m u l t i p l e s p i n i n t e r a c t i o n s i s n e g l i -g i b l e . R a d i c a l s c r e a t e d i n e p i t h e r m a l r e a c t i o n s (R^ i n the g e n e r a l r e a c t i o n scheme of Figure 6) would o n l y be d e t e c t a b l e i n the t r a n s v e r s e f i e l d experiment i f they e x i s t e d o v e r at l e a s t one Larmor p r e c e s s i o n p e r i o d . The p r e c e s s i o n p e r i o d o f muonium is c o n s i d e r e d t o be t h e lower l i m i t f o r the p r e c e s s i o n p e r i o d o f a muonic r a d i c a l , and the r a d i c a l must e x i s t f o r at l e a s t ~50 nsec t o be d i r e c t l y o b s e r v a b l e . I t i s - 37 -p o s s i b l e t h a t s h o r t c h e m i c a l l i f e t i m e s f o r p o l y a t o m i c muonic r a d i c a l s have p r e v e n t e d t h e i r d i r e c t d e t e c t i o n i n p a s t e f f o r t s ; ' r a d i c a l p r e c e s s i o n ' ( o t h e r than t h a t o f muonium) has never been e x p e r i m e n t a l l y o b s e r v e d i n MSR e x p e r i m e n t s . Another p o s s i b l e r e ason c o u l d be t h a t t h e p r o b a b i l i t y o f h o t - r a d i c a l f o r m a t i o n (h^) may be e x t r e m e l y s m a l l i n t h e s u b s t r a t e s used. R a d i c a l s formed by t h e r m a l r e a c t i o n s ( R 2 ) °f muonium w i t h t h e s u b s t r a t e w i l l o n l y be o b s e r v a b l e w i t h s a t i s f a c t i o n o f the f o l l o w i n g c r i t e r i o n : the muonium i n v o l v e d must have a v e r y s h o r t c h e m i c a l l i f e t i m e ("C <f< 77 ) so t h a t the phase coherence o f t h e muon ensemble i s not d e s t r o y e d . A g a i n , d i r e c t d e t e c t i o n e x p e r i m e n t s have not been s u c c e s s f u l . To date t h e r e has been no r e p o r t o f t h e d i r e c t d e t e c t i o n Z5 o f muonic r a d i c a l s . P e r c i v a l e t a l . i n v e s t i g a t e d degassed samples o f t e t r a m e t h y l e t h y l e n e , b u t a d i e n e , i s o b u t e n e , i s o p r e n e , m a l e i c a c i d , f u m a r i c a c i d , and carbon d i s u l f i d e . In no case were s i g n i f i c a n t s i g n a l s o b s e r v e d . - 38 -IV. INDIRECT EVIDENCE OF MUONIC RADICALS The i n d i r e c t e v i d e n c e f o r the p a r t i c i p a t i o n o f muonic r a d i c a l s i n r e a c t i n g systems comes from e x p e r i m e n t s u s i n g the ' r e s i d u a l muon p o l a r i z a t i o n ' t e c h n i q u e d e v e l o p e d by Brewer, F l e m i n g , and Gygax Whereas i n the d i r e c t method one conducts o b s e r v a t i o n s i m m e d i a t e l y f o l l o w i n g t h e r m a l i z a t i o n o f muonic s p e c i e s Mu, R^, and D^ ( r e c a l l f i g u r e 6), which o c c u r s e s s e n t i a l l y at time z e r o , the i n d i r e c t method i n v o l v e s o b s e r v a t i o n at a l a t e r t i m e , when ( i n c e r t a i n c a s e s ) the muonic s p e c i e s have a l l reacted- t o form the d i a m a g n e t i c p r o d u c t s , D^, and D^. At t h i s time the muons p r e c e s s j u s t as i f they had begun a t t = 0 w i t h an apparent i n i t i a l u + p o l a r i z a t i o n c a l l e d t h e ' r e s i d u a l p o l a r i z a t i o n ' : i t i s g e n e r a l l y reduced and r o t a t e d w i t h r e s p e c t t o t h e a c t u a l i n i t i a l p o l a r i z a t i o n . One may i n t e r p r e t t h a t the muons have undergone a p e r i o d o f r a p i d s p i n r . e v o l u t i o n w h i l e ' p a s s i n g t h r o u g h ' muonium o r .muonic r a d i c a l s , b e f o r e e n t e r i n g the d i a m a g n e t i c environment. Thus the 'amplitude' and 'phase' o f t h e s e muons' p o l a r i z a t i o n d i f f e r from t h o s e o f a h y p o t h e t i c a l ensemble p r e c e s s i n g as f r e e muons s i n c e time z e r o . As one o f a s e r i e s o f s i m i l a r e x p e r i m e n t s (which a l l sug-g e s t e d t h e p a r t i c i p a t i o n o f muonic r a d i c a l s ) Brewer and co-- 3*\ -workers* measured the r e s i d u a l a m p l i t u d e and phase as f u n c -t i o n s o f t h e bromine c o n c e n t r a t i o n i n l i q u i d benzene. In t h i s system 'hot' muonium s h o u l d r e a c t w i t h t h e s o l v e n t t o g i v e d i a m a g n e t i c p r o d u c t w i t h p r o b a b i l i t y h^, whereas t h e r m a l r e a c t i o n o f Mu w i t h benzene l e a d s t o muonic c y c l o h e x a d i e n y l r a d i c a l R 2 ( k ^ = k|(CgHg)). The bromine scavenges b o t h t h e r -mal muonium t o g i v e p r o d u c t ( k Q = k ^ ( B r 2 ) ) and R 2 t o g i v e p r o d u c t Dg ( k 2 = k 2 ( B r 2 ) ) . These workers d i d not d i s c u s s r a d i c a l f o r m a t i o n v i a t h e hot atom r o u t e ( R ^ ) . T h e i r m u l t i -p arameter f i t t o t h e e x p e r i m e n t a l d a t a gave e x c e l l e n t q u a l i -t a t i v e e v i d e n c e o f t h e i n v o l v e m e n t o f r a d i c a l s i n t h e r e a c t i n g system. R e a n a l y s i s o f t h e i r d a t a by P e r c i v a l s u g g e s t e d t h a t r a d i c a l f o r m a t i o n v i a the hot-atom r o u t e ( w i t h p r o b a b i l i t y h^) was a l s o p o s s i b l e , and showed t h a t t h e r e i s a c o n t i n u o u s s e t o f p a i r s o f v a l u e s o f the r a t e s k^ and k| s a t i s f y i n g t h e m u l t i - p a r a m e t e r ' f i t s t o t h e d a t a . Thus, w h i l e o n l y t e n t a t i v e e s t i m a t e s o f t h e r a t e c o n s t a n t s were a v a i l a b l e , t h e p a r t i c i -p a t i o n o f muonic r a d i c a l s seems t o have been at l e a s t q u a l i -t a t i v e l y demonstrated. A s i d e from t h e p o s s i b l e a m b i g u i t i e s i n m u l t i - p a r a m e t e r f i t s t o r e s i d u a l phase and a m p l i t u d e measurements a l o n e , t h e a n a l y s e s r e l i e d on assumed r a d i c a l s t r u c t u r e s and h y p e r f i n e f r e q u e n c i e s f o r which t h e r e i s no d i r e c t e v i d e n c e . The h y p e r f i n e f r e q u e n c i e s were e s t i m a t e d from t h o s e o f known p r o t o n i c r a d i c a l s by m u l t i p l i c a t i o n by t h e r a t i o o f t h e muon's magnetic moment o v e r t h e p r o t o n ' s magnetic moment. - Ho -V . DIRECT DETECTION EXPERIMENTAL SCHEME A) Method o f R a d i c a l I d e n t i f i c a t i o n F o r t r a n s v e r s e f i e l d s t h e r e can be o s c i l l a t i o n s a t t h e muon Larmor f r e q u e n c y CJ^. i n d i a m a g n e t i c s p e c i e s and at t h e f o u r t r a n s i t i o n f r e q u e n c i e s ( E q u a t i o n s 111-15, 16, 17, 18) o f muonium and t h e r a d i c a l s . F o r z e r o f i e l d 6 J l t and C J a 3 are z e r o and (as p r e v i o u s l y mentioned) f o r nonzero weak f i e l d s ( t h i s e x p e r i m e n t ) t h e y appear a t £ J _ - - n . ( r e c a l l E q u a t i o n 111-15); the f r e q u e n c y d i f f e r e n c e 2.-H- i n c r e a s e s w i t h i n c r e a -s i n g f i e l d but i t a l s o i n c r e a s e s w i t h d e c r e a s i n g h y p e r f i n e f r e q u e n c y Us , where the s u b s c r i p t r e p r e s e n t s muonium o r r a d i c a l . As mentioned e a r l i e r t he h y p e r f i n e f r e q u e n c y 6 J r i n t h e r a d i c a l w i l l be l e s s than t h a t i n "vacuum" muonium ( ( J 0 ) • Thus, t h e f r e q u e n c i e s U , A and U A 3 (which may e a s i l y be o b s e r v e d f o r not too l a r g e s p e c i f i c f i e l d s ~X_ , o f Equa-t i o n 111-12) w i l l be " s p l i t " more i n a r a d i c a l than i n muonium i n a g i v e n e x t e r n a l f i e l d , and t h e i r d i f f e r e n c e may be used t o d i s t i n g u i s h between t h e two p a r a m a g n e t i c s p e c i e s . A l s o , t h e n o r m a l l y u n o b s e r v a b l e h i g h f r e q u e n c i e s (AJ/((. and C J - j ^ ( r e c a l l F i g u r e 7) approach £J $ f o r z e r o f i e l d and they may i n f a c t be o b s e r v a b l e f o r s m a l l CJS and low f i e l d s . - 41 -B) Example: I d e n t i f i c a t i o n o f Muonium i n Q u a r t z In t h e MSR e x p e r i m e n t a l system d e s c r i b e d below, q u a r t z i s r e g u l a r l y used as a s t a n d a r d t a r g e t , i n wh i c h q u a s i - f r e e muonium i s o b s e r v e d , t o ensure p r o p e r o p e r -a t i o n o f the system. In t h i s example r e s u l t s were o b t a i n e d f o r muonium i n q u a r t z at low f i e l d ( — 7 G). Next, t h e experiment was r e p e a t e d i n a moderate f i e l d (—70 G) t o i l l u s t r a t e t h e s p l i t t i n g e f f e c t ( E q u a t i o n .-111-24 ) i n muonium. The s p l i t t i n g f r e q u e n c y i n muonium can be r e s o l v e d above about 4Q G; t h e minimum n e c e s s a r y f i e l d s h o u l d be lo w e r f o r o t h e r r a d i c a l s p e c i e s . i ) Q u a r t z i n Low E x t e r n a l F i e l d F i g u r e 9 shows t h e r e s u l t o f a " X ^ - m i n i m i z a t i o n f i t o f e x p e r i m e n t a l d a t a t o the e x p r e s s i o n f o r Mu i n weak f i e l d ( E q u a t i o n 111-27 ). u s i n g t h e ( t ) g i v e n i n E q u a t i o n ( I I I , 3 1 ) . The d a t a i s from muonium i n q u a r t z i n 6.5 G e x t e r n a l f i e l d . The f i t t i n g program y i e l d e d a v a l u e o f t h e r e l a x a t i o n t ime T 2 = 2.5 +/- 0.1 usee, as w e l l as f o r t h e o t h e r parameters o f t h e Mu h i s t o g r a m e x p r e s s i o n ( E q u a t i o n 111-27), based on t h e known muon l i f e t i m e . The f r e q u e n c y a n a l y s i s i s f a c i l i t a t e d by use o f t h e F o u r i e r t e c h n i q u e , y i e l d i n g t h e F o u r i e r t r a n s f o r m shown i n F i g u r e 10. i F i e l d = 6.5 G Frequency =9.08 MHz T 2 = 2.5 usee i ; I 1 : I . i 1 0 .05 .1 .15 .2 .25 .3 .35 'TIME (MICROSEC) F i g u r e 9: Asymmetry P l o t f o r Muonium i n Fused Q u a r t z The e x p e r i m e n t a l _ h i s t o g r a m was f i t t o the form FUSED QUARTZ IN LOW FIELD SFTi[RIGHT) 7.E-4 6.E-4 5.E-4 4.E-4 3.E-4 2. E-4 1 .E-4 -1 .E-4 -5 10 15 FREQUENCY (MHZ) 20 25 30 F i g u r e 10: F o u r i e r T r a n s f o r m Spectrum of Qu a r t z Data a t Low F i e l d , The peak at 9.08 MHz i s from muonium p r e c e s s i o n i n an e x t e r n a l f i e l d o f 6.5 G. - *tH~ -i i ) Two-Frequency P r e c e s s i o n of Muonium i n a Moderate E x t e r n a l M a g n e t i c F i e l d F i g u r e 11 shows the F o u r i e r t r a n s f o r m spectrum f o r muonium i n q u a r t z i n a 67.5 G e x t e r n a l f i e l d : r e c a l l i n g the d i s c u s s i o n o f E q u a t i o n (111-23), t h e f r e q u e n c i e s £J ) X and are e x p e c t e d t o appear at £J_ + SL . The f r e q u e n c y d i f f e r e n c e 2 .T2- 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 t h e h y p e r f i n e f r e q u e n c y D0 . T a k i n g t h e f r e q u e n c y d i f f e r e n c e between the two peaks as 2_n- and the p o s i t i o n midway between them as the Larmor f r e q -uency £J_ , and i n s e r t i n g t h e s e v a l u e s i n t o E q u a t i o n (111-25) y i e l d s a v a l u e f o r the muonium h y p e r f i n e f r e q u e n c y i n q u a r t z of 4000 MHz, which i s i n a c c e p t a b l e agreement w i t h the v a l u e f o r f r e e muonium i n vacuum, V0 = 4463 MHz. HU IN QUARTZ. (RIGHT) .00175 -2.5E-4 -20 0 20 F i g u r e 11: 40 100 120 140 60 80 FREQUENCY (MHZ) F o u r i e r T r a n s f o r m Spectrum o f Qua r t z Data at Moderate E x t e r n a l F i e l d shows s p l i t t i n g o f the 160 180 Mu p r e c e s s i o n . - f 6 -C) S p i n D e n s i t y P r e d i c t i o n s The s p l i t t i n g f r e q u e n c y 2_n. may be used as a d i a g n o s t i c a i d i n t he i d e n t i f i c a t i o n o f muonic r a d i c a l s s i n c e t h e h y p e r f i n e f r e q u e n c y (which i s d i r e c t l y p r o p o r t i o n a l t o t h e s p i n den-s i t y at t h e muon) may be d e r i v e d from an e x p e r i m e n t a l measure-ment. In o r d e r t o c o r r o b o r a t e the i d e n t i f i c a t i o n i t i s a l s o d e s i r a b l e t o p r e d i c t the v a l u e o f CJr~ , which would a l s o be u s e f u l i n a s s i g n i n g a t e n t a t i v e s t r u c t u r e f o r t h e r a d i c a l . C o n v e r s e l y , a t h e o r e t i c a l p r e d i c t i o n o f ( J r f o r a p a r t i c u l a r r a d i c a l can be used t o p r e d i c t t h e v a l u e o f Sl-f o r a p a r t i c u l a r s t r e n g t h of e x t e r n a l magnetic f i e l d . In o t h e r words, i t i s n e c e s s a r y t o e s t i m a t e the minimum e x t e r n a l f i e l d needed t o ' s p l i t ' t he r a d i c a l Larmor f r e q u e n c y i n o r d e r t o d i s t i n g u i s h the r a d i c a l from muonium. For example, t h e s p l i t t i n g f r e q u e n c y i n muonium i n a 35 G e x t e r n a l f i e l d can b a r e l y be r e s o l v e d (~0.5 MHz); f o r a r a d i c a l w i t h u = 0.01 C J Q t h e same magnitude o f s p l i t t i n g would be e x p e c t e d at 3G. Thus i n a 10 G f i e l d t he r a d i c a l would be v i s i b l y ' s p l i t ' w h i l e muonium would n o t . In the o t h e r extreme, i f the s p i n d e n s i t y at t h e muon - 1*7 -was e x t r e m e l y s m a l l i n a p a r t i c u l a r r a d i c a l , t h e ' s p l i t t i n g ' even a t t h e l o w e s t p r a c t i c a l e x t e r n a l f i e l d s t r e n g t h ( ~ 1 G, l i m i t e d by i n h o m o g e n e i t y ) c o u l d c o n c i e v a b l y be t o o l a r g e t o be o b s e r v e d — i n p r i n c i p l e t h e h y p e r f i n e f r e q u e n c y o f t h i s r a d i c a l c o u l d be d e t e c t e d by an ex p e r i m e n t i n z e r o e x t e r n a l f i e l d w i t h t h e use o f a p o s i t r o n c o u n t e r p o s i t i o n e d a l o n g t h e beam a x i s . The h y p e r f i n e f r e q u e n c y C J r i n a p a r t i c u l a r r a d i c a l can be p r e d i c t e d by m u l t i p l y i n g t h e h y p e r f i n e f r e q u e n c y i n muonium (2TT x 4463 MHz) by t h e s p i n d e n s i t y at t h e muon i n the r a d i c a l s p e c i e s . The s p i n d e n s i t y p r e d i c t i o n a t t h e muon i n a p o l y -a t o m i c r a d i c a l s h o u l d be i d e n t i c a l t o t h a t f o r a hydrogen n u c l e u s i f t h e bond l e n g t h s a re assumed t o be t h e same. With t h i s a ssumption, c o m p u t a t i o n s were performed on p r o t o n i c a n a l o g s of the a n t i c i p a t e d muonic r a d i c a l s . - 4-8 -D) S e l e c t i o n of C h e m i c a l s The s u b s t a n c e s C 0 2 , S 0 2 , and C S 2 were chosen f o r s t u d y 12 1G 32 p r i m a r i l y because the dominant i s o t o p e s C , 0 , and S a l l have z e r o n u c l e a r s p i n . Assuming t h a t muonium can t a k e p a r t i n an a d d i t i o n r e a c t i o n w i t h each s p e c i e s , the r a d i c a l s formed might be c h a r a c t e r i z e d by h y p e r f i n e c o u p l i n g between t h e muon and u n p a i r e d e l e c t r o n s i m i l a r t o t h a t seen i n f r e e muonium. E) Temperature C o n s i d e r a t i o n s F ree r a d i c a l s , h a v i n g u n p a i r e d e l e c t r o n s , a re e x t r e m e l y r e a c t i v e i n g e n e r a l . S i n c e c h e m i c a l p r o c e s s e s s h o u l d be impeded at v e r y low t e m p e r a t u r e s , e f f o r t s were made t o conduct t h e ex p e r i m e n t s at 4.2 K. T h i s was c o n s i d e r e d t o be o f v i t a l i m p o r t a n c e w i t h r e g a r d t o d i f f u s i o n i n t h e l a t t i c e , s i n c e t h e pr e s e n c e of even t r a c e s o f pa r a m a g n e t i c i m p u r i t i e s would be^ e x p e c t e d t o d e s t r o y the r a d i c a l . P r i o r t o t h e a v a i l a b i l i t y o f t h e h e l i u m c r y o s t a t d e s c r i b e d below, C S 2 was i n v e s t i g a t e d at ambient t e m p e r a t u r e u s i n g an a v a i l a b l e , t a r g e t c e l l , a l s o d e s c r i b e d below. CCv, was e a s i l y i n v e s t i g a t e d as dry i c e at 195 K, and was a l s o used i n c o n t a c t w i t h l i q u i d n i t r o g e n (77 K) i n a low d e n s i t y foam p l a s t i c s h e a t h . - H -V I ) MOLECULAR ORBITAL CALCULATION OF SPIN DENSITIES A) Computer Programs In o r d e r t o p r e d i c t t h e u n p a i r e d e l e c t r o n s p i n d e n s i t y a t t h e muon ( t o w h i c h t h e v a l u e o f Ur i s d i r e c t l y p r o p o r t i o n a l ) i n s e v e r a l p o s s i b l e muonic r a d i c a l s , LCAO-MO-SCF c a l c u l a t i o n s were p e r f o r m e d on i s o m e r i c s t r u c t u r e s o f t h e s p e c i e s H C 0 2 , HCSg, and HSO2. F o r t h e f i r s t s p e c i e s , an INDO/2 open s h e l l c a l c u l a t i o n was p e r f o r m e d u s i n g a b a s i s s e t l i m i t e d t o s- and p- S l a t e r t y p e o r b i t a l s . T h i s program was not p a r a m e t e r i z e d t o p e r f o r m c a l c u l a t i o n s on m o l e c u l e s c o n t a i n i n g second row e l e m e n t s , so i n t h e case o f HCS 2 and H S 0 2 a CNDO/2 open s h e l l c a l c u l a t i o n was p e r f o r m e d u s i n g a b a s i s s e t l i m i t e d t o s-, p-, and d- S l a t e r t y p e o r b i t a l s . However, i n _ t h e p r e s e n t a p p l i -c a t i o n t h e CNDO/2 method was u n s a t i s f a c t o r y , s i n c e t h e appr o x -i m a t i o n s i n v o l v e d were too-extreme t o g i v e a p r o p e r account o f th e s p i n p o l a r i z a t i o n c o n t r i b u t i o n t o t h e e l e c t r o n s p i n d e n s i t y a t t h e p r o t o n . T h i s p r o b l e m was most s e r i o u s f o r c a l c u l a t i o n s on T T - r a d i c a l s , i n whi c h r e t e n t i o n o f o n e - c e n t r e exchange i n t e g -r a l s ( o m i t t e d i n CNDO/2) was n e c e s s a r y f o r i n t r o d u c t i o n o f any s p i n d e n s i t y a t a l l i n t o t h e 6 -system. The CNDO/2 method, however, s h o u l d at l e a s t p r o v i d e f a i r e s t i m a t e s o f t h e s p i n d e n s i t y a t t h e p r o t o n i n d'-type r a d i c a l s ( i n which t h e u n p a i r e d e l e c t r o n was p r i m a r i l y a s s o c i a t e d w i t h a m o l e c u l a r o r b i t a l w i t h n o n - v a n i s h i n g a m p l i t u d e at t h e n u c l e a r p o s i t i o n i n h ydrogen). - so -Only t h e i s o t r o p i c p a r t o f t h e h y p e r f i n e i n t e r -a c t i o n i n the hydrogen c o u l d be c o n s i d e r e d s i n c e o n l y one atomic o r b i t a l b a s i s f u n c t i o n was a l l o w e d f o r hydrogen ( I s ) . - 51 -B) HS0 2 CNDO/2 c a l c u l a t i o n s were performed on t h r e e i s o m e r i c s t r u c t u r e s shown i n F i g u r e 12 u s i n g the known s t r u c t u r a l p arameters f o r S 0 2 and an assumed bond l e n g t h f o r S-H or 0-H of 1.33 A and 0.99 A, r e s p e c t i v e l y . The c a l c u l a t e d s p i n d e n s i t i e s on each atom are g i v e n i n p a r e n t h e s e s . ( 0 - 3 l ) H F i g u r e 12: S p i n D e n s i t y  D i s t r i b u t i o n i n HSOp Isomers 1.33 A 0.322)^ 0 ' (0.18.) \ l o i r / O 0 n I K J.M-3 A 0 (o. is) $(0.71) (0.17) O n r H lo.oo) - 52. -The s p e c i e s formed i n the near uv p h o t o l y s i s o f an H I / S 0 2 m i x t u r e i n an argon m a t r i x has been i d e n t i f i e d by EPR as t h e symmetric 6 - r a d i c a l I . The wor k e r s a l s o p e r f o r m e d INDO/2 c a l c u l a t i o n s ( u s i n g a b a s i s s e t l i m i t e d t o s- and p- S l a t e r t y p e o r b i t a l s ) on s t r u c t u r e I which was found t o have minimum energy when t h e H-S bond i s d i r e c t e d a t 45° t o the SC>2 p l a n e . C a l c u l a t i o n s were a l s o p e r f ormed on t h e as y -mmetric form, a l t h o u g h t h e SOH bond a n g l e was not s p e c i f i e d . An assumed a n g l e i s g i v e n f o r p o s s i b l e s t r u c t u r e s I I and I I I . F o r s t r u c t u r e I t h e i r INDO c a l c u l a t i o n i n d i c a t e d a p o s i t i v e s p i n d e n s i t y i n the hydrogen I s o r b i t a l o f 0.3 which i s i n e x c e l l e n t agreement w i t h our CNDO p r e d i c t i o n . For t he asymmetric form they found the s p i n d e n s i t y i n t h e hydrogen I s o r b i t a l t o be about a f a c t o r o f 10 smal-l e r . In our CNDO c a l c u l a t i o n s t he c o r r e s p o n d i n g s p i n den-s i t i e s i n the 77" - r a d i c a l s t r u c t u r e s I I and I I I i s e r r o -n e o u s l y p r e d i c t e d t o be z e r o ( s i n c e c o n f i g u r a t i o n a l i n t e r -a c t i o n i s not ac c o u n t e d f o r i n t h e program). C o n f i g u r a t i o n a l i n t e r a c t i o n would t r a n s f e r some s p i n d e n s i t y from t h e 7T-system (which i s p e r p e n d i c u l a r t o t h e S 0 2 p l a n e ) t o the hydrogen I s o r b i t a l . The c o m p a r a t i v e s t a b i l i t i e s o f t h e d i f f e r e n t s t r u c t u r e s cannot be p r e d i c t e d from the c a l c u l a t e d t o t a l e n e r g i e s s i n c e 3^ the CNDO/INDO method g i v e s u n s a t i s f a c t o r y energy e s t i m a t e s - S3 -INDO/2 open s h e l l c a l c u l a t i o n s were p e r f o r m e d on s t r u c t u r e s IV, V, and VI (and on v a r i a t i o n s o f t h e s e ) shown i n F i g u r e 13 . The c a l c u l a t e d s p i n d e n s i t i e s a r e g i v e n i n p a r e n t h e s e s . F i g u r e 13: S p i n D e n s i t y D i s t r i b u t i o n i n HC0 o Isomers 0 (°- 31) Q (OM) H (o-o\) - St -The OCO bond a n g l e s were o b t a i n e d from a CNDO/2 s t u d y of HC0 2 o p t i m i z e d g e o m e t r i e s ( w i t h r e s t r i c t i o n t o t h e p l a n a r f o r m s ) , and are i n f a i r agreement w i t h the v a l u e s d e r i v e d 1 Q 1 7 _ from ESR C - 0 s t u d i e s o f the C 0 2 r a d i c a l a n i o n ( i s o e l e c -t r o n i c w i t h HC0 2) formed by x- and V- i r r a d i a t i o n o f s i n g l e c r y s t a l HCOONa at room t e m p e r a t u r e , which y i e l d e d v a l u e s of 138° ' and 134° " r e s p e c t i v e l y . However, an ESR C stu d y o f the C0~ r a d i c a l i o n p r e p a r e d by t h e d e p o s i t i o n o f sodium on s o l i d C 0 2 a t 77 K s u g g e s t s an a n g l e o f 121 . V a r i a t i o n of t he OCO a n g l e over t h e quoted v a l u e s was shown t o have o n l y a s l i g h t e f f e c t (±1%) on t h e s p i n d e n s i t y a t the hy d r o -gen n u c l e u s . S t r u c t u r e IV i s p r e d i c t e d t o be a ^ - r a d i c a l w i t h s p i n d e n s i t y i n t h e oxygen atoms l o c a l i z e d i n t h e i n - p l a n e p - o r b i t a l s , i n agreement w i t h p r e v i o u s l y mentioned s t u d i e s , as w e l l as w i t h an ESR study o f t h e DOOC-CH=CH-COO" r a d i c a l t r a p p e d i n a s i n g l e c r y s t a l o f m a l e i c a c i d - d 2 i r r a d i a t e d at 77 K, and a l s o i n a s i m i l a r s t u d y u s i n g s u c c i n i c a c i d . However, i t s h o u l d be p o i n t e d out t h a t minor s t r u c t u r a l v a r i a t i o n s between c a r b o n y l -type r a d i c a l s can cause a 6 t o TT i n v e r s i o n The s m a l l s p i n d e n s i t i e s at the hydrogen n u c l e u s i n s t r u c t -u r e s V and VI i s due t o t h e l o c a l i z a t i o n o f the u n p a i r e d e l e c t r o n d e n s i t y i n an i n - p l a n e m o l e c u l a r o r b i t a l o f the t e r m i n a l 0 and the C atom, w i t h l i t t l e i n t e r a c t i o n w i t h t he o t h e r 0 atom. - 55 -Whether t h e symmetric s t r u c t u r e i s p r e f e r r e d o v e r t h e s t r u c t u r e i n which hydrogen i s bonded t o a t e r m i n a l oxygen has been the s u b j e c t o f c o n s i d e r a b l e c o n t r o v e r s y . An ESR st u d y and a gas-phase u l t r a v i o l e t s tudy o f t h e p r o t o n a t e d c a r b o x y l r a d i c a l b o th f a v o u r the symmetric form where t h e hydrogen i s bonded t o carb o n . However, a stu d y o f e x c e s s -e n e r g i e s i n the e l e c t r o n - i m p a c t i n d u c e d d i s s o c i a t i o n s o f a c e t i c a c i d and o f i t s isomer methyl formate suggest t h a t the COOH s t r u c t u r e i s s t a b l e , whereas the HC0 2 s t r u c t u r e i s not. . T h i s view i s s u p p o r t e d by an i n f r a r e d a b s o r p t i o n s t u d y o f s t r u c t u r a l i n t e r m e d i a t e s ( i n c o r p o r a t i n g i s o t o p i c s u b s t i t u t i o n s ) i n t h e r e a c t i o n of OH w i t h a CO m a t r i x at 14 K which f a v o u r s the c i s - and t r a n s - isomers A MINDO/2 computation o f the t o t a l e n e r g i e s o f the s t r u c t u r e s i n F i g u r e \hr f a v o u r s the O - p r o t o n a t i o n over the C - p r o t o n a t i o n and a l s o s u g g e s t s t h a t t h e t r a n s - isomer s h o u l d be more s t a b l e (by 10 k c a l / m o l ) than the c i s - isomer"'' . - S6 -D) HCS 2 CNDO/2 comp u t a t i o n s were performed on t h e s t r u c t u r e s V I I , V I I I , and IX shown i n F i g u r e 14 . S p i n d e n s i t i e s a r e g i v e n i n p a r e n t h e s e s . F i g u r e 14: S p i n D e n s i t y ^ ^ D i s t r i b u t i o n i n HCSp Isomers / /.S33A ( o . o i ) / - 57 -The SCS bond a n g l e and C-S bond l e n g t h were o b t a i n e d from 13 -an ESR C s t u d y o f t h e C S 2 r a d i c a l i o n p r e p a r e d by d e p o s i t i n g sodium on s o l i d C S 2 at 77 K i n a r o t a t i n g c r y o s t a t . The 3z C-H bond l e n g t h i s assumed t o be 1.08 A , and t h e S-H bond Z<\< l e n g t h t o be 1.33 A . F o r s t r u c t u r e s V I I I and IX t h e CSH o bond a n g l e i s assumed t o be 96.5 from comparison w i t h t h e s t r u c t u r e s of HSSR and H^CSH. V a r i a t i o n o f t h e o u t - o f - p l a n e CSH bond a n g l e from 0°-30° had l i t t l e e f f e c t on t h e s p i n d e n s i t y d i s t r i b u t i o n o r on the t o t a l energy. - 5 * -V I I ) EXPERIMENTAL A) Beam Source i ) P r o d u c t i o n T a r g e t The i n t e r m e d i a t e energy ( t y p i c a l l y 500 MeV) p r o t o n beam l i n e BL1 at TRIUMF produces t h r e e beams o f p i o n s and muons at the p r o d u c t i o n t r a g e t T2 shown i n F i g u r e 15. The M20 second-ary beam l i n e f o r 'muon s p i n r e s e a r c h ' a c c e p t s p i o n s e m i t t e d at 55° from the p r o d u c t i o n t a r g e t . The p i o n momentum i s v a r i -a b l e from e s s e n t i a l l y z e r o up t o about 170 MeV/c w i t h a r e s o -l u t i o n o f about ± 2.5%. T h i s i s a c h i e v e d w i t h t u n i n g magnets. The e n t i r e beam l i n e i s under vacuum. i i ) C o n v e n t i o n a l Muons In t h e ' c o n v e n t i o n a l mode', s t o p p i n g muons a r e produce d by t r a n s p o r t i n g t h e p i o n beam o v e r a d i s t a n c e l o n g enough f o r a s i z a b l e f r a c t i o n t o d e c a y - i n - f l i g h t i n t o muons, form-i n g a p o l a r i z e d beam. When magnet B2 i s tuned f o r muons from f o r w a r d - d e c a y i n g p i o n s a t 170 MeV/c, t h e c h a n n e l p r o d u c e s about 10^ u + s t o p s / s e c i n a t h i c k 50 cm^ t a r g e t f o r e v e r y uA of 500 MeV p r o t o n s on a 10 cm b e r y l l i u m T2 p r o d u c t i o n t a r g e t . The r e l a t i v e l y low (60%) p o l a r i z a t i o n o f t h e s e s t o p p e d muons i s due to c o n t a m i n a t i o n by a l a r g e f l u x of ' c l o u d muons'. These a r e randomly p o l a r i z e d muons coming from off-momentum - 51 -- fcO -p i o n s which decay i n t h e v i c i n i t y o f the t a r g e t . F o r a 'backward muon' t u n i n g the p o l a r i z a t i o n i s improved and t h e r e i s l e s s p i o n c o n t a m i n a t i o n , but t h e e q u i v a l e n t muon r a t e i s low e r e d by a f a c t o r o f 10-20. C o n v e n t i o n a l muons are o f s u i t a b l e momentum f o r s t o p p i n g a s i z a b l e f r a c t i o n w i t h i n a few c e n t i m e n t e r s t h i c k n e s s o f l i q u i d and s o l i d t a r g e t s o f common d e n s i t i e s ( i e . about u n i t y ) . They were used i n t h e s e e x p e r i m e n t s i n c o n j u n c t i o n w i t h a l i q u i d h e l i u m c r y o s t a t , d e s c r i b e d below, and a l s o i n t h e e x p e r i m e n t s on C 0 2 at 195 K and 77 K. i i i ) S u r f a c e Muons The M20 ch a n n e l i s a l s o o p e r a t e d i n the ' s u r f a c e mode' which o f f e r s two o r d e r s of magnitude g r e a t e r s t o p p i n g - u + d e n s i t y o v e r t h a t o f a c o n v e n t i o n a l beam, and n e a r l y 100% l o n g i t u d i n a l p o l a r i z a t i o n . ' T h i s i s a c h i e v e d by t u n i n g . f o r a momentum < 30 MeV/c so t h a t muons are a c c e p t e d which come d i r e c t l y from the p r o d u c t i o n t a r g e t as a r e s u l t o f p i o n s s t o p p i n g and d e c a y i n g near t h e t a r g e t s u r f a c e . The p i o n c a p t u r e s t e p o f the c o n v e n t i o n a l mode i s e l i m i n a t e d , and th e s e ' s u r f a c e ' muons are c o l l e c t e d d i r e c t l y i n t o a n e a r l y monochromatic beam o f 4.1 MeV energy, the f l u x i n t h i s mode 3 + b e i n g 5 x 10 u /sec-uA on T2. The range o f t h e s e muons i s about 27 cm i n Argon gas a t one atmosphere ( i d e a l f o r gas phase e x p e r i m e n t s ) and o n l y a few m i l l i m e t e r s i n con-densed p h a s e s , ( i d e a l f o r r a r e m a t e r i a l s t u d i e s ) . In t h e - a -p r e s e n t a p p l i c a t i o n ' s u r f a c e muons' a r e u s e f u l f o r t h e i r h i g h p o l a r i z a t i o n and use w i t h t a r g e t s o f low volume, wh i c h u s u a l l y can be b e t t e r p u r i f i e d i n s m a l l amounts. T h i s beam t u n i n g method was used i n t h e i n v e s t i g a t i o n o f l i q u i d CSD a t room t e m p e r a t u r e , i n a d d i t i o n t o t h e ' s t a n d a r d ' q u a r t z sample. B) H e l m h o l t z C o i l s The t r a n s v e r s e magnetic f i e l d was produce d by a p a i r of H e l m h o l t z c o i l s o f 24" d i a m e t e r , powered by l o w - d r i f t power s u p p l i e s , and w a t e r - c o o l e d . The f i e l d was u n i f o r m i n the t a r g e t a r e a t o b e t t e r t h a n 0.5% v a r i a t i o n o v e r a range of about 6 G t o n e a r l y 100 G. - (.1. -Teflon taper plug -and tubing —Teflon cell Teflon taper plug -and tubing Pfexigla: F i g u r e 16: S u r f a c e Mode Target C e l l - 63 -C) Tar g e t Systems i ) C o n v e n t i o n a l Mode C e l l In the ( c o n v e n t i o n a l mode) h e l i u m t e m p e r a t u r e e x p e r i m e n t s the samples were c o n t a i n e d i n T e f l o n b o t t l e s o f 60 ml c a p a c i t y w i t h T e f l o n c l o s u r e s . The c y l i n d r i c a l b o t t l e s had an o u t e r d i a m e t e r o f l i " ( f o r placement i n a c r y o s t a t e x t e n s i o n o f 1 3/4" i n t e r n a l d i a m e t e r ) and were 3.2" i n h e i g h t . The w a l l t h i c k n e s s was about 2 mm. A f t e r c l o s u r e , the b o t t l e s were s e a l e d w i t h T e f l o n t a p e . The t a r g e t b o t t l e was p l a c e d w i t h i n t h e c r y o s t a t ( d e s c r i b e d i n VI-D ) which was a d j u s t e d t o pos-i t i o n t he b o t t l e at t h e c e n t e r o f t h e H e l m h o l t z c o i l s . i i ) S u r f a c e Mode C e l l In t h e s u r f a c e mode experiment w i t h l i q u i d CSg, the sample was c o n t a i n e d i n a T e f l o n c e l l o f about 50 ml capa-c i t y . T h i s ' d i s c - s h a p e d ' c e l l (shown i n F i g u r e 16) had an i n t e r n a l w i d t h o f about 4 mm, and p r e s e n t e d a t h i n (.005!') window t o t h e i n c o m i n g beam, w h i l e t h e back o f t h e c e l l was about 6mm t h i c k . The c e l l was equ i p p e d w i t h a d e v i c e f o r c o n t i n u o u s d e g a s s i n g d u r i n g t h e ex p e r i m e n t . - 6*t -i i i ) C 0 2 T a r g e t In t he 195 K experiment on CC>2 i n the c o n v e n t i o n a l mode, a b l o c k o f dry i c e , about 6,!" l e n g t h p e r edge, was p l a c e d d i r e c t l y at the c e n t e r o f the H e l m h o l t z c o i l s . The 77 K experiment on C 0 2 i n t h e c o n v e n t i o n a l mode was conducted by p u t t i n g a^  b l o c k o f dry i c e i n d i r e c t con-t a c t w i t h l i q u i d n i t r o g e n w i t h i n a t h e r m a l l y i n s u l a t e d l o w - d e n s i t y foam p l a s t i c s h e a t h . i v ) Q u a r t z R e f e r e n c e T a r g e t At the s t a r t o f each e x p e r i m e n t a l run a f u s e d q u a r t z p l a t e o f about J" t h i c k n e s s was p o s i t i o n e d a t the c e n t e r o f the H e l m h o l t z . c o i l s f o r use as a s t a n d a r d t a r g e t . - bS -D) C r y o s t a t The aluminum and copper l i q u i d h e l i u m c r y o s t a t was d e s i g n e d by Dr. Ken Nagamine o f the U n i v e r s i t y o f Tokyo. The T e f l o n t a r g e t b o t t l e ( o f S e c t i o n V T I - C - i ) was lo w e r e d t o the bottom o f a c y l i n d r i c a l copper e x t e n s i o n tube ( o f 1 3/4" d i a m e t e r w i t h w a l l s o f 1/32" t h i c k n e s s ) i n t h e base of the dewar system, t o a p o s i t i o n at the c e n t e r o f t h e H e l m h o l t z c o i l s . The c e n t r a l dewar h o l d i n g t h e t a r g e t b o t t l e and l i q u i d h e l i u m was s h i e l d e d by a n o t h e r dewar c o n t a i n i n g l i q u i d n i t r o g e n , w i t h a vacuum envelope on b o t h s i d e s o f t h e n i t r o g e n dewar. The o u t e r w a l l s o f the c r y o -s t a t e x t e n s i o n had two s e t s o f 5 m i l M y l a r windows a l o n g t h e beam a x i s . F o r a l l e x p e r i m e n t s i n v o l v i n g t h e c r y o s t a t , t h e temp-e r a t u r e o f l i q u i d h e l i u m at.S-.T.P. (4.2 K) was used. - u -E) E x p e r i m e n t a l D e t a i l s of the C o n v e n t i o n a l Mode The e x p e r i m e n t a l arrangement f o r c o n v e n t i o n a l mode i s shown i n F i g u r e 17 . i ) D e g r a d a t i o n and C o l l i m a t i o n o f t h e Beam The i n c i d e n t p o s i t i v e muons l e f t t he beam p i p e t h r o u g h a 5 m i l M y l a r window, p a s s i n g t h r o u g h 8 i " o f p o l y e t h y l e n e degrader t o reduce p i o n c o n t a m i n a t i o n . The beam was c o l l i -mated t h r o u g h a 1" d i a m e t e r h o l e i n a l e a d b r i c k w a l l o f 2" t h i c k n e s s t o reduce the random background e v e n t s . i i ) S c i n t i l l a t o r C o u n t e r s P l a s t i c s c i n t i l l a t o r s ( w i t h p h o t o m u l t i p l i e r s ) were a r r a n g e d around the s t o p p i n g t a r g e t a r e a as shown i n t h e f i g u r e . Three s e t s o f p o s i t r o n d e t e c t i o n a r r a y s a r e shown f o r c o n v e n i e n c e o f i l l u s t r a t i o n , but i n f a c t o n l y two s e t s were used i n each e x p e r i m e n t : t h e ' L e f t ' and ' R i g h t ' a r r a y s were used w i t h the dry i c e t a r g e t , w h i l e the ' L e f t ' and 'Zero degree' a r r a y s were used i n t h e 4.2 K e x p e r i m e n t s . The ' L e f t ' and ' R i g h t ' a r r a y s were each eq u i p p e d w i t h a t h i c k (2") g r a p h i t e a b s o r b e r between t h e c o u n t e r s t o reduce a c c i d e n t a l s and t o d i s c r i m i n a t e a g a i n s t low-energy decay p o s i t r o n s , t h e r e b y r a i s i n g t h e e x p e r i m e n t a l asymmetry. Back-ground e v e n t s and u + s t o p s i n t h e c r y o s t a t were reduced by u s i n g a d e f i n i n g c o u n t e r 'D' i n c o n f o r m a t i o n w i t h t h e t a r g e t . F i g u r e 17: Apparatus Used With C o n v e n t i o n a l Muons y^^mm^mo POSITRON DEGRADER 1 I z I 1 T E - 6 8 -The 'Zero degree' c o u n t e r was equipped w i t h a -J" aluminum a b s o r b e r t o r a i s e the asymmetry. The TM c o u n t e r was used i n the d e t e c t i o n o f incoming muons. i i i ) L o g i c System The s i g n a t u r e o f a s t o p p i n g muon was l o g i c a l l y d e f i n e d as _ 'u ' = TM.D.X which r e p r e s e n t s a s i m u l t a n e o u s t w o f o l d c o i n c i d e n c e i n t h e 'TM' and 'D' c o u n t e r s and an a n t i c o i n c i d e n c e i n the 'X' coun-t e r . The s i g n a t u r e o f a decay p o s i t r o n p a s s i n g t h r o u g h t h e ' L e f t ' , ' R i g h t ' , o r 'Zero degree' c o u n t e r s was ' e L = 4-L 2.L 3.(D^-TM s t r e t c h e d ) ' eR' = R l - R 2 - R 3 - ( n ~ ™ s t r e t c h e d ^ * e o ' = X - Z - T E " ( s t r e t c h e d ) • The p u l s e s ' u + ' and ' e + ' were used as g a t e s i n c o i n c i -dence w i t h t i m i n g p u l s e s from c o u n t e r s 'D' and 'X' t o form s t a r t i n g and s t o p p i n g p u l s e s f o r an EG&G TDC100 time d i g i t i z e r . T h i s ' c l o c k ' d i g i t i z e d t h e time i n t e r v a l w hich might span s e v e r a l m i c r o s e c o n d s . The time r e s o l u t i o n of t h e e n t i r e system was on the o r d e r o f 1 nsec. Time z e r o was d e f i n e d f o r each - &1 -run by t a k i n g a few thousand e v e n t s w i t h v e t o e s removed from t h e c o i n c i d e n c e s , a l l o w i n g b o t h 1 u + ' and ' e + ' t o be t r i g g e r e d by a s i n g l e p a r t i c l e p a s s i n g t h r o u g h the a p p r o p r i a t e c o u n t e r a r r a y s w i t h o u t s t o p p i n g . The system was then r e s e t b e f o r e t a k i n g d a t a . i v ) Data A q u i s i t i o n A CAMAC e l e c t r o n i c hardware system was used as a ' s w i t c h -b o a r d ' f o r d i s p a t c h i n g the d i g i t i z e d time i n t e r v a l a l o n g w i t h s e v e r a l d i a g n o s t i c l o g i c b i t s , whose f u n c t i o n s were t o e l i m -i n a t e s p u r i o u s e v e n t s o r a m b i g u i t i e s , t o the d a t a a q u i s i t i o n system. A B i - R a MBD-11 p r e - p r o c e s s o r i n t e r f a c e s t h e CAMAC and the PDP-11/40 computer upon which the MSR d a t a a q u i s i t i o n and a n a l y s i s system i s based. The MBD i s a f a s t minicomputer ( 3 o o « ^ ) which h a n d l e s a l l CAMAC o p e r a t i o n s , p e r f o r m s i n i t i a l d a t a s c r e e n i n g ( u s i n g programs down-loaded from t h e PDP-11), and t r a n s m i t s m o d i f i e d d a t a d i r e c t l y i n t o t h e memory o f the PDP-11. The.time i n t e r v a l s from each o f t h e two e x p e r i m e n t a l c h a n n e l s were s e p a r a t e l y r o u t e d t o one o f two h i s t o g r a m s w i t h i n the PDP-11 memory. Each h i s t o g r a m c o n t a i n s two t h o u -sand b i n s , u s u a l l y w i t h a w i d t h o f 1 o r 2 nsec p e r b i n f o r h i g h and low f i e l d runs r e s p e c t i v e l y . A t y p i c a l MSR e x p e r -- 7o -iment accumulates on t h e o r d e r o f one m i l l i o n e v e n t s p e r h i s t o g r a m . The PDP-11 i s used t o ex e c u t e v a r i o u s p r o c e s s c o n t r o l , d i a g n o s t i c , and a n a l y s i s t a s k s under the RSX-11D s o f t w a r e . An e x p e r i m e n t a l c o n t r o l program based on a g r a p h i c a l d i s p l a y w i t h l i g h t - p e n commands i s used. T h i s system can run s e v e r a l independent e x p e r i m e n t s s i m u l t a n e o u s l y , w i t h o n - l i n e f e e d -back t o e x p e r i m e n t e r s . The PDP-11 uses two RK05 d i s c d r i v e u n i t s , t h e f i r s t m a i n l y f o r system s o f t w a r e and t h e second m a i n l y f o r d a t a memory. The e x p e r i m e n t a l d a t a i s l a t e r t r a n s l a t e d i n t o b i n a r y and EBCDIC code and w r i t t e n onto 9-channel magnetic tape f o r a n a l y s i s at the UBC Computing C e n t e r on the IBM System 370/168 computer. F i g u r e 18: A p p a r a t u s Used With S u r f a c e Muons 3 2 u S U R F A C E fJL B E A M V A C U U M P I P E - 12. -F) E x p e r i m e n t a l D e t a i l s o f the S u r f a c e Mode The t a r g e t and c o u n t e r s were a r r a n g e d as shown i n f i g -u r e 11 . I n c i d e n t s u r f a c e muons l e f t t he e v a c u a t e d beam p i p e t h r o u g h a t h i n m ylar window, t r i g g e r e d the t h i n (15 m i l ) p l a s t i c s c i n t i l l a t o r , and st o p p e d e i t h e r i n the s t a n d a r d q u a r t z t a r g e t o r i n the T e f l o n c e l l ( o f s e c t i o n V l - C - i v ) p o s i t i o n e d i n the c e n t e r of t h e H e l m h o l t z c o i l s . The two s e t s o f decay p o s i t r o n c o u n t e r s were s i t u a t e d a t 90° t o t h e i n c i d e n t muon beam. The s i g n a t u r e o f a s t o p p i n g muon was l o g i c a l l y d e f i n e d (and p u l s e - h e i g h t d i s c r i m i n a t e d t o e l i m i n a t e p o s i t r o n s ) as + l The s i g n a t u r e s of a decay p o s i t r o n e x i t i n g t h r o u g h e i t h e r t h e ' L e f t ' o r ' R i g h t ' c o u n t e r a r r a y s were ' e L ' = L 1 - L 2 , L 3 and 'e*' = R ^ R ^ R g . + + + The 'u ' and 'e T ' o r 'e ' p u l s e s were used t o s t a r t and s t o p L ti the time d i g i t i z e r and a s s o c i a t e d e l e c t r o n i c s w h i c h have j u s t been d e s c r i b e d i n t h e l a s t s e c t i o n s . - 7 3 -G) P r e p a r a t i o n o f C h e m i c a l s A n a l y t i c a l grade carbon d i s u l f i d e ( A l d r i c h ) was used w i t h o u t f u r t h e r p u r i f i c a t i o n ( o t h e r than d e g a s s i n g ) . Mass s p e c t r o s c o p i c a n a l y s i s showed t h a t i t c o n t a i n e d n e g l i g i b l e amounts of i m p u r i t i e s . The carbon d i s u l f i d e was p r e p a r e d by d e g a s s i n g o v e r a p e r i o d o f 45 m i n u t e s : dry argon was p a s s e d t h r o u g h a s i n t e r e d g l a s s b u b b l e r i n t o a 250 ml volume of the l i q u i d . A f t e r d e g a s s i n g , the carbon d i s u l f i d e was t r a n s f e r r e d w i t h i n an i n e r t system o f T e f l o n and P y r e x i n t o the T e f l o n t a r g e t b o t t l e ( o f S e c t i o n V l l - C - i ) w hich was s e a l e d under an i n e r t atmosphere. In p r e p a r a t i o n f o r t h e s u r f a c e mode e x p e r i m e n t , carbon d i s u l f i d e was degassed w i t h argon w i t h i n t h e s p e c i a l l y d e s i g n e d (by Dr. L. Vaz) t h i n - w a l l e d T e f l o n c e l l ( o f S e c t i o n V H - C - i i ) f o r about 45 m i n u t e s . The d e g a s s i n g p r o c e d u r e c o n t i n u e d t h r o u g h o u t t h e e x p e r i m e n t . S u l f u r d i o x i d e (Matheson) o f 99.9% p u r i t y was t r a n s f e r -r e d t h r o u g h T e f l o n t u b i n g i n t o t h e T e f l o n t a r g e t b o t t l e ( s e c t i o n V l - C - i ) immersed i n a dry i c e / a c e t o n e b a t h under a dry n i t o g e n atmosphere. The gas r e a d i l y l i q u i f i e d (b.p. - 1 0 P C ) , and a s c i n t e r e d g l a s s b u b b l e r tube was i n s e r t e d i n t o the b o t t l e . C o o l dry argon gas was b u b b l e d t h r o u g h t h e l i q u i d f o r . t h i r t y minutes t o remove gaseous i m p u r i t i e s . Dry i c e ( L i q u i d C a r b o n i c L t d . ) o f 98% p u r i t y was used i n the C 0 9 e x p e r i m e n t . - 7+ -V I I I . DISCUSSION OF EXPERIMENTAL RESULTS A) S u r f a c e Mode Experiment on Fused Q u a r t z at 300 K The e x p e r i m e n t s conducted at low and moderate e x t e r n a l t r a n s v e r s e f i e l d s have been d e s c r i b e d i n s e c t i o n V-B, and F i g u r e s 9, 10, and 11 i l l u s t r a t e the r e s u l t s . Measurement o f t h e peak l o c a t i o n s i n the F o u r i e r t r a n s f o r m spectrum f o r two-frequency muonium p r e c e s s i o n i n t h e 67.5 G experiment gave V 1 2 = 91.3 ± 0.5 MHz y 2 3 = 96.2 ± 0.5 MHz so -£}; = 2.2 ± 0.5 MHz U s i n g Eqn. 111-25 g i v e s V = 4024 ± 800 MHz O which i s w i t h i n e x p e r i m e n t a l e r r o r of t h e a c c e p t e d v a l u e of 4463 MHz f o r muonium i n vacuum. R e c a l l i n g E q u a t i o n s (111-32,33) which r e l a t e the h y p e r -f i n e c o u p l i n g t o the mean atomic r a d i u s , one can say t h a t the mean r a d i u s a Q o f t h e muonium atom i s the same i n q u a r t z as i n vacuum. T h i s s u g g e s t s t h a t t h e Mu atom r e s i d e s i n i n t e r s t i t i a l s i t e s ( i n f u s e d q u a r t z ) t h a t a re o f l a r g e r d i m e n s i o n s than 1 2 a Q and which have n e g l i g i b l e v a l e n c e e l e c t r o n d e n s i t i e s . - i r -B) S u r f a c e Mode Experiment i n C S 2 at 300 K Immediately f o l l o w i n g a s t a n d a r d i z a t i o n run on f u s e d q u a r t z , l i q u i d C S 2 was i n v e s t i g a t e d at 300 K. The d a t a showed no s i g n i f i c a n t peaks ( a s i d e from a s m a l l s i g n a l from ^ 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 ) , s u g g e s t i n g a r a p i d r e l a x a t i o n t i m e T 2 < ~50 ns. A l t h o u g h i t i s not p o s s i b l e t o d i s t i n g u i s h e l e c t r o n i c r e l a x a t i o n from c h e m i c a l r e l a x a t i o n u s i n g t h i s t e c h n i q u e , t h e l a t t e r mechanism i s e x p e c t e d t o be s i g n i f i c a n t : muonium has o n l y been seen i n l i q u i d s i n t h e case o f t r i p l y -[1 d i s t i l l e d w a t e r . I n s t e a d o f p u r s u i n g t h e i n v e s t i g a t i o n i n the l i q u i d o phase, we d e c i d e d t o t r y u s i n g s o l i d C S 2 (m.p. - I l l C ) : the problem o f d i f f u s i o n o f muonic s p e c i e s t o i m p u r i t y s i t e s (a p o s s i b l e cause o f r a p i d c h e m i c a l r e l a x a t i o n ) i s l e s s e n e d , as e v i d e n c e d by the o b s e r v a t i o n o f muonium i n i c e ( d e s p i t e 2.0 no s p e c i a l p u r i f i c a t i o n ) . C ) C o n v e n t i o n a l Mode Ex p e r i m e n t s on C S 2 and S 0 2 at Helium Temperature U n f o r t u n a t e l y , t h e a t t e m p t s t o p e r f o r m e x p e r i m e n t s at 4.2 K i n the c o n v e n t i o n a l mode were p l a g u e d by i n s t r u -m ental d i f f i c u l t i e s , b e l i e v e d t o be p a r t i a l l y due t o d e f e c t -i v e o p e r a t i o n o f the time d i g i t i z e r , and p a r t i a l l y due t o - -a r e l a t i v e l y weak f l u x o f i n c o m i n g muons (which s e v e r e l y l i m i t e d the amount o f d a t a a v a i l a b l e i n t i m e ) . The exp-e r i m e n t a l s e s s i o n was t e r m i n a t e d when t h e a l l o t e d 'beam time.' e x p i r e d . U n f o r t u n a t e l y t h e r e was no subsequent o p p o r t u n i t y t o r e p e a t the experiment and c o n s e q u e n t l y no m e a n i n g f u l r e s u l t s can be r e p o r t e d here. D) C o n v e n t i o n a l Mode Experiments on C 0 2 The F o u r i e r t r a n s f o r m spectrum shown i n F i g u r e 1*} shows the p r e c e s s i o n d a t a o b t a i n e d when c o n v e n t i o n a l muons were s t o p p e d i n a b l o c k o f dry i c e at 195 K i n a 7.5 G .ex-t e r n a l f i e l d . A ^ - m i n i m i z a t i o n f i t t o t h e e x p e r i m e n t a l d a t a gave a v a l u e o f T 2 = 0.4 ± 0.1 jusec, i n agreement w i t h the o r i g i n a l experiment by My a s i s h c h e v a et a l . These w o r k e r s assumed t h a t pure s o l i d C 0 2 i s c h e m i c a l l y i n e r t w i t h r e s p e c t t o muonium, and a s s e r t e d t h a t the o b s e r v e d s i g n a l i s a s s o c i -a t e d w i t h a q u a s i - f r e e muonium atom l o c a t e d i n a ' s p a c i o u s ' i n t e r s t i t a l vacancy. We have found s u p p o r t f o r t h i s assumption ( w i t h r e g a r d So t o t h e r m a l r e a c t i o n s ) i n a p u l s e r a d i o l y s i s - u v e x periment conducted on a s o l u t i o n o f 0.2N s u l f u r i c a c i d s a t u r a t e d w i t h C0 2, which i n d i c a t e d t h a t s o l v a t e d e l e c t r o n s r e a c t p r e f e r e n t -i a l l y w i t h H + t o produce H a t o m s — t h e r e was no a b s o r p t i o n at 250 nm ( e x p e c t e d f o r t h e CO~ r a d i c a l o r i t s p r o t o n a t e d f o r m ) , FROZEN C02 e LDV FIELD .0012 . 1 1 r 5 10 . 15 20 25 30 FREQUENCY [MHZ) Figure 19: Fourier Transform Spectrum of CO,, Data at 195 K in 7.5 G External F i e l d , f i t over 0.75 p.sec i n t e r v a l . - 7* -i n d i c a t i n g t h a t t h e r a t e o f t h e r e a c t i o n H + C 0 2 * HC0 2 6 - 1 1 was l e s s than 10 M s e c _ x a t ambient t e m p e r a t u r e s . I t i s not u n r e a s o n a b l e t o assume t h a t the analogous r e a c t i o n f o r muonium i n t h e s o l i d C 0 2 s u b s t r a t e i s n e g l i g i b l e on t h e t i m e s c a l e o f t h e MSR e x p e r i m e n t . Even w i t h t h i s a s s umption, i t i s s t i l l p o s s i b l e t h a t the o b s e r v e d s i g n a l i s a s s o c i a t e d w i t h an e p i t h e r m a l l y formed r a d i c a l : at 7 G, the s i g n a l f o r a r a d i c a l w i t h 6J r ^ o.o7.CJ0 would not be r e s o l v a b l y s p l i t , and so c o u l d not be d i s t i n g u i s h e d from muonium. With t h i s i n mind, t h e experiment was r e p e a t e d (On a s e p a r a t e o c c a s i o n ) i n a magnetic f i e l d o f 20 G, and t h e t e m p e r a t u r e 77 K was used ( i n an attempt t o l e n g t h e n the T 2 r e l a x a t i o n t i m e ) . W h i l e t h e v a l u e of T 2 d i d not change a p p r e c i a b l y , - we were s u p r i s e d t o o b serve an apparent s p l i t - , t i n g o f t h e s i g n a l (see F i g u r e 2 0 ) . F i t t i n g the same d a t a o v e r a 50% l o n g e r time window d e c r e a s e d t h e r e l a t i v e power of t h i s s i g n a l , s u g g e s t i n g r a p i d r e l a x a t i o n (see F i g u r e 2 1 ) . I t i s i n t e r e s t i n g t o compare F i g u r e 20 w i t h t h e s i g n a l s i , 5 1 o b s e r v e d i n p-type s i l i c o n i n the same f i e l d (and at 4.2 K) F i g u r e 22. shows the s p l i t t i n g i n S i ( i n which the h y p e r f i n e 1.4E-1 1.2E-4 H ] .E-4 8.E-5 £ 6.E-5 o 4.E-5 2.E-5 -2.E-5 -20 F i g u r e 20: -0 20 40 60 80 FREQUENCY (MHZ) 100 120 110 160 180 F o u r i e r T r a n s f o r m Spectrum o f COg Data at 77 K  i n 20 G E x t e r n a l F i e l d f i t over 1 ^isec i n t e r v a l ; the peak a t 23 MHz i s a c h a r a c t e r i s t i c " n o i s e " peak due t o t h e r f s t r u c t u r e o f the c y c l o t r o n beam, which " l e a k s " i n t o t h e d a t a t h r o u g h the a c c i d e n t a l background. F i g u r e 21: F o u r i e r T r a n s f o r m Spectrum of CO^ Data at 77 K  i n 20 G E x t e r n a l F i e l d f i t over 1.5 psec i n t e r v a l F i g u r e 2.2: F o u r i e r T r a n s f o r m Spectrum o f S i Data (Ref.52) i n 20 G F i e l d , shows two-frequency p r e c e s s i o n . - 22. -c o u p l i n g i s 0.45 - 0.02 o f the v a l u e f o r muonium i n vacuum). D i g r e s s i n g m o m e n t a r i l y , i t s h o u l d be e x p l a i n e d t h a t t h e s m a l l h y p e r f i n e c o u p l i n g i n Mu i n p-type s i l i c o n i s due t o an i n c r e a s e d a tomic r a d i u s . T h i s i n t u r n i s due t o s c r e e n i n g by v a l e n c e band e l e c t r o n s from n e i g h b o u r i n g l a t t i c e s i t e s . The amount of s p l i t t i n g f o r the C 0 2 peaks ( F i g u r e 20) i s about t h e same as t h a t f o r t h e S i peaks. I f t h e phenomenon seen i n t h e C 0 2 d a t a i s not an a r t i f a c t , i t might be e i t h e r a s s o c i a t e d w i t h ' s w e l l i n g ' o f muonium atom i n t h e i n t e r s t i t i a l s i t e s , o r w i t h t h e p r e s e n c e of a muonic r a d i c a l : t h e l a t t e r p o s s i b i l i t y i s i n t e r e s t i n g w i t h r e g a r d t o a ( c a u t i o u s ) compar-i s o n o f t h e INDO p r e d i c t i o n f o r the symmetric r a d i c a l I (see F i g u r e 1 3 ) , w i t h t h e v a l u e (~0.4) c a l c u l a t e d from the s p l i t t i n g o f t h e peaks i n t h e C 0 2 d a t a . The experiment was r e p e a t e d i n about 40 G e x t e r n a l f i e l d ( F i g u r e 2 3 ) . Whereas the peaks would be e x p e c t e d i n t h e v i c i n i t y o f 55.7 MHz ( t h e v a l u e o f k)_in t h i s f i e l d ) we were s u r p r i s e d t o o b s e r v e f o u r p o s s i b l y s i g n i f i c a n t peaks i n a much h i g h e r f r e q u e n c y r e g i o n . No i n t e r p r e t a t i o n i s g i v e n as t o t h e s i g n i f i c a n c e ( i f any) of t h e peaks i n t h i s C 0 2 d a t a w i t h o u t f u r t h e r e x p e r i m e n t a l i n v e s t i g a t i o n o v e r a s e r i e s of e x t e r n a l f i e l d v a l u e s . I t s h o u l d be n o t e d t h a t "anomalous" peaks i n m i l d l y p-type s i l i c o n have been o b s e r v e d which have a p e c u l i a r f i e l d dependence. These a r e c u r r e n t l y under i n v e s t i g a t i o n Sx and have not y e t been f u l l y i n t e r p r e t e d . DRY ICE AT 40 GAUSS 1.75E-4 i 1 V 1.5E-4 1.25E-4 l.E-4 7.5E-5 5.E-5 2.5E-5 -2.5E-5 -20 20 40 60 80 FREQUENCY (MHZ) 100 120 140 160 180 F i g u r e 23 F o u r i e r T ransform Spectrum o f COp Data i n 40 G E x t e r n a l F i e l d f i t o v e r 500 n s e c s . -84-IX. CONCLUSIONS M o l e c u l a r o r b i t a l c a l c u l a t i o n s were performed on assumed ge o m e t r i e s f o r s e v e r a l p r o t o n i c a n a l o g s o f t h e a n t i c i p a t e d p r o d u c t s formed by a d d i t i o n o f muonium t o t h e compounds C 0 2 , CSg, and S 0 2 . The p r e d i c t e d s p i n d e n s i t i e s a t t h e p r o t o n (analogous t o t h e muon) i n t h e s e s t r u c t u r e s were c a l c u l a t e d , and s u g g e s t e d t h a t the r a d i c a l s c o u l d be d i s t i n g u i s h e d from muonium by v i r t u e o f a c l e a r l y d i f f e r e n t h y p e r f i n e c o u p l i n g c o n s t a n t . S e v e r a l t r a n s v e r s e f i e l d MSR e x p e r i m e n t s were pe r f o r m e d i n which muons were i m p l a n t e d i n C 0 2 , CS 2, and S 0 2 at d i f f e r e n t t e m p e r a t u r e s (and d i f f e r e n t e x t e r n a l f i e l d v a l u e s ) . Due t o e x p e r i m e n t a l d i f f i c u l t i e s and t h e r a r i t y o f 'beam t i m e ' , i n t e r -p r e t a b l e d a t a was o n l y o b t a i n e d i n the e x p e r i m e n t s on C S 2 (300 K, 7 G ) , C 0 2 (195 K, 7.5 G), and t e n t a t i v e l y i n the e x p e r -iments, on C 0 2 (77 K, 20 G) and C 0 2 (77 K, 40 G). No s i g n i f i c a n t peaks were found i n t h e F o u r i e r t r a n s -form spectrum of t h e C S 2 (300 K, 7 G) d a t a . A s i g n i f i c a n t peak was seen i n t h e spectrum o f t h e C 0 2 (195 K, 7.5 G) d a t a which i s e i t h e r due t o Larmor p r e c e s s i o n o f t h e muon s p i n i n muonium o r i n a p o l y a t o m i c muonic r a d i c a l . The t e n t a t i v e i n t e r p r e t a t i o n o f the C 0 2 (77 K, 20 G) d a t a i s t h a t t h e o b s e r -ved peaks may be a s s o c i a t e d w i t h a p o l y a t o m i c muonic r a d i c a l . -85-The peaks o b s e r v e d i n the F o u r i e r t r a n s f o r m spectrum o f t h e COg (77 K, 40 G) d a t a cannot be i n t e r p r e t e d i n terms o f t h e t h e o r y g i v e n i n t h i s paper. In o r d e r t o o b t a i n c o n c l u s i v e i n f o r m a t i o n about t h e p o s s i b l e i d e n t i f i c a t i o n o f muonic r a d i c a l s i n C S 2 and S 0 2 , and about t h e so u r c e o f t h e s i g n a l s d e t e c t e d i n C 0 2 , t h e ex p e r i m e n t s on s o l i d - p h a s e s u b s t r a t e s s h o u l d be r e - a t t e m p t e d at l ow.temperature over a s e r i e s o f e x t e r n a l f i e l d v a l u e s . In c o n c l u s i o n , an improved e x p e r i m e n t a l system i s proposed: s o l i d - p h a s e t a r g e t s s h o u l d be p r e p a r e d by f r e e z i n g p u r i f i e d gaseous C 0 9 o r S 0 2 ( o r s p r a y i n g pure C S 2 ) onto a c o l d copper p l a t e ( w i t h i n an ev a c u a t e d chamber and i n t h e r m a l c o n t a c t w i t h a c r y o s t a t ) t o p r o v i d e t h i n - f i l m (~4 mm) t a r g e t s f o r use w i t h ' s u r f a c e ' m u o n s — s e v e r a l advantages o v e r t h e use of ' c o n v e n t i o n a l ' muons are app a r e n t : i . P u r i f i c a t i o n o f t h e samples t o a g r e a t e r e x t e n t may j . - be f a c i l i t a t e d s i n c e f a r l e s s t a r g e t volume i s r e q u i r e d . i i . E x t e r n a l magnetic f i e l d inhomogeneity i s m i n i m i z e d s i n c e a s m a l l e r t a r g e t a r e a i s r e q u i r e d (due t o t h e s m a l l 'spot' f o c u s o f the ' s u r f a c e ' muon beam). i i i . 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