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UBC Theses and Dissertations

A systematic study of muon capture Suzuki, Takenori 1980

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I,'  A SYSTEMATIC STUDY OF MUON CAPTURE  by Takenori  Suzuki  a.Sc., U n i v e r s i t y of Tokyo, 1970 M . S c , U n i v e r s i t y 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 October, 1980 T a k e n o r i Suzuki, 1980  r  In p r e s e n t i n g an the  advanced Library  I further for  his  of  this  written  shall  agree  at make  that  thesis  it  freely  permission  purposes  for  in p a r t i a l  the U n i v e r s i t y  It  financial  is  University  of  British  October 14, 1980  of  Columbia,  British  by  for  gain  Columbia  shall  the  requirements  reference copying  of  I agree and  that  not  copying  be a l l o w e d  or  for  that  study.  this  thesis  t h e Head o f my D e p a r t m e n t  understood  PHYSICS  207S Wesbrook Place Vancouver, Canada V6T 1WS  of  for extensive  permission.  of  fulfilment  available  may be g r a n t e d  representatives.  Department The  thesis  degree  scholarly  by  this  or  publication  without  my  i i  Abstract  elements (  6  Negative  mucn  lifetimes  including  four  pairs  Li,7Li, ^ B ,  electronics  wiich  agreement  with  by  produced  the  M20  elements in  Be,  Our  for in  results  predicted that  the  the by  Na, 1 3  C,  Li, in  6  1 8  the  of  muons  captured  analysis.  Our  agreed  well  are  higher  of  systematic situation.  C,  Dy  Er.  Li  muon  accuracy  errors,  heavy  which  and  muon good Muons  were  provided  X-ray  and a r e gives  measured  a l l  has  been  measurements  were effects  was n o  isotope  effect  agreement Our  is  was the  i s not  in  also  large  in  ratios.  deduced  by  to  and  23  fields.  metallic The  number  lifetime  The  confidence  the  expected  dependence  very  C.  confirm  that  capture  periodic  in  magnetic  stopped  measurements. liable  strong  were  the  measurements  smaller than  angle was  with  light  achieved  isotope  nuclei  added  for  Strong  atomic  reproduced  which  set-up  in  ns,  accuracy  good  rates  beam the  were  Jonker.  each element  earlier  targets  positive  pions  new  in  Cabifcbo  measure by  and  in  the  48  2197.120±0.077 ns. of  there  were  capture  result  with  and  Lodder  of  in  experimental the  improved and  negative to  decay  and K,  effect  quenching  of  Cl,  odd-Z  order  An  and  from  in  He.  Li  even-odd  isotope  2197,0±0.7  muon l i f e t i m e s  7  measured  TRIUMF.  and 0 , but  by  be  value  B,  values  The  at  against  to  backward  H and  of  oxides  accepted  negative  increase the  checked  measured  the  0 , F,  performed observed  was  except  N,  were  beam c h a n n e l The  The  8  logic  been  separated  * B , * 2 _ , i 3 c ,1 6 0 , i 0 ) .  1  lifetime,  were  of  have  results  and however  different to  the  overall  i i i  TABLE  OF  AB S I R & C T T A B L E OF CONTENT'S L I S T OF F I G U R E S L I S T OF T A B L E S ACKNOWLEDGEMENTS CHAPTER I.A  I,  I. B I.C I. D CHAPTER II. A II.B II.C II.D II.E II. F  II,  CONTENTS  —  Introduction 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 Matter F r e e Muon D e c a y Bound Mucn D e c a y Muon C a p t u r e i n N u c l e i  i i i i i vi v i i v i i i in  E x p e r i m e n t a l Method and S e t - u p Muon Beam L i n e S c i n t i l l a t i o n C o u n t e r s and Geometry 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 — Targets E l e c t r o n i c s and T i m i n g C o n s i d e r a t i o n R u n n i n g P r o c e d u r e a n d Run R e c o r d  CHAPTER I I I , D a t a A n a l y s i s III. A Data A n a l y s i s Procedure III. B Magnetic F i e l d Effect III. C Mucn S t o p p i n g R a t e E f f e c t III. D 2 n d Muon R e j e c t i o n III.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 Dead Time c f E l e c t r o n i c s • III. 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 III. G H y p e r f i n e E f f e c t (hf) i n a Decay Curve CHAPTER I V , IV. A IV.B IV.C IV.D (a) (b) (c) (d) (e) (f) (g) (h) (i)  E x p e r i m e n t a l R e s u l t s and D i s c u s s i o n s of L i f e t i m e Measurements 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 Mucn 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 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 and System C a l i b r a t i o n 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 Elements L i t h i u m ( 6 L i and 7 L i ) Beryllium B o r o n (i ° B a n d i » B ) C a r b o n (* 2 C a n d 1 3 C ) Nitrogen Oxygen ( i 6 0 and ia ) Fluorine Search f o r the hf T r a n s i t i o n i n Be, 1 0 B , i i B , 1 3 C , N , Na a n d C l F r o m Z= 1 1 (Na) t o Z = 83 ( B i ) 0  1 1 4 8 15 24 25 3 1 34 35 39 49 53 53 57 6 1 64 67 69 72 77 85 88 92 94 94 97 98 99 100 101 101 104 107  iv  IV.E IV.F IV. G  P r i m a k o f f F o r m u l a i n Muon C a p t u r e The Even-Odd Z E f f e c t i n Heavy N u c l e i 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 C a p t u r e  109 112 123  CHAPTER V, Muon C a p t u r e i n C h e m i c a l Compounds V. A Introduction V.B Muon A t o m i c C a p t u r e fiatio by t h e L i f e t i m e Method  129 129  CHAPTER V I , Summary  139  References  143  131  V  List  of  Figures  Figure 1-1,  Page  Energy  Spectrum  decay.  The  units 1-2,  of  Energy muon muons  1-3,  x  axis  (muon  decay in  in  negative  positrons shows  carbon.  titanium  is  energy  muons  Also  i n C,  Ti,  and  The  M20  II-2,  Experimental  II-3,  Time  of  stopped  beam  Fe  7  positive  the  asymmetry  Cu,  decay  and  negative  cf  negative —  decay  and  electrons  set-up  Pb.  12  e l e c t r o n s from  negative 13 26  and  decay  spectrum  of  electron counters  incident  mucn s i g n a l s data  beam  taking  II-5,  Electronics  logic  II- 6,  Timings  difinitions  30  system  40 43  of  1,Positive  muon  decay  curve  III-2,Negative  muon  decay  curve  III-3,Stopping  rate  dependence  events  44 55  in with  Cr203 and  56 without  rejections distortion  29  and  •  S i m p l i f i e d MSB  III-4,Lifetime  9  from  (Huff61).  II-4,  III-  in  line  flight  and  momentum  for  spectra of  muons II- l,  positoron  muon  shown.  s p e c t r a of  Pb  positive  >  asymmetry  Theoretical in  the  from  mass) / 2 .  dependent  Experimental  I- 4,  cf  62 in  positive  muon  decay  curve  65  Figure  Page  III- 5,Hyperfine rate,  doublet  Ec c a p t u r e  disappearance rate  frcm  F+{F~)  Ratio  IV-2,  The TBIUMF d a t a  IV-3,  c f bound  Past  findings fitted  decay  Absolute from is  rate  to  sign  and E  free  decay  rate  89 and  formula.  summarized  114  by E c k h a u s e  e t a l . (ECK66)  and t h e  formula  of experimental  115 capture  rates  from  the  formula  deviations  117  of experimental  the Goulard-Primakoff  formula.  capture Figure  rates IV-4  redrawned.  The n o r m a l i z e d  IV-7,  Reduced graph  capture  has been  The n e u t r o n This  1 18 deviations rates shown  excess  of  versus  odd-Z atomic  by K c h y a m a  versus  e x c e s s t e r m i s named  atomic  nuclei number.  Atomic  capture  120 This  a n d F u j i i (KOH79)  —  125  number.  P a u l i e x c l u s i o n term  Primakoff. V-1,  total  shews t h e  to the Primakoff  to the Primakoff  IV-6,  I-V-8,  rate,  conversion  74  are f i t t e d  Goulard-Primakcff IV-5,  decay  Rh i s  state.  Goulard-Primakoff Deviations  Ed  atom.  The + v e ( - v e )  Goulard-Primakoff  are  IV-4,  muonic  rate,  rate.  I V - 1,  the  of  by 126  ratio  in metallic  oxides.  135  List  of Tables  Table  Page  II-1,  Counter  Geometry  II-2,  List  II-3,  M e a n i n g s c f Symbols i n L o g i c  o f T a r g e t s and  {figure I I - 4,  Bun  and  Efficiency  33  T h e i r Form  36-37  Diagram  II-5)  42  Becords (Total Events)  I I I - 1,• P o s i t i v e  5 1-52  Muon L i f e t i m e s o f F o u r  Electron  Telescope I I I - 2,  Carbon  I V - 1,  Besults  60  Background  Effect  cf Lifetime  i n Light  Measurements  Elements in This  Experiment  78-79  IV-2,  Summary o f Muon L i f e t i m e s and  IV- 3 ,  Past P o s i t i v e  IV-4,  N e g a t i v e Muon L i f e t i m e s i n C a r b o n  IV-5 (1) , C a p t u r e (2),  The  Bates i n  Mucn C a p t u r e The  IV-7,  Fitting  I V - 8,  V- 1,  6  L i and  Bates  B a t e s by  Besults  7  93  l i  Lodder  96 t o the  and  total  Jonker  i n Various Nuclei  f o r the P r i m a k o f f  (4. 16) )  Formula  ( e g u a t i o n (4.18))  in  Capture  Metallic  105-106  113  B e s u l t s f o r the G o u l a r d - P r i m a k o f f  atom  96  Formula  Fitting  Per  80-84 86  of M u l t i p o l e s  Hyperfine Effects  (equation  Capture  Mucn Measurements  Contribution  IV-6,  71  Batios  Oxides  A(Z/0)  113 o f muons 134  viii  ACKNOWLEDGEMENT'S  I only  f o r h i s help  guidance thank  members o f  help  Professor  David  not  t h e s i s , but also f o r h i s  p h y s i c a l phenomena.  the supervising committee, for their  F.Measday  I  would  like  Professors  a d v i c e and e f f o r t  to  D.S.Beder,  in  reading  work.  many  would  like  t o thank  t h e MSB d a t a  of  this  invaluable two-week  taking  experiment.  assistance of  experiment.  MSB g r u o p ,  assistance  through I  also  of  Dr.D.G.Fleming) , Dr.E.B.Jchnscn, experiment express  many  frcm f i v e  a n d TCKYO have  thanks  Finally encourage ment.  due t o t h e o t h e r  and D.Spencer  the l a s t members  of  E.Kiefl, for their  I  groups,  MSB g r o u p  to a l l of  during  many  years  this  work.  the above  I  DE.J.B.Warren,  would  for their  Ycshiko  Without  (Dr.D.C.Walker,  (Dr.T.Yamazaki),  completed.  my w i f e  Dr.J.M.Poutissou,  OBC c h e m i s t r y  (Dr.B.M.Pearce),  n o t been  thank  Dr.M.Hasinoff,  kind advice  UVIC TRIUMF  would  throughout  the  t h e MSB m e e t i n g .  for their  targets  Roalsvig  Dr.D.G.Fleming,  wish t o thank  and D r . M . S a l o m o n  their  w h i c h was e s s e n t i a l f o r t h e  are also  B.Ng,  Dr.D.M.Garner  i s my p l e a s u r e t o a c k n o w l e d g e  Dr.Jan-Per  Dr.D.C.Walker,  and  and i n p a r t i c u l a r f o r  system It  Thanks  G. M a r s h a l l , B . J . M i k u l a ,  a loan  Dr.J.H.Brewer  enlightening discussions  with  success  the  to  i n completing t h i s  and B . L . W h i t e  I for  grateful  i n understanding  F. W . D a l b y , this  am m o s t  this  like  to  cooperation.  f o r h e r many  years  of  1  CHAPTEE  I  Introduction  I.A  Discovery in  The  muon  (AND38)  was t h o u g h t  tc  in  the  by  difficult  explain  earth's Yukawa have in al.  been  the  negative muons  who  muons  did  not  discovery  of  are  Thus the  and  muens mass  of  fact  light  by  decay  that  that  are are the  Behavior  work  ratio  Lattes  et  products  in  the  are  modern 105.6  and they  absorption that  nucleus.  from It  is  and now  use  MeV/c2  experience  of the  The  resolved  mesons  atoms  et  clear  muons  the  should  with  Conversi  became  ways-  the  was b e c a u s e  interaction  pions.  Yukawa  mass  penetrated  reactions  the  forces was  nuclear  the  the  nuclear  i t  it  a l . (LAT47)  many  mesons i n  p a r t i c l e s of  with  that of  the  it  was f o u n d ,  This  cf  of  and  However,  had  nuclear  strongly  electron)  for  strong  elements,  electrons net  it  the  the  the  are  When i t  (YUK35).  via  observed  pions  Anderson  absorption.  Through  They  similar tc  leptons  1935  quickly  pions  were t h e  understood  the  interact  contradiction. rays  in  measured in  and i t s  responsible  responsible for  atmosphere.  (CON47),  meson  without  absorbed  by  cosmic r a y s .  Yukawa  atmosphere mesons  Muon  Matter  as p r e d i c t e d to  the  was d i s c o v e r e d  Neddermeyer  be  of  the  cosmic now  muons  -which  classified  of  the (206.8  the  term. times  weak  and  as  2  the  electromagnetic  interactions  but  not  the  strong  inte raction. The conveniently The  1,  divided  slowing  discussed  dcwn  in  High  behavior  detail  the  by  to  a  few  mainly  by  collisions  end  this  its  A few The  in  depend gas,  The  whether  are  states  of  lowest  state  have  (WU69).  been  (FER47).  the  almost The  lose  equal  between  energy  electrons.  muon's  slowing  their  energy to  the  and  a  the few  valence  down t i m e  IO7-9  At  is  10  in  the  °  sec.  _ 1  with  sec.  the  The  electrons details  material  of  a n d come this  is  a metal,  and e l e c t r o m a g n e t i c  cascade:  eventualy  a particular of  the  e m i s s i o n of transition  processes is  MeV  atomic  energy  10-*3  capture  muons  i.e.  stages  be  rest:  about on  duration  may  to  process  insulator,  etc.  Atomic  the  is  mucns e x c h a n g e  rest  with  material i s to  matter  four  Teller  of  when  velocity.„  keV  and  tens  stage,  velocity  following  in  keV:  several  of  muons  and i t s  Fermi  with  condensed  4,  into  Mucns  electron  3,  negative  mechanism  energy  keV,  2,  of  about  10~13  Disappearance:  atom  muonic  atomic  between  between  trapped  the  sec.  and  into  c a s c a d e down  atom.  Auger  electrons  the lower  highly  higher  )  are  levels  levels.  The  excited to  the  processes dominant and  ( in  radiative  cascade  time  3  Most  of  the  atom  and  nucleus light  muons  they frcm  either this  elements,  microseconds, muons  to  this  stages  will  the  (FER47) to  the  the  the  Z-law,  so  the  called  However,  the  experiments  (SEN58,  periodicity  of  (ZIN66),  clarifying  incomplete  cf  the  interaction.  In  2.2 muons,  heavy  elements  it  the  third  rate  of  for  takes  and t h e  thus  the  was  by  was  Fermi  the about  fourth  net  capture it  was  been  by  to  which rate  its  Teller  a  subsequent a  metallic the  capture  structure.  progress SCH78),  chemical effect  in  atomic by  that  chemical  (DAN79,  atom  observed  realized  in  according  an  in the  considerable  observed  and  supported  by t h e  process  muons  proposed.  capture  Bai63),  affected  has  for  negative  proportional  Z-law  capture  energy  have of  calculations  while  the  now  be  atomic  and  early  is  weak  by  in  the  s t i l l  detailed remains  (SCH77) . There  kinetic  the  there the  explanation  captured  muonic  positive  "Z-law'1  ECK62,  strongly  though  the  of  of  probability  number. ,  Even  the  was i n v e s t i g a t e d  would  is  In  are  of  approximately  lifetime  capture  ccmpcund  process  via  takes  physics  chemical  oxides  or  orbit  (ns).  atomic  compounds and  IS  be d i s c u s s e d .  The chemical  decay  disappear.,  thesis,  the  orbit  it  80 n a n o s e c o n d s In  reach  muons  believed  been  muons  when  (HAF74)  kinetic that  several attempts  the  captured  suggested  energy energy  is is  by  the  that  s t i l l less  to  the  calculate atom.  Although  capture.occurs  hundreds than  the  of  15 e V  eV, in  it the  4  case of makes  the  it  easier to  structure  scheme  hydrogen  atom  understand  on t h e  capture  I.E  Free  A muon  is  >  +  y  +  +  Because t h i s in  magnetic  acment  momentum  vector.  work,  turns  it  does  are  »• e  +  out  to  twc  + v  te  + v  of  molecular  a pion.  The  decay  their  on t h e  energy  y  +  at  effect  ,  *  y~  hypothesis spectrum  (TI049-1). has  the  The  only  of  for  spin  and  the MSB  the  muon d e c a y s  into  recently  ( W i l l i s et quantum  ,  decay  n  in  t-06  by  the  electrons law  of  been c o n f i r m e d  by  for  Wheeler  interaction  the  al.(WIL80-1))  number  Tiomno and  (1.2) y  simple additive  a  v  with  was c o n f i r m e d  forbidding  Fermi  its  is  + v e  l  Universal  muon  essential for  The  e~ + v  necessitating a v ).  is  thesis.  conserved,  v  namely  inconvenience  this  energy  LAMEF  decay  state,  the  anti-aligned)  this  an  decay  conservation  experiments  (or  (1.1) parity,  y  three-particle  the  the  neutrinos.  e  observation  helicity  Although  and  in  of  energy  +  y~  conserve  aligned  an e l e c t r o n  +  not  a particular  described in  leptcn  product  IT" - H *  experiments  and  effect  kinetic  Decay  decay  ,  decay  produced  This  lower  process.  Muon  the  the  The  is  ir  y  (LE079).  ( for  anti-muons  decay  products  (TI049-2)  which the  instance has  to  and  proposed  coupling  be  a  5  constants are  of  beta  decay,  muon  of  t h e same  order  cf  scheme  can then  be e x p r e s s e d  decay  and n u c l e a r  magnitude.  The weak  by t h e f o l l o w i n g  muon  capture  interaction picture  (Puppi  triangle)  (n,p)  Eeta  Decay  Muon  (e,v )  —  e  Muon  The described  Hamiltonian  by t h e f o l l o w i n g  of  and of  runs  the  weak  1  the s c a l a r ,  (Michel  interaction  + H , C  a polarized  vector,  decay  electron  expressed  spectrum  tensor,  of  (SAC75)  axial  and G i s a c o u p l i n g  (see i n d e t a i l  Hence,  interaction  (1  and t h e asymmetry  muon.  (1.2) i s  '  (1.3) l e a d s to t h e energy  spectrum)  process  four-fermion  pseudo-scalar interactions,  Hamiltonian  of  over  V y  the decay  = /  i  (y, )  Decay  H |I{ViV^/i^i^v where  Capture  The  constant  section IV.A). spectrum term  term  general  the polarized  B(X)  The M(X)  f o r the  formula positive  of  3)  vector,  decay  the  muon  i s  as  d N ( X , P , g ) c x [M (X) * B (X) c o s (g) } X 2 d X  where  '  P i s the  mucn p o l a r i z a t i o n ,  g the  angle  (1.4)  between  the  6  decay  electron In  data  points  figure  curve.  experimental  spectrum (MIC57,  SAC75)  parameter. neutrino values  .  1979  = 2 (X)  and  theories  shown  at  energy  by M i c h e l  (SAC75)  (BAB65)  Thus  of t h e  peak  SAC 7 5 ) .  two-component  The  and Fryberger  respectively..  (FEY68) The  the experiments  experimental are  TEIUMF  are i n  good  prediction,. positive  muons,  the  i s g i v e n fcy  = 2 (X) *{2 z  with  (1.5)  t o be 0 . 7 5 by t h e  the theoretical  the same,as  muon  the  The t h e o r e t i c a l  in units  (KIN57,  ( 1 - X ) +4 6 ( ( 4 / 3 ) 2 - 1 ) }  <5 i s t h e a s y m m e t r y  positive  with  following  has been  the case of p o l a r i z e d  E (X)  spectrum  P i s the s o - c a l l e d Michel  and 0 . 7 6 2 ± 0 . 0 0 8 ,  term  be 0 . 7 5 ,  (SUZ79). muons  along  muon,.  TEIUMF were . p r e s e n t e d  momentum  i s 0.749±0.003.  asymmetry  at  energy  the  £6 ( 1 - X ) +4 p i ( 4 / 3 ) X - 1 ) }  2 .  by B a r d o n  with  and the  of  t o be  and V-A  In  to  in  P i s predicted  found  agreement  where  figure  measured  ( 5 2 . 8 MeV/c)  0.750±0.003 result  This  X i s the electron  momentum  direction  TEIUMF a r e shown  f o r the p o s i t i v e  M(X)  where  at  results  CAP c o n f e r e n c e  and t h e s p i n  1-1, t h e e x p e r i m e n t a l  measured  theoretical  the  momentum  parameter. p  .  At  Again  TEIUMF,  <s i s  the  a 84% beam p o l a r i z a t i o n  (1.6)  predicted  polarized  was s t o p p e d  in a  1.0  MOMENTUM(ny2) Figure I - l , Energy spectrum of positrons from positive muon decay. shows the positron momentum i n units of (muon mass)/2.  8  carbon  target  measured.  This  asymmetry titanium  and t h e is  muon a s y m m e t r y , well the  with  In is  electrons  figure  asymmetry along  1-2  muons  in  data  a n a l y s i s of  <S i s e g u a l  to  0 . 753 + 0 . 0 0 5 .  finding  of  with  a carbon  From t h e  was the  and  the  a  positive  This  agrees  0.752±0.Q08 and a l s o  not  usual counter  measured. of  the  The  experiment,  angular  the  electron  distribution  of  form  d N ( P , g ) <=>< { 1 + A P c o s (g)} dq  where  A is  is  an  equation for  of  a magnetic  the  the  asymmetry the  field.  e l e c t r o n momentum  and  muon  (1.7)  P the  muon p o l a r i z a t i o n .  p r e c e s s i o n under  Ihe  integration  (X)  between  of  0 and  the  P= 1 ( n a m e l y  I.C  The  equation  muon i n  the  probability  100% beam  bound  1 gives  frcm  Muon  polarization).  Decav.  muon d e c a y h a s a a free  K o r b i t of than  for  (1.6)  ( 1. 8)  Bound  characteristics  This  influence  A = 1/3 when  with  value. the  is  dependent  negative  Fryberger's  predicted  energy  shown i n  s p e c t r a of target.  energy  a free  the  muon  few  decay.  muonic atom  muon d u e  to  the  different First,  a  has a l o w e r  negative decay  reduced phase  space.  9  1.0r  1  i  r  i  1  1  1  1  1  r  /I  inC  If  /  0.5 >-  jj~  •Q15 / r in Ti •0.10 •005  hLU  • /  o  /  0  4  I  i  *  in C  •0.0  <  o o  o, ^  T h e o r e t ical  Asy m metry  -0.3  0.0  J  L  I  I  I  I  0.5  L  1.0  MOMENTUM(ny2) Figure 1-2, Energy dependent asymmetry f o r positive and negative muon decay i n carbon. Also the asymmetry of negative muons i n titanium i s shown.  10  The  decay  rate  Ed(+)  The  energy  free  MeV  positive  <x (mucn mass)  mucn i s  5  o f t h e bound muon i s e q u a l t o t h e e n e r g y  muon  orbit  of t h e f r e e  (105.6 MeV) minus t h e b i n d i n g  o f t h e muonic atom  which  energy  of the K  reaches a value  of about  12  i n uranium. . That i s  Ed (-) <=< (muon m a s s - b i n d i n g  This  of the  corresponds t o the reduction  accessible motion  t o t h e decay  energy)  o f t h e phase  products.  c f t h e bound muon i n t h e K o r b i t , t h e d e c a y  a D o p p l e r e f f e c t and t h e maximum e n e r g y  the  cut-off  energy  (=52.8 MeV) o f decay  muons.. Hence, t h e e n e r g y stretches  spectrum  t o the high-energy  probability  and t h e d e c a y  side.  electron  affected  by t h e n u c l e a r coulomb  spectrum  i s shifted into  number o f t h e t a r g e t In  TEIUMF  nucleus  Thirdly,  (SUZ79),  energy  muon  free  decay  t h e decay  spectrum a r e  side  as the atomic  increase.  copper,  there  decay  electron  and l e a d . . B e f o r e t h e  had been two e x p e r i m e n t s  e t a l . (CUL61) f o r an i r o n  f o r a copper t a r g e t .  from  than  The peak of t h e  f i g u r e 1-3, t h e r e a r e f o u r  measurement  electrons  energy  electron  i s greater  o f t h e bound  field.  t h e lower  from c a r b o n , t i t a n i u m ,  by C u l l i g a n (BEI68)  space  S e c o n d l y , due t o t h e  has  spectra  5  target  and B e i l i n  The TEIUMF e x p e r i m e n t  was t h e  11  first  attempt  spectrum effects energy with  to demonstrate  the v a r i a t i o n of  f o r the various n u c l e i . above  Huff's  theory  shown i n f i g u r e theoretical  TEIUMF  (HUF6 1 ) .  1-4.  curve  at  in the figure.  have  shown g o o d  The  agreement  His t h e o r e t i c a l curves are  As d i s c u s s e d  must  energy  The s e c o n d a n d t h i r d  are c l e a r l y demonstrated  spectra obtained  the  take  into  in section I.B,  account  the  the  detector  resolution  and energy  loss  i n the electron counters i n  to  the theory  with  the experiment.  compare  reported muon  that  decay  the theory  spectra In  i s i n gocd agreement  the experiment  e l e c t r o n s are d i f f e r e n t elements,  electrons in  to high  must  the atomic capture  of  heavy  i t  of  compound,  the  like  energy  the l i g h t e r element.  electrons  frcm  compound  target  with  already the  bound  ratio  in a  (SUZ79).  chemical decay  We h a v e  order  t h e heavy  be n o t e d  lead,  that  for  the energy  different  the r a t i o  of  the loss  element  i s larger than  In  than  the  of low energy  constituent  that  nuclei.  low energy  electrons i s greater Thus,  spectra  ratio decay  i n the chemical  frcm the l i g h t  element  constituent. a negative the  c a s c a d e i n t h e muo.nic a t o m .  (SUZ79)  i s the f i r s t  dependence 1-2, are  muon l o s e s  of  t h e asymmetry  two asymmetry shown.  asymmetry  attempt  polarization quickly I h e TEIUMF  spectra f o r carbon  muons..  done  f o r an i r o n  energy In  and t i t a n i u m  The c a l c u l a t i o n o f t h e e n e r g y h a s been  experiment  at measuring the of negative  target  during  figure targets  dependent 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 muons in carbon, titanium, copper, and lead.  F i g u r e 1-4,  T h e o r e t i c a l s p e c t r a of decay e l e c t r o n s from n e g a t i v e muons i n l e a d , antimony and i r o n (HUF61)  14  Mathews  (GIL60).  asymmetry  at  the  The spinless  n u c l e i has  behavior  energy by  cf  negative  I.A.  During  to  is  excited their  rest,  atom.  cf  and  During 50% c f  carbon,  15%.  (MAN6 1 ) . .  muons the  Furthermore, the  lose  When of  the  undergo  mucn a n d  depolarization.  about  ground the  the  they 1/3  muonic  is  shown  Due  cf  occurs  the  of  via  the  orbits,  nuclear  nucleus  spins the with  the  Auger  the  muons  estimated  to  be  If  is  the  in  good  nucleus  between  the the  cascade. .  hyperfine  produces  case about  interaction, the  lower  muonic  the  below.  of  initial  in  this  this  into  Thus,  during  state,  in  processes i n  interaction to  energy  l o s e most  residual polarization as  in  high  kinetic  trapped  state  polarization.  Consequently, in  from  many t r a n s i t i o n s  a spin-spin  ground  are  and r a d i a t i v e  the  depolarization  their  The  depolarization  muons  enly  nucleus.  the  the  polarization  is  of  for  discussed  process  muonic a t o m ,  reach the  of  has been  down  most  but  the  experiments  at  matter  slewing  remaining  host  muons  in  cascade i n  there  the  additional  negative  Mann a n d R o s e  final  with  and  between  and  orbits  estimate  a spin,  muons  the the  This  agreement has  by  muons  the  zero. .  analyzed  retainig  finally  to  theoretically  electrons  higher  down  been  states  Then t h e  orbits,  drops  muons  muons  polarization,  in  end  the  negative  negligible.  processes  lose  the  with  bound  value.  energy  that  of  (SHM59)  collisions  stage  high  calculation predicts  residual polarization  Scmushkevich  section  Their  a  coupling strong  residual polarization  of  a spin i s  be  expected  to  15  much of  s m a l l e r than  1 9  F  4±45fc  (1=1/2),  carbon  the residual polarization  residual polarizations  and t i t a n i u m  a r e 20±3%  TEIUMF e x p e r i m e n t  been the  i n the spinless nucleus.  In the case  i s reported  t o be  (AST61) . The  the  that  investigated total  findings  were  titanium,  the  TEIUMF  for  this  energy. better  time  well.  result  spectrum This  e t a l . (DZH72),  from have  who m e a s u r e d  by e g u a t i o n  the case  However,  (1.7).  cf carbon,  i n the case  by a f a c t o r  In the case large will  errors  -which a r e r e l a t e d  of  Their  both  of  2.  titanium, The r e a s o n  of t i t a n i u m ,  the  e s p e c i a l l y at low  be r e p e a t e d  muon beam i n o r d e r  at  to reduce  to the R.F.  TEIUMF  with  a  the accidental period i n the  spectrum.  Muon C a p t u r e  Conversi positive  the lifetime  hand,  Nuclei  measured  mucns i n c a r b o n  of negative  cf positive decay  in  e t a l . (CCN47)  and negative  same a s t h a t other  shows  measurement  quality  In  i s smaller  i s not c e r t a i n .  I.D  that  polarizations  in  1 9 . 4 ± 1 . \% a n d 1 5 . 5 ± 1 . S % f o r c a r b o n a n d  agree  coincidences  These  expressed  respectively.  experiments  asymmetry  (SUZ79).  (A)  muons  a n d 7±3%, r e s p e c t i v e l y ,  by D z h u r a e v  asymmetry  of negative  muons  electrons  muons  the lifetime  and i r o n .  i n carbon  They  the negative  found  was a l m o s t  (2.2 microseconds) •  from  of  muons  the  On t h e in  iron  16  were  not  detected  after  one  that  the  negative  mucns  were  within  a  studied rate  microsecond.  been  the  then,  delay.  by  the  the  for  basic  process  p —>  n •  most of  This  iron  proved  nucleus  muon c a p t u r e  and t h e o r e t i c a l l y  determined  The  captured  Since  experimentally  has  microsecond  and t h e  has  been  capture  nuclei.  muon  capture  in  a nucleus  is  reaction: +  y~  which  in  the  case  (a,z)  cf  v  bound —>  • y~  (1.9) y  protons (&,Z-1)  in •  a nucleus  becomes: (1,10)  v  y  This  reaction  leads  to  resonance  states  de-excite  with  The  theoretical  first  capture  rate  expressed  the  in  the  at  nuclear  about  20  emission  the  exited  MeV of  nucleus  capture  rate  Rc(Z,A) = constant*  excitation)  one  approach  to  was  states  or  more  (mainly which  made  by  then  neutrons  c a l c u l a t e the  giant  (K&P58).  total  Wheeler  (WHE49).  He  by  E |¥(at each proton) | all protons  (1.11)  2  2 where  ¥  is  proportional  the to  muon Z3,  wave f u n c t i o n . so  Be (Z,A)  In  this  orbit the  is  part  eguation  the  is  |y|  that (Zeff) *  Z  i n s i d e the of  Now,  is  (1.  r e p l a c e d by  nucleus  for  wave f u n c t i o n  Zeff,  heavier  which  is  because  the  n u c l e i and inside  the  muonic  12)  K  therefore nucleus  is  17  modified is  because  i t sees  approximately  overestimates  for light  elements,  rate  f o r heavy  elements.  the  a neutron  principle. calculate excited heen the  He e m p l o y e d  mucn c a p t u r e  disappearance the  decay  Bt  where  Q (Z)  account atom heavy  cf  will  rate  rate,  Bt,  to  formula to  has  overcome  formula  for  the  more  was made  by  Sens e t  lifetime of  which  systematically  of  negative  the l i f e t i m e  i s composed rate,  of Be,  factor  muons  i s the two  rate  i s reduced  utilizing  l i f e t i m e s of  which  total  components,  ie  discussed earlier  and so t h e decay  taken  -59)  (1.13)  the negative  Bd i s  the  a l . (SEN57,  = B e + Q (Z) « E d  nuclei).  to  accessible  be d i s c u s s e d i n  that  total  i n order  (G0U74)  study  Rd, and the capture  i s the Huff  muon  which  Pauli  a l l  This  the Primakoff  the factor  positive the  nucleus.  experiment  The i n v e r s e  rate,  the  for  law  i t  approximation  elements  theories  the apparent  i n matter.  from  and P r i m a k o f f from  but  (Zeff)*  V.  first  determined  stop  These  i n Chapter The  total  deviation  elements.  matrix  The  a simple formula  originating  the daughter  by G o u l a r d  systematic  detail  who  of  derived  a closure  the t r a n s i t i o n  improved  heavy  (PEI59)  excess term  states  charge.  valid  Primakoff has  a reduced  to  t h e CPT  muon  which  i s bound  (by u p t o  which  i n the  20% f o r  b e t h e same a s t h a t theorem  takes  for  implies  the that  p a r t i c l e s and a n t i - p a r t i c l e s a r e  18  identical. elements linear  from  their  and  measurements  by  the  original  error  numbers,  can  have  a small  for  light  measurements  the  transion  Primakoff matrix  by the  this  a factor general  result  with  a  Fcldy model,  capture  in  nuclei.  of  rate  in  of  of  this for  i s the  the  past  thesis. the  outside 1963  have  to  the 2197.13  ±  of  muon  decay  rate  c a l c u l a t e d decay  rate,  positive  We t h e r e f o r e approached  The  GOU71,  believe that  with  some  theoretical direct  model  transitions  can  developments  be  instead  is  Total  than  the  used t o of  a l l  caution..  c a l c u l a t i o n of  DUP75).  usually higher The  formula.  difference  i n the the  Most  value  in  and  findings  micrcscopic picture  (LUY63,  3.  IV-2  2 ns  been s e v e r a l  with the  trend  ±  the  improved  past  accepted  29  measurements  with  Table  showed rates  a l . (ECK66).  2203  theory.  2 cr  of  the  in  Primakcff  muon h a s c h a n g e d  change  model a r e  of  et  the  s h o u l d be  have  model c a l c u l a t i o n by  the  the  performed  (from  As  There  rates  years,  capture  by  of  a l . (SEN59)  (Z=92)  number  values  a marked e f f e c t  especially  since  a large  positive  ns t o d a y ) .  two  predicted  been  et  uranium  be l i s t e d . i n  bars  Sens  reduced  Eckhause  intervening of  early  as  of  to  the  averaged  will  lifetime  0.08  between  n u c l e i have  summarized  the  (Z=6)  experiment,  instruments  In  carbon  excess term,  different  been  measurements  relation  neutron After  The  the  the  shell  muon  capture  experiments understand  comparing  the  experiment. and  Walecka  which c a l c u l a t e s the  (FOL64) giant  developed  dipole  a  resonance  resonance  (GDR)  19  excitation  induced  experimental manipulate section. nuclei, are  for  1 6  *He,  applied 0 and  were  result  fcr  6  higher  well  Li  in  6  and  their  and  Jonker.  7  L i  were  experiment  nuclei  It  also  total  energy  capture  and o b t a i n e d  Bc(E')  <=><  for  by  remeasured well  for  later  their  value  and  et  of  was  the  the r e s u l t s  that  Li  6  Their  value  Recently  the  and Jonker  rate  by B a r d i n  with  rates  10% a n d  rate,  Lodder  l i their  7  value.  the follwing  (E»)+  good  and i n c l u d i n g  the experimental  i n terms  P*  C  capture  capture  a l . (BAB78) of  Lodder  our measurements  in  calculation.  e t a l . (CHE73)  rate  l 2  to the capture  muon  than  be shown  support  was i n  s e m i - e m p i r i c a l method.  agreed  will  transitions  the experiments  experiment.  whereas  Christillin the  (WAL75)  was s m a l l e r  and  magic  the theory  to  to  cross  the allowed  t h e model  with  reactions  the doubly  *He,  than  to the experimental Li  an  The c a l c u l a t e d c a p t u r e  the t o t a l  e t a l . (ECK63)  comparable  these  agreed  to  i n which  the Foldy-Walecka  Eckhause  rates  >Ca,  model  Applying  investigated  with  this  contribution  used  o f the mucn c a p t u r e  the experiment.  respectively. allowed  4(  They  the photc-nuclear  In the case of  0 and * ° C a  (LOD67) Li  1 6  with  calculation  7  section of  the d i p o l e . p a r t  suppressed.  25%, the  cross  They  agreement  i n muon c a p t u r e .  of  have  attempted  a mean n u c l e a r  simple . r e l a t i o n  (Zeff)*(H  1 C2P2  )  to  give  excitation  20  where  P i s the neutrino  energy E'  and C a c o n s t a n t .  agreed  with  other  hand,  while  t h e GDE  (CAN74).  E'  In  increased to energy  i s expected  photo-excitaticn  muon  capture  in  photo-excitaticn calculations  neutrino neutron  and  i n muon  that to  MeV.  capture,  the  the  energy  for  for  i s c l e a r from  their  i s suppressed i n the  no e x p e r i m e n t s  excitation  from  13 MeV  c a l c u l a t i o n s by  It  excitation  On t h e  a n d t h e GDR of  28 MeV w h e r e a s 17  that  elements,  excitation  to  i n muon c a p t u r e  i s unfortunately  spectrum  the decay  because  i m p o s s i b l e and t h e of the n u c l e u s  gives  information. Bernabeu  uncertainty  rates.  is  level  spectroscopy  ambiguous  the  Ni  T h e r e .have b e e n  t h e T+1  energy  than  the average  t h e 1+1  photo-excitation. investigate  6 4  nuclei.  i s only  are excited  According  i t i s only  that  occurring  t o be l a r g e r  e t a l . (NAL74),  excitation  calculation indicated  excitation  (Tz=T+1)  (CHR75).  t h e mean  4 5 MeV i n t h e h e a v y  t h e GBB p r o c e s s  energy  E•  i n the l i g h t  i n photo  isospin levels  Nalcioglu  Their  t h e GDR e n e r g y  higher  the  momentum,  of  (BER73)  the neutrino  Khoyama a n d F u j i i  calculated the t o t a l  method.  They  performed  elements  frcm  Z= 11  reproduced  has proposed  to  (KOH76, capture  an i m p o r t a n t  -7S) rates  which  avoids  i n the t o t a l  capture  adopted  model  this  using the  statistical  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  Z=92 a n d t h e i r  the experimental Before  energy  a model  completing  predicted  capture  data  within  this  s e c t i o n we s h o u l d  c o m p l i c a t i o n which  confuses  rates  15%. . discuss  the.comparison  of  21  experiment in  the  1S  resulting states.  with  theory.  crbit  has i t s  in For  proton,  the  predicted  x=1.2  state and,  (MUK77).  The  CEBN-Bolcgna They  muonic of  process rapid to  the  liquid  conversion  time  the  82 n s  muon  is  Experimentally Bc+<100  is  state,  is  in  1.2  a pyp  given  3/4>«Bc~ +  It  has  (Bc+)  a  been  from  the  interaction Bc~=635  /sec by  the  Bc~=651±57 / s e c . (8  the  atm,  293  a statistical  there  is  triplet  300  the  microseconds at  0.5  capture  m o l e c u l e and  in  the  the state  atm a  capture  1/4«Ec+  460±20 / s e c  (EAE80)  a complex  n u c l e u s has  a non-zero  probability  of  by  Bc(CM)=  capture  a  mixture  K,  For  as  scattering  frcm the gas at  K)  muon-proton  hydrogen,  (MAT71).  by  mutual  was m e a s u r e d  Through the and  (hf)  which  shows  that  /sec. If  the  =  in  hydrogen  8 atm  bound  Be ( o r t h o m o l e c u l e ) Bc(OM)  (I),  at  V-xA  rate  muonic atoms For  and  for  rate  hydrogen  formed  m u c n i c atom  state.  on t h e  capture  hydrogen,  states.  spin  muon i s c a p t u r e d  particles.  capture  pure  the  two  singlet  gaseous  nuclear  hyperfine  the  who o b t a i n e d  initially  and s i n g l e t  singlet  pressure  rate  are  between  calculated  (AIB69)  muon  termed  1/sec  F=0  the  the  depends  the  to  state  ultrapure  c c n v e r s i c n of  the  the  a system of  atoms  triplet  that  i s egual  from  the  a spin,  coupled to  a negative  s p i n s of  group  In  spin  probability  singlet  employed  target.  the  when  theoretically  triplet  with  example,  of  cwn  a nucleus with  possible states  capture  orientation  F=1  two  For  of  a negative  nuclear  muon  in  the  spin  22  nucleus and  also  depends  F~=I-1/2o  effect  Bernstein  f o r a model  external higher  proton  hf s t a t e  fact,  a fast  Auger  electrons  transition  b.y  Winston rate  without  w h i c h i s more  (WIN63)  i s so fast  the lowest  will  be l i s t e d  from  twc hf s t a t e s .  determine fast  that  energy  limited  t h e muons  state.  i n Table  the conversion  only  conversion  small  i t i s much h a r d e r  detecting  decay  gamma  rays  fluorine  has  ( see s e c t i o n I I I . G  are the rates  therefore been  readily  experiment. method  determines employed  only  The s t a n d a r d  (MSB),  for  method  ).  of than  calculated  captured  the capture  rates  measurements  FAV70)..  Because  determination the effect  i n t h e decay  F  to  of  i s  of the hf  electron  the rate  by  neutrons  or  f o r c h l o r i n e and r a t e s and  So f a r , t h e c o n v e r s i o n 1 9  (Z>10)  nuclei  several  Only  the  for various  by d e t e c t i n g  method  which measures  the relaxation  this  were  comparable t o capture  observable.  determined  with  to determine  electrons than  i s , in  faster  are normally  Since  (<0.01)  spectrum,  rates  (WIN63,  nuclei.  from t h e  f o r heavy e l e m e n t s  the experimental  for light  i s very  100 t i m e s  have been  rates  a n d an  the ejection  The r a t e  IV-6 along  There  conversion,  that  this  But t h e r e  through  conversion  who s h o w e d  from  the  These  core  a conversion  than  F+=I+1/2  calculated  hf s t a t e .  (TEL59)  momenta  a spinless  allowing  to the lower  rate.  angular  et al.(BER58)  c o n s i s t i n g of  conversion  Ml  the  on the t o t a l  b y a muon  rate  capture  i s t h e muon  spin  resonance  t h e p r e c e s s i o n damping and  rate.  to obtain  Bavart  e t a l . (FAV70)  the conversion  rates  for  6  L i ,  23  7  Li,  9  Be,  1 0  B  and  These  " B .  results  are  listed in  Table  IV-6.  The  present  experiment  to  nuclei  muon a t o m i c  The  and  The  Chapter are  determine  experimental  II.  data IV,  theoretical rate,  and  theories  in  experiment  a detailed  mean  and  is  muon  ratios  method  lifetimes in in  are  discussed in  d e s c r i p t i o n of  metallic  Chapter  results  and n u c l e a r  detail.  Chapter  V deals  of  made.  In  the of  atomic the  Chapter  presented.  and  with  nuclear  experimental VI,  the  oxides.  III.  ,  capture  Chapter In rates  the muon  results  summary  an  complex  described in  lifetime  aspects  is  the  set-ups  a comparison is  is  capture  analysis  the  reported  work  of  capture with  this  the  24  CHAPTER Experimental  In method  used  discuss  this  in this  will In  employed  muons  channel  II-2, by  a  Decay  electron  as a stop stop  computer  signal.  s i g n a l s was s t o r e d  of  were  mucns  used  of the h i s t o g r a m .  was c a l i b r a t e d  counter I I - 1 and  signal for a  detected  by  to the clock  between  the s t a r t  i n the histogram  was o b t a i n e d data  and  by a PDP-11/40  f o r MSR e x p e r i m e n t s  This  four  t o p (5,8) and  s i g n a l was s e n t  i n a histogram  i n a target  by a  at  and t h e  chi-squared  analysis will  be  III.  When t h e d a t a system  were  right (5,7),  2000 c h a n n e l s  i n Chapter  a start  difference  which i s e x t e n s i v e l y  minimization discussed  The t i m e  muon  s i g n a l w h i c h was d e f i n e d  t h e muons  l e f t (5,6),  and t h e  in figures  muon  of t h e  sections.  by t h e s t e p p e d  a r e shown  and t h e e l e c t r o n  TEIUMF.. . T h e r e lifetime  provided  from  we s h a l l  m e a s u r e m e n t s we  c o i n c i d e n c e produced  telescopes:  bottom (5,S),  lifetime  A stopped  electrons  experimental  and d e t a i l e d f e a t u r e s  T h e beam l i n e  experiment  (1,2,3,4,J5)  clock.,  the  were  respectively.  section  i n the following  (M20) a t T E I U M F . of t h i s  describe the  In the f i r s t  s e r i e s of  which  and Set-up  we s h a l l  procedure  be g i v e n  this  Method  work.  the general  equipment  set-up  chapter  II  taking  was s t a r t e d ,  by m e a s u r i n g  lifetime  w h i c h i s knewn  positive  muon  precisely  lifetime.was  the  the positive (BRI78).  obtained  after  detection muon  When t h e c o r r e c t several  runs,  the  25  positive  muon  changing  the  polarity  Then,  the  beginning  at  beam  was s w i t c h e d of  magnets  of  the  lifetime  This  was  used  at  least,  once  a day,  was  measured  in  the  two  experiment  second  week week  reproduced  frcm the  established different  performed  on  Throughout  these  micro-amperes production  15  shown and a  strip,  have  target  a low was  in  to  carbon  lifetime, in  During  7/10,  system,  lifetimes  and,  system.,  3/10  the  made.  which  was more  than  80  BeamLine  cf  T2,  measurements  electron  the  The  which  section.. high  of  muon c h a n n e l  10 cm l o n g  a relatively  frcm  was  system  lifetime  by  measured.  500 M e V .  mm i n c r o s s  the  beam  line..  i n carbon  detection  muon  muon  experiments,  target,  lifetime  1979),  positive  stopped  at  muon  week  28/10  negative  series the  M20 beam  muon  the  (first to  were  Muon  The  by  the  targets  II. A  beryllium  21/10  check  muon  the  measurement  negative  to  correct  and  cf  negative  as a c a l i b r a t i o n of the  order  the  negative  measurements, lifetime  to  muon (M20)  proton  prcton  the  beam  Since  beam  a  rate  contamination for  i n the  this  was  20  a  pion  water  cooled  direction,  for  was  TEIUMF.  struck  beryllium  production  specially selected  at  current  c o n s i s t e d of in  lifetimes  and  targets negative pion  lifetime  5 mm  have pions  beam,  such  26  Figure I I - l ,  The M20 beam l i n e .  27  experiment. The a s e r i e s cf set  with  guadrupole  two  different  bending  modes  conventional modes,  and  muon  cloud  pions For  between  selected  the  same  called  momentum  than  from  decay  target. come  As  to  very  is thin  magnet 170  muons for  MeV/c  BI  are  between  B1  and B 2 , The  pion  of  beam.  pions  they  at  rest  do n o t  from  muons  the  pions  have  29 M e V / c  B1.  the  are into  the  direction  larger are  surface  are  (smaller)  produced of  the  T2  c n n u c l e i when  muons  and  The  energy  )  of  a  undergo  decay  muons  a  magnet  with  p i o n beam  on t h e  cloud  muons  which  which  as  bending  and t h e  muons o n l y .  ( 4 MeV,  two  follows.  defined  allowed to  into  only  are  absorbed  decay  hand,  for  Surface  pions are  positive  low  muons  three  were a v a i l a b l e  the  the  was  cloud,  first  of  with  so t h i s of  and so t h e y  they mode  surface  stop  in  targets. In  These  the  were  other  a decay  by  negative  very  by  a fraction  (backward)  possible for  muons  mcdes  and  magnet.  There  the  modes,  set  the  rest,  On  beam  and the.momentum  muon b e a m :  d i r e c t i o n as(to)  forward  the  muons  B2  (opposite)  (Q1-Q9)  three  target  focused the  (B1,E2).  produced  T2  line  modes.  The  momentum  by t h e  magnets  conventional  are  decay  magnets  surface  conventional  in-flight  team  a positive  team.  muons  particular  is  for  c l o u d and  negative The  M20 s e c o n d a r y  this were  the for  experiment, s e l e c t e d by  backward the  first  muon  backward setting  the  momentum.  bending  muons  magnet  were  seccnd Since  employed..  bending  a momentum  was f i x e d ,  the  of  28  expected chosen  backward  for  muon  the f o l l o w i n g  electron  contamination  compared  with  associated are  degraders  The muon was  protons,  thin,  easily  spectrum  beam i s s h o w n  in  figure  II-3.  with  the  contamination  Although  muons  pulse height  i n the  remove  the  diameter  beam  very  lead  defined  to  a CH2 d e g r a d e r reduce  (TOF)  by a  (1,2,3)  a 20 m i c r o - a m p e r e  Thirdly,  muons using  negative  Since t h i s  TOF  spectrum  counter than  beam t h e r e  S2,  the  of  the  that were  mostly  2 . 5 cm i n t h i c k n e s s was  the energy  of the  muons  and to  W i t h a 2 . 5 cm  c o i n c i d e n c e was n e a r l y current  i n the  which  the incoming negative  proton  pions  the  few p i o n s i n t h e beam.  collimator,  background  of  r e j e c t i o n of  muon  the  advantage.  was much l o w e r  i n the backward  and e l e c t r o n s ,  placed  (<2%)  low  (8%)  i n the t a r g e t s  an i m p o r t a n t  flight  taken  beam  a n d gammas  the background.  stopped  mode was  had very  are absorbed  of  beam.  for  were  muon  This  When t h e n e g a t i v e  the pions  neutrons,  it  Secondly,  time  electron  rate  (>80%).  s i g n i f i c a n t l y to  which  First,  was r e d u c e d .  were  MeV/c.  i n the negative  i n a degrader,  l e w momentum  was 87  reasons.  modes  pious  producing  contribute with  other  with  stopped  nucleus  momentum  o n t h e T2  muon  beam  1000/sec target.  29  Concrete • Wall  M20 i  Bedim Variable C H 2 D e g r a d e r  wmnm^imnim V////////A  S1 L e a d  Shielding  &  \ V////////A  Collimator  S 7  (Right )  S6(Left)  M i l M e t a l Shielding —  S 4  Decay E l e c t r o n Counters  s s  a  (Top)  S 9 ( Bottom)  F i g u r e I I - 2 , E x p e r i m e n t a l set-up and decay e l e c t r o n  counters.  30  140 x 1 0i  r  i  r  yu Peak  100  X 102  e Peak 50  Without S 4 Veto  -40  O u  .  0  0  _!_L  • •..  • •. •  i•  10 20 30 40 CHANNEL NUMBERS  F i g u r e I I - 3 , Time of f l i g h t signals.  W i t h S4 Veto  50  spectrum of i n c i d e n t beam and-stopped muon  31  II.B  S c i n t i l l a t i o n Counters  In dimensions counters Nuclear Since  experiment,  and e f f i c i e n c i e s  were  made c f  Enterprises  a l l  much c a r e S1:  this  was t a k e n  Counter  S1  in  are  and  in  were  Table  scintillator  viewed  was s u p p l i e d their  Geometry  counters  given  a plastic  Ltd.)  information  nine  and  by  from  d e s i g n and  was  big enough  to  was  made t h i c k e r  RCA  II-1.  8575  use.  made  by  phototubes.. counters,  In  the  whose These  (NE110  plastic  cover  used  particular:  beam  collimator. S2:  Counter  S2  electrons, pulse  height  higher had  little  energy  pulse heights  heights.  The  muons  ranged from  e l e c t r o n s from  Slow  than  loss  order  muons and  analysis.  pulse  for  slow  pulse height  and t h e  the  were  by  and d o u b l e  muons  showed  30 t o  muons.  plastic  lower  t y p i c a l pulse  250 t o  height  mV.  a slow  muon  which stopped  variable  in  for  ordinary  pulse  height  S2 a n d t h e  event  was p l a c e d i n f r o n t  lead collimator in  order  to  e l e c t r o n t e l e s c o p e s so t h a t  did  contribute  as a carbon background  S3  defining  was t h e  counter  of  avoid  to  Counter  height  a double  visible not  muon's  A pulse  600 mV w a s c o n s i d e r e d a s  S2  scintillator  6 0 0 mV a n d t h e 150  Electrons  than the  than  Counter  distinguish muons  ordinary  in  to  double  larger  rejected.  S3:  muons,  in  of  or  was the  i t  this  muon  being  counter  source..  muons a n d  was  32  visible  to  the  mucns s t o p p e d as  good  events  in  thickness  S4:  the  and t h i s  histogram.  the  counter  plastic  S3,  In S3  S4  was  came t h r o u g h  the  these  order to  negative  were  counted background  minimize  was made o f  scintillator  b i g enough  When  caused carbon  cm t h i c k n e s s a l u m i n u m  Counter which  inside counter  mucn e v e n t s  background,  0.001  electron telescopes.  0.07  the  cm  and c o v e r e d  with  only  foil.  to  cover  target  any  particles  a n d was u s e d a s a  veto  counter. S5:  Counter  S5 h a d  thickness was  wall,  used i n  also  it  was  scattered towards  a cylindrical 20 cm l o n g  a l l four a veto  counter  electron  cylindrical  counter  between  electron  S6-S9:  the  Counters  shape  (see  imbalance were  S6,  S7,  20 cm i n  used to  the  telescopes. S 5 was t o  The  t e l e s c o p e s and t o  S8 and  £9 w e r e  made  i n the  electron  telescopes.  shown  in figure  angle  for  new  phototubes  The  configuration  II-2.  a point  cylindrical  source at  counter  the  This  to  to  of  set-up the  any  of  these had  center  identical any they  same  counter  counters  60 % s o l i d of  the  S5.  tvwo week  experiment,  there  a  counters.  Also, the  using  imbalance  save  avcid  get  off  i d e a of  minimize  order  efficiencies.  It  the  beam w h i c h s e t  II-l) in  by  diameter. .  reject  Table  viewed  During  and  0 . 3 cm  electron telescope coincidences,  p a r t i c l e s from  the  shape w i t h  was  a  is  33  Table  Symbol  II-1  Counter  Geometry  (Name)  Size  S1 S2(thick  counter)  S3 ( d e f i n i n g S4 ( v e t o  counter)  counter)  S5(cylindrical S6(left  E  counter)  S7 ( r i g h t  E  S8 ( t o p  counter)  E  S9 ( B o t t o m  1)  counter)  The  counter)  E  Counter)  counter  source.  efficiency  and  Efficiency  ( cm)  Efficiency  10x 1 0 x 0 . 6  99,9 %  6. 4 (dia) x1. 2  99.9  5 . 0 ( d i a ) x O . 07  99.6  30x45x1. 2  99.9  20 ( d i a )  99.8  x0.3  20x20x0.6  99.9  20x20x0.6  99.9  20x20x0.6  99.9  20X20X0.6  99.9  test  was made by  using  1  a Ru  electron  34  possibility  cf  drifting  the  of  coincidences and  printed  out  the  which  was  flux  In  to  cylinders With  position field, and four  the  cf  beam  reduce  the  magnetic  used i n s i d e  correct  the  electron  as  line  was  telescopes.  of  field with  the at  the  only  of  1  Gauss),  leakage the  of  target.  Mu  metal  counter  the  S5..  target  small muon by  a  precessed  (about  thin  this  affected  will  run.  muon  near  two  scalers  Collimator  as the  field.,  achieved  This  the  magnets  Even  muons  and  important  visual  every  field  well  magnetic  on  of  measurement  and o u t s i d e  0.05G..  lifetime  Field  magnetic  earth  p r e c e s s i o n of  of  of  lifetime  the  cylinders,  end  including  rates  monitored  polarization, the  the  failures  counting  the  from  was down t c  the  the  because  were  these  at  Shielding  a high  by  so  were  a record  case of  created  magnetic order  as  with  target  electronics  rejections  the  muon  or  voltage,  Mu M e t a l  Fcr  in  high  and  II.C  positive  counter  magnetic lifetime  averaging  be d i s c u s s e d i n  the  section  III-E. The in  diameter.  collimator between cm d = 2 . 5  M20 In  14  order  cm i n  counters cm)  beam l i n e  was  S1  to  collimate  length and  placed  formed  S2,  and and  between  3.8  a broad the cm i n  another counters  beam  beam,  a  spot  10  lead  diameter  was  used  lead collimater S2  and  cm  S3.  (L=7  35  II.D  Targets  In and  this  9 pcwder  with  targets  targets  targets Table  UVIC  of  mixed  II-2.  groups:  UBC  group  standard varied  of  the  beam  the  density  size  of  were  thickness.  expensive  or  from to  chosen.  mucns i n  and  ( s m a l l Z)  long  a chi-squared Since in  the  that get  in  of  the  group, a  the  the  in a  material  simple  electron  components  chosen  When i t  a combination  a decay  cover (metal)  was  i n the  target.  a target  to  s h e e t s 0.00 3  container  lifetime  was  substance  of  small  spectrum  short  were  lead  diameter,  plastic  such a c h e m i c a l compound, lifetime  of  enough  (stainless)  which had For  Warren's  Since the  large  in  five  material..  ends  muon  from  cm i n  2  listed  thickness  was  mylar  is  were  the  was 2.5  material of  difficult  were  both  a negative  negative  target  at  c h e m i c a l compounds Z  beam  together  diameter  cm a n d  target  targets  The  Dr  metal,  27  there  borrowed  group,  group.  the  also,  information  were  w a s 9.5  thin  The  different  large  MSE  the  made o f  target  Johson's  of  s p o t . . Windows  was q u i t e  by  Dr  3 liquid,  a s i n g l e element  targets  container  so t h a t  and  the  Tokyo  carefully  form,  All  which d e f i n e d  standard  cm i n  Half  the  the  container  Agar.  Chemistry,  with  were  c h e m i c a l compounds.  29  target  there  composed of  in  and  collimator  experiment,  easily  Z  of  (large  Z)  separated  minimization. the  i 0 target 8  same f o r m  was  was  used  in  made  in  order  Agar to  form,  compare  a the  1  6  0  36  Table  11-2(1)  List  of Targets  and Their  Form  z  Element (Isotope Ratio)  Form  Container Material  Size(cm)1  Owner2  3  Li-6 Li-7  Powder Powder Plate Powder Powder Plate Powder Liquid Water Agar Agar Powder Plate Powder Powder Red Rod Plate Granular Powder Powder Liquid Stick Granular Plate Disk Granular Powder Plate Stick Plate Plate Powder Powder Powder Plate Plate Plate Plate Plate Plate Plate  SS SS Ni p l a t e d Brass Brass  7. 2Dx9. 5 7. 2Dx9. 5 13x13x0.7 6Dx1. 3 6Dx1. 3 10x10x2 2. 5Dx5 7.5DX15 9 . 5Dx5 5x5x1 5x5x1 9 . 5Dx5 13x13x1.3 9.5Dx5 9 . 5Dx4 9. 5Dx7. 6 3.8DX7. 6 10x10x2 9. 5Dx2. 5 9.5Dx3.8 9.5Dx3. 8 8x8x5 9.5Dx7.6 9.5Dx5.0 10x8x0.5 5x4x0.5 6.0Dx1. 5 9. 5Dx2. 5 7x7x0.5 0. 5Dx5. 0 5Dx1. 0 10x10x0.5 6.5DX7. 5 6 . 0 D X 1. 4  TINA TINA UVIC TINA TINA TINA Johnson TINA TINA J chnson Johnson TINA TINA TINA TINA TINA T I NA TINA CHEM TINA TINA CHEM TINA TINA TINA UVIC CHEM TINA TOKYO TOKYO TOKYO TOKYO CHEM Warren TINA TOKYO TINA TOKYO TOKYO TOKYO TOKYO TINA  4 5 6 7 8 9  11 12 13 14 15 16 17 19 20 22 23 24 25 26 27 28 29 30 32 35 40 41 42 47 48 49 50  (95.6%) (98.2%)  Be B - 10 ( 9 6 . 2%) B-11 (9 7.25E) C-12 (Natural) C-13 (99.9%) N 0 - 1 6 (H20) 0 - 1 6 (H20) 0 - 1 8 ( 9 8 . 5%H20) F--LiF --C2F4 — CaF2 --PbF Na Mg Al Si P S Cl—CC14 K Ca Ti V cr Mn—Mn02 Fe Co Ni Cu Zn Ge—Ge02 Br—NH4Er Zr Nb Mo Ag Cd In Sn  Brass SS Brass Brass Plastic Plastic Plastic Plastic Plastic Plastic Plastic Plastic Plastic Plastic Plastic  Plastic Plastic  9.5DX5  6x6x0.7 10x8x0.5 8x10x0.2 5x5x0.5 5x5x0.5 5x5x0.5 13x 8 x 0 . 5  37  Table  I I-2(2)  z  Element (Isotope  53 56 60 64 66 68 74 80 82 83  I Ba—BaO Nd--Nd0 Gd  *  Er W Hg—HgO Pb Bi  14 15  20 22 24 29 30 32 48 50 82  1) 2)  Other  i  of Targets  oxide targets  CG2 ( D r y I c e ) Na202 MgO A1203 SiO 2 P205 C a (GH) 2 Ti0 2 Cr203 Cr03 CuO ZnO Geo CdO Sn02 Pb02 Pb304  and T h e i r  Form  Form  Container Material  S i z e (cm)  Powder Powder Pcwder Stick Stick Stick Powder Powder plate plate  Plastic Plastic Plastic  9.5Dx2. 5  Eatio)  Dy  6 1 1 12 13  List  f o r muon Sclid Powder Powder Pcwder Pcwder Powder Pcwder Powder Powder Pcwder Powder Powder Pcwder Powder Powder Pcwder Powder  Plastic Plastic  atomic  Plastic Plastic Plastic Plastic Plastic Plastic Plast i c Plastic Plastic Elastic Plastic Plastic Plastic Plastic Plastic Plastic  1  9.5DX2-5  9.5Dx2. 0.5Dx5 0 . 5Dx5 0.5Dx5 6Dx1.4 9. 5Dx2. 10x8x0. 1 0x8x0. capture  5  5 2 5  Owner2  TINA CHEM CHEM TOKYO TOKYO TOKYO CHEM TOKYO TINA TINA  experiment  10x10x20 9.5Dx2. 5 9.5DX10  9.5Dx2. 5 9.5Dx2. 5 9. 5Dx2. 5 9.5DX2.5 9.5DX2.5  9. 5Dx2» 5 9.5DX2. 5  9.5Dx2. 5 S.5DX2. 5 6 . 0 D X 1. 3  9.5Dx2. 5 S. 5Dx2. 5 9.5DX2. 5 9.5DX2. 5  D=diameter Owner, group and group 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 . Measday ) 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 . U V I C — U . o f V i c t o r i a and TEIUMF, ( 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. Yamazaki) Johnson R . R . - - U B C P i o n S c a t t e r i n g Group Leader W a r r e n J . B . — U B C Muon X - r a y G r o u p Leader  CHEM CHEM Warren CHEM Warren CHEM Warren Warren TINA CHEM CHEM CHEM Warren CHEM CHEM CHEM TOKYO  Fleming)  38  lifetimes liquid fit  It  1 6  and  o  nitrogen  the  steel  in  target  targets  reduce  the  a vacuum  container.  The  cm t h i c k n e s s stopped  in  made  of  0.3  was  able  heat  space two  of  container  c y l i n d r i c a l counter  to  had  *a0  It  conduction the  containers  windows.  The  was  made.of  loss  inner  order  ends  of  of  keep  liguid  nitrogen  windows  to  two  outer 0.0 1  containers  were  This  a three  nitrogen.  of  reduce  the  for  the  to  stainless  liquid  and  cm t h i c k n e s s s t a i n l e s s s t e e l .  to  A  s p e c i a l l y designed  had t h i n  stainless steel in  the  was  S5.  between  similar composition.  made muons  container  hour  experiment.  the of  All  targets  were  of  counter  S5. . Since the  center the  background  plastic  container  container. counted  shape  with  long  i t  was  which  and  case the  the  and  a metal  the  holder  lifetime important  In  order  consisted  thickness cf  were  beryllium  same  background for  In  runs.  The  background In  holder and  the  case  to  of  holder  brass  and  for  size  cr  for  the  was  used  at one  for  the  metal container  the  were  boron  and  targets,  atomic  background  with *3C  and  capture  the  in  dummy same  targets..  copper  used f c r  nitrogen  light  background,  copper  were  the  carbon  l i q u i d nitrogen the  was  the  target  know t h e  used  of  the  estimate  empty  runs  for  holder  source.  and l i t h i u m  thickness  target  target  measurements  to of  the  a p l a s t i c holder  same b a c k g r o u n d  histogram.  targets  the  Hence  as the  elements, the  sources,  p l a c e d on  In  plates  the  target  was  used  oxygen  targets.  experiments,  39  metallic  oxide  with  standard  the  background  of  targets size  these of  heavy  powder,  in  the  II.  In  our  was e m p l o y e d .  Garner  (GAK79) . . T h e  figure  described  II-4. as  (for  carbon  from  instance  lifetime  Zn  powder,  S  container.  and  Timing  system  was  s i m p l i f i e d data main  The  containers  Consideration  functions  the  MSE  explained taking of  the  data  taking  in detail  system i s system  by  shown  are  follows  1.  muon  2.  electron  i d e n t i f y muons and s e n d s t a r t  lcgic  rejection 4.  . The  The  plastic  above.  l i f e t i m e experiment,  system  in  plastic  in  was e s t i m a t e d  elements  Electronics  E  enclosed  mentioned  targets  measurements etc)  were  clock  in a target to a c l o c k ,  d e t e r m i n e a good 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 stop s i g n a l to the c l o c k .  logic  lcgic  stopped signals  -  f i n d any e v e n t w h i c h s a t i s f i e s rejection logic, determine the s t a r t  the  a t i m e i n t e r v a l between and t h e s t o p s i g n a l s ,  5 . . C AM AC  s t o r e a l l i n f o r m a t i o n needed 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 to a c t i v a t e a Microprogrammed Branch Driver (MBD),  6. .  c o n t r o l data t a k i n g system, read 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 the i n f o r m a t i o n to PDP-11/40,  MBD  PDP-11/40  process data stored i n the r e c o r d d a t a on a d i s k f i l e  MBD, and renew  MUON COUNTERS S1 S2 S3 S4 ELECTRON COUNTERS S5 S6 S7  MUON START  LOGIC UJ _i m  <  o  S 8  S9  M 2 0 EXPERIMENT AREA  MU  GATE  ELECTRON LOGIC L R  _L__i_  2ND MU > 2ND E REJECTION  CLOCK  ^ 4 *  STOP '  h AT  GRAPHIC DISPLAY  MUGATE  DATA  CAMAC L R T B  LAM DATA  CLEAR  EJECTION  MSR Figure  I I - 4 , S i m p l i f i e d MSR  COUNTING  data t a k i n g system.  DATA  & MBD-11  PDP-11/40 DISK  ROOM  o  4 1  histograms 8.  magnetic tape  Figure for  the  muon,  II-5  the  names and  II-3.  figure  II-6,  Incident  coincidence  and  (=M)  gate(GI) with a  of  long (short)  signals  (GJ);  no and  (M , G J ,P2,  produce  same  was a l w a y s there  was  there  muons,  made  sure there  good  mucns.  In  this  while  the  Since  way,  the  were no the  determined target  muon s i g n a l  within  by  in  Table  events  (PUG)  a  (1,2,3)  a  (1/2,3,4,5)  If  gates  sent  to  gate  (GJ) ,  a good  the  computer pre-muons  G2 g a t e  Gl  a  stretched  gate  (32  cr  kept  busy  muon  G1  The  for  no  generator  muon e v e n t .  length  dealing  no MBD  muon g a t e s ,  was  muon  were  (G2),  muons s t o p p e d i n gate  of  microseconds  there  a gate  Two  a  w h i c h was  32(16)  are  by  opened  rejections  was a g o o d  whenever  listed  d e f i n i t i o n s of  the  (G4).  o r i g i n a l muon  microseconds). stopped  was  logics.  means a n a n t i - c o i n c i d e n c e  protection  a 2nd-muon,  as t h e  in  pulse height no  created  and  measurement.  muon g a t e  if  symbols are  generator  pre-muons  MBD , G 6 )  another  were ; t h e  length  and  gate  lifetime  (MEjD)  signal  if  muons  stopped  a pile-up  2nd-mucns  pre-muons  The  terminal,  the e l e c t r o n i c s  rejection  p a r t i c l e s were  stopped  S4(S5).  of  timings  c o i n c i d e n c e , w h e r e .4(5)  counter  graphic  shows a s c h e m a t i c s of  meanings  explained.  the  at the end of e x p e r i m e n t , transfer data from the d i s k t o tape to keep i t p e r m a n e n t l y and t c a n a l y z e i t offline.  e l e c t r o n and the  Equipment In  -  on  to and  G4,  G1  gate  target  and,  by  the  same  16 track  of  the  was p r o c e s s i n g d a t a ,  and  before  next  accepting the  was c r e a t e d  only  by  a  good  Table  Symbol  II-3  Meanings of  Symbols  in  Logic  Name  Diagram  Model  —'D'OuD—  Delay  D  Leading  DL(DH)  Lower (Higher)  C  Constant  COI  Coincidence Logic  F  Logic  LF  Linear  PUG  Pile  Up  GG  Gate  Generator  S1-S9  Counter  —X)  anticoincidence of  0—•  Inverted  PH  Pulse  SAW  Saw  INC  Incident  ST  With  G  Ordinary  P  Pile  A1-A4  Telescope I d e n t i f i c a t i o n  Edge  Discriminator Disc,  Fraction  Fan-In  and  Fan-In Gate  level  LBS-621BL  Discriminator  ORTEC-EGG  934  LES-465 Fan-Out  LBS-429  and F a n - O u t  LES-428F  Generator  EGG-GP100/NL LES-222  Name i n  Table  II-1  Logic  N  Output  Height  Electron Mucn  Rejection without  C o i n c i d e n c e of  (1,2,3)  Anti-Coincidence  Up  LES-621BL  Gate Gate  from from  PUG  (1,2,3,4,5) or  GG  PUG Input  Muon  Gate  43  RESET C 2 1 2  CLOCK START  PATTERN REJECTION UNIT GATE C 2 1 2 C 2 1 2  Figure I I - 5 , Electronic logic.  C 2 1 2  STROBO  CLOCK STOP  44  (1) Good event Stopped Muon  ( T i m e in jj s e c ) t=0  muon  f ( Start  gateCGD  t  Electron event Electron  signal  MBD  busy gate  |32  V (Stop i i i  gate(G5)  LAM  Clock)  Clock) i  > >  V I  Protection  i  ^ 4 j  gate  j-15 -  Pre-muon  ( 3 ) 2-nd  Yt<o gate  V t=o J Extended gate  1  muon  Stopped 2-nd  1  i i i  (2) P r e - muon  Pre-muon  50-J  i i  muon  muon  Yt2~  P i l e up g a t e t2+ New muon (4) 2-nd  electron  Electron Electron 2-nd  gate  event gate  electron  Figure II-6, Timings and d i f i n i t i o n s of events.  V  3 2  45  muon the by  and  applied  pattern the  tc  unit  a  was  as  a start  was d e t e r m i n e d  by  a constant  showed  signal. counter  fraction  type  In fed  the  into  counter  gate,  the  CAMAC  crate,  p r o c e s s i n g of  generated  by  a C212  activated  the  generated  to  the  MBD.  produce  the  reset  created  at  logic. was  it  busy the  and  it  the  counter  data  was s e n t  start  output  This  better  to  signal  was  fed  discriminator  timing  to  compared  the  the  After  the  in  the  to  a  the  gate,  LAM  a  the  end  protection  gate  inhibit  of  CAMAC c r a t e  (G6)  the the  to  a  was  and  was n o  a clear pulse at  good  signal  there  the  was s e t . .  CAMAC c r a t e  was a c t i v a t e d ,  the  the  s i g n a l and  4 microseconds f o r  to  within  Then,  unit  if  This  electron  pattern  hand,  unit  muon g a t e MBD  four  the  muon g a t e ,  about  s u p p l i e d from  in  S5  discriminator. .  as a s t o p the  other  counter  e l e c t r o n event  muon  pattern  took  cf  the  cf  was o p e n e d .  mounted  the  signal,  end  of  a clock  unit  output  fraction  g a t e (G5)  On  the  was a g o o d  end of  within  Since  of  discriminator.  identification bit  event  timing  whose  timings  an e l e c t r o n  at  logic.  S3  constant  When t h e r e  Furthermore,  electron  The  jitter  s i g n a l was s e n t  signal  the  muon s i g n a l ,  electron logic,  determined  telescope  muon  on t h e  discriminator.  another  telescopes.  event  during  was a good  a s m a l l e r time  leading-edge  muon  gate  computer.  a clock  was  unit  protected  When t h e r e  into  pattern  good  was the  the  gate. MBD  was  c l o c k and MBD  to  the  busy  inhibit  the  muon  46  Two p i l e - u p rejection  were  rejection  i s given  stopped  muons  rejections  employed.  The d e f i n i t i o n  in figure  and good  II-6.  electrons  2nd-electrons, .respectively. iy  the  pile-up-of  pile-up  cf  examined the  pile  if  there  up a s  seconds  quite  will  a muon  1.7  (muons)  of  level.  c o n s i d e r e d as slow  inhibit  data  rejection,  slow  probability for  taking  lifetimes  of  logic  The t e s t  for  muon  life  and  the was  between  runs  changed  The p i l e - u p  i n the l i f e t i m e  showed  30 ( 2 5 0 )  S2 a t  a  and  s i g n a l of band  mV t o  of  or  counter  the  gate  mostly  muons  1000 / s e c mucn s t o p p i n g  mV. . a s than  and  6 0 0 mV  were  G2 was g e n e r a t e d  rejected,  within  S2  electrons  150 ( 6 0 0 )  double  the  high  a l l p a r t i c l e s higher  t w o muons  rejection  by  16 o r 3 2 m i c r o s e c o n d s .  were  nano  measurements  was made  the bright  muons  by 3  of  III.  rejection  occurred,  muons  having  muon  the output  vcltage,  this  of  determined  pile-up  1500/sec.  in section II.B,  If  were  This  S2 a n d S 3 w i t h  In  was l o c a t e d f r c m  rejected.  small  rate  pulse height  kV h i g h  mentioned were  the positive  cf counters  discriminator  events  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  be d i s c u s s e d i n C h a p t e r  coincidence  pile-up  coincidence instead  rejections.  a s e r i o u s problem  The  with  were  (1,2,3),  at  2nd-muons  the p o s i t i v e  pile-up  the  The p i l e - u p  coincidence.  by c o m p a r i n g  of  height  a r e named a s 2 n d - m u o n s  The  (1,2,3,4,5)  (1,2,3)  two d i f f e r e n t  that,  was  a  a  and one p u l s e  because  20 n s w a s  rate,  By  this the  extremely  w h i c h was t h e  to  47  standard  stopping If  were the  there  in this  were  s e t i n the p a t t e r n unit  was i g n o r e d In  to  rate  determine  only  a TDC-100  clock  a  1 GHz  shop  i n t h e summer  week  experiment  new  clock  assured  employed page.  measurement,  made  of  1979,  i n October,  the p o s i t i v e  Thus,  Before  a clock  by t h i s  was  t h e summer runs  clock.  in  of of  important 1979, the  A new c l o c k  the beginning  1979,  muon l i f e t i m e .  in the  series of  lifetime  with  a time  convenience, experiment  of  t h e two were  tested  Frcm t h e t e s t ,  with  The l i n e a r i t y  of  t h e two c l o c k s  agreement  by t h e t e s t  in this  At  better  was u s e d .  For  stored  s c a l e r w a s 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  c l o c k showed  lifetime.  bits  soft-ware.  was a v a i l a b l e a n d t e s t  with  new  rejection  and a l l i n f o r m a t i o n  interval.  c a l i b r a t i o n were  measuring  unit  by  system  by  rejection events,  the l i f e t i m e a time  experiment.  the p o s i t i v e  the  muon  measurements,  the  t h e new c l o c k w a s  calibrator  the ultimate  (ORTEC-650) .  logic  i s summarized  w h i c h was  i n the  following  48  Sjajynarj o f  INCIDENT STOPPED STAET STOP  MUON MOON  Event  Definitions  (come  into  target  (stop  i n target  )—(1,2,3,4,5)  (GOOD MUON) ( n o p r e m u o n (GOOD E L E C T R O N ) - - ( 5 , 6 )  Event  rejected  region)—(1,2,3)  r e j e c t i o n ) — (1,2, 3, 4 , 5,(n) or  (5,7)  or  (5,8)  cr  (5,9)  i f  PEE  MUON—(1,2,3,4,5)  within  16(32)  microsec before  2nd  MUON--(1,2,3,4,5)  within  16(32)  microsec after  TWO C O I N C I D E N T  ( o r SLOW) — (2«,3)  2nd  ELECTEON--^two  Gate  created  STOPPED  MUGN  GOOD MUON  End  of  G1  MUONS with  S2 p u l s e  within  16(32)  up g a t e ) — G l  ( c r SLOW)  (normal  GOOD E L E C T R O N  STAET  height  > 6 0 0 mV  microsec a f t e r  STAET  by  (Pile  TWO C O I N C I D E N T  SIOPs  STAET  gate)--G4  (normal  + G5—G6  MUON  (MUON g a t e (Pile  (gate  g a t e ) — G5  (protection  up  16 o r 3 2 m i c r o s e c )  gate)—G2  for pattern (ELECTRON  of  muon  unit)  gate)  logic)  Note: 32(16)  microsecond gate  longer (shorter) 2 means 2'  means  than  was u s e d f o r  measurments  of  lifetimes  300 n s .  the discriminator l e v e l i s  35 mV (DL  in figure  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  II-5).  figure.II-5).  49  II.F  Sunning  There each  of  week  ,  Procedure  was a t w o - w e e k  o n e week  duration.  the experiment  break  The M 2 0  2.  D i s c r i m i n a t o r l e v e l s and h i g h  3.  the  TDC-100  comparing  the r e s u l t s ,  for  t h e new c l o c k  new  logic  scheme,  TDC-100  (Lam s i g n a l ,  clock,  days  lifetime  was m e a s u r e d  effect  s c h e m e s a n d beam  was e x a m i n e d  w a s made  with after  was e m p l o y e d  gate,  rates.  by s t o p p i n g  logic  of the  rejection time).  the p o s i t i v e  different  for  the o l d logic  ( 1 / 3 o f o u r beam  t o c a l i b r a t e the system,  rejection  checked. .  the development  In order  with  counters  a t TRIUMF.  from  protection  three  steps:  Since the e l e c t r o n i c  was d i f f e r e n t  etc) took  were  t h e new c l o c k  cf experiments.  for the  of  measurement built  first  muons.  voltages  a n d t h e new c l o c k  series  created  4.  muon l i f e t i m e  the  of the  was s e t f o r p o s i t i v e  a d j u s t e d and e l e c t r o n i c s l o g i c s  The p o s i t i v e  two e x p e r i m e n t s  i n the following  1.  were  between  at t h e b e g i n n i n g  was d o n e  beam l i n e  and Bun R e c o r d  muon  conditions of  The m a g n e t i c  positive  field  pions i n a  target. 5.  The M 2 0  beam l i n e  6.  at the beginning measurements,  was s e t f o r n e g a t i v e of t h e n e g a t i v e  the negative  measured and t h i s calibration  during  muon  was r e p e a t e d the l i f e t i m e  muon  muons. lifetime  lifetime  i n c a r b o n was  once a day a s a measurements.  50  7.  T a r g e t s were changed  after  g a t e -was a d j u s t e d s o t h a t measurement had a 32(16) long  lifetime  carbon 8.,  (short)  microsecond  frcm  a disk  and t h e muon lifetime  gate.  For the  elements, the  were made f o r e a c h  target*  one week r u n , a l l d a t a file  t o a magnetic  were  t a p e f o r an  analysis.  After  t h e one. week b r e a k , t h e e x p e r i m e n t  the  procedure  run  took  and  accepted electrons  II-4.  runs  A t t i e end o f t h e f i r s t  offline  a long  measurements o f l i g h t  background  transfered  enough e v e n t s  as s t a t e d  two h o u r s .  above e x c e p t  s t e p 3.. N o r m a l l y one  Numbers o f s t o p p e d i n histograms  followed  muons, good  are l i s t e d  muons  i n Table  Table 11-4(1)  Bun B e c o r d s  z  Element  Inc  Mu  3  Li-6 Li-7 Be B-10 B- 1 1 C- 12 C- 13 N 0- 16 0-16 (Agar) 0-18 (Agar) F-LiF -C2F4 -CaF2 - EbF Na Mg Al Si  14.4 17. 7 4. 6 8. 1 8. 8 3. 6 5.5 5.7 9.0 10. 0 8.3 7.3 3. 6 3. 1 5. 8 4. 7 8. 9 5.9 3. 2 5. 7 5.6 3. 9 4.3 4. 7 5. 5 6. 8 4. 5 4. 2 3. 8 6. 6 3. 2 3.2 4. 2 4.4 3. 2  x10* 12. 1 14. 7 4.1 4. 1 4.0 2.9 2. 5 5.6 8.7 3.9 3.2 4.9 2.9 2. 5 5.0 4.2 6.7 5. 1 2.7 4.7 4. 9 3.7 3.6 4.2 4, 1 2.9 3.8 1.8 3.6 4.7 2.9 2.7 3.9 2.6 2.9  4. 5 4. 1 3. 5 4.5 4.4  3.4 3.4 1.7 2.5 2.0  X106  4 5 6 7 8 9  11 12 13 14 15 16 17 19 20 22 23 24 25 26 27 28 29 30 32 35 40 41 42 47 48 49  JP  S C1-CC14 K Ca Ti V Cr Mn-Mn02 Fe Co Ni Cu Zn Ge-Ge02 Br-NH4Er Zr Nb Mo Ag Cd In  Stop  (Total  Mu  Events)  Tot  E  Accepl  X103  X103  5,630 6,800 2,024 1,312 1,210 1 ,320 820 1,640 2,780 1, 17C 1,060 1,940 1,019 500 470 1 ,290 2,090 86C 50 6 815 '710 614 510 550 365 300 299 490 103 261 105 175 165 662 503  4,580 5,900 1,531 1 ,100 1,023 1,100 570 1,230 2,236 956 885 1,550 842 4 10 370 1,0 50 1 ,640 740 420 6 20 550 505 425 454 310 250 254 430 74 210 84 121 112 490 392 573 150 152 79. 113 130  176 180 97 142 160  T a b l e .11-4(1)  Bun R e c o r d s  Z  Element  I n c Mu  50 53 56 60 64 66 68 74 80 82 83  Sn I Ba-BaO Nd-NdO Gd Dy Er  2.4 5. 5 4. 3 5. 8 3. 9 4. 5 4.8 3.8 6.0 4.1 3.1  X106  W  Hg-HgO Pb Bi  * Other 6 11 12 13 14 15 20 22 24 29 30 32 48 50 82  oxide t a r g e t s  C02 Na20 2 MgO A1203 SiC2 P205 Ca(OH) 2 Ti02 Cr203 Cr03 CuO ZnO GeO CdO Sn02 Pb02 Pb304  Stop  (Total  Mu  X 1 0 *  1.6 4.9 3.7 2. 2 2.5 3.5 3.9 2.9 5. 2 3.4 2.0 f c r muon a t o m i c  Events)  Tot E  X103 110 217 402 591 132 230 158 199 427 118 137 capture  4.0  3,.4  1 ,487  3. 2 4. 6 2. 2 4. 7 4. 3 3. 4 3. 9 5. 5 1.6 3. 5 6. 1 11.6 5.6 4. 6 3.5  2.9 4.2 1.0 3.4 3,8 2.2 3.5 5. 1 1.3 2.7 3.7 9.7 5.0 3.8 3.0  9 13 1 ,421 343 1,232 1 ,129 589 696 1 , 195 141 463 993 1,553 1,015 439 238  Accepted E  X103 88 179 323 447 106 195 134 169 333 95 109 experiment 1 , 182 718 1 ,1 13 278 989 891 451 548 935 111 362 735 1,214 776 342 188  53  CHAPTER Data  III.A  All 470  Analysis  Data  Analysis  Procedure  data  analysis  was p e r f o r m e d  V/6 c o m p u t e r .  which  III  A computer  program  a t CERN,  was u s e d  was d e v e l o p e d  o n t h e OBC  called  Amdahl  MINOIT  (JAM71),  for a chi-sguared  minimization. Two of  fitting  the chi-sguared  histogram,  three  background  were  procedures  minimization  parameters:  was d o n e  case  a negative.mucn  parameters due  to  very  Then,  first  lifetime,  quickly  b y MINOIT  elements  amplitude,  were  appeared  Therefore,  was f i x e d found  since the  parameters. were  muon  and  spectrum,  there  for the t a i l  In the case  of a p o s i t i v e  for three  histogram,  capture.  the background  several  fitting  f i t a n d more e v e n t s  to the nuclear  fitted  employed.  searched f o r the e n t i r e  fitting of  were  more  In than  at earlier  the four  times  t h e b a c k g r o u n d was  of each  and o t h e r  for the front  histogram.  parameters part  for  of the  spectrum. Figure curve.  After  events.  events  a typical there  of the background  i s roughly  came  shows  26 m i c r o s e c o n d s ,  A ratio  (B/N ( 0 ) )  TII-1  mainly  equal  to  are only  muon  These  decay  background  to the amplitude  3x10~*.  f r c m random  positive  a t T=0  background  coincidences with  charged  54  particles  scattered  were a l s o  some b a c k g r o u n d  experiment cosmic  Linac. 3x10  - 5  The ,  There  was  ratio  was  detector was  23  detector equal to  was  MHz,  about  mentioned  1x10~*. 2  III-2  20  the  t h e r e was  no  e v e r y beam bunch  of S a c l a y s E l e c t r o n 1  Balandin  "IT s o l i d  was  equal to  by a f a c t o r (BAL75),  of  who  angle... T h e i r  S i n c e the s o l i d  10. built  B/N (0)  angle of  our  beam r e p e t i t i o n  rate  o f f i g u r e I I I - 1 seems  t o t h e o t h e r good  above,  the background and  was  i n the f i t t i n g found  30 m i c r o s e c o n d s .  microseconds  and  t h e chromium, oxygen,  lifetimes  because  measurements  16 m i c r o s e c o n d s , t h e r e a r e o n l y  12  the  after  only  shows the n e g a t i v e muon e x p e r i m e n t i n  and  fixed  by  TT r a d i a n s and t h e  As mentioned  spectrum, between  affected  abcve.  After  events.  with a 4  when compared  Figure Cr203.  by  t h e B/N(0) r a t i o  satisfactory  The  S a c l a y ' s experiment  an e x p e r i m e n t  There  cosmic r a y s .  T h i s was  beam s t r u c t u r e of  counting area.  i s s m a l l e r t h a n our r a t i o  also  a Cerenkov  from  microseconds  B/N (0) r a t i o  which  M20  (DUC73) was  events.  beam f o r 500  t o the s p e c i a l  i n the events  made a t S a c l a y  ray background  incoming due  around  was  fitted and  from  cf  this  the f l a t  f o r t h e chromium carbon  carbon.  section  Then t h e s p e c t r u m  amplitude c f the background o f oxygen and  background  between  lifetime,  amplitude, keeping as w e l l  as t h e  0  100000  "i  i  r  10000 k JU  0  2  4  6  8  10  12  14  1  Decay  +  16  18  T I M E (MICRO SEC) Figure I I I - l ,  P o s i t i v e muon decay curve.  r  i  r  26  28  Spectrum  20 . 22  24  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 s t a r t s i g n a l s from the  muon stops i n the t a r g e t  electrons positive  and stop s i g n a l s from  were recorded as a histogram.  In the case of  muons, the histogram shows a l i f e t i m e of  microseconds.  Without  a magnetic  field  decay  2.2  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 p o s i t i v e muons, Bg the time independent background If and  there i s not a strong d e p o l a r i z a t i o n  i f the t a r g e t  field,  The new  N(t)=N(0)«[1  where a,w phase,  i s under  equation (3. 1)  precession.  and N (0) the amplitude a t t=0.  must be m o d i f i e d due t o the muon eguation i s given by  (3.2)  and p> are an asymmetry, an angular frequency and a In our p o s i t i v e muon l i f e t i m e  measurement, carbon, which depolarization  the  of a magnetic  + &«cos (wt+p) } »exp (-t/Tm) + Bg  respectively.  polarized  the i n f l u e n c e  of muons  (SWa58),  was  does net show any mucn used as a t a r g e t .  I f a highly  muon does not show any d e p o l a r i z a t i o n i n a  asymmetry a i s c l o s e to 0.33.  In the t a r g e t  target,  r e g i o n of  58  our  experimental  because Under with  of  muon  magnetic  shielding,  magnetic  10 muon  apparent  field,  lifetime  field  was q u i t e  as discussed like  precess  lifetimes.  This  0 . 0 5 G,  in section positive  by 0 . 0 9 r a d i a n s  II.C.  muons  (5  precession affects  and t h e f o l l o w i n g  small  degrees) the  approximation  can  made  Tm = T m ( 0 ) * [ 1  where or  the  100% p o l a r i z a t i o n  within  be  Mu m e t a l  a small a  set-up,  + (-)  vice  versa.  has  which  the f i r s t  In  Since  stopped pions  sources,  to  arranged  distortion  and  has a Since  four  as  of the four  lifetimes lifetime  effect.  the magnetic  as i f  In  by 7 n s .  and the average  they  this  were  field  effect,  positive  among  case,  the  pions  muons.  are i d e a l unpolarized  in lifetimes  i s given  N(t)=Np(0)«  the average  detector  f o r 0.05G  symmetrically,  i n the t a r g e t  i s expected.  electrons  order  the l i f e t i m e  check  in a target stopped  w=85,500*0.05/sec  order  (3.3)  the l e f t (right)  distortion  second  no d i f f e r e n c e  telescopes decay  were  order  order  to  the.first  in section II.B,  a negligible  were  A=0.33,  changes  telescopes  discussed cancels  With  microseconds,  effect,  electron  + 0 . 5 « (A«w«Tm (0) ) 2}  s i g n c a n be a p p l i e d  Tm(0)=2.2 0.3%  ± A«w«Tm(0)  muon  electron  the d i s t r i b u t i o n  of  by  {exp(-t/Tp) (Tp -  -  exp(-t/Tm)}  Tm)  + Bg  ( 3 . 4)  59  where  Tm (Tp)  lifetimes becomes decay  is  negligible  curve  telescopes as  muon ( p i o n )  (=260 n s ) ,  the  and,  Table  for  10  then,  Muon  the  pion  from  equation  the  (3.4)  are  lifetimes  listed.  The  of  pion  shows  four  decay the  same  electron  summary  Error  of  the  table  Eeam  Counters L and R  T and  Standard d e v i a t i o n of each e l e c t r o n t e l e s c o p e from the average l i f e t i m e  6.4  ns  5.0  ns  Statistical  4.4  ns  4.4  ns  4.6  ns  2. 4  ns  1.4  ns  3.0ns  4. 4  ns  4.4  ns  0.0  ns  0.0  ns  error  Magnetic f i e l d e f f e c t a quadratic relation Pion  beam  Standard  Magnetic Consequently, to  the  magnetic  (tcp-bottom)  distortion  corresponds  measurement  428  ER)  .showed  the  center  lifetime  of  with  the the  effect distortion  is  roughly  electron to  a flux  target,  the  seems t o  muon ns  average in  Since  (Hewlett  between  be  the  4.6(2.4)  G.  meter  te  of  0.02 field  good  lifetime  for  t e l e s c o p e s and  0.03(0.02)  f i e l d to  distortion  measurement.  the  field  left-right  field  error  field  B  by  deviation  Statistical  field  10  fcllcws.  Beam  due  After  (3.1).  III-1, runs  lifetime.  contribution  as e q u a t i o n  In  is  the  the  the the  magnetic  Packard and  0.05  from  agreement  Model G  near  the with  the  Table  P o s i t i v e Muon Telescopes  Lifetimes  cf  Four  ( in Left  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)  Electron  nanosec)  Eight  Top  Bottom  Average  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) 2198. 1 (2.2) (-6.0) 2187.2 2195.8 (-8.6) 2195.4 2196.4 (-1.0)  21S7.7  2198. 1  (-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)  2195,2 2198.4 2197. 1 2196.6 2198.4 2195.4 2197.0(0.7)  1)  All positive target.  *)  These  data  ( )  shows  the  muon  were  lifetimes  taken  deviation  by  from  were  stopping the  measured pions i n  average.  in  the  the  carbon target.  61  We w i s h t o e m p h a s i z e its  polarization  As  while  less  than  measurements to  this  single  effect  of  etc; the  negative would  of  III.C  If  III-3,  (a)  to  be s h o r t e r  the rate  Rate  properly,  without than  microseconds Before  if  we h a d u s e d a  due t o f a u l t y  data  was r e p e a t e d  transfer  and none  of  Effect  discussed i n section lifetime  stopping rate.  on t h e p o s i t i v e  determined In  figure  muon l i f e t i m e i s  experiments:  r e j e c t i o n scheme  which i s t h e f i n a l  logic,  rejection of  a stop  i n t h e l i f e t i m e due  (On a f e w o c c a s i o n s o n e o r  t h e muon  for a higher  effect  a good  i s  t h e r e s u l t s a r e a l w a y s an  rejection  f o r the two f o l l o w i n g with  atom..  used.)  t h e bad event  electronics (b)  .were l o s t  Stopping  i s not working  tends  shown  Muon  loses  Thus f o r t h e l i f e t i m e  1 ns even  telescopes.  were  i n t h e muonic  the error  c a s e s t h e measurement  p a r t i a l data  H.E  te about  the histograms  i n these  muons  whereas i n f a c t  a l l four  muon  the residual polarization  20% c f t h e i n i t i a l .  telescopes  average two  of  the negative  i t c a s c a d e s down  discussed i n section I.D,  always  that  bad e v e n t s  signal into or  w h i c h come  the taxget  by about  later 8  longer.  the f i n a l  e l e c t r o n i c s l o g i c was c o m p l e t e d ,  2210  Figure III-3,  Stopping r a t e dependence w i t h and without r e j e c t i o n s .  63  the  LAM s i g n a l was p r o d u c e d  microseconds  after  by a TDC-100 c l o c k 4  an e l e c t r o n s t o p  4 microseconds f o r the pattern (the  electronics logic  Actually, within the  i n order  a muon  end of  Since, the  gate,  rejection  cf  (b),  at  between  without  rejection  no s y s t e m a t i c  good  positive they  muon  muon  there  start. than  was no  Figure  c f t h e muon  III-3  lifetime  On t h e o t h e r  hand,  up t c 5 0 0 0 / s e c w i t h  case of  was  kept  rate  was a b o u t  was v a r i e d  negative  below  there  the  rate  a 20 m i c r o - a m p e r e target.  with  proton  group  i n the p o s i t i v e  This  rate  In t h i s  the rate  was a l s o t h e  a 2 . 5 cm d i a m e t e r current  and  experiment, life  dependence.  rate  the  (DUC73)  muon  measurements,  w h i c h was t h e s a f e  effect.  mucn beam r a t e  production  only  1500/sec.  accurately  stopping  as t h e Saclay  muon l i f e t i m e  1000/sec  measured  a 7000/sec  sc as to investigate  stopping  negative  with  (BAL75)  t h e same r e s u l t  rate  the  group  lifetime  stopping  measurements  and  the gate,  scheme.  dependence  Russian  obtained  whose  muon  muon  t h e LAM s i g n a l c a m e e a r l i e r  dependence  rate  a good  at  logic. The  the  II-E)..  o r 2nd e l e c t r o n s  t h e two s i g n a l s .  rate  is  another  b y t h e MBD  in section  2 n d muons  the end of  shows t h e s t r o n g t h e good  given  took  be r e a d  32 m i c r o s e c o n d s a f t e r  s i g n a l produced  proper  to  It  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  the gate  i n the case  unit  has been  t o check  event.  the  time In  rate  to avoid maximum collimator  on a b e r y l l i u m  the  64  III.D  2 n d Muon  Without  Rejection  proper  r e j e c t i o n s of  bad e v e n t s ,  there  a distortion  i n the histogram  as discussed i n the l a s t  section.  crder  the distortion,  In  chi-sguared different the  minimization  initial  analyses  analyses III-4 for  to examine  times  was f i x e d  .were  taken  (a)  with  (b)  without  (c)  with  According section  this  stopping muon  dependence  of  detail  of  t h e 2nd muon  c h o i c e of  b i z a r r e . . In  a typical  the  beam,  incoming  scheme  logic,  there  logic  Figure time  T1  II-6  height  were  Let  by t h e  beam  t h e 2nd (1,2,3)  us d i s c u s s  which  t h e 2 n d muon  8.6x106  rejections:  f o r the d e f i n i t i o n s ) .  by t h e i n c o m i n g  run with  beam.  and the  Alternatively  logic  (b),  described in  s i g n a l i s generated  rejection  (a) ,  2 n d muon  are four  the pulse  muon e v e n t s .  there  i n which  by t h e i n c o m i n g  (1,2,3,4,5).  the stopping  this  the  same a s I I I - B  the ultimate  (see f i g u r e  s i g n a l c a n be p r o d u c e d  instead  Thus,  same a s I I I - B  bad e v e n t s ,  2nd e l e c t r o n ,  events  The e n d o f  on t h e i n i t i a l  scheme,  rejection  i n the f i n a l  muon  several  a n d 30 m i c r o s e c o n d s .  are generated  rejections  for  cases:  t h e summary  logic,  T1  r e j e c t i o n of  2nd m u o n , t h e  made  the  the histogram.  rejection  t h e good  II.E,  pre-muon In  between  t h e good  to  of  were  a t 30 m i c r o s e c o n d s .  three  rejections  the  (Tl)  shows t h e l i f e t i m e  the f o l l o w i n g  analyses  i s  in  some  may seem rejection  incoming  muons  by  through  2230 |  2220  muon rejection by stopped muon  t  2-nd  m u o n r e j e c t i o n by i n c o m i ng m u o n  }  No rejection  i  LO  c LU  2-nd  2210  u2200 LL  t^2190 i  i  2180  t 2170h  2160  (MICRO  0  .  2  4  INITIAL T I M E ( T o ) O F  igure III-4,  6 DATA  SEC)  8 FITTING  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 decay c u r v e .  66  the lead c o l l i m a t o r , 0.4x10 g e n e r a t e d , and 6 . 4 x 1 0 If  6  6  2nd muon s i g n a l s  (74%) muons s t o p p e d  t h e 2nd muon s i g n a l had been p r o d u c e d  muons, 0 . 2 5 x 1 0  6  2nd mucn s i g n a l s  were  i n the target.  from  the stopped  w o u l d have b e e n  generated.  P r o d u c i n g t h e 2nd muon r e j e c t i o n s i g n a l s f r o m t h e i n c o m i n g beam, t h e r e was an e x t r a a b o u t 6% c f 2 . 4 x 1 0  6  0.15x10  6  rejections.  T h i s was  e l e c t r o n events accepted i n the  histogram. I n - p r i n c i p l e , 2nd muon r e j e c t i o n by t h e i n c o m i n g muons seems b e t t e r  t h a n t h e r e j e c t i o n by t h e s t o p p e d  muons  i n a t a r g e t , b e c a u s e t h e f o r m e r r e j e c t i o n d o e s n o t a l l o w any two mucns c o m i n g i n t o t h e t a r g e t Since a large in are  a r e a w i t h i n t h e muon g a t e .  number o f p a r t i c l e s i n t h e i n c o m i n g  beam ( 2 6 %  t h e t y p i c a l c a s e shown above) go t h r o u g h t h e t a r g e t and 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 o f t h e s e  muons may n o t a f f e c t t h e s p e c t r u m the incoming  a s 2nd muons*  beam i s used f o r t h e 2nd muon r e j e c t i o n , many  good e v e n t s a r e u n n e c e s s a r i l y r e j e c t e d . lifetime  Thus, i f  This caused  a  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 p r o p e r r e j e c t i o n o f .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 , . is  shorter  i n f r o n t o f the spectrum  The l i f e t i m e  and l o n g e r i n t h e t a i l . .  67  III.E  Distortion  from Counter E f f i c i e n c y and  Dead Time of E l e c t r o n i c s  The e f f i c i e n c i e s of counters are l i s t e d II-1..  i n Table  Since the (1,2,3) c o i n c i d e n c e which monitors the  incoming  beam has 99.4% e f f i c i e n c y ,  0.6% of incoming  would not be detected even i f they stopped These muons can be considered as undetected cause a d i s t o r t i o n  problem.  muons  i n the t a r g e t . . 2nd muons and so  In order to f i n d the degree of  the d i s t o r t i o n , an e m p i r i c a l approach can be a p p l i e d . . Figure I I I - 4  shows the stopping r a t e dependence of  lifetime  with  detected  mucns f e l l o w a Poisson d i s t r i b u t i o n , t h e d i s t o r t i o n  due  and without r e j e c t i o n s .  to undetected  Since undetected and  muons can be estimated by  Poisson d i s t r i b u t i o n of undetected muons w i t h i n twice the time of the muon gate Tdis=  where  DT <»  Poisson d i s t r i b u t i o n of stopping muons w i t h i n twice the time of the muon gate  = DT •  (1-E)»N»2*Tm*exp {- (1-E) •N»2»Tm} ; N»2«Tm«exp (-N»2»Tm)  ET=  empirical lifetime  E =  counter  N =  stopping muon r a t e ,  Tm=  mucn gate  distortion,  efficiency,  (32 microseconds).  (3.5)  68  At 5000/sec stopping r a t e , the l i f e t i m e d i s t o r t i o n with no rejection eguation 0.2  i s about  25 ns, from f i g u r e I I I - 4 , and  (3.5), the d i s t o r t i o n due t o undetected  ns f o r a 99.4%  undetected  counter e f f i c i e n c y .  from muorfs i s  However only 25% of  muons c o n t r i b u t e to the d i s t o r t i o n because  of the  2nd e l e c t r o n r e j e c t i o n by the e l e c t r o n t e l e s c o p e s with the 2 TT r a d i a n s o l i d a n g l e . efficiency  of 99.1%  C o n s i d e r i n g t h a t the counter  was  measured with a ruthenium  e l e c t r o n source and the e f f i c i e n c y f e r muons was  4  MeV  b e t t e r than  that f o r e l e c t r o n s , the d i s t o r t i o n due to undetected muons was  l e s s than 0.05  ns..  So i t was  5000/sec stopping rate I f two  n e g l i g i b l e at or below the  used.  muons came i n t o  the t a r g e t r e g i o n w i t h i n  10  ns, the pulse height r e j e c t i o n could e l i m i n a t e the event from a histogram. more than  However, i f the second  mucn came a f t e r  10 ns but l e s s than the e l e c t r o n i c s dead-time  (about 60 ns f e r a counter o u t p u t ) , the pulse h e i g h t and  the  2nd muon r e j e c t i o n c o u l d not r e j e c t the event.. I n c i d e n t muons were monitored.by muon s i g n a l was  counters S i , S2 and S3, and the 2nd  generated by a p i l e - u p gate generator  (PUG).  Thus, the dead times cf a LBS-621BL l e a d i n g edge type discriminator  (S1 and  S2), an ORTEC-934 constant f r a c t i o n  discriminator  (S3) and an EGG-100 (PUG)  must be c o n s i d e r e d .  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 i n the d e t e r m i n a t i o n 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 find  t w o muons  the probability  distribution the  part  in  lifetime  (3.5).  It  rate  h a s been muon  caused  below  by t h e r a t e Since  effect from I-C,  B,  muon  N,  backgroumd  i s  0)  i n the mesonic  muon  were  decay  negative for  Cr203.  t h e muon systematic  lose  III.B  experiment  of  background.  i s the d e f i n i n g  i n the  their the  i s small.  magnetic For  discussed i n  of n e g a t i v e  muons  respectively.  the systematic  measurement  i s the carbon  source  the  atcm s t a g e ,  }5% a n d 5%,  cause of  lifetime  of  muons  the r e s i d u a l p o l a r i z a t i o n s  main  Lifetime  was n e g l i g i b l e a s s h o w n  the negative  t h e bound  and t i t a n i u m The  Muon  1000/sec a n d t h e  discussed in section  Be,  by o n e  distortion  measurements,  field  negative  rate,  c a n be  discussed in section III.A  guickly  carbon  to  Poisson  the lifetime  for the analysis  polarization  section  effect  on t h e l i f e t i m e  lifetime  was k e p t  section.  example,  this  changes  of Negative  procedure  the negative  former  60 n s , t h e  a n d , f o r 5000/sec s t o p p i n g  2.5x10-*.. A l s o ,  is  Analysis  The  distortion  within  In order  small.  III. F  stopping  two muons  and the e f f e c t  5  negligibly  muon  of  by e q u a t i o n  10  30 n s c a n be r e j e c t e d .  c a n be a p p l i e d  probability  estimated  In  within  error  light  elements  The m a i n  counter  i n the  S3.  (Li,  carbon  Also,  the  in  70  light  guide  background  S 5 , and w r a p p i n g  counter  SU and S5 c a n be c a r b o n  counters carbon  of c y l i n d r i c a l  background  depends on t h e t a r g e t  sources.  size  T h e r e f o r e , carbon  after  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  by  using a duplicated target  fitting  of the l i g h t  subtracted III-2,  the f i t t i n g  background runs  results  t h e carbon  are l i s t e d .  of small correction.  background in  enclosed  decay  electron target,  There  by a few n s f o r t h e  into  spectrum  account  following  eguation.  compound f i t t i n g of  t h e powder o r t h e c h e m i c a l  the c o n t r i b u t i o n  frcm  the elements of  compounds must be i n c l u d e d  Thus, f i g u r e I I I - 2 i s f i t t e d t o  equation  Ne (t) = A (Cr) «exp {-t/T (Cr)}  • A (0) »exp [-t/T (0)} (3.6)  + A (C) • e x p [ - t / I ( C ) } + Bg  where A and T a r e t h e a m p l i t u d e element  a s shown  pcwder t a r g e t s were  In the l i f e t i m e  from  m a t e r i a l s and c h e m i c a l  the f i t t i n g  II-D,  were c h e m i c a l  i n Table I I - 2 .  as l i s t e d  container  the  In T a b l e  The u n c e r t a i n t y o f t h e c a r b o n  mentioned i n s e c t i o n  i n containers.  compound  in  was  The c a r b o n  d e t e r m i n a t i o n i s a l s o .taken  As  the  background  III-2.  Table  targets  element  o f t h e background run.  c o r r e c t i o n s have changed t h e l i f e t i m e s case  were made  made o f brass,„ I n t h e l i f e t i m e  element,  using the r e s u l t  The  and i t s  thickness. every  tapes of  (Cr, 0 ,  C) .  In this  and t h e l i f e t i m e  fitting,  of each  T(C) and T<0) a r e  71  Table  III-2  Carbon Background  L i f e t i m e without C Background  Effect  i n Light  % of C Background  Elements  L i f e t i m e with C Background 2. 0 n s e c  1.0 (±0.5) %  2177.0 ±  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  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  1.3  1.6 (±0. 5)  1795.4 ± 2. 0  1865.4 + 3.0  13.0(±2.0)  1844.0 ± 4. 5  Li-6  2175.9 ±  Li-7  0 (H20) 1799.6 ± 0-18  1. 5 n s e c  1) The numbers i n p a r e n t h e s e s a r e t h e e s t i m a t e s u n c e r t a i n t y i n the carbon background.  ±  3. 0  of the  72  fixed.  although  counter  and c o n t a i n e r ,  curve rate  is negligible. of  recent  negative  studied  the absolute  =0.996  complete  i n CH2.  amplitude  i s also In  weighted  fitting  of  telescopes, J3INUIT  phenomenon  intensity  of  ± 0.007.  u  e  t  of o  t o heavy i s that Zinov  muonic  result  the negative  this  fast  average  of  four  i s taken  ,  using  from  Vitale  et  a l . (ZIN64)  obtained  the of  four  hydrogen hydrogen target.  H2O  muon  obtained  the weights  X-rays  muon f r o m  the negative  electron spectra  of  has indicated the  curve  lifetimes,  transfer  elements. . a  and  transfer,  n e g l i g i b l e i n a decay to determine  i n the decay  K series  carbon,  Their  plastic  of the high  that  (CH2)and pure  E  order  decay  hydrogen  we n o t e  in the  component  i s because  from  transfer  carbon  lifetimes, by t h e  electron  s u p p l i e d from  the  program.  III.G  In discussed. by  This  muons  a hydro-carbon  almost  the  the hydrogen  As c o n f i r m a t i o n  A(CH2)/A(C)  to  i s a l s o hydrogen  d i s c u s s i o n of t h i s  (VIT80).  from  there  atom  resulting arrival  s e c t i o n I.D This  detecting  muonic  Hyperfine  the hf  electrons.  their  i n two h f s t a t e s .  i n the K o r b i t ,  At  Curve  i n n u c l e i has been  how t h e e f f e c t  Muons  own s p i n  i n a Decay  effect  section explains  decay have  (hf), E f f e c t  i s  i n the K o r b i t  obtained of  coupled to the nuclear t=0,  t h e muons  the time  populate  of  the spin  their  t h e two  states  73  statistically higher  and then undergo the hf t r a n s i t i o n from the  l e v e l to the lower l e v e l .  been c a l c u l a t e d by Winston results  are l i s t e d  experimental  negligible  (WIN63) f o r various n u c l e i .  i n Table IV-6 along with  results.  t h e r e i s an e f f e c t  The c o n v e r s i o n r a t e s have  In a histogram  His  past  of decay e l e c t r o n s ,  from t h i s conversion and t h i s i s not  forfluorine  i n particular.  T h i s w i l l be  d i s c u s s e d i n s e c t i o n IV.D. F i g u r e I I I - 5 shows the hf doublet definitions  c f Rh, B+, R~ and D.  F + and F~ s t a t e s s t a t i s t i c a l l y  and the  a t t=0, muons populate the  as f o l l o w s  n+= ( 1 + 1 ) / ( 2 1 + 1 )  n-= 1/(21+1)  The  (3.7)  muon p o p u l a t i o n s N+(t) and N~ (t) of F+ and F~ s t a t e s are  determined by  d — N+(t) = - (Bh + B+)«N+(t) dt d —  N-(t)  = Bh»N+(t) - E-»N-(t)  (3.8-1)  (3.8-2)  dt  The  time spectrum of decay e l e c t r o n s , Ne (t) , i s given by  Ne (t)=Bd« {N+ (t) + N"(t) }  (3.9)  Nuclear Level  Nucleus  A  R  = Rd + R c  +  D = R"-R = R c - Rc  Rh J R  gure I I I - 5 ,  +  = Rd + Rc~  H y p e r f i n e d o u b l e t o f muonic atom. Rh i s c o n v e r s i o n r a t e , Rc c a p t u r e r a t e , Rd decay r a t e , and R t o t a l disappearance r a t e . The +ve(-ve) s i shows the r a t e from F=I+l/2 (F=I-l/2) s t a t e .  +  +  75  Since Eh>>D f o r most n u c l e i and  (WIN63) , from eguations (3.8)  ( 3 . 9 ) , we have the simple form  Ne (t) =const« {1 - Ae«exp (-Bh«t) } «exp (-E"«t) Ae=n+«D/Bh.  (3.10) (3.11)  Since 1=1/2 and D/Eh=0.02 f o r i « F (WIN63), the hf e f f e c t Ae i s e g u a l t o 0.015, which i s q u i t e a s m a l l e f f e c t . In the case cf a nucleus which has t h e hf e f f e c t , equations  (3.6) and (3.10) are combined t o 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  This i s used f o r the chi-squared minimization.  (3.12)  The average  capture,  (Ec)av, and t o t a l disappearance r a t e s of the hf  doublet,  (Et)av, are d e f i n e d by  (Ec) av=n •Ec* + n~«Ec-  (3.13)  (Et) av=n + »E+ + n~»R-  (3. 14)  +  T  =1/(Et)av  where T i s the mean l i f e .  (3.15)  These equations w i l l be a p p l i e d  i n s e c t i o n IV,. D. The measurements  of capture events  (neutrons or  gamma rays) i s s u i t a b l e f o r experiments on the hf e f f e c t i n  76  muon capture equation  (WIN61).  In the capture process, Ae i n  (3.10) i s replaced by An which i s g i v e n by  An=n+«D/Ec-  From equations  (3. 16)  (3.11) and  (3.16),  An=Ae» (Eh/Ec-)  (3.17)  For most n u c l e i , Eh>>Ec , thus, the capture _  measurements show a l a r g e hf e f f e c t .  event  In the case of  l 9  F,  An=25«Ae  and  the l a r g e enhancement o f the hf e f f e c t has been observed  i n the neutron  and gamma ray measurement  (WIN63) .  77  Experimental of  Our muons  In  IV-2  Table  results rates, 0.7  our r e s u l t  of  measurement  elements  (Ee,  been  made  measurements positive away  from  error  cf  in  for  0, 1 3  C,  F,  lifetime  which  factor  improved  errors,  along  of  accepted  our capture  2197.0  a n d new  ±  muon  the accuracy  f o r many  of  the  light  measurements  Many  past  especially for the  value.  studied  of IV-1. .  with  t h e bound  was many s t a n d a r d  and the c o r r e c t a s shown  i n Table  lifetime,  0 , Dy a n d E r .  our system h a s been  obtained  muon  N a , C l , K)  1 8  rates  our c a l c u l a t i o n of  experiment,  has been  the c u r r e n t l y  III,  In  this  had s y s t e m a t i c  mucn  Chapter  been  N,  IV-1.  a r e shown  correction In  and c a p t u r e  n u c l e i are l i s t e d  the p o s i t i v e  are employed.  B,  Measurements  for lifetimes  i n Table  lifetime  have  and D i s c u s s i o n s  measurements  n s , and t h e H u f f  decay  Eesults  i n complex past  listed  IV  Lifetime  results  negative  CHAPTER  The  deviations  systematic  carefully,  positive  i n the following  muon  as d i s c u s s e d  l i f e t i m e has  section  IV.A.  Table IV-1(1)  z  R e s u l t s o f L i f e t i m e Measurements i n This Experiment  Huff Fac. (Q)  (A-Z) / 2 i  1. 0 1.0 1.0 1,. 0 1.0  0. 25 0. 2857 0. 2778 0.25 0. 2727  Mean L i f e ( ns )  C a p t u r e Rate ( x l C /sec)  Li-6 Li-7 Be B-10 B-il 1  2177.0±2.0 2188.3±2.0 2162.1±2.0 2070.7±3.0 2096. 1 ± 3 . 0  4. 18±0.45 1.81±0.45 7.35±0,45 2.8U0.07 2.22±0.07  x l O "3 x10- 3 x10~ 3 x10- 2 x10- 2  C C-13 N 0 0-18  2026. 3+ 1.5 2029.1±3.0 1906.8±3.0 1795. 4 + 2.0 1344.0±4.5  3.88±0.05 3.77±0.07 6.93±0.C8 10.36±0.04 8.80±0. 15  x10- 2 1. 0 x 1 0 - 2 1.0 x10- 2 1.0 x10- 2 0. 998 x l O - 2 0. 998  11  F-LiF F-C2F4 F-CaF2 F-PtF2 Na  1464.7+4.0 1458.8+4.0 1463.2±5.0 1462.2 + 6.0 1204. 0±2.0  0.228±0.002 0.23U0.002 0.229±0.003 0.230±0.003 0.377±0.001  0. 998 0. 998 0. 998 0. 998 0. 996  0.2632 0. 2632 0. 2632 0.2632 0. 26  12 13 14 15 16  Mg Al Si P S  1067.2±2.0 864. 0±1.0 756.0±1.0 6 1 1. 2±1.0 554.7±1.0  0.484±0.002 0.705±0.001 0. 87 1±0.002 1. 185±0.003 1. 35210.C03  0. 995 0. 993 0. 992 0.99 1 0.990  0.2533 0.2593 0.2510 0. 2581 0. 2507  17 19 20 22  Cl K ca Ti  560.8±2.0 437. 0± 1.0 332. 7+1.5 329. 3± 1.3  1.333±0. 006 1.839±0.005 2.557±0.C14 2.590+0.012  0. 989 0.987 0. 985 0. 981  0. 2605 0.2570 0.2505 0. 2705  23 24 25 26 27  V cr Mn Fe Co  284. 5±2.0 255.3±2.0 232. 5 i 2 . 0 206. 0± 1.0 185.8±1.0  3.069±0.025 3.472±0.031 3.857±0.C37 4.4 10±0.024 4.940±0.029  0. 980 0. 978 0. 976 0. 975 0. 9 7 1  0. 2745 0.2695 0.2727 0.2675 0.2712  28 29 30 32 35  Ni Cu Zn Ge Br  156.9± 1.0 163.5H.G 159, 4 ± 1 . 0 180.0±2.0 13 3. 3± 1.0  5.932±0.041 5.676+0 .037 5.834±0.C39 5. 1 18±0.062 7.069±0.G56  0.969 0. 967 0.965 0.96 0 0.952  0. 26 18 0.2721 0. 2709 0. 28 0.2810  3 4 5 6 7 8  9  Element  6  0. 25 0.2692 0.25 0. 25 0.2778  79  Table  Element  IV-1(2)  Mean L i f e ( ns )  R e s u l t s of L i f e t i m e Measurements in This Experiment  Capture Rate (x106 /sec)  Huff Fac. (Q)  (A-Z)/2A  40 41 42 47  Zr Nb Mo Ag  110. 0 ± 1 . 0 K 9 2. 7 ± 1 .~* 99.6±1. 5 87. 0 ± 1 .5  8. 1. 0. 1.  6 6 3 ± 0 .083 0 3 6 ± 0 . 0 18 X 1 0 9 6 1 ± 0 . 0 15 X 1 0 1 0 7 ± 0 .020 X10  0. 9 4 0  0.2810  0 . 93 9 0.936 0. 9 2 5  0.2796 0. 28 10 0.2823  48 49 50 53 56  ca  9 0 . 7 ± 1. 5 84.6±1. 5 9 2. 1 + 1. 5 83.4±1. 5 96.611. 5  1. 1. 1. 1. 0.  0 6 0 ± 0 . 0 18 1 4 0 ± 0 . 021 0 4 4 ± 0 . 018 1 5 8 ± 0 . 021 9 9 4 ± 0 . 0 16  X10 X10 X10 X10 X10  0. 921 0. 9 2 0 0. 9 1 8 0.910 0.902  0.2869 0.2868 0.2867 0. 2 9 13 0.2959  60 64 66 68 74  Nd Gd  1. 2 5 0 ± 0 . G 3 3 1 . 1 8 2 ± 0 . 022 1. 2 2 9 ± 0 . C 1 8 1. 3 0 4 ± 0 . 0 2 7 1. 2 3 7 + 0 . 0 2 4  X10 X10 X10 XI 0 X10  0. 8 9 5 0. 8 8 5 0.880 0. 875 0,. 86 0  0 . 29 19 0.2964  Er W  77. 5 ± 2 . 0 81.8±1. 5 78.8±1. 1 74. 4 ± 1 .5 7 8 . 4 ± 1 .5  80 82 83  Hg Pb Bi  76.2±1. 5 72. 3 ± 1 . 1 74.2±1. 0  1. 2 7 4 ± 0 . 0 2 6 X10 1 . 3 4 5 ± 0 . 021 X10 1 . 3 1 0 ± 0 - 0 18 X 1 0  0. 8 4 8 0. 844 0. 8 4 0  0. 3 0. 3 0 2 2 0.3014  In Sn I Ba  Dy  0.2969 0.2968 0.2984  Table I V - 2 ( 1 ) Element  Z  (Zeff) 1 (1.0) 2 (1.98)  Muon L i f e t i m e s and Capture Rates  Mean L i f e ( ns )  Capture Rate (IO* /sec)  2A  651±57 x 1 0 ~ 0. 2195.6±0. 3 2194.97±0.15 467±43 x 1 0 - 6 2 198±2 He-3 2170+ 170 (-430) x10~6 0, 1667 x10~ 0. 1667 1410±140 x l O - 6 0. 25 He-4 336±75 375+30 (-300) X 1 0 - 6 X10-6 0. 25 Li-6 2173 +5 6 100± 1400 x10-6 2 175.310. 4 4678H04 2177.0±2.0 4180±450 x10~ 2194 ±4 1800±1100 X10-6 0. 2857 Li-7 2 186. 8±0. 4 2260±104 x10" X10-6 2188.3±2.0 1810±440 2140 ±20 0.2778 0.018 ±0.0 1 Ee 2156 +10 0.010 ±0.002 0.OC59±0.0O02 2169.0±1. 0 0.0074±0.0005 2 162. 1±2.0 0.0265±0.0015 0. 25 2C82 ±6 E- 10 0.0278±0. 0007 2070.7±3.0 0.02 18±0.00 16 0.2727 2102 ±6 B-11 0.0219±0.0007 2096.1±3.0 0. 044 ±0.01 0 0.25 2020 ±20 C 0.0373±0.00 11 2043 ±3 2041 G.0361±0.00 13 ±5 2040 ±30 0. 037 ±0.007 2025 ±4 0.0397±0.00 13 2035 ±8 0.0365±0.0020 2060 ±30 0.0303±0.007 0. 0376±0.0004 2030.0± 1. 6 •0.0388±0.0005 2026.3±1.5 0.0376±0.0007 0. 2692 C- 13 2029.1±3.0 O.C86 ±0.011 0.25 1860 ±20 N 0. 065 ±0.004 1927 ±13 C. 0602±0.0008 1940.5±2.8 0.06S3±0.0008 1906.8±3.0 0. 159 ±0.0 14 0.25 1640 ±30 0 C.098 ±0.003 1812 ±12 1810 ±20 0.0S8 ±G..005 1795.4±2.0 0.1026±0.0006 1844.0±4.5 C. 0880±0.00 15 0. 2778 0-18 1420 ±40 0.254 ±0.022 0. 2632 F 1450 ±200. 235 ±0.010 1458 ±13 C.231 ±0.006 1462.7±5. 0 0.229 ±0.001 F data show l i f e t i m e s f o r lower hf s t a t e s . s e c t i o n IV.D (g) ) H  6  6  3  (2^94)  6  3  6  4  (3.89)  5 (4. 81)  6 (5.72)  7 (6.61)  8 (7.49)  9  (8.32)  (These See  Ref s.  -19-28- 1417715171026* 10-26* - 1- 10-  -29* - 10* -10* - 1- 3- 4- 5-10-13- 16-29* * - 1-10-29* - 1- 10- 16* * - 1- 8-13*  Table  z  IV-2'(2)  Element  (Zeff)  10 (9.i i i )  Ne  11 (9. 95)  Na  1 2 ( 1 0 . 69) Mg  13(11. 48) ftl  14 (12. 22) S i  15(12. 90) P 16(13- 64) S 17(14. 24) C l 18(14. 89) Ar 19 (15. 53) K 2 0 ( 1 6 . 15) Ca- 40  Ca- 44 2 2 ( 1 7 . 38) T i 23 (18. 04) V  2 4 ( 1 8 . 49) Cr  2 5 ( 1 9 . 06) Mn  Muon L i f e t i m e s  and C a p t u r e  Mean L i f e ( ns )  C a p t u r e Rate (10 /sec)  1520  0.204 ±0.0 10 0. 167 ±0.030 0. 30 ±0.02 0. 235 ±0.005 C.3 67 ±0.015 0.3772±0.0014 0.507 ±0.020 0.4 80 ± 0 . 0 0 2 0.52 ±0.02 0;4641±0.0018 0.69 1 ±0.020 0. 662 ±0.003 0. 6 5 0 ± 0 , 0 1 5 0.705'4±0.00 13 0.777 ± 0 . 0 2 5 0.8 50 ±0.003 ±0.04 0.86 C.8712±0.0018 1. 054 ±0.05 1.121 ±0.005 1. 185 ± 0 . 0 0 3 1.39 ±0.09 1.3 1 ±0.03 1.352 ±0.003 1.39 ±0.09 1.333 ±0.006 1.20 ±0.08 ±0.12 1.99 1.839 ±0.005 2.55 ±0.05 2.549 ±0.063 2. 977 ±0.008 2.286 ± 0 . 0 5 0 2.557 ±0.014 1. 793 ± 0 . 0 4 0 2.63 ±0.06 ±0.04 2.60 2. 590 ±0.012 3.37 ±0,06 3.24 ±0.07 3.OS ±0.05 3. 069 ±0.025 3.24 ±0.08 3. 33 ±0.06 3.472 ±0.031 3. 67 ±0.08 3.98 ±0.05 3. 857 ±0.037  ±23  1450 ±10 1190 ±20 1204.0±2. 0 1040 ±20 107 1 ±2 102 1 ±25 1067.2±2.0 880 ±10 864 ±2 905 ±12 864. 0±1. 0 810 ±10 767 ±2 758 ±20 756.0±1.0 660 ±20 635 ±2 61 1. 2±1. 0 540 ±20 567.4±8.4 554. 7±1. 0 540 ±20 560.8±2.0 410 ±20 437.0±1„0 333 ±7 333 ±7 335.9±0. 9 365 ±8 332. 7±1. 5 445 ±8 330 ±7 327. 3±4. 5 329.3±1.3 264 ±4 27 1 ±5 282.6±3. 2 284.5±2.0 276 ±6 264.5±3.2 255.3±2. 0 239 ±4 225. 5±2. 3 232.5±2. 0  6  Rates  Ref s, 2A  0. 2522 -11- 12-22-290.2609 - 1-  *  0,2533 - 1- 4- 18-  *  0.2593 -  *  148-  0.2510 - 1- 4-180.2581 -  *  *  14-  0. 2507 - 1-180.2605 -  * *  1-  -220.2573 - 10. 25  *  - 1- 6-21-25-  *  0.2727 - 60. 2705 - 1- 18-  *  0. 2745 - 1- 5-18-  *  0.2695 - 1- 18-  *  0. 2727 - 1-18-  *  T a b l e I V - 2 (3) z (Zeff)  Element  26 (19.59) Fe  27(20jJ3)  Co  28 (20.66) N i  29 (21.12) Cu  Cu- 63 30 (21 .6 1) Zn  31 (22.02) Ga 32 (22^43) Ge 33 (22.84) as 34(23.24) Se 3 5 (23s_6 5) B r - 79 E r - 81 Er 37 (24.47) Rb 38(24.85) Sr S r - 88 39 (25.23) Y 4 0 ( 2 5 . 6 J ) Zr 41(25.9S)  Nb  42 (26.37) Mo 45(27.32) Rh 46 (27.63) Pd 47(27.95) Ag  Muon L i f e t i m e s and C a p t u r e  Mean L i f e ( ns ) 201 ±4 196 ±8 207 ±3 206.7±2.4 206.0±1.0 188 ±3 184.Oil. 7 185,. 8±1. 0 154 ±3 158 ±3 159,. 1±3. 1 156.9±1.0 160 ±4 169±6 164.0±2. 3 163, 5± 2. 4 163.5+1.0 162. 1±1. 4 161 +4 169 ±4 16 1. 2±1. 1 159,. 4±1. 0 163.0±1.6 167. 4±1. 8 180. 0±2. 0 153.8 + 1. 7 163.0±1. 2 133.7±6.5 125. 3±7.9 133, 3± 1. 0 136i,5±2. 7 130. 1+2. 3 142.0±5.5 120.2+1.4 110.8±0. 8 110.0±1.0 92. 3±1. 1 92.7±1.5 105 ±2 103.5±0.7 99.6±1.5 95.8±0.6 96.0+0.6 85 ±3 88.7±0.9 88.6±1.1 87.0±1. 5  Rates  C a p t u r e Rate (IO /sec)  JAzZl 2A  4.53  ±0.0 1  0.2675  1.38 4. 40 4.4 11 4. 89 4.96 4. 940 6. 03 5.9 5.83 5.932 5, 79 5.47 5.66 5.6 7 5.676 5.72 5. 76 5. 5 5.76 5. 834 5. 70 5.54 5. 119 6.07 5.70 7.03 7. 53 7,. 06 9 6.89 7.25 6.6 1 7.89 8, 59 8.663 10. 40 10.36 9.09 5.23 9.6 14 10.01 10. 00 11.25 10. 86 10.88 11.07  ±0.07 ±0.05 ±0.024 +0.09 ±0.05 ±0,029 ±0.14 ±0. 1 ±0.11 ±0.041 ±0*16 ±0.20 ±0.09 ±0.09 ±0.037 ±0.05 ±0.17 ±0, 1 ±0.05 ±0.039 ±0.06 ±0.06 ±0.061 ±0.0 7 ±0.05 ±0. 34 ±0.48 ±0.056 ±0.13 ±0.14 ±0. 27 ±0.11 ±0.07 ±0.083 ±0.14 ±0. 17 ±0.18 ±0.07 ±0. 15 ±0.07 ±0.07 ±0.5 ±0. 13 ±0. 14 ±0.20  6  0.2712 0. 2618  0.2721  0.2698 0.2709  0.2779 0. 28 0. 28 0. 2850 0.2785 0. 2840 0.2810 0. 2838 0.2834 0.2841 0.2809 0.2810 0.2796 0.2810 0. 28 16 0.2841 0. 2823  Ref s,  12518-  -* 5-- 18*  1- 5- *181- 8- 9-- 18-  *  - 18-  1- 5- *18-  - 18-  - *18- 1818- 20-- 20*  - 1818- 18- 9- 18-* - *9-  118-  -*  - 18-  - 181- 9- 18-*  Table  z  Element  (Zeff)  48(28.20)  Cd  4 9 (28^4 2) In 50 (28.64) Sn 51 (28.79) Sb 52 (29.03) l e 53 (29^27) I 55 (29.75) Cs 56 (29,9 9) Ea 57 58 59 60  IV-2(4)  (30.22) (30.36) (30.53) (30.69)  La Ce Pr Nd °  62 (3-1.0 1) Sm 64 (31. 34) Gd 65 (31 .48) 66 (31.62) 67(31.76) 68 (31.90) 72 (32.47) 73 (32.6 1) 74 (32.76)  Tb Dy Ho Er Hf Ta W  79 (33.64) au 80 (33.8 1) Hg 81 (34.2 1) T l 82 (34. 18) Pb  RPbi  Muon L i f e t i m e s and C a p t u r e  Mean L i f e ( ns ) 95 ±5 90.5±0. 8 90.7±1. 5 84.8±0.8 84.6±1. 5 92 ±3 89,9±1.0 92. 1±1. 5 91.7±1. 1 105.5±1. 2 86. 1±0.7 83.4±1.5 87.8±1. 9 94.5±0.7 96.6±1.5 89.9±0.7 84.4±0.7 72. 1 + 0. 6 78,5±0.8 77.5±2.0 79.2±1.0 80.1+1.0 8 1.8±1. 5 76.2+0.7 78.8 + 1. 1 74.9±0.6 74.4±1.5 74.5± 1. 3 75. 5±0. 6 81 ±2 72 ±3 74.3+1.2 78. 4±1. 5 75.6±0. 5 76.2± 1.5 76. 2±1. 5 75 +4 70.3±0.9 82 ±5 67 ±3 74.9±0. 4 73.2±1.2 72.311. 1 71.510.4  Rates  Capture Rate ( I O /sec)  Jlzzi 2a  10.05 ±0. 5 10. 63 ±0. 11 10. 61 ±0.18 1 1.37 10. 13 11.40 ±0.21 10. 5 10.4 10.70 ±0. 14 10.44 10.18 10. 19 ±0.14 9. 06 10. 11 1 1. 20 ±0. 1 1 11. 58 ±0.22 10. S8 ±0.25 10. 18 ±0. 1 0 9.94 1±0.16 10.71 ±0. 10 11. 44 ±0. 11 13.45 ±0. 13 12. 32 ±0. 14 12.50 ±0.33 12.22 ±0. 17 12. 09 ±0. 16 11.82 ±0.22 12.73 ±0, 13 12. 29 ±0. 18 12. 95 ±0. 13 13. 04 ±0. 27 13. 03 ±0,2 1 12. 86 ±0. 13 11.9 ±0.3 13. 5 ±0.6 13.07 ±0.21 12.36 ±0.24 13.39 ±0. 1 1 12.74 ±0.26 12.74 ±0.26 12. 90 ±0.75 13. 83 ±0. 20 11.70 ±0.75 14. 50 ±0.7 12. 98 ±0. 10 13.27 ±0.22 13.45 ±0,21 13.61 ±0. 10  0.2869 -  6  Ref s  0.2868 0.2867 -  * * *  19959-  0.2907 - 90. 2964 -180.29 13 - 9-  *  0. 2932 0.2959 0.2950 0.2928 0. 2908 0.2919  -  0. 2937 0.2964 0,2956 0.2969 0.2970 0.2968 0. 2982 0.2983 0.2984  -  *  * * *  999999999-  - 9-  *  - 18- 9- 1- 5-18-  *  0. 2995 - 90. 3 - 18-  *  0.3019 - 1- 90. 3022 - 1- 5- 9-18-  *  -  9-  Table IV-2(5) z (Zeff)  Element  83 ( 3 4 . 0 )  Bi  9 0 (34.J3)  Th-232  9 2 ( 3 4 . 94)  0 -235  Mean L i f e ( ns )  Np Pu-239 Pu-242  and C a p t u r e R a t e s  Capture Rate (106 /sec)  79 +5 73.3 + 0.4 74.2±1.0 80.4±2. 0 79. 2±2. 0 78 ±4 75.4±1. 9 88 ±4 8 1 . 5 + 2. 0 73.5±2. 0 71.3±0. 9 77.5±2. 0 73.4+2.8 70.1±0.7 75.4±0. 9  0 -238 93 ( 3 5 . 0 5 ) 9 4 (35.J6)  Muon L i f e t i m e s  12.20 +0.75 1 3 . 2 6 ± 0 , . 10 13.10 ± 0 . 1 8 12.1 ±0.3 12.2 ±0.3 (12,4 ± 0 . 6 ) 12.9 ± 0 . 3 10.9 ± 0 . 5 (11.9 ± 0 . 3 ) 13.2 ± 0 . 4 (13.6 ± 0 . 2 ) (12.5 ± 0 . 3 ) 13.3 ± 0 . 4 (13.9 ±0.2) (12.9 ± 0 . 2 )  R e f s, 2A 0.3014 0.3061  -  *  19-  -23-240. 3043 - 2 3 0.3043 - 2 4 0.3068 1-23-240.3038 -270.3033 - 2 3 -24-270. 3058 - 2 7 -  References: (SEN59) ,  - 2-  (BAR59) ,  - 3-  (REI60) ,  - 4-  (LAT6 1) ,  - 5-  (BLA62) ,  - 6-  (CRA62) ,  -  (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) ,  -29Note:  (MAE80)  -  1-  7-  *: D e n o t e s t h e r e s u l t s o f t h i s e x p e r i m e n t . ( Z e f f ) with u n d e r l i n e s are e s t i m a t e d v a l u e s . ( ) : Numbers a r e n e t g i v e n i n r e f e r e n c e s and e s t i m a t e d capture rates cr l i f e t i m e s . 1) RPb = r a d i o g e n i c  lead  (88%Pb-206,9%Pb-207,3%Pb-208)  from  85  IV.A  P o s i t i v e Muon L i f e t i m e i n Carbon  In t h i s experiment the p o s i t i v e 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 t a k i n g system, s i n c e the l i f e t i m e has been measured p r e c i s e l y a t s e v e r a l l a b o r a t o r i e s as shown i n Table I V - 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 P a r t i c l e P r o p e r t i e s (KEL80).  Before  I960,  there was d i f f i c u l t y i n the d e t e c t i o n of microsecond  time  i n t e r v a l s , because a delayed c o i n c i d e n c e or a time t o pulse height converter distributicns.  (TAC) was employed to determine Swanson  time  (SWA60) pointed out t h a t there was a  n o n - l i n e a r i t y c f 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 o f 0.6%  i n the IAC.  high freguency  After  1960, a d i g i t a l technigue with a  o s c i l l a t o r became common and was able to  reduce the systematic e r r o r i n the t i m i n g of the i n t e r v a l s . However, i t was pointed out by Lundy still  (LUN62) t h a t there was  a s y s t e m a t i c e r r o r due to the time dependent  background caused  by 2nd muons.  As shown i n Table I V - 3 , an  a c c u r a t e measurement was done by E a l a d i n e t a l . (BAL74) by using a p o s i t r o n d e t e c t o r with a 4  ir r a d i a n s o l i d angle. .  In t h i s experiment, as d i s c u s s e d i n Chapter I I I , the s y s t e m a t i c e r r o r s have been s t u d i e d c a r e f u l l y by checking  the event r e j e c t i o n e f f e c t s , the stopping muon r a t e  e f f e c t , and the magnetic f i e l d e f f e c t . concluded  I t has been  that the systematic e r r o r i n the p o s i t i v e muon  Table IV-3  A u t h e r and  P a s t P o s i t i v e Muon  Eefs.  Lifetimes  Year  Eesult  ( ns )  al.  (BEL51)  1951  2220 ± 20  E.W.Swanscn e t a l .  (SWA 59)  1959  2261 ± 7  J.Fisher  et a l .  (FIS59)  1959  2200 + 15  J.C.Sens  eta l .  (SEN59)  1959  2210 ± 20  e t a l . . (BEI60)  1960  2211 ± 3  J.L.Lathrcp eta l .  (LAT6 1)  1961  2203 + 2  E.A.Lundy  et a l .  (LUN62)  1962  2203 ± 4  S.L.Meyer  eta l .  (MEY63)  1963  2198 ±  (ECK63)  1963  2202 ± 4  (EAE64)  1964  2 197 ± ' 2  E . W . W i l l i a m s e t a l . (WIL72)  1972  2200.26 i  J.Duclos eta l .  (DUC73)  1973  2197.3 ±  M . P . B a l a n d i n e t a l .(EAL74)  1974  2 197. 1 11 ± 0.08  (BAE78)  1978  2196. 8 + 0. 4  (EAE79)  1979  2197. OSI ± 0. 14  (SUZ80)  1S79  2 197.0 + 0.7  E ATA Group (KEL80)  1980  2 197. 120± 0.077  W.E.Bell e t .  E.A.Eeiter  M.Eckhause J.Barlow  G.Eardin  eta l .  eta l .  et a l . .  TEIUMF  Particle  Decay  rate  0.455141  ± 0.000016  2  ±  0.81 0.4  x10* s~»  87  lifetime  is  in  III-1  Table  negligible. and  the  is  in  good  This coupling  interaction,  result  Soos  of  positive  10  muon  runs  are  lifetime  ± 0 . 7  agreement  constant,  lifetimes  average  T>( + ) =2 1 9 7 . 0 which  The  with  and  for  is ( 4 . 1)  c a n be  Gm,  listed  the  applied  a muon  Sirlin  accepted in  calculating  decay.  (RO07 1)  value.  Assuming  derived  the  the V-A  following  relation  (Gm)2  192 • ( TT ) 3 • T(+)  =  Gm  =  1 . 4 3 5 6 (7)  where  Shrock  formula  erg«cm3  3.8614x10-ii  cm  -ft  =  1.0545x10~27  erg«sec  d  = 0.00422  T (+)  =  for  rate  10-*»  =  Gm. =  have  number  1 . 4 3 5 8 2 (4)  defined Rd(+)  =  muon by  x  et  lifetime equation  (4.551  Gm w i t h  a l . (BA174)  for  10-*«  correction,R0071)  ns  determined  Balandin  Their  the  (radiative  219 7 . 0 ( 1 . 0 )  (SHE78) by  d)  8 « (Me/Mm) 2 )  -fa/ ( M e » c )  For decay  x  -  (CR072)  Wang  +  (4.2) (1  = 2 0 6 . 7 6 8 2 (5)  obtained  Gm  tiz»c«(1  • (Mm»Me*c) s :  Mm/Me  and  lifetime  (He«n")s  Gm  and  the  precise  their  new  is  erg»cm3 given (4.2)  ± 0.002) x10s  by  ( 4 . 1) ,  the  muon  is /sec  (4.3)  88  IV.B  Muon  as rate and  Capture  Bate  and i t s accuracy  discussed i n section I . C ,  i s n e t t h e same the r e l a t i o n  Bd (-)  as the free  between  The b o u n d  positive  t h e two r a t e s  muon  mucn d e c a y  decay rata  i s written as  = Q (Z) « B d ( + ) = Q(Z)/T( +)  where for  Q (Z)  i s called  t h e bound  a bound The  muon  theory  (BLA62-2, bound  muon  effect  result  heavy  factor  elements  =  with  Oberall  h a s been  obtained  measurements  a simple  the K crbit thus  for a point  form  the effective  charge.  Hence  t h e bound  Calculations  by H u f f  In  Huff's  much  formula  i n t h e heavy  and U b e r a l l were  atom  charge,  becomes  Uberall's  effect  values  nucleus.  of the mesonic  the  werk  rate.  ( 4 . 5)  f e r t h e mucn c a p t u r e ,  this  decay  that  c a l c u l a t e d t h e muon  He o b t a i n e d  responsible  overestimates  predicts  subsequent  (OBE60)  theory  1 - 0 . 5 (Z/137) 2  the n u c l e u s ,  nuclear  Huff's  has a reduced  agreement  Also,  (Huf60).  i n t h e mescnic atoms  i n the nucleus.  elements,  inside  decay  i s i n gcod  Q (Z)  This  a Huff  i n heavy  YAM74).  (4.4)  a r e shown employed  i s  For formed  which i s smaller  than  (4.6) nuclei.  i n figure  and l i s t e d  IV-1. in  Table  89  T  ATOMIC Figure  IV-1,  NUMBER(Z)  R a t i o of bound decay r a t e to f r e e decay r a t e .  90  IV-].  In muon capture experiment, disappearance  the t o t a l  r a t e , the n u c l e a r capture r a t e , and the decay  rate, a r e f r e g u e n t l y  used.  F o r reasons  of convenience,  those  r e l a t i o n s are summarized i n the f o l l o w i n g .  Decay r a t e of f r e e muons; Rd (+) =1/T ( + ) , T(+): Total  p o s i t i v e or negative f r e e muon l i f e t i m e < 2 1 9 7 . 0 ns)  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 Nuclear capture r a t e  + Rd {-)  ; Rc=Rt - Rd(-) = 1/T(-) - Q(Z)/T( + )  ( 4 . 6 )  When the n u c l e a r capture r a t e i s obtained from l i f e t i m e measurements, eguation T (-) ; l i s t e d T (+) ;  ( 4 . 6 ) i s used.  i n Tables I V - 1 and I V - 2  2 1 S 7 . 0 ± 0 . 7  ns (our measurement)  Q (Z) ; f i g u r e I V - 1 , Huff  The  factor  accuracy of the t o t a l disappearance  rate i s  d e f i n e d by  dRt/fit = 1/-/(Ne)  where Ne i s the t o t a l number of e l e c t r o n e v e n t s .  ( 4 . 7 )  From  91  equation the  (4.6),  the capture  approximation  expressed  For  c f Q(Z) = 1.  Ec i s e q u a l t o  The a c c u r a c y  of  R-Ed  with  Ec i s  as  dEc  1  Ec-  Rev  example,  approximate lifetime  rate  / Et2  E d 2  Ne-  Ne +  i n the case of numbers  6  L i ,  and eguations  we h a v e for  the  following  a 0.1% a c c u r a c y  of  measurement  T <-) = 2 1 7 5 . 0 ± 2 . C Et =Ed=4.5x10  5  (0.1%)  /sec  Ec=5000 / s e c Ne~=Ne+=4x106  events  dRc/Ec=Ed/Rc«A/(2/Ne)  Thus heavy less Ec  the accuracy elements than  Ne+.  c f Rc i n  (Z>20) ,  L i i s about  Rc i s g r e a t e r  Therefore,  i s . approximated  6  (4.9)  6 %.  than  the accuracy of  In the case  Rd a n d N e - i s the capture  events,  gives  a 1 % accuracy  which i s e q u i v a l e n t  measurement  rate  (4.10)  /  (4.10)  much  by  d E c / B c = ]/ J(He-)  Equation  of  i n a lead  to a  target.  o f Ec f o r  1% a c c u r a c y  Ne-=10*  total  in a lifetime  92  IV.C  Negative and  The throughout the  System  lifetime  this  from  separate  runs  determined the  assures  Carbon  IV-4,  The w e i g h t e d  of  along  IV-1.  seven  with  average  frcm  t h e mean.  i n the t a b l e ,  the system  are guite  was w o r k i n g  a  i s  of each  of  i n the  small  properly  result  of the  The e r r o r  The c h a n g e s  times  was u s e d a s  t h e s t a t i s t i c s and t h e d e v i a t i o n s  a s shown  that  The r e s u l t s  i n Table  1979.  runs  in  several  since the l i f e t i m e  the system.  of  was m e a s u r e d  i s recorded i n Table  frcm  different  lifetime,  i n carbon  are l i s t e d  the spring  Measurements  Calibration  experiment,  c a l i b r a t i o n of  measurements  Mucin L i f e t i m e  and i t  throughout  this  experiment. As l i s t e d three  precise  Lathrop  et  i n Table  measurements  a l . , and E e i t e r  IV-2,  for  1 2  around  C  by E c k h a u s e  et a l . .  of the p o s i t i v e  1960, there et a l . ,  measurements  the  lifetime  are  2 2 0 2 + 4 n s , 2 2 0 3 ± 2 n s a n d 2 2 1 1 ±3 n s , r e s p e c t i v e l y ,  all  disagree  with  the presently  0.08  ns.  It  and,  from  the point  negative be m o r e system to  seems t h e i r  muon  with  which  be 2197.18  cf  lifetime  reliable.  muon,  Their  systems  view  ± 0 . 1 2 ns  were  of system  i n carbon  The S a c l a y they  as shewn  accepted  group  determined (DUC80,  would  i n Table  value  not w e l l  of  for  IV-3, which  2197.13  ±  calibrated  c a l i b r a t i o n , our appear  has a w e l l  the p o s i t i v e  BAE79).  are  Their  therefore  to  calibrated muon value  lifetime f o r the  Table  IV-4  Run #  1979  SEEING  1979  FALL  Negative  Events ( x10*  )  Muon  lifetimes in  Carbon  Lifetime ( ns )  1.6  2026.5  ± 1.6  1178  1.0  2026.0  +  1 197  0.9  2025. 2 + 2.2  1259  0.6  2026. 1 ± 2.7  1264  0.5  2025. 3 + 2.9  1272  0.8  2023.5  1275  0.5  2026, 3 + 2.9  1291  0.6  2030.3  ± 2.7  Total  6.5  2026.3  ±  2. 1  ± 2.3  1.5  94  negative mucn l i f e 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 i n adequate agreement  with Eckhause's r e s u l t  of 2025±4 ns and the  f i n d i n q of the Saclay group, but disagrees with the two r e s u l t s of 2043±3 ns by R e i t e r and 204 1±5 ns by Lathrop. Although i f one s u b t r a c t s o f f 14 ns and 6 ns muon l i f e t i m e d e v i a t i o n from the accepted  (their  value),  r e s p e c t i v e l y , the agreement i s b e t t e r , but t h i s minded  positive  simple  procedure i s not n e c e s s a r i l y v a l i d because almost  c e r t a i n l y there would have been d i f f e r e n t s y s t e m a t i c  errors.  Within e r r o r , our capture r a t e b a r e l y o v e r l a p s with past measurements  as shown i n Table IV-2.  The c a l c u l a t i o n by Walecka r a t e of 0.35x10  (WAL75) gave a capture  /sec which i s lower than our r e s u l t  s  (0.388±0.005) x10s by 6%.  IV.D  Negative Muon L i f e t i m e  Measurements  i n 48 Elements  (a) Lithium  (6Li  7  and  The f i r s t  Li)  measurement was made by Eckhause et  a l . (ECK63) but t h e i r r e s u l t s had l a r g e errors.„ Furthermore, their result  f o r L i was i n c o n s i s t e n t with the t h e o r e t i c a l 6  estimate by Lodder and Jcnker  (LOD67), which i n d i c a t e d  f u r t h e r experiments would be u s e f u l .  that  Recently, c o n s i d e r a b l y  g r e a t e r p r e c i s i o n 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  experimental  capture r a t e s i s g i v e n i n Table I V - 5 ( 1 ) .  shown i n T a b l e I I I - 2 , background. carbon Our  As  c u r d a t a depend on t h e c a r b o n  A c c o r d i n g t o t h e c a r t o n b a c k g r o u n d r u n , a 1.0 %  background i s allowed  results,  i n the r e s u l t s  without the carbon  Saclay's r e s u l t s , The  background, agree w e l l  which a r e f r e e from t h e c a r b o n  capture  average capture  of Table I V - 5 .  rate.  rate,  hyperfine states according  background.  shown i n T a b l e I V - 5 ,  At f i r s t negative  with  i s an  muons p o p u l a t e t h e  to a s t a t i s t i c a l  distribution.  Then t h e r e i s a c h a n g e i n t h e p o p u l a t i o n due t o t h e transition  between t h e h y p e r f i n e s t a t e s .  For lithium,  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 experiment, /sec  t h a t t h e c o n v e r s i o n r a t e was l e s s t h a n  o f which t h e c o n v e r s i o n  microseconds. experiment  was l o n g e r t h a n 50  I n order to e x p l a i n t h e p a r t i a l capture  cf L i 6  (PRI77) and Hwan hyperfine  time  2x10*  6  He (g. s. )  (=1600 / s e c )  rate  (DEU68) , P r i m a k o f f  (HWA78) added a 16 % e f f e c t f r o m t h 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  rate.  S i n c e t h e c c n v e r s i c n r a t e i s v e r y s m a l l and t h e t r a n s i t i o n occurs  w i t h i n m i l l i seconds, our experiment,  events  a p p e a r w i t h i n 25 m i c r o s e c o n d s ,  find  the hyperfine The  valid  simple formula  between  6  o f P r i m a k o f f , w h i c h w i l l be  has a neutron  frcm t h e P a u l i p r i n c i p l e  f o r Z>6. L i and  i s not adequate t o  transitions.  shown i n t h e n e x t C h a p t e r , originates  i n which a l l  excess  term. . This  and i s c l a i m e d t o be  The d i f f e r e n c e o f t h e t o t a l c a p t u r e 7  L i i s mainly  due t o t h e a l l o w e d  rate  transition  96  Table IV-5(1)  Capture Rates i n L i - 6 and L i - 7  Li-6  (LOD67)  Theory  (/sec)  Li-7  (/sec)  Ec (7) /Be (6)  3480  2080  0. 60  6100±1400  1800± 1 100  0.30±0- 19  468C±120  2260±120  0.48±0.03  4 180±450  18 10±440  0. 43±0. 11  Experiment Eckhause (ECK63) Saclay  (EAE78)  TEIUMF  Table IV-5 (2)  The D i f f e r e n t C o n t r i b u t i o n t o the T o t a l Muon Capture Bate by Lodder and Jonker (L0D67) (unit i n /sec)  Isotope  Allowed  Li-6  1248  Li-7  Dipole  Other Belativistic M u l t i p o l e Term  Ec (Total)  1263 (1044)  621  348  3480 (3261)  1 182  620  281  2083 (±12%)  97  in  6  L i according t o Lodder's c a l c u l a t i o n  l a b l e IV-5(2).  (LOD67) as shown i n  The neutron excess term i n P r i m a k o f f s  formula p r e d i c t s the i s o t o p e e f f e c t , Ec(7)/Rc(6) =0.48, which i s c l o s e t o our measurement, Be (7)/Be (6) =0,.43±0. 02.  <fc) B e r y l l i u m There have teen three measurements of the n e g a t i v e muon l i f e t i m e i n Be by Sens  (SEN58) , Eckhause e t a l . (ECK63),  and Martino et a l . (MAB80), who o b t a i n e d l i f e t i m e s of 2140±20 ns, 2 156±10 ns, and 2169.Otl.O  ns, r e s p e c t i v e l y .  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 r e s u l t  from Martino and Duclos i s l o n g e r than ours by 7 ns.. T h i s disagreement can not tie explained with the h y p e r f i n e Since Be has a n e g a t i v e magnetic  effect.  moment as shown i n Table  IV-6, the h y p e r f i n e s t a t e with F =I+1/2 i s lower i n energy +  than the hyperfine s t a t e with F =I-1/2.. In the l i f e t i m e -  measurements at S a c l a y , the d e t e c t i o n of the decay e l e c t r o n s s t a r t e d a few microseconds a f t e r the muons stopped, so t h e i r experiment  may have detected decay e l e c t r o n s from the lower  hyperfine l e v e l T  +  (F+). From Table IV-6, i t i s evident t h a t  (lifetime i n F  state).  +  state) i s l o n g e r than T  -  ( l i f e t i m e i n F~  Since our experiment s t a r t e d t a k i n g data d i r e c t l y  a f t e r muons stepped i n a t a r g e t , we were measuring the mean l i f e t i m e , Tmean.  However, the h y p e r f i n e t r a n s i t i o n time has  been determined e x p e r i m e n t a l l y t e be longer than 20 microseconds by Favart e t al.(FAV70) , so t h a t , within a few  98  microseconds, the h y p e r f i n e Assuming  that  data t a k i n g the  the t r a n s i t i o n  starts  hyperfine  lifetime longer right  measured  t i m e i s 20 m i c r o s e c o n d s and t h e  would  be l e s s  by t h e S a c l a y  No t h e o r e t i c a l  Eoron  This  with  their  result  calculation  good  ("B  in  1 0  i s shorter  t h e 7 nsec  h a s been made f o r  and M B )  B  and  within than  1 1  B.  Our r e s u l t  error;  their  measured  a s shown  in  i n the case  result  l l  the negative B  agrees  of ° B o u r 1  by two s t a n d a r d  The c a p t u r e r a t e s and i s o t o p e  agreement  i s i n the  i n Be.  result  deviations.  be a b o u t 2 n s e c  correction  E c k h a u s e e t a l . (ECK63) have muon l i f e t i m e s  stop,  20%, and t h e  but i n s u f f i c i e n t t o e x p l a i n  muon c a p t u r e  (c)  than  t h e muon  group s h o u l d  t h a n t h e mean l i f e t i m e . direction  would n o t be l a r g e .  at 4 microseconds a f t e r  effect  discrepancy. the  effect  effects  are i n  below.  i«B  H B  Rc(11)/Rc(10)  Eckhause  life cap  2082±6 n s 25,800±1500 / s e c  2 1 0 2 ± 6 ns 2 1 , 2 0 0 ± 1 5 0 0 / s e c 0.82±0.08  TBIUMF  life cap  207C.7±2.0 ns 27,760±490 /sec  2 0 9 6 . 1 ± 2 . 0 ns 21,910±480 / s e c 0.79±0.02  T h e r e i s no t h e o r e t i c a l  calculation  which c a n be compared  99  with  the t o t a l  (d)  Carbon Tlie  IV.C. such  muon c a p t u r e  (*2C  of  Our measurement  difference effect  1 2  C  i n Table  between  i s egual  C  l 2  to  theory  which  implemented  expected  isotope  ratio  i s equal  capture states et  rates with  f o r l i m i t e d numbers  a l . (DES78) ,  agrees  approach  by s e v e r a l  succeeded  the  results  rate  authors  in reproducing  c a n be u t i l i z e d  isotope  and C,  except  C  result.  i s no  and t h e From  been  principle,  the  i s not  The t o t a l  reported  muon  between  by  Desgrolard  and i m p u l s e  between  (LOY63,  isotope  the  of t r a n s i t i o n s  Although  1 2  C  that and  l 3  there C  the s h e l l  G0U71,  JOS72,  qualitatively  i s no  and t h i s  f  model DUP75)  the a c t u a l experimental  has  values,  i n discussing  isotopes  of L i ,  B,  the  Q values  of  and,  l 2  C  may b e o n e o f  C  reasons  been  observed  structures,  and 0 have 1 3  have  The d i f f e r e n c e  for level  The  values  l 3  the Pauli  model  effects  and 0 i n c u r e x p e r i m e n t .  nuclei  and  there  first  rates. Strong  B,  IV-1,  calculations indicate  our experiments.  not  capture  Their  i n the capture  with  have  using the s h e l l  approximation. difference  parity  i n * 3 C i s the  to 0.7 1 which  our experimental  t h e same  discussed in section  0.97±0.03.  Primakoff  with  °B and " B .  of the l i f e t i m e  in lifetimes  compatible  1  has been  As l i s t e d  Be ( 1 3 ) / E c (12)  in  and i ^ C )  lifetime  measurement.  rates  different  a r e t h e same. f o r t h e same  for  Li,  between  these  i s the Q  value.  Q values, These  muon  but  same Q  capture  rate  100  in  and  12c  i 3  (e)  Nitrogen The  with  great  does  not  IV-2,  muon  lifetime  precision in  agree  but  our  Eckhause. 1a )  (FUJ79) •  C  with  higher  value  than  our  rate cf  our  the  microseconds  target,  it  possible that  than and  transition.  ours,  because  muon  lifetime  shorter  than  in  had  shorter we h a d which  water  than  varied to  generally  is  model  Using  1905ns  to  significantly  the  muon  functions.  1.09x10s  /sec,  There  no  exceeds  other  muon  lifetimes  as  in  a target.  behavior  The  calculated total  the  experimental value.  shorter  their  target  be (NH^Cl),  nitrogen, we  We b e l i e v e  of  of  using  the  by  been  shell  capture  results  that  the  c a l c u l a t i o n has  (KIS73),  the  is  would  in  by  moment  state  r e l i a b l e because  N  the  be  Consequently,  k theoretical  theoretical  in  c h e m i c a l compounds  more  capture  taking  magnetic  If  of  (nearly  should  lifetime  1925ns.  nitrogen  value  affected  state.  the  the  stopped  hyperfine  hyperfine  determining  equipment.  find  wave  is  lower  Table  1.8%  is  result  c o n s i s t e n t and r e a s o n a b l e  electronic to  from  result  result  in  data  a positive  contamination, also.  with is  measured  lifetime  shown  muons  their  has  the  higher  use l i q u i d  result  made  ours  difficulty  decided our  the  in  as  their  tie  their  so,  Our  group  Since  after  nitrogen  the  (NHi+I)  If  has been  overlaps  Saclay  result.  a few  hyperfine  results,  just  started  is  nitrogen  experiment.  previous  capture  The  in  rate, 70  %.  10 1  (f)  Oxygen As  muon  (i60  shown  lifetime  in  a considerably  for  1 6  (water  measurements, the by  previous Walecka  His  which  is  0.  1 8  of  1 6  C  c l o s e to is  the  target  in  the  above  calculation.  is  0.80+0.01.  equal  ratio It  of  seems  structure both  0.60, that are  i 2 c - i 3  (g)  this  to  C  in  light  more a D C  i  by  the  0  - i 8  The  isotope is  quite  0  the  result result  error  limits was  resonance 1.07x10s  of  in  the  model.  /sec,  muon  Agar,  the  There effect  1 6  0  lifetime carbon  is  the  no  E c ( 1 8 ) / R c (16) from  Primakoff"s  details  of  lifetime  different  since this  /sec.  measurement  fixed  of  made  1 . 0 1 8 ± 0 . 0 0 5 x105  target.  elements  cf  formula.  the  formula  the  nuclear  fails  for  .  Fluorine hf  effect  nucleus,  as  demonstrated  (3.12).  the  c a l c u l a t e d by  The  histogram  of  is  lifetime  using  important,  i 6  0  1 6  was f o r m e d  This  which i s  large  measurement  water  theoretical  in  result  form  the  the  our  the  recent  Foldy-Walecka  rate  target  from  although two  of  Our  A t h e o r e t i c a l attempt  first  same  measurements  previously.  than  within  our  was d e t e r m i n e d  made  lower  fall  three  accuracy.  using the  Since t h i s  obtained  is  muon c a p t u r e  guite  background  been  measurements.  Ours in  dees  (WAL75)  result  IV-2,  improved  target) it  *80)  Table  * 6 0 have  has  0  in  and  cf The  decay data  cf  muon  capture  by  e l e c t r o n s has analyses  of  the  Winston been  c a n be  expected  (WIN63);  hence  fitted  to  equation  histograms  of  four  in the  102  c h e m i c a l compounds g i v e the mean l i v e s disappearance results  rates  (R~) o f t h e l o w e r  ( l — ) and t h e hf s t a t e s .  The  are l i s t e d i n the f o l l o w i n g  Compound  T~ ( ns )  R(x10 /sec)  • Rc~=R—Rd (x10 /sec)  6  s  LiF C2F4 CaF2 PbF2  1464. 7±4.0 1458. 8 ± 4 . 0 1463. 2±5. 0 1464.2 + 6. 0  0. 6 8 3 ± 0 . 002 0.686±0.002 0. 6 8 3 ± 0 . 0 0 2 0. 683±0.003  0. 2 2 8 ± 0 . 0 0 2 0. 2 3 0 ± 0 . 0 0 2 0. 2 2 8 ± 0 . 0 0 3 0. 228±0.003  Average  1462. 7±5. 0  0. 6 8 4 ± 0 . 002  0.229±0.003  As  discussed i n section  the  hf t r a n s i t i o n  see  this  data  effect  effect  clearly  points within  .have b e t t e r  than  (Ae) i s a b o u t  1 % statistics. o  t h e mucn  effect  decay  study.  than  (WIN6 3) whose h i s t o g r a m  ours  (=200 ns) must  has 8000 e l e c t r o n  events  f o r the hf  r e s u l t s are  Eh= (8. 8 ± 4 . 0) x10* / s e c , . Winston  histogram, the  I n our F d a t a l i s t e d  i n F a t t=0, can be used  The f i t t i n g  In order t o  of the t r a n s i t i o n  a b o v e , o n l y t h e L i F d a t a , which from  0.015.  i n a decaj electron  t h e time  a  I I I . G , the amplitude of  Ae = 0. 0 1 7±0. 0 10 had f i v e  times  (4.11) more  events  obtained  Eh= (6.3± 1. 8) x 10* / s e c , ( from  electron  data )  Eh= (5. 8±0. 8) x 106 / s e c , ( from  neutral  Ae=0. 026±0. 0 07  data )  An=0. 30 ±0.02  (4. 12)  103  Although  cur results  results  (4. 12),  determine  our data  t h e hf e f f e c t The  from  (4.11)  capture  the following  E"(I-1/2)  -  does n o t have terms.  rates  relations  B + ( I + 1/2)  Eav  a r e i n agreement  with  enough  Winston's  statistics  to  Eh a n d A e .  of the hf doublet (BEB58,  are estimated  PB.I59)  1 (• (2I+1)/I = 0. 9 4 5 » - « K Z I - ( 2 I + 1 ) / ( I + 1)  :I=L+1/2 :I=L-1/2 ( 4 . 13)  where  the definitions  section  III.G*  Bernstein, BLYP  Since  (Bevalue  0.77±0.13. (3.14)  Bc +) / ( B c ) a v  was d e t e r m i n e d Osing  these  and ( 3 . 1 5 ) ,  summarized  as  and Eav have (4.13)  and P r i m a k o f f ,  In the case -  E-  eguation  L e e , Yang,  estimate.  This  cf B+,  c f F,  1=1/2  Our  named t h e  so  that  = 0.42  (4.14)  experimentally  two v a l u e s  by W i n s t o n  and e g u a t i o n s  our r e s u l t s and Winston's  t o be  (3.13),  results are  )  2. 3 1 ± 0 . 0 6  (electron)  2.29+0.02  Tmean (ns)  Ec+ ( u p p e r ) (x10 /sec) s  1584± 1 1 1663±20 1590±5 1667±20  1. 5 7 ± 0 . 0 4 i 1. 1 8 ± 0 . 0 9 2 1 .56±0.02i 1. 1 7 ± 0 . 0 9 2  0 . 4 2 from e q u a t i o n (4.13) (BLYP e s t i m a t e ) 0 . 7 7 ± 0 . 1 3 , Winston's experimental value  results  Table hf  by  i s often  and Z=9,  in  follows  Winston (neutral  1, 2,  given  was d e r i v e d this  B e - (lower) (xlOs / s e c )  TBIUMF  been  agree  with  I V - 2 , the past  state  Winston's  measurements  a r e l i s t e d . . Our r e s u l t  neutron of  a n d gamma d a t a .  lifetimes  shows  In  of the lower  agreement  with the  104  other  measurements.  (h)  Search  f o r the hf N,  i3C,  In nuclei  with  estimates  Table a spin  transitions  N Na Cl  As  the  According  rates  effect  our data  were  and a r e l i s t e d  at  s  order  to  spectrum, even  small  -)  the spectrum  or  the  hf  be o b s e r v e d  Amp*  (F A V 7 0) (FAV70) (FAV70) fit fit (KIN63) (KIN63)  i n our (3.12).  of the  at  t=0  5000 3500 3500 2000 4000 3000 2000  (3.6)  for various of  transition  nuclei,  the n u c l e i .  i n t h e decay  has t o have  f o r the n u c l e i which  experimental  0.01 or less,.  clearly  for  theoretical  tc equation  Eef .  the hf  f o r most  see the e f f e c t  B, »»B,  states  any i n d i c a t i o n  t=0 i n e g u a t i o n  Ae i s e s t i m a t e d  Ae i s v e r y  1 0  below.  0.05 fixed 0.2 fixed 0.33 f i x e d (0. 2±0.2) ( 1 . 2 ± 1 . 5) 14 fixed 8 fixed  t o be a r o u n d  could  fitted  do n o t show  Eh (106  i s expected which  (WIN63)  i t i s possible that  discussed i n section III.G,  that  t=0  to  obtained  Amplitude  (Ae) in  is listed.  0.006±0.002 0.001±0.002 0.001±0.003 0.01 ± 0 . 0 1 0. 0 0 8 ± 0 . 0 1 0.01 ±0.02 0.01 ±0.02  H B  1)  hf  Ae  Element Be log  of  (FAV70),  Thus  results  hyperfine  I V - 6 , the information  of n u c l e i l i s t e d above  experiment.  in Be, ,  and C l .  of the conversion  determinations  The  Na,  transitions  more  than  seem t c be g o o d  coefficient  From i t  Table  i s  IV-6  evident  Thus,  in  electron 104  events  candidates  at for  105  Table IV-6(1)  Element  S p i n Moment  I i (3,6) L i (3,7) Be (4,9) B(5,10) B<5, 11)  1+ 3/23/23+ 3/2-  C(6,13) N(7,14) F ( 9 , 19)  1/2- 0.70 0.40 1+ 1/2 + 2. 63  0.82 3.26 - 1 . 18 1.80 2. 69  Na (11, 23) 3/2 + 2. 22 A l (13, 27) 5/2 + 3.64 P(15,31)  1/2 + 1. 13  Cl(17,35)  3/2 + 0.82  K(19,39)  3/2 + 0.39  The h y p e r f i n e e f f e c t s  D/Rav  Ani  i n various  nuclei  Aei  Rh(10  <0.0 22 <0.022 <0. 0 52 0.21±0.052 0.251 0. 3 3 ± 0 . 0 5 2  0.843 0. £ 3 3  6  /se<  0.513 1.2* -0.2 13  0. 24 0.43  0.009 0.0 17  0.423 0. 76* 0.77+0.13i - 0 . 143 0. 183 0.28* 0. 253 0. 37* -0.093 - 0 . 14* -0.083 - 0 . 11*  0.24 0.36 0.30±0.02 0.08 0.09 0. 14 0. 16 0.22 -0.06 -0.06 -0.05 -0.07  0. 58±0. 085 0.01 0.63±0, 186 0.0 15 0.026±0. 007 14i 0.002 41i 0.001 0.002 0.003 58i 0. 004 -0. 01 8i - 0 . 01 -0.00 5 2 2 i -0.001  Note: 1, W i n s t o n d a t a o r e s t i m a t e ( W I N 6 3 ) 2, F a v a r t e t a l . (FAV70) 3, BLYP 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 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 ) 1  T a b l e I V - 6 (2) Elem  D/Rav  Hyperfine Effect Rc~ (/sec) (T- n s )  i n Lifetime  Li Be  0.633  72601130 (2162.3±0.7) 10500±560 (2147,. 5±2, 7)  and C a p t u r e R a t e  Rc+ (/sec) (T+ n s )  (Rc) av (/sec) (Tmean ns)  3260±80 (2181.2±0.5) 5730±300 (216S.7+2.0)  4678±104 {2175.3±0.4) 7 4680H20 (2186.8±Q.4)f 7500±400 ( 2 1 6 2 . 1±2.0)  *Li 7  (BER58)  106  Table  I V - 6 (3)  Hyperfine  Elem  D/Rav  Rc(T~  I  0 £  I I  B  0. 513 1. 2 * -0.21 3  Effect  (10Vsec) ns)  0. 4 2 3  0.229±0.003 (1463±5)  0. 156±0.002 (163516) 0. 1 1810.002 (174616) 0.11710.009 (1749130) 0 . 4 3 5 1 0 . 001 (1 1 2 3 1 2 ) 0.59010.001 ( 957H) 0.53610.001 (100911) 0.93510.003 ( 71911) 0 . 8 4 1 1 0 . 003 ( 77111) 1 . 4 6 0 1 0 . 004 ( 52211) 1.53810.004 ( 50 211) 1.99410.006 ( 40811) 2.05610.006 ( 39811)  0 . 7 7 ± 0 . 13i - 0 . 143  Al  0 . 183 0. 28* 0. 253 0. 37*  Cl  -0.093 -0.14* -0.083 -0.11*  Rc+(106/sec) (T+ n s )  0.01794+C.0004 (2114. ±2) 0.0122±0.0003 (2140±2) 0.0397±0.0008 ( 2 0 2 113)  0. 76*  Na  L i f e t i m e and Capture  0.0293±0.005 (2064. ±3) 0.0389±0.0007 (2024i4) 0.03 18±0.0008 (2054i3)  N F  in  0.377+0.001  JJ204±21  0.705*0.001  JJ64±J1  1. 1 8 5 ± 0 . 0 0 3 ( 6 1 1 ± 1) 1 . 3 3 3 ± 0 . 003  JJ56JJJ1 1. 839±0.005 (437±1l  Rate  (Rc)av (106/sec) (Tmean n s ) 0.028110.0005 (2070.713.0) 0.0222+0.0005 (2096.113.0) 0 . 0 2221400 0.038310.0007 (2029. 113.0) 0.06 9910.0004 (1906.813.0) 0. 17510.003 (159016) 0 . 14510. 003 (166615) 0.14510.008 (1667120) 0.41310.001 (115112) 0.63810.001 ( 9 15+1) 0.606+0.001 ( 94211) 0.99710.003 ( 68811) 0.97210.003 ( 72311) 1.41310.003 ( 536H) 1.45610.003 ( 52211) 1.93610.005 ( 41811) 1.97410.005 ( 412±1)  Note: 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 , BLYP 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, Winston's neutral data(WIN63) 6, W i n s t o n ' s e l e c t r o n data(WIN63) 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 underlined are our experimental r e s u l t s e x c e p t L i and 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  the  hf e f f e c t  eguation small  ( 3 . 1) ,  difficult lifetime  the  suitable  method  are  also  n u c l e i by t h e  are F  (i)  From The  i s slow  appear  within  results  time,  microseconds..  There  have  the short  hf  Z=11(Na) following  zero  and t h i s  of  t h e most method..  the hf e f f e c t s  ( F e f o r N a n d Cu f o r near  i s also  and e s t i m a t e s  i n N and * 3 C .  candidates,  Z=83 ( B i ) o n t h e b a s i s  4  and C l f o r t h e l i f e t i m e running  It  (for instance L i ,  From t h e t a b l e  be d e t e c t e d .  the small  i n our  for light  events  f o r times  separate  of events  As  the effect  of the hf e f f e c t s  distortion  spectrum.  Ae.  experimental  materials  i s too  to obtain  experimental  possible  decay  This  enough  are summarized.  n u c l e i could  container  to  most  targets  estimates  number  i f the conversion  IV-6, p a s t  sufficient these  the t o t a l  t c measure  hf e f f e c t  c f N a , by u s i n g  by t h e e l e c t r o n  i s not large  B ) , because Table  In the case  Ae i s c a l c u l a t e d t o b e 0 . 0 0 3 .  above,  experiments  In  Cl) .  t o be d e t e r m i n e d  summarized  Be,  (eg F ,  With  in  been no Although  these  l i f e t i m e s i n the 1 3  C)  give  makes i t  large difficult  effect.  to Z= 83(Bi) remarks  may b e made  of the r e s u l t s  from  obtained  Z=11(Na)  to  i n our  experiment. (1)  As l i s t e d good  agreement  nuclei (2)  i n Table  between  Our l i f e t i m e  I V - 2 , o u r measurements  with  past  Z=11  and 8 3 .  measurements  measurements  i n N a , K,  are i n f a i r l y  f o r most  and C l have  of the  been  108  made w i t h g r e a t are  precision.  i n agreement w i t h e a r l i e r  within  error,  longer than lifetime targets  but o u r r e s u l t  the e a r l i e r  frcm  different  both  atomic  difference  i n the l i f e t i m e  with  Er.  nuclei. past  results,  there should  measurement  be no  f o r the element  t a r g e t and when i t i s  However  be  metal.  i n Dy and E r seem t o be  a r e compared w i t h  our two  a l l nuclei  Z effect  have g u i t e  i n Dy,  been s t u d i e d and t h i s even-odd  I f the  measurements o f l i f e t i m e s  when t h e y  Adding  lifetimes  should  The l i f e t i m e s  reasonable  Our  our r e s u l t  germanium  These are the f i r s t and  compound  compound  element t a r g e t i t s e l f .  f o r the  the previous r e s u l t .  numbers, t h e n  when i t i s i n a c h e m i c a l  (3)  Our v a l u e  were t h e same.  of a chemical  (SEN59)  in K i s substantially  than  oxides  i n Na and C l  measurements  were Ge02 and Geo, and t h e muon  constituents  checked  lifetimes  measurement.  i n Ge i s l a r g e r  obtained  an  The  other rare e a r t h  measurements o f Dy and E r t o between Z=64 and Z=68 have  now  makes i t p o s s i b l e t o d i s c u s s t h e  i n rare earth nuclei  (see s e c t i o n  IV.F) . (4)  From  T a b l e I V - 2 , i t i s e v i d e n t t h a t t h e odd Z n u c l e i  for  Z>40 show s y s t e m a t i c a l l y l a r g e r c a p t u r e  the  even Z n u c l e i .  experiment  support  Past  measurements  the f a c t  than  the estimated  value  (FIL63)  t h a t the c a p t u r e  Nb (Z=4 1,A=93) i s a n o m a l o u s l y from  higher  rates  than  and o u r rate i n  ( 10.35±0.17 x10 )  the Primakoff  6  formula  109  (9.35x10*) the  large  (WA175). capture  Watson  rate  vanishing  of  this  be d i s c u s s e d  will  total  IV.E  capture  rata  number  A and atomic  started Fujii  with  nuclecn  i n a complex Z  nucleon  constants  follow  the  conserved  are  well  In  nucleus with  their  (Axial  electron-muon  defined.  Heff, work,  t h e mass  nucleon  lepton-bare  and the coupling Also,  the nucleon coupling  The H a m i l t o n i a n  he  deduced by the  universality.  current,  muon  In h i s derivation,  vector),  and e l e c t r o n - b a r e  Capture  for the total  (PBI59).  (FUJ59).  vector  with the  Hamiltcnian,  i s V and A  muon-bare  comparing  i n Muon N u c l e a r  a formula  the effective  coupling  I n s e c t i o n IV.F,  d e t a i l by  rates  Formula  number  and P r i m a k o f f  that  formula.  derived  Ec(A,Z)  Qc.  i n more  Primakoff  Primakoff  angle  capture  Goulard-Primakoff  has suggested  i n Nb c o u l d b e d u e t o t h e  the Cabibbo  experimental  (HA175)  i s as f o l l o w s  assuming constants  (F0J59,  PEI59) H  - -  A  l + _i=2^L  y eff  T  /  2  /  2  ±  z =  T 1  ; x  {  G  -  y M. V  +  i  G  P ^a. A i  a-vo.-v } 6 ( r - r . ) x x  P  (4.14)  with r  y  -  „  u  t  i  j  .  2mp  P % ~= l  g £ - g £  - g j ( i + y  p  - y  n  ) } - £ -  p  (A.15)  110  In T  equation ,  ]  cf , a  and  ±  angular  r  r  and  which t r a n s f o r m  T  +  for the lepton  , T ~  state  of  closure  eguations  state  and f i n a l  approximation.  excited  excited  accessible  into  state  and  matrix  element  Rc(1,1)  states of  i s performed.  the reduction  i s proportional  estimated  factor  the square between  of  the  the f i n a l  a l l daughter  a n d t h e sum o v e r  Using  i s t h e muon c a p t u r e  {(A-Z)/2A}g,  nucleus  an i - t h n u c l e o n  In the approximation  this  nucleus  a l l the  approximation,  of  phase  g(A-Z)/(2A)}  rate  value  with of  4.  embodies  A=2Z,  to the f r a c t i o n  the bracket  Therefore,  i n hydrogen,  parameter.  the P a u l i  for g i s equal  (4.16)  to 3  and  The s e c o n d  exclusion principle  cf neutrons. (PRI59).  The  Hence  reduces the capture  the P a u l i  K  space f o r the neutrino  g i s the nucleon-nucleon correlation  and  into  neutrino  obtained  represents  term,  operators  a leptcn  (4.15),  R c (A , Z) = ( Z e f f ) * R c ( 1 , 1) K {1 -  where  f o r t h e l e p t o n and  n u c l e i w a s c a l c u l a t e d by t h e  b y t h e muon c a p t u r e  states  Primakoff  (4.14)  transition  initial  energeticaly  and the i - t h  are isobaric spin  muon  and s p i n  (FUJ5S) .  mucn c a p t u r e  states  neutrino;  operators  are space c o - o r d i n a t e s  a lepton  With  are  unit  a n d an i - t h n u c l e o n p r o t o n  neutron  the  i s t h e momentum o f t h e  a r e 2x2 m a t r i x  i - t h nucleon;  state  v  momentum o p e r a t o r s  nucleon; the  (4.14),  exclusion term  for a rate  i s a  by a larqe  111  effect  f o r heavy In  the  nuclei.  order  Primakoff  to  compare  formula,  our experimental  eguation  (4.16)  results  with  i s parameterized  as  follows  Ec ( A , Z ) = ( Z e f f ) * X ( 1 )  The  effective  nuclei Table in  by F o r d IV-2.  et  equation  i n Table  i n Table  lighter  and  are net included.  agrees The  well  with  Z=7  IV-7.  i s reproduced  Without  agree  well  gave with  If equation  1-2/X(2)= becomes  vector  value  current  For  (4.16)  excess  breaks  For  close to t h i s  2  3  8  U,  down. Z/A  Z=8  X (2)  Primakoff.  X (1) = 161  / s e c and IV-7.  hypothesis, and  his theory  (FEI59),. satisfies  The c o n d i t i o n  i s about  condition  The  as shown i n T a b l e  CVC  term  (ECK66) ,  between  fitting  f o r g by  (CVC)  f i t  fittings,  nuclei  of  in  the best  was u s e d .  these  has shown  the assumption of  the  interpolation  X (1) = 137 / s e c , s o t h e e x p e r i m e n t  the neutron  0.36.  In  by t h e e x p e r i m e n t  the conserved  calculation  MINUIT  The r e s u l t  the estimated  of  provided  measurments  and odd p r o t c n  c a l c u l a t i o n by P r i m a k o f f  this  =1,  than  and p a s t  program  most  which a r e not  underlined.  to cur data  (4.17)  results are listed  by t h e l i n e a r  IV-2  elements Z=22  Their  charges,  minimization  are l i s t e d  X (2) ( A - Z ) / (2k)}  calculated for  are obtained  ( 4 . 17)  a chi-squared results  been  The e f f e c t i v e  and shewn  -  a l . (FOE62).  the reference,  method of  c h a r g e s have  [1  (A-Z)g/(2A) implies  0.39, thus  f o r heavy  nuclei.  Z/A Hence  Z/A=  112  higher  order  nuclei.  Pauli  Goulard  c o r r e c t i o n s become  and  Primakoff  R c ( A , Z ) = X (1) ( Z e f f ) • {1  (G0U74)  A  +  necessary  A-Z  where  factors are  2A  X (i)  (A-Z)  X(2)  are  better IV-2  the  IV-3  chi-sguare figures, same  Table  i s  than  the  best  fits  From  Tables  the  evident  curves IV-7  the  kinematic  a l l existing IV-7  formula  Table  that  to  X(1),  and  gives  Primakoff  fitting in  In  IV-8, a  the  formulae  is  Figures  best  and I V - 8 .  two  i t  little  formula.  for  data  From t h e show  two  almost  the  behavior*  as Z>40  show  light  The  stated  larger  elements  shown  is in  states  Even-Odd Z  in  odd  tc  rates Z,  the  hf  s i n c e the  eguation  (4.13),  illustrated  by  nearly  the  figures  of  and  the  same.  IV-4  the the  effect. effect  and  i„n Heavy  the  than  most  small,  are  Effect  section IV.D,  capture  with  be a t t r i b u t e d  effect  hf  IV-8.  listed  IV.F  can  constants.  The  fit  show  fits  it  (4.18)  Goulard-Primakoff  chi-sguare  and  are  included. in  that  4)  X(3)  2A  )X(4)}  8ZA  (i= 1 t o  listed  clear  A-2Z  •  heavy  obtained  2Z -(  for  is  odd-Z  For  IV-5.  1/Z  capture  heavy  In rates  n u c l e i the  rates  hf  to  1/Z,  as  from  the  two  dependence Figure  for  nuclei.  proportional  capture  This  nuclei  even-Z large  Nuclei  IV-4  is shows  Table  IV-7,  Fitting  Results for  TEIUMF  Data*  Past  Formula  58  X(1)  170  170  X(2)  3 . 125  3 . 125  4.6%  5 . 8%  cf  data  (exp-f i t ) /exp  Our  2)  Past  Table  listed in  experimental results  1)  results  IV-8,  s u m m a r i z e d by  Fitting Results Formula  for  cf  IV-1.  a l . (ECK66).  Goulard-Primakoff  ( 4 . 18)  TRIUMF  Number  Table  Eckhause et  Data*  Eata  X(1)  Past  Results2  30  58  261  252  X(2)  -0.040  -0.038  X(3)  - 0 . 26  - 0 . 24  X(4)  3.24  3'. 2 3  (Exp-Fit)  2)  4 . 1%  /Exp  see Table  IV -7  above.  (4.16)  Results2  30  Number  1),  Primakoff  5.6%  CD Ul  +  ( I R I U M F Data)  +  2°  \ ^^Goulard-Primakoff  Win <  + ++.  cr LU  Primakoff  P in j Q_  U ' L O _ |  Q U  LD  i 2.4  r 2.5  ~~I  1  2.6  1 — 2.7  (fl-Z)/2fl  F i g u r e IV-2,  The TRIUMF d a t a a r e f i t t e d formula.  2.8  2 . 9  ,  3.0  3.1  CX10" ) 1  to the Primakoff and the G o u l a r d -  Primakoff  i g u r e IV-3,  Past f i n d i n g s summarized by Eckhause et al.(ECK66) are f i t t e d Primakoff and the Goulard-Primakoff formula.  to the  116  deviations  of  experimental  Goulard-Primakoff  (G-P)  plotting  against  the  that  pattern  of  the  effects.  In  comparison  this  formula.  In  are  frcm the  taken  experimental than  Z=10  formula  Z=8  as  IV-5, shown. data  absolute  the  hf  average  clearly  for  (PRI59, of is  from  rates,  as  the  (Rc)av,  and  the  for  conversions  frcm  the  higher  hf  fluorine.  The  than  the  formula  G-P  between  (Rc)av  with  the  from and  the  large  experiments  Rc~  average  (eg  20% i n  capture  numbers  most  1/Z  rates  of  the  odd-Z  formula..  dependence This  table,  capture  the  of by  from Due  to hf  nuclei  estimates differences  because the (Rc)av..  is  lower in  of  the  rates  nuclei.  levels  caused  than  number  deviations  P) ,  smaller  been  G-P  l e v e l to  are  The  figure  have  the  hf  set  because  In  the  light  lcwer  G-P  TRIUMF  (4.13))..  In  listed  heavier  the  eguation IV-6.  from  that  a  a l . (ECK66).  atomic  with  Table  decay  the  IV-4  from  are  muons  the  nuclei heavier  figure  Rc~,  a l l  used f o r  and  GOU74).  clear  agrees BLYP  shell  discussion below,  only  decrease  are  now  illustrate  with  et  atcmic  Z=40 d e v i a t e s  (see  data  to  lacking in  level,  level,  deals  and  it  tendency  capture  lower  fast  IV-5,  interactions  understood  the  this  valid  authors  deviations  increases, the  be  order  Eckhause  the  deviations  From f i g u r e Z=10  data  the  we a r e  results  n u c l e i with from  in  connected  experimental  excluded  the  Z  TfilUMF  of  from  Note t h a t  is  a l l  reference  seems t o  between  Since  deviation  the  rates  number  comparison,  c l a i m e d by the  atomic  r e s u l t s of  are  the  formula.  section,  between the  capture  theory  by  (EX-TH)/EX  • Odd-Z * Even-Z  0.2  0.1  X  O  <  0.0  J  >  LU Q  x. X  X  *  •  -0.1  -02  10 Figure IV-4,  20  30 40 ATOMIC  50 60 70 NUMBER (Z)  80  90  Deviations of experimental capture rates from the Goulard-Primakoff formula.  100  Odd-Z Even-Z  EX-TH|/EX 0.2  \  • \  O  \  i—i > UJ Q  • -7-1  V  \  ^ z \  •  \ \,  \  UJ I—  0.1  _J  O  •  00  \  \  m < •x  0.0 _2 10 F i g u r e IV-5,  §_  20  30 40 ATOMIC  50 60 70 N U M B E R (Z)  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 from the formula.  F i g u r e IV-4 i s redrawned.  80  90  100 co  Goulard-Primakoff  11  Figure only.  In  this  IV-6  shows  figure,  the  data odd  points  for  data  points  data  + Even  odd-Z are  nuclei  normalized  as  follows Odd In  the  Z  nuclei  rates is  and  example,  of  turn  as  are  the  Z=70,  Nb  3% a n d  the  hf  capture  rate  Cabibbo  angle  al.(SAL74) (>1016 high odd  in  fields nuclei  these  could  (Qc).  hf  and  are  has be  easily  CaMbbo  and  by  not  suggested the  large  in  deviations, IV-6,  Z=30  In have  that  the  (4.13)  enough  to  rate).  the  large  vanishing  Qc t o  Between  large  capture  external  angle  achieved  For  equation  was p r o p o s e d  a strong  figure  as e x p e c t e d .  (=large  tc  in  respectively.  estimated  due  large  nuclei.  anomalously  are  the  figure  Z=10  of  by  the  Salam  total  mucn c a p t u r e  rate  is  et  magnetic  field  vanish.  Such  interior  of  the  (S0B75). The  of  even-Z  6.5%  In  2%,  an  concept  that  some  3% a n d  effect  have  difference  formula  IV-5.  effects  This  causes the  c a n be  for  have  deviation  (WAT75) Nb  G-P  n u c l e i between the  the  data}/2  neighboring  the  small  o.5%  (Z+1)  manipulation,  in figure  effects  who s h o w e d  gauss)  be  Ho(Z=67)  to  anomalous  Watson  to  seems t o  to  explain  this  only  due  The  aliout  After  odd-Z  deviation. be  and i t s  shown  deviations  Z=35 a n d  and  effect,  odd-Z  out  Tb(Z=65)  deviations  large  even-odd  odd-Z n u c l e i from  IV-5  figure,  (Z-1)  the  between  respectively,  this  {Even  important.  deviations  these  -  d i s c u s s i o n of  capture  IV-4  data  9  proportional  to  OQ  e ro  P O  CD  m o o ~n  031  RELATIVE O  DEVIATION  P  l\j  121  { G m » c o s (Qc) } 2  (BLI73).  from  (4.2),  eguaticn  constant  The c o u p l i n g c o n s t a n t ,  i s related  Gv i n a b e t a  decay  to the vector  Gm,  obtained  coupling  ty  G v=Gm « c o s (Qc) We e x p e c t  the effect  Rc(odd The  angle,  i s equal  eguation  (4.19)  theoretical rate angle  i s  the  vanishing  of  Qc t o  be g i v e n  A ) / R c ( e v e n ft) = 1 / c o s 2 (Qc)  Cabibbo  (R0074) ,  of  determined to  9% h i g h e r  about  rate.  than  i s quenched,  (4.19)  eight  hyperon  0,234±0.003 radians*  predicts  capture  from  it  beta-decays  Using  this  angle,  a 6% i n c r e a s e i n t h e  In the case  the t h e o r e t i c a l could  by  explain  o f Nb o u r  capture  rate.  the  larger  If  Cabibbo  experimental  values. If rates  (>5%)  heavier this  this have  than  does  i s a universal t c be o b s e r v e d  Z=40.  But i t  net hold  discussed  true  between  structure.  Thus  we h a v e  to choose  nuclear  structure.  2 = 4 5 a n d Z=55 seen  in figure  formula expected  by  Also  to  capture  discuss  figure  Figure  o r Z=63 IV-6,  IV-8  there  and Z=75 s a t i s f y these  nuclei  the vanishing the vanishing  of of  Cabibbo  Z  effect,  affected  nuclei  this  i s not such a l a r g e  As  and n u c l e a r  that  deviate  that  is a  the even-odd  shows  IV-6  nuclei.  n u c l e i which are not s t r o n g l y  2%.. This  from  muon  capture  t h e odd n u c l e i  heavy  section IV.G,  nuclear  of  from  f o r many o d d - Z  i n order  the large  f o r most  i s evident  i n the following  correlation  rule,  between  condition.  from  the  deviation  by  As  G-P as  angle,.  the Cabibbo  angle  has been  122  investigated  i n actinide  al.(PAR78).  according to their  muon c a p t u r e  rates  a l . (JOH77) vanishing Wilcke  are reproduced  by adding  of the Cabibbo  i n actinide  model  of  is  and Z g l i n s k i  I.D,  the giant  actinide the  resonance  excitations  model  rates  hypothesis  gauss)  of  i n odd-A  calculation magnetic  gauss.  for  very It  each  According  to  resonance  t h e d i p o l e and  As d i s c u s s e d i n well  for  are better  section total  seems t h a t  in  explained  by  multipole  the vanishing  i n odd heavy  f o r the vanishing  in conclusion,  of the Cabibbo  angle  Cabibbo magnetic  to the  (LEE78),  nuclei  magnetic  of  high  According  by L e e a n d K h a n n a  field  of the  c f an u l t r a  nuclei.  Hence t h e a c t u a l  Finally, vanishing  model,  dipole  Pb b o t h  which i n c l u d e s h i g h e r  (1016  enough  alternate  In their  excitations.  nuclei.  field  high  d e s c r i b e d by t h e  works  i s based on t h e a s s u m p t i o n  5x10l*  capture  of C a , the giant  angle  internal  that  the large  by  (WIL80-2).  The  elaborate  paper  are important.  n u c l e i the capture  et  t h e i n c r e a s e due t o t h e  But t h e r e c e n t  i n the case of  in light  total  by J o h n s o n  i s t h e sum o f t h e r a t e s  resonance.model  rates  measured  u  (KOZ78).  resonance  i n the case  resonances  muon c a p t u r e  rate  of g i a n t  d o m i n a n t , whereas  cctupole  h a s shown  mucn c a p t u r e  results,  angle.  nuclei are well  Kozlowski  multipolarity their  23  et  calculation, the large  and 239p  in  e t a l . (WIL80-2)  total  Parthasarathy  ^U  rates  the  nuclei ty  recent  the  i s less  than  f i e l d 'may n o t b e  the Cabibbo  angle.  the concept  i n mucn c a p t u r e  of the has not  been  123  proved  and i n f a c t  against total  i t .  Since  nuclear  r a t e and n u c l e a r s t r u c t u r e ,  t h e even-odd Z e f f e c t  Nuclear  In t h i s and n u c l e a r Figure (figures  Ac  formula  b  E  |  ^  In f i g u r e capture  I / £ l<»|J2  (|vba|)|a>|*  'strength'  (Iv-ba|)| >|*  (4-20)  a  U  r a t e s i n equation capture  rates  as f o l l o w s  I V - 7 , the experimental  experimental  plot  on t h e f o l l o w i n g  IV-7 i s e q u a l t o t h e t o t a l  I ^  D=  capture  has been p r e s e n t e d by  I* / £ |<b|j"  of the n u c l e a r t r a n s i t i o n  *- M  between  • y  y a x i s of f i g u r e  (S  Capture  the Primakoff  (KOH79), and i s b a s e d  = The  from  This plot  f o r t o t a l capture  = K - ^ f ^  i n Muon  t e examined.  IV-7 i s d i f f e r e n t  Kohyama and F u j i i  when  account.  the c o r r e l a t i o n  structure will  IV-2 and I V - 3 ) .  general  into  Structure Effect  section,  between  i n muon c a p t u r e , t h e  s t r u c t u r e has t o be t a k e n  IV.G  i s slightly  there i s a strong c o r r e l a t i o n  mucn c a p t u r e  considering  rates  the weight o f t h e evidence  results  (4.20).  r a t e s reduced  a r e used  f o r the  In the f i g u r e , the by  (Zeff)*  increase  124  linearly  until  transition  matrix  protons  and  protons  in  capture  and,  protons  in  reduction the  Z =30,  A-Z  for  the  (Ar,  structure  heavy  nuclei,  nucleus takes  figure the  by  has  part the  of  small  linearly  only  The  to  the  Z,  of  from  the  the  a fraction  in  nuclear  a contribution  case  Z  Z  muon the  Z  muon c a p t u r e .  effective  Kr,  cf  Xe).  atomic  chance  this  nuclear  structure.  versus Pauli  IV-8,  atomic  maxima  closed  shell  and,  the  expected. the  shell  large This  charge,  measurements their the  reduced ether  is  in  Pauli  the  total  capture hand,  can  of be  of  the  to  This  Zeff,  in  in  the  atomic  mean  the  nuclear  capture  c h a r a c t e r i s t i c s of by  neutron This  amount  in  is  the  to  the  nucleus  IV-8.. nuclei  In  figure,  the  Although  be  muon rates  caputure are  minima  in  the  have  rates  been in  expected  to  figure  IV-8  rate  of  no  Kr be  IV-7  nuclear  reduced capture  there  this  the  causes o s c i l l a t i o n s i n figure reflect  the  atomic near  i n h i b i t i o n can  clearly  the  called  formula..  correspond of  figure  excess  Primakoff  exclusion  and,  closed  that  affect  explained  the  oscillation  the  not  the  plotted.  results  small.  of  one  muon c a p t u r e  effect  In  anomalously  a clear  does  accidentally  experimental  effect.  is  strength  the  this  amount  number  figure,  maxima,  is  closed shells  This  the  exclusion  there  But  the  By  figure  IV-7,  minima c o r r e s p o n d  rates.  On  the  constant.  nucleus.  shells  is  capture In  implemented  surprisingly,  and  become  nucleus contribute  for  In  In  muon  neutrons.  the  is  and t h e n  and very  are  Xe, small.  located  Ar  .125  1Q  xLOO ;  1  1  1  i  i  1  1  Nb(N=52)  Ni(N=30)  Pr(N=82)  X  Zeff « \  Ca , X *<  cn •  UJ  •  cr  • * •  CL  X '  /  •  •  I V  X  X  *" X  ? t  ?  •  U 5  *  v  Ar  t Kr Z=36  Xe  Q_ X UJ  • Odd-Z x Even-Z  Q  LU  U  -  •  Q  X  U  t "X,  0  1  0  1  10  F i g u r e IV-7,  i  i  i  20 30 4 0 50 60 70 ATOMIC NUMBER (Z)  i  80 90  Reduced c a p t u r e r a t e s v e r s u s atomic number. T h i s graph i s adapted from Kohyama and F u j i i ( K O H 7 9 ) .  0.31  N=126  ,x  0.30  N = 8 2  X  Q27  X  X«X  J  *•  X/  N=20  <  -X  •\x  N=50  0.29 028  •u-  ...  X  ". N=2S  /  *  »x  X N. x  x  ^  I  Kr  x  t  t Xe Z-54  • Odd-Z * Even-Z  Z=36  I  < 026  Rn Z-86  02 5 10  20  30 40 50 60 70 ATOMIC NUMBER (Z)  Figure IV-8, The neutron excess versus atomic number. P a u l i exclusion term by Primakoff.  80  This excess term i s named  90  127  near the  the  nuclei  minima,  the  experimental  and  capture  be  to  have  larger  Ca  Pr  have  neutron  nuclei. have  8,  neutron  20,  different process  is  process  is  neutrcns capture  (28), are  numbers  rather  frcm  other  (1.10).  produced rates.  rates.  numbers  of  the  G-P  Nb(4 1 , 9 3 ) ,  There (eg  for  are  Ni  large  Although  muon c a p t u r e  and  of  the  Pauli  Nb.  In  these  and a f f e c t s have  is  Y are  rates of  exceed  do n o t  magic  nuclei the  muon  magic show  deviate similar not  the  magic  case  do n o t  are  is  the  they  Z  the  affect  a  in  against  IV-8  Y (39,89)  rates  egual  basic  capture  the  some n u c l e i w h i c h but  to  to  numbers  remains  rates  Z  nuclei  inhibition  in  and  Y (39,89))  magic  having  the  inhibition seems  Ni  numbers  Nuclei  N equal  figure  still  capture  formula.  the  this  neutron  from  small  effect  large  capture  Although,  twc,  The  The  complex  exclusion  n u c l e i having  the  and  N or  capture,  for  Pr(N=82).  neutron  anomalously  muon  IV-8  than  c h a r a c t e r i s t i c s which  relatively  still  capture  have  muon  figure  numbers.  the  by  closed shell  126..  the  Nb(N=52),  is  ( 1 14),  Thus the  numbers,  82,  and  by  magic  number  (1.9)  explains  (28,50)  inhibition  number  rates  proton  magic  Nb(41,93)  capture  or  by  small for  and  weak  Ni (28,51),  numbers.  In  Frcm  and  50,  the  magic  nuclei.  expressed  This  neutron  (40),  a magic  C a ( N = 20)  Ni(N=30)  tc  near  At  large.  Ca ( 2 0 , 4 0 ) ,  numbers  to  apparently number.  and  correspond  N equal  from  seem t c  l i s t e d below..  s m a l l and  appear  2,  the  rates  is  Pr ( 5 9 , 1 4 1 )  Nb  for  inhibition  numbers  IV-7,  parentheses or  Pauli  magic  figure  numbers to  nuclear  Frcm  other and  with  extremely to  anomalous  128  like  Nb.  nuclear  This  seems t o be due t o t h e d i f f e r e n c e  magnetic  Y has a small  negative  magnetic  Nb h a s a l a r g e  positive  magnetic  ( = - 0 . 137) ,  whereas  moment  (=6.167).  In the case  moment,  t h e F+=I+1/2 h f s t a t e  state.  Since  effects to  there  the capture  rate  from  for the nuclei  Nb, although  of the negative i s lower  than  i s a rapid conversion F+  there  magnetic  t h e F~=I-1/2  from  F-  t o F+  s e e m s t c be s u p p r e s s e d .  with  b e one o f t h e r e a s o n s  from  their  moments.  moment  Y,  in  negative  magnetic  f o r the different has been  in  The h f  moments  behavior  no e s t i m a t e  hf  appear  of Y  of i t s  magnitude. The strontium  isotcpes  a l . (FRI79). charge  nuclear  Their  radius  charge  have  been  radii  o f molybdenum and  measured  experiment  that  the nuclear  i s 1% l a r g e r  than  that  of  magic number  50.  From  Mo (Z=4 2 , N = 50)  which h a s the neutron  their  protons  number  becomes  moves weaker  increase. Since  i n a nucleus  s e e m t o b e more t i g h t l y  neutrons  away f r o m  This  the radius  muonic  wave f u n c t i o n  s o t h e muon  exact teen  distribution pointed  radius  rate  will  of the protons  c u t by E c k h a u s e  et  magic  t h e number  the binding tends  of  force  to  f o r Nb (Z=4 1 , N = 5 2 ) .  S crbit  i s comparable  capture  b u t , when  of the protons  of t h e muonic  cm) a n d t h e n u c l e a r  a neutron  number,  seems t o be t h e c a s e  (10~13  and  with  bound  a magic  and the r a d i u s  et  has suggested  c f Mc ( Z = 4 2 , N = 5 2 )  result,  by F r i c k e  i n Nb i s 6 . 4  i s about  6 fermi,  in size be v e r y  fermi the  t o the nucleus sensitive  i n the nucleus. al.(ECK66).  to the This has  129  CHAPTER V Muon  V.A  relative  atomic  (Z1)  m  Fermi-Teller rates  i s given  n  (FER47)  probability  Z c f each  capture  (Z2)  and T e l l e r  capture  number  so c a l l e d atomic  i n Chemical  Compounds  Introduction  Fermi the  Capture  atom  proposed  a model i n  was p r o p o r t i o n a l  to the  i n a c h e m i c a l compound.  Z law implies cf negative  that  muons  the ratio  in a  This of  compound  by  W(Z1/Z2)= ( m « Z 1 ) / ( n * Z 2 )  It  s c o n became  experimental was that  clear  oxides  have  minima  correspond  capture  indicated that affects  made  and t h e c a p t u r e e t a l . (ZIN66) rates  f a r , there  have  Most  studies  by d e t e c t i n g  process . demonstrated  i n the metallic The p o s i t i o n s  metals.  The  of the  experimental  the electronic structure  the atomic  capture  rate  been, a s i g n i f i c a n t  c o l l e c t e d b y many g r o u p s  inconsistent. been  Zinov  to the a l k a l i  compounds So  data  (BEI63)  d i d not explain the  a periodic characteristic.  clearly  chemical  atomic  (5.1)  the Z-law  complicated*  the relative  results  that  observations  much more  which  but they  were  of the atomic  t h e muonic  K X-rays  of  of  muons.  amount  of  often  capture  rates  ( t h e Lyman  have  130  series).  In  X-ray  been  has  captured. BAI63), decay  this  In  the  K orbit.  and  very  atomic  from  muons earlier  targets  were  method  rate  of  a negative longer  spent  measured. been  muons muon  than  (1204  ns),  it  spectrum  into  the  (SEN58,  mcst  experiments  has  in in  the is  numbers  was o b t a i n e d  which  Ihese  intensity  the  rate  their  In  of  by of  their  the  present study  lifetime easy  oxygen  to  ns)  and m e t a l  in  the Since  the  is  in elements  decompose  life  statistics  metallic oxides. (1795  muons  detecting  poor  to  the  ECK62,  had  applied  oxygen  of  the  heavier decay  constituents  by  lifetimes.  As  discussed in Chapter  approxinaticn  that  orbit  their  without  capture  to  capture  sodium  using  equal  atomic  significantly  electron  be  the  experiments  their  of  to  sum o f  earlier  capture  lifetime  tlie  some  few  experiment,  than  assumed  electrons  the  method,  during  the  a l l  muons  trapped  disappearance cascade.  by  Within  number  of  muons  deduced  from  should  be  egual  to  obtained  muonic  X-ray.  that  I,  the  it  is a  in  an atom  decay, this  decay from  good  or  the  K  nuclear  approximation,  electron the  reach  the  spectrum  intensity  of  the1  131  V.B  Muon the  In decay in  from  obtain  spectrum,  e l e m e n t s most  nucleus.  Thus,  Capture  Lifetime  order t o  electron  heavy  Atomic  the nucleus with  Method  t h e number  we m u s t  number  the atomic  o f muons  from  a  correct for the fact  o f t h e muons  the t o t a l  R a t i o b%  of  are absorbed  that  by t h e  decay e l e c t r o n s ,  number  Z i s given  Ne-(Z),  by  Q (Z) « R d Ne~(Z)=  R c (Z)  •Nm-(Z) « E 1 * E 2 ( Z )  + Q (Z) « R d  where  t h e d e f i n i t i o n s of Q , R d and Rc a r e g i v e n  (4.4:)  and  effect the  Nm-(Z)  with  Z.  angle, decay  1-3  seen  that  efficiency including the  muons  showed C,  of  low energy  of  heavy  Ti,  correction  than  muon.  Hence,  i n the case of  i s a c c o u n t e d f o r by E 2 ( Z ) .  we h a v e  t c know  spectrum  C u , a n d Pb  energy  the energy  loss  of  (SUZ79). spectra i n  due t o t h e  the rate  of t h e  i s larger light  and  i n the  the peaks of t h e energy  electrons i n the target  elements  trapped  the energy  elements are shifted to lower cf the negative  eguations  E 2 (Z) i s t h e c o r r e c t i o n f o r  of negative  Figure  by  electrons in the target,  e l e c t r o n s i n the t a r g e t s  .binding  E2(Z),  solid  cf low energy  i s clearly  heavy  i s the counter  i s t h e number  nucleus  It  E1  of l i m i t e d  loss  decay  (4.5),  (5.2)  i n the case  elements..  In order f o r decay  loss  to  This  determine  electrons  132  in  the target,  the  counter  electrons  plastic  walls  telescope.  decay  can experience  spectrum P b ^  ,  electrons. by H u f f  electrons in  C r  Cr  2  °3 '  n  e  c  u  energy  t  Z smaller  Z=30,  capture  values  of  is  11  For example,  rate E2 (Z)  Since  the t o t a l  always  are severe  appear  in  respectively.  are small  they  energy  of  MeV a n d t h e l o s s  while  Thus  spectrum  18 MeV a n d t h e l o s s e s  The c o r r e c t i o n s  constituents.  atomic two  than  that  the calculated  i n Pb a n d 0 a r e 2635 a n d 11%, t  and  and a v e r a g e d . .  i s employed. i s  lengths  i n the energy  I n our a n a l y s i s ,  energy  a n d 2 . 4 % i n 0.  heavy  energy  container,  path  are estimated  (HUF6 1)  the cut off  the target  The d i f f e r e n t  we c a n c a l c u l a t e t h e c u t o f f of  of  decay Also,  i s 4% i n  f o r oxides  i n oxides  with  with  corrections i n the  as t h e d i f f e r e n c e  and E2(0), the c o r r e c t i o n s  between  tend  t o be  smaller. Negative either of  i n t h e m e t a l (Z)  t h e decay  decomposed this  electron  into  i n m e t a l l i c oxides  spectrum,  Ne-(Z)  capture  rates  By t h e a n a l y s i s  the spectrum  c a n be  a n d N e ~ (0) a r e o b t a i n e d . . from  p e r atom  eguation in Z 0 m  n  (5.2).  i s defined  W (Z/0) = { n « N m ~ (Z)} / [ m » N m - (0)}  In  the f i t t i n g  and,  frcm  of  the spectrum,  equations  (5.2)  trapped  and t h e oxygen components.  a n d Nm~ (0) a r e f o u n d  atomic  Z 0\ , a r e  o r i n t h e o x i d e (0).  the metal  manipulation,  Nm-(Z) of  muons  equation  and ( 5 . 3 ) ,  From Thus,  The  ratio  by  ( 5 . 3)  (3.6)  we g e t  h a s been  used  133  /Z\ W - = \0/  where A (Z) and  n m  •  Q(0)  •  Q(Z)  (Q ( 0 ) ,  E2(Z)  E2 ( 0 ) ) , One  the d i f f i c u l t y  E2(Z)  (5.4)  A(0)  respectively.  are almost e q u a l to the  of t h e m e t a l and I n the case  of t h e s h o r t c o m i n g s i n s e p a r a t i n g the  different atomic  Assuming A (C)/A(0)  In  a Monte C a r l o programme  was  =0.25, 4 x 1 0  as a t a r g e t  muons o u t  s  of  t r i a l s were c a p t u r e d i n o x y g e n and t h e numbers o f  muons was created  e s t i m a t e d a t 3.99x10  spectrum.  C a r l o and  s  by  f i t t i n g the a r t i f i c i a l l y  Since the d i f f e r e n c e  t h e f i t t i n g i s o n l y 0.3%,  enough s t a t i s t i c s , having  method i s  numbers.  2  s  ZOO,  lifetime  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 )  5x10  of  v a l u e s f o r oxygen  of the l i f e t i m e  with s i m i l a r  to study t h i s problem,  material.  the  b e c a u s e o f t h e s m a l l bound muon e f f e c t .  components f o r elements order  A(Z)  •  A (0) a r e t h e a m p l i t u d e s  o x y g e n component a t t=0, Q (Z) and  E2(0)  we c a n s e p a r a t e  between t h e  i t seems t h a t i f we  have  e v e n t s e v e n f o r compounds  c c m p c n e n t s w i t h n e a r l y t h e same Z, s u c h  h a v e measured a muon a t o m i c  Monte  capture r a t i c  as C0 »  We  2  i n dry  ice.  The  result  seems g u i t e r e a s o n a b l e , when i t i s c o m p a r e d w i t h  atomic  capture r a t i c  c f o x i d e s w i t h B o r Be  (SCH78-2)  the  near  C. Our  r e s u l t s are l i s t e d  p a s t r e s u l t s o f X-ray  i n T a b l e V-1  along  m e a s u r e m e n t s done by p r e v i o u s  with workers.  Table  V-1, P e r Atom C a p t u r e M e t a l l i c Oxides  R a t i o s A(Z/0) o f Muons i n  z  ZmOn  TRIUMF  6 1 1 12 13  C02 Na202 MgO A1202  0. 43 0.87 0. 80 0.84  14  Si02  0.96 ± 0,04  + 0.02 + C.02 + 0.0 2  ± 0.03  0.87 + 0.03 1.49 + 0.06  22  P205 Ca (OH) 2 CaO CaO Ti02  24  Cr203  2. 63 ± 0, 1 3  15 20  25 29 30 32 48  2. 17 + 0. 1 1  Cr03 Mn02 CuO  2.96 ± 0.20 3.00 ± 0. 17 4.06 ± 0. 23  ZnO Geo GeC2 CdO  2. 39 2. 20 2.40 1. 93  + 0. 10  ± 0. 12 ± 0. 13 + 0.07  50 56  Sn02 BaO  2. 15 + 0. 11 2. 27 ± 0.09  60 80 82  Nd02 HgO Pb0 2  4. 13 ± 0,29 3. 75 ± 0.29 3. 21 ± 0.23  Pb304  3.87 + 0. 29  References : (1) ZIN66 (2) SEN58 (3) MAU77 (4) KNI75 (5) D AN 77 (6) BAI63  Past R e s u l t  0.0 7 0.06 0. 0 6 0.07 + 0.05 + 0.07 + 0. 11  0.83 0.85 0.65 0.79 0.57 0.86 0.93  ± ± ± ±  1. 36 1.45 2.70 1. 90 3,00 2.04  ± 0. 10 + 0.09 + 0.20 ± 0. 10 + 0. 17 ± 0. 1 1  3.60 ± 0.40 6. 14 ± 0. 8 5 2.66 ± 0.32 6.70 2. 47 2. 50 3.17 2.27 1. 45  + 1, 50 ± 0. 22 + 0. 2 8 ± 0. 24 ± 0. 22 ± 0. 18  4. 17 ± 0.30 4. 10 + 0. 4 2  Ref.  (D (1) (2)  (D  (2) (3) (2) (1) (4) (1) (4)  (D  (4)  (D  (6)  (D (D  (4) (5)  (D (D  (5)  (D  (5)  7-Or jfi Zinov  6-0  Vaeilyev  et al  £  Daniel  — ——  Daniel  ^  Triumf  — —  Schneuwly et al  eq(5.6)  5-0  40 NJ|O  3-0  2-0  1-0  10  20  30  ATOMIC  40  50  60  NUMBER ( Z )  F i g u r e V - l , Atomic c a p t u r e r a t i o i n m e t a l l i c oxides.  136  In  figure  V-1,  theoretical our  our r e s u l t s ,  curves  (ZIN66,  The  predicts Daniel ratio  twice  the  capture  with  / Zl  \  Z2  formula  ratio  experiments  elements  the experimental  the  Z-law  capture  Zl  rates. capture  matter.  His  of  and T e l l e r  Fermi  as a Fermi  p e r atom  gas.  i n the case  of  He a  in  obtained binary  a n d Z2  (Z 1) i / 3 » l n ( 0 . 5 7 » Z 1)  (5.5)  /  (Z2)  gives  better  i / 3 * l n (0.  57«Z2)  agreement  c h e m i c a l bend  have  metal  spectra  performed  X-ray  a c a l c u l a t i o n of the atomic  cascade i n t e n s i t i e s . .  a l . (KES67)  the  with the  that  than  the Z-law  as  shown  V-1. The  pure  various  = \  figure  and  i s evident  explains the  on the t r e a t m e n t  elements  W  It  b u t i n heavy  the electrons are treated  compound  in  Z-law  muens i n c o n d e n s e d  i s based  atomic  This  Z<30,  performed  f o r negative  together. agreement  the values of  (DAN75)  calculation which  belcw  measurements  DAN77) .  Fermi-Teller  qualitatively  the  a r e shewn  r e s u l t s a r e i n adeguate  measurements  in  past  also  Zinov  affects  e l a l . (ZIN66)  shown  that  t h e muonic  T i have  more  transitions  i n titanium  the systematic  oxides.  the s t r u c t u r e  X-ray from  Schneuwly  measurements  of  and K e s s l e r  K-series high  spectra  orbits  than  e t a l . (SCH78-1)  of c a p t u r e  et  ratios  in  137  selected  compounds  confirmed role  that  theory  valence  atomic  sulfur  capture  to take  electrons  al.(SCH78-2) curve  nitrogen,  the chemical structure  i n the muonic  successful and  of  into  reproduces  plays  process.  account  was p r o p o s e d  a n d , a s shown  and s e l e n i u m , and important  The  first  the effect  by S c h n e u w l y  in figure  the p e r i o d i c i t y  an  V-1,  core  et  their  observed  of  theoretical  i n the  experiments. Recently, correlation atomic  between  capture  (5.5)  atomic to  being  (EAN79)  radii  high  that  and a t o m i c  f o r atoms  account  there  with  i s a  strong  radii  with  small  radii  a model which t a k e s and m o d i f i e d  the  the  h i s formula  ( Z l ) i / 3 « l n ( 0 . 5 7 - Z 1 ) » R (Z2) =  (  * Z2 '  B (Z)  As shown  agreement  (Z2)  in figure of  than  Schneuwly atomic  and D a n i e l capture  interpreting  radius  the atomic  Even t h o u g h ,  6 )  V » l n ( 0 . 5 7 - Z 2 ) » B (Z 1)  V-1,  eguation  5 .  3  i s the atomic  periodicity  the  capture  proposed  into  / Zl \  Z.  shown  give  w  where  has been  atomic  rate  (DAN78) . . D a n i e l actual  i t  f o r a n atom  equation  capture  cf  atomic  number  (5.6) c l e a r l y g i v e s  rate  and g i v e s  the  better  ( 5 . 5) . as discussed  have r e v e a l e d  rate,  there  the experiments.  above,  the important  i s s t i l l In  the theories  of  features  difficulty  our experimental  of  in results,  138  it  i s  evident  the.same  that  element  reproduce  this  are  radii  model,  which takes  gives  different  explain  Thus,  the  further rate.  tc  for  oxides  only  different the  of  the  solve  the  weakly  valency  these  different  states.  models  observed  in  will  chemical effects  different  for  However  the  of  can  into  ratios  are  oxides  Schneuwly's  effect  capture  development  model  via the  same e l e m e n t .  differences  theoretical  in  Daniel's  c h e m i c a l bond  p r e d i c t e d by the  ratios  different.  slightly different  differences to  capture  difference  atomic  also  the  not  account, the  the large  enough  experiments..  have t o  be  pursued  in the.atomic  capture  139  CHAPTER  VI  S ummar y  Our in  various  Forty  large  measurements  n u c l e i have  eight  somewhat  lifetime  elements  larger  number  differences  than  due  tc  groups.  For  due  important,  and  previous  in  lifetime. lifetimes shifted  agrees  the  Hence, in  the  lifetime  in  2nd  the  determined with  the  group  muons  of  our  various  2nd e l e c t r o n s very  few  muon  r e s u l t s of  negative  muon  systematic  system  accepted  The  was  value  of  have  errors  positive  2 197.0  are  groups  positive  by  This  the  the  affected  a  measurment,  and  muon l i f e t i m e . by  bound  before.1  removes  among  experiments  past  n u c l e i were  one  lifetime  determination  positive  well  to  muons  which i s  attempted  errors  the  errors  altogether,  been  by  systematic  systematic  succeeded  has  measurements  negative  many s u c c e s s f u l r e s u l t s .  were s t u d i e d  survey  of  experimental  produced  for  which  muon  ±0.7  ns  which  2197.120±0.077  ns  (KEL80) . We h a v e lifetimes  in  improved  many l i g h t  a n d new  determinations  Most  our  cf  findings.  i  the  accuracy  elements were  measurements In  the  case of  made  are 6  (Ee,  Li  in  for  of  B, 1 3  C,  adeguate  and  7  Li,  negative  N, 1 8  0,  F,  0 ,  Dy,  Na,  was  Cl,  and  agreement  there  muon  a  Sens e t a l . ( S E N 5 9 ) had 30 e l e m e n t s i n 1959.  with  K)  Er. past  140  disagreement and  the  recent  between t h e  experiment  with  calculation. and  0,  ours  and  was  of p a r t i a l by  their  no  partial  muon c a p t u r e  capture  r a t e as d e m o n s t r a t e d  might be  of the based Nb  due 6  Cabibbo angle on  the  which has  discussed  nuclear  Z=68.  with  has  no  1 2  i n L i , B,  observed  C  and  * C  using  a  i n C. have  3  difference  shell  i n the  This prediction  G)  our  for  pointed  out  muon c a p t u r e o f an  (WAT75) which c a u s e s  (WAT75, SA174).  IV.F,  this  The  werk.  effect  rates  ultra the  t h e odd-Z n u c l e i  from  been no  even-Z n u c l e i ,  the  vanishing of  study  In  Z=55 and  high  vanishing  discussion  However  order effect between  show s l i g h t l y the  than  was  rate in as  seems t o have a  t h e even-odd  between Z=45 and  total  t h a t odd-Z heavy  presence  in this  the  experiment.  nuclear structure.  r a t e s than  as e x p e c t e d  theoretical  observed  rates in  by  to t h e  been c o n f i r m e d  although  capture  was  larger total  structure effects,  investigated  two  o b s e r v a t i o n of a l a r g e n u c l e a r capture  in section  correlation  there  (10*  The  r a t e seems t o h o l d even f o r t h e  shewing  nuclei  field  the  isotope effect  isotopes.  R e c e n t l y , i t was  magnetic  with  results indicated  (LOD67)  (EAR78), a r e i n  D e s g r o l a r d e t al.(DES78)  r a t e s f o r these  even-Z heavy  also  capture  capture  nuclei  Bardin's  A large isotope e f f e c t  been p e r f o r m e d model,  and  e a c h o t h e r and  however, t h e r e  Calculations  calculation  c f E c k h a u s e e t a l . (ECK63).  experiments,  agreement  Lodder-Jonker  to avoid has  any  been  Z=64 and larger  amount i s not  the C a b i b b o a n g l e .  as l a r g e Since  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  total  effect  muon c a p t u r e  should  be i n v e s t i g a t e d  Our c a p t u r e compared  of  the l a t t e r  experimental  data  the Primakoff  chi-sguared  in detail  r a t e s determined  with t h e P r i m a k o f f  As e x p e c t e d , the  r a t e i n e v e n and odd n u c l e i , t h e .  formula,  minimization  t h i s i n mind.  by l i f e t i m e s  and G o u l a r d - P r i m a k o f f  theory  than  with  gave a s l i g h t l y  the former  theory.  better f i t to  theory.  I n the case  the parameters obtained were  were  by t h e  i n good a g r e e m e n t w i t h h i s  estimate. It perform decay  the l i f e t i m e  spectrum  information atomic given  was n e c e s s a r y  about  lifetimes  rates.  by t h e r a t i o (5.4)).  metallic  compound, but a l s o  The r e l a t i v e  we have e x t e n d e d  was t h e f i r s t  investigating  attempt  Z=30 showed  agreement  of the type  Z 0 .  the periodic  with e a r l i e r  atomic  X-ray  measurements, a l t h o u g h  lower  than  rate  t h e X-ray  f o r atoms  lifetime  method In  atcmic  with  capture  i n eguation  (3.6)  (see  to include  capture  Our r e s u l t s  method i n rates i n  between Z=6  m n  dependence and were i n good capture  r a t e s o b t a i n e d by  our r e s u l t s  measurements. Z larger  ratio i s  initially.  the l i f e t i m e  s y s t e m a t i c a l l y t h e atomic  oxides  In a  t h e i n f o r m a t i o n on muon  our experiment  to apply  to  there i s not only the  t h a n had been a n t i c i p a t e d  1c  and  f o r some e l e m e n t s .  of the a m p l i t u d e s  many more compounds This  measurements  of a chemical  capture  eguation  t o use a c h e m i c a l compound  than  a t TEIUMF d u r i n g  c o n c l u s i o n we n o t e  around  Z=50 were  The muon a t o m i c 30 w i l l  capture  be s t u d i e d by t h e  t h e f a l l o f 1980. t h a t t h i s t h e s i s h a s made a  142  significant capture  by  physical but  c o n t r i b u t i o n to atoms  effects  which can  basic  equipment.  wherever  important  a l s o to  which have  Both and  types  feature  cf  tie  base not  different studied of  so g r e a t  possible.  data  muon c a p t u r e  be c o n v e n i e n t l y  systematic 'errors check  but  the  This  muon  interests  u t i l i z i n g the are  same  fraught  has been t a k e n  c o n s e r v a t i s m may  experimental  in  nuclei;  scientific  experiment care  by  only  technique.  to  be t h e  with double most  143  References  ALB69  a . A l b e r i g i - Q u a r a t a , A . B e r t i n , G.Matone, F.Palmonari, G. T o r e l l i , F . D a l p i a z , A . P l a c c i o , and E . Z a v a t t i n i , P h y s . R e v . J 7 7 , 21 18 (196 9)  AND38  C.D.Andersen and S.H.Neddermeyer, Phys.Rev. 50,263 (1 963) , 5^,584 ( 1937), 54,88 (1938)  AST61  a . a s t b u r y , P.M.Hattersiey, M.Hussain, M.A.R.Kemp, H. Muirhead, and T.Woodhead, Proc. Phys. Soc. 78, 1 144 (1961)  AUE65  L.E.Auerbach, R . J . E s t e r l i n g , J . l . L a c h , and N.H.Lipman Phys.Rev.J38B, 127 (1965)  BAI63  B . J . S . B a i j a l , J.A.Diaz, S.N.Kaplan, and R.V.Pyle, Nuovo Cimento 30, 711 (1963)  BAL75  M.P,Balandin, V.M.Grebenyuk, V.G.Zinov, A.D.Konin, and A. N.Poncmarev, Sov. Phys. JETP 40,8 11 (1975)  BAR59  W.A.Barrett, F.E.Holmstrom, and J.W.Kenffel Phys.Rev.JJ3,6e1(1959)  BAR64  J.Barlcw, J.C.Sens, P.J.Duke, Phys.Lett. 9,84 (1964)  BAR65  M.Bardcn, P.Norton, J.Peoples, A.M.Sachs,J.L.Franzini Phys.Rev. L e t t . J J , 449 (1 965)  BAR78  G.Bardin, J.Duclos, J.Joseph, A.Magnon, J.Martino, E . Z a v a t t i n i , Phys.Lett.79B,52(19 78)  BAR79  G.Bardin, e t a l . . High Energy Physics and Nuclear Conference (1979) C o n t r i b u t i o n 5B16  BAR80  G.Bardin, J.Duclos, A.Magncn, J.Martino, A.Richter, E . Z a v a t t i n i , A.Bertin, M . P i c c i n i n i , A . V i t a l e , and D.Measday, CERN-EP/80-121  R . E . H i l l , D.A.Jenkins,  and M.A.R.Kemp  (Submitted t o Nuclear Physics A)  BEI68  P . E . E e i l i n , Nuovo Cimento 54A,87 1 (1968)  BEL51  W.E.Bell and E.H.Hincks, Phys. Rev. 84, 1243 (1951)  BEE73-1 J.Eernabeu, Nucl.Phys.A20J,41 (1 S73) BER73-2 A . E e r t i n ,  A.Vitale,  and A . P l a c c i  Phys,.Rev. A7,22 14 (197 3) R . E i z z a r i , Nuovo Cimento  33,1497(1964)  1 I . M . E l a i r , H.Muirhead, and T.Woodhead, Prcc.Phys.Sec.80,945(1962) 2 I . M . B l a i r , H.Muirhead, and T.Woodhead, Proc.Phys.Soc.80,938 (1962) R . J . B l i n - S t c y l e , Fundamental I n t e r a c t i o n s and the Nucleus, North-Holland P u b l i s h i n g Comp. (1973) J.H.Brewer, K.M.Crowe, F.N.Gygax, and A.Schenck, Muon P h y s i c s v o l . 3 , ed. V.Hughes and C.S.Wu, New York Academic Press (1975) C. Ericman e t a l . ( P a r t i c l e Phys.Lett.75B, 1 (1978)  Data Group),  F. Cannata and N.C.Mukhopadhyay , Phys. Rev.C_10,379 (1974) P . C h r i s t i l l i n , A . D e l l a f i o r e , and M.Rosa-Clot, Phys. Rev. L e t t . 3 J , 101 2 (1973) P . C h r i s t i l l i n , A . D e l l a f i o r e , and M.Rosa-Clot, Phys. Rev. CJ 2,6 9 1 ( 1975) E.Clementel and G.Puppi, Nuovo Cimento  5,505(1948)  M.Conversi, E . P a n c i n i , and O . P i c c i o n i , Phys. Be v. 6 8, 232 (1945) , 7 J , 209 (1947) G. C c n f o r t o , C R u i k i a , and E . Z a v a t t i n i , Phys.Lett.4,239 (1963) W.A.Cramer, V . L . T e l e g d i , R.Winston, and E. A.Lundy, Nuovo Cimento 24, 546 (1962) K.M.Crewe, J.F.Hague, J.E.Rothberg, A.Schenck, D. L . W i l l i a m s , R.W.Williams, and K.K.Young, Phys. Rev. D5, 2145 (1972) G. C u l l i g a n , e t a l . , D.Harting, N.H.Lipraann., and G . T i b e l l , Conf.Int.on Elementary P a r t i c l e s , Aix-de-Provence, 71,143(196 1), T h i s i s c i t e d i n "Muons" by A.C.Weisenberg  (North-Holland,Amsterdam, 1967) a  H. D a n i e l , Phys.Rev.Lett.24, 1649 (1975) H.Daniel, W.Denk, F. J . Hart mann , J.J.Reidy and  145  fl.Wilhelm,  Phys.Lett.7JB,60(1977)  DAN78  H . D a n i e l , W.Denk, F . J . H a r t m a n n , W.Wilhelm, T . v o n E g i d y , P h y s . B e v . L e t t . 4 J , 8 5 3 (1978)  DAN79  H.Daniel,  DES78  P.Desgrclard, Nucvc Cimento  DEU68  J.P.Deutsch, L.Grenacs, P.Igo-Kemenes, and P . C . M a c g , P h y s . L e t t . 2 6 E , 3 1 5 ( 1 9 6 8 )  DIL71  L . d i L e l l a , I.Hammerman, and P h y s . R e v . L e t t . 2 7 , 8 3 0 ( 1971)  DUC73  J . D u c l o s , A . M a g n o n , and Phys.Lett.47E,491(1973)  DUC80  J . D u c l o s , E x o t i c Atoms ' 7 9 , F u n d a m e n t a l I n t e r a c t i o n and S t r u c t u r e c f M a t t e r , e d . K . C r o w e , J.Duclos, G . F i o r e n t i n i , and G . T o r e l l i , P l e n u m P u b l i s h i n g C o r p o r a t i o n (1980)  DUP75  D.Duplain, B.Goulard, P h y s . R e v . C J 2 , 2 8 (1975)  DZH72  A.A.Dzhuraev, Yu.V.Obukhcv, Sov.Phys.JEIP  ECK62  M . E c k h a u s e , T. A . F i l i p p a s , R . B . S u t t o n , R.E.Welsh, a n d T . A . R o m a now s k i , N u o v o C i m e n t o 2 4 , 6 6 6 ( 1 9 6 2 )  ECK63  M.Eckhause, T , A . F i l i p p a s , P h y s . R e v . J 3 2 / 4 2 2 (1963)  ECK66  M.Eckhause, R . T . S i e g e l , N u c l . P h y s . 8 J , 57 5 ( 1 9 6 6 )  FAL62  I.V.Falcrakin, A.I.Filippov, M.M.Kulyukin, E.Pontecorvo, Yu.A.Scherbakov, R.M.Sulyaev, V . M . I s u p k o - S i t n i k o v , and 0 . A . Z a i m i d o r o g a , P h y s . L e t t . J , 3 1 8 (1S62) , 3 , 2 2 9 ( 1 9 6 2 ) , 6 , 1 0 0 ( 1 9 6 3 )  FAV70  D.Favart et a l . Phys.Rev.Lett.25,1348(1970)  FER47  E.Fermi  FIL63  T.A.Filippas, P.Pabit, P h y s . L e t t . 6 , 118(1S63)  Z. P h y s i k  and  and  A 2 9 J , 29 ( 1 9 7 9 )  P.A.M.Guichcn, 4 3 A , 4 7 5 (1978)  and  J.Joseph  P.Lipnik,  L.M.Bosenstein  J.Eicard  and  J.Joseph,  V.S.Evseev, G.G.Myasishcheva, and V . S . R o g a n o v , 35,748(1972)  E.Teller,  R.B.Sutton  R.E.Welsh,  and  and  R.E.Welsh  T.A.Filippas,  P h y s . R e v . 7 2 , 3 9 9 (1947) and  R.I.Siegel,  146  FIS59  J . F i s h e r , B . I e c n t i c , A.Lundby, E.Meunier, and J . P . S t r c o t , P h y s . E e v . L e t t . 3 , 3 4 9 (1959)  FIS71  E.Fischback, and J . S m i t h ,  FOE62  K.W.Ford  FE.I79  G . F r i c k e , G . M a l l o t , A . E u e t s c h i , L . A> S c h a l l e r , L . S c h e l l e n b e r g , H . S c h n e u w l y , and E . B . S h e r a , SIN A n n u a l E e p o r t 1 9 7 9 , P a g e C37  FBY68  D.Fryberger,  FUJ59  A.Fujii  FUJ79  A.Fujii,  GAE79  D.Garner,  GIL60  V.Gilinsky  GOU71  B . G o u l a r d , J . J o s e p h , and F.O.l'edoyen P h y s . B e v . L e t t * 21, 1 2 3 8 ( 1 9 7 1 )  GOU74  B.Gculard  GEA80  E.D.Graves, B.A.Lamers, A,Nagl, H.Uberall, V . D e v a n a t h a n , and P . E . S u b r a m n n i a n , C a n . J . P h y s . . 5 8 , 4 8 (1980)  HAF74  P.K.Haff  HAS76  O.Hashimoto, S.Nagamiya, P h y s . L e t t . 6 2 B , 2 33 ( 1 9 7 6 )  HAB77  E . D . H a r t , C.E.Cox, G.W.Dodson, M.Eckhause, J.B.Kane, M . S . P a n d e y , A . M . B u s h t o n , E. T . S i e g e l , a n d E . E . W e l s h P h y s . E e v . L e t t . 3 9 , 399 ( 1 9 7 7 )  HUF61  E.W.Huff,  HWA78  W-Y.P.Hwan,  JAM7 1  F.James Interim  J0H77  M.W.Johnson, W.U.Schroder, J . E.Huizenga, W.K.Hensley, D . G . P e r r y a n d J . C . B r o w n e , P h y s . B e v . C 1 5 , 2 169 ( 1 9 7 7 )  J0S72  J.Joseph, F.Ledoyen, and B . G o u l a r d , P h y s . E e v . C 6 , 174 2 ( 197 2)  M.M.Nieto, H.Primakoff, C.K.Scott, P h y s . E e v . L e t t . 2 7 , 1 4 C 3 (1971)  and J . G . W i l l s ,  N u c l . P h y s . 35 , 2 9 5 ( 1 9 6 2 )  P h y s . B e V . J 6 6 , 1 3 9 7 (1 9 6 8)  and H . P r i m a k o f f , Private  Nuovc  Cimento  12,327(1959)  communication  P h . D . t h e s i s (1979) , and J . M a t h e w s ,  UBC C h e m i s t r y  Dept.  P h y s . B e v . 1 2 0 , 1450 (1960)  and H . P r i m a k o f f ,  P h y s . E e v . C _ 1 0 , 2 0 3 4 (1 9 7 4 )  and T . A . T o m b r e l l o ,  A n n . P h y s . 8 6 , 178 ( 1 9 7 4 )  K.Nagamine,  and  T.Yamazaki,  A n n . P h y s . 1 6 , 2 8 8 ( 196 1) P h y s . B e v . C_17, 1 7 9 9 (1 S78)  a n d M . E o o s , M I N U I T , CEEN C o m p u t e r Programme L i b r a r y (1971)  7600  147  KAP58  S.N.Kaplan, B.J.Mover, E h y s . Ee v . _ M 2 , 9 6 8 ( 1 958)  and  KEL80  E . L . K e l l y e t a l . ( P a r t i c l e Data Eev.Mod.Phys.52,S1(1980)  KES67  D.Kessler, H.L.Anderson, M.S.Dixit, H.J.Evans, E.J.McKee, C.K. Hargrove, B.D.Earton, E. P . H i n c k s , J . D . M c A n d r e w , P h y s . R e v . L e t t . J 8 , 1 1 79 ( 1 9 6 7 )  KIN57  T.Kinoshita  KIS73  H.E.Kissener, A.Aswad, H.U.Jager, N u c l . P h y s . A 2 J 5 , U2U (1 S73)  KNI76  J.D.Knight, C.J.Orth, H.Daniel, K.Springer, P h y s . B e v . AJ2,43 (1S76)  KCH76  Y.Kchyama and A . F u j i i , S u p p l e m e n t c f t h e P r o g . T h e o r . P h y s . 6 0 , 171  and A . S i r l i n ,  E.V.Pyle Group)  and  E h y s . E e v . J _ 0 7 , 593 (1957) and  E.A.Eramzhian,  M . E . S c h i l l a c i , B»A.Naumann, and H . B . K n c w l e s ,  (1976)  KCH79  Y . K c h y a m a and A . F u j i i , TEIUMF E e p o r t (submitted tc Nuclear Physics)  K0Z78  T . K o z l o w s k i and A . Z g l i n s k i , Nucl.Phys.A305,368(1978)  LAT47  C.M.G.Lattes, H.Muirhead, G . P . S . O c c h i a l i n i , C . F . P c w e l l , N a t u r e ( L o n d o n ) 1 5 9 , 6 9 4 (1 9 4 7 )  LAT6 1  J.L.Lathrop, E.A,Lundy, V.L.Telegdi, E.Winston, D. D. Y o v a n o v i t c h , P h y s . E e v . L e t t . 7 , 107 ( 1 9 6 1)  LEE78  H.C.Lee  LE079  M . L e o n , L o s A l a m o s R e p o r t L A - U R - 7 9 - 1 2 3 5 (1979) ( E x o t i c Atoms ' 7 9 , F u n d a m e n t a l I n t e r a c t i o n and Structure cf Matter, e d . K . C r o w e , J . D u c l o s , G . F i o r e n t i n i , and G . T o r e l l i , P l e n u m P u b l i s h i n g C o r p o r a t i o n , NY  LOD67  A.Lcdder  LUN62  E.A.Lundy,  LUY63  J.R.Iuyten, H.P.C.Rood, N u c l * P h y s . 4 j , 2 3 1 (1963) ,  MAN61  E.A.Mann  and  F.C.Khanna,  TEI-PP-79-41  and  Can.J.Phys.56,149(1978)  and C . C . J c n k e r ,  N u c l . P h y s . B 2 , 3 8 3 (1967) P h y s . L e t t . VS, 3 10 ( 1 9 6 5 )  P h y s . Re v . J 2 5 , 16 86 (1 9 62)  and M . E . B o s e ,  and  and H.A.Tolhoek, 7 0 , 6 4 1 (1965) P h y s . B e v . J 2 J , 293 (1961)  148  MAB80  J.Martino  and J . D u c l o s ,  Private  MAT71  G.Matone,  Lett.Nuovo  MAU77  L.F.Mausner, E.A.Naumann, J . A . M o n a r d , and S . N . K a p l a n , P h y s . R e v . A J 5 , 4 79(1977)  MEY63  S.L.Meyer, E.W.Anderson, E . B l e s e r , L.M.Lederman, J . L . R o s e n , J . E o t h h e r g , and I-T.Wang P h y s . E e v . J 3 2 , 2693 (1963)  MIC57  L.Michel,  MUK77  N.C.Mukhopadhyay,  NAL74  O . N a l c i c g l u , D.J.Rowe, and N u c l . P h y s . A 2 J 8 , 495 (1974)  PAE78  E . P a r t h a s a r a t h y and V . N . S r i d h a r , C a n . J . P h y s . 5 6 , 1606 ( 1 9 7 8 )  PET63  V . I . P e t r u k h i n and . Y u . D . P r o k o s h k i n , N u c v c C i m e n t o 2 8 , 9 9 (1963)  POV70  H.P.Povel, H.Koch, a n d G. B a c k e n s t o s s ,  PRI59  H.Primakcff,  PEI77  H . P r i m a k o f f , AIP Conference Nc37, Weak I n t e r a c t i o n P h y s i c s - 1 9 7 7 p 8 5  REI60  R . A . R e i t e r , T. A . R c m a n o w s k i , R . B . S u t t o n , E . G . C h i d l e y , P h y s . Be v . L e t t . 5 , 2 2 (1960)  R0071  M.Rcos  E0074  M.EOOS,  ROS63  J . L . E c s e n , E.W.Anderson, S.L.Meyer, J.E.Eothberg, P h y s . B e v . j 1 3 2 , 2 6 S 1 (1963)  SAC75  A . M . S a c h s a n d A . S i r l i n , Mucn P h y s i c s v o l 2 , e d . V . W . H u g h e s a n d C . S . W u ( A c a d e m i c P r e s s 1975)  SAL74  A . S a l a m a n d . J, S t r a t h d e e ,  SCH77  H.Schneuwly, Proceeding of the 1st course I n t e r n a t i o n a l School of Physics of E x o t i c e d . G . F i o r e n t i n i a n d G . T o r e l l i , 255 (1977)  SCH78-1  H.Schneuwly,  Cimento  communication  (1980)  2,151(1971)  Rev.Med.Phys.,29,223(1957) Physics  Reports  3 0 C , 1 (1977)  C.Ngo-Trong  W.D.Hamilton, S.Charalambus, P h y s . L e t t . 3 3 B , 6 2 0 (1970)  R e v . M o d . P h y s . J J , 802 (1959)  and A . S i r l i n ,  and  Nucl.Phys.B29,296(1971)  N u c l . P h y s . B 7 7 , 420 (1974)  T.Dubler,  E.J.Bleser, L.M.Lederman, and I - T . W a n g ,  Nature  K.Kaeser,  2 5 2 , 5 6 9 (1974) of t h e Atoms,  B.Eobert-Tissort,  149  L . f l . S c h a l l e r / and L . S c h e l l e n b e r g P h y s . L e t t . 6 6 A , 168 ( 1 9 7 8 ) SCH78-2  H.Schneuwly, V.I.Pokrovsky, N u c l . P h y s . & 3 1 2 , 4 19 (1 97 8)  SCH79  W.U.Schroder, W.W.Wilcke, M.W.Johnson, D . H i l s c h e r , J . H . H u i z e n g a , J . C . B r o w n e , and D . G . P e r r y P h y s . E e v . L e t t . 4 3 , 6 7 2 (1979)  SEN57  J . C . S e n s , R . A . S w a n s o n , V . L . T e l e g d i , arid D . D . Y o v a n o v i t c h , P h y s . R e v . J O 7 , 1464 (19 57)  SEN58  J.C.Sens,  R.A.Swanson,  D.D.Yovanovitch,  Nuovo  SEN59  J.C.Sens,  SHM59  I.M.Shmushkevich,  SHR78  R. E . S h r o c k  L.I.Ponomarev,  V.L.Telegdi, Cimento  Phys.Rev.JJ3,679  and  and  and  7,536(1958)  (1959)  Nucl.Phys.JJ,419(1959)  L.L.Wang,  P h y s . R e v . L e t t . 4 J , 169 2 ( 1 9 7 8 ) SUR75  P.Suranyi  and R . A . H e d i n g e r ,  SUZ79  T.Suzuki  et  a l . , CAP  C o n g r e s s , paper  SUZ80  T.Suzuki  et  a l . , CAP  C o n g r e s s , p a p e r AD4  SWA58  R.A.Swanson,  P h y s . B e v . J J 2 , 5 8 0 (1S58)  SWA59  R.A.Swanson,  R.A.Lundy,  D. D. Y o v a n o v i t c h ,  Phys.Lett.56B,151(1975)  V.L.Telegdi,  EC3  Vancouver  1979  Hamilton  1980  and  P h y s . R e v . L e t t . 2 , 4 3 0 ( 19 59)  SWA60  R.S.Swanson,  R e v . S c i . I n s t r u m . 3 J , 1 49 (1 9 6 0 )  TEL59  V.L.Telegdi,  P h y s . Re v . L e t t . 3 , 59 ( 1 9 5 9 )  TIM49-1  J.Timno  and J . A . W h e e l e r ,  Re v . M o d . E h y s . 2 J , 144 ( 1 9 4 9 )  TIM49-2  J.Timno  and J . A . W h e e l e r ,  Eev.Mod.Ehys.2J,153(1949)  TUR63  L.Turner,  UBE60 VIT80  H . U b e r a l l , P h y s . R e v . 1 1 9 , 3 6 5 (1 9 6 0 ) A . V i t a l e , E x o t i c Atoms ' 7 9 , F u n d a m e n t a l I n t e r a c t i o n and S t r u c t u r e c f M a t t e r e d . K . C r o w e , J . D u c l o s , G . F i o r e n t i n i , and G . T o r e l l i , P l e n u m P u b l i s h i n g C o r p o r a t i o n (1980) J . D . W a l e c k a , Muon P h y s i c s , e d . V . W. H u g h e s a n d C . S . W u , Academic Press 1975  WAL75  Bull.Am.Phys.Soc.Ser.II#8,324(1963)  150  WAT75  P.J.S.Watscn,  Phys. L e t t . 5JB, 43 1 (1 S75)  WHE49  J.ft.Wheeler,  Eev.Mod.Phys.2J,133(1949)  WIL72  E.W.Williams  and D . L . W i l l i a m s , P h y s . Rev. D6,737 (1972)  WIL80-1  S . E . W i l l i s , V.W.Hughes, P.Nemethy, R.L.Burman, D.R.F.Cochran, J . S . F r a n k , E.P.Bedwine, J . D u c l o s , H.Kaspar, C . K . H a r g r o v e , and U.Moser Phys.Rev.Lett.44,522(1980)  WIL80-2 W.W.Wilcke, M.W.Johnson, W.U.Schroder, D.Hilscher, J . R . B i r k e l u n d , J . R . H u i z e n g a , J.C.Browne, and D . G . P e r r y , Phys.Rev.C21,2019 (1S8 0) WIN61  R.Winston and V . L . T e l e . g d i Phys.Rev. L e t t . 7, 104 (1961)  WIN63  R . W i n s t c n , Phy s. Re v. J J 9 , 27 6 6 ( 1 96 3)  WU69  C.S. Wu and L . W i l e t s ,  YAM74  T.Yamazaki, K.Sugimoto,  YUK35  H.Yukawa, P h y s i c o - M a t h e m a t i c a l S o c i e t y o f J a p a n (Nippon S u g a k u - b u t s u r i g a k k a w a i K i z i ) .17,48 (1935)  ZIN64  V . G . Z i n o v , A.D.Konin, and A . I . M u k h i n , S o v . P h y s . J E T P J 9 , 1292 ( 1964)  ZIN66  V . G . Z i n o v , A.D.Konin, and A.I.Mukhin, Sov.J.NucliPhys.2,613(1966)  Ann. Re v. N u c l . S c i . 19 ,527 (1969)  S.Nagamiya, O.Hashimoto, K . N a k a i , and K.M.Crowe, P h y s . L e t t . 5 3 B , 1 1 7 ( 1 9 7 4 )  

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