UBC Theses and Dissertations

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UBC Theses and Dissertations

A systematic study of muon capture 1980

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I,' A SYSTEMATIC STUDY OF MUON CAPTURE a.Sc., University of Tokyo, 1970 M.Sc, University of B r i t i s h Columbia, 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIRMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF GRADUATE STUDIES (DEPARTMENT OF PHYSICS) WE ACCEPT THIS THESIS AS CONFORMING TO THE REQUIRED STANDARDS THE UNIVERSITY OF BRITISH COLUMBIA by Takenori Suzuki r October, 1980 Takenori Suzuki, 1980 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f PHYSICS The U n i v e r s i t y o f B r i t i s h C o l u m b i a 207S Wesbrook Place Vancouver, Canada V6T 1WS October 14, 1980 i i A b s t r a c t N e g a t i v e mucn l i f e t i m e s h a v e b e e n m e a s u r e d i n 4 8 e l e m e n t s i n c l u d i n g f o u r p a i r s o f s e p a r a t e d i s o t o p e t a r g e t s ( 6 L i , 7 L i , ^ B , 1 * B , * 2_, i 3 c ,1 6 0 , i 8 0 ) . T h e e x p e r i m e n t a l s e t - u p a n d e l e c t r o n i c s l o g i c w e r e c h e c k e d a g a i n s t t h e p o s i t i v e muon l i f e t i m e , w i i c h was m e a s u r e d t o b e 2 1 9 7 , 0 ± 0 . 7 ns, i n g o o d a g r e e m e n t w i t h t h e a c c e p t e d v a l u e o f 2 1 9 7 . 1 2 0 ± 0 . 0 7 7 n s . M u o n s w e r e p r o d u c e d b y t h e b a c k w a r d d e c a y o f p i o n s w h i c h w e r e p r o v i d e d b y t h e M20 beam c h a n n e l a t T R I U M F . T h e n e g a t i v e muon l i f e t i m e s w e r e m e a s u r e d f o r a l l l i g h t e l e m e n t s e x c e p t H a n d H e . An i m p r o v e d a c c u r a c y h a s b e e n a c h i e v e d i n B e , N , 0 , F , N a , C l , a n d K , a n d new m e a s u r e m e n t s w e r e p e r f o r m e d f o r 1 3 C , 1 8 C , Dy a n d E r . S t r o n g i s o t o p e e f f e c t s w e r e o b s e r v e d i n L i , B , a n d 0 , b u t t h e r e w a s n o i s o t o p e e f f e c t i n C . O u r r e s u l t s i n 6 L i a n d 7 L i w e r e i n g o o d a g r e e m e n t w i t h t h e p r e d i c t e d v a l u e s b y L o d d e r a n d J o n k e r . O u r m e a s u r e m e n t s c o n f i r m t h a t t h e e v e n - o d d e f f e c t i n h e a v y n u c l e i i s n o t s t r o n g a n d t h e i n c r e a s e o f t h e o d d - Z c a p t u r e r a t e s i s s m a l l e r t h a n t h a t e x p e c t e d f r o m t h e q u e n c h i n g o f t h e C a b i f c b o a n g l e i n l a r g e m a g n e t i c f i e l d s . The n e g a t i v e muon beam was a l s o s t o p p e d i n 2 3 m e t a l l i c o x i d e s i n o r d e r t o m e a s u r e t h e a t o m i c c a p t u r e r a t i o s . T h e n u m b e r o f m u o n s c a p t u r e d b y e a c h e l e m e n t w a s d e d u c e d by l i f e t i m e a n a l y s i s . O u r r e s u l t r e p r o d u c e d t h e p e r i o d i c d e p e n d e n c e a n d a g r e e d w e l l w i t h e a r l i e r X - r a y m e a s u r e m e n t s . T h e r e s u l t s h o w e v e r a r e o f h i g h e r a c c u r a c y a n d a r e l i a b l e t o v e r y d i f f e r e n t s y s t e m a t i c e r r o r s , w h i c h g i v e s a d d e d c o n f i d e n c e t o t h e o v e r a l l s i t u a t i o n . i i i T A B L E OF CONTENTS AB S I R & C T — i i T A B L E OF CONTENT'S i i i L I S T OF F I G U R E S v i L I S T OF T A B L E S v i i ACKNOWLEDGEMENTS v i i i CHAPTER I , I n t r o d u c t i o n 1 I . A D i s c o v e r y c f t h e Muon a n d i t s B e h a v i o r i n M a t t e r 1 I . B F r e e Muon D e c a y 4 I . C B o u n d M u c n D e c a y 8 I . D Muon C a p t u r e i n N u c l e i 15 CHAPTER I I , E x p e r i m e n t a l M e t h o d a n d S e t - u p 24 I I . A Muon Beam L i n e 25 I I . B S c i n t i l l a t i o n C o u n t e r s a n d G e o m e t r y 3 1 I I . C Mu M e t a l S h i e l d i n g o f F i e l d a n d C o l l i m a t o r — 34 I I . D T a r g e t s 3 5 I I . E E l e c t r o n i c s a n d T i m i n g C o n s i d e r a t i o n 39 I I . F R u n n i n g P r o c e d u r e a n d R u n R e c o r d 4 9 C H A P T E R I I I , D a t a A n a l y s i s 5 3 I I I . A D a t a A n a l y s i s P r o c e d u r e 53 I I I . B M a g n e t i c F i e l d E f f e c t 57 I I I . C M u c n S t o p p i n g R a t e E f f e c t 6 1 I I I . D 2 n d Muon R e j e c t i o n 64 I I I . E D i s t o r t i o n f r o m C o u n t e r E f f i c i e n c y a n d D e a d T i m e c f E l e c t r o n i c s •  6 7 I I I . F A n a l y s i s o f N e g a t i v e Muon L i f e t i m e 6 9 I I I . G H y p e r f i n e E f f e c t ( h f ) i n a D e c a y C u r v e 72 C H A P T E R I V , E x p e r i m e n t a l R e s u l t s a n d D i s c u s s i o n s o f L i f e t i m e M e a s u r e m e n t s 77 I V . A P o s i t i v e Muon L i f e t i m e i n C a r b o n 85 I V . B M u c n C a p t u r e R a t e a n d i t s A c c u r a c y 8 8 I V . C N e g a t i v e Muon L i f e t i m e M e a s u r e m e n t i n C a r b o n a n d S y s t e m C a l i b r a t i o n 92 I V . D N e g a t i v e Muon L i f e t i m e M e a s u r e m e n t s i n 48 E l e m e n t s 9 4 (a) L i t h i u m ( 6 L i a n d 7 L i ) 94 (b) B e r y l l i u m 9 7 (c) B o r o n (i ° B a n d i » B ) 98 (d) C a r b o n (* 2 C a n d 1 3 C ) 99 (e) N i t r o g e n 100 ( f ) O x y g e n ( i 6 0 a n d ia 0) 101 (g) F l u o r i n e 101 (h) S e a r c h f o r t h e h f T r a n s i t i o n i n B e , 1 0 B , i i B , 1 3 C , N , Na a n d C l 104 ( i ) F r o m Z= 1 1 (Na) t o Z = 8 3 ( B i ) 107 i v IV.E P r i m a k o f f Formula i n Muon Capture 109 IV.F The Even-Odd Z E f f e c t i n Heavy N u c l e i 112 IV. G N u c l e a r S t r u c t u r e E f f e c t i n Muon Capture 123 CHAPTER V, Muon Capture i n C h e m i c a l Compounds 129 V. A I n t r o d u c t i o n 129 V.B Muon Atomic Capture fiatio by t h e L i f e t i m e Method 131 CHAPTER V I , Summary 139 R e f e r e n c e s 143 V L i s t o f F i g u r e s F i g u r e P a g e 1 - 1 , E n e r g y S p e c t r u m c f p o s i t r o n s f r o m p o s i t i v e muon d e c a y . The x a x i s s h o w s t h e p o s i t o r o n momentum i n u n i t s o f (muon m a s s ) / 2 . > 7 1 - 2 , E n e r g y d e p e n d e n t a s y m m e t r y f o r p o s i t i v e a n d n e g a t i v e muon d e c a y i n c a r b o n . A l s o t h e a s y m m e t r y c f n e g a t i v e m u o n s i n t i t a n i u m i s s h o w n . — 9 1 - 3 , E x p e r i m e n t a l e n e r g y s p e c t r a o f d e c a y e l e c t r o n s f r o m n e g a t i v e muons i n C , T i , C u , a n d P b . 12 I - 4 , T h e o r e t i c a l s p e c t r a o f d e c a y e l e c t r o n s f r o m n e g a t i v e m u o n s i n P b a n d Fe ( H u f f 6 1 ) . 13 I I - l , T h e M20 beam l i n e 26 I I - 2 , E x p e r i m e n t a l s e t - u p a n d d e c a y e l e c t r o n c o u n t e r s 29 I I - 3 , T i m e o f f l i g h t s p e c t r u m o f i n c i d e n t beam a n d s t o p p e d mucn s i g n a l s • 30 I I - 4 , S i m p l i f i e d MSB d a t a t a k i n g s y s t e m 40 I I - 5 , E l e c t r o n i c s l o g i c 43 I I - 6 , T i m i n g s a n d d i f i n i t i o n s o f e v e n t s 44 I I I - 1 , P o s i t i v e muon d e c a y c u r v e 55 I I I - 2 , N e g a t i v e muon d e c a y c u r v e i n C r 2 0 3 56 I I I - 3 , S t o p p i n g r a t e d e p e n d e n c e w i t h a n d w i t h o u t r e j e c t i o n s 62 I I I - 4 , L i f e t i m e d i s t o r t i o n i n p o s i t i v e muon d e c a y c u r v e 65 F i g u r e P a g e I I I - 5 , H y p e r f i n e d o u b l e t o f m u o n i c a t o m . Rh i s c o n v e r s i o n r a t e , E c c a p t u r e r a t e , E d d e c a y r a t e , a n d E t o t a l d i s a p p e a r a n c e r a t e . The + v e ( - v e ) s i g n s h e w s t h e r a t e f r c m F + { F ~ ) s t a t e . 74 I V - 1 , R a t i o c f b o u n d d e c a y r a t e t o f r e e d e c a y r a t e 89 I V - 2 , T h e T B I U M F d a t a a r e f i t t e d t o t h e P r i m a k o f f a n d t h e G o u l a r d - P r i m a k o f f f o r m u l a . 114 I V - 3 , P a s t f i n d i n g s s u m m a r i z e d by E c k h a u s e e t a l . ( E C K 6 6 ) a r e f i t t e d t o t h e P r i m a k o f f a n d t h e G o u l a r d - P r i m a k o f f f o r m u l a 115 I V - 4 , D e v i a t i o n s o f e x p e r i m e n t a l c a p t u r e r a t e s f r o m t h e G o u l a r d - P r i m a k c f f f o r m u l a 117 I V - 5 , A b s o l u t e d e v i a t i o n s o f e x p e r i m e n t a l c a p t u r e r a t e s f r o m t h e G o u l a r d - P r i m a k o f f f o r m u l a . F i g u r e I V - 4 i s r e d r a w n e d . 1 18 I V - 6 , The n o r m a l i z e d d e v i a t i o n s o f o d d - Z n u c l e i 1 2 0 I V - 7 , R e d u c e d c a p t u r e r a t e s v e r s u s a t o m i c n u m b e r . T h i s g r a p h h a s b e e n s h o w n by K c h y a m a a n d F u j i i (KOH79) — 125 I - V - 8 , The n e u t r o n e x c e s s v e r s u s a t o m i c n u m b e r . T h i s e x c e s s t e r m i s n a m e d P a u l i e x c l u s i o n t e r m by P r i m a k o f f . 126 V - 1 , A t o m i c c a p t u r e r a t i o i n m e t a l l i c o x i d e s . 1 3 5 L i s t of Tables Table Page I I - 1 , Counter Geometry and E f f i c i e n c y 33 I I - 2 , L i s t of Targets and T h e i r Form 36-37 I I - 3 , Meanings cf Symbols i n Logic Diagram {figure II-5) 42 I I - 4, Bun Becords ( T o t a l Events) 5 1-52 I I I - 1,• P o s i t i v e Muon L i f e t i m e s of Four E l e c t r o n Telescope 60 I I I - 2, Carbon Background E f f e c t i n L i g h t Elements 71 IV- 1, B e s u l t s cf L i f e t i m e Measurements i n This Experiment 78-79 IV-2, Summary of Muon L i f e t i m e s and Capture Bates 80-84 IV- 3 , Past P o s i t i v e Mucn Measurements 86 IV-4, Negative Muon L i f e t i m e s i n Carbon 93 IV-5 (1) , Capture Bates i n 6 L i and 7 l i 96 (2), The C o n t r i b u t i o n of M u l t i p o l e s to the t o t a l Mucn Capture Bates by Lodder and Jonker 96 IV-6, The Hyperfine E f f e c t s i n Various N u c l e i 105-106 IV-7, F i t t i n g B e s u l t s f o r the Primakoff Formula (equation (4. 16) ) 113 IV- 8, F i t t i n g B e s u l t s f o r the Goulard-Primakoff Formula (eguation (4.18)) 113 V- 1, Per atom Capture B a t i o s A(Z/0) of muons i n M e t a l l i c Oxides 134 v i i i ACKNOWLEDGEMENT'S I am m o s t g r a t e f u l t o P r o f e s s o r D a v i d F . M e a s d a y n o t o n l y f o r h i s h e l p i n c o m p l e t i n g t h i s t h e s i s , b u t a l s o f o r h i s g u i d a n c e i n u n d e r s t a n d i n g p h y s i c a l p h e n o m e n a . I w o u l d l i k e t o t h a n k m e m b e r s o f t h e s u p e r v i s i n g c o m m i t t e e , P r o f e s s o r s D . S . B e d e r , F . W . D a l b y , a n d B . L . W h i t e f o r t h e i r a d v i c e a n d e f f o r t i n r e a d i n g t h i s w o r k . I w o u l d l i k e t o t h a n k D r . J . H . B r e w e r a n d D r . D . M . G a r n e r f o r many e n l i g h t e n i n g d i s c u s s i o n s a n d i n p a r t i c u l a r f o r t h e i r h e l p w i t h t h e MSB d a t a t a k i n g s y s t e m w h i c h was e s s e n t i a l f o r t h e s u c c e s s o f t h i s e x p e r i m e n t . I t i s my p l e a s u r e t o a c k n o w l e d g e t h e i n v a l u a b l e a s s i s t a n c e o f D r . J a n - P e r R o a l s v i g t h r o u g h o u t t h e l a s t t w o - w e e k e x p e r i m e n t . T h a n k s a r e a l s o d u e t o t h e o t h e r m e m b e r s o f t h e MSB g r u o p , D r . D . C . W a l k e r , D r . D . G . F l e m i n g , E . K i e f l , G . M a r s h a l l , B . J . M i k u l a , B . N g , a n d D . S p e n c e r f o r t h e i r many y e a r s a s s i s t a n c e t h r o u g h t h e MSB m e e t i n g . I a l s o w i s h t o t h a n k D r . M . H a s i n o f f , D r . J . M . P o u t i s s o u , a n d D r . M . S a l o m o n f o r t h e i r k i n d a d v i c e d u r i n g t h i s w o r k . W i t h o u t a l o a n o f t a r g e t s f r c m f i v e g r o u p s , OBC c h e m i s t r y ( D r . D . C . W a l k e r , D r . D . G . F l e m i n g ) , U V I C T R I U M F ( D r . B . M . P e a r c e ) , D E . J . B . W a r r e n , D r . E . B . J c h n s c n , a n d TCKYO MSB g r o u p ( D r . T . Y a m a z a k i ) , t h i s e x p e r i m e n t w o u l d h a v e n o t b e e n c o m p l e t e d . I w o u l d l i k e t o e x p r e s s many t h a n k s t o a l l o f t h e a b o v e f o r t h e i r c o o p e r a t i o n . F i n a l l y I t h a n k my w i f e Y c s h i k o f o r h e r many y e a r s o f e n c o u r a g e m e n t . 1 C H A P T E E I I n t r o d u c t i o n I . A D i s c o v e r y o f t h e Muon a n d i t s B e h a v i o r i n M a t t e r T h e muon was d i s c o v e r e d b y A n d e r s o n a n d N e d d e r m e y e r (AND38) i n c o s m i c r a y s . When i t w a s f o u n d , i t was t h o u g h t t c be t h e m e s o n r e s p o n s i b l e f o r n u c l e a r f o r c e s a s p r e d i c t e d by Y u k a w a i n 1 9 3 5 ( Y U K 3 5 ) . H o w e v e r , i t was d i f f i c u l t t o e x p l a i n t h e f a c t t h a t i t h a d p e n e t r a t e d t h e e a r t h ' s a t m o s p h e r e w i t h o u t a b s o r p t i o n . T h i s w a s b e c a u s e t h e Y u k a w a m e s o n s r e s p o n s i b l e f o r t h e s t r o n g i n t e r a c t i o n s h o u l d h a v e b e e n a b s o r b e d q u i c k l y v i a n u c l e a r r e a c t i o n s w i t h a t o m s i n t h e a t m o s p h e r e . T h r o u g h t h e w o r k c f C o n v e r s i e t a l . ( C O N 4 7 ) , who m e a s u r e d t h e r a t i o o f n u c l e a r a b s o r p t i o n o f n e g a t i v e m u o n s i n l i g h t e l e m e n t s , i t b e c a m e c l e a r t h a t t h e m u o n s d i d n o t i n t e r a c t s t r o n g l y w i t h t h e n u c l e u s . T h e d i s c o v e r y o f p i o n s by L a t t e s e t a l . ( L A T 4 7 ) r e s o l v e d t h e c o n t r a d i c t i o n . T h e y o b s e r v e d t h a t t h e muons f r o m c o s m i c r a y s w e r e t h e d e c a y p r o d u c t s o f t h e p i o n s . I t i s now u n d e r s t o o d t h a t p i o n s a r e t h e Y u k a w a m e s o n s a n d muons - w h i c h a r e s i m i l a r t c e l e c t r o n s i n many w a y s - a r e now c l a s s i f i e d a s l e p t o n s a n d a r e n e t m e s o n s i n t h e m o d e r n u s e o f t h e t e r m . T h u s m u e n s a r e p a r t i c l e s o f m a s s 1 0 5 . 6 M e V / c 2 ( 2 0 6 . 8 t i m e s t h e m a s s o f t h e e l e c t r o n ) a n d t h e y e x p e r i e n c e t h e weak a n d 2 t h e e l e c t r o m a g n e t i c i n t e r a c t i o n s b u t n o t t h e s t r o n g i n t e r a c t i o n . The b e h a v i o r o f n e g a t i v e m u o n s i n m a t t e r may be c o n v e n i e n t l y d i v i d e d i n t o t h e f o l l o w i n g f o u r s t a g e s ( W U 6 9 ) . The s l o w i n g d c w n m e c h a n i s m a n d i t s d u r a t i o n h a v e b e e n d i s c u s s e d i n d e t a i l b y F e r m i a n d T e l l e r (FER47). 1 , H i g h e n e r g y t o a f e w k e V : M u c n s w i t h s e v e r a l t e n s o f MeV l o s e t h e i r e n e r g y m a i n l y b y c o l l i s i o n s w i t h a t o m i c e l e c t r o n s . A t t h e e n d o f t h i s s t a g e , when t h e m u o n ' s e n e r g y i s a f e w k e V , i t s v e l o c i t y i s a l m o s t e q u a l t o t h e v a l e n c e e l e c t r o n v e l o c i t y . „ T h e s l o w i n g d o w n t i m e i n t h e c o n d e n s e d m a t e r i a l i s b e t w e e n I O 7 - 9 a n d 1 0 _ 1 ° s e c . 2, A f e w keV t o r e s t : The m u c n s e x c h a n g e e n e r g y w i t h e l e c t r o n s a n d c o m e t o r e s t i n a b o u t 1 0 - *3 s e c . T h e d e t a i l s o f t h i s p r o c e s s d e p e n d o n w h e t h e r t h e m a t e r i a l i s a m e t a l , i n s u l a t o r , g a s , e t c . 3, A t o m i c c a p t u r e a n d e l e c t r o m a g n e t i c c a s c a d e : T h e m u o n s a r e e v e n t u a l y t r a p p e d i n t o h i g h l y e x c i t e d s t a t e s o f a p a r t i c u l a r a t o m a n d c a s c a d e d o w n t o t h e l o w e s t s t a t e o f t h e m u o n i c a t o m . A u g e r p r o c e s s e s ( i . e . e m i s s i o n o f a t o m i c e l e c t r o n s ) a r e d o m i n a n t i n t h e t r a n s i t i o n b e t w e e n t h e h i g h e r l e v e l s a n d r a d i a t i v e p r o c e s s e s b e t w e e n t h e l o w e r l e v e l s . The c a s c a d e t i m e i s a b o u t 1 0 ~ 1 3 s e c . 4 , D i s a p p e a r a n c e : 3 M o s t o f t h e muons r e a c h t h e IS o r b i t o f t h e m u o n i c a t o m a n d t h e y e i t h e r d e c a y o r a r e c a p t u r e d by t h e n u c l e u s f r c m t h i s o r b i t v i a t h e w e a k i n t e r a c t i o n . I n l i g h t e l e m e n t s , i t t a k e s a p p r o x i m a t e l y 2 . 2 m i c r o s e c o n d s , t h e l i f e t i m e o f p o s i t i v e m u o n s , f o r t h e m u o n s t o d i s a p p e a r . , I n h e a v y e l e m e n t s i t t a k e s a b o u t 8 0 n a n o s e c o n d s ( n s ) . I n t h i s t h e s i s , t h e p h y s i c s o f t h e t h i r d a n d t h e f o u r t h s t a g e s w i l l b e d i s c u s s e d . The a t o m i c c a p t u r e r a t e o f n e g a t i v e m u o n s i n c h e m i c a l c o m p o u n d s was i n v e s t i g a t e d by F e r m i a n d T e l l e r ( F E R 4 7 ) a n d t h e s o c a l l e d " Z - l a w ' 1 was p r o p o s e d . a c c o r d i n g t o t h e Z - l a w , t h e p r o b a b i l i t y f o r c a p t u r e b y a n a t o m i n a c h e m i c a l c c m p c u n d w o u l d be p r o p o r t i o n a l t o i t s a t o m i c n u m b e r . , H o w e v e r , t h e Z - l a w was n e t s u p p o r t e d b y s u b s e q u e n t e x p e r i m e n t s ( S E N 5 8 , E C K 6 2 , B a i 6 3 ) , w h i c h o b s e r v e d a p e r i o d i c i t y o f t h e a t o m i c c a p t u r e r a t e i n t h e m e t a l l i c o x i d e s ( Z I N 6 6 ) , a n d t h u s i t was r e a l i z e d t h a t t h e c a p t u r e p r o c e s s i s s t r o n g l y a f f e c t e d by t h e c h e m i c a l s t r u c t u r e . E v e n t h o u g h t h e r e h a s b e e n c o n s i d e r a b l e p r o g r e s s i n c l a r i f y i n g t h e c a p t u r e p r o c e s s ( D A N 7 9 , S C H 7 8 ) , t h e d e t a i l e d e x p l a n a t i o n c f t h e o b s e r v e d c h e m i c a l e f f e c t s t i l l r e m a i n s i n c o m p l e t e ( S C H 7 7 ) . T h e r e h a v e b e e n s e v e r a l a t t e m p t s t o c a l c u l a t e t h e k i n e t i c e n e r g y o f muons when c a p t u r e d b y t h e a t o m . A l t h o u g h e a r l y c a l c u l a t i o n s (HAF74) s u g g e s t e d t h a t t h e c a p t u r e . o c c u r s w h i l e t h e m u o n s k i n e t i c e n e r g y i s s t i l l h u n d r e d s o f e V , i t i s now b e l i e v e d t h a t t h e e n e r g y i s l e s s t h a n 15 e V i n t h e 4 c a s e o f t h e h y d r o g e n a t o m ( L E 0 7 9 ) . T h e l o w e r k i n e t i c e n e r g y m a k e s i t e a s i e r t o u n d e r s t a n d t h e e f f e c t o f t h e m o l e c u l a r s t r u c t u r e o n t h e c a p t u r e p r o c e s s . I . E F r e e Muon D e c a y A muon i s t h e d e c a y p r o d u c t o f a p i o n . T h e d e c a y s c h e m e i s i r + > y + + , IT" - H * y~ + (1.1) B e c a u s e t h i s d e c a y d o e s n o t c o n s e r v e p a r i t y , t h e muon i s p r o d u c e d i n a p a r t i c u l a r h e l i c i t y s t a t e , n a m e l y i t s s p i n a n d m a g n e t i c a c m e n t a r e a l i g n e d ( o r a n t i - a l i g n e d ) w i t h t h e momentum v e c t o r . A l t h o u g h t h i s e f f e c t i s e s s e n t i a l f o r MSB w o r k , i t t u r n s o u t t o t e a n i n c o n v e n i e n c e f o r t h e e x p e r i m e n t s d e s c r i b e d i n t h i s t h e s i s . T h e muon d e c a y s i n t o a n e l e c t r o n a n d t w c n e u t r i n o s . y + »• e + + v + v , y~ * e~ + v + v (1.2) e y e y T h i s t h r e e - p a r t i c l e d e c a y h y p o t h e s i s was c o n f i r m e d b y t h e o b s e r v a t i o n o n t h e e n e r g y s p e c t r u m o f t h e d e c a y e l e c t r o n s a n d t h e i r e n e r g y ( T I 0 4 9-1). T h e s i m p l e a d d i t i v e l a w o f l e p t c n c o n s e r v a t i o n h a s o n l y r e c e n t l y b e e n c o n f i r m e d b y e x p e r i m e n t s a t L A M E F ( W i l l i s e t a l . ( W I L 8 0 - 1 ) ) ( f o r i n s t a n c e i n t h e y + d e c a y t h e q u a n t u m n u m b e r f o r a n t i - m u o n s h a s t o b e c o n s e r v e d , n e c e s s i t a t i n g a v l n t - 0 6 d e c a y p r o d u c t s a n d f o r b i d d i n g a v ) . T i o m n o a n d W h e e l e r ( T I 0 4 9 - 2 ) p r o p o s e d a v U n i v e r s a l F e r m i i n t e r a c t i o n , i n w h i c h t h e c o u p l i n g 5 c o n s t a n t s o f b e t a d e c a y , muon d e c a y a n d n u c l e a r muon c a p t u r e a r e o f t h e s a m e o r d e r c f m a g n i t u d e . T h e w e a k i n t e r a c t i o n s c h e m e c a n t h e n b e e x p r e s s e d b y t h e f o l l o w i n g p i c t u r e ( P u p p i t r i a n g l e ) ( n , p ) E e t a D e c a y Muon C a p t u r e (e,v e) — ( y , V y ) Muon D e c a y T h e H a m i l t o n i a n o f t h e d e c a y p r o c e s s (1 . 2 ) i s d e s c r i b e d b y t h e f o l l o w i n g f o u r - f e r m i o n i n t e r a c t i o n ( S A C 7 5 ) H = / | I { V i V ^ / i ^ i ^ v 1 + H , C' ( 1' 3 ) w h e r e i r u n s o v e r t h e s c a l a r , v e c t o r , t e n s o r , a x i a l v e c t o r , a n d p s e u d o - s c a l a r i n t e r a c t i o n s , a n d G i s a c o u p l i n g c o n s t a n t o f t h e w e a k i n t e r a c t i o n ( s e e i n d e t a i l s e c t i o n I V . A ) . T h e H a m i l t o n i a n (1 . 3 ) l e a d s t o t h e e n e r g y s p e c t r u m t e r m M(X) ( M i c h e l s p e c t r u m ) a n d t h e a s y m m e t r y t e r m B ( X ) f o r t h e d e c a y o f a p o l a r i z e d m u o n . H e n c e , The g e n e r a l f o r m u l a o f t h e d e c a y e l e c t r o n s p e c t r u m o f t h e p o l a r i z e d p o s i t i v e muon i s e x p r e s s e d a s d N ( X , P , g ) c x [M (X) * B (X) c o s (g) } X 2 d X (1.4) w h e r e P i s t h e mucn p o l a r i z a t i o n , g t h e a n g l e b e t w e e n t h e 6 d e c a y e l e c t r o n momentum a n d t h e s p i n d i r e c t i o n o f t h e m u o n , . I n f i g u r e 1-1, t h e e x p e r i m e n t a l e n e r g y s p e c t r u m d a t a p o i n t s m e a s u r e d a t TEIUMF a r e s h o w n a l o n g w i t h t h e t h e o r e t i c a l c u r v e . T h i s f i g u r e a n d t h e f o l l o w i n g e x p e r i m e n t a l r e s u l t s m e a s u r e d a t TEIUMF w e r e . p r e s e n t e d a t t h e CAP c o n f e r e n c e i n 1979 ( S U Z 7 9 ) . T h e t h e o r e t i c a l e n e r g y s p e c t r u m f o r t h e p o s i t i v e m u o n s h a s b e e n s h o w n b y M i c h e l ( M I C 5 7 , S A C 7 5 ) t o be M(X) = 2 (X) 2 . £6 ( 1 - X ) +4 p i ( 4 / 3 ) X - 1 ) } ( 1 . 5 ) w h e r e X i s t h e e l e c t r o n momentum i n u n i t s o f t h e p e a k momentum ( 5 2 . 8 M e V / c ) a n d P i s t h e s o - c a l l e d M i c h e l p a r a m e t e r . . P i s p r e d i c t e d t o b e 0 . 7 5 b y t h e t w o - c o m p o n e n t n e u t r i n o a n d V - A t h e o r i e s ( K I N 5 7 , SAC 7 5 ) . The e x p e r i m e n t a l v a l u e s f o u n d b y B a r d o n ( B A B 6 5 ) a n d F r y b e r g e r ( F E Y 6 8 ) a r e 0 . 7 5 0 ± 0 . 0 0 3 a n d 0 . 7 6 2 ± 0 . 0 0 8 , r e s p e c t i v e l y . . T h e T E I U M F r e s u l t i s 0 . 7 4 9 ± 0 . 0 0 3 . T h u s t h e e x p e r i m e n t s a r e i n g o o d a g r e e m e n t w i t h t h e t h e o r e t i c a l p r e d i c t i o n , . I n t h e c a s e o f p o l a r i z e d p o s i t i v e m u o n s , t h e a s y m m e t r y t e r m ( S A C 7 5 ) i s g i v e n fcy E (X) = 2 (X)  z*{2 ( 1 - X ) +4 6 ( ( 4 / 3 ) 2 - 1 ) } ( 1 . 6 ) w h e r e <5 i s t h e a s y m m e t r y p a r a m e t e r . A g a i n <s i s p r e d i c t e d t o b e 0 . 7 5 , t h e s a m e , a s p . A t T E I U M F , t h e p o l a r i z e d p o s i t i v e muon w i t h a 84% beam p o l a r i z a t i o n w a s s t o p p e d i n a 1.0 MOMENTUM(ny2) Figure I - l , Energy spectrum of positrons from positive muon decay. shows the positron momentum in units of (muon mass)/2. 8 c a r b o n t a r g e t a n d t h e e n e r g y d e p e n d e n t a s y m m e t r y was m e a s u r e d . T h i s i s s h o w n i n f i g u r e 1-2 a l o n g w i t h t h e a s y m m e t r y s p e c t r a o f n e g a t i v e m u o n s i n a c a r b o n a n d a t i t a n i u m t a r g e t . F r o m t h e d a t a a n a l y s i s o f t h e p o s i t i v e muon a s y m m e t r y , <S i s e g u a l t o 0 . 753 + 0 . 005 . T h i s a g r e e s w e l l w i t h F r y b e r g e r ' s f i n d i n g o f 0.752±0.Q08 a n d a l s o w i t h t h e p r e d i c t e d v a l u e . I n t h e u s u a l c o u n t e r e x p e r i m e n t , t h e e l e c t r o n e n e r g y i s n o t m e a s u r e d . T h e a n g u l a r d i s t r i b u t i o n o f e l e c t r o n s i s o f t h e f o r m d N ( P , g ) <=>< {1+ A P c o s (g)} dq (1.7) w h e r e A i s t h e a s y m m e t r y a n d P t h e muon p o l a r i z a t i o n . T h i s i s a n e q u a t i o n f o r t h e muon p r e c e s s i o n u n d e r t h e i n f l u e n c e o f a m a g n e t i c f i e l d . I h e i n t e g r a t i o n o f e q u a t i o n (1.6) f o r t h e e l e c t r o n momentum (X) b e t w e e n 0 a n d 1 g i v e s A = 1/3 ( 1. 8) when P= 1 ( n a m e l y 100% beam p o l a r i z a t i o n ) . I . C B o u n d Muon D e c a v . The b o u n d muon d e c a y h a s a f e w d i f f e r e n t c h a r a c t e r i s t i c s f r c m a f r e e muon d e c a y . F i r s t , a n e g a t i v e muon i n t h e K o r b i t o f t h e m u o n i c a t o m h a s a l o w e r d e c a y p r o b a b i l i t y t h a n a f r e e muon d u e t o t h e r e d u c e d p h a s e s p a c e . 9 1.0r i 1 r i 1 1 1 1 1 r 0.5 /I If inC / >- h- LU < o / I 4 jj~ in C • / r in Ti / 0 * i o o •Q15 •0.10 •005 •0.0 o, ^ -0.3 Theoret ical A s y m m e t r y J L I I I I L 0.0 0.5 MOMENTUM(ny2) 1.0 Figure 1-2, Energy dependent asymmetry for positive and negative muon decay in carbon. Also the asymmetry of negative muons in titanium is shown. 10 The decay r a t e of the f r e e p o s i t i v e mucn i s Ed(+) <x (mucn mass) 5 The energy of the bound muon i s equal to the energy of the fr e e muon (105.6 MeV) minus the bin d i n g energy of the K o r b i t of the muonic atom which reaches a value of about 12 MeV i n uranium. . That i s Ed (-) <=< (muon mass-binding e n e r g y ) 5 This corresponds t o the r e d u c t i o n of the phase space a c c e s s i b l e t o the decay products. Secondly, due to the motion c f the bound muon i n the K o r b i t , the decay e l e c t r o n has a Doppler e f f e c t and the maximum energy i s g r e a t e r than the c u t - o f f energy (=52.8 MeV) of decay e l e c t r o n s from f r e e muons.. Hence, the energy spectrum of the bound muon decay s t r e t c h e s t o the high-energy s i d e . T h i r d l y , the decay p r o b a b i l i t y and the decay e l e c t r o n energy spectrum are a f f e c t e d by the n u c l e a r coulomb f i e l d . The peak of the spectrum i s s h i f t e d i n t o the lower energy s i d e as the atomic number of the t a r g e t nucleus i n c r e a s e . In f i g u r e 1-3, t h e r e are fou r decay e l e c t r o n s p e c t r a from carbon, t i t a n i u m , copper, and l e a d . . Before the TEIUMF measurement (SUZ79), there had been two experiments by C u l l i g a n et a l . (CUL61) f o r an i r o n t a r g e t and B e i l i n (BEI68) f o r a copper t a r g e t . The TEIUMF experiment was the 11 f i r s t a t t e m p t t o d e m o n s t r a t e t h e v a r i a t i o n o f t h e e n e r g y s p e c t r u m f o r t h e v a r i o u s n u c l e i . The s e c o n d a n d t h i r d e f f e c t s a b o v e a r e c l e a r l y d e m o n s t r a t e d i n t h e f i g u r e . T h e e n e r g y s p e c t r a o b t a i n e d a t T E I U M F h a v e s h o w n g o o d a g r e e m e n t w i t h H u f f ' s t h e o r y (HUF6 1 ) . H i s t h e o r e t i c a l c u r v e s a r e s h o w n i n f i g u r e 1 - 4 . A s d i s c u s s e d i n s e c t i o n I . B , t h e t h e o r e t i c a l c u r v e m u s t t a k e i n t o a c c o u n t t h e d e t e c t o r r e s o l u t i o n a n d e n e r g y l o s s i n t h e e l e c t r o n c o u n t e r s i n o r d e r t o c o m p a r e t h e t h e o r y w i t h t h e e x p e r i m e n t . We h a v e a l r e a d y r e p o r t e d t h a t t h e t h e o r y i s i n g o c d a g r e e m e n t w i t h t h e b o u n d muon d e c a y s p e c t r a ( S U Z 7 9 ) . I n t h e e x p e r i m e n t o f t h e a t o m i c c a p t u r e r a t i o i n a c h e m i c a l c o m p o u n d , i t m u s t b e n o t e d t h a t t h e e n e r g y s p e c t r a o f d e c a y e l e c t r o n s a r e d i f f e r e n t f o r d i f f e r e n t n u c l e i . I n t h e h e a v y e l e m e n t s , l i k e l e a d , t h e r a t i o o f l o w e n e r g y e l e c t r o n s t o h i g h e n e r g y e l e c t r o n s i s g r e a t e r t h a n t h e r a t i o i n t h e l i g h t e r e l e m e n t . T h u s , t h e l o s s o f l o w e n e r g y d e c a y e l e c t r o n s f r c m t h e h e a v y e l e m e n t c o n s t i t u e n t i n t h e c h e m i c a l c o m p o u n d t a r g e t i s l a r g e r t h a n t h a t f r c m t h e l i g h t e l e m e n t c o n s t i t u e n t . a n e g a t i v e muon l o s e s p o l a r i z a t i o n q u i c k l y d u r i n g t h e c a s c a d e i n t h e m u o . n i c a t o m . I h e TEIUMF e x p e r i m e n t ( S U Z 7 9 ) i s t h e f i r s t a t t e m p t a t m e a s u r i n g t h e e n e r g y d e p e n d e n c e o f t h e a s y m m e t r y o f n e g a t i v e m u o n s . . I n f i g u r e 1 - 2 , t w o a s y m m e t r y s p e c t r a f o r c a r b o n a n d t i t a n i u m t a r g e t s a r e s h o w n . T h e c a l c u l a t i o n o f t h e e n e r g y d e p e n d e n t a s y m m e t r y h a s b e e n d o n e f o r a n i r o n t a r g e t by G i l i n s k y a n d 0.5 MOMENTUM(nry2) Figure 1-3, Experimental energy spectra of decay electrons from negative in carbon, titanium, copper, and lead. muons Figure 1-4, Theoretical spectra of decay electrons from negative muons in lead, antimony and iron (HUF61) 14 M a t h e w s ( G I L 6 0 ) . T h e i r c a l c u l a t i o n p r e d i c t s t h a t t h e a s y m m e t r y a t t h e h i g h e n e r g y e n d d r o p s down t o z e r o . . The r e s i d u a l p o l a r i z a t i o n o f n e g a t i v e muons f o r s p i n l e s s n u c l e i h a s b e e n t h e o r e t i c a l l y a n a l y z e d by S c m u s h k e v i c h (SHM59) a n d Mann a n d R o s e (MAN6 1 ) . . The b e h a v i o r c f n e g a t i v e m u o n s i n m a t t e r h a s b e e n d i s c u s s e d i n s e c t i o n I . A . D u r i n g t h e s l e w i n g down p r o c e s s f r o m h i g h e n e r g y t o r e s t , t h e m u o n s l o s e m o s t o f t h e i r k i n e t i c e n e r g y by c o l l i s i o n s w i t h e l e c t r o n s b u t t h e d e p o l a r i z a t i o n i n t h i s s t a g e i s n e g l i g i b l e . When t h e m u o n s a r e t r a p p e d i n t o e x c i t e d b o u n d s t a t e s o f t h e m u o n i c a t o m , t h e y l o s e m o s t o f t h e i r p o l a r i z a t i o n , r e t a i n i g e n l y a b o u t 1/3 c f t h e i n i t i a l v a l u e . T h e n t h e m u o n s u n d e r g o many t r a n s i t i o n s v i a A u g e r p r o c e s s e s i n h i g h e r o r b i t s a n d r a d i a t i v e p r o c e s s e s i n l o w e r o r b i t s , a n d f i n a l l y r e a c h t h e g r o u n d s t a t e o f t h e m u o n i c a t o m . D u r i n g t h e c a s c a d e i n t h e m u o n i c o r b i t s , t h e m u o n s l o s e 5 0 % c f t h e r e m a i n i n g p o l a r i z a t i o n . T h u s , i n t h e c a s e c f c a r b o n , t h e f i n a l p o l a r i z a t i o n i s e s t i m a t e d t o b e a b o u t 15%. T h i s e s t i m a t e o f t h e r e s i d u a l p o l a r i z a t i o n i s i n g o o d a g r e e m e n t w i t h e x p e r i m e n t s a s s h o w n b e l o w . I f t h e n u c l e u s h a s a s p i n , t h e r e i s a s p i n - s p i n i n t e r a c t i o n b e t w e e n t h e m u o n s a n d t h e h o s t n u c l e u s . Due t o t h i s i n t e r a c t i o n , t h e a d d i t i o n a l d e p o l a r i z a t i o n o c c u r s d u r i n g t h e c a s c a d e . . F u r t h e r m o r e , a t t h e g r o u n d s t a t e , t h e h y p e r f i n e c o u p l i n g b e t w e e n t h e mucn a n d n u c l e a r s p i n s p r o d u c e s a s t r o n g d e p o l a r i z a t i o n . C o n s e q u e n t l y , t h e r e s i d u a l p o l a r i z a t i o n o f n e g a t i v e m u o n s i n t h e n u c l e u s w i t h a s p i n i s e x p e c t e d t o b e 15 much s m a l l e r t h a n t h a t i n t h e s p i n l e s s n u c l e u s . I n t h e c a s e o f 1 9 F (1= 1 / 2 ) , t h e r e s i d u a l p o l a r i z a t i o n i s r e p o r t e d t o b e 4±45fc ( A S T 6 1 ) . T h e r e s i d u a l p o l a r i z a t i o n s o f n e g a t i v e muons i n c a r b o n a n d t i t a n i u m a r e 20±3% a n d 7±3%, r e s p e c t i v e l y , f r o m t h e T E I U M F e x p e r i m e n t ( S U Z 7 9 ) . T h e s e p o l a r i z a t i o n s h a v e b e e n i n v e s t i g a t e d b y D z h u r a e v e t a l . ( D Z H 7 2 ) , who m e a s u r e d t h e t o t a l a s y m m e t r y (A) e x p r e s s e d b y e g u a t i o n ( 1 . 7 ) . T h e i r f i n d i n g s w e r e 1 9 . 4 ± 1 . \% a n d 1 5 . 5 ± 1 . S % f o r c a r b o n a n d t i t a n i u m , r e s p e c t i v e l y . I n t h e c a s e c f c a r b o n , b o t h e x p e r i m e n t s a g r e e w e l l . H o w e v e r , i n t h e c a s e o f t i t a n i u m , t h e T E I U M F r e s u l t i s s m a l l e r b y a f a c t o r o f 2 . The r e a s o n f o r t h i s i s n o t c e r t a i n . I n t h e c a s e o f t i t a n i u m , t h e a s y m m e t r y s p e c t r u m s h o w s l a r g e e r r o r s e s p e c i a l l y a t l o w e n e r g y . T h i s m e a s u r e m e n t w i l l b e r e p e a t e d a t TEIUMF w i t h a b e t t e r q u a l i t y muon beam i n o r d e r t o r e d u c e t h e a c c i d e n t a l c o i n c i d e n c e s - w h i c h a r e r e l a t e d t o t h e R . F . p e r i o d i n t h e t i m e s p e c t r u m . I . D Muon C a p t u r e i n N u c l e i C o n v e r s i e t a l . (CCN47) m e a s u r e d t h e l i f e t i m e o f p o s i t i v e a n d n e g a t i v e m u c n s i n c a r b o n a n d i r o n . T h e y f o u n d t h a t t h e l i f e t i m e o f n e g a t i v e m u o n s i n c a r b o n w a s a l m o s t t h e same a s t h a t c f p o s i t i v e m u o n s ( 2 . 2 m i c r o s e c o n d s ) • On t h e o t h e r h a n d , d e c a y e l e c t r o n s f r o m t h e n e g a t i v e m u o n s i n i r o n 16 w e r e n o t d e t e c t e d a f t e r o n e m i c r o s e c o n d d e l a y . T h i s p r o v e d t h a t t h e n e g a t i v e m u c n s w e r e c a p t u r e d by t h e i r o n n u c l e u s w i t h i n a m i c r o s e c o n d . S i n c e t h e n , t h e muon c a p t u r e h a s b e e n s t u d i e d e x p e r i m e n t a l l y a n d t h e o r e t i c a l l y a n d t h e c a p t u r e r a t e h a s b e e n d e t e r m i n e d f o r m o s t n u c l e i . T h e b a s i c p r o c e s s o f muon c a p t u r e i n a n u c l e u s i s t h e r e a c t i o n : y~ + p — > n • v ( 1 . 9 ) y w h i c h i n t h e c a s e c f b o u n d p r o t o n s i n a n u c l e u s b e c o m e s : (a,z) • y~ —> ( & , Z - 1 ) • v ( 1 , 1 0 ) y T h i s r e a c t i o n l e a d s t o n u c l e a r e x i t e d s t a t e s ( m a i n l y g i a n t r e s o n a n c e s t a t e s a t a b o u t 2 0 MeV e x c i t a t i o n ) w h i c h t h e n d e - e x c i t e w i t h t h e e m i s s i o n o f o n e o r m o r e n e u t r o n s ( K & P 5 8 ) . T h e f i r s t t h e o r e t i c a l a p p r o a c h t o c a l c u l a t e t h e t o t a l c a p t u r e r a t e i n t h e n u c l e u s w a s made b y W h e e l e r ( W H E 4 9 ) . He e x p r e s s e d t h e c a p t u r e r a t e b y R c ( Z , A ) = c o n s t a n t * E |¥(at each proton) | 2 ( 1 . 1 1 ) a l l protons 2 w h e r e ¥ i s t h e muon wave f u n c t i o n . N o w , |y| i s p r o p o r t i o n a l t o Z 3 , s o t h a t B e ( Z , A ) ( Z e f f ) * ( 1 . 12) I n t h i s e g u a t i o n Z i s r e p l a c e d b y Z e f f , b e c a u s e t h e m u o n i c K o r b i t i s i n s i d e t h e n u c l e u s f o r h e a v i e r n u c l e i a n d t h e r e f o r e t h e p a r t o f t h e w a v e f u n c t i o n w h i c h i s i n s i d e t h e n u c l e u s i s 17 m o d i f i e d b e c a u s e i t s e e s a r e d u c e d c h a r g e . T h e ( Z e f f ) * l a w i s a p p r o x i m a t e l y v a l i d f o r l i g h t e l e m e n t s , b u t i t o v e r e s t i m a t e s t h e r a t e f o r h e a v y e l e m e n t s . P r i m a k o f f ( P E I 5 9 ) d e r i v e d a s i m p l e f o r m u l a w h i c h h a s a n e u t r o n e x c e s s t e r m o r i g i n a t i n g f r o m t h e P a u l i p r i n c i p l e . He e m p l o y e d a c l o s u r e a p p r o x i m a t i o n i n o r d e r t o c a l c u l a t e t h e t r a n s i t i o n m a t r i x e l e m e n t s f o r a l l a c c e s s i b l e e x c i t e d s t a t e s o f t h e d a u g h t e r n u c l e u s . T h i s f o r m u l a h a s h e e n i m p r o v e d by G o u l a r d a n d P r i m a k o f f (G0U74) t o o v e r c o m e t h e s y s t e m a t i c d e v i a t i o n f r o m t h e P r i m a k o f f f o r m u l a f o r t h e h e a v y e l e m e n t s . T h e s e t h e o r i e s w i l l b e d i s c u s s e d i n m o r e d e t a i l i n C h a p t e r V . T h e f i r s t e x p e r i m e n t t o s t u d y s y s t e m a t i c a l l y t h e t o t a l mucn c a p t u r e r a t e was made by S e n s e t a l . ( S E N 5 7 , - 5 9 ) who d e t e r m i n e d t h e a p p a r e n t l i f e t i m e o f n e g a t i v e muons w h i c h s t o p i n m a t t e r . T h e i n v e r s e o f t h e l i f e t i m e i s t h e t o t a l d i s a p p e a r a n c e r a t e , B t , w h i c h i s c o m p o s e d o f t w o c o m p o n e n t s , t h e d e c a y r a t e , R d , a n d t h e c a p t u r e r a t e , B e , i e B t = B e + Q (Z) « E d ( 1 . 1 3 ) w h e r e Q (Z) i s t h e H u f f f a c t o r d i s c u s s e d e a r l i e r w h i c h t a k e s a c c o u n t c f t h e f a c t o r t h a t t h e n e g a t i v e muon i s b o u n d i n t h e a t o m a n d s o t h e d e c a y r a t e i s r e d u c e d (by u p t o 20% f o r h e a v y n u c l e i ) . Bd i s t a k e n t o b e t h e s a m e a s t h a t f o r t h e p o s i t i v e muon u t i l i z i n g t h e CPT t h e o r e m w h i c h i m p l i e s t h a t t h e t o t a l l i f e t i m e s o f p a r t i c l e s a n d a n t i - p a r t i c l e s a r e 18 i d e n t i c a l . T h e m e a s u r e m e n t s o f S e n s e t a l . ( S E N 5 9 ) i n 29 e l e m e n t s f r o m c a r b o n (Z=6) t o u r a n i u m (Z=92) s h o w e d t h e l i n e a r r e l a t i o n b e t w e e n t h e r e d u c e d c a p t u r e r a t e s a n d n e u t r o n e x c e s s t e r m , a s p r e d i c t e d b y t h e P r i m a k c f f f o r m u l a . A f t e r t h e i r e x p e r i m e n t , a l a r g e n u m b e r o f m e a s u r e m e n t s i n d i f f e r e n t n u c l e i h a v e b e e n p e r f o r m e d w i t h i m p r o v e d i n s t r u m e n t s a n d a v e r a g e d v a l u e s o f t h e p a s t f i n d i n g s h a v e b e e n s u m m a r i z e d by E c k h a u s e e t a l . ( E C K 6 6 ) . M o s t o f t h e p a s t m e a s u r e m e n t s w i l l b e l i s t e d . i n T a b l e I V - 2 o f t h i s t h e s i s . I n t h e i n t e r v e n i n g y e a r s , t h e a c c e p t e d v a l u e f o r t h e l i f e t i m e o f t h e p o s i t i v e muon h a s c h a n g e d o u t s i d e t h e o r i g i n a l e r r o r b a r s ( f r o m 2 2 0 3 ± 2 n s i n 1 9 6 3 t o 2 1 9 7 . 1 3 ± 0 . 0 8 n s t o d a y ) . A s t h e c a p t u r e r a t e i s t h e d i f f e r e n c e o f t w o n u m b e r s , a s m a l l c h a n g e i n t h e p o s i t i v e muon d e c a y r a t e c a n h a v e a m a r k e d e f f e c t i n t h e c a l c u l a t e d d e c a y r a t e , e s p e c i a l l y f o r l i g h t n u c l e i . We t h e r e f o r e b e l i e v e t h a t a l l e a r l y m e a s u r e m e n t s s h o u l d b e a p p r o a c h e d w i t h s o m e c a u t i o n . . T h e r e h a v e b e e n s e v e r a l t h e o r e t i c a l d e v e l o p m e n t s s i n c e t h e P r i m a k o f f t h e o r y . T h e d i r e c t c a l c u l a t i o n o f t h e t r a n s i o n m a t r i x w i t h t h e m i c r c s c o p i c p i c t u r e i s t h e s h e l l m o d e l c a l c u l a t i o n ( L U Y 6 3 , G O U 7 1 , D U P 7 5 ) . T o t a l muon c a p t u r e r a t e s b y t h i s m o d e l a r e u s u a l l y h i g h e r t h a n t h e e x p e r i m e n t s by a f a c t o r o f 2 c r 3 . T h e m o d e l c a n be u s e d t o u n d e r s t a n d t h e g e n e r a l t r e n d o f t r a n s i t i o n s i n s t e a d o f c o m p a r i n g t h e r e s u l t w i t h a e x p e r i m e n t . F c l d y a n d W a l e c k a ( F O L 6 4 ) d e v e l o p e d a r e s o n a n c e m o d e l , w h i c h c a l c u l a t e s t h e g i a n t d i p o l e r e s o n a n c e (GDR) 19 e x c i t a t i o n i n d u c e d i n muon c a p t u r e . T h e y u s e d a n e x p e r i m e n t a l c r o s s s e c t i o n o f t h e p h o t c - n u c l e a r r e a c t i o n s t o m a n i p u l a t e t h e d i p o l e . p a r t o f the m u c n c a p t u r e c r o s s s e c t i o n . T h e y a p p l i e d t h i s m o d e l t o t h e d o u b l y m a g i c n u c l e i , * H e , 1 6 0 a n d 4 ( > C a , i n w h i c h t h e a l l o w e d t r a n s i t i o n s a r e s u p p r e s s e d . I n t h e c a s e o f * H e , t h e t h e o r y was i n g o o d a g r e e m e n t w i t h t h e e x p e r i m e n t . T h e c a l c u l a t e d c a p t u r e r a t e s f o r 1 6 0 a n d * ° C a w e r e h i g h e r t h a n t h e e x p e r i m e n t s by 10% a n d 2 5 % , r e s p e c t i v e l y . A p p l y i n g t h e m o d e l t o l 2 C a n d i n c l u d i n g t h e a l l o w e d c o n t r i b u t i o n (WAL75) t o t h e c a p t u r e r a t e , t h e c a l c u l a t i o n a g r e e d w e l l w i t h e x p e r i m e n t . L o d d e r a n d J o n k e r (LOD67) i n v e s t i g a t e d t h e t o t a l muon c a p t u r e r a t e f o r 6 L i a n d 7 L i w i t h t h e F o l d y - W a l e c k a s e m i - e m p i r i c a l m e t h o d . T h e i r r e s u l t f c r 6 L i was s m a l l e r t h a n t h e e x p e r i m e n t a l v a l u e o f E c k h a u s e e t a l . ( E C K 6 3 ) w h e r e a s f o r 7 l i t h e i r v a l u e w a s c o m p a r a b l e t o t h e e x p e r i m e n t a l v a l u e . R e c e n t l y t h e c a p t u r e r a t e s i n 6 L i a n d 7 L i w e r e r e m e a s u r e d b y B a r d i n e t a l . ( B A B 7 8 ) a n d t h e i r e x p e r i m e n t a g r e e d w e l l w i t h t h e r e s u l t s o f L o d d e r a n d J o n k e r . I t w i l l b e s h o w n l a t e r t h a t o u r m e a s u r e m e n t s i n t h e s e n u c l e i a l s o s u p p o r t t h e i r c a l c u l a t i o n . C h r i s t i l l i n e t a l . (CHE73) h a v e a t t e m p t e d t o g i v e t h e t o t a l c a p t u r e r a t e i n t e r m s o f a mean n u c l e a r e x c i t a t i o n e n e r g y a n d o b t a i n e d t h e f o l l w i n g s i m p l e . r e l a t i o n P* 1 B c ( E ' ) <=>< ( Z e f f ) * ( H ) ( E » ) + C 2 P 2 20 w h e r e P i s t h e n e u t r i n o m o m e n t u m , E• t h e mean e x c i t a t i o n e n e r g y a n d C a c o n s t a n t . T h e i r c a l c u l a t i o n i n d i c a t e d t h a t E ' a g r e e d w i t h t h e GDR e n e r g y i n t h e l i g h t n u c l e i . On t h e o t h e r h a n d , E ' i n c r e a s e d t o 4 5 MeV i n t h e h e a v y e l e m e n t s , w h i l e t h e GDE e n e r g y i n p h o t o e x c i t a t i o n i s o n l y 13 MeV ( C A N 7 4 ) . I n t h e GBB p r o c e s s o c c u r r i n g i n muon c a p t u r e , t h e h i g h e r i s o s p i n l e v e l s (Tz=T+1) a r e e x c i t e d a n d t h e GDR e n e r g y i s e x p e c t e d t o b e l a r g e r t h a n t h a t o f t h e p h o t o - e x c i t a t i c n ( C H R 7 5 ) . A c c o r d i n g t o c a l c u l a t i o n s by N a l c i o g l u e t a l . ( N A L 7 4 ) , t h e a v e r a g e e x c i t a t i o n e n e r g y f o r t h e muon c a p t u r e i n 6 4 N i i s 28 MeV w h e r e a s f o r p h o t o - e x c i t a t i c n i t i s o n l y 17 M e V . I t i s c l e a r f r o m t h e i r c a l c u l a t i o n s t h a t t h e 1+1 e x c i t a t i o n i s s u p p r e s s e d i n t h e p h o t o - e x c i t a t i o n . T h e r e . h a v e b e e n n o e x p e r i m e n t s t o i n v e s t i g a t e t h e T+1 l e v e l e x c i t a t i o n i n muon c a p t u r e b e c a u s e n e u t r i n o s p e c t r o s c o p y i s u n f o r t u n a t e l y i m p o s s i b l e a n d t h e n e u t r o n e n e r g y s p e c t r u m f r o m t h e d e c a y o f t h e n u c l e u s g i v e s a m b i g u o u s i n f o r m a t i o n . B e r n a b e u (BER73) h a s p r o p o s e d a m o d e l w h i c h a v o i d s t h e u n c e r t a i n t y o f t h e n e u t r i n o e n e r g y i n t h e t o t a l c a p t u r e r a t e s . K h o y a m a a n d F u j i i ( K O H 7 6 , - 7 S ) a d o p t e d t h i s m o d e l a n d c a l c u l a t e d t h e t o t a l c a p t u r e r a t e s u s i n g t h e s t a t i s t i c a l m e t h o d . T h e y p e r f o r m e d n u m e r i c a l c a l c u l a t i o n s f o r 35 e l e m e n t s f r c m Z= 11 t o Z=92 a n d t h e i r p r e d i c t e d c a p t u r e r a t e s r e p r o d u c e d t h e e x p e r i m e n t a l d a t a w i t h i n 15%. . B e f o r e c o m p l e t i n g t h i s s e c t i o n we s h o u l d d i s c u s s a n i m p o r t a n t c o m p l i c a t i o n w h i c h c o n f u s e s t h e . c o m p a r i s o n o f 21 e x p e r i m e n t w i t h t h e o r y . F o r a n u c l e u s w i t h a s p i n , t h e muon i n t h e 1S c r b i t h a s i t s cwn s p i n c o u p l e d t o t h e n u c l e a r s p i n r e s u l t i n g i n t w o p o s s i b l e s t a t e s t e r m e d t h e h y p e r f i n e ( h f ) s t a t e s . F o r e x a m p l e , when a n e g a t i v e muon i s c a p t u r e d b y a p r o t o n , t h e c a p t u r e p r o b a b i l i t y d e p e n d s o n t h e m u t u a l o r i e n t a t i o n o f t h e s p i n s o f t h e t w o p a r t i c l e s . I t h a s b e e n p r e d i c t e d t h e o r e t i c a l l y t h a t t h e c a p t u r e r a t e (Bc+) f r o m t h e F=1 t r i p l e t s t a t e i s e g u a l t o 1 / s e c f o r V - x A i n t e r a c t i o n w i t h x = 1 . 2 a n d , f r o m t h e F=0 s i n g l e t s t a t e , B c ~ = 6 3 5 / s e c ( M U K 7 7 ) . The s i n g l e t s t a t e c a p t u r e r a t e w a s m e a s u r e d b y t h e C E B N - B o l c g n a g r o u p ( A I B 6 9 ) who o b t a i n e d B c ~ = 6 5 1 ± 5 7 / s e c . T h e y e m p l o y e d u l t r a p u r e g a s e o u s h y d r o g e n (8 a t m , 2 9 3 K) a s a t a r g e t . I n a s y s t e m o f p u r e h y d r o g e n , t h e m u o n - p r o t o n m u o n i c a t o m s a r e i n i t i a l l y f o r m e d i n a s t a t i s t i c a l m i x t u r e o f t r i p l e t a n d s i n g l e t s t a t e s . T h r o u g h t h e s c a t t e r i n g p r o c e s s b e t w e e n t h e m u c n i c a t o m a n d h y d r o g e n , t h e r e i s t h e r a p i d c c n v e r s i c n o f t h e m u o n i c a t o m s f r c m t h e t r i p l e t s t a t e t o t h e s i n g l e t s t a t e . F o r h y d r o g e n g a s a t 300 K , t h e c a l c u l a t e d c o n v e r s i o n t i m e i s 1 . 2 m i c r o s e c o n d s a t 0 . 5 a t m o f p r e s s u r e a n d 82 n s a t 8 atm ( M A T 7 1 ) . F o r c a p t u r e i n a l i q u i d t h e muon i s b o u n d i n a p y p m o l e c u l e a n d t h e c a p t u r e r a t e Be ( o r t h o m o l e c u l e ) i s g i v e n b y B c ( O M ) = 3 / 4 > « B c ~ + 1 / 4 « E c + E x p e r i m e n t a l l y B c ( C M ) = 4 6 0 ± 2 0 / s e c ( E A E 8 0 ) w h i c h s h o w s t h a t B c + < 1 0 0 / s e c . I f a c o m p l e x n u c l e u s h a s a n o n - z e r o n u c l e a r s p i n ( I ) , t h e c a p t u r e p r o b a b i l i t y o f a n e g a t i v e muon i n t h e 22 n u c l e u s a l s o d e p e n d s o n t h e t o t a l a n g u l a r m o m e n t a F + =I+1/2 a n d F~=I-1/2o B e r n s t e i n e t a l . ( B E R 5 8 ) c a l c u l a t e d t h i s e f f e c t f o r a m o d e l c o n s i s t i n g o f a s p i n l e s s c o r e a n d an e x t e r n a l p r o t o n w i t h o u t a l l o w i n g a c o n v e r s i o n f r o m t h e h i g h e r h f s t a t e t o t h e l o w e r h f s t a t e . B u t t h e r e i s , i n f a c t , a f a s t c o n v e r s i o n ( T E L 5 9 ) t h r o u g h t h e e j e c t i o n o f A u g e r e l e c t r o n s w h i c h i s m o r e t h a n 1 0 0 t i m e s f a s t e r t h a n t h e M l t r a n s i t i o n r a t e . T h e s e c o n v e r s i o n r a t e s w e r e c a l c u l a t e d b.y W i n s t o n (WIN63) who s h o w e d t h a t f o r h e a v y e l e m e n t s (Z>10) t h e r a t e i s s o f a s t t h a t t h e m u o n s a r e n o r m a l l y c a p t u r e d f r o m t h e l o w e s t e n e r g y s t a t e . T h e r a t e f o r v a r i o u s n u c l e i w i l l b e l i s t e d i n T a b l e I V - 6 a l o n g w i t h t h e c a p t u r e r a t e s f r o m t w c h f s t a t e s . T h e r e h a v e b e e n s e v e r a l m e a s u r e m e n t s t o d e t e r m i n e t h e c o n v e r s i o n r a t e s ( W I N 6 3 , F A V 7 0 ) . . B e c a u s e o f t h e f a s t c o n v e r s i o n , 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 i s l i m i t e d o n l y f o r l i g h t n u c l e i . S i n c e t h e e f f e c t o f t h e h f c o n v e r s i o n i s v e r y s m a l l ( < 0 . 0 1 ) i n t h e d e c a y e l e c t r o n s p e c t r u m , i t i s m u c h h a r d e r t o d e t e r m i n e t h e r a t e b y d e t e c t i n g d e c a y e l e c t r o n s t h a n b y d e t e c t i n g n e u t r o n s o r gamma r a y s ( s e e s e c t i o n I I I . G ) . O n l y f o r c h l o r i n e a n d f l u o r i n e a r e t h e r a t e s c o m p a r a b l e t o c a p t u r e r a t e s a n d t h e r e f o r e r e a d i l y o b s e r v a b l e . S o f a r , t h e c o n v e r s i o n r a t e h a s b e e n d e t e r m i n e d o n l y f o r 1 9 F b y a muon c a p t u r e e x p e r i m e n t . T h e s t a n d a r d m e t h o d i s t h e muon s p i n r e s o n a n c e m e t h o d ( M S B ) , w h i c h m e a s u r e s t h e p r e c e s s i o n d a m p i n g a n d d e t e r m i n e s t h e r e l a x a t i o n r a t e . B a v a r t e t a l . (FAV70) e m p l o y e d t h i s m e t h o d t o o b t a i n t h e c o n v e r s i o n r a t e s f o r 6 L i , 23 7 L i , 9 B e , 1 0 B a n d " B . T h e s e r e s u l t s a r e l i s t e d i n T a b l e I V - 6 . T h e p r e s e n t w o r k i s a d e t a i l e d d e s c r i p t i o n o f a n e x p e r i m e n t t o d e t e r m i n e t h e mean muon l i f e t i m e s i n c o m p l e x n u c l e i a n d muon a t o m i c c a p t u r e r a t i o s i n m e t a l l i c o x i d e s . T h e e x p e r i m e n t a l s e t - u p s a n d m e t h o d a r e d e s c r i b e d i n C h a p t e r I I . T h e d a t a a n a l y s i s i s d i s c u s s e d i n C h a p t e r I I I . , I n C h a p t e r I V , t h e l i f e t i m e r e s u l t s a n d n u c l e a r c a p t u r e r a t e s a r e r e p o r t e d i n d e t a i l . C h a p t e r V d e a l s w i t h t h e t h e o r e t i c a l a s p e c t s o f t h e a t o m i c a n d n u c l e a r muon c a p t u r e r a t e , a n d a c o m p a r i s o n o f t h e e x p e r i m e n t a l r e s u l t s w i t h t h e t h e o r i e s i s m a d e . I n C h a p t e r V I , t h e s u m m a r y o f t h i s e x p e r i m e n t i s p r e s e n t e d . 24 CHAPTER I I E x p e r i m e n t a l M e t h o d a n d S e t - u p I n t h i s c h a p t e r we s h a l l d e s c r i b e t h e e x p e r i m e n t a l m e t h o d u s e d i n t h i s w o r k . I n t h e f i r s t s e c t i o n we s h a l l d i s c u s s t h e g e n e r a l p r o c e d u r e a n d d e t a i l e d f e a t u r e s o f t h e e q u i p m e n t w i l l b e g i v e n i n t h e f o l l o w i n g s e c t i o n s . I n t h i s s e r i e s o f l i f e t i m e m e a s u r e m e n t s we e m p l o y e d muons w h i c h w e r e p r o v i d e d b y t h e s t e p p e d muon c h a n n e l (M20) a t T E I U M F . T h e beam l i n e a n d t h e c o u n t e r s e t - u p o f t h i s e x p e r i m e n t a r e s h o w n i n f i g u r e s I I - 1 a n d I I - 2 , r e s p e c t i v e l y . A s t o p p e d muon s i g n a l w h i c h w a s d e f i n e d b y a (1 , 2 , 3 , 4 , J 5 ) c o i n c i d e n c e p r o d u c e d a s t a r t s i g n a l f o r a c l o c k . , D e c a y e l e c t r o n s f r o m t h e muons w e r e d e t e c t e d b y f o u r e l e c t r o n t e l e s c o p e s : l e f t ( 5 , 6 ) , r i g h t ( 5 , 7 ) , t o p (5 , 8 ) a n d b o t t o m ( 5 , S ) , a n d t h e e l e c t r o n s i g n a l was s e n t t o t h e c l o c k a s a s t o p s i g n a l . T h e t i m e d i f f e r e n c e b e t w e e n t h e s t a r t a n d t h e s t o p s i g n a l s w a s s t o r e d i n a h i s t o g r a m b y a P D P-11/ 4 0 c o m p u t e r w h i c h i s e x t e n s i v e l y u s e d f o r MSR e x p e r i m e n t s a t TEIUMF. . . T h e r e w e r e 2 0 0 0 c h a n n e l s i n t h e h i s t o g r a m a n d t h e l i f e t i m e o f m u c n s i n a t a r g e t was o b t a i n e d b y a c h i - s q u a r e d m i n i m i z a t i o n o f t h e h i s t o g r a m . T h i s d a t a a n a l y s i s w i l l b e d i s c u s s e d i n C h a p t e r I I I . When t h e d a t a t a k i n g was s t a r t e d , t h e d e t e c t i o n s y s t e m was c a l i b r a t e d b y m e a s u r i n g t h e p o s i t i v e muon l i f e t i m e w h i c h i s k n e w n p r e c i s e l y ( B R I 7 8 ) . When t h e c o r r e c t p o s i t i v e muon l i f e t i m e . w a s o b t a i n e d a f t e r s e v e r a l r u n s , t h e 25 p o s i t i v e muon beam was s w i t c h e d t o t h e n e g a t i v e muon beam b y c h a n g i n g t h e p o l a r i t y o f m a g n e t s c f t h e M20 beam l i n e . . T h e n , a t t h e b e g i n n i n g o f n e g a t i v e muon l i f e t i m e m e a s u r e m e n t s , t h e l i f e t i m e m e a s u r e m e n t i n c a r b o n w a s m a d e . T h i s l i f e t i m e w a s u s e d a s a c a l i b r a t i o n o f t h e s y s t e m a n d , a t l e a s t , o n c e a d a y , t h e n e g a t i v e muon l i f e t i m e i n c a r b o n was m e a s u r e d i n o r d e r t o c h e c k t h e d e t e c t i o n s y s t e m . , D u r i n g t h e t w o w e e k e x p e r i m e n t ( f i r s t week f r c m 3 / 1 0 t o 7 / 1 0 , s e c o n d week f r c m 2 1 / 1 0 t o 2 8 / 1 0 1 9 7 9 ) , t h e s y s t e m , w h i c h r e p r o d u c e d t h e c o r r e c t p o s i t i v e muon l i f e t i m e , was e s t a b l i s h e d a n d t h e n e g a t i v e muon l i f e t i m e s i n more t h a n 80 d i f f e r e n t t a r g e t s w e r e m e a s u r e d . I I . A Muon B e a m L i n e T h e s e r i e s c f m e a s u r e m e n t s o f muon l i f e t i m e s was p e r f o r m e d o n t h e s t o p p e d muon c h a n n e l (M20) a t T E I U M F . T h r o u g h o u t t h e s e e x p e r i m e n t s , t h e p r o t o n c u r r e n t was 20 m i c r o - a m p e r e s a t 5 0 0 M e V . T h e p r c t o n beam s t r u c k a p i o n p r o d u c t i o n t a r g e t , T 2 , w h i c h c o n s i s t e d o f a w a t e r c o o l e d b e r y l l i u m s t r i p , 10 cm l o n g i n t h e beam d i r e c t i o n , a n d 5 mm by 15 mm i n c r o s s s e c t i o n . . S i n c e b e r y l l i u m t a r g e t s h a v e s h o w n a r e l a t i v e l y h i g h p r o d u c t i o n r a t e f o r n e g a t i v e p i o n s a n d h a v e a l o w e l e c t r o n c o n t a m i n a t i o n i n t h e p i o n b e a m , s u c h a t a r g e t was s p e c i a l l y s e l e c t e d f o r t h i s l i f e t i m e 26 Figure I I - l , The M20 beam l i n e . 27 e x p e r i m e n t . T h e M20 s e c o n d a r y t e a m l i n e f o c u s e d t h e beam w i t h a s e r i e s c f g u a d r u p o l e m a g n e t s ( Q 1 - Q 9 ) a n d t h e . m o m e n t u m was s e t w i t h t w o b e n d i n g m a g n e t s ( B 1 , E 2 ) . T h e r e w e r e t h r e e d i f f e r e n t m o d e s f o r a p o s i t i v e muon b e a m : c l o u d , c o n v e n t i o n a l a n d s u r f a c e m o d e s . On t h e o t h e r h a n d , o n l y t w o m o d e s , c l o u d a n d c o n v e n t i o n a l m o d e s , w e r e a v a i l a b l e f o r a n e g a t i v e muon t e a m . T h e t h r e e m c d e s a r e d e f i n e d a s f o l l o w s . T h e c l o u d m u o n s a r e p r o d u c e d b y a d e c a y f r o m t h e c l o u d o f p i o n s b e t w e e n t h e T 2 t a r g e t a n d t h e f i r s t b e n d i n g m a g n e t B 1 . F o r c o n v e n t i o n a l muons a f r a c t i o n o f t h e p i o n s w i t h a p a r t i c u l a r momentum s e t b y B I a r e a l l o w e d t o u n d e r g o t h e i n - f l i g h t d e c a y b e t w e e n B1 a n d B 2 , a n d t h e m u o n s a r e s e l e c t e d b y t h e B2 m a g n e t . T h e muons w h i c h d e c a y i n t o t h e same ( o p p o s i t e ) d i r e c t i o n a s ( t o ) t h e p i o n beam d i r e c t i o n a r e c a l l e d f o r w a r d ( b a c k w a r d ) m u o n s w h i c h h a v e l a r g e r ( s m a l l e r ) momentum t h a n t h e p i o n b e a m . S u r f a c e muons a r e p r o d u c e d f r o m t h e d e c a y o f p i o n s a t r e s t o n t h e s u r f a c e o f t h e T 2 t a r g e t . A s n e g a t i v e p i o n s a r e a b s o r b e d c n n u c l e i w h e n t h e y c o m e t o r e s t , t h e y do n o t d e c a y i n t o muons a n d s o t h i s mode i s p o s s i b l e f o r p o s i t i v e m u o n s o n l y . T h e e n e r g y o f s u r f a c e m u o n s i s v e r y l o w ( 4 M e V , 29 M e V / c ) a n d s o t h e y s t o p i n v e r y t h i n t a r g e t s . I n t h i s e x p e r i m e n t , b a c k w a r d muons w e r e e m p l o y e d . . T h e s e m u o n s w e r e s e l e c t e d b y s e t t i n g t h e s e c c n d b e n d i n g m a g n e t f o r t h e b a c k w a r d muon m o m e n t u m . S i n c e a momentum o f 170 M e V / c f o r t h e f i r s t b e n d i n g m a g n e t was f i x e d , t h e 28 e x p e c t e d b a c k w a r d muon momentum was 87 M e V / c . T h i s mode was c h o s e n f o r t h e f o l l o w i n g r e a s o n s . F i r s t , i t h a d v e r y l o w e l e c t r o n c o n t a m i n a t i o n i n t h e n e g a t i v e muon beam (8%) c o m p a r e d w i t h o t h e r modes ( > 8 0 % ) . S e c o n d l y , t h e b a c k g r o u n d a s s o c i a t e d w i t h p i o u s was r e d u c e d . When t h e n e g a t i v e p i o n s a r e s t o p p e d i n a d e g r a d e r , t h e p i o n s a r e a b s o r b e d i n t h e n u c l e u s p r o d u c i n g n e u t r o n s , p r o t o n s , a n d gammas w h i c h c o n t r i b u t e s i g n i f i c a n t l y t o t h e b a c k g r o u n d . T h i r d l y , m u o n s w i t h l e w momentum w e r e s t o p p e d e a s i l y i n t h e t a r g e t s u s i n g d e g r a d e r s w h i c h w e r e t h i n , a n i m p o r t a n t a d v a n t a g e . T h e t i m e o f f l i g h t s p e c t r u m (TOF) o f t h e n e g a t i v e muon beam i s s h o w n i n f i g u r e I I - 3 . S i n c e t h i s TOF s p e c t r u m was t a k e n w i t h t h e p u l s e h e i g h t r e j e c t i o n o f c o u n t e r S 2 , t h e e l e c t r o n c o n t a m i n a t i o n (<2%) was much l o w e r t h a n t h a t o f t h e b e a m . A l t h o u g h i n t h e b a c k w a r d muon beam t h e r e w e r e m o s t l y m u o n s a n d e l e c t r o n s , a CH2 d e g r a d e r 2 . 5 cm i n t h i c k n e s s was p l a c e d i n t h e beam t o r e d u c e t h e e n e r g y o f t h e muons a n d t o r e m o v e t h e v e r y f e w p i o n s i n t h e b e a m . W i t h a 2 . 5 cm d i a m e t e r l e a d c o l l i m a t o r , t h e i n c o m i n g n e g a t i v e muon beam r a t e d e f i n e d b y a ( 1 , 2 , 3 ) c o i n c i d e n c e was n e a r l y 1 0 0 0 / s e c f o r a 20 m i c r o - a m p e r e p r o t o n c u r r e n t o n t h e T2 t a r g e t . 29 M20 i Bedim C o n c r e t e • W a l l V a r i a b l e C H 2 D e g r a d e r S 1 wmnm^imnim L e a d Shielding V////////A \ V////////A & C o l l i m a t o r S 7 ( R i g h t ) S 6 ( L e f t ) M i l M e t a l S h i e l d i n g — S 4 Decay Electron Counters s s a (Top) S 9 ( Bottom) Figure II-2, Experimental set-up and decay electron counters. 30 140 x10 i r i r 100 yu Peak O u 50 0 0 _!_L X 102 -40 e Peak W i t h o u t S 4 V e t o . W i t h S 4 V e t o • •. • • • . . i• 10 20 30 4 0 CHANNEL NUMBERS 50 Figure II-3, Time of f l i g h t spectrum of incident beam and-stopped muon sign a l s . 31 I I . B S c i n t i l l a t i o n C o u n t e r s a n d G e o m e t r y I n t h i s e x p e r i m e n t , n i n e c o u n t e r s w e r e u s e d w h o s e d i m e n s i o n s a n d e f f i c i e n c i e s a r e g i v e n i n T a b l e I I - 1 . T h e s e c o u n t e r s w e r e made c f a p l a s t i c s c i n t i l l a t o r ( N E 1 1 0 made by N u c l e a r E n t e r p r i s e s L t d . ) a n d v i e w e d b y RCA 8 5 7 5 p h o t o t u b e s . . S i n c e a l l i n f o r m a t i o n was s u p p l i e d f r o m p l a s t i c c o u n t e r s , much c a r e was t a k e n i n t h e i r d e s i g n a n d u s e . I n p a r t i c u l a r : S 1 : C o u n t e r S1 was b i g e n o u g h t o c o v e r t h e b e a m c o l l i m a t o r . S 2 : C o u n t e r S 2 was made t h i c k e r i n o r d e r t o d i s t i n g u i s h e l e c t r o n s , m u o n s , s l o w m u o n s a n d d o u b l e m u o n s b y p u l s e h e i g h t a n a l y s i s . S l o w a n d d o u b l e muons s h o w e d h i g h e r p u l s e h e i g h t t h a n o r d i n a r y m u o n s . E l e c t r o n s h a d l i t t l e e n e r g y l o s s i n t h e p l a s t i c s c i n t i l l a t o r a n d t h e p u l s e h e i g h t s w e r e l o w e r t h a n t h e m u o n ' s p u l s e h e i g h t s . The t y p i c a l p u l s e h e i g h t f o r o r d i n a r y m u o n s r a n g e d f r o m 2 5 0 t o 6 0 0 mV a n d t h e p u l s e h e i g h t f o r e l e c t r o n s f r o m 30 t o 150 mV. A p u l s e h e i g h t l a r g e r t h a n 6 0 0 mV w a s c o n s i d e r e d a s a d o u b l e muon o r a s l o w muon w h i c h s t o p p e d i n S2 a n d t h e e v e n t was r e j e c t e d . C o u n t e r S 2 was p l a c e d i n f r o n t o f t h e v a r i a b l e l e a d c o l l i m a t o r i n o r d e r t o a v o i d i t b e i n g v i s i b l e t o e l e c t r o n t e l e s c o p e s s o t h a t t h i s c o u n t e r d i d n o t c o n t r i b u t e a s a c a r b o n b a c k g r o u n d s o u r c e . . S 3 : C o u n t e r S 3 was t h e d e f i n i n g c o u n t e r o f m u o n s a n d was 32 v i s i b l e t o t h e e l e c t r o n t e l e s c o p e s . When n e g a t i v e m u c n s s t o p p e d i n s i d e c o u n t e r S 3 , t h e s e w e r e c o u n t e d a s g o o d mucn e v e n t s a n d t h i s c a u s e d c a r b o n b a c k g r o u n d e v e n t s i n t h e h i s t o g r a m . I n o r d e r t o m i n i m i z e t h e b a c k g r o u n d , t h e c o u n t e r S 3 was made o f 0 . 0 7 cm t h i c k n e s s p l a s t i c s c i n t i l l a t o r a n d c o v e r e d w i t h o n l y 0 . 0 0 1 cm t h i c k n e s s a l u m i n u m f o i l . S 4 : C o u n t e r S4 was b i g e n o u g h t o c o v e r a n y p a r t i c l e s w h i c h came t h r o u g h t h e t a r g e t a n d was u s e d a s a v e t o c o u n t e r . S 5 : C o u n t e r S5 h a d a c y l i n d r i c a l s h a p e w i t h 0 . 3 cm t h i c k n e s s w a l l , 20 cm l o n g a n d 20 cm i n d i a m e t e r . . I t was u s e d i n a l l f o u r e l e c t r o n t e l e s c o p e c o i n c i d e n c e s , a l s o i t w a s a v e t o c o u n t e r u s e d t o r e j e c t t h e s c a t t e r e d p a r t i c l e s f r o m t h e beam w h i c h s e t o f f t o w a r d s t h e e l e c t r o n t e l e s c o p e s . T h e i d e a o f u s i n g a c y l i n d r i c a l c o u n t e r S 5 was t o m i n i m i z e a n y i m b a l a n c e b e t w e e n t h e e l e c t r o n t e l e s c o p e s a n d t o s a v e c o u n t e r s . S 6 - S 9 : C o u n t e r s S 6 , S 7 , S 8 a n d £9 w e r e made o f i d e n t i c a l s h a p e ( s e e T a b l e I I - l ) i n o r d e r t o a v c i d a n y i m b a l a n c e i n t h e e l e c t r o n t e l e s c o p e s . A l s o , t h e y w e r e v i e w e d by new p h o t o t u b e s t o g e t t h e same c o u n t e r e f f i c i e n c i e s . T h e c o n f i g u r a t i o n o f t h e s e c o u n t e r s i s s h o w n i n f i g u r e I I - 2 . T h i s s e t - u p h a d 6 0 % s o l i d a n g l e f o r a p o i n t s o u r c e a t t h e c e n t e r o f t h e c y l i n d r i c a l c o u n t e r S 5 . D u r i n g t h e tvwo w e e k e x p e r i m e n t , t h e r e w a s a 3 3 T a b l e I I - 1 C o u n t e r G e o m e t r y a n d E f f i c i e n c y S y m b o l (Name) S i z e ( cm) E f f i c i e n c y 1 S1 10x 1 0 x 0 . 6 9 9 , 9 % S 2 ( t h i c k c o u n t e r ) 6 . 4 ( d i a ) x 1 . 2 9 9 . 9 S3 ( d e f i n i n g c o u n t e r ) 5 . 0 ( d i a ) x O . 07 9 9 . 6 S4 ( v e t o c o u n t e r ) 3 0 x 4 5 x 1 . 2 9 9 . 9 S 5 ( c y l i n d r i c a l c o u n t e r ) 20 ( d i a ) x 0 . 3 9 9 . 8 S 6 ( l e f t E c o u n t e r ) 2 0 x 2 0 x 0 . 6 9 9 . 9 S7 ( r i g h t E c o u n t e r ) 2 0 x 2 0 x 0 . 6 9 9 . 9 S8 ( t o p E c o u n t e r ) 2 0 x 2 0 x 0 . 6 9 9 . 9 S9 ( B o t t o m E C o u n t e r ) 2 0 X 2 0 X 0 . 6 9 9 . 9 1) T h e c o u n t e r e f f i c i e n c y t e s t was made b y u s i n g a Ru e l e c t r o n s o u r c e . 34 p o s s i b i l i t y c f c o u n t e r o r e l e c t r o n i c s f a i l u r e s i n c l u d i n g d r i f t i n g o f t h e h i g h v o l t a g e , s o c o u n t i n g r a t e s o f i m p o r t a n t c o i n c i d e n c e s a n d r e j e c t i o n s w e r e m o n i t o r e d o n v i s u a l s c a l e r s a n d p r i n t e d o u t a s a r e c o r d a t t h e e n d o f e v e r y r u n . I I . C Mu M e t a l S h i e l d i n g o f F i e l d a n d C o l l i m a t o r F c r t h e c a s e o f t h e l i f e t i m e m e a s u r e m e n t o f a p o s i t i v e muon w i t h a h i g h p o l a r i z a t i o n , t h e muon p r e c e s s e d i n t h e t a r g e t b e c a u s e c f t h e m a g n e t i c f i e l d ( a b o u t 1 G a u s s ) , w h i c h was c r e a t e d by t h e e a r t h a s w e l l a s t h e l e a k a g e o f m a g n e t i c f l u x f r o m t h e beam l i n e m a g n e t s n e a r t h e t a r g e t . I n o r d e r t o r e d u c e t h e m a g n e t i c f i e l d . , t w o t h i n Mu m e t a l c y l i n d e r s w e r e u s e d i n s i d e a n d o u t s i d e o f t h e c o u n t e r S 5 . . W i t h t h e s e c y l i n d e r s , t h e m a g n e t i c f i e l d a t t h e t a r g e t p o s i t i o n was d o w n t c 0 . 0 5 G . . E v e n w i t h t h i s s m a l l m a g n e t i c f i e l d , t h e p r e c e s s i o n o f m u o n s a f f e c t e d t h e muon l i f e t i m e a n d t h e c o r r e c t l i f e t i m e was a c h i e v e d o n l y b y a v e r a g i n g t h e f o u r e l e c t r o n t e l e s c o p e s . T h i s w i l l b e d i s c u s s e d i n s e c t i o n I I I - E . The M20 beam l i n e f o r m e d a b r o a d beam s p o t 10 cm i n d i a m e t e r . I n o r d e r t o c o l l i m a t e t h e b e a m , a l e a d c o l l i m a t o r 14 cm i n l e n g t h a n d 3 . 8 cm i n d i a m e t e r was u s e d b e t w e e n c o u n t e r s S1 a n d S 2 , a n d a n o t h e r l e a d c o l l i m a t e r (L=7 cm d = 2 . 5 cm) was p l a c e d b e t w e e n c o u n t e r s S 2 a n d S 3 . 35 I I . D T a r g e t s I n t h i s e x p e r i m e n t , t h e r e w e r e 3 l i q u i d , 27 m e t a l , a n d 9 p c w d e r t a r g e t s c o m p o s e d o f a s i n g l e e l e m e n t t o g e t h e r w i t h t a r g e t s o f 29 c h e m i c a l c o m p o u n d s . a l s o , t h e r e w e r e 2 t a r g e t s m i x e d i n A g a r . A l l t a r g e t i n f o r m a t i o n i s l i s t e d i n T a b l e I I - 2 . H a l f o f t h e t a r g e t s w e r e b o r r o w e d f r o m f i v e g r o u p s : UBC C h e m i s t r y , D r J o h s o n ' s g r o u p , D r W a r r e n ' s g r o u p , UVIC g r o u p a n d t h e T o k y o MSE g r o u p . T h e d i a m e t e r o f a s t a n d a r d t a r g e t c o n t a i n e r w a s 9.5 cm a n d t h e t h i c k n e s s v a r i e d w i t h t h e d e n s i t y o f t a r g e t m a t e r i a l . . S i n c e t h e l e a d c o l l i m a t o r w h i c h d e f i n e d t h e beam was 2.5 cm i n d i a m e t e r , t h e s t a n d a r d s i z e o f t h e t a r g e t s was l a r g e e n o u g h t o c o v e r t h e beam s p o t . . W i n d o w s a t b o t h e n d s o f t h e p l a s t i c ( m e t a l ) c o n t a i n e r w e r e made o f t h i n m y l a r ( s t a i n l e s s ) s h e e t s 0.00 3 cm i n t h i c k n e s s . The m a t e r i a l o f t h e c o n t a i n e r w a s c h o s e n c a r e f u l l y s o t h a t a n e g a t i v e muon l i f e t i m e i n t h e m a t e r i a l was q u i t e d i f f e r e n t f r o m t h a t i n t h e t a r g e t . When i t was e x p e n s i v e o r d i f f i c u l t t o g e t a t a r g e t i n a s i m p l e s u b s t a n c e f o r m , c h e m i c a l c o m p o u n d s w h i c h h a d a c o m b i n a t i o n o f s m a l l Z a n d l a r g e Z w e r e c h o s e n . F o r a d e c a y e l e c t r o n s p e c t r u m o f n e g a t i v e m u c n s i n s u c h a c h e m i c a l c o m p o u n d , s h o r t ( l a r g e Z) a n d l o n g ( s m a l l Z) l i f e t i m e c o m p o n e n t s w e r e e a s i l y s e p a r a t e d b y a c h i - s q u a r e d m i n i m i z a t i o n . S i n c e t h e i 8 0 t a r g e t was made i n A g a r f o r m , a 1 6 0 t a r g e t i n t h e same f o r m was u s e d i n o r d e r t o c o m p a r e t h e 36 T a b l e 1 1 - 2 ( 1 ) L i s t o f T a r g e t s a n d T h e i r F o r m z E l e m e n t - F o r m C o n t a i n e r S i z e ( c m ) 1 O w n e r 2 ( I s o t o p e R a t i o ) M a t e r i a l 3 L i - 6 ( 9 5 .6%) P o w d e r SS 7 . 2 D x 9 . 5 T I N A L i - 7 ( 9 8 .2%) P o w d e r SS 7 . 2 D x 9 . 5 TINA 4 B e P l a t e N i p l a t e d 1 3 x 1 3 x 0 . 7 UVIC 5 B - 10 ( 9 6 . 2%) P o w d e r B r a s s 6 D x 1 . 3 T I N A B - 1 1 (9 7.25E) P o w d e r B r a s s 6 D x 1 . 3 T I N A 6 C - 1 2 ( N a t u r a l ) P l a t e 1 0 x 1 0 x 2 TINA C - 1 3 ( 9 9 . 9 % ) P o w d e r B r a s s 2 . 5 D x 5 J o h n s o n 7 N L i q u i d SS 7 . 5 D X 1 5 T I N A 8 0 - 1 6 (H20) W a t e r B r a s s 9 . 5 D x 5 TINA 0 - 1 6 (H20) A g a r 5 x 5 x 1 J c h n s o n 0 - 1 8 ( 9 8 . 5%H20) A g a r 5 x 5 x 1 J o h n s o n 9 F - - L i F P o w d e r B r a s s 9 . 5 D x 5 TINA - - C 2 F 4 P l a t e 1 3 x 1 3 x 1 . 3 T I N A — C a F 2 P o w d e r P l a s t i c 9 . 5 D x 5 TINA - - P b F P o w d e r P l a s t i c 9 . 5 D x 4 TINA 11 Na Red P l a s t i c 9 . 5 D x 7 . 6 T I N A 12 Mg R o d 3 . 8 D X 7 . 6 TI NA 13 A l P l a t e 1 0 x 1 0 x 2 TINA 14 S i G r a n u l a r P l a s t i c 9 . 5 D x 2 . 5 CHEM 15 P P o w d e r P l a s t i c 9 . 5 D x 3 . 8 TINA 16 S P o w d e r P l a s t i c 9 . 5 D x 3 . 8 T I N A 17 C l — C C 1 4 L i q u i d P l a s t i c 8 x 8 x 5 CHEM 19 K S t i c k P l a s t i c 9 . 5 D x 7 . 6 T I N A 20 C a G r a n u l a r P l a s t i c 9 . 5 D x 5 . 0 T I N A 22 T i P l a t e 1 0 x 8 x 0 . 5 T I N A 23 V D i s k 5 x 4 x 0 . 5 U V I C 24 c r G r a n u l a r P l a s t i c 6 . 0 D x 1 . 5 CHEM 2 5 M n — M n 0 2 P o w d e r P l a s t i c 9 . 5 D x 2 . 5 T I N A 26 F e P l a t e 7 x 7 x 0 . 5 TOKYO 27 C o S t i c k 0 . 5 D x 5 . 0 TOKYO 28 N i P l a t e 5 D x 1 . 0 TOKYO 29 C u P l a t e 1 0 x 1 0 x 0 . 5 TOKYO 30 Z n P o w d e r 6 . 5 D X 7 . 5 CHEM 3 2 G e — G e 0 2 P o w d e r P l a s t i c 6 . 0 D X 1. 4 W a r r e n 3 5 B r — N H 4 E r P o w d e r P l a s t i c 9 . 5 D X 5 TINA 40 Z r P l a t e 6 x 6 x 0 . 7 TOKYO 41 Nb P l a t e 1 0 x 8 x 0 . 5 T I N A 42 Mo P l a t e 8 x 1 0 x 0 . 2 TOKYO 47 Ag P l a t e 5 x 5 x 0 . 5 TOKYO 48 C d P l a t e 5 x 5 x 0 . 5 TOKYO 49 I n P l a t e 5 x 5 x 0 . 5 TOKYO 50 S n P l a t e 13x 8 x 0 . 5 TINA 37 T a b l e I I - 2 ( 2 ) L i s t o f T a r g e t s a n d T h e i r F o r m z E l e m e n t F o r m C o n t a i n e r S i z e (cm) 1 O w n e r 2 ( I s o t o p e E a t i o ) M a t e r i a l 53 I P o w d e r P l a s t i c 9 . 5 D x 2 . 5 T I N A 56 B a — B a O P o w d e r P l a s t i c 9.5DX2 - 5 CHEM 6 0 N d - - N d 0 P c w d e r P l a s t i c 9 . 5 D x 2 . 5 CHEM 64 G d S t i c k 0 . 5 D x 5 TOKYO 66 D y S t i c k 0 . 5 D x 5 TOKYO 68 E r S t i c k 0 . 5 D x 5 TOKYO 74 W P o w d e r P l a s t i c 6 D x 1 . 4 CHEM 80 H g — H g O P o w d e r P l a s t i c 9 . 5 D x 2 . 5 TOKYO 82 Pb p l a t e 1 0 x 8 x 0 . 2 TINA 83 B i p l a t e 1 0 x 8 x 0 . 5 T I N A * i O t h e r o x i d e t a r g e t s f o r muon a t o m i c c a p t u r e e x p e r i m e n t 6 CG2 ( D r y I c e ) S c l i d 1 0 x 1 0 x 2 0 CHEM 1 1 N a 2 0 2 P o w d e r P l a s t i c 9 . 5 D x 2 . 5 CHEM 12 MgO P o w d e r P l a s t i c 9 . 5 D X 1 0 W a r r e n 1 3 A 1 2 0 3 P c w d e r P l a s t i c 9 . 5 D x 2 . 5 CHEM 14 S i O 2 P c w d e r P l a s t i c 9 . 5 D x 2 . 5 W a r r e n 1 5 P 2 0 5 P o w d e r P l a s t i c 9 . 5 D x 2 . 5 CHEM 20 C a (GH) 2 P c w d e r P l a s t i c 9 . 5 D X 2 . 5 W a r r e n 22 T i 0 2 P o w d e r P l a s t i c 9 . 5 D X 2 . 5 W a r r e n 24 C r 2 0 3 P o w d e r P l a s t i c 9 . 5 D x 2 » 5 TINA C r 0 3 P c w d e r P l a s t i c 9 . 5 D X 2 . 5 CHEM 29 CuO P o w d e r E l a s t i c 9 . 5 D x 2 . 5 CHEM 30 ZnO P o w d e r P l a s t i c S . 5 D X 2 . 5 CHEM 32 G e o P c w d e r P l a s t i c 6 . 0 D X 1 . 3 W a r r e n 4 8 CdO P o w d e r P l a s t i c 9 . 5 D x 2 . 5 CHEM 50 S n 0 2 P o w d e r P l a s t i c S . 5 D x 2 . 5 CHEM 82 P b 0 2 P c w d e r P l a s t i c 9 . 5 D X 2 . 5 CHEM P b 3 0 4 P o w d e r P l a s t i c 9 . 5 D X 2 . 5 TOKYO 1) D = d i a m e t e r 2) O w n e r , g r o u p a n d g r o u p l e a d e r : T I N A - - U B C P h y s i c s D e p t . , ( D . F . M e a s d a y ) C H E M — U B C C h e m i s t r y MSB G r o u p , ( D. W a l k e r a n d D. F l e m i n g ) U V I C — U . o f V i c t o r i a a n d T E I U M F , ( M . P e a r c e ) T O K Y O - U . c f T o k y o MSE G r o u p , ( T . Y a m a z a k i ) J o h n s o n R . R . - - U B C P i o n S c a t t e r i n g G r o u p L e a d e r W a r r e n J . B . — U B C Muon X - r a y G r o u p L e a d e r 38 l i f e t i m e s i n 1 6 o a n d * a 0 t a r g e t s o f s i m i l a r c o m p o s i t i o n . A l i q u i d n i t r o g e n t a r g e t c o n t a i n e r was s p e c i a l l y d e s i g n e d t o f i t t h e c y l i n d r i c a l c o u n t e r S 5 . I t was m a d e . o f s t a i n l e s s s t e e l t o r e d u c e t h e h e a t c o n d u c t i o n l o s s o f l i q u i d n i t r o g e n . I t h a d a v a c u u m s p a c e b e t w e e n t h e i n n e r a n d t h e o u t e r c o n t a i n e r . The t w o c o n t a i n e r s h a d t h i n w i n d o w s made o f 0 . 0 1 cm t h i c k n e s s s t a i n l e s s s t e e l i n o r d e r t o r e d u c e m u o n s s t o p p e d i n t h e w i n d o w s . T h e e n d s o f t h e t w o c o n t a i n e r s w e r e made o f 0 . 3 cm t h i c k n e s s s t a i n l e s s s t e e l . T h i s c o n t a i n e r was a b l e t o k e e p l i g u i d n i t r o g e n f o r a t h r e e h o u r e x p e r i m e n t . A l l t a r g e t s w e r e p l a c e d o n t h e t a r g e t h o l d e r a t t h e c e n t e r o f c o u n t e r S 5 . . S i n c e t h e t a r g e t h o l d e r w a s o n e o f t h e b a c k g r o u n d s o u r c e s , a p l a s t i c h o l d e r was u s e d f o r t h e p l a s t i c c o n t a i n e r a n d a m e t a l h o l d e r f o r t h e m e t a l c o n t a i n e r . H e n c e t h e h o l d e r a n d t h e t a r g e t c o n t a i n e r w e r e c o u n t e d a s t h e s a m e b a c k g r o u n d s o u r c e . I n l o n g l i f e t i m e m e a s u r e m e n t s f o r t h e l i g h t e l e m e n t s , i t was i m p o r t a n t t o know t h e c a r b o n b a c k g r o u n d i n t h e h i s t o g r a m . I n o r d e r t o e s t i m a t e t h e b a c k g r o u n d , dummy t a r g e t s w h i c h c o n s i s t e d o f b r a s s c r c o p p e r w i t h t h e s a m e s h a p e a n d t h i c k n e s s w e r e u s e d f o r b o r o n a n d * 3 C t a r g e t s . . I n t h e c a s e c f b e r y l l i u m a n d l i t h i u m t a r g e t s , c o p p e r p l a t e s w i t h t h e same t h i c k n e s s a n d s i z e w e r e u s e d f c r t h e b a c k g r o u n d r u n s . T h e e m p t y l i q u i d n i t r o g e n t a r g e t was u s e d f o r t h e b a c k g r o u n d r u n s o f t h e n i t r o g e n a n d o x y g e n t a r g e t s . I n t h e c a s e o f t h e a t o m i c c a p t u r e e x p e r i m e n t s , 39 m e t a l l i c o x i d e t a r g e t s w e r e e n c l o s e d i n p l a s t i c c o n t a i n e r s w i t h t h e s t a n d a r d s i z e m e n t i o n e d a b o v e . T h e c a r b o n b a c k g r o u n d o f t h e s e t a r g e t s was e s t i m a t e d f r o m l i f e t i m e m e a s u r e m e n t s o f h e a v y e l e m e n t s ( f o r i n s t a n c e Zn p o w d e r , S p o w d e r , e t c ) i n t h e p l a s t i c c o n t a i n e r . I I . E E l e c t r o n i c s a n d T i m i n g C o n s i d e r a t i o n I n o u r l i f e t i m e e x p e r i m e n t , t h e MSE d a t a t a k i n g s y s t e m was e m p l o y e d . T h e s y s t e m was e x p l a i n e d i n d e t a i l by G a r n e r (GAK79) . . T h e s i m p l i f i e d d a t a t a k i n g s y s t e m i s s h o w n i n f i g u r e I I - 4 . . T h e m a i n f u n c t i o n s o f t h e s y s t e m a r e d e s c r i b e d a s f o l l o w s 1. 2. muon l c g i c e l e c t r o n l o g i c i d e n t i f y m u o n s s t o p p e d i n a t a r g e t a n d s e n d s t a r t s i g n a l s t o a c l o c k , d e t e r m i n e a g o o d e l e c t r o n a s s o c i a t e d w i t h t h e s t o p p e d muon a n d s e n d a s t o p s i g n a l t o t h e c l o c k . r e j e c t i o n l c g i c - f i n d a n y e v e n t w h i c h s a t i s f i e s t h e r e j e c t i o n l o g i c , 4 . c l o c k 5 . . C AM AC 6. . MBD P D P-11/ 4 0 d e t e r m i n e a t i m e i n t e r v a l b e t w e e n t h e s t a r t a n d t h e s t o p s i g n a l s , s t o r e a l l i n f o r m a t i o n n e e d e d f o r p r o c e s s i n g d a t a a n d s e n d a LAM s i g n a l t o a c t i v a t e a M i c r o p r o g r a m m e d B r a n c h D r i v e r ( M B D ) , c o n t r o l d a t a t a k i n g s y s t e m , r e a d a l l i n f o r m a t i o n s t o r e d i n CAMAC a n d s e n d t h e i n f o r m a t i o n t o P D P - 1 1 / 4 0 , p r o c e s s d a t a s t o r e d i n t h e MBD, r e c o r d d a t a o n a d i s k f i l e a n d r e n e w M U O N C O U N T E R S S1 S2 S3 S 4 ELECTRON C O U N T E R S S 5 S 6 S7 S 8 S9 UJ _ i m < o M 2 0 EXPERIMENT AREA M U O N L O G I C M U G A T E E L E C T R O N L O G I C L R _ L _ _ i _ 2 N D M U > 2ND E R E J E C T I O N ^ 4 * START CLOCK STOP ' h MUGATE C A M A C L R T B EJECTION A T L A M & DATA CLEAR GRAPHIC D I S P L A Y DATA MBD-11 PDP-11/40 D A T A D I S K M S R C O U N T I N G R O O M Figure II-4, Simplified MSR data taking system. o 4 1 h i s t o g r a m s o n t h e g r a p h i c t e r m i n a l , 8 . m a g n e t i c t a p e - a t t h e e n d o f e x p e r i m e n t , t r a n s f e r d a t a f r o m t h e d i s k t o t a p e t o k e e p i t p e r m a n e n t l y a n d t c a n a l y z e i t o f f l i n e . F i g u r e I I - 5 s h o w s a s c h e m a t i c s o f t h e e l e c t r o n i c s f o r t h e m u o n , t h e e l e c t r o n a n d t h e r e j e c t i o n l o g i c s . E q u i p m e n t n a m e s a n d m e a n i n g s o f s y m b o l s a r e l i s t e d i n T a b l e I I - 3 . I n f i g u r e I I - 6 , t i m i n g s a n d d e f i n i t i o n s o f e v e n t s a r e e x p l a i n e d . I n c i d e n t p a r t i c l e s w e r e d e t e r m i n e d b y a ( 1 , 2 , 3 ) c o i n c i d e n c e a n d s t o p p e d m u o n s i n t h e t a r g e t by a ( 1 / 2 , 3 , 4 , 5 ) (=M) c o i n c i d e n c e , w h e r e . 4 ( 5 ) m e a n s a n a n t i - c o i n c i d e n c e o f c o u n t e r S 4 ( S 5 ) . T h e s t o p p e d muon s i g n a l o p e n e d a muon g a t e ( G I ) o f a p i l e - u p g a t e g e n e r a t o r (PUG) w h i c h was d e a l i n g w i t h 2 n d - m u c n s a n d p r e - m u o n s w i t h i n 3 2 ( 1 6 ) m i c r o s e c o n d s f o r a l o n g ( s h o r t ) l i f e t i m e m e a s u r e m e n t . I f t h e r e w e r e n o p r e - m u o n s ( G J ) ; n o p u l s e h e i g h t r e j e c t i o n s ( G 2 ) , n o MBD b u s y s i g n a l s (MEjD) a n d n o p r o t e c t i o n g a t e s (GJ) , a g o o d muon s i g n a l (M , G J ,P2, MBD , G 6 ) was s e n t t o a g a t e g e n e r a t o r t o p r o d u c e a n o t h e r muon g a t e ( G 4 ) . Two muon g a t e s , G1 a n d G 4 , w e r e ; t h e s a m e i f t h e r e was a g o o d muon e v e n t . T h e G1 g a t e was a l w a y s c r e a t e d w h e n e v e r m u o n s s t o p p e d i n a t a r g e t a n d , i f t h e r e was a 2 n d - m u o n , t h e g a t e was s t r e t c h e d b y t h e s a m e l e n g t h a s t h e o r i g i n a l muon g a t e l e n g t h (32 c r 16 m i c r o s e c o n d s ) . I n t h i s w a y , t h e G l g a t e k e p t t r a c k o f t h e s t o p p e d m u o n s , w h i l e t h e c o m p u t e r was p r o c e s s i n g d a t a , a n d made s u r e t h e r e w e r e n o p r e - m u o n s b e f o r e a c c e p t i n g t h e n e x t g o o d m u c n s . S i n c e t h e G2 g a t e w a s c r e a t e d o n l y by a g o o d T a b l e I I - 3 M e a n i n g s o f S y m b o l s i n L o g i c D i a g r a m S y m b o l Name M o d e l —'D'OuD— D e l a y D L e a d i n g E d g e D i s c r i m i n a t o r L E S - 6 2 1 B L DL(DH) L o w e r ( H i g h e r ) D i s c , l e v e l L B S - 6 2 1 B L C C o n s t a n t F r a c t i o n D i s c r i m i n a t o r O R T E C - E G G 9 3 4 C O I C o i n c i d e n c e L o g i c L E S - 4 6 5 F L o g i c F a n - I n a n d F a n - O u t L B S - 4 2 9 L F L i n e a r F a n - I n a n d F a n - O u t L E S - 4 2 8 F PUG P i l e Up G a t e G e n e r a t o r E G G - G P 1 0 0 / N L GG G a t e G e n e r a t o r L E S - 2 2 2 S 1 - S 9 C o u n t e r Name i n T a b l e I I - 1 —X) a n t i c o i n c i d e n c e o f L o g i c N 0—• I n v e r t e d O u t p u t PH P u l s e H e i g h t R e j e c t i o n SAW Saw E l e c t r o n w i t h o u t C o i n c i d e n c e o f Muon G a t e I N C I n c i d e n t M u c n ( 1 , 2 , 3 ) ST W i t h A n t i - C o i n c i d e n c e ( 1 , 2 , 3 , 4 , 5 ) G O r d i n a r y G a t e f r o m PUG o r GG P P i l e Up G a t e f r o m PUG A 1 - A 4 T e l e s c o p e I d e n t i f i c a t i o n I n p u t 43 R E S E T C 2 1 2 C L O C K START PATTERN UNIT GATE C 2 1 2 REJECTION C 2 1 2 C 2 1 2 STROBO C L O C K STOP Figure II-5, Electronic logic. 44 (1) Good e v e n t S topped m u o n M u o n g a t e C G D E l e c t r o n e v e n t E l e c t r o n g a t e ( G 5 ) L A M s igna l M B D busy g a t e P r o t e c t i o n ga te (2 ) P r e - m u o n P r e - m u o n P r e - m u o n g a t e ( 3 ) 2-nd m u o n Stopped m u o n 2 - n d m u o n P i l e up ga te N e w m u o n g a t e ( 4 ) 2-nd e l e c t r o n E l e c t r o n e v e n t E l e c t r o n gate 2-nd e l e c t r o n 1 t = 0 ( T i m e in jj s e c ) f ( S t a r t C l o c k ) t | 3 2 Yt<o V t=o Y t 2 ~ V V ( S t o p C l o c k ) i i i > i > V I i ^ 4 j 5 0 - J i i j -15 - 1 i i i J Extended gate t2+ 3 2 Figure II-6, Timings and difinitions of events. 4 5 muon a n d a p p l i e d t c a p a t t e r n u n i t g a t e o n t h e CAMAC c r a t e , t h e p a t t e r n u n i t w a s p r o t e c t e d d u r i n g t h e p r o c e s s i n g o f d a t a b y t h e c o m p u t e r . When t h e r e w a s a g o o d muon s i g n a l , i t w a s s e n t t o a c l o c k a s a s t a r t s i g n a l . The t i m i n g o f t h e s t a r t s i g n a l was d e t e r m i n e d b y c o u n t e r S 3 w h o s e c o u n t e r o u t p u t was f e d i n t o a c o n s t a n t f r a c t i o n d i s c r i m i n a t o r . T h i s d i s c r i m i n a t o r s h o w e d a s m a l l e r t i m e j i t t e r a n d b e t t e r t i m i n g c o m p a r e d t o a l e a d i n g - e d g e t y p e d i s c r i m i n a t o r . I n t h e e l e c t r o n l o g i c , t h e o u t p u t c f c o u n t e r S5 was f e d i n t o a n o t h e r c o n s t a n t f r a c t i o n d i s c r i m i n a t o r . . T h i s c o u n t e r d e t e r m i n e d t h e t i m i n g s o f t h e f o u r e l e c t r o n t e l e s c o p e s . When t h e r e was a g o o d e l e c t r o n e v e n t w i t h i n t h e muon g a t e , a n e l e c t r o n g a t e (G5) was o p e n e d . T h e n , t h e g o o d e v e n t s i g n a l was s e n t t o a c l o c k a s a s t o p s i g n a l a n d a t e l e s c o p e i d e n t i f i c a t i o n b i t i n t h e p a t t e r n u n i t w a s s e t . . F u r t h e r m o r e , a t t h e e n d o f t h e muon g a t e , a LAM s i g n a l w a s g e n e r a t e d b y a C 2 1 2 u n i t m o u n t e d i n t h e CAMAC c r a t e a n d a c t i v a t e d t h e MBD. On t h e o t h e r h a n d , i f t h e r e w a s n o g o o d e l e c t r o n e v e n t w i t h i n t h e muon g a t e , a c l e a r p u l s e w a s g e n e r a t e d t o r e s e t t h e p a t t e r n u n i t a t t h e e n d o f t h e g a t e . S i n c e i t t o o k a b o u t 4 m i c r o s e c o n d s f o r t h e MBD t o p r o d u c e t h e b u s y s i g n a l , t h e p r o t e c t i o n g a t e (G6) w a s c r e a t e d a t t h e e n d c f muon g a t e t o i n h i b i t t h e c l o c k a n d t h e muon l o g i c . A f t e r t h e MBD w a s a c t i v a t e d , t h e MBD b u s y s i g n a l was s u p p l i e d f r o m t h e CAMAC c r a t e t o i n h i b i t t h e muon l o g i c . 4 6 Two p i l e - u p r e j e c t i o n s a n d o n e p u l s e h e i g h t r e j e c t i o n w e r e e m p l o y e d . T h e d e f i n i t i o n o f t h e p i l e - u p r e j e c t i o n i s g i v e n i n f i g u r e I I - 6 . T h e p i l e - u p e v e n t s o f s t o p p e d m u o n s a n d g o o d e l e c t r o n s a r e named a s 2 n d - m u o n s a n d 2 n d - e l e c t r o n s , . r e s p e c t i v e l y . T h e 2 n d - m u o n s w e r e d e t e r m i n e d i y t h e p i l e - u p - o f a ( 1 , 2 , 3 , 4 , 5 ) c o i n c i d e n c e i n s t e a d o f t h e p i l e - u p c f a ( 1 , 2 , 3 ) c o i n c i d e n c e . T h i s p i l e - u p l o g i c was e x a m i n e d by c o m p a r i n g t h e p o s i t i v e muon l i f e t i m e s b e t w e e n t h e t w o d i f f e r e n t p i l e - u p r e j e c t i o n s . The t e s t r u n s s h o w e d t h a t , i f t h e r e w e r e t o o many r e j e c t i o n s b y t h e d e f i n i t i o n o f p i l e up a s ( 1 , 2 , 3 ) , t h e p o s i t i v e muon l i f e c h a n g e d b y 3 n a n o s e c o n d s a t a muon r a t e o f 1 5 0 0 / s e c . The p i l e - u p r e j e c t i o n was q u i t e a s e r i o u s p r o b l e m i n t h e l i f e t i m e m e a s u r e m e n t s a n d w i l l b e d i s c u s s e d i n C h a p t e r I I I . T h e p u l s e h e i g h t r e j e c t i o n was made b y t h e c o i n c i d e n c e c f c o u n t e r s S2 a n d S 3 w i t h S2 a t a h i g h d i s c r i m i n a t o r l e v e l . I n t h e o u t p u t s i g n a l o f c o u n t e r S 2 w i t h 1 . 7 kV h i g h v c l t a g e , t h e b r i g h t b a n d o f e l e c t r o n s ( m u o n s ) was l o c a t e d f r c m 30 ( 2 5 0 ) mV t o 150 ( 6 0 0 ) mV. . a s m e n t i o n e d i n s e c t i o n I I . B , a l l p a r t i c l e s h i g h e r t h a n 6 0 0 mV w e r e c o n s i d e r e d a s s l o w muons o r d o u b l e m u o n s a n d w e r e r e j e c t e d . I f t h i s o c c u r r e d , t h e g a t e G2 was g e n e r a t e d t o i n h i b i t d a t a t a k i n g f o r 16 o r 3 2 m i c r o s e c o n d s . By t h i s r e j e c t i o n , s l o w m u o n s w e r e m o s t l y r e j e c t e d , b e c a u s e t h e p r o b a b i l i t y h a v i n g t w o m u o n s w i t h i n 20 n s w a s e x t r e m e l y s m a l l f o r 1000 / s e c mucn s t o p p i n g r a t e , w h i c h w a s t h e 47 s t a n d a r d s t o p p i n g r a t e i n t h i s e x p e r i m e n t . I f t h e r e w e r e r e j e c t i o n e v e n t s , r e j e c t i o n b i t s w e r e s e t i n t h e p a t t e r n u n i t a n d a l l i n f o r m a t i o n s t o r e d i n t h e u n i t was i g n o r e d b y s o f t - w a r e . I n t h e l i f e t i m e m e a s u r e m e n t , a c l o c k w a s i m p o r t a n t t o d e t e r m i n e a t i m e i n t e r v a l . B e f o r e t h e s u m m e r o f 1 9 7 9 , o n l y a T D C - 1 0 0 c l o c k was a v a i l a b l e a n d t e s t r u n s o f t h e s y s t e m c a l i b r a t i o n w e r e made by t h i s c l o c k . A new c l o c k w i t h a 1 GHz s c a l e r was a s s e m b l e d b y t h e TRIOMF e l e c t r o n i c s s h o p i n t h e s u m m e r o f 1 9 7 9 , A t t h e b e g i n n i n g o f t h e t w o week e x p e r i m e n t i n O c t o b e r , 1 9 7 9 , t h e t w o c l o c k s w e r e t e s t e d b y m e a s u r i n g t h e p o s i t i v e muon l i f e t i m e . F r c m t h e t e s t , t h e new c l o c k s h o w e d b e t t e r a g r e e m e n t w i t h t h e p o s i t i v e muon l i f e t i m e . T h u s , i n t h e s e r i e s o f l i f e t i m e m e a s u r e m e n t s , t h e new c l o c k was u s e d . T h e l i n e a r i t y o f t h e new c l o c k w a s a s s u r e d b y t h e t e s t w i t h a t i m e c a l i b r a t o r ( O R T E C - 6 5 0 ) . F o r c o n v e n i e n c e , t h e u l t i m a t e l o g i c w h i c h was e m p l o y e d i n t h i s e x p e r i m e n t i s s u m m a r i z e d i n t h e f o l l o w i n g p a g e . 4 8 S j a j y n a r j o f E v e n t D e f i n i t i o n s I N C I D E N T MUON (come i n t o t a r g e t r e g i o n ) — ( 1 , 2 , 3 ) STOPPED MOON ( s t o p i n t a r g e t ) — ( 1 , 2 , 3 , 4 , 5 ) STAET (GOOD MUON) ( n o p r e m u o n r e j e c t i o n ) — ( 1 , 2 , 3 , 4 , 5 , ( n ) STOP (GOOD ELECTRON) - - ( 5 , 6 ) o r ( 5 , 7 ) o r ( 5 , 8 ) c r ( 5 , 9 ) E v e n t r e j e c t e d i f P E E M U O N — ( 1 , 2 , 3 , 4 , 5 ) w i t h i n 1 6 ( 3 2 ) m i c r o s e c b e f o r e STAET 2 n d M U O N - - ( 1 , 2 , 3 , 4 , 5 ) w i t h i n 1 6 ( 3 2 ) m i c r o s e c a f t e r STAET TWO C O I N C I D E N T ( o r SLOW) MUONS — ( 2 « , 3 ) w i t h S2 p u l s e h e i g h t > 6 0 0 mV 2 n d E L E C T E O N - - ^ t w o S I O P s w i t h i n 1 6 ( 3 2 ) m i c r o s e c a f t e r STAET G a t e c r e a t e d b y STOPPED MUGN ( P i l e up g a t e ) — G l (MUON g a t e 16 o r 3 2 m i c r o s e c ) TWO C O I N C I D E N T ( c r SLOW) MUON ( P i l e up g a t e ) — G 2 GOOD MUON ( n o r m a l g a t e ) - - G 4 ( g a t e f o r p a t t e r n u n i t ) GOOD E L E C T R O N ( n o r m a l g a t e ) — G5 (ELECTRON g a t e ) E n d o f G1 + G 5 — G 6 ( p r o t e c t i o n o f muon l o g i c ) N o t e : 3 2 ( 1 6 ) m i c r o s e c o n d g a t e was u s e d f o r m e a s u r m e n t s o f l i f e t i m e s l o n g e r ( s h o r t e r ) t h a n 3 0 0 n s . 2 m e a n s t h e d i s c r i m i n a t o r l e v e l i s 35 mV (DL i n f i g u r e I I - 5 ) . 2 ' m e a n s t h e d i s c r i m i n a t o r l e v e l i s 6 0 0 mV (DH i n f i g u r e . I I - 5 ) . 49 I I . F S u n n i n g P r o c e d u r e a n d B u n R e c o r d T h e r e w a s a t w o - w e e k b r e a k b e t w e e n t w o e x p e r i m e n t s e a c h o f o n e w e e k d u r a t i o n . at t h e b e g i n n i n g o f t h e f i r s t week , t h e e x p e r i m e n t was d o n e i n t h e f o l l o w i n g s t e p s : 1 . The M 2 0 beam l i n e was s e t f o r p o s i t i v e m u o n s . 2 . D i s c r i m i n a t o r l e v e l s a n d h i g h v o l t a g e s o f c o u n t e r s w e r e a d j u s t e d a n d e l e c t r o n i c s l o g i c s w e r e c h e c k e d . . 3. T h e p o s i t i v e muon l i f e t i m e m e a s u r e m e n t w a s made w i t h t h e T D C - 1 0 0 a n d t h e new c l o c k b u i l t a t T R I U M F . a f t e r c o m p a r i n g t h e r e s u l t s , t h e new c l o c k w a s e m p l o y e d f o r t h e s e r i e s c f e x p e r i m e n t s . S i n c e t h e e l e c t r o n i c l o g i c f o r t h e new c l o c k was d i f f e r e n t f r o m t h e o l d l o g i c c r e a t e d f o r t h e T D C - 1 0 0 c l o c k , t h e d e v e l o p m e n t o f t h e new l o g i c (Lam s i g n a l , p r o t e c t i o n g a t e , r e j e c t i o n s c h e m e , e t c ) t o o k t h r e e d a y s ( 1 / 3 o f o u r beam t i m e ) . 4. I n o r d e r t o c a l i b r a t e t h e s y s t e m , t h e p o s i t i v e muon l i f e t i m e was m e a s u r e d w i t h d i f f e r e n t c o n d i t i o n s o f r e j e c t i o n s c h e m e s a n d beam r a t e s . T h e m a g n e t i c f i e l d e f f e c t was e x a m i n e d by s t o p p i n g p o s i t i v e p i o n s i n a t a r g e t . 5 . T h e M 2 0 b e a m l i n e was s e t f o r n e g a t i v e m u o n s . 6. a t t h e b e g i n n i n g o f t h e n e g a t i v e muon l i f e t i m e m e a s u r e m e n t s , t h e n e g a t i v e muon l i f e t i m e i n c a r b o n was m e a s u r e d a n d t h i s was r e p e a t e d o n c e a d a y a s a c a l i b r a t i o n d u r i n g t h e l i f e t i m e m e a s u r e m e n t s . 50 7. Targets were changed a f t e r enough events and the muon gate -was ad j u s t e d so t h a t a long (short) l i f e t i m e measurement had a 32(16) microsecond gate. For the long l i f e t i m e measurements of l i g h t elements, the carbon background runs were made f o r each t a r g e t * 8., At t i e end of the f i r s t one week run, a l l data were t r a n s f e r e d frcm a disk f i l e to a magnetic tape f o r an o f f l i n e a n a l y s i s . A f t e r the one. week break, the experiment f o l l o w e d the procedure as s t a t e d above except step 3.. Normally one run took two hours. Numbers of stopped muons, good muons and accepted e l e c t r o n s i n histograms are l i s t e d i n Table I I - 4 . Table 11-4(1) Bun Becords ( T o t a l Events) z Element Inc Mu Stop Mu Tot E Accepl X 1 0 6 x10* X 1 0 3 X 1 0 3 3 L i - 6 14.4 12. 1 5,630 4,580 L i - 7 17. 7 14. 7 6,800 5,900 4 Be 4. 6 4.1 2,024 1,531 5 B-10 8. 1 4. 1 1,312 1 ,100 B- 1 1 8. 8 4.0 1,210 1,023 6 C- 12 3. 6 2.9 1 ,320 1,100 C- 13 5.5 2. 5 820 570 7 N 5.7 5.6 1,640 1,230 8 0- 16 9.0 8.7 2,780 2,236 0-16 (Agar) 10. 0 3.9 1, 17C 956 0-18 (Agar) 8.3 3.2 1,060 885 9 F - L i F 7.3 4.9 1,940 1,550 -C2F4 3. 6 2.9 1,019 842 -CaF2 3. 1 2. 5 500 4 10 - EbF 5. 8 5.0 470 370 11 Na 4. 7 4.2 1 ,290 1,0 50 12 Mg 8. 9 6.7 2,090 1 ,640 13 Al 5.9 5. 1 86C 740 14 S i 3. 2 2.7 50 6 420 15 JP 5. 7 4.7 815 6 20 16 S 5.6 4. 9 '710 550 17 C1-CC14 3. 9 3.7 614 505 19 K 4.3 3.6 510 425 20 Ca 4. 7 4.2 550 454 22 T i 5. 5 4, 1 365 310 23 V 6. 8 2.9 300 250 24 Cr 4. 5 3.8 299 254 25 Mn-Mn02 4. 2 1.8 490 430 26 Fe 3. 8 3.6 103 74 27 Co 6. 6 4.7 261 210 28 Ni 3. 2 2.9 105 84 29 Cu 3.2 2.7 175 121 30 Zn 4. 2 3.9 165 112 32 Ge-Ge02 4.4 2.6 662 490 35 Br-NH4Er 3. 2 2.9 503 392 40 Zr 573 41 Nb 4. 5 3.4 176 150 42 Mo 4. 1 3.4 180 152 47 Ag 3. 5 1.7 97 79. 48 Cd 4.5 2.5 142 113 49 In 4.4 2.0 160 130 Table .11-4(1) Bun Records ( T o t a l Events) Z Element Inc Mu Stop Mu Tot E Accepted E X106 X 1 0 * X103 X103 50 Sn 2.4 1.6 110 88 53 I 5. 5 4.9 217 179 56 Ba-BaO 4. 3 3.7 402 323 60 Nd-NdO 5. 8 2. 2 591 447 64 Gd 3. 9 2.5 132 106 66 Dy 4. 5 3.5 230 195 68 Er 4.8 3.9 158 134 74 W 3.8 2.9 199 169 80 Hg-HgO 6.0 5. 2 427 333 82 Pb 4.1 3.4 118 95 83 B i 3.1 2.0 137 109 * Other oxide t a r g e t s f c r muon atomic capture experiment 6 C02 4.0 3,.4 1 ,487 1 , 182 11 Na20 2 12 MgO 3. 2 2.9 9 13 718 13 A1203 4. 6 4.2 1 ,421 1 ,1 13 14 SiC2 2. 2 1.0 343 278 15 P205 4. 7 3.4 1,232 989 20 Ca(OH) 2 4. 3 3,8 1 ,129 891 22 Ti02 3. 4 2.2 589 451 24 Cr203 3. 9 3.5 696 548 Cr03 5. 5 5. 1 1 , 195 935 29 CuO 1.6 1.3 141 111 30 ZnO 3. 5 2.7 463 362 32 GeO 6. 1 3.7 993 735 48 CdO 11.6 9.7 1,553 1,214 50 Sn02 5.6 5.0 1,015 776 82 Pb02 4. 6 3.8 439 342 Pb304 3.5 3.0 238 188 5 3 CHAPTER I I I D a t a A n a l y s i s I I I . A D a t a A n a l y s i s P r o c e d u r e A l l d a t a a n a l y s i s was p e r f o r m e d o n t h e OBC A m d a h l 470 V/6 c o m p u t e r . A c o m p u t e r p r o g r a m c a l l e d M I N O I T ( J A M 7 1 ) , w h i c h was d e v e l o p e d a t C E R N , was u s e d f o r a c h i - s g u a r e d m i n i m i z a t i o n . Two f i t t i n g p r o c e d u r e s w e r e e m p l o y e d . I n t h e c a s e o f t h e c h i - s g u a r e d m i n i m i z a t i o n f i t t i n g o f a p o s i t i v e muon h i s t o g r a m , t h r e e p a r a m e t e r s : l i f e t i m e , a m p l i t u d e , a n d b a c k g r o u n d w e r e s e a r c h e d f o r t h e e n t i r e s p e c t r u m , s i n c e t h e f i t t i n g was d o n e v e r y q u i c k l y f o r t h r e e p a r a m e t e r s . I n t h e c a s e o f a n e g a t i v e . m u c n h i s t o g r a m , t h e r e w e r e m o r e t h a n f o u r p a r a m e t e r s t o f i t a n d m o r e e v e n t s a p p e a r e d a t e a r l i e r t i m e s d u e t o t h e n u c l e a r c a p t u r e . T h e r e f o r e , t h e b a c k g r o u n d w a s f i t t e d f i r s t b y M I N O I T f o r t h e t a i l o f e a c h h i s t o g r a m . T h e n , t h e b a c k g r o u n d was f i x e d a n d o t h e r p a r a m e t e r s f o r s e v e r a l e l e m e n t s w e r e f o u n d f o r t h e f r o n t p a r t o f t h e s p e c t r u m . F i g u r e T I I - 1 s h o w s a t y p i c a l p o s i t i v e muon d e c a y c u r v e . A f t e r 26 m i c r o s e c o n d s , t h e r e a r e o n l y b a c k g r o u n d e v e n t s . A r a t i o o f t h e b a c k g r o u n d t o t h e a m p l i t u d e a t T=0 (B/N ( 0 ) ) i s r o u g h l y e q u a l t o 3 x 1 0 ~ * . T h e s e b a c k g r o u n d e v e n t s c a m e m a i n l y f r c m r a n d o m c o i n c i d e n c e s w i t h c h a r g e d 54 p a r t i c l e s s c a t t e r e d around i n the M20 counting area. There were a l s o some background events from cosmic r a y s . The experiment made at Saclay (DUC73) was a f f e c t e d only by the cosmic ray background events. T h i s was because there was no incoming beam f o r 500 microseconds a f t e r every beam bunch due to the s p e c i a l beam s t r u c t u r e of S a c l a y 1 s E l e c t r o n L i n a c . The B/N (0) r a t i o of Saclay's experiment was equal to 3 x 1 0 - 5 , which i s s m a l l e r than our r a t i o by a f a c t o r of 10. There was a l s o an experiment by Balandin (BAL75), who b u i l t a Cerenkov d e t e c t o r with a 4 "IT s o l i d angle... T h e i r B/N (0) r a t i o was equal to 1x10~*. Since the s o l i d angle of our d e t e c t o r was about 2 TT radians and the beam r e p e t i t i o n r a t e was 23 MHz, the B/N(0) r a t i o of f i g u r e III-1 seems s a t i s f a c t o r y when compared to the other good measurements mentioned abcve. F i g u r e I I I - 2 shows the negative muon experiment i n Cr203. A f t e r 16 microseconds, there are only background events. As mentioned above, i n the f i t t i n g c f t h i s spectrum, the background was found from the f l a t s e c t i o n between 20 and 30 microseconds. Then the spectrum between 0 and 12 microseconds was f i t t e d f o r the chromium l i f e t i m e , and the chromium, oxygen, and carbon amplitude, keeping f i x e d the amplitude c f the background as w e l l as the l i f e t i m e s of oxygen and carbon. 100000 10000 k "i r i 1 r i r JU+ D e c a y S p e c t r u m 0 2 4 6 8 10 12 14 16 18 20 . 22 24 26 28 TIME (MICRO SEC) Figure I I I - l , Positive muon decay curve. COUNTS 9£ 57 III.E Magnetic F i e l d E f f e c t The time i n t e r v a l s between the start signals from the muon stops i n the target and stop signals from decay electrons were recorded as a histogram. In the case of posit i v e muons, the histogram shows a l i f e t i m e of 2.2 microseconds. Without a magnetic f i e l d e f f e c t , the histogram shows a decay curve which i s simply expressed as N <t) =N (0) «exp (-t/Tm) + Bg (3.1) where Tm i s the l i f e t i m e of positive muons, Bg the time independent background and N (0) the amplitude at t=0. If there i s not a strong depolarization of muons and i f the target i s under the influence of a magnetic f i e l d , equation (3. 1) must be modified due to the muon precession. The new eguation i s given by N(t)=N(0 ) « [ 1 + &«cos (wt+p) } »exp (-t/Tm) + Bg (3.2) where a,w and p> are an asymmetry, an angular frequency and a phase, respectively. In our positive muon l i f e t i m e measurement, carbon, which does net show any mucn depolarization (SWa58), was used as a target. I f a highly polarized muon does not show any depolarization i n a target, the asymmetry a i s close to 0.33. In the target region of 58 o u r e x p e r i m e n t a l s e t - u p , t h e m a g n e t i c f i e l d was q u i t e s m a l l b e c a u s e o f Mu m e t a l s h i e l d i n g , a s d i s c u s s e d i n s e c t i o n I I . C . U n d e r a s m a l l m a g n e t i c f i e l d , l i k e 0 . 0 5 G , p o s i t i v e m u o n s w i t h a 100% p o l a r i z a t i o n p r e c e s s b y 0 . 0 9 r a d i a n s (5 d e g r e e s ) w i t h i n 10 muon l i f e t i m e s . T h i s p r e c e s s i o n a f f e c t s t h e a p p a r e n t muon l i f e t i m e a n d t h e f o l l o w i n g a p p r o x i m a t i o n c a n b e made Tm = T m ( 0 ) * [ 1 ± A « w « T m ( 0 ) + 0 . 5 « (A«w«Tm (0) ) 2} ( 3 . 3 ) w h e r e + (-) s i g n c a n b e a p p l i e d t o t h e l e f t ( r i g h t ) d e t e c t o r o r v i c e v e r s a . W i t h A = 0 . 3 3 , w = 8 5 , 5 0 0 * 0 . 0 5 / s e c f o r 0 . 0 5 G a n d T m ( 0 ) = 2 . 2 m i c r o s e c o n d s , t h e . f i r s t o r d e r d i s t o r t i o n h a s a 0 . 3 % e f f e c t , w h i c h c h a n g e s t h e l i f e t i m e b y 7 n s . S i n c e f o u r e l e c t r o n t e l e s c o p e s w e r e a r r a n g e d s y m m e t r i c a l l y , a s d i s c u s s e d i n s e c t i o n I I . B , t h e a v e r a g e o f t h e f o u r l i f e t i m e s c a n c e l s t h e f i r s t o r d e r d i s t o r t i o n a n d t h e a v e r a g e l i f e t i m e h a s a n e g l i g i b l e s e c o n d o r d e r e f f e c t . I n o r d e r t o c h e c k t h e m a g n e t i c f i e l d e f f e c t , p i o n s w e r e s t o p p e d i n a t a r g e t a s i f t h e y w e r e p o s i t i v e m u o n s . S i n c e p i o n s s t o p p e d i n t h e t a r g e t a r e i d e a l u n p o l a r i z e d muon s o u r c e s , n o d i f f e r e n c e i n l i f e t i m e s among t h e e l e c t r o n t e l e s c o p e s i s e x p e c t e d . I n t h i s c a s e , t h e d i s t r i b u t i o n o f d e c a y e l e c t r o n s i s g i v e n by { e x p ( - t / T p ) - e x p ( - t / T m ) } N ( t ) = N p ( 0 ) « + B g ( 3 . 4) (Tp - Tm) 59 w h e r e Tm (Tp) i s t h e muon ( p i o n ) l i f e t i m e . A f t e r 10 p i o n l i f e t i m e s (=260 n s ) , t h e c o n t r i b u t i o n f r o m t h e p i o n d e c a y b e c o m e s n e g l i g i b l e a n d , t h e n , e q u a t i o n ( 3 . 4 ) s h o w s t h e s a m e d e c a y c u r v e a s e q u a t i o n ( 3 . 1 ) . I n T a b l e I I I - 1 , t h e l i f e t i m e s o f f o u r e l e c t r o n t e l e s c o p e s f o r 10 r u n s a r e l i s t e d . The s u m m a r y o f t h e t a b l e i s a s f c l l c w s . Beam E r r o r Muon Eeam S t a n d a r d d e v i a t i o n o f e a c h e l e c t r o n t e l e s c o p e f r o m t h e a v e r a g e l i f e t i m e S t a t i s t i c a l e r r o r M a g n e t i c f i e l d e f f e c t by a q u a d r a t i c r e l a t i o n P i o n beam S t a n d a r d d e v i a t i o n S t a t i s t i c a l e r r o r M a g n e t i c f i e l d e f f e c t C o u n t e r s L a n d R T a n d B 6 . 4 n s 5 . 0 n s 4 . 4 n s 4 . 4 n s 4 . 6 n s 1 . 4 n s 4 . 4 n s 0 . 0 n s 2 . 4 n s 3 . 0 n s 4 . 4 n s 0 . 0 n s C o n s e q u e n t l y , t h e d i s t o r t i o n o f t h e muon l i f e t i m e d u e t o t h e m a g n e t i c f i e l d i s r o u g h l y 4 . 6 ( 2 . 4 ) n s f o r t h e l e f t - r i g h t ( t c p - b o t t o m ) e l e c t r o n t e l e s c o p e s a n d t h e d i s t o r t i o n c o r r e s p o n d s t o 0 . 0 3 ( 0 . 0 2 ) G . S i n c e t h e m a g n e t i c f i e l d m e a s u r e m e n t w i t h a f l u x m e t e r ( H e w l e t t P a c k a r d M o d e l 4 2 8 ER) . s h o w e d t h e f i e l d t o t e b e t w e e n 0 . 0 2 a n d 0 . 0 5 G n e a r t h e c e n t e r o f t h e t a r g e t , t h e a v e r a g e f i e l d f r o m t h e l i f e t i m e d i s t o r t i o n s e e m s t o be i n g o o d a g r e e m e n t w i t h t h e f i e l d m e a s u r e m e n t . T a b l e P o s i t i v e Muon L i f e t i m e s c f F o u r E l e c t r o n T e l e s c o p e s ( i n n a n o s e c ) L e f t E i g h t T o p B o t t o m A v e r a g e 2202.7 (4. 4) (+4.6) 221 1. 3 ( + 5.5) 2193.3 (-3. 1) 219 1.8 ( -6.3) 2188. 3 (-6.9) 2202. 4 (+4.0) 2202. 9 (+5.8) 220 1. 7 (+5. 1) * 2197.8 ( -0.6) * 219 7.3 (+1.9) 2 19 3. 4 (4.4) (-4-7) 2188.8 (-7.0) 2194. 3 (-2.1) 2203. 6 (+5.5) 2200. 0 ( + 4. 8) 2 19 1. 2 (-7.8) 2191. 7 (-5.4) 2193.4 (-3.2) 2197.2 (-1.2) 2196.8 (+1.4) 2204.3 (4. 4) ( + 6.2) 21 95.7 (-0.1) 2202. 7 (+6.3) 2199.4 (+1.3) 2197.4 ( + 2.2) 2201.6 ( + 3.2) 2203.7 (+6,6) 2202*9 ( + 6. 3) 2195.8 (-2.6) 2192.0 (-3.4) 2192.1 (4.4) (-6.0) 2187.2 (-8.6) 2195.4 (-1.0) 21S7.7 (-0.4) 2195.1 (-0. 1) 21S8.5 (+0. 1) 2190. 1 (-7.0) 2188.4 (-8.2) 2202. 6 ( + 4.2) 2195.4 ( 0.0) 2198. 1 (2.2) 2195.8 2196.4 2198. 1 2195,2 2198.4 2197. 1 2196.6 2198.4 2195.4 2197.0(0.7) 1) A l l p o s i t i v e muon l i f e t i m e s w e r e m e a s u r e d i n t h e c a r b o n t a r g e t . * ) T h e s e d a t a w e r e t a k e n by s t o p p i n g p i o n s i n t h e t a r g e t . ( ) s h o w s t h e d e v i a t i o n f r o m t h e a v e r a g e . 61 We w i s h t o e m p h a s i z e t h a t t h e n e g a t i v e muon l o s e s i t s p o l a r i z a t i o n w h i l e i t c a s c a d e s d o w n i n t h e m u o n i c a t o m . . A s d i s c u s s e d i n s e c t i o n I . 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 s a l w a y s l e s s t h a n 20% c f t h e i n i t i a l . T h u s f o r t h e l i f e t i m e m e a s u r e m e n t s o f n e g a t i v e m u o n s t h e e r r o r i n t h e l i f e t i m e d u e t o t h i s e f f e c t w o u l d t e a b o u t 1 n s e v e n i f we h a d u s e d a s i n g l e t e l e s c o p e s w h e r e a s i n f a c t t h e r e s u l t s a r e a l w a y s a n a v e r a g e o f a l l f o u r t e l e s c o p e s . (On a f e w o c c a s i o n s o n e o r t w o o f t h e h i s t o g r a m s .were l o s t d u e t o f a u l t y d a t a t r a n s f e r e t c ; i n t h e s e c a s e s t h e m e a s u r e m e n t was r e p e a t e d a n d n o n e o f t h e p a r t i a l d a t a w e r e u s e d . ) I I I . C Muon S t o p p i n g R a t e E f f e c t I f t h e b a d e v e n t r e j e c t i o n d i s c u s s e d i n s e c t i o n H . E i s n o t w o r k i n g p r o p e r l y , t h e muon l i f e t i m e d e t e r m i n e d t e n d s t o be s h o r t e r f o r a h i g h e r s t o p p i n g r a t e . I n f i g u r e I I I - 3 , t h e r a t e e f f e c t o n t h e p o s i t i v e muon l i f e t i m e i s s h o w n f o r t h e t w o f o l l o w i n g e x p e r i m e n t s : (a) w i t h a g o o d r e j e c t i o n s c h e m e w h i c h i s t h e f i n a l e l e c t r o n i c s l o g i c , (b) w i t h o u t r e j e c t i o n o f b a d e v e n t s w h i c h c o m e l a t e r t h a n a s t o p s i g n a l i n t o t h e t a x g e t b y a b o u t 8 m i c r o s e c o n d s o r l o n g e r . B e f o r e t h e f i n a l e l e c t r o n i c s l o g i c w a s c o m p l e t e d , 2210 Figure III-3, Stopping rate dependence with and without r e j e c t i o n s . 6 3 t h e LAM s i g n a l was p r o d u c e d b y a T D C - 1 0 0 c l o c k 4 m i c r o s e c o n d s a f t e r an e l e c t r o n s t o p e v e n t . I t t o o k a n o t h e r 4 m i c r o s e c o n d s f o r t h e p a t t e r n u n i t t o be r e a d b y t h e MBD ( t h e e l e c t r o n i c s l o g i c h a s b e e n g i v e n i n s e c t i o n I I - E ) . . A c t u a l l y , i n o r d e r t o c h e c k 2 n d m u o n s o r 2 n d e l e c t r o n s w i t h i n a muon g a t e , t h e LAM s i g n a l h a d t o l i e g e n e r a t e d a t t h e e n d o f t h e g a t e 3 2 m i c r o s e c o n d s a f t e r a g o o d muon s t a r t . S i n c e , i n t h e c a s e c f ( b ) , t h e LAM s i g n a l c a m e e a r l i e r t h a n t h e s i g n a l p r o d u c e d a t t h e e n d o f t h e g a t e , t h e r e w a s n o p r o p e r r e j e c t i o n b e t w e e n t h e t w o s i g n a l s . F i g u r e I I I - 3 s h o w s t h e s t r o n g r a t e d e p e n d e n c e c f t h e muon l i f e t i m e w i t h o u t t h e g o o d r e j e c t i o n s c h e m e . On t h e o t h e r h a n d , t h e r e i s n o s y s t e m a t i c r a t e d e p e n d e n c e up t c 5 0 0 0 / s e c w i t h t h e g o o d l o g i c . T h e R u s s i a n g r o u p ( B A L 7 5 ) m e a s u r e d a c c u r a t e l y t h e p o s i t i v e muon l i f e t i m e w i t h a 7 0 0 0 / s e c s t o p p i n g r a t e a n d t h e y o b t a i n e d t h e same r e s u l t a s t h e S a c l a y g r o u p (DUC73) w h o s e s t o p p i n g r a t e w a s a b o u t 1 5 0 0 / s e c . I n t h i s e x p e r i m e n t , t h e muon r a t e was v a r i e d o n l y i n t h e p o s i t i v e muon l i f e t i m e m e a s u r e m e n t s s c a s t o i n v e s t i g a t e t h e r a t e d e p e n d e n c e . I n t h e c a s e o f n e g a t i v e muon l i f e t i m e m e a s u r e m e n t s , t h e r a t e was k e p t b e l o w 1 0 0 0 / s e c w h i c h w a s t h e s a f e r a t e t o a v o i d t h e muon s t o p p i n g r a t e e f f e c t . T h i s was a l s o t h e maximum n e g a t i v e mucn beam r a t e w i t h a 2 . 5 cm d i a m e t e r c o l l i m a t o r a n d a 20 m i c r o - a m p e r e p r o t o n c u r r e n t o n a b e r y l l i u m p r o d u c t i o n t a r g e t . 64 I I I . D 2 n d Muon R e j e c t i o n W i t h o u t p r o p e r r e j e c t i o n s o f b a d e v e n t s , t h e r e i s a d i s t o r t i o n i n t h e h i s t o g r a m a s d i s c u s s e d i n t h e l a s t s e c t i o n . I n c r d e r t o e x a m i n e t h e d i s t o r t i o n , t h e c h i - s g u a r e d m i n i m i z a t i o n a n a l y s e s w e r e made f o r s e v e r a l d i f f e r e n t i n i t i a l t i m e s ( T l ) o f t h e h i s t o g r a m . T h e e n d o f t h e a n a l y s e s was f i x e d a t 30 m i c r o s e c o n d s . T h u s , t h e a n a l y s e s .were t a k e n b e t w e e n T1 a n d 30 m i c r o s e c o n d s . F i g u r e I I I - 4 s h o w s t h e l i f e t i m e d e p e n d e n c e o n t h e i n i t i a l t i m e T1 f o r t h e f o l l o w i n g t h r e e c a s e s : (a) w i t h t h e g o o d r e j e c t i o n s c h e m e , same a s I I I - B (a) , (b) w i t h o u t r e j e c t i o n o f b a d e v e n t s , s a m e a s I I I - B ( b ) , ( c ) w i t h t h e g o o d r e j e c t i o n s c h e m e i n w h i c h 2 n d muon r e j e c t i o n s a r e g e n e r a t e d b y t h e i n c o m i n g b e a m . A c c o r d i n g t o t h e s u m m a r y o f t h e u l t i m a t e l o g i c d e s c r i b e d i n s e c t i o n I I . E , i n t h e f i n a l l o g i c , t h e r e a r e f o u r r e j e c t i o n s : t h e 2 n d m u o n , t h e 2 n d e l e c t r o n , t h e p u l s e h e i g h t a n d t h e p r e - m u o n r e j e c t i o n s ( s e e f i g u r e I I - 6 f o r t h e d e f i n i t i o n s ) . I n t h i s l o g i c , t h e 2nd muon s i g n a l i s g e n e r a t e d b y t h e s t o p p i n g muon e v e n t s ( 1 , 2 , 3 , 4 , 5 ) . A l t e r n a t i v e l y t h e 2 n d muon s i g n a l c a n be p r o d u c e d by t h e i n c o m i n g beam ( 1 , 2 , 3 ) i n s t e a d o f t h e s t o p p i n g muon e v e n t s . L e t u s d i s c u s s i n s o m e d e t a i l t h i s c h o i c e o f r e j e c t i o n l o g i c w h i c h may s e e m b i z a r r e . . I n a t y p i c a l r u n w i t h t h e 2 n d muon r e j e c t i o n b y t h e i n c o m i n g b e a m , t h e r e w e r e 8 . 6 x 1 0 6 i n c o m i n g m u o n s t h r o u g h 2230 2220 LO c L U 2210 u 2 2 0 0 L L t ^2190 2180 2170h 2160 | 2 - n d m u o n r e j e c t i o n by s t o p p e d m u o n i t 2-nd m u o n reject ion by i n c o m i ng m u o n } No r e j e c t i o n t i i ( M I C R O S E C ) 0 . 2 4 6 8 IN IT IAL T I M E ( T o ) O F D A T A F I T T I N G igure III-4, Lifetime d i s t o r t i o n i n p o s i t i v e muon decay curve. 66 t h e l e a d c o l l i m a t o r , 0.4x10 6 2nd muon s i g n a l s were g e n e r a t e d , and 6.4x10 6 (74%) muons stopped i n the t a r g e t . I f the 2nd muon s i g n a l had been produced from the stopped muons, 0.25x10 6 2nd mucn s i g n a l s would have been gen e r a t e d . P r o d u c i n g the 2nd muon r e j e c t i o n s i g n a l s from the i n c o m i n g beam, t h e r e was an e x t r a 0.15x10 6 r e j e c t i o n s . T h i s was about 6% c f 2.4x10 6 e l e c t r o n e v e n t s a c c e p t e d i n the h i s t o g r a m . I n - p r i n c i p l e , 2nd muon r e j e c t i o n by the i n c o m i n g muons seems b e t t e r than the r e j e c t i o n by t h e stopped muons i n a t a r g e t , because the former r e j e c t i o n does not a l l o w any two mucns coming i n t o the t a r g e t a rea w i t h i n t h e muon g a t e . S i n c e a l a r g e number of p a r t i c l e s i n the incoming beam (26% i n the t y p i c a l case shown above) go through the t a r g e t and are d e t e c t e d by v e t o c o u n t e r s (S4 and S 5 ) , most of t h e s e muons may not a f f e c t the spectrum as 2nd muons* Thus, i f the incoming beam i s used f o r the 2nd muon r e j e c t i o n , many good e v e n t s a re u n n e c e s s a r i l y r e j e c t e d . T h i s caused a l i f e t i m e d i s t o r t i o n by 3 ns (=0.015% d i s t o r t i o n ) . I f t h e r e i s no prop e r r e j e c t i o n of .bad e v e n t s ( f i g u r e I I I - 1 b) , t h e r e i s a l a r g e d i s t o r t i o n , . The l i f e t i m e i s s h o r t e r i n f r o n t o f the spectrum and l o n g e r i n the t a i l . . 67 III.E Distortion from Counter E f f i c i e n c y and Dead Time of Electronics The e f f i c i e n c i e s of counters are l i s t e d i n Table I I - 1 . . Since the (1,2,3) coincidence which monitors the incoming beam has 99 .4% e f f i c i e n c y , 0.6% of incoming muons would not be detected even i f they stopped i n the target.. These muons can be considered as undetected 2nd muons and so cause a d i s t o r t i o n problem. In order to find the degree of the d i s t o r t i o n , an empirical approach can be applied.. Figure I I I - 4 shows the stopping rate dependence of l i f e t i m e with and without r e j e c t i o n s . Since undetected and detected mucns fellow a Poisson d i s t r i b u t i o n , the d i s t o r t i o n due to undetected muons can be estimated by Poisson d i s t r i b u t i o n of undetected muons within twice the time of the muon gate Tdis= DT <» Poisson d i s t r i b u t i o n of stopping muons within twice the time of the muon gate (1-E)»N»2*Tm*exp {- (1-E) •N»2»Tm} = DT • ; (3.5) N»2«Tm«exp (-N»2»Tm) where ET= empirical l i f e t i m e d i s t o r t i o n , E = counter e f f i c i e n c y , N = stopping muon rate, Tm= mucn gate (32 microseconds). 68 At 5000/sec stopping rate, the l i f e t i m e d i s t o r t i o n with no re j e c t i o n i s about 25 ns, from figure III-4, and from eguation (3.5), the d i s t o r t i o n due to undetected muorfs i s 0.2 ns for a 99.4% counter e f f i c i e n c y . However only 25% of undetected muons contribute to the d i s t o r t i o n because of the 2nd electron rejection by the electron telescopes with the 2 TT radian s o l i d angle. Considering that the counter e f f i c i e n c y of 99.1% was measured with a ruthenium 4 MeV electron source and the e f f i c i e n c y f e r muons was better than that for electrons, the d i s t o r t i o n due to undetected muons was less than 0.05 ns.. So i t was n e g l i g i b l e at or below the 5000/sec stopping rate used. If two muons came into the target region within 10 ns, the pulse height rejection could eliminate the event from a histogram. However, i f the second mucn came after more than 10 ns but less than the electronics dead-time (about 60 ns fer a counter output), the pulse height and the 2nd muon rejection could not reject the event.. Incident muons were monitored.by counters S i , S2 and S3, and the 2nd muon signa l was generated by a pile-up gate generator (PUG). Thus, the dead times cf a LBS-621BL leading edge type discriminator (S1 and S2), an ORTEC-934 constant fraction discriminator (S3) and an EGG-100 (PUG) must be considered. From the dead time measurements, the LES-621BL showed a dead time of 60 ns, the OETEC-934 40 ns and the EGG-100 18 ns. Conseguently, the dead time in the determination of the 2nd muon r e j e c t i o n was 60 ,ns. Even with t h i s system, more than 69 5052 o f t w o m u o n s w i t h i n 30 n s c a n be r e j e c t e d . I n o r d e r t o f i n d t h e p r o b a b i l i t y o f two m u o n s w i t h i n 60 n s , t h e P o i s s o n d i s t r i b u t i o n c a n be a p p l i e d a n d , f o r 5000/ s e c s t o p p i n g r a t e , t h e p r o b a b i l i t y i s 2 . 5 x 1 0 - * . . A l s o , t h i s e f f e c t c a n b e e s t i m a t e d b y e q u a t i o n ( 3 . 5 ) . I t c h a n g e s t h e l i f e t i m e by o n e p a r t i n 10 5 a n d t h e e f f e c t o n t h e l i f e t i m e d i s t o r t i o n i s n e g l i g i b l y s m a l l . I I I . F A n a l y s i s o f N e g a t i v e Muon L i f e t i m e T h e p r o c e d u r e f o r t h e a n a l y s i s o f t h e n e g a t i v e muon l i f e t i m e h a s b e e n d i s c u s s e d i n s e c t i o n I I I . A f o r C r 2 0 3 . I n t h e n e g a t i v e muon l i f e t i m e m e a s u r e m e n t s , t h e muon s t o p p i n g r a t e was k e p t b e l o w 1000/ s e c a n d t h e s y s t e m a t i c d i s t o r t i o n c a u s e d b y t h e r a t e was n e g l i g i b l e a s s h o w n i n t h e f o r m e r s e c t i o n . S i n c e t h e n e g a t i v e m u o n s l o s e t h e i r p o l a r i z a t i o n g u i c k l y i n t h e m e s o n i c a t c m s t a g e , t h e m a g n e t i c f i e l d e f f e c t d i s c u s s e d i n s e c t i o n I I I . B i s s m a l l . F o r e x a m p l e , f r o m t h e b o u n d muon d e c a y e x p e r i m e n t d i s c u s s e d i n s e c t i o n I - C , t h e r e s i d u a l p o l a r i z a t i o n s o f n e g a t i v e m u o n s i n c a r b o n a n d t i t a n i u m w e r e }5% a n d 5%, r e s p e c t i v e l y . The m a i n c a u s e o f t h e s y s t e m a t i c e r r o r i n t h e n e g a t i v e muon l i f e t i m e m e a s u r e m e n t o f l i g h t e l e m e n t s ( L i , B e , B , N , 0) i s t h e c a r b o n b a c k g r o u n d . The m a i n c a r b o n b a c k g r o u m d s o u r c e i s t h e d e f i n i n g c o u n t e r S3. A l s o , t h e 70 l i g h t guide of c y l i n d r i c a l counter S5 , and wrapping tapes of counters SU and S5 can be carbon background sources. The carbon background depends on the t a r g e t s i z e and i t s t h i c k n e s s . T h e r e f o r e , carbon background runs were made a f t e r every muon l i f e t i m e d e t e r m i n a t i o n i n a l i g h t element by using a d u p l i c a t e d t a r g e t made of brass,„ In the l i f e t i m e f i t t i n g of the l i g h t element, the carbon background was su b t r a c t e d using the r e s u l t of the background run. In Table I I I - 2 , the f i t t i n g r e s u l t s are l i s t e d . The carbon c o r r e c t i o n s have changed the l i f e t i m e s by a few ns f o r the case o f s m a l l c o r r e c t i o n . The u n c e r t a i n t y of the carbon background determination i s a l s o .taken i n t o account as shown i n Table I I I - 2 . As mentioned i n s e c t i o n II-D, pcwder t a r g e t s were encl o s e d i n c o n t a i n e r s . There were chemical compound t a r g e t s as l i s t e d i n Table I I - 2 . In the l i f e t i m e f i t t i n g of the decay e l e c t r o n spectrum from the powder or the chemical compound t a r g e t , the c o n t r i b u t i o n frcm the elements of co n t a i n e r m a t e r i a l s and chemical compounds must be i n c l u d e d i n the f i t t i n g e g u a t i o n . Thus, f i g u r e I I I - 2 i s f i t t e d to the f o l l o w i n g equation Ne (t) = A (Cr) «exp {-t/T (Cr)} • A (0) »exp [-t/T (0)} + A (C) •exp[-t/I(C) } + Bg (3.6) where A and T are the amplitude and the l i f e t i m e of each element (Cr, 0 , C) . In t h i s f i t t i n g , T(C) and T<0) are 71 Table I I I - 2 Carbon Background E f f e c t i n L i g h t Elements L i f e t i m e without % of L i f e t i m e with C Background C Background C Background L i - 6 2175.9 ± 1. 5 nsec 1.0 (±0.5) % 2177.0 ± 2. 0 nsec L i - 7 2186.9 + 1.5 1.0 ( + 0. 5) 2188.3 + 2. 0 Be 2 160.8 + 1.3 1.5 (±0. 5) 2162.0 + 2. 0 B-10 2067.0 + 2. 0 7.5 (±1.0) 2070.7 ± 3. 0 B-11 208.9.6 ± .2. 0 7.5 (+1.0) 2096.1 ± 3. 0 C-13 2028. 1 ± 3. 0 6.8(±1.0) 2029. 1 ± 3. 0 N 1909. 1 ± 2.0 1.6 (±0. 5) 1906.8 + 3. 0 0 (H20) 1799.6 ± 1.3 1.6 (±0. 5) 1795.4 ± 2. 0 0-18 1865.4 + 3.0 13.0(±2.0) 1844.0 ± 4. 5 1) The numbers i n parentheses are the estimates of the u n c e r t a i n t y i n the carbon background. 72 f i x e d . a l t h o u g h t h e r e i s a l s o h y d r o g e n i n t h e p l a s t i c c o u n t e r a n d c o n t a i n e r , t h e h y d r o g e n c o m p o n e n t i n t h e d e c a y c u r v e i s n e g l i g i b l e . T h i s i s b e c a u s e o f t h e h i g h t r a n s f e r r a t e o f n e g a t i v e m u o n s f r o m h y d r o g e n t o h e a v y e l e m e n t s . . a r e c e n t d i s c u s s i o n o f t h i s p h e n o m e n o n i s t h a t o f V i t a l e ( V I T 8 0 ) . A s c o n f i r m a t i o n we n o t e t h a t Z i n o v e t a l . ( Z I N 6 4 ) s t u d i e d t h e a b s o l u t e i n t e n s i t y o f m u o n i c K s e r i e s X - r a y s f r o m a h y d r o - c a r b o n ( C H 2 ) a n d p u r e c a r b o n , a n d o b t a i n e d A ( C H 2 ) / A ( C ) = 0 . 9 9 6 ± 0 . 0 0 7 . T h e i r r e s u l t h a s i n d i c a t e d t h e a l m o s t c o m p l e t e t r a n s f e r o f t h e n e g a t i v e muon f r o m h y d r o g e n t o c a r b o n i n C H 2 . E u e t o t h i s f a s t t r a n s f e r , t h e h y d r o g e n a m p l i t u d e i s a l s o n e g l i g i b l e i n a d e c a y c u r v e o f H 2 O t a r g e t . I n o r d e r t o d e t e r m i n e t h e n e g a t i v e muon l i f e t i m e s , t h e w e i g h t e d a v e r a g e o f f o u r l i f e t i m e s , o b t a i n e d by t h e f i t t i n g o f d e c a y e l e c t r o n s p e c t r a f r o m f o u r e l e c t r o n t e l e s c o p e s , i s t a k e n , u s i n g t h e w e i g h t s s u p p l i e d f r o m t h e J3INUIT p r o g r a m . I I I . G H y p e r f i n e ( h f ) , E f f e c t i n a D e c a y C u r v e I n s e c t i o n I . D t h e h f e f f e c t i n n u c l e i h a s b e e n d i s c u s s e d . T h i s s e c t i o n e x p l a i n s how t h e e f f e c t i s o b t a i n e d b y d e t e c t i n g d e c a y e l e c t r o n s . M u o n s i n t h e K o r b i t o f t h e m u o n i c a t o m h a v e t h e i r own s p i n c o u p l e d t o t h e n u c l e a r s p i n r e s u l t i n g i n t w o h f s t a t e s . A t t = 0 , t h e t i m e o f t h e i r a r r i v a l i n t h e K o r b i t , t h e m u o n s p o p u l a t e t h e t w o s t a t e s 73 s t a t i s t i c a l l y and then undergo the hf t r a n s i t i o n from the higher l e v e l to the lower l e v e l . The conversion rates have been calculated by Winston (WIN63) for various nuclei. His resu l t s are l i s t e d in Table IV-6 along with past experimental r e s u l t s . In a histogram of decay electrons, there i s an e f f e c t from t h i s conversion and t h i s i s not ne g l i g i b l e for fl u o r i n e i n p a r t i c u l a r . This w i l l be discussed i n section IV.D. Figure III-5 shows the hf doublet and the de f i n i t i o n s cf Rh, B+, R~ and D. a t t=0, muons populate the F + and F~ states s t a t i s t i c a l l y as follows n+= (1+1)/(21+1) n-= 1/(21+1) (3 .7) The muon populations N+(t) and N~ (t) of F+ and F~ states are determined by d — N+(t) = - (Bh + B+)«N+(t) (3.8-1) dt d — N-(t) = Bh»N+(t) - E-»N-(t) (3.8-2) d t The time spectrum of decay electrons, Ne (t) , i s given by Ne (t)=Bd« {N+ (t) + N"(t) } (3.9) N u c l e a r L e v e l N u c l e u s A Rh R + = Rd + R c + D = R " - R + = R c - R c + J R = Rd + Rc~ gure III-5, Hyperfine doublet of muonic atom. Rh i s conversion rate, Rc capture rate, Rd decay rate, and R t o t a l disappearance rate. The +ve(-ve) s i shows the rate from F=I+l/2 (F=I-l/2) state. 75 Since Eh>>D for most nuclei (WIN63) , from eguations (3.8) and (3 . 9 ) , we have the simple form Ne (t) =const« {1 - Ae«exp (-Bh«t) } «exp (-E"«t) (3.10) Ae=n+«D/Bh. (3.11) Since 1=1/2 and D/Eh=0.02 for i«F (WIN63), the hf ef f e c t Ae i s egual to 0.015, which i s quite a small e f f e c t . In the case cf a nucleus which has the hf e f f e c t , equations (3.6) and (3.10) are combined to y i e l d the following equation Ne(t)=Eg + A < 1) «exp (-t/T (1) ) + A (2) «exp (-t/T (2) ) + A(3) »exp (- t/T (3) ) • {1 - A (4) «exp (-Bh*t) J (3.12) This i s used for the chi-squared minimization. The average capture, (Ec)av, and t o t a l disappearance rates of the hf doublet, (Et)av, are defined by (Ec) av=n+ •Ec* + n~«Ec- (3.13) (Et) av=n + »E+ + n~»R- (3. 14) T =1/(Et)av (3.15) where T i s the mean l i f e . These equations w i l l be applied in section IV,. D. The measurements of capture events (neutrons or gamma rays) i s suitable for experiments on the hf eff e c t in 76 muon capture (WIN61). In the capture process, Ae i n equation (3.10) i s replaced by An which i s given by An=n+«D/Ec- (3. 16) From equations (3.11) and (3.16), An=Ae» (Eh/Ec-) (3.17) For most nuclei, Eh>>Ec_, thus, the capture event measurements show a large hf e f f e c t . In the case of l 9 F , An=25«Ae and the large enhancement of the hf e f f e c t has been observed in the neutron and gamma ray measurement (WIN63) . 77 CHAPTER I V E x p e r i m e n t a l E e s u l t s a n d D i s c u s s i o n s o f L i f e t i m e M e a s u r e m e n t s O u r r e s u l t s f o r l i f e t i m e s a n d c a p t u r e r a t e s o f n e g a t i v e muons i n c o m p l e x n u c l e i a r e l i s t e d i n T a b l e I V - 1 . . I n T a b l e I V - 2 p a s t m e a s u r e m e n t s a r e s h o w n a l o n g w i t h o u r r e s u l t s l i s t e d i n T a b l e I V - 1 . I n o u r c a l c u l a t i o n o f c a p t u r e r a t e s , o u r r e s u l t o f t h e p o s i t i v e muon l i f e t i m e , 2 1 9 7 . 0 ± 0 . 7 n s , a n d t h e H u f f c o r r e c t i o n f a c t o r o f t h e b o u n d muon d e c a y a r e e m p l o y e d . I n t h i s e x p e r i m e n t , t h e a c c u r a c y o f t h e l i f e t i m e m e a s u r e m e n t h a s b e e n i m p r o v e d f o r many l i g h t e l e m e n t s ( E e , B , N , 0 , F , N a , C l , K) a n d new m e a s u r e m e n t s h a v e b e e n made f o r 1 3 C , 1 8 0 , Dy a n d E r . M a n y p a s t m e a s u r e m e n t s h a d s y s t e m a t i c e r r o r s , e s p e c i a l l y f o r t h e p o s i t i v e mucn l i f e t i m e w h i c h was many s t a n d a r d d e v i a t i o n s a w a y f r o m t h e c u r r e n t l y a c c e p t e d v a l u e . T h e s y s t e m a t i c e r r o r c f o u r s y s t e m h a s b e e n s t u d i e d c a r e f u l l y , a s d i s c u s s e d i n C h a p t e r I I I , a n d t h e c o r r e c t p o s i t i v e muon l i f e t i m e h a s b e e n o b t a i n e d a s s h o w n i n t h e f o l l o w i n g s e c t i o n I V . A . Table IV-1(1) R e s u l t s of L i f e t i m e Measurements i n T h i s Experiment z Element Mean L i f e Capture Rate Huff Fac. (A-Z) /2i ( ns ) ( x l C 6 /sec) (Q) 3 L i - 6 2177.0±2.0 4. 18±0.45 xlO" 3 1. 0 0. 25 L i - 7 2188.3±2.0 1.81±0.45 x10- 3 1.0 0. 2857 4 Be 2162.1±2.0 7.35±0,45 x10~ 3 1.0 0. 2778 5 B-10 2070.7±3.0 2.8U0.07 x10-2 1,. 0 0.25 B-il 1 2096. 1 ± 3 . 0 2.22±0.07 x10- 2 1.0 0. 2727 6 C 2026. 3+ 1.5 3.88±0.05 x10-2 1. 0 0. 25 C-13 2029.1±3.0 3.77±0.07 x10- 2 1.0 0.2692 7 N 1906.8±3.0 6.93±0.C8 x10- 2 1.0 0.25 8 0 1795. 4 + 2.0 10.36±0.04 x10-2 0. 998 0. 25 0-18 1344.0±4.5 8.80±0. 15 xlO-2 0. 998 0.2778 9 F - L i F 1464.7+4.0 0.228±0.002 0. 998 0.2632 F-C2F4 1458.8+4.0 0.23U0.002 0. 998 0. 2632 F-CaF2 1463.2±5.0 0.229±0.003 0. 998 0. 2632 F-PtF2 1462.2 + 6.0 0.230±0.003 0. 998 0.2632 11 Na 1204. 0±2.0 0.377±0.001 0. 996 0. 26 12 Mg 1067.2±2.0 0.484±0.002 0. 995 0.2533 13 A l 864. 0±1.0 0.705±0.001 0. 993 0.2593 14 S i 756.0±1.0 0. 87 1±0.002 0. 992 0.2510 15 P 6 1 1. 2±1.0 1. 185±0.003 0.99 1 0. 2581 16 S 554.7±1.0 1. 35210.C03 0.990 0. 2507 17 C l 560.8±2.0 1.333±0. 006 0. 989 0. 2605 19 K 437. 0± 1.0 1.839±0.005 0.987 0.2570 20 ca 332. 7+1.5 2.557±0.C14 0. 985 0.2505 22 T i 329. 3± 1.3 2.590+0.012 0. 981 0. 2705 23 V 284. 5±2.0 3.069±0.025 0. 980 0. 2745 24 c r 255.3±2.0 3.472±0.031 0. 978 0.2695 25 Mn 232. 5i2. 0 3.857±0.C37 0. 976 0.2727 26 Fe 206. 0± 1.0 4.4 10±0.024 0. 975 0.2675 27 Co 185.8±1.0 4.940±0.029 0. 971 0.2712 28 Ni 156.9± 1.0 5.932±0.041 0.969 0. 26 18 29 Cu 163.5H.G 5.676+0 .037 0. 967 0.2721 30 Zn 159, 4±1. 0 5.834±0.C39 0.965 0. 2709 32 Ge 180.0±2.0 5. 1 18±0.062 0.96 0 0. 28 35 Br 13 3. 3± 1.0 7.069±0.G56 0.952 0.2810 79 T a b l e I V - 1 ( 2 ) R e s u l t s o f L i f e t i m e M e a s u r e m e n t s i n T h i s E x p e r i m e n t E l e m e n t M e a n L i f e C a p t u r e R a t e H u f f F a c . ( A - Z ) / 2 A ( n s ) ( x 1 0 6 / s e c ) (Q) 40 Z r 110. 0 ± 1 . 0 8. 6 6 3 ± 0 . 083 0. 940 0 . 2 8 1 0 41 Nb 9 2. 7 ± 1 . K ~* 1. 0 3 6 ± 0 . 0 18 X10 0. 93 9 0 . 2 7 9 6 42 Mo 9 9 . 6 ± 1 . 5 0. 9 6 1 ± 0 . 0 15 X10 0 . 9 3 6 0. 28 10 47 Ag 87. 0 ± 1 . 5 1. 1 0 7 ± 0 . 020 X10 0. 925 0 . 2 8 2 3 48 c a 9 0 . 7± 1. 5 1. 0 6 0 ± 0 . 0 18 X10 0. 921 0 . 2 8 6 9 49 I n 8 4 . 6 ± 1 . 5 1. 1 4 0 ± 0 . 021 X10 0. 920 0 . 2 8 6 8 50 S n 9 2. 1 + 1. 5 1. 0 4 4 ± 0 . 018 X10 0. 918 0 . 2 8 6 7 53 I 8 3 . 4 ± 1 . 5 1. 1 5 8 ± 0 . 021 X10 0.910 0. 29 13 56 B a 9 6 . 6 1 1 . 5 0. 9 9 4 ± 0 . 0 16 X10 0.902 0 . 2 9 5 9 60 Nd 77. 5 ± 2 . 0 1. 2 5 0 ± 0 . G33 X10 0. 895 0. 29 19 64 Gd 8 1 . 8± 1 . 5 1 . 1 8 2 ± 0 . 022 X10 0. 885 0.2964 66 Dy 7 8 . 8 ± 1 . 1 1. 2 2 9 ± 0 . C18 X10 0.880 0 . 2 9 6 9 68 E r 74. 4 ± 1 . 5 1. 3 0 4 ± 0 . 027 XI 0 0. 875 0 . 2 9 6 8 74 W 78. 4 ± 1 . 5 1. 2 3 7 + 0 . 024 X10 0,. 86 0 0 . 2 9 8 4 80 Hg 7 6 . 2 ± 1 . 5 1. 2 7 4 ± 0 . 026 X10 0. 848 0. 3 82 P b 72. 3 ± 1 . 1 1 . 3 4 5 ± 0 . 021 X10 0. 844 0. 3022 83 B i 7 4 . 2 ± 1 . 0 1 . 3 1 0 ± 0 - 0 18 X10 0. 840 0 . 3 0 1 4 Table IV-2 ( 1 ) Muon Lifetimes and Capture Rates Z (Zeff) Element Mean L i f e ( ns ) Capture Rate (IO* /sec) 2A Ref s. 1 (1.0) H 2 (1.98) He-3 He-4 3 (2^94) Li-6 3 Li-7 4 (3.89) Ee 5 (4. 81) E- 10 B-11 6 (5.72) C 2195.6±0. 3 2194.97±0.15 2 198±2 651±57 467±43 x 1 0 ~ 6 x 1 0 - 6 C- 13 7 (6.61) N 8 (7.49) 0 0-18 9 (8.32) F (These F data See section 2173 +5 2 175.310. 4 2177.0±2.0 2194 ±4 2 186. 8±0. 4 2188.3±2.0 2140 ±20 2156 +10 2169.0±1. 0 2 162. 1±2.0 2C82 ±6 2070.7±3.0 2102 ±6 2096.1±3.0 2020 ±20 2043 2041 2040 2025 2035 2060 ±3 ±5 ±30 ±4 ±8 ±30 2170+ 170 (-430) x10~6 1410±140 336±75 375+30 (-300) 6 100± 1400 4678H04 4180±450 1800±1100 2260±104 1810±440 0.018 0.010 0, 0. 0. 2030.0± 1. 6 2026.3±1.5 2029.1±3.0 1860 ±20 1927 ±13 1940.5±2.8 1906.8±3.0 1640 ±30 1812 ±12 1810 ±20 1795.4±2.0 1844.0±4.5 1420 ±40 1450 ±20- 1458 ±13 1462.7±5. 0 show l i f e t i m e s IV.D (g) ) 0. -19- -28- - 14- 17- 7- 15- 17- 10- 26- * 10- -26- * 0.2778 - 1- - 10- -29- 0. 0. 1667 1667 25 25 2857 x10~ 6 x l O - 6 X 1 0 - 6 X 1 0 - 6 x10-6 x10~ 6 X 1 0 - 6 x10" 6 X 1 0 - 6 ±0.0 1 ±0.002 0.OC59±0.0O02 0.0074±0.0005 * 0.0265±0.0015 0. 25 - 10- 0.0278±0. 0007 * 0.02 18±0.00 16 0.2727 -10- 0.0219±0.0007 * 0. 044 ±0.01 0 0.25 - 1- 0.0373±0.00 11 - 3- G.0361±0.00 13 - 4- 0. 037 ±0.007 - 5- 0.0397±0.00 13 -10- 0.0365±0.0020 -13- 0.0303±0.007 - 16- 0. 0376±0.0004 -29- •0.0388±0.0005 * 0.0376±0.0007 0. 2692 * O.C86 ±0.011 0.25 - 1- 0. 065 ±0.004 -10- C. 0602±0.0008 -29- 0.06S3±0.0008 * 0. 159 ±0.0 14 0.25 - 1- C.098 ±0.003 - 10- 0.0S8 ±G..005 - 16- 0.1026±0.0006 * C. 0880±0.00 15 0. 2778 * 0.254 ±0.022 0. 2632 - 1- 0. 235 ±0.010 - 8- C.231 ±0.006 -13- 0.229 ±0.001 * for lower hf states. Table IV-2'(2) Muon L i f e t i m e s and Capture Rates z (Zeff) Element Mean L i f e ( ns ) Capture Rate (10 6 /sec) 2A Ref s, 10 (9. i i i ) Ne 1520 ±23 0.204 ±0.0 10 0. 2522 -11- 0. 167 ±0.030 - 12- 0. 30 ±0.02 -22- 1450 ±10 0. 235 ±0.005 -29- 11 (9. 95) Na 1190 ±20 C.3 67 ±0.015 0.2609 - 1- 1204.0±2. 0 0.3772±0.0014 * 12(10. 69) Mg 1040 ±20 0.507 ±0.020 0,2533 - 1- 107 1 ±2 0.4 80 ±0.002 - 4- 102 1 ±25 0.52 ±0.02 - 18- 1067.2±2.0 0;4641±0.0018 * 13(11. 48) ftl 880 ±10 0.69 1 ±0.020 0.2593 - 1- 864 ±2 0. 662 ±0.003 - 4- 905 ±12 0. 650±0,015 - 8- 864. 0±1. 0 0.705' 4±0.00 13 * 14 (12. 22) S i 810 ±10 0.777 ±0.025 0.2510 - 1- 767 ±2 0.8 50 ±0.003 - 4- 758 ±20 0.86 ±0.04 -18- 756.0±1.0 C.8712±0.0018 * 15(12. 90) P 660 ±20 1. 054 ±0.05 0.2581 - 1- 635 ±2 1.121 ±0.005 - 4- 61 1. 2±1. 0 1. 185 ±0.003 * 16(13- 64) S 540 ±20 1.39 ±0.09 0. 2507 - 1- 567.4±8.4 1.3 1 ±0.03 -18- 554. 7±1. 0 1.352 ±0.003 * 17(14. 24) C l 540 ±20 1.39 ±0.09 0.2605 - 1- 560.8±2.0 1.333 ±0.006 * 18(14. 89) Ar 1.20 ±0.08 -22- 19 (15. 53) K 410 ±20 1.99 ±0.12 0.2573 - 1- 437.0±1„0 1.839 ±0.005 * 20(16. 15) Ca- 40 333 ±7 2.55 ±0.05 0. 25 - 1- 333 ±7 2.549 ±0.063 - 6- 335.9±0. 9 2. 977 ±0.008 -21- 365 ±8 2.286 ±0.050 -25- 332. 7±1. 5 2.557 ±0.014 * Ca- 44 445 ±8 1. 793 ±0.040 0.2727 - 6- 22(17. 38) T i 330 ±7 2.63 ±0.06 0. 2705 - 1- 327. 3±4. 5 2.60 ±0.04 - 18- 329.3±1.3 2. 590 ±0.012 * 23 (18. 04) V 264 ±4 3.37 ±0,06 0. 2745 - 1- 27 1 ±5 3.24 ±0.07 - 5- 282.6±3. 2 3.OS ±0.05 -18- 284.5±2.0 3. 069 ±0.025 * 24(18. 49) Cr 276 ±6 3.24 ±0.08 0.2695 - 1- 264.5±3.2 3. 33 ±0.06 - 18- 255.3±2. 0 3.472 ±0.031 * 25(19. 06) Mn 239 ±4 3. 67 ±0.08 0. 2727 - 1- 225. 5±2. 3 3.98 ±0.05 -18- 232.5±2. 0 3. 857 ±0.037 * Table IV-2 (3) Muon L i f e t i m e s and Capture Rates z Element Mean L i f e Capture Rate J A z Z l Ref s, (Zeff) ( ns ) (IO 6 /sec) 2A 26 (19.59) Fe 201 ±4 4.53 ±0.0 1 0.2675 1- 196 ±8 - 2-207 ±3 1.38 ±0.07 - 5-206.7±2.4 4. 40 ±0.05 - 18-206.0±1.0 4.4 11 ±0.024 * 27(20jJ3) Co 188 ±3 4. 89 +0.09 0.2712 - 5-184.Oil. 7 4.96 ±0.05 - 18- 185,. 8±1. 0 4. 940 ±0,029 * 28 (20.66) Ni 154 ±3 6. 03 ±0.14 0. 2618 - 1-158 ±3 5.9 ±0. 1 - 5-159,. 1±3. 1 5.83 ±0.11 - 18-156.9±1.0 5.932 ±0.041 * 29 (21.12) Cu 160 ±4 5, 79 ±0*16 0.2721 - 1-169±6 5.47 ±0.20 - 8-164.0±2. 3 5.66 ±0.09 - 9-163, 5± 2. 4 5.6 7 ±0.09 - 18- 163.5+1.0 5.676 ±0.037 * Cu-63 162. 1±1. 4 5.72 ±0.05 0.2698 - 18- 30 (21 .6 1) Zn 161 +4 5. 76 ±0.17 0.2709 - 1-169 ±4 5. 5 ±0, 1 - 5-16 1. 2±1. 1 5.76 ±0.05 - 18-159,. 4±1. 0 5. 834 ±0.039 * 31 (22.02) Ga 163.0±1.6 5. 70 ±0.06 0.2779 - 18- 32 (22^43) Ge 167. 4±1. 8 5.54 ±0.06 0. 28 - 18-180. 0±2. 0 5. 119 ±0.061 * 33 (22.84) as 153.8 + 1. 7 6.07 ±0.0 7 0. 28 - 18-34(23.24) Se 163.0±1. 2 5.70 ±0.05 0. 2850 - 18-3 5 (23s_6 5) Br- 79 133.7±6.5 7.03 ±0. 34 0.2785 -20-Er- 81 125. 3±7.9 7. 53 ±0.48 0. 2840 - 20- Er 133, 3± 1. 0 7,. 06 9 ±0.056 0.2810 * 37 (24.47) Rb 136i,5±2. 7 6.89 ±0.13 0. 2838 - 18-38(24.85) Sr 130. 1+2. 3 7.25 ±0.14 0.2834 - 18-Sr- 88 142.0±5.5 6.6 1 ±0. 27 0.2841 - 18-39 (25.23) Y 120.2+1.4 7.89 ±0.11 0.2809 - 9-40(25.6J) Zr 110.8±0. 8 8, 59 ±0.07 0.2810 - 18-110.0±1.0 8.663 ±0.083 * 41(25.9S) Nb 92. 3±1. 1 10. 40 ±0.14 0.2796 - 9-92.7±1.5 10.36 ±0. 17 * 42 (26.37) Mo 105 ±2 9.09 ±0.18 0.2810 1- 103.5±0.7 5.23 ±0.07 - 18-99.6±1.5 9.6 14 ±0. 15 * 45(27.32) Rh 95.8±0.6 10.01 ±0.07 0. 28 16 - 18- 46 (27.63) Pd 96.0+0.6 10. 00 ±0.07 0.2841 - 18-47(27.95) Ag 85 ±3 11.25 ±0.5 0. 2823 - 1-88.7±0.9 10. 86 ±0. 13 - 9-88.6±1.1 10.88 ±0. 14 - 18-87.0±1. 5 11.07 ±0.20 * Table IV-2(4) Muon L i f e t i m e s and Capture Rates z Element Mean L i f e Capture Rate J l z z i Ref s (Zeff) ( ns ) ( I O 6 /sec) 2a 48(28.20) Cd 95 ±5 10.05 ±0. 5 0.2869 - 1- 90.5±0. 8 10. 63 ±0. 11 - 9- 90.7±1. 5 10. 61 ±0.18 * 4 9 (28^4 2) In 84.8±0.8 1 1.37 10. 13 0.2868 - 9- 84.6±1. 5 11.40 ±0.21 * 50 (28.64) Sn 92 ±3 10. 5 10.4 0.2867 - 5- 89,9±1.0 10.70 ±0. 14 - 9- 92. 1±1. 5 10.44 10.18 * 51 (28.79) Sb 91.7±1. 1 10. 19 ±0.14 0.2907 - 9- 52 (29.03) l e 105.5±1. 2 9. 06 10. 11 0. 2964 -18- 53 (29^27) I 86. 1±0.7 1 1. 20 ±0. 1 1 0.29 13 - 9- 83.4±1.5 11. 58 ±0.22 * 55 (29.75) Cs 87.8±1. 9 10. S8 ±0.25 0. 2932 - 9- 56 (29,9 9) Ea 94.5±0.7 10. 18 ±0. 1 0 0.2959 - 9- 96.6±1.5 9.94 1±0.16 * 57 (30.22) La 89.9±0.7 10.71 ±0. 10 0.2950 - 9- 58 (30.36) Ce 84.4±0.7 11. 44 ±0. 11 0.2928 - 9- 59 (30.53) Pr 72. 1 + 0. 6 13.45 ±0. 13 0. 2908 - 9- 6 0 (30.69) Nd 78,5±0.8 12. 32 ±0. 14 0.2919 - 9- ° 77.5±2.0 12.50 ±0.33 * 62 (3-1.0 1) Sm 79.2±1.0 12.22 ±0. 17 0. 2937 - 9- 64 (31. 34) Gd 80.1+1.0 12. 09 ±0. 16 0.2964 - 9- 8 1.8±1. 5 11.82 ±0.22 * 65 (31 .48) Tb 76.2+0.7 12.73 ±0, 13 0,2956 - 9- 66 (31.62) Dy 78.8 + 1. 1 12. 29 ±0. 18 0.2969 * 67(31.76) Ho 74.9±0.6 12. 95 ±0. 13 0.2970 - 9- 68 (31.90) Er 74.4±1.5 13. 04 ±0. 27 0.2968 * 72 (32.47) Hf 74.5± 1. 3 13. 03 ±0,2 1 0. 2982 - 18- 73 (32.6 1) Ta 75. 5±0. 6 12. 86 ±0. 13 0.2983 - 9- 74 (32.76) W 81 ±2 11.9 ±0.3 0.2984 - 1- 72 ±3 13. 5 ±0.6 - 5- 74.3+1.2 13.07 ±0.21 -18- 78. 4±1. 5 12.36 ±0.24 * 79 (33.64) au 75.6±0. 5 13.39 ±0. 1 1 0. 2995 - 9- 80 (33.8 1) Hg 76.2± 1.5 12.74 ±0.26 0. 3 - 18- 76. 2±1. 5 12.74 ±0.26 * 81 (34.2 1) T l 75 +4 12. 90 ±0.75 0.3019 - 1- 70.3±0.9 13. 83 ±0. 20 - 9- 82 (34. 18) Pb 82 ±5 11.70 ±0.75 0. 3022 - 1- 67 ±3 14. 50 ±0.7 - 5- 74.9±0. 4 12. 98 ±0. 10 - 9- 73.2±1.2 13.27 ±0.22 -18- 72.311. 1 13.45 ±0,21 * RPbi 71.510.4 13.61 ±0. 10 - 9- Table IV-2(5) Muon L i f e t i m e s and Capture Rates z E l e m e n t Mean L i f e C a p t u r e R a t e R e f s , ( Z e f f ) ( n s ) ( 1 0 6 / s e c ) 2A 8 3 ( 3 4 . 0 ) B i 79 +5 1 2 . 2 0 + 0 . 7 5 0 . 3 0 1 4 - 1- 7 3 . 3 + 0 . 4 1 3 . 2 6 ± 0 , . 10 - 9 - 7 4 . 2 ± 1 . 0 1 3 . 1 0 ± 0 . 1 8 * 9 0 (34.J3) T h - 2 3 2 8 0 . 4 ± 2 . 0 1 2 . 1 ± 0 . 3 0 . 3 0 6 1 - 2 3 -7 9 . 2 ± 2 . 0 1 2 . 2 ± 0 . 3 - 2 4 - 9 2 ( 3 4 . 94) 0 - 2 3 5 78 ±4 ( 1 2 , 4 ± 0 . 6 ) 0 . 3 0 4 3 - 2 3 - 7 5 . 4 ± 1 . 9 1 2 . 9 ± 0 . 3 0 . 3 0 4 3 - 2 4 - 0 - 2 3 8 8 8 ±4 1 0 . 9 ± 0 . 5 0 . 3 0 6 8 - 1 - 8 1 . 5 + 2. 0 ( 1 1 . 9 ± 0 . 3 ) - 2 3 - 7 3 . 5 ± 2 . 0 1 3 . 2 ± 0 . 4 - 2 4 - 9 3 ( 3 5 . 0 5 ) Np 7 1 . 3 ± 0 . 9 ( 1 3 . 6 ± 0 . 2 ) 0 . 3 0 3 8 - 2 7 - 9 4 ( 3 5 . J 6 ) P u - 2 3 9 7 7 . 5 ± 2 . 0 ( 1 2 . 5 ± 0 . 3 ) 0 . 3 0 3 3 - 2 3 - 7 3 . 4 + 2 . 8 1 3 . 3 ± 0 . 4 - 2 4 - 7 0 . 1 ± 0 . 7 ( 1 3 . 9 ± 0 . 2 ) - 2 7 - P u - 2 4 2 7 5 . 4 ± 0 . 9 ( 1 2 . 9 ± 0 . 2 ) 0 . 3 0 5 8 - 2 7 - References: - 1- (SEN59) , - 2- (BAR59) , - 3- (REI60) , - 4- (LAT6 1) , - 5- (BLA62) , - 6- (CRA62) , - 7- (FAL62) , - 8- (ECK62) , - 9- (FIL63) , -10- (ECK63) , - 1 1- (R0S63) , -12- (CON63) , -13- (WIN63) , - 14- (MEY63) , - 15- (BIZ64) , -16- (BAR64) , -17- (AUE65) , - 18- (ECK66) , - 19- (ALB69) , -20- (POV70) , -21- (DIL71) , -22- (EER73-2) ,-23- (HAS76) , -24- (JOH77) , -25- (HAR77), -26- (BAR78) , -27- (SCH79), -28- (BAR 79) , -29- Note: (MAE80) *: Denotes the r e s u l t s of t h i s experiment. (Zeff) with u n d e r l i n e s are estimated v a l u e s . ( ) : Numbers are net given i n r e f e r e n c e s and estimated from capture r a t e s c r l i f e t i m e s . 1) RPb = r a d i o g e n i c l e a d (88%Pb-206,9%Pb-207,3%Pb-208) 85 IV.A Positive Muon Lifetime i n Carbon In t h i s experiment the positive muon l i f e t i m e (T (+)) was used to c a l i b r a t e the experimental set-up and the data taking system, since the l i f e t i m e has been measured precisely at several laboratories as shown i n Table IV - 3 . The.accepted value cf the l i f e t i m e i s 2197.120±0.077 ns i n the Beview of Pa r t i c l e Properties (KEL80). Before I960, there was d i f f i c u l t y i n the detection of microsecond time i n t e r v a l s , because a delayed coincidence or a time to pulse height converter (TAC) was employed to determine time d i s t r i b u t i c n s . Swanson (SWA60) pointed out that there was a non-linearity cf 1 to 2 % and a c a l i b r a t i o n i n s t a b i l i t y of 0.6% i n the IAC. After 1960, a d i g i t a l technigue with a high freguency o s c i l l a t o r became common and was able to reduce the systematic error i n the timing of the in t e r v a l s . However, i t was pointed out by Lundy (LUN62) that there was s t i l l a systematic error due to the time dependent background caused by 2nd muons. As shown i n Table IV - 3 , an accurate measurement was done by Ealadin et a l . (BAL74) by using a positron detector with a 4 ir radian s o l i d angle. . In t h i s experiment, as discussed in Chapter I I I , the systematic errors have been studied c a r e f u l l y by checking the event rejection e f f e c t s , the stopping muon rate e f f e c t , and the magnetic f i e l d e f f e c t . I t has been concluded that the systematic error i n the positive muon Table IV-3 Past P o s i t i v e Muon L i f e t i m e s Auther and E e f s . Year E e s u l t ( ns ) W.E.Bell e t . a l . (BEL51) 1951 2220 ± 20 E.W.Swanscn et a l . (SWA 59) 1959 2261 ± 7 J . F i s h e r et a l . (FIS59) 1959 2200 + 15 J.C.Sens et a l . (SEN59) 1959 2210 ± 20 E . A . E e i t e r et a l . . (BEI60) 1960 2211 ± 3 J . L . L a t h r c p e t a l . (LAT6 1) 1961 2203 + 2 E.A.Lundy et a l . (LUN62) 1962 2203 ± 4 S.L.Meyer et a l . (MEY63) 1963 2198 ± 2 M.Eckhause et a l . (ECK63) 1963 2202 ± 4 J.Barlow et a l . (EAE64) 1964 2 197 ± ' 2 E.W.Williams e t a l . (WIL72) 1972 2200.26 i ± 0.81 J.Duclos et a l . (DUC73) 1973 2197.3 ± 0.4 M.P.Balandin et a l . (EAL74) 1974 2 197. 1 1 1 ± 0.08 G.Eardin et a l . . (BAE78) 1978 2196. 8 + 0. 4 (EAE79) 1979 2197. OS I ± 0. 14 TEIUMF (SUZ80) 1S79 2 197.0 + 0.7 P a r t i c l e E ATA Group (KEL80) 1980 2 197. 120± 0.077 Decay rate 0.455141 ± 0.000016 x10* s~» 87 l i f e t i m e i s n e g l i g i b l e . T h e l i f e t i m e s o f 10 r u n s a r e l i s t e d i n T a b l e I I I - 1 a n d t h e a v e r a g e p o s i t i v e muon l i f e t i m e i s T>( + ) =2 1 9 7 . 0 ± 0 . 7 ( 4 . 1) w h i c h i s i n g o o d a g r e e m e n t w i t h t h e a c c e p t e d v a l u e . T h i s r e s u l t c a n b e a p p l i e d i n c a l c u l a t i n g t h e c o u p l i n g c o n s t a n t , Gm, f o r a muon d e c a y . A s s u m i n g V - A i n t e r a c t i o n , S o o s a n d S i r l i n (RO07 1) d e r i v e d t h e f o l l o w i n g r e l a t i o n 192 • ( TT ) 3 ( H e « n " ) s t i z » c « ( 1 + d) ( G m ) 2 = • : • ( 4 . 2 ) T(+) ( M m » M e * c ) s (1 - 8 « (Me/Mm) 2 ) Gm = 1 . 4 3 5 6 (7) x 1 0 - * » e r g « c m 3 w h e r e Mm/Me = 2 0 6 . 7 6 8 2 (5) ( C R 0 7 2 ) -fa/ ( M e » c ) = 3 . 8 6 1 4 x 1 0 - i i cm -ft = 1 . 0 5 4 5 x 1 0 ~ 2 7 e r g « s e c d = 0 . 0 0 4 2 2 ( r a d i a t i v e c o r r e c t i o n , R 0 0 7 1 ) T (+) = 219 7 . 0 ( 1 . 0 ) n s S h r o c k a n d Wang ( S H E 7 8 ) h a v e d e t e r m i n e d Gm w i t h t h e p r e c i s e l i f e t i m e o b t a i n e d b y B a l a n d i n e t a l . ( B A 1 7 4 ) a n d t h e i r new f o r m u l a f o r Gm. T h e i r n u m b e r f o r Gm i s Gm = 1 . 4 3 5 8 2 (4) x 1 0 - * « e r g » c m 3 F o r t h e muon l i f e t i m e g i v e n b y ( 4 . 1) , t h e muon d e c a y r a t e d e f i n e d by e q u a t i o n ( 4 . 2 ) i s R d ( + ) = ( 4 . 5 5 1 ± 0 . 0 0 2 ) x 1 0 s / s e c ( 4 . 3 ) 88 I V . B Muon C a p t u r e B a t e a n d i t s a c c u r a c y a s d i s c u s s e d i n s e c t i o n I . C , The b o u n d muon d e c a y r a t e i s n e t t h e same a s t h e f r e e p o s i t i v e mucn d e c a y r a t a a n d t h e r e l a t i o n b e t w e e n t h e t w o r a t e s i s w r i t t e n a s Bd (-) = Q (Z) « B d ( + ) = Q ( Z ) / T ( + ) ( 4 . 4 ) w h e r e Q (Z) i s c a l l e d a H u f f f a c t o r ( H u f 6 0 ) . H u f f ' s t h e o r y f o r t h e b o u n d muon d e c a y i n t h e m e s c n i c a t o m s p r e d i c t s t h a t a b o u n d muon i n h e a v y e l e m e n t s h a s a r e d u c e d d e c a y r a t e . T h e t h e o r y i s i n g c o d a g r e e m e n t w i t h s u b s e q u e n t m e a s u r e m e n t s ( B L A 6 2 - 2 , Y A M 7 4 ) . A l s o , O b e r a l l (OBE60) c a l c u l a t e d t h e muon b o u n d e f f e c t i n t h e n u c l e u s . He o b t a i n e d a s i m p l e f o r m Q (Z) = 1 - 0 . 5 ( Z / 1 3 7 ) 2 ( 4 . 5) T h i s r e s u l t h a s b e e n o b t a i n e d f o r a p o i n t n u c l e u s . F o r h e a v y e l e m e n t s , t h e K c r b i t o f t h e m e s o n i c a t o m i s f o r m e d i n s i d e t h e n u c l e u s , t h u s t h e e f f e c t i v e c h a r g e , w h i c h i s r e s p o n s i b l e f e r t h e mucn c a p t u r e , b e c o m e s much s m a l l e r t h a n t h e n u c l e a r c h a r g e . H e n c e U b e r a l l ' s f o r m u l a ( 4 . 6 ) o v e r e s t i m a t e s t h e b o u n d e f f e c t i n t h e h e a v y n u c l e i . C a l c u l a t i o n s b y H u f f a n d U b e r a l l a r e s h o w n i n f i g u r e I V - 1 . I n t h i s w e r k H u f f ' s v a l u e s w e r e e m p l o y e d a n d l i s t e d i n T a b l e 89 T ATOMIC NUMBER(Z) Figure IV-1, Ratio of bound decay rate to free decay rate. 9 0 IV-]. In muon capture experiment, the t o t a l disappearance rate, the nuclear capture rate, and the decay rate, are freguently used. For reasons of convenience, those re l a t i o n s are summarized in the following. Decay rate of free muons; Rd (+) =1/T ( + ) , T(+): positive or negative free muon l i f e t i m e < 2 1 9 7 . 0 ns) Total disappearance rate; Rt=1/T(-) T(-): negative muon l i f e t i m e i n nucleus Rt=Rc + Q (Z)«Rd (+) =Rc + Rd {-) Nuclear capture rate ; Rc=Rt - Rd(-) = 1/T(-) - Q(Z)/T( + ) ( 4 . 6 ) When the nuclear capture rate i s obtained from l i f e t i m e measurements, eguation ( 4 . 6 ) i s used. T (-) ; l i s t e d in Tables IV-1 and I V - 2 T (+) ; 2 1 S 7 . 0 ± 0 . 7 ns (our measurement) Q (Z) ; figure I V - 1 , Huff factor The accuracy of the t o t a l disappearance rate i s defined by dRt/fit = 1/-/(Ne) ( 4 . 7 ) where Ne i s the t o t a l number of electron events. From 9 1 e q u a t i o n ( 4 . 6 ) , t h e c a p t u r e r a t e E c i s e q u a l t o R - E d w i t h t h e a p p r o x i m a t i o n c f Q ( Z ) = 1 . T h e a c c u r a c y o f E c i s e x p r e s s e d a s d E c 1 / E t 2 E d 2 E c - R e v N e - Ne + F o r e x a m p l e , i n t h e c a s e o f 6 L i , we h a v e t h e f o l l o w i n g a p p r o x i m a t e n u m b e r s a n d e g u a t i o n s f o r a 0 . 1 % a c c u r a c y o f l i f e t i m e m e a s u r e m e n t T <-) = 2 1 7 5 . 0 ± 2 . C ( 0 . 1 % ) E t = E d = 4 . 5 x 1 0 5 / s e c E c = 5 0 0 0 / s e c N e ~ = N e + = 4 x 1 0 6 e v e n t s d R c / E c = E d / R c « A / ( 2 / N e ) ( 4 . 9 ) T h u s t h e a c c u r a c y c f R c i n 6 L i i s a b o u t 6 % . I n t h e c a s e o f h e a v y e l e m e n t s (Z>20) , R c i s g r e a t e r t h a n Rd a n d N e - i s much l e s s t h a n N e + . T h e r e f o r e , t h e a c c u r a c y o f t h e c a p t u r e r a t e E c i s . a p p r o x i m a t e d by d E c / B c = ]//J(He-) ( 4 . 1 0 ) E q u a t i o n ( 4 . 1 0 ) g i v e s a 1 % a c c u r a c y o f E c f o r N e - = 1 0 * t o t a l e v e n t s , w h i c h i s e q u i v a l e n t t o a 1% a c c u r a c y i n a l i f e t i m e m e a s u r e m e n t i n a l e a d t a r g e t . 92 I V . C N e g a t i v e Mucin L i f e t i m e M e a s u r e m e n t s i n C a r b o n a n d S y s t e m C a l i b r a t i o n The l i f e t i m e i n c a r b o n was m e a s u r e d s e v e r a l t i m e s t h r o u g h o u t t h i s e x p e r i m e n t , s i n c e t h e l i f e t i m e w a s u s e d a s t h e c a l i b r a t i o n o f t h e s y s t e m . T h e r e s u l t s o f s e v e n m e a s u r e m e n t s a r e l i s t e d i n T a b l e I V - 4 , a l o n g w i t h a r e s u l t f r o m t h e s p r i n g o f 1 9 7 9 . T h e w e i g h t e d a v e r a g e o f t h e s e p a r a t e r u n s i s r e c o r d e d i n T a b l e I V - 1 . T h e e r r o r i s d e t e r m i n e d f r c m t h e s t a t i s t i c s a n d t h e d e v i a t i o n s o f e a c h o f t h e d i f f e r e n t r u n s f r c m t h e m e a n . T h e c h a n g e s i n t h e l i f e t i m e , a s s h o w n i n t h e t a b l e , a r e g u i t e s m a l l a n d i t a s s u r e s t h a t t h e s y s t e m was w o r k i n g p r o p e r l y t h r o u g h o u t t h i s e x p e r i m e n t . A s l i s t e d i n T a b l e I V - 2 , a r o u n d 1 9 6 0 , t h e r e a r e t h r e e p r e c i s e m e a s u r e m e n t s f o r 1 2 C by E c k h a u s e e t a l . , L a t h r o p e t a l . , a n d E e i t e r e t a l . . T h e i r m e a s u r e m e n t s f o r t h e l i f e t i m e o f t h e p o s i t i v e m u o n , a s s h e w n i n T a b l e I V - 3 , a r e 2 2 0 2 + 4 n s , 2 2 0 3 ± 2 n s a n d 2 21 1 ±3 n s , r e s p e c t i v e l y , w h i c h a l l d i s a g r e e w i t h t h e p r e s e n t l y a c c e p t e d v a l u e o f 2 1 9 7 . 1 3 ± 0 . 0 8 n s . I t s e e m s t h e i r s y s t e m s w e r e n o t w e l l c a l i b r a t e d a n d , f r o m t h e p o i n t c f v i e w o f s y s t e m c a l i b r a t i o n , o u r n e g a t i v e muon l i f e t i m e i n c a r b o n w o u l d a p p e a r t h e r e f o r e t o be m o r e r e l i a b l e . The S a c l a y g r o u p h a s a w e l l c a l i b r a t e d s y s t e m w i t h w h i c h t h e y d e t e r m i n e d t h e p o s i t i v e muon l i f e t i m e t o b e 2 1 9 7 . 1 8 ± 0 . 1 2 n s ( D U C 8 0 , B A E 7 9 ) . T h e i r v a l u e f o r t h e T a b l e I V - 4 N e g a t i v e M u o n l i f e t i m e s i n C a r b o n R u n # E v e n t s ( x 1 0 * ) L i f e t i m e ( n s ) 1979 S E E I N G 1 . 6 2 0 2 6 . 5 ± 1 . 6 1979 F A L L 1178 1 . 0 2 0 2 6 . 0 + 2 . 1 1 197 0 . 9 2 0 2 5 . 2 + 2 . 2 1 2 5 9 0 . 6 2 0 2 6 . 1 ± 2 . 7 1264 0 . 5 2 0 2 5 . 3 + 2 . 9 1272 0 . 8 2 0 2 3 . 5 ± 2 . 3 1 2 7 5 0 . 5 2 0 2 6 , 3 + 2 . 9 1291 0 . 6 2 0 3 0 . 3 ± 2 . 7 T o t a l 6 . 5 2 0 2 6 . 3 ± 1 . 5 94 negative mucn life t i m e i n carbon i s 2030.0 ±1.6 ns (MAR80),. Our r e s u l t of 2026.3±1.5 ns i s in adequate agreement with Eckhause's r e s u l t of 2025±4 ns and the findinq of the Saclay group, but disagrees with the two r e s u l t s of 2043±3 ns by Reiter and 204 1±5 ns by Lathrop. Although i f one subtracts o f f 14 ns and 6 ns (their positive muon l i f e t i m e deviation from the accepted value), r e s p e c t i v e l y , the agreement i s better, but th i s simple minded procedure i s not necessarily v a l i d because almost c e r t a i n l y there would have been dif f e r e n t systematic errors. Within error, our capture rate barely overlaps with past measurements as shown in Table IV-2. The ca l c u l a t i o n by Walecka (WAL75) gave a capture rate of 0.35x10s /sec which i s lower than our result (0.388±0.005) x10s by 6%. IV.D Negative Muon Lifetime Measurements in 48 Elements (a) Lithium ( 6 L i and 7 L i ) The f i r s t measurement was made by Eckhause et a l . (ECK63) but t h e i r results had large errors.„ Furthermore, their r e s u l t for 6 L i was inconsistent with the th e o r e t i c a l estimate by Lodder and Jcnker (LOD67), which indicated that further experiments would be useful. Recently, considerably greater precision was achieved i n a measurement by the Saclay group (BAR78). A comparison of the t h e o r e t i c a l and 95 e x p e r i m e n t a l c a p t u r e r a t e s i s g i v e n i n Table I V - 5 ( 1 ) . As shown i n Table I I I - 2 , c ur d a t a depend on the carbon background. A c c o r d i n g t o t h e c a r t o n background r u n , a 1.0 % carbon background i s a l l o w e d i n the r e s u l t s of Table I V - 5 . Our r e s u l t s , w i t h o u t the carbon background, agree w e l l w i t h S a c l a y ' s r e s u l t s , which are f r e e from t h e c a r b o n background. The c a p t u r e r a t e , shown i n Table I V - 5 , i s an average c a p t u r e r a t e . At f i r s t n e g a t i v e muons p o p u l a t e t h e h y p e r f i n e s t a t e s a c c o r d i n g t o a s t a t i s t i c a l d i s t r i b u t i o n . Then t h e r e i s a change i n t h e p o p u l a t i o n due t o the t r a n s i t i o n between the h y p e r f i n e s t a t e s . F o r l i t h i u m , F a v a r t e t a l . (FAV70) showed, by a muon p r e c e s s i o n e x p e r i m e n t , t h a t the c o n v e r s i o n r a t e was l e s s t h a n 2x10* /sec o f which the c o n v e r s i o n time was l o n g e r than 50 mi c r o s e c o n d s . I n o r d e r t o e x p l a i n t h e p a r t i a l c a p t u r e r a t e e x p e r i m e n t c f 6 L i - 6 He (g. s. ) (=1600 /sec) (DEU68) , P r i m a k o f f (PRI77) and Hwan (HWA78) added a 16 % e f f e c t from the h y p e r f i n e c o n v e r s i o n t o the s t a t i s t i c a l l y averaged r a t e . S i n c e t h e c c n v e r s i c n r a t e i s very s m a l l and the t r a n s i t i o n o c c u r s w i t h i n m i l l i seconds, our exp e r i m e n t , i n which a l l events appear w i t h i n 25 mi c r o s e c o n d s , i s not adequate t o f i n d t h e h y p e r f i n e t r a n s i t i o n s . The s i m p l e f o r m u l a o f P r i m a k o f f , which w i l l be shown i n t h e next C h a p t e r , has a neutron e x c e s s term. . T h i s o r i g i n a t e s frcm t h e P a u l i p r i n c i p l e and i s c l a i m e d t o be v a l i d f o r Z>6. The d i f f e r e n c e o f the t o t a l c a p t u r e r a t e between 6 L i and 7 L i i s m a i n l y due t o t h e a l l o w e d t r a n s i t i o n 96 Table IV-5(1) Capture Rates in Li-6 and Li-7 Li-6 (/sec) Li-7 (/sec) Ec (7) /Be (6) Theory (LOD67) 3480 2080 0. 60 Experiment Eckhause (ECK63) 6100±1400 1800± 1 100 0.30±0- 19 Saclay (EAE78) 468C±120 2260±120 0.48±0.03 TEIUMF 4 180±450 18 10±440 0. 43±0. 11 Table IV-5 (2) The Different Contribution to the Total Muon Capture Bate by Lodder and Jonker (L0D67) (unit i n /sec) Isotope Allowed Dipole Other B e l a t i v i s t i c Ec (Total) Multipole Term Li-6 1248 1263 621 348 3480 (1044) (3261) Li-7 1 182 620 281 2083 (±12%) 97 i n 6 L i according to Lodder's cal c u l a t i o n (LOD67) as shown i n la b l e IV-5(2). The neutron excess term i n Pri m a k o f f s formula predicts the isotope e f f e c t , Ec(7)/Rc(6) =0.48, which i s close to our measurement, Be (7)/Be (6) =0,.43±0. 02. <fc) Beryllium There have teen three measurements of the negative muon l i f e t i m e i n Be by Sens (SEN58) , Eckhause et a l . (ECK63), and Martino et a l . (MAB80), who obtained l i f e t i m e s of 2140±20 ns, 2 156±10 ns, and 2169.Otl.O ns, respectively. Our r e s u l t of 2 162. 1±1.8 ns i s i n good agreement with the e a r l i e r measurements of Sens and Eckhause et a l . , but the re s u l t from Martino and Duclos i s longer than ours by 7 ns.. This disagreement can not tie explained with the hyperfine e f f e c t . Since Be has a negative magnetic moment as shown i n Table IV-6, the hyperfine state with F+=I+1/2 i s lower in energy than the hyperfine state with F-=I-1/2.. In the li f e t i m e measurements at Saclay, the detection of the decay electrons started a few microseconds after the muons stopped, so th e i r experiment may have detected decay electrons from the lower hyperfine l e v e l (F+). From Table IV-6, i t i s evident that T + ( l i f e t i m e i n F + state) i s longer than T - (lifetime i n F~ st a t e ) . Since our experiment started taking data d i r e c t l y after muons stepped in a target, we were measuring the mean l i f e t i m e , Tmean. However, the hyperfine t r a n s i t i o n time has been determined experimentally te be longer than 20 microseconds by Favart et al.(FAV70) , so that, within a few 98 microseconds, the hyp e r f i n e e f f e c t would not be l a r g e . Assuming that the t r a n s i t i o n time i s 20 microseconds and the data t a k i n g s t a r t s at 4 microseconds a f t e r the muon s t o p , the h y p e r f i n e e f f e c t would be l e s s than 20%, and the l i f e t i m e measured by the Saclay group should be about 2 nsec longer than the mean l i f e t i m e . T h i s c o r r e c t i o n i s i n the r i g h t d i r e c t i o n but i n s u f f i c i e n t to e x p l a i n the 7 nsec d i s c r e p a n c y . No t h e o r e t i c a l c a l c u l a t i o n has been made f o r the muon capture i n Be. (c) Eoron ("B and M B ) Eckhause et a l . (ECK63) have measured the negative muon l i f e t i m e s i n 1 0 B and 1 1 B . Our r e s u l t i n l l B agrees with t h e i r r e s u l t w i t h i n e r r o r ; i n the case of 1°B our r e s u l t i s s h o r t e r than t h e i r r e s u l t by two standard d e v i a t i o n s . The capture r a t e s and i s o t o p e e f f e c t s are i n good agreement as shown below. i«B H B Rc(11)/Rc(10) Eckhause l i f e 2082±6 ns 2102±6 ns cap 25,800±1500 /sec 21,200±1500 / s e c 0.82±0.08 TBIUMF l i f e 207C.7±2.0 ns 2096.1±2.0 ns cap 27,760±490 /sec 21,910±480 /sec 0.79±0.02 There i s no t h e o r e t i c a l c a l c u l a t i o n which can be compared 99 w i t h t h e t o t a l muon c a p t u r e r a t e s i n 1 ° B a n d " B . (d) C a r b o n ( * 2 C a n d i ^ C ) T l i e l i f e t i m e o f 1 2 C h a s b e e n d i s c u s s e d i n s e c t i o n I V . C . O u r m e a s u r e m e n t o f t h e l i f e t i m e i n * 3 C i s t h e f i r s t s u c h m e a s u r e m e n t . A s l i s t e d i n T a b l e I V - 1 , t h e r e i s n o d i f f e r e n c e i n l i f e t i m e s b e t w e e n l 2 C a n d l 3 C a n d t h e i s o t o p e e f f e c t Be ( 1 3 ) / E c (12) i s e g u a l t o 0 . 9 7 ± 0 . 0 3 . F r o m t h e P r i m a k o f f t h e o r y w h i c h i m p l e m e n t e d t h e P a u l i p r i n c i p l e , t h e e x p e c t e d i s o t o p e r a t i o i s e q u a l t o 0 . 7 1 w h i c h i s n o t c o m p a t i b l e w i t h o u r e x p e r i m e n t a l r e s u l t . T h e t o t a l muon c a p t u r e r a t e s f o r l i m i t e d n u m b e r s o f t r a n s i t i o n s b e t w e e n s t a t e s w i t h t h e s a m e p a r i t y h a v e b e e n r e p o r t e d by D e s g r o l a r d e t a l . ( D E S 7 8 ) , u s i n g t h e s h e l l m o d e l a n d i m p u l s e a p p r o x i m a t i o n . T h e i r c a l c u l a t i o n s i n d i c a t e t h a t t h e r e i s n o d i f f e r e n c e i n t h e c a p t u r e r a t e b e t w e e n 1 2 C a n d l 3 C f a n d t h i s a g r e e s w i t h o u r e x p e r i m e n t s . A l t h o u g h t h e s h e l l m o d e l a p p r o a c h b y s e v e r a l a u t h o r s ( L O Y 6 3 , G 0 U 7 1 , J O S 7 2 , DUP75) h a s n o t s u c c e e d e d i n r e p r o d u c i n g t h e a c t u a l e x p e r i m e n t a l v a l u e s , t h e r e s u l t s c a n b e u t i l i z e d q u a l i t a t i v e l y i n d i s c u s s i n g c a p t u r e r a t e s . S t r o n g i s o t o p e e f f e c t s h a v e b e e n o b s e r v e d f o r L i , B , a n d 0 i n c u r e x p e r i m e n t . T h e d i f f e r e n c e b e t w e e n t h e s e n u c l e i a n d C , e x c e p t f o r l e v e l s t r u c t u r e s , i s t h e Q v a l u e . T h e i s o t o p e s o f L i , B , a n d 0 h a v e d i f f e r e n t Q v a l u e s , b u t t h e Q v a l u e s o f l 2 C a n d , 1 3 C a r e t h e s a m e . T h e s e same Q v a l u e s may b e o n e o f r e a s o n s f o r t h e s a m e muon c a p t u r e r a t e 100 i n 12c a n d i 3 C ( F U J 7 9 ) • (e) N i t r o g e n The muon l i f e t i m e i n n i t r o g e n h a s b e e n m e a s u r e d w i t h g r e a t p r e c i s i o n i n o u r e x p e r i m e n t . O u r l i f e t i m e r e s u l t d o e s n o t a g r e e w i t h p r e v i o u s r e s u l t s , a s s h o w n i n T a b l e I V - 2 , b u t o u r c a p t u r e r a t e j u s t o v e r l a p s w i t h t h e v a l u e o f E c k h a u s e . T h e v a l u e c f t h e S a c l a y g r o u p i s 1 . 8 % ( n e a r l y 1 a ) h i g h e r t h a n o u r r e s u l t . S i n c e t h e i r d a t a t a k i n g s t a r t e d a f e w m i c r o s e c o n d s a f t e r t i e muons s t o p p e d i n t h e t a r g e t , i t i s p o s s i b l e t h a t t h e i r r e s u l t i s a f f e c t e d by t h e h y p e r f i n e t r a n s i t i o n . I f s o , t h e i r r e s u l t s h o u l d b e s h o r t e r t h a n o u r s , b e c a u s e n i t r o g e n h a s a p o s i t i v e m a g n e t i c moment a n d t h e muon l i f e t i m e i n t h e l o w e r h y p e r f i n e s t a t e i s s h o r t e r t h a n i n t h e h i g h e r h y p e r f i n e s t a t e . I f t h e i r t a r g e t (NHi+I) h a d w a t e r c o n t a m i n a t i o n , t h e l i f e t i m e w o u l d be s h o r t e r t h a n o u r s a l s o . U s i n g c h e m i c a l c o m p o u n d s ( N H ^ C l ) , we h a d d i f f i c u l t y d e t e r m i n i n g muon l i f e t i m e s i n n i t r o g e n , w h i c h v a r i e d f r o m 1 9 0 5 n s t o 1 9 2 5 n s . C o n s e q u e n t l y , we d e c i d e d t o u s e l i q u i d n i t r o g e n a s a t a r g e t . We b e l i e v e t h a t o u r r e s u l t i s s i g n i f i c a n t l y m o r e r e l i a b l e b e c a u s e o f t h e g e n e r a l l y c o n s i s t e n t a n d r e a s o n a b l e b e h a v i o r o f t h e e l e c t r o n i c e q u i p m e n t . k t h e o r e t i c a l c a l c u l a t i o n h a s b e e n made t o f i n d t h e muon c a p t u r e i n N ( K I S 7 3 ) , u s i n g s h e l l m o d e l wave f u n c t i o n s . The c a l c u l a t e d t o t a l c a p t u r e r a t e , 1 . 0 9 x 1 0 s / s e c , e x c e e d s t h e e x p e r i m e n t a l r e s u l t s b y 70 % . T h e r e i s n o o t h e r t h e o r e t i c a l v a l u e . 10 1 ( f ) O x y g e n ( i 6 0 a n d * 8 0 ) As s h o w n i n T a b l e I V - 2 , t h r e e m e a s u r e m e n t s o f t h e muon l i f e t i m e i n * 6 0 h a v e b e e n made p r e v i o u s l y . O u r r e s u l t h a s a c o n s i d e r a b l y i m p r o v e d a c c u r a c y . a l t h o u g h o u r r e s u l t f o r 1 6 0 ( w a t e r t a r g e t ) i s l o w e r t h a n t w o r e c e n t m e a s u r e m e n t s , i t d e e s f a l l w i t h i n t h e l a r g e e r r o r l i m i t s o f t h e p r e v i o u s m e a s u r e m e n t s . A t h e o r e t i c a l a t t e m p t was made b y W a l e c k a (WAL75) u s i n g t h e F o l d y - W a l e c k a r e s o n a n c e m o d e l . H i s r e s u l t o f muon c a p t u r e r a t e i n 1 6 0 i s 1 . 0 7 x 1 0 s / s e c , w h i c h i s g u i t e c l o s e t o o u r r e s u l t o f 1 . 0 1 8 ± 0 . 0 0 5 x 1 0 5 / s e c . O u r s i s t h e f i r s t m e a s u r e m e n t o f t h e muon l i f e t i m e i n 1 8 0 . S i n c e t h i s t a r g e t w a s f o r m e d i n A g a r , t h e c a r b o n b a c k g r o u n d was d e t e r m i n e d b y t h e l i f e t i m e m e a s u r e m e n t o f t h e 1 6 C t a r g e t i n t h e same f o r m u s i n g t h e f i x e d 1 6 0 l i f e t i m e o b t a i n e d a b o v e f r o m t h e w a t e r t a r g e t . T h e r e i s n o t h e o r e t i c a l c a l c u l a t i o n . T h e i s o t o p e e f f e c t E c ( 1 8 ) / R c (16) i s e q u a l t o 0 . 8 0 + 0 . 0 1 . T h i s i s q u i t e d i f f e r e n t f r o m t h e r a t i o o f 0 . 6 0 , w h i c h i s c a l c u l a t e d b y P r i m a k o f f " s f o r m u l a . I t s e e m s t h a t i n l i g h t e l e m e n t s t h e d e t a i l s c f t h e n u c l e a r s t r u c t u r e a r e m o r e i m p o r t a n t , s i n c e t h i s f o r m u l a f a i l s f o r b o t h i 2 c - i 3 C a D C i i 6 0 - i 8 0 . (g) F l u o r i n e T h e h f e f f e c t c f muon c a p t u r e c a n b e e x p e c t e d i n t h i s n u c l e u s , a s d e m o n s t r a t e d b y Winston ( W I N 6 3 ) ; h e n c e t h e h i s t o g r a m c f d e c a y e l e c t r o n s h a s b e e n f i t t e d t o e q u a t i o n ( 3 . 1 2 ) . T h e d a t a a n a l y s e s o f t h e h i s t o g r a m s o f f o u r 102 chemical compounds give the mean l i v e s ( l—) and the disappearance r a t e s (R~) of the lower hf s t a t e s . The r e s u l t s are l i s t e d i n the f o l l o w i n g Compound T~ R- • Rc~=R—Rd ( ns ) (x10 6 /sec) (x10 s /sec) L i F 1464. 7±4.0 0. 683±0. 002 0. 228±0.002 C2F4 1458. 8±4. 0 0.686±0.002 0. 230±0.002 CaF2 1463. 2±5. 0 0. 683±0.002 0. 228±0.003 PbF2 1464.2 + 6. 0 0. 683±0.003 0. 228±0.003 Average 1462. 7±5. 0 0. 684±0. 002 0.229±0.003 As d i s c u s s e d i n s e c t i o n I I I . G , the amplitude of the hf t r a n s i t i o n e f f e c t (Ae) i s about 0.015. In order to see t h i s e f f e c t c l e a r l y i n a decaj e l e c t r o n histogram, the data p o i n t s wi t h i n the time of the t r a n s i t i o n (=200 ns) must .have b e t t e r than a 1 % s t a t i s t i c s . I n our F data l i s t e d above, only the L i F odata, which has 8000 e l e c t r o n events from the mucn decay i n F at t=0, can be used f o r the hf e f f e c t study. The f i t t i n g r e s u l t s are Eh= (8. 8±4. 0) x10* / s e c , . Ae = 0. 0 1 7±0. 0 10 (4.11) Winston (WIN6 3) whose histogram had f i v e times more events than ours obtained Eh= (6.3± 1. 8) x 10* /sec, Ae=0. 026±0. 0 07 (4. 12) ( from e l e c t r o n data ) Eh= (5. 8±0. 8) x 106 / s e c , An=0. 30 ±0.02 ( from n e u t r a l data ) 103 A l t h o u g h c u r r e s u l t s ( 4 .11) a r e i n a g r e e m e n t w i t h W i n s t o n ' s r e s u l t s ( 4 . 1 2 ) , o u r d a t a d o e s n o t h a v e e n o u g h s t a t i s t i c s t o d e t e r m i n e t h e h f e f f e c t t e r m s . E h a n d A e . The c a p t u r e r a t e s o f t h e h f d o u b l e t a r e e s t i m a t e d f r o m t h e f o l l o w i n g r e l a t i o n s ( B E B 5 8 , P B . I 5 9 ) E " ( I - 1 / 2 ) - B + ( I + 1/2) 1 (• ( 2 I + 1 ) / I : I = L + 1 / 2 = 0 . 9 4 5 » - « K E a v Z I - ( 2 I + 1 ) / ( I + 1) : I = L - 1 / 2 ( 4 . 13) w h e r e t h e d e f i n i t i o n s c f B + , E - a n d E a v h a v e b e e n g i v e n i n s e c t i o n I I I . G * S i n c e e g u a t i o n ( 4 . 1 3 ) was d e r i v e d b y B e r n s t e i n , L e e , Y a n g , a n d P r i m a k o f f , t h i s i s o f t e n n a m e d t h e B L Y P e s t i m a t e . I n t h e c a s e c f F , 1 = 1 / 2 a n d Z = 9 , s o t h a t ( B e - - B c + ) / ( B c ) a v = 0 . 4 2 ( 4 . 1 4 ) T h i s v a l u e was d e t e r m i n e d e x p e r i m e n t a l l y by W i n s t o n t o b e 0 . 7 7 ± 0 . 1 3 . O s i n g t h e s e t w o v a l u e s a n d e g u a t i o n s ( 3 . 1 3 ) , ( 3 . 1 4 ) a n d ( 3 . 1 5 ) , o u r r e s u l t s a n d W i n s t o n ' s r e s u l t s a r e s u m m a r i z e d a s f o l l o w s B e - ( l o w e r ) Ec+ ( u p p e r ) Tmean ( x l O s / s e c ) ( x 1 0 s / s e c ) ( n s ) W i n s t o n ( n e u t r a l ) 2. 3 1±0.06 1 . 5 7 ± 0 . 0 4 i 1584± 1 1 1 . 18±0 . 0 9 2 1663±20 T B I U M F ( e l e c t r o n ) 2 . 2 9 + 0 . 0 2 1 .56±0.02i 1590±5 1 . 1 7 ± 0 . 0 9 2 1667±20 1 , 0 . 4 2 f r o m e q u a t i o n ( 4 . 1 3 ) ( B L Y P e s t i m a t e ) 2 , 0 . 7 7 ± 0 . 1 3 , W i n s t o n ' s e x p e r i m e n t a l v a l u e O u r r e s u l t s a g r e e w i t h W i n s t o n ' s n e u t r o n a n d gamma d a t a . I n T a b l e I V - 2 , t h e p a s t m e a s u r e m e n t s o f l i f e t i m e s o f t h e l o w e r h f s t a t e a r e l i s t e d . . O u r r e s u l t s h o w s a g r e e m e n t w i t h t h e 104 o t h e r m e a s u r e m e n t s . (h) S e a r c h f o r t h e h f t r a n s i t i o n s i n B e , , 1 0 B , » » B , i 3 C , N , N a , a n d C l . I n T a b l e I V - 6 , t h e i n f o r m a t i o n o f h f s t a t e s f o r n u c l e i w i t h a s p i n i s l i s t e d . A c c o r d i n g t o t h e t h e o r e t i c a l e s t i m a t e s o f t h e c o n v e r s i o n r a t e s (WIN63) o r e x p e r i m e n t a l d e t e r m i n a t i o n s ( F A V 7 0 ) , i t i s p o s s i b l e t h a t t h e h f t r a n s i t i o n s o f n u c l e i l i s t e d a b o v e c o u l d b e o b s e r v e d i n o u r e x p e r i m e n t . T h u s o u r d a t a w e r e f i t t e d t c e q u a t i o n ( 3 . 1 2 ) . T h e r e s u l t s o b t a i n e d do n o t s h o w a n y i n d i c a t i o n o f t h e h y p e r f i n e e f f e c t a n d a r e l i s t e d b e l o w . E l e m e n t Ae Eh (106 s - ) E e f . Amp* a t t=0 Be 0 . 0 0 6 ± 0 . 0 0 2 0 . 0 5 f i x e d (F A V 7 0) 5 0 0 0 l o g 0 . 0 0 1 ± 0 . 0 0 2 0 . 2 f i x e d ( F A V 7 0 ) 3 5 0 0 H B 0 . 0 0 1 ± 0 . 0 0 3 0 . 3 3 f i x e d ( F A V 7 0 ) 3 5 0 0 0 . 0 1 ± 0 . 0 1 ( 0 . 2 ± 0 .2) f i t 2 0 0 0 N 0 . 0 0 8 ± 0 . 0 1 ( 1 . 2 ± 1 . 5) f i t 4 0 0 0 Na 0 . 0 1 ± 0 . 0 2 14 f i x e d ( K I N 6 3 ) 3 0 0 0 C l 0 . 0 1 ± 0 . 0 2 8 f i x e d ( K I N 6 3 ) 2 0 0 0 1) A m p l i t u d e a t t = 0 i n e g u a t i o n ( 3 . 6 ) A s d i s c u s s e d i n s e c t i o n I I I . G , t h e h f t r a n s i t i o n c o e f f i c i e n t (Ae) i s e x p e c t e d t o b e a r o u n d 0 . 0 1 o r l e s s , . F r o m T a b l e I V - 6 i n w h i c h Ae i s e s t i m a t e d f o r v a r i o u s n u c l e i , i t i s e v i d e n t t h a t A e i s v e r y s m a l l f o r m o s t o f t h e n u c l e i . T h u s , i n o r d e r t o s e e t h e e f f e c t c l e a r l y i n t h e d e c a y e l e c t r o n s p e c t r u m , t h e s p e c t r u m h a s t o h a v e m o r e t h a n 1 0 4 e v e n t s a t t = 0 e v e n f o r t h e n u c l e i w h i c h s e e m t c b e g o o d c a n d i d a t e s f o r 105 T a b l e IV-6(1) The h y p e r f i n e e f f e c t s i n v a r i o u s n u c l e i Element S p i n Moment D/Rav A n i Aei Rh(10 6 /se< I i (3,6) 1 + 0.82 <0.0 22 L i (3,7) 3/2- 3.26 0.843 <0.022 Be (4,9) 3/2- -1 . 18 0. £ 3 3 <0. 0 52 B(5,10) 3 + 1.80 0.21±0.052 B<5, 11) 3/2- 2. 69 0.513 0. 24 0.009 0 . 2 51 1.2* 0.43 0.0 17 0. 33±0 .052 C(6,13) 1/2- 0.70 -0.2 13 N(7,14) 1 + 0.40 F ( 9 , 19) 1/2 + 2. 63 0.423 0.24 0.01 0. 58±0. 085 0. 76* 0.36 0.0 15 0.63±0, 186 0.77+0.13i 0.30±0.02 0.026±0. 007 Na (11, 23) 3/2 + 2. 22 -0. 143 0.08 0.002 14i A l (13, 27) 5/2 + 3.64 0. 183 0.09 0.001 4 1 i 0.28* 0. 14 0.002 P(15,31) 1/2 + 1. 13 0. 253 0. 16 0.003 58i 0. 37* 0.22 0. 004 Cl ( 1 7 , 3 5 ) 3/2 + 0.82 -0.093 -0.06 -0. 01 8 i - 0 . 14* -0.06 -0. 01 K(19,39) 3/2 + 0.39 -0.083 -0.05 -0.00 5 22i - 0 . 11* -0.07 -0.001 2, 3, 4, 5, 6, ( W I N 6 3 ) Note: 1, W i n s t o n 1 d a t a or e s t i m a t e F a v a r t e t a l . (FAV70) BLYP e q u a t i o n ( t e x t e q u a t i o n (4.11), P r i m a k o f f ' s e s t i m a t e quoted i n WIN63 Winston's n e u t r a l data(WIN63) Winston's e l e c t r o n data(WIN63) Berstein (BER58) Table IV-6 (2) H y p e r f i n e E f f e c t i n L i f e t i m e and Capture Rate Elem D/Rav Rc~ (/sec) (T- ns) Rc+ (/sec) (T+ ns) (Rc) av (/sec) (Tmean ns) * L i 7 L i Be 72601130 (2162.3±0.7) 0.633 10500±560 (2147,. 5±2, 7) 3260±80 (2181 .2±0 .5 ) 5730±300 (216S.7+2 .0 ) 4678±104 {2175 .3±0 .4 ) 7 4 6 8 0 H 2 0 ( 2 1 8 6 . 8 ± Q . 4 )f 7500±400 (2162. 1±2.0) 106 T a b l e I V - 6 (3) H y p e r f i n e E f f e c t i n L i f e t i m e a n d C a p t u r e R a t e E l e m D / R a v R c - ( 1 0 V s e c ) (T~ n s ) R c + ( 1 0 6 / s e c ) (T+ n s ) ( R c ) a v ( 1 0 6 / s e c ) ( T m e a n n s ) I 0 £ I I B N F Na A l C l 0 . 5 1 3 0 . 0 2 9 3 ± 0 . 0 0 5 ( 2 0 6 4 . ± 3 ) 1. 2 * 0 . 0 3 8 9 ± 0 . 0 0 0 7 ( 2 0 2 4 i 4 ) - 0 . 2 1 3 0 . 0 3 1 8 ± 0 . 0 0 0 8 ( 2 0 5 4 i 3 ) 0 . 4 2 3 0 . 7 6 * 0 . 7 7 ± 0 . 1 3 i - 0 . 143 0 . 183 0 . 2 8 * 0 . 2 5 3 0 . 3 7 * - 0 . 0 9 3 - 0 . 1 4 * - 0 . 0 8 3 - 0 . 1 1 * 0 . 2 2 9 ± 0 . 0 0 3 ( 1 4 6 3 ± 5 ) 0 . 3 7 7 + 0 . 0 0 1 J J 2 0 4±21 0 . 7 0 5 * 0 . 0 0 1 J J 6 4±J1 1. 1 8 5 ± 0 . 0 0 3 ( 6 1 1 ± 1) 1 . 3 3 3 ± 0 . 0 0 3 JJ56JJJ1 1 . 8 3 9 ± 0 . 0 0 5 ( 4 3 7 ± 1 l 0 . 0 1 7 9 4 + C . 0 0 0 4 ( 2 1 1 4 . ± 2 ) 0 . 0 1 2 2 ± 0 . 0 0 0 3 ( 2 1 4 0 ± 2 ) 0 . 0 3 9 7 ± 0 . 0 0 0 8 ( 2 0 2 113) 0 . 1 5 6 ± 0 . 0 0 2 ( 1 6 3 5 1 6 ) 0 . 1 1 8 1 0 . 0 0 2 ( 1 7 4 6 1 6 ) 0 . 1 1 7 1 0 . 0 0 9 ( 1 7 4 9 1 3 0 ) 0 . 4 3 5 1 0 . 001 (1 1 2 3 1 2 ) 0 . 5 9 0 1 0 . 0 0 1 ( 9 5 7 H ) 0 . 5 3 6 1 0 . 0 0 1 ( 1 0 0 9 1 1 ) 0 . 9 3 5 1 0 . 0 0 3 ( 7 1 9 1 1 ) 0 . 8 4 1 1 0 . 0 0 3 ( 7 7 1 1 1 ) 1 . 4 6 0 1 0 . 0 0 4 ( 5 2 2 1 1 ) 1 . 5 3 8 1 0 . 0 0 4 ( 50 211) 1 . 9 9 4 1 0 . 0 0 6 ( 4 0 8 1 1 ) 2 . 0 5 6 1 0 . 0 0 6 ( 3 9 8 1 1 ) 0 . 0 2 8 1 1 0 . 0 0 0 5 ( 2 0 7 0 . 7 1 3 . 0 ) 0 . 0 2 2 2 + 0 . 0 0 0 5 ( 2 0 9 6 . 1 1 3 . 0 ) 0 . 0 2 2 2 1 4 0 0 0 . 0 3 8 3 1 0 . 0 0 0 7 ( 2 0 2 9 . 1 1 3 . 0 ) 0 . 0 6 9 9 1 0 . 0 0 0 4 ( 1 9 0 6 . 8 1 3 . 0 ) 0 . 1 7 5 1 0 . 0 0 3 ( 1 5 9 0 1 6 ) 0 . 1 4 5 1 0 . 0 0 3 ( 1 6 6 6 1 5 ) 0 . 1 4 5 1 0 . 0 0 8 ( 1 6 6 7 1 2 0 ) 0 . 4 1 3 1 0 . 0 0 1 ( 1 1 5 1 1 2 ) 0 . 6 3 8 1 0 . 0 0 1 ( 9 15+1) 0 . 6 0 6 + 0 . 0 0 1 ( 9 4 2 1 1 ) 0 . 9 9 7 1 0 . 0 0 3 ( 6 8 8 1 1 ) 0 . 9 7 2 1 0 . 0 0 3 ( 7 2 3 1 1 ) 1 . 4 1 3 1 0 . 0 0 3 ( 5 3 6 H ) 1 . 4 5 6 1 0 . 0 0 3 ( 5 2 2 1 1 ) 1 . 9 3 6 1 0 . 0 0 5 ( 4 1 8 1 1 ) 1 . 9 7 4 1 0 . 0 0 5 ( 4 1 2 ± 1 ) N o t e : 1 , W i n s t o n ' d a t a o r e s t i m a t e (WIN63) 2 , F a v a r t e t a l . (FAV70) 3 , B L Y P e q u a t i o n ( t e x t e q u a t i o n ( 4 . 1 1 ) , B e r s t e i n (BER58) 4 , P r i m a k o f f ' s e s t i m a t e q u o t e d i n WIN63 5 , W i n s t o n ' s n e u t r a l d a t a ( W I N 6 3 ) 6 , W i n s t o n ' s e l e c t r o n d a t a ( W I N 6 3 ) 7 , S a c l a y g r o u p d a t a (EAR78) — L i f e t i m e s u n d e r l i n e d a r e o u r e x p e r i m e n t a l r e s u l t s e x c e p t L i a n d a l l o t h e r l i f e t i m e s a r e e s t i m a t e d v a l u e s . 107 t h e h f e f f e c t (eg F , C l ) . I n t h e c a s e c f N a , by u s i n g e g u a t i o n ( 3 . 1) , Ae i s c a l c u l a t e d t o b e 0 . 0 0 3 . T h i s i s t o o s m a l l t o b e d e t e r m i n e d b y t h e e l e c t r o n d e c a y s p e c t r u m . A s s u m m a r i z e d a b o v e , t h e t o t a l n u m b e r o f e v e n t s i n o u r e x p e r i m e n t s i s n o t l a r g e e n o u g h t o o b t a i n A e . I t i s a l s o d i f f i c u l t t c m e a s u r e t h e e f f e c t f o r l i g h t n u c l e i b y t h e l i f e t i m e m e t h o d i f t h e c o n v e r s i o n i s s l o w ( f o r i n s t a n c e L i , B e , B ) , b e c a u s e m o s t e v e n t s a p p e a r w i t h i n 4 m i c r o s e c o n d s . . I n T a b l e I V-6, p a s t e x p e r i m e n t a l r e s u l t s a n d e s t i m a t e s o f t h e h f e f f e c t a r e s u m m a r i z e d . F r o m t h e t a b l e t h e m o s t s u i t a b l e t a r g e t s a r e F a n d C l f o r t h e l i f e t i m e m e t h o d . . W i t h s u f f i c i e n t e x p e r i m e n t a l r u n n i n g t i m e , t h e h f e f f e c t s i n t h e s e n u c l e i c o u l d be d e t e c t e d . T h e r e h a v e b e e n n o e s t i m a t e s o f t h e h f e f f e c t s i n N a n d * 3 C . A l t h o u g h t h e s e a r e a l s o p o s s i b l e c a n d i d a t e s , t h e s h o r t l i f e t i m e s i n t h e c o n t a i n e r m a t e r i a l s (Fe f o r N a n d Cu f o r 1 3 C ) g i v e l a r g e d i s t o r t i o n f o r t i m e s n e a r z e r o a n d t h i s m a k e s i t d i f f i c u l t t o s e p a r a t e t h e s m a l l h f e f f e c t . ( i ) F r o m Z = 1 1 ( N a ) t o Z = 8 3 ( B i ) The f o l l o w i n g r e m a r k s may b e made f r o m Z = 1 1 ( N a ) t o Z=83 ( B i ) o n t h e b a s i s o f t h e r e s u l t s o b t a i n e d i n o u r e x p e r i m e n t . (1) A s l i s t e d i n T a b l e I V - 2 , o u r m e a s u r e m e n t s a r e i n f a i r l y g o o d a g r e e m e n t w i t h p a s t m e a s u r e m e n t s f o r m o s t o f t h e n u c l e i b e t w e e n Z=11 a n d 8 3 . (2) O u r l i f e t i m e m e a s u r e m e n t s i n N a , K , a n d C l h a v e b e e n 108 made with g r e a t p r e c i s i o n . The l i f e t i m e s i n Na and C l are i n agreement with e a r l i e r measurements (SEN59) w i t h i n e r r o r , but our r e s u l t i n K i s s u b s t a n t i a l l y l o n g e r than the e a r l i e r measurement. Our value f o r the l i f e t i m e i n Ge i s l a r g e r than the previous r e s u l t . Our t a r g e t s were Ge02 and Geo, and the muon l i f e t i m e s obtained frcm both oxides were the same. I f the c o n s t i t u e n t s of a chemical compound have g u i t e d i f f e r e n t atomic numbers, then t h e r e should be no d i f f e r e n c e i n the l i f e t i m e measurement f o r the element when i t i s i n a chemical compound t a r g e t and when i t i s an element t a r g e t i t s e l f . However our r e s u l t should be checked with germanium metal. (3) These are the f i r s t measurements of l i f e t i m e s i n Dy, and E r . The l i f e t i m e s i n Dy and Er seem to be reasonable when they are compared with other r a r e e a r t h n u c l e i . Adding our two measurements of Dy and Er to past r e s u l t s , a l l n u c l e i between Z=64 and Z=68 have now been s t u d i e d and t h i s makes i t p o s s i b l e t o d i s c u s s the even-odd Z e f f e c t i n r a r e e a r t h n u c l e i (see s e c t i o n IV.F) . (4) From Table IV-2, i t i s e v i d e n t that the odd Z n u c l e i f o r Z>40 show s y s t e m a t i c a l l y l a r g e r capture r a t e s than the even Z n u c l e i . Past measurements (FIL63) and our experiment support the f a c t t h a t the capture r a t e i n Nb (Z=4 1,A=93) i s anomalously higher ( 10.35±0.17 x10 6) than the estimated value from the Primakoff formula 109 ( 9 . 3 5 x 1 0 * ) ( W A 1 7 5 ) . W a t s o n (HA175) h a s s u g g e s t e d t h a t t h e l a r g e c a p t u r e r a t e i n Nb c o u l d b e d u e t o t h e v a n i s h i n g o f t h e C a b i b b o a n g l e Q c . I n s e c t i o n IV. F , t h i s w i l l be d i s c u s s e d i n m o r e d e t a i l b y c o m p a r i n g e x p e r i m e n t a l t o t a l c a p t u r e r a t e s w i t h t h e G o u l a r d - P r i m a k o f f f o r m u l a . I V . E P r i m a k o f f F o r m u l a i n Muon N u c l e a r C a p t u r e P r i m a k o f f d e r i v e d a f o r m u l a f o r t h e t o t a l muon c a p t u r e r a t a E c ( A , Z ) i n a c o m p l e x n u c l e u s w i t h t h e m a s s n u m b e r A a n d a t o m i c n u m b e r Z ( P B I 5 9 ) . I n h i s d e r i v a t i o n , h e s t a r t e d w i t h t h e e f f e c t i v e H a m i l t c n i a n , H e f f , d e d u c e d b y F u j i i a n d P r i m a k o f f ( F U J 5 9 ) . I n t h e i r w o r k , t h e l e p t o n - b a r e n u c l e c n c o u p l i n g i s V a n d A ( A x i a l v e c t o r ) , a n d t h e m u o n - b a r e n u c l e o n a n d e l e c t r o n - b a r e n u c l e o n c o u p l i n g c o n s t a n t s f o l l o w e l e c t r o n - m u o n u n i v e r s a l i t y . A l s o , a s s u m i n g t h e c o n s e r v e d v e c t o r c u r r e n t , t h e n u c l e o n c o u p l i n g c o n s t a n t s a r e w e l l d e f i n e d . The H a m i l t o n i a n i s a s f o l l o w s ( F 0 J 5 9 , P E I 5 9 ) - - A H y l T+ _i=2^L z T ; { G y M. + G P ^ a . e f f / 2 / 2 ± = 1 x V i A i - a-vo.-v } 6 ( r - r . ) (4.14) P x x w i t h r y - „ u t i j . 2mp P % ~= l g £ - g £ - g j ( i + y p - y n ) } - £ - (A.15) p 110 I n e q u a t i o n ( 4 . 1 4 ) , v i s t h e momentum o f t h e n e u t r i n o ; T , ]± a n d cf , a a r e 2 x 2 m a t r i x u n i t o p e r a t o r s a n d s p i n a n g u l a r momentum o p e r a t o r s f o r t h e l e p t o n a n d t h e i - t h n u c l e o n ; r a n d r a r e s p a c e c o - o r d i n a t e s f o r t h e l e p t o n a n d t h e i - t h n u c l e o n ; T + , T ~ a r e i s o b a r i c s p i n o p e r a t o r s w h i c h t r a n s f o r m a l e p t o n muon s t a t e i n t o a l e p t c n n e u t r i n o s t a t e a n d a n i - t h n u c l e o n p r o t o n s t a t e i n t o a n i - t h n u c l e o n n e u t r o n s t a t e ( F U J 5 S ) . W i t h e g u a t i o n s ( 4 . 1 4 ) a n d ( 4 . 1 5 ) , t h e s q u a r e o f t h e mucn c a p t u r e t r a n s i t i o n m a t r i x e l e m e n t b e t w e e n t h e s t a t e s o f i n i t i a l a n d f i n a l n u c l e i w a s c a l c u l a t e d by t h e c l o s u r e a p p r o x i m a t i o n . I n t h e a p p r o x i m a t i o n a l l e n e r g e t i c a l y a c c e s s i b l e s t a t e s o f t h e f i n a l d a u g h t e r n u c l e u s a r e e x c i t e d b y t h e muon c a p t u r e a n d t h e sum o v e r a l l t h e e x c i t e d s t a t e s i s p e r f o r m e d . U s i n g t h i s a p p r o x i m a t i o n , P r i m a k o f f o b t a i n e d R c (A , Z) = ( Z e f f ) * R c ( 1 , 1) K {1 - g ( A - Z ) / ( 2 A ) } ( 4 . 1 6 ) w h e r e R c ( 1 , 1 ) i s t h e muon c a p t u r e r a t e i n h y d r o g e n , K r e p r e s e n t s t h e r e d u c t i o n o f p h a s e s p a c e f o r t h e n e u t r i n o a n d g i s t h e n u c l e o n - n u c l e o n c o r r e l a t i o n p a r a m e t e r . T h e s e c o n d t e r m , { ( A - Z ) / 2 A } g , e m b o d i e s t h e P a u l i e x c l u s i o n p r i n c i p l e a n d i s p r o p o r t i o n a l t o t h e f r a c t i o n c f n e u t r o n s . T h e e s t i m a t e d v a l u e f o r g i s e q u a l t o 3 ( P R I 5 9 ) . H e n c e f o r a n u c l e u s w i t h A = 2 Z , t h e b r a c k e t r e d u c e s t h e c a p t u r e r a t e b y a f a c t o r o f 4 . T h e r e f o r e , t h e P a u l i e x c l u s i o n t e r m i s a l a r q e 111 e f f e c t f o r h e a v y n u c l e i . I n o r d e r t o c o m p a r e o u r e x p e r i m e n t a l r e s u l t s w i t h t h e P r i m a k o f f f o r m u l a , e g u a t i o n ( 4 . 1 6 ) i s p a r a m e t e r i z e d a s f o l l o w s E c ( A , Z ) = ( Z e f f ) * X ( 1 ) [1 - X (2) ( A - Z ) / (2k)} ( 4 . 1 7 ) T h e e f f e c t i v e c h a r g e s h a v e b e e n c a l c u l a t e d f o r m o s t o f t h e n u c l e i b y F o r d e t a l . ( F O E 6 2 ) . T h e i r r e s u l t s a r e l i s t e d i n T a b l e I V - 2 . T h e e f f e c t i v e c h a r g e s , w h i c h a r e n o t p r o v i d e d i n t h e r e f e r e n c e , a r e o b t a i n e d b y t h e l i n e a r i n t e r p o l a t i o n m e t h o d a n d s h e w n i n T a b l e I V - 2 u n d e r l i n e d . F o r t h e b e s t f i t o f e q u a t i o n ( 4 . 17) t o c u r d a t a a n d p a s t m e a s u r m e n t s ( E C K 6 6 ) , a c h i - s q u a r e d m i n i m i z a t i o n p r o g r a m M I N U I T w a s u s e d . T h e r e s u l t s a r e l i s t e d i n T a b l e I V - 7 . I n t h e s e f i t t i n g s , e l e m e n t s l i g h t e r t h a n Z=7 a n d o d d p r o t c n n u c l e i b e t w e e n Z=8 a n d Z=22 a r e n e t i n c l u d e d . T h e r e s u l t o f f i t t i n g X (2) a g r e e s w e l l w i t h t h e e s t i m a t e d v a l u e f o r g b y P r i m a k o f f . The c a l c u l a t i o n b y P r i m a k o f f h a s s h o w n X (1) = 161 / s e c a n d t h i s i s r e p r o d u c e d by t h e e x p e r i m e n t a s s h o w n i n T a b l e I V - 7 . W i t h o u t t h e c o n s e r v e d v e c t o r c u r r e n t (CVC) h y p o t h e s i s , h i s c a l c u l a t i o n g a v e X (1) = 137 / s e c , s o t h e e x p e r i m e n t a n d t h e o r y a g r e e w e l l w i t h t h e a s s u m p t i o n o f CVC ( F E I 5 9 ) , . I f t h e n e u t r o n e x c e s s t e r m s a t i s f i e s ( A - Z ) g / ( 2 A ) = 1 , e q u a t i o n ( 4 . 1 6 ) b r e a k s d o w n . The c o n d i t i o n i m p l i e s Z/A= 1 - 2 / X ( 2 ) = 0 . 3 6 . F o r 2 3 8 U , Z/A i s a b o u t 0 . 3 9 , t h u s Z/A b e c o m e s c l o s e t o t h i s c o n d i t i o n f o r h e a v y n u c l e i . H e n c e 112 h i g h e r o r d e r P a u l i c o r r e c t i o n s b e c o m e n e c e s s a r y f o r h e a v y n u c l e i . G o u l a r d a n d P r i m a k o f f ( G 0 U 7 4 ) o b t a i n e d A ( A - Z ) R c ( A , Z ) = X (1) ( Z e f f ) • {1 + X ( 2 ) X ( 3 ) 2Z 2A A - Z A - 2 Z - ( • ) X ( 4 ) } ( 4 . 1 8 ) 2A 8ZA w h e r e X ( i ) ( i = 1 t o 4) a r e c o n s t a n t s . I n X ( 1 ) , k i n e m a t i c f a c t o r s a r e i n c l u d e d . T h e b e s t f i t s t o a l l e x i s t i n g d a t a a r e l i s t e d i n T a b l e I V - 8 . F r o m T a b l e s I V - 7 a n d I V - 8 , i t i s c l e a r t h a t t h e G o u l a r d - P r i m a k o f f f o r m u l a g i v e s a l i t t l e b e t t e r c h i - s g u a r e f i t t h a n t h e P r i m a k o f f f o r m u l a . F i g u r e s I V - 2 a n d I V - 3 show t h e f i t t i n g c u r v e s f o r t h e b e s t c h i - s g u a r e f i t s l i s t e d i n T a b l e I V - 7 a n d I V - 8 . F r o m t h e t w o f i g u r e s , i t i s e v i d e n t t h a t t h e t w o f o r m u l a e s h o w a l m o s t t h e s a m e b e h a v i o r * I V . F T h e E v e n - O d d Z E f f e c t i „ n H e a v y N u c l e i a s s t a t e d i n s e c t i o n I V . D , t h e o d d - Z n u c l e i f o r Z>40 s h o w l a r g e r c a p t u r e r a t e s t h a n t h e e v e n - Z n u c l e i . I n l i g h t e l e m e n t s w i t h o d d Z , m o s t o f t h e l a r g e c a p t u r e r a t e s c a n be a t t r i b u t e d t c t h e h f e f f e c t . F o r h e a v y n u c l e i t h e h f e f f e c t i s s m a l l , s i n c e t h e e f f e c t i s p r o p o r t i o n a l t o 1 / Z , a s s h o w n i n e g u a t i o n ( 4 . 1 3 ) , a n d t h e c a p t u r e r a t e s f r o m t h e t w o h f s t a t e s a r e n e a r l y t h e s a m e . T h i s 1/Z d e p e n d e n c e i s i l l u s t r a t e d b y f i g u r e s I V - 4 a n d I V - 5 . F i g u r e I V - 4 s h o w s T a b l e I V - 7 , F i t t i n g R e s u l t s f o r P r i m a k o f f F o r m u l a ( 4 . 1 6 ) T E I U M F D a t a * P a s t R e s u l t s 2 N u m b e r c f d a t a 30 5 8 X ( 1 ) 170 170 X ( 2 ) 3 . 125 3 . 1 2 5 ( e x p - f i t ) / e x p 4 . 6 % 5 . 8% 1) O u r e x p e r i m e n t a l r e s u l t s l i s t e d i n T a b l e I V - 1 . 2) P a s t r e s u l t s s u m m a r i z e d b y E c k h a u s e e t a l . ( E C K 6 6 ) . T a b l e I V - 8 , F i t t i n g R e s u l t s f o r G o u l a r d - P r i m a k o f f F o r m u l a ( 4 . 18) TRIUMF D a t a * P a s t R e s u l t s 2 N u m b e r c f E a t a 30 58 X ( 1 ) 2 6 1 2 5 2 X ( 2 ) - 0 . 0 4 0 - 0 . 0 3 8 X ( 3 ) - 0 . 26 - 0 . 24 X ( 4 ) 3 . 2 4 3' . 2 3 ( E x p - F i t ) / E x p 4 . 1% 5 . 6 % 1 ) , 2) s e e T a b l e I V - 7 a b o v e . CD Ul 2° W i n < cr L U P in j Q_ U ' L O _ | Q U LD 2 . 4 + + ( I R I U M F Data) \ ^^Goulard-Primakoff + ++. Primakoff i r 2 . 5 ~~I 1 1 — 2 . 6 2 . 7 ( f l - Z ) / 2 f l 2 . 8 2 . 9 , 3 . 0 CX10" 1 ) 3 . 1 Figure IV-2, The TRIUMF data are f i t t e d to the Primakoff and the Goulard- Primakoff formula. igure IV-3, Past findings summarized by Eckhause et al.(ECK66) are f i t t e d to the Primakoff and the Goulard-Primakoff formula. 116 d e v i a t i o n s o f e x p e r i m e n t a l c a p t u r e r a t e s f r o m t h e G o u l a r d - P r i m a k o f f ( G - P ) f o r m u l a . N o t e t h a t we a r e now p l o t t i n g a g a i n s t t h e a t o m i c n u m b e r Z i n o r d e r t o i l l u s t r a t e t h a t t h e p a t t e r n o f d e v i a t i o n i s c o n n e c t e d w i t h s h e l l e f f e c t s . I n t h i s s e c t i o n , a l l T f i l U M F d a t a a r e u s e d f o r a c o m p a r i s o n b e t w e e n t h e e x p e r i m e n t a l r e s u l t s a n d t h e G - P f o r m u l a . I n t h e c o m p a r i s o n , d a t a l a c k i n g i n t h e TRIUMF s e t a r e t a k e n f r c m t h e r e f e r e n c e o f E c k h a u s e e t a l . ( E C K 6 6 ) . T h e e x p e r i m e n t a l r e s u l t s o f n u c l e i w i t h a t c m i c n u m b e r s s m a l l e r t h a n Z=10 a r e e x c l u d e d f r o m t h e d i s c u s s i o n b e l o w , b e c a u s e t h e f o r m u l a s e e m s t o b e v a l i d o n l y f o r n u c l e i h e a v i e r t h a n Z=8 a s c l a i m e d b y t h e a u t h o r s ( P R I 5 9 , G O U 7 4 ) . I n f i g u r e I V - 5 , t h e a b s o l u t e d e v i a t i o n s o f f i g u r e I V - 4 h a v e b e e n s h o w n . F r o m f i g u r e I V - 5 , i t i s c l e a r t h a t m o s t o f t h e o d d - Z d a t a b e t w e e n Z=10 a n d Z=40 d e v i a t e s f r o m t h e G - P f o r m u l a . . S i n c e t h e d e v i a t i o n s d e c r e a s e a s t h e a t o m i c n u m b e r i n c r e a s e s , t h i s t e n d e n c y a g r e e s w i t h t h e 1/Z d e p e n d e n c e o f t h e h f i n t e r a c t i o n s ( s e e B L Y P e g u a t i o n ( 4 . 1 3 ) ) . . T h i s i s u n d e r s t o o d c l e a r l y f r o m T a b l e I V - 6 . I n t h e t a b l e , t h e a v e r a g e c a p t u r e r a t e s , ( R c ) a v , a n d t h e c a p t u r e r a t e s f r o m t h e l o w e r l e v e l , R c ~ , a r e l i s t e d f o r l i g h t n u c l e i . Due t o f a s t c o n v e r s i o n s f r c m t h e h i g h e r h f l e v e l t o t h e l o w e r h f l e v e l , a l l m u o n s d e c a y f r o m t h e l c w e r h f l e v e l s i n n u c l e i h e a v i e r t h a n f l u o r i n e . The l a r g e d e v i a t i o n s o f e s t i m a t e s b y t h e G - P f o r m u l a f r o m e x p e r i m e n t s a r e c a u s e d b y d i f f e r e n c e s b e t w e e n ( R c ) a v a n d R c ~ ( e g 20% i n P) , b e c a u s e t h e t h e o r y d e a l s w i t h t h e a v e r a g e c a p t u r e r a t e s ( R c ) a v . . 0.2 0.1 O < 0.0 > LU Q -0.1 - 0 2 ( EX -TH ) /EX X X • • O d d - Z * E v e n - Z J x. X * 10 20 30 4 0 5 0 6 0 70 ATOMIC NUMBER (Z) 80 90 100 Figure IV-4, Deviations of experimental capture rates from the Goulard-Primakoff formula. EX-TH|/EX Odd-Z Even-Z 0.2 O i—i > UJ Q UJ I— _ J O 0 0 m < \ • \ 0.1 0.0 \ • V - 7-1 \ ^ z \ • \ \ , \ \ • \ _2 §_ • x 10 20 30 4 0 5 0 60 70 ATOMIC NUMBER (Z) 8 0 9 0 100 co Figure IV-5, Absolute deviations of experimental capture rates from the Goulard-Primakoff formula. Figure IV-4 i s redrawned. 11 9 F i g u r e I V - 6 s h o w s d a t a p o i n t s f o r o d d - Z n u c l e i o n l y . I n t h i s f i g u r e , t h e o d d d a t a p o i n t s a r e n o r m a l i z e d a s f o l l o w s O d d Z d a t a - { E v e n ( Z - 1 ) d a t a + E v e n (Z+1) d a t a } / 2 I n t h e d i s c u s s i o n o f t h e e v e n - o d d e f f e c t , t h e d i f f e r e n c e o f c a p t u r e r a t e s b e t w e e n o d d - Z a n d i t s n e i g h b o r i n g e v e n - Z n u c l e i i s i m p o r t a n t . A f t e r t h i s m a n i p u l a t i o n , t h e l a r g e d e v i a t i o n s o f o d d - Z n u c l e i f r o m t h e G - P f o r m u l a i n f i g u r e I V - 4 a n d I V - 5 t u r n o u t t o b e s m a l l f o r some n u c l e i . F o r e x a m p l e , T b ( Z = 6 5 ) a n d H o ( Z = 6 7 ) h a v e 3% a n d 6 . 5 % d e v i a t i o n s , r e s p e c t i v e l y , a s s h o w n i n f i g u r e I V - 5 . I n f i g u r e I V - 6 , t h e s e d e v i a t i o n s a r e o n l y o . 5 % a n d 2 % , r e s p e c t i v e l y . I n t h i s f i g u r e , t h e o d d - Z n u c l e i b e t w e e n Z=10 a n d Z=30 h a v e l a r g e d e v i a t i o n s d u e t o t h e h f e f f e c t a s e x p e c t e d . B e t w e e n Z=35 a n d Z = 7 0 , Nb s e e m s t o h a v e a n a n o m a l o u s l y l a r g e d e v i a t i o n . T h e h f e f f e c t s a r e e s t i m a t e d by e q u a t i o n ( 4 . 1 3 ) t o b e a l i o u t 3% a n d t h e s e e f f e c t s a r e n o t l a r g e e n o u g h t o e x p l a i n t h e a n o m a l o u s d e v i a t i o n ( = l a r g e c a p t u r e r a t e ) . W a t s o n (WAT75) h a s s u g g e s t e d t h a t t h e l a r g e c a p t u r e r a t e i n Nb c o u l d be d u e t c t h e v a n i s h i n g o f t h e C a b i b b o a n g l e ( Q c ) . T h i s c o n c e p t was p r o p o s e d b y S a l a m e t a l . ( S A L 7 4 ) who s h o w e d t h a t a s t r o n g e x t e r n a l m a g n e t i c f i e l d ( > 1 0 1 6 g a u s s ) c a u s e s t h e C a M b b o a n g l e Qc t o v a n i s h . S u c h h i g h f i e l d s c a n b e e a s i l y a c h i e v e d i n t h e i n t e r i o r o f t h e o d d n u c l e i ( S 0 B 7 5 ) . The t o t a l mucn c a p t u r e r a t e i s p r o p o r t i o n a l t o OQ e ro RELATIVE DEVIATION P O P O l\j CD m o ~n o 0 3 1 121 { G m » c o s (Qc) } 2 ( B L I 7 3 ) . The c o u p l i n g c o n s t a n t , G m , o b t a i n e d f r o m e g u a t i c n ( 4 . 2 ) , i s r e l a t e d t o t h e v e c t o r c o u p l i n g c o n s t a n t Gv i n a b e t a d e c a y t y G v=Gm « c o s (Qc) We e x p e c t t h e e f f e c t o f t h e v a n i s h i n g o f Qc t o b e g i v e n b y R c ( o d d A ) / R c ( e v e n ft) = 1 / c o s 2 (Qc) ( 4 . 1 9 ) T h e C a b i b b o a n g l e , d e t e r m i n e d f r o m e i g h t h y p e r o n b e t a - d e c a y s ( R 0 0 7 4 ) , i s e q u a l t o 0 , 2 3 4 ± 0 . 0 0 3 r a d i a n s * U s i n g t h i s a n g l e , e g u a t i o n ( 4 . 1 9 ) p r e d i c t s a b o u t a 6% i n c r e a s e i n t h e t h e o r e t i c a l c a p t u r e r a t e . I n t h e c a s e o f Nb o u r c a p t u r e r a t e i s 9% h i g h e r t h a n t h e t h e o r e t i c a l r a t e . I f t h e C a b i b b o a n g l e i s q u e n c h e d , i t c o u l d e x p l a i n l a r g e r e x p e r i m e n t a l v a l u e s . I f t h i s i s a u n i v e r s a l r u l e , t h e l a r g e c a p t u r e r a t e s (>5%) h a v e t c b e o b s e r v e d f o r m o s t o f t h e o d d n u c l e i h e a v i e r t h a n Z = 4 0 . B u t i t i s e v i d e n t f r o m f i g u r e I V - 6 t h a t t h i s d o e s n e t h o l d t r u e f o r many o d d - Z h e a v y n u c l e i . A s d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n I V . G , t h e r e i s a c o r r e l a t i o n b e t w e e n n u c l e a r muon c a p t u r e a n d n u c l e a r s t r u c t u r e . T h u s i n o r d e r t o d i s c u s s t h e e v e n - o d d Z e f f e c t , we h a v e t o c h o o s e n u c l e i w h i c h a r e n o t s t r o n g l y a f f e c t e d by n u c l e a r s t r u c t u r e . F i g u r e I V - 8 s h o w s t h a t n u c l e i b e t w e e n 2 = 4 5 a n d Z=55 o r Z=63 a n d Z=75 s a t i s f y t h i s c o n d i t i o n . A s s e e n i n f i g u r e I V - 6 , t h e s e n u c l e i d e v i a t e f r o m t h e G - P f o r m u l a b y 2 % . . T h i s i s n o t s u c h a l a r g e d e v i a t i o n a s e x p e c t e d f r o m t h e v a n i s h i n g o f C a b i b b o a n g l e , . A l s o t h e v a n i s h i n g o f t h e C a b i b b o a n g l e h a s b e e n 122 i n v e s t i g a t e d i n a c t i n i d e n u c l e i t y P a r t h a s a r a t h y e t a l . ( P A R 7 8 ) . a c c o r d i n g t o t h e i r c a l c u l a t i o n , t h e l a r g e t o t a l muon c a p t u r e r a t e s i n  23^U a n d 239p u m e a s u r e d b y J o h n s o n e t a l . ( J O H 7 7 ) a r e r e p r o d u c e d b y a d d i n g t h e i n c r e a s e d u e t o t h e v a n i s h i n g o f t h e C a b i b b o a n g l e . B u t t h e r e c e n t p a p e r b y W i l c k e e t a l . ( W I L 8 0 - 2 ) h a s s h o w n t h a t t h e l a r g e c a p t u r e r a t e s i n a c t i n i d e n u c l e i a r e w e l l d e s c r i b e d b y t h e a l t e r n a t e m o d e l o f K o z l o w s k i a n d Z g l i n s k i ( K O Z 7 8 ) . I n t h e i r m o d e l , t h e t o t a l mucn c a p t u r e r a t e i s t h e sum o f t h e r a t e s f o r e a c h m u l t i p o l a r i t y o f g i a n t r e s o n a n c e e x c i t a t i o n s . A c c o r d i n g t o t h e i r r e s u l t s , i n t h e c a s e o f C a , t h e g i a n t d i p o l e r e s o n a n c e i s d o m i n a n t , w h e r e a s i n t h e c a s e o f P b b o t h t h e d i p o l e a n d c c t u p o l e r e s o n a n c e s a r e i m p o r t a n t . As d i s c u s s e d i n s e c t i o n I . D , t h e g i a n t r e s o n a n c e . m o d e l w o r k s v e r y w e l l f o r t o t a l muon c a p t u r e r a t e s i n l i g h t n u c l e i . I t s e e m s t h a t i n a c t i n i d e n u c l e i t h e c a p t u r e r a t e s a r e b e t t e r e x p l a i n e d by t h e r e s o n a n c e m o d e l w h i c h i n c l u d e s h i g h e r m u l t i p o l e e x c i t a t i o n s ( W I L 8 0 - 2 ) . The h y p o t h e s i s o f t h e v a n i s h i n g o f t h e C a b i b b o a n g l e i s b a s e d o n t h e a s s u m p t i o n c f a n u l t r a h i g h m a g n e t i c f i e l d ( 1 0 1 6 g a u s s ) i n o d d - A n u c l e i . A c c o r d i n g t o t h e r e c e n t e l a b o r a t e c a l c u l a t i o n by L e e a n d K h a n n a ( L E E 7 8 ) , t h e i n t e r n a l m a g n e t i c f i e l d i n o d d h e a v y n u c l e i i s l e s s t h a n 5 x 1 0 l * g a u s s . H e n c e t h e a c t u a l m a g n e t i c f i e l d 'may n o t b e h i g h e n o u g h f o r t h e v a n i s h i n g o f t h e C a b i b b o a n g l e . F i n a l l y , i n c o n c l u s i o n , t h e c o n c e p t o f t h e v a n i s h i n g o f t h e C a b i b b o a n g l e i n mucn c a p t u r e h a s n o t b e e n 123 proved and i n f a c t the weight of the evidence i s s l i g h t l y a g a i n s t i t . Since there i s a s t r o n g c o r r e l a t i o n between t o t a l mucn capture r a t e and n u c l e a r s t r u c t u r e , when c o n s i d e r i n g the even-odd Z e f f e c t i n muon c a p t u r e , the n u c l e a r s t r u c t u r e has to be taken i n t o account. IV.G Nuclear S t r u c t u r e E f f e c t i n Muon Capture In t h i s s e c t i o n , the c o r r e l a t i o n between capture r a t e s and n u c l e a r s t r u c t u r e w i l l te examined. Fi g u r e IV-7 i s d i f f e r e n t from the Primakoff p l o t ( f i g u r e s IV-2 and IV-3). T h i s p l o t has been presented by Kohyama and F u j i i (KOH79), and i s based on the f o l l o w i n g g e n e r a l formula f o r t o t a l c a p t u r e r a t e s A c = K - ^ f ^ b E | ^ I* / £ |<b|j" (|vba|)|a>|* = • y The y a x i s of f i g u r e IV-7 i s equal t o the t o t a l ' s t r e n g t h ' of the nucl e a r t r a n s i t i o n as f o l l o w s (S * - M I ^ I 2 / £ l<»|J- ( I v -ba | ) | a >|* (4-20) D= U In f i g u r e IV-7, the experimental r e s u l t s are used f o r the capture r a t e s i n equation (4.20). In the f i g u r e , the exp e r i m e n t a l capture r a t e s reduced by ( Z e f f ) * i n c r e a s e 124 l i n e a r l y u n t i l Z = 3 0 , a n d t h e n b e c o m e c o n s t a n t . T h e n u c l e a r t r a n s i t i o n m a t r i x f o r muon c a p t u r e h a s a c o n t r i b u t i o n f r o m Z p r o t o n s a n d A - Z n e u t r o n s . I n t h e c a s e o f s m a l l Z , t h e Z p r o t o n s i n t h e n u c l e u s c o n t r i b u t e l i n e a r l y t o t h e muon c a p t u r e a n d , f o r h e a v y n u c l e i , o n l y a f r a c t i o n o f t h e Z p r o t o n s i n t h e n u c l e u s t a k e s p a r t i n t h e muon c a p t u r e . T h i s r e d u c t i o n i s i m p l e m e n t e d by t h e e f f e c t i v e c h a r g e , Z e f f , i n t h e n u c l e u s . I n f i g u r e I V - 7 , t h e r e i s a c l e a r o s c i l l a t i o n a n d , s u r p r i s i n g l y , t h e m i n i m a c o r r e s p o n d t o t h e a t o m i c c l o s e d s h e l l s ( A r , K r , X e ) . B u t t h i s d o e s n o t mean t h a t t h e s t r u c t u r e c f t h e a t o m i c c l o s e d s h e l l s a f f e c t n u c l e a r c a p t u r e r a t e s . By c h a n c e t h i s i s o n e o f t h e c h a r a c t e r i s t i c s o f t h e n u c l e a r s t r u c t u r e . T h i s c a n be e x p l a i n e d b y f i g u r e I V - 8 . . I n f i g u r e I V - 8 , t h e a m o u n t o f t h e n e u t r o n e x c e s s i n n u c l e i v e r s u s a t o m i c n u m b e r i s p l o t t e d . T h i s a m o u n t i s c a l l e d t h e P a u l i e x c l u s i o n s t r e n g t h i n t h e P r i m a k o f f f o r m u l a . . I n t h i s f i g u r e , t h e m a x i m a a c c i d e n t a l l y c o r r e s p o n d t o t h e a t o m i c c l o s e d s h e l l a n d , i n muon c a p t u r e o f t h e n u c l e u s n e a r t h e m a x i m a , t h e l a r g e P a u l i e x c l u s i o n i n h i b i t i o n c a n be e x p e c t e d . T h i s e f f e c t c a u s e s o s c i l l a t i o n s i n f i g u r e I V - 7 a n d t h e e x p e r i m e n t a l r e s u l t s c l e a r l y r e f l e c t t h e n u c l e a r s h e l l e f f e c t . I n t h e f i g u r e , t h e r e d u c e d c a p t u r e r a t e o f A r i s a n o m a l o u s l y s m a l l . A l t h o u g h t h e r e h a v e b e e n n o m e a s u r e m e n t s o f t o t a l muon c a p u t u r e r a t e s i n K r a n d X e , t h e i r r e d u c e d c a p t u r e r a t e s a r e e x p e c t e d t o be v e r y s m a l l . On t h e e t h e r h a n d , t h e m i n i m a i n f i g u r e I V - 8 a r e l o c a t e d .125 1 Q xLOO cn UJ cr CL U 5 Q_ X U J Q LU U Q U 0 ; 1 1 Z e f f Ca , * < 1 Ni(N=30) X « \ X v • i i 1 1 Nb(N=52) Pr (N=82) • • * • • * • X ' • / A r I V *" X ? t Kr Z=36 X X ? t Xe • Odd-Z x Even-Z • X t - " X , 1 1 i i i i 0 10 20 30 40 50 60 70 80 90 ATOMIC NUMBER (Z) Figure IV-7, Reduced capture rates versus atomic number. This graph i s adapted from Kohyama and Fujii(KOH79). 0.31 0.30 0.29 028 < Q27 I < 026 02 5 N=20 ". N=2S X Nx. N=126 ,x... X - X N = 8 2 •u- X X « X J N = 5 0 • \ x *• X/ X * / »x x x ^ I Kr Z = 3 6 t X e Z - 5 4 t Rn Z - 8 6 • Odd-Z * Even-Z 10 20 30 40 50 60 70 80 90 ATOMIC NUMBER (Z) Figure IV-8, The neutron excess versus atomic number. This excess term is named Pauli exclusion term by Primakoff. 127 n e a r t h e n u c l e i w i t h n u c l e a r m a g i c n u m b e r s l i s t e d b e l o w . . A t t h e m i n i m a , t h e P a u l i i n h i b i t i o n i s s m a l l a n d t h e e x p e r i m e n t a l c a p t u r e r a t e s s e e m t c b e l a r g e . F r c m f i g u r e I V - 7 , C a ( 2 0 , 4 0 ) , N i ( 2 8 , 5 1 ) , N b ( 4 1 , 9 3 ) a n d P r ( 5 9 , 1 4 1 ) a p p e a r t o h a v e l a r g e r c a p t u r e r a t e s t h a n o t h e r n u c l e i . C a a n d P r h a v e n e u t r o n m a g i c n u m b e r s , a n d N i a n d Nb h a v e n e u t r o n n u m b e r s n e a r m a g i c n u m b e r s . The m a g i c n u m b e r s c o r r e s p o n d t c n e u t r o n o r p r o t o n n u m b e r N o r Z e g u a l t o 2 , 8 , 2 0 , ( 2 8 ) , ( 4 0 ) , 5 0 , 8 2 , ( 1 1 4 ) , 1 2 6 . . T h e n u m b e r s i n p a r e n t h e s e s a r e r a t h e r weak m a g i c n u m b e r s . N u c l e i h a v i n g Z o r N e q u a l t o a m a g i c n u m b e r h a v e c h a r a c t e r i s t i c s w h i c h a r e d i f f e r e n t f r c m o t h e r n u c l e i . I n muon c a p t u r e , t h e b a s i c p r o c e s s i s e x p r e s s e d b y ( 1 . 9 ) a n d f o r c o m p l e x n u c l e i t h e p r o c e s s i s ( 1 . 1 0 ) . T h u s t h e e x c l u s i o n i n h i b i t i o n a g a i n s t n e u t r c n s p r o d u c e d b y t h e muon c a p t u r e s e e m s t o a f f e c t t h e c a p t u r e r a t e s . F r c m f i g u r e I V - 8 t h i s i n h i b i t i o n i s a p p a r e n t l y s m a l l f o r n u c l e i h a v i n g N e q u a l t o a m a g i c n u m b e r . T h i s e x p l a i n s t h e r e l a t i v e l y l a r g e c a p t u r e r a t e s f o r C a ( N = 20) a n d P r ( N = 8 2 ) . A l t h o u g h , i n t h e c a s e o f N i ( N = 3 0 ) a n d N b ( N = 5 2 ) , t h e n e u t r o n n u m b e r s e x c e e d t h e m a g i c n u m b e r s ( 2 8 , 5 0 ) b y t w c , f r o m f i g u r e I V - 8 t h e P a u l i i n h i b i t i o n i s s t i l l s m a l l f o r N i a n d N b . I n t h e s e n u c l e i t h e c l o s e d s h e l l e f f e c t s t i l l r e m a i n s a n d a f f e c t s t h e muon c a p t u r e r a t e s . T h e r e a r e s o m e n u c l e i w h i c h h a v e m a g i c n u m b e r s o f n e u t r o n (eg Y ( 3 9 , 8 9 ) ) b u t t h e y d o n o t show a n o m a l o u s l y l a r g e c a p t u r e r a t e s a n d do n o t d e v i a t e e x t r e m e l y f r o m t h e G - P f o r m u l a . A l t h o u g h Y ( 3 9 , 8 9 ) i s s i m i l a r t o N b ( 4 1 , 9 3 ) , t h e muon c a p t u r e r a t e s o f Y a r e n o t a n o m a l o u s 128 l i k e N b . T h i s s e e m s t o b e d u e t o t h e d i f f e r e n c e i n t h e i r n u c l e a r m a g n e t i c m o m e n t s . Y h a s a s m a l l n e g a t i v e m a g n e t i c moment ( = - 0 . 137) , w h e r e a s Nb h a s a l a r g e p o s i t i v e m a g n e t i c moment ( = 6 . 1 6 7 ) . I n t h e c a s e o f t h e n e g a t i v e m a g n e t i c m o m e n t , t h e F+=I+1/2 h f s t a t e i s l o w e r t h a n t h e F ~ = I - 1 / 2 h f s t a t e . S i n c e t h e r e i s a r a p i d c o n v e r s i o n f r o m F - t o F + i n Y , t h e c a p t u r e r a t e f r o m F+ s e e m s t c be s u p p r e s s e d . T h e h f e f f e c t s f o r t h e n u c l e i w i t h n e g a t i v e m a g n e t i c m o m e n t s a p p e a r t o b e o n e o f t h e r e a s o n s f o r t h e d i f f e r e n t b e h a v i o r o f Y f r o m N b , a l t h o u g h t h e r e h a s b e e n no e s t i m a t e o f i t s m a g n i t u d e . The n u c l e a r c h a r g e r a d i i o f m o l y b d e n u m a n d s t r o n t i u m i s o t c p e s h a v e b e e n m e a s u r e d b y F r i c k e e t a l . ( F R I 7 9 ) . T h e i r e x p e r i m e n t h a s s u g g e s t e d t h a t t h e n u c l e a r c h a r g e r a d i u s c f Mc (Z= 4 2 , N = 5 2 ) i s 1% l a r g e r t h a n t h a t o f Mo (Z=4 2 , N = 5 0 ) w h i c h h a s t h e n e u t r o n m a g i c n u m b e r 5 0 . F r o m t h e i r r e s u l t , p r o t o n s i n a n u c l e u s w i t h a n e u t r o n m a g i c n u m b e r s e e m t o be m o r e t i g h t l y b o u n d b u t , w h e n t h e n u m b e r o f n e u t r o n s m o v e s a w a y f r o m a m a g i c n u m b e r , t h e b i n d i n g f o r c e b e c o m e s w e a k e r a n d t h e r a d i u s o f t h e p r o t o n s t e n d s t o i n c r e a s e . T h i s s e e m s t o b e t h e c a s e f o r Nb (Z=4 1 , N = 5 2 ) . S i n c e t h e r a d i u s o f t h e m u o n i c S c r b i t i n Nb i s 6 . 4 f e r m i ( 1 0 ~ 1 3 cm) a n d t h e n u c l e a r r a d i u s i s a b o u t 6 f e r m i , t h e m u o n i c wave f u n c t i o n i s c o m p a r a b l e i n s i z e t o t h e n u c l e u s a n d s o t h e muon c a p t u r e r a t e w i l l be v e r y s e n s i t i v e t o t h e e x a c t d i s t r i b u t i o n o f t h e p r o t o n s i n t h e n u c l e u s . T h i s h a s t e e n p o i n t e d c u t b y E c k h a u s e e t a l . ( E C K 6 6 ) . 129 CHAPTER V Muon C a p t u r e i n C h e m i c a l C o m p o u n d s V . A I n t r o d u c t i o n F e r m i a n d T e l l e r ( F E R 4 7 ) p r o p o s e d a m o d e l i n w h i c h t h e r e l a t i v e c a p t u r e p r o b a b i l i t y was p r o p o r t i o n a l t o t h e a t o m i c n u m b e r Z c f e a c h a t o m i n a c h e m i c a l c o m p o u n d . T h i s s o c a l l e d F e r m i - T e l l e r Z l a w i m p l i e s t h a t t h e r a t i o o f a t o m i c c a p t u r e r a t e s c f n e g a t i v e muons i n a c o m p o u n d (Z1) m ( Z 2 ) n i s g i v e n by W ( Z 1 / Z 2 ) = ( m « Z 1 ) / ( n * Z 2 ) ( 5 . 1 ) I t s c o n b e c a m e c l e a r t h a t t h e Z - l a w d i d n o t e x p l a i n t h e e x p e r i m e n t a l o b s e r v a t i o n s ( B E I 6 3 ) a n d t h e c a p t u r e p r o c e s s . was much m o r e c o m p l i c a t e d * Z i n o v e t a l . ( Z I N 6 6 ) d e m o n s t r a t e d t h a t t h e r e l a t i v e a t o m i c c a p t u r e r a t e s i n t h e m e t a l l i c o x i d e s h a v e a p e r i o d i c c h a r a c t e r i s t i c . T h e p o s i t i o n s o f t h e m i n i m a c o r r e s p o n d t o t h e a l k a l i m e t a l s . The e x p e r i m e n t a l r e s u l t s c l e a r l y i n d i c a t e d t h a t t h e e l e c t r o n i c s t r u c t u r e o f c h e m i c a l c o m p o u n d s a f f e c t s t h e a t o m i c c a p t u r e r a t e o f m u o n s . So f a r , t h e r e h a v e b e e n , a s i g n i f i c a n t a m o u n t o f d a t a c o l l e c t e d b y many g r o u p s b u t t h e y w e r e o f t e n i n c o n s i s t e n t . M o s t s t u d i e s o f t h e a t o m i c c a p t u r e r a t e s h a v e b e e n made b y d e t e c t i n g t h e m u o n i c K X - r a y s ( t h e L y m a n 130 s e r i e s ) . I n t h i s m e t h o d , t l i e sum o f t h e i n t e n s i t y o f t h e X - r a y h a s b e e n a s s u m e d t o b e e q u a l t o t h e n u m b e r s o f m u o n s c a p t u r e d . I n some e a r l i e r e x p e r i m e n t s ( S E N 5 8 , E C K 6 2 , B A I 6 3 ) , t h e a t o m i c c a p t u r e r a t e was o b t a i n e d b y d e t e c t i n g d e c a y e l e c t r o n s f r o m m u o n s w h i c h s p e n t m c s t o f t h e i r l i f e i n t h e K o r b i t . I h e s e e a r l i e r e x p e r i m e n t s h a d p o o r s t a t i s t i c s a n d v e r y f e w t a r g e t s w e r e m e a s u r e d . I n t h e p r e s e n t e x p e r i m e n t , t h e i r m e t h o d h a s b e e n a p p l i e d t o s t u d y t h e a t o m i c c a p t u r e r a t e o f m u o n s i n m e t a l l i c o x i d e s . S i n c e t h e l i f e t i m e o f a n e g a t i v e muon i n o x y g e n ( 1 7 9 5 n s ) i s s i g n i f i c a n t l y l o n g e r t h a n t h e l i f e t i m e i n e l e m e n t s h e a v i e r t h a n s o d i u m ( 1 2 0 4 n s ) , i t i s e a s y t o d e c o m p o s e t h e d e c a y e l e c t r o n s p e c t r u m i n t o t h e o x y g e n a n d m e t a l c o n s t i t u e n t s b y u s i n g t h e i r l i f e t i m e s . A s d i s c u s s e d i n C h a p t e r I , i t i s a g o o d a p p r o x i n a t i c n t h a t a l l m u o n s t r a p p e d i n a n a t o m r e a c h t h e K o r b i t w i t h o u t t h e i r d i s a p p e a r a n c e b y d e c a y , o r n u c l e a r c a p t u r e d u r i n g t h e c a s c a d e . W i t h i n t h i s a p p r o x i m a t i o n , t h e n u m b e r o f muons d e d u c e d f r o m t h e d e c a y e l e c t r o n s p e c t r u m s h o u l d b e e g u a l t o t h a t o b t a i n e d f r o m t h e i n t e n s i t y o f t h e 1 m u o n i c X - r a y . 131 V . B Muon A t o m i c C a p t u r e R a t i o b% t h e L i f e t i m e M e t h o d I n o r d e r t o o b t a i n t h e n u m b e r o f m u o n s f r o m a d e c a y e l e c t r o n s p e c t r u m , we m u s t c o r r e c t f o r t h e f a c t t h a t i n h e a v y e l e m e n t s m o s t o f t h e m u o n s a r e a b s o r b e d by t h e n u c l e u s . T h u s , t h e t o t a l n u m b e r o f d e c a y e l e c t r o n s , N e - ( Z ) , f r o m t h e n u c l e u s w i t h t h e a t o m i c n u m b e r Z i s g i v e n b y Q (Z) « R d N e ~ ( Z ) = •Nm-(Z) « E 1 * E 2 ( Z ) ( 5 . 2 ) R c (Z) + Q (Z) « R d w h e r e t h e d e f i n i t i o n s o f Q , R d a n d R c a r e g i v e n b y e g u a t i o n s ( 4 . 4 : ) a n d ( 4 . 5 ) , E1 i s t h e c o u n t e r e f f i c i e n c y i n c l u d i n g t h e e f f e c t o f l i m i t e d s o l i d a n g l e , E 2 (Z) i s t h e c o r r e c t i o n f o r t h e l o s s c f l o w e n e r g y d e c a y e l e c t r o n s i n t h e t a r g e t , a n d N m - ( Z ) i s t h e n u m b e r o f n e g a t i v e m u o n s t r a p p e d i n t h e n u c l e u s w i t h Z . F i g u r e 1 - 3 s h o w e d t h e e n e r g y s p e c t r u m o f d e c a y e l e c t r o n s i n t h e t a r g e t s C , T i , C u , a n d P b ( S U Z 7 9 ) . I t i s c l e a r l y s e e n t h a t t h e p e a k s o f t h e e n e r g y s p e c t r a i n h e a v y e l e m e n t s a r e s h i f t e d t o l o w e r e n e r g y d u e t o t h e . b i n d i n g c f t h e n e g a t i v e m u o n . H e n c e , t h e r a t e o f t h e l o s s o f l o w e n e r g y e l e c t r o n s i n t h e t a r g e t i s l a r g e r i n t h e c a s e o f h e a v y e l e m e n t s t h a n i n t h e c a s e o f l i g h t e l e m e n t s . . T h i s c o r r e c t i o n i s a c c o u n t e d f o r by E 2 ( Z ) . I n o r d e r t o d e t e r m i n e E 2 ( Z ) , we h a v e t c know t h e e n e r g y l o s s f o r d e c a y e l e c t r o n s 132 i n t h e t a r g e t , p l a s t i c w a l l s o f t h e t a r g e t c o n t a i n e r , a n d t h e c o u n t e r t e l e s c o p e . The d i f f e r e n t p a t h l e n g t h s t h a t e l e c t r o n s c a n e x p e r i e n c e a r e e s t i m a t e d a n d a v e r a g e d . . T h u s we c a n c a l c u l a t e t h e c u t o f f e n e r g y i n t h e e n e r g y s p e c t r u m o f d e c a y e l e c t r o n s . I n o u r a n a l y s i s , t h e c a l c u l a t e d e n e r g y s p e c t r u m b y H u f f (HUF6 1) i s e m p l o y e d . F o r e x a m p l e , i n P b ^ , t h e c u t o f f e n e r g y i s 18 MeV a n d t h e l o s s e s o f d e c a y e l e c t r o n s i n Pb a n d 0 a r e 2635 a n d 11%, r e s p e c t i v e l y . A l s o , i n C r 2 ° 3 ' t n e c u t e n e r g y i s 11 MeV a n d t h e l o s s i s 4% i n C r a n d 2 . 4 % i n 0. The c o r r e c t i o n s a r e s m a l l f o r o x i d e s w i t h Z s m a l l e r t h a n Z = 3 0 , w h i l e t h e y a r e s e v e r e i n o x i d e s w i t h h e a v y c o n s t i t u e n t s . S i n c e t h e t o t a l c o r r e c t i o n s i n t h e a t o m i c c a p t u r e r a t e a l w a y s a p p e a r a s t h e d i f f e r e n c e b e t w e e n t w o v a l u e s o f E2 (Z) a n d E 2(0), t h e c o r r e c t i o n s t e n d t o be s m a l l e r . N e g a t i v e m u o n s i n m e t a l l i c o x i d e s Z 0\ , a r e t r a p p e d e i t h e r i n t h e m e t a l (Z) o r i n t h e o x i d e (0). By t h e a n a l y s i s o f t h e d e c a y e l e c t r o n s p e c t r u m , t h e s p e c t r u m c a n be d e c o m p o s e d i n t o t h e m e t a l a n d t h e o x y g e n c o m p o n e n t s . F r o m t h i s m a n i p u l a t i o n , N e - ( Z ) a n d N e ~ (0) a r e o b t a i n e d . . T h u s , N m - ( Z ) a n d Nm~ (0) a r e f o u n d f r o m e g u a t i o n ( 5 . 2 ) . T h e r a t i o o f a t o m i c c a p t u r e r a t e s p e r a t o m i n Z m 0 n i s d e f i n e d by W (Z/0) = { n « N m ~ (Z)} / [ m » N m - (0)} ( 5 . 3) I n t h e f i t t i n g o f t h e s p e c t r u m , e q u a t i o n ( 3 . 6 ) h a s b e e n u s e d a n d , f r c m e q u a t i o n s ( 5 . 2 ) a n d ( 5 . 3 ) , we g e t 1 3 3 /Z\ n Q(0) E2(0) A(Z) W - = • • • (5.4) \0/ m Q(Z) E2(Z) A(0) where A (Z) and A (0) are the a m p l i t u d e s of t h e metal and the oxygen component a t t=0, r e s p e c t i v e l y . I n the case of ZOO, Q (Z) and E2(Z) are almost e q u a l t o the v a l u e s f o r oxygen (Q ( 0 ) , E2 ( 0 ) ) , because of t h e s m a l l bound muon e f f e c t . One of t h e s h o r t c o m i n g s of the l i f e t i m e method i s the d i f f i c u l t y i n s e p a r a t i n g the d i f f e r e n t l i f e t i m e components f o r elements w i t h s i m i l a r atomic numbers. I n o r d e r to s t u d y t h i s problem, a Monte C a r l o programme was w r i t t e n t c s i m u l a t e a run w i t h dry i c e (C0 2) as a t a r g e t m a t e r i a l . Assuming A (C)/A(0) =0.25, 4x10 s muons out of 5 x 1 0 s t r i a l s were c a p t u r e d i n oxygen and t h e numbers of muons was e s t i m a t e d a t 3.99x10 s by f i t t i n g the a r t i f i c i a l l y c r e a t e d spectrum. S i n c e t h e d i f f e r e n c e between the Monte C a r l o and the f i t t i n g i s o n l y 0.3%, i t seems t h a t i f we have enough s t a t i s t i c s , we can s e p a r a t e e v e n t s even f o r compounds h a v i n g ccmpcnents w i t h n e a r l y t h e same Z, such as C0 2» We have measured a muon atomic c a p t u r e r a t i c i n dry i c e . The r e s u l t seems g u i t e r e a s o n a b l e , when i t i s compared w i t h the atomic c a p t u r e r a t i c c f o x i d e s w i t h B or Be (SCH78-2) near C. Our r e s u l t s are l i s t e d i n Table V-1 a l o n g w i t h p a s t r e s u l t s o f X-ray measurements done by p r e v i o u s w o r k e r s . Table V-1, Per Atom Capture R a t i o s A(Z/0) of Muons i n M e t a l l i c Oxides z ZmOn TRIUMF Past R e s u l t Ref. 6 C02 0. 43 + 0.02 1 1 Na202 0.87 + C.02 12 MgO 0. 80 + 0.0 2 0.83 ± 0.0 7 (D 13 A1202 0.84 ± 0.03 0.85 ± 0.06 (1) 0.65 ± 0. 0 6 (2) 14 Si02 0.96 ± 0,04 0.79 ± 0.07 (D 0.57 + 0.05 (2) 0.86 + 0.07 (3) 15 P205 0.87 + 0.03 0.93 + 0. 11 (2) 20 Ca (OH) 2 1.49 + 0.06 CaO 1. 36 ± 0. 10 (1) CaO 1.45 + 0.09 (4) 22 Ti02 2. 17 + 0. 1 1 2.70 + 0.20 (1) 1. 90 ± 0. 10 (4) 24 Cr203 2. 63 ± 0, 1 3 3,00 + 0. 17 (D 2.04 ± 0. 1 1 (4) Cr03 2.96 ± 0.20 25 Mn02 3.00 ± 0. 17 29 CuO 4.06 ± 0. 23 3.60 ± 0.40 (D 6. 14 ± 0. 8 5 (6) 30 ZnO 2. 39 + 0. 10 2.66 ± 0.32 (D 32 Geo 2. 20 ± 0. 12 GeC2 2.40 ± 0. 13 48 CdO 1. 93 + 0.07 6.70 + 1, 50 (D 2. 47 ± 0. 22 (4) 2. 50 + 0. 2 8 (5) 50 Sn02 2. 15 + 0. 11 3.17 ± 0. 24 (D 56 BaO 2. 27 ± 0.09 2.27 ± 0. 22 (D 1. 45 ± 0. 18 (5) 60 Nd02 4. 13 ± 0,29 80 HgO 3. 75 ± 0.29 82 Pb0 2 3. 21 ± 0.23 4. 17 ± 0.30 (D 4. 10 + 0. 4 2 (5) Pb304 3.87 + 0. 29 References : (1) ZIN66 (2) SEN58 (3) MAU77 (4) KNI75 (5) D AN 77 (6) BAI63 N J | O 7-Or 6-0 5-0 4 0 3-0 2-0 1-0 jfi Zinov Vaeilyev et al £ Daniel — — — Daniel e q (5 .6 ) ^ Triumf — — Schneuwly et al 10 20 30 4 0 50 6 0 ATOMIC NUMBER ( Z ) Figure V - l , Atomic capture r a t i o i n m e t a l l i c oxides. 136 I n f i g u r e V - 1 , o u r r e s u l t s , p a s t m e a s u r e m e n t s a n d v a r i o u s t h e o r e t i c a l c u r v e s a r e s h e w n t o g e t h e r . I t i s e v i d e n t t h a t o u r r e s u l t s a r e i n a d e g u a t e a g r e e m e n t w i t h t h e X - r a y m e a s u r e m e n t s ( Z I N 6 6 , DAN77) . T h e F e r m i - T e l l e r Z - l a w e x p l a i n s t h e e x p e r i m e n t s q u a l i t a t i v e l y b e l c w Z < 3 0 , b u t i n h e a v y e l e m e n t s t h e Z - l a w p r e d i c t s t w i c e t h e v a l u e s o f t h e e x p e r i m e n t a l c a p t u r e r a t e s . D a n i e l (DAN75) p e r f o r m e d a c a l c u l a t i o n o f t h e a t o m i c c a p t u r e r a t i o f o r n e g a t i v e m u e n s i n c o n d e n s e d m a t t e r . H i s c a l c u l a t i o n i s b a s e d o n t h e t r e a t m e n t o f F e r m i a n d T e l l e r i n w h i c h t h e e l e c t r o n s a r e t r e a t e d a s a F e r m i g a s . He o b t a i n e d t h e a t o m i c c a p t u r e r a t i o p e r a t o m i n t h e c a s e o f a b i n a r y c o m p o u n d w i t h e l e m e n t s Z l a n d Z2 / Z l \ (Z 1) i / 3 » l n ( 0 . 5 7 » Z 1) W = ( 5 . 5 ) \ Z2 / (Z2) i / 3 * l n ( 0 . 5 7 « Z 2 ) T h i s f o r m u l a g i v e s b e t t e r a g r e e m e n t t h a n t h e Z - l a w a s s h o w n i n f i g u r e V - 1 . T h e c h e m i c a l b e n d a l s o a f f e c t s t h e s t r u c t u r e o f t h e c a s c a d e i n t e n s i t i e s . . Z i n o v e l a l . ( Z I N 6 6 ) a n d K e s s l e r e t a l . ( K E S 6 7 ) h a v e s h o w n t h a t t h e m u o n i c X - r a y K - s e r i e s s p e c t r a i n p u r e m e t a l T i h a v e m o r e t r a n s i t i o n s f r o m h i g h o r b i t s t h a n t h e s p e c t r a i n t i t a n i u m o x i d e s . S c h n e u w l y e t a l . ( S C H 7 8 - 1 ) p e r f o r m e d t h e s y s t e m a t i c m e a s u r e m e n t s o f c a p t u r e r a t i o s i n 137 s e l e c t e d c o m p o u n d s o f n i t r o g e n , s u l f u r a n d s e l e n i u m , a n d c o n f i r m e d t h a t t h e c h e m i c a l s t r u c t u r e p l a y s a n i m p o r t a n t r o l e i n t h e m u o n i c a t o m i c c a p t u r e p r o c e s s . T h e f i r s t s u c c e s s f u l t h e o r y t o t a k e i n t o a c c o u n t t h e e f f e c t o f c o r e a n d v a l e n c e e l e c t r o n s w a s p r o p o s e d by S c h n e u w l y e t a l . ( S C H 7 8 - 2 ) a n d , a s s h o w n i n f i g u r e V - 1 , t h e i r t h e o r e t i c a l c u r v e r e p r o d u c e s t h e p e r i o d i c i t y o b s e r v e d i n t h e e x p e r i m e n t s . R e c e n t l y , i t h a s b e e n s h o w n t h a t t h e r e i s a s t r o n g c o r r e l a t i o n b e t w e e n a t o m i c c a p t u r e a n d a t o m i c r a d i i w i t h t h e a t o m i c c a p t u r e r a t e b e i n g h i g h f o r a t o m s w i t h s m a l l r a d i i (DAN78) . . D a n i e l (EAN79) p r o p o s e d a m o d e l w h i c h t a k e s t h e a c t u a l a t o m i c r a d i i i n t o a c c o u n t a n d m o d i f i e d h i s f o r m u l a ( 5 . 5 ) t o g i v e / Z l \ ( Z l ) i / 3 « l n ( 0 . 5 7 - Z 1 ) » R (Z2) w = ( 5 . 6 ) * Z2 ' (Z2) V 3 » l n ( 0 . 5 7 - Z 2 ) » B (Z 1) w h e r e B (Z) i s t h e a t o m i c r a d i u s f o r a n a t o m c f a t o m i c n u m b e r Z . A s s h o w n i n f i g u r e V - 1 , e q u a t i o n ( 5 . 6 ) c l e a r l y g i v e s t h e p e r i o d i c i t y o f t h e a t o m i c c a p t u r e r a t e a n d g i v e s b e t t e r a g r e e m e n t t h a n e g u a t i o n ( 5 . 5) . E v e n t h o u g h , a s d i s c u s s e d a b o v e , t h e t h e o r i e s o f S c h n e u w l y a n d D a n i e l h a v e r e v e a l e d t h e i m p o r t a n t f e a t u r e s o f t h e a t o m i c c a p t u r e r a t e , t h e r e i s s t i l l d i f f i c u l t y i n i n t e r p r e t i n g t h e e x p e r i m e n t s . I n o u r e x p e r i m e n t a l r e s u l t s , 138 i t i s e v i d e n t t h a t t h e c a p t u r e r a t i o s i n d i f f e r e n t o x i d e s o f t h e . s a m e e l e m e n t a r e d i f f e r e n t . D a n i e l ' s m o d e l c a n r e p r o d u c e t h i s d i f f e r e n c e o n l y w e a k l y v i a t h e d i f f e r e n t a t o m i c r a d i i f o r d i f f e r e n t v a l e n c y s t a t e s . S c h n e u w l y ' s m o d e l , w h i c h t a k e s t h e c h e m i c a l b o n d e f f e c t i n t o a c c o u n t , a l s o g i v e s s l i g h t l y d i f f e r e n t c a p t u r e r a t i o s f o r t h e d i f f e r e n t o x i d e s o f t h e same e l e m e n t . H o w e v e r t h e d i f f e r e n c e s p r e d i c t e d by t h e s e m o d e l s a r e n o t l a r g e e n o u g h t o e x p l a i n t h e d i f f e r e n c e s o b s e r v e d i n t h e e x p e r i m e n t s . . T h u s , t h e t h e o r e t i c a l d e v e l o p m e n t w i l l h a v e t o b e p u r s u e d f u r t h e r t c s o l v e t h e c h e m i c a l e f f e c t s i n t h e . a t o m i c c a p t u r e r a t e . 139 CHAPTER VI S ummar y O u r l i f e t i m e m e a s u r e m e n t s f o r n e g a t i v e muons b o u n d i n v a r i o u s n u c l e i h a v e p r o d u c e d many s u c c e s s f u l r e s u l t s . F o r t y e i g h t e l e m e n t s w e r e s t u d i e d a l t o g e t h e r , w h i c h i s a s o m e w h a t l a r g e r s u r v e y t h a n h a s b e e n a t t e m p t e d b e f o r e . 1 T h i s l a r g e n u m b e r o f m e a s u r e m e n t s b y o n e g r o u p r e m o v e s t h e d i f f e r e n c e s d u e t c s y s t e m a t i c e r r o r s among v a r i o u s e x p e r i m e n t a l g r o u p s . F o r t h e l i f e t i m e m e a s u r m e n t , s y s t e m a t i c e r r o r s d u e t o 2 n d muons a n d 2 n d e l e c t r o n s a r e i m p o r t a n t , a n d i n p r e v i o u s e x p e r i m e n t s v e r y f e w g r o u p s h a v e s u c c e e d e d i n t h e d e t e r m i n a t i o n o f t h e p o s i t i v e muon l i f e t i m e . H e n c e , t h e p a s t r e s u l t s o f n e g a t i v e muon l i f e t i m e s i n n u c l e i w e r e a f f e c t e d b y s y s t e m a t i c e r r o r s w h i c h s h i f t e d t h e p o s i t i v e muon l i f e t i m e . The p o s i t i v e muon l i f e t i m e d e t e r m i n e d b y o u r s y s t e m was 2 1 9 7 . 0 ± 0 . 7 n s w h i c h a g r e e s w e l l w i t h t h e a c c e p t e d v a l u e o f 2 1 9 7 . 1 2 0 ± 0 . 0 7 7 n s ( K E L 8 0 ) . We h a v e i m p r o v e d t h e a c c u r a c y o f n e g a t i v e muon l i f e t i m e s i n many l i g h t e l e m e n t s ( E e , B , N , 0 , F , N a , C l , K) a n d new d e t e r m i n a t i o n s w e r e made f o r 1 3 C , 1 8 0 , D y , a n d E r . M o s t c f o u r m e a s u r e m e n t s a r e i n a d e g u a t e a g r e e m e n t w i t h p a s t f i n d i n g s . I n t h e c a s e o f 6 L i a n d 7 L i , t h e r e w a s a i Sens et al.(SEN59) had 30 elements i n 1959. 1 4 0 disagreement between the Lodder-Jonker c a l c u l a t i o n (LOD67) and the experiment cf Eckhause et a l . (ECK63). The two r e c e n t experiments, ours and Bardin's (EAR78), are i n agreement with each other and a l s o with the t h e o r e t i c a l c a l c u l a t i o n . A l a r g e i s o t o p e e f f e c t was observed i n L i , B, and 0, however, there was no i s o t o p e e f f e c t observed i n C. C a l c u l a t i o n s of p a r t i a l capture r a t e s i n 1 2 C and * 3C have been performed by Desgrolard et al.(DES78) using a s h e l l model, and t h e i r r e s u l t s i n d i c a t e d no d i f f e r e n c e i n the capture r a t e s f o r these i s o t o p e s . T h i s p r e d i c t i o n f o r the p a r t i a l muon capture r a t e seems to hold even f o r the t o t a l capture r a t e as demonstrated by our experiment. Recently, i t was pointed out that odd-Z heavy n u c l e i might be shewing l a r g e r t o t a l muon capture r a t e s than even-Z heavy n u c l e i due to the presence of an u l t r a h i g h magnetic f i e l d (10* 6 G) (WAT75) which causes the v a n i s h i n g of the Cabibbo angle (WAT75, SA174). The d i s c u s s i o n was based on the o b s e r v a t i o n of a l a r g e nuclear capture r a t e i n Nb which has been confirmed i n t h i s werk. However as d i s c u s s e d i n s e c t i o n IV.F, t h i s e f f e c t seems t o have a c o r r e l a t i o n with n u c l e a r s t r u c t u r e . In order to avoid any n u c l e a r s t r u c t u r e e f f e c t s , the even-odd e f f e c t has been i n v e s t i g a t e d between Z=45 and Z=55 and between Z=64 and Z=68. although the odd-Z n u c l e i show s l i g h t l y l a r g e r capture r a t e s than even-Z n u c l e i , the amount i s not as l a r g e as expected from the v a n i s h i n g of the Cabibbo angle. Since there has been no study cf the n u c l e a r s t r u c t u r e e f f e c t s on 141 the t o t a l muon capture r a t e i n even and odd n u c l e i , the. e f f e c t should be i n v e s t i g a t e d i n d e t a i l with t h i s i n mind. Our capture r a t e s determined by l i f e t i m e s were compared with the Primakoff and Goulard-Primakoff theory. As expected, the l a t t e r theory gave a s l i g h t l y b e t t e r f i t to the experimental data than the former t h e o r y . In the case of the Primakoff formula, the parameters obtained by the chi - s g u a r e d minimization were i n good agreement with h i s estim a t e . I t was necessary to use a chemical compound to perform the l i f e t i m e measurements f o r some elements. In a decay spectrum of a chemical compound, there i s not only the i n f o r m a t i o n about l i f e t i m e s but al s o the i n f o r m a t i o n on muon atomic capture r a t e s . The r e l a t i v e atcmic capture r a t i o i s given by the r a t i o of the amplitudes i n eguation (3.6) (see eguation (5.4)). we have extended our experiment to i n c l u d e many more compounds than had been a n t i c i p a t e d i n i t i a l l y . T h i s was the f i r s t attempt to apply the l i f e t i m e method i n i n v e s t i g a t i n g s y s t e m a t i c a l l y the atomic capture r a t e s i n m e t a l l i c oxides of the type Z 0 . Our r e s u l t s between Z=6 1 c m n and Z=30 showed the p e r i o d i c dependence and were i n good agreement with e a r l i e r atomic capture r a t e s obtained by X-ray measurements, although our r e s u l t s around Z=50 were lower than the X-ray measurements. The muon atomic capture r a t e f o r atoms with Z l a r g e r than 30 w i l l be s t u d i e d by the l i f e t i m e method at TEIUMF duri n g the f a l l of 1980. In c o n c l u s i o n we note that t h i s t h e s i s has made a 142 s i g n i f i c a n t c o n t r i b u t i o n t o t h e d a t a b a s e n o t o n l y i n muon c a p t u r e b y a t o m s b u t a l s o t o muon c a p t u r e b y n u c l e i ; p h y s i c a l e f f e c t s w h i c h h a v e d i f f e r e n t s c i e n t i f i c i n t e r e s t s b u t w h i c h c a n be c o n v e n i e n t l y s t u d i e d u t i l i z i n g t h e s a m e b a s i c e q u i p m e n t . B o t h t y p e s o f e x p e r i m e n t a r e f r a u g h t w i t h s y s t e m a t i c ' e r r o r s a n d s o g r e a t c a r e h a s b e e n t a k e n t o d o u b l e c h e c k w h e r e v e r p o s s i b l e . T h i s c o n s e r v a t i s m may b e t h e m o s t i m p o r t a n t f e a t u r e c f t i e e x p e r i m e n t a l t e c h n i q u e . 143 References ALB69 a . Alberigi-Quarata, A.Bertin, G.Matone, F.Palmonari, G. 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