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Pion transfer in gaseous hydrogen Noble, Anthony James 1986

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PION TRANSFER IN GASEOUS HYDROGEN by ANTHONY JAMES NOBLE •Sc. (Math/Phys.), The University of New Brunswick, 1983  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Physics . We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA January 1986  © Anthony James Noble ,  1 986  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or by his or her representatives.  It is  understood that copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  PHYSICS  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  DE-6(3/81)  13/01/86  ABSTRACT.  The pressure of n  H2,  D2  IT  +  0  experiment gas  consisted  of  stopping  t a r g e t to measure the  and HD were  gas. The  detected  negative  pions  in  a  high  t r a n s f e r r a t e ir-p •*• ir-d i n mixtures  gamma rays from the decay of the I T i n ir-p •*• 0  in  coincidence  using  two  large  sodium  iodide  crystals. The pionic  probability  hydrogen  A  ratio  =  0.21  in  an  ±0.04. equal  internal  ratio  level.  be  t r a n s f e r r e d to a deuteron  described  These  mix  of  values H2  i n terms  2  2  and  implied  of  D2  was  that  a  indicated  the  F(H D )  measured to be F(HD)  F(H D )/F(HD)  transfer  about a 60%  pion  from  that  2  2  =  a  phenomenological  by B and A . F i t s to the data y i e l d e d B = 0.77  c a p t u r e r a t i o f o r HD was The  a  complex was  model parameterized and  that  hydrogen 0.45  ±0.14 capture  ±0.01.  The  = 0.355 ±0.021. there  was  likely  to  be  i n the breakup of ir-HD f a v o u r i n g the ir-d complex at  - iii -  TABLE OF CONTENTS.  Abstract  i i  Table of Contents L i s t of Tables L i s t of Figures Acknowledgements  i i i v vi viii  1.  Introduction and Motivation  1  2.  Theory  4  2.1  I n i t i a l Slowing Down  5  2.2  Coulomb Capture  6  2.3  De-excitation  16  2.4  Transfer  19  2.5  Nuclear Capture  22  2.6  The H2D2 and HD Systems  25  2.7  Summary of Previous Hydrogen Measurements  29  3.  The Experiment  31  3.1  Overview of Experimental Setup  32  3.2  Target Design  33  3.3  Selection of Beam Parameters  35  3.4  Gas Preparation, Handling and Mixing  38  3.5  Electronics and Data Acquisition  42  -  4.  Analysis  47  4.1  Determination of Gas Concentration  48  4.1.1  V i r i a l Corrections  49  4.1.2  Concentration Error Analysis  53  4.2  4.3  5.  iv -  Analysis of the Data  54  4.2.1  Time Cuts  55  4.2.2  RF Cuts  57  4.2.3  Energy Cuts  4.2.4  The Stop D e f i n i t i o n  65  4.2.5  F i t t i n g the Stop Region  71  4.2.6  Comment on Error Analysis and Combination of Data. 76  Calculation of the Hydrogen Capture Ratio  ..59  78  Results and Discussion  83  5.1  A Comparison of the Results to the Literature  87  5.2  Limits on the Molecular Breakup Rates i n HD  88  5.3  The Future of These Measurements  90  5.4  Summary  91  References  93  - v -  LIST OF TABLES.  Table 4.1  V i r i a l y corrected deuterium gas concentration  52  Table 4.2  Stopping p r o f i l e of target  65  Table 4.3  Hydrogen capture ratios  80  Table 5.1  Comparison of results with previous measurements  87  - vi-  LIST OF FIGURES.  Figure 2.1  P e r i o d i c i t y of the muon capture r a t i o i n oxides  11  Figure 2.2  H Z T T - Potential  13  Figure 2.3  Rate diagram f o r HZir- system  14  Figure 2.4  Rate diagram f o r H2D2 mixtures  26  Figure 2.5  Rate diagram f o r HD  26  Figure 3.1  Experimental  33  Figure 3.2  Target design  34  Figure 3.3  Scintillator detail  35  Figure 3.4  TRIUMF M13 beam l i n e  37  Figure 3.5  Apparatus f o r HD manufacture  39  Figure 3.6  Gas Manifold  40  Figure 3.7  Electronics  Figure 4.1  TINA time spectrum  56  Figure 4.2  RF time spectrum  58  Figure 4.3  TINA coincidence spectrum  60  Figure 4.4  TINA singles spectrum  61  setup, viewed from above  diagram  43  Figure 5.4a F i t to TINA radiative capture peak  63  Figure 5.4b F i t to MINA radiative capture peak  ....64  Figure 4.6  Scatterplot  of ES3 and ES4 f o r pulser strobe  67  Figure 4.7  Scatterplot  of ES3 and ES4 f o r non-pulser  68  Figure 4.8  Schematic of ES3 vs. ES4  69  Figure 4.9  Energy d i s t r i b u t i o n of S3 before cuts  73  Figure 4.10 Energy d i s t r i b u t i o n of S4 before cuts  73  Figure 4.11 Energy d i s t r i b u t i o n of S3 after cuts  74  strobe  - vii-  Figure 4.12  Energy d i s t r i b u t i o n of S4 after cuts  74  Figure 5.1  Hydrogen capture r a t i o i n mixtures of H2 and D2  84  Figure 5.2  Transfer probability i n mixtures of H2 and D2  85  Figure 5.3  Limit of molecular breakup rate  89  - viii -  ACKNOWLEDGEMENTS.  I would his  help  l i k e to thank my supervisor, Professor D.F. Measday f o r  and encouragement  throughout  the analysis and during the  preparation of this thesis. I would also l i k e to thank Dr D. Horvath, Dr M. Salomon and Dr K. Aniol f o r discussions about the analysis and their  tireless  help  during  the s h i f t  work. I am also  indebted to  S h i r v e l Stanislaus, Dr F. Entezami, Dr J . Smith and Dr D. Livesey f o r t h e i r assistance during the experiment. I would l i k e to thank NSERC for their f i n a n c i a l assistance during my term as a masters student. F i n a l l y , I would l i k e to thank my friends, especially Shirley, who suffered  with  patience  writing of my thesis.  and understanding  during  the dark age of the  Chapter 1  Introduction and Motivation.  When a pion  stops  molecular,  atomic,  subdivided  into many stages, and  sees  the  only  processes. stopping  and  i n matter  final  Hence  nuclear  products  parameters  as  theoretical  studies  levels.  a  capture mechanism can  i t i s the job of the physicist  have  similar  possible.  The  to unravel these mutually  experiments  i n groups of  i t i s involved i n interactions at  focused  their  compounds so as  From  such  phenomenological  who  interrelated  attention  on  pions  to eliminate as many  experiments model  be  and  describing  extensive the  life  history of pions i n matter can be developed. By  studying  relative  the pionic  strengths  capture  or  nuclear  capture.  of  competing  collisionally The  capture mechanism one processes  induced  monitors  transfer  of  a  like and  pion's  can  determine  radiative Stark  progress  and  Auger  enhancement in a  the  of  condensed  medium which are available to experimentalists are the X-Rays emitted as the exotic pionic atom de-excites as i t cascades  down towards the  nucleus and the diverse reaction products from nuclear capture. The  knowledge of the pion stopping schedule has  interest  to more than  just  the  academic. At  first  proved glance  to be of one  would  suppose that a pion would stop i n a mechanical mixture of gases l i k e +  2H  2  ^H^.  i n much the same way Experiment  as f o r a chemical compound l i k e  N  2  hydrazine  shows us however that this i s not the case. There i s a  substantial suppression of capture on the hydrogen i n hydrazine due to the proximity of the nitrogen atoms. proven  to  molecules.  be  a useful  tool  In this way  i n probing  the  pionic chemistry has  electronic  structure of  - 2 -  It  i s also  correlated  to the  muons i n oxides these  power  the  atomic  shell  structure  capture p r o b a b i l i t y . This was  i t i s seen  probability which  that  first  i s strongly observed with  and has since been seen i n many other compounds. In  1  compounds  capture  clear  can  2  that  i s similar  be  the  oscillatory  to observed  explained  by  character of  oscillations  examining  the  the  of stopping  electronic  shell  structure. In mixtures of hydrogen isotopes i t i s found that a stopped y- can form muonic molecules  from which the nuclei  can fuse, an  exothermic  reaction which has been proposed as a macroscopic source of energy. By examining  pionic  capture one  can  deduce  information about  analogous  processes i n the muon catalyzed fusion reactions. The l o n g l i f e time and absence of a strong i n t e r a c t i o n allow a muon to catalyze as many as 1 0 0 fusions  i n mixtures  of deuterium  and  tritium.  In the theory of muon  induced fusion ddy and d t u complexes are formed v i a an excited resonant molecule of the form [ d d u - d 2 e ] . The resonant mechanism greatly enhances the rate of formation. The d d u and d t p can then fuse yielding neutrons, helium,  and  often  ejecting  catalyze more fusions.  the muon. This muon may  then recycle and  Knowledge of the transfer process between d y  and ty i s c r i t i c a l  to the understanding of the o v e r a l l mechanism, and  it  studies  i s hoped  that  of pions w i l l  help clear  up  some of  the  mysteries. At brain  a more p r a c t i c a l l e v e l , i n the medical treatment of deep seated and  pelvic  tumours pions have proven  to be very useful. Since  upon being captured by nucleus the entire pion rest mass Is given up to heavy  fragments  one  can  maximize  the  damage  to  the  tumour  while  minimizing the e f f e c t i v e dosage to the intervening healthy tissue. This  - 3 -  is  in  contrast  to  the  traditional  method  of  treatment  by  y ray -  i r r a d i a t i o n for which the r e l a t i v e body dosage f a l l s off with depth, so that  the  overlying healthy  tumour. A  tissue  better understanding  i s more heavily damaged  of  the  allow optimization of the pion therapy In this experiment we mixtures  of H ,  D  2  stopping  mechanism  the will  technique.  studied the stopping mechanism of pions i n  and HD gases. We  2  pion  than  investigated very simple  molecules  i n an attempt to determine fundamental parameters which would allow us to extract r e a l physics from the data.  The general procedure to date  i n the l i t e r a t u r e appears to be the systematic measurement of a whole host of complex molecules  from which general trends can be determined  but no simple physics p r i n c i p l e . Experimentally which  were  relationship  we  captured of  FH D  measured on  the f°  r  t n e  the  proton.  high F H  D  Fy^  we  re-examined  / F H D ratio.  We  relative  2 2  measuring  fraction  of  stopped  determined H,/D, z  the  FX  previously  a  pions  functional  concentration.  By  z  observed  3  anomalously  - 4 -  " Chapter 2  Theory.  During the i n i t i a l capture process a negative pion can replace an electron about a nucleus to form an exotic atom. Since the Bohr radius i s inversely proportional to the mass, and a pion i s much heavier than an  electron,  the  pionic  orbits  eventually become very  small.  l i f e t i m e of pionic hydrogen i s i n the order of a picosecond, on the  The  (depending  environment).  In order to discuss the processes of pion capture we subdivide the stopping mechanism into several stages. In most cases these stages w i l l be competing with other processes. Here we try to present the possible mechanisms which  and  support  discuss or  the  theoretical  contradict  them. We  models which have been developed To get an understanding  and  will  experimental predictions also  examine some of  the  to f i t the wealth of data available.  of the entire process and because most of the  data are not of this form, we w i l l not l i m i t discussion to mixtures of hydrogen isotopes. The  primary  source  of energy  stage where i t i s slowed thermal  electrons by  electrons  from  It  interactions, may  then  be  principally captured  by  ejecting  into  excited  mesomolecular or mesoatomic orbits via an Auger t r a n s i t i o n . The distribution  first  from a r e l a t i v i s t i c v e l o c i t y to that of the  Coulomb  atoms.  loss for the pion i s i n the  of the pion w i l l  be determined  by c o l l i s i o n a l l y  final  induced  de_excitations or transfers and the density of electronic states about each  atom. Once  the  pion  reaches  the  lower  energy  states i t s wave  function begins to overlap with the nucleus and i t can then be captured v i a the strong i n t e r a c t i o n .  - 5 -  §2.1  I n i t i a l Slowing Down. In  the  first  stage,  where  the  pion has  lots  of  energy,  small  amounts of energy are given up to the electron cloud of the medium i n the  form  of  parameterized  excitation by  the  or  dissociation.  velocity  and  charge  The of  process  the  can  pion,  v  be  and  z  respectively, and by the number of electrons i t sees which i s given by N, The  the number of atoms per cm  and Z the atomic number of the medium.  3  only other parameter i s how  t i g h t l y bound the electrons are which  i s given by the average i o n i z a t i o n potential I. Then the energy loss i s given by the Bethe-Bloch  _ dE  dX  4Tie z ZN 4  =  z  1  „  2  7— m v e  equation *;  ,„  • B ,  . .  (2.1)  where B i s the stopping number and i s a logarithmic term which varies slowly with energy.  ln(2m  v ) 2  B =  This  i s the  added correction higher  order  ln(l-B ) - B 2  simplest  2  •  (2.2)  form of B, more elaborate treatments  terms for s h e l l e f f e c t s , density e f f e c t s , and  c o r r e c t i o n s . We 5  see  from  dependence on Z so that i n mixtures  (2.1)  have other  that there i s a linear  the pion w i l l  be more l i k e l y  to  stop near the heavier atoms. Equation (2.1) i s only v a l i d for p a r t i c l e v e l o c i t i e s greater than the thermal electron v e l o c i t i e s ; v > v  t h  « oc ,  (2.3)  - 6 -  where a i s the fine structure constant, a = 1/137. Of course i t i s also possible that the pion loses large amounts of  energy  by  velocities  interacting  strongly with  a  nucleus,  but at  the mean free path f o r hadronic interactions  these  i s very long  and hence this process i s r e l a t i v e l y rare.  §2.2  Coulomb Capture. By Coulomb capture one means the t r a n s i t i o n from the continuum to  the discrete spectrum. This i s by f a r the least well understood  process  i n the o v e r a l l picture of a stopping pion. This i s due to the fact that we do not understand  the t r a n s i t i o n mechanism and we do not have a good  f e e l i n g for energy losses at low energies. It i s s t i l l an open question whether consider  one should  treat  the transfer  the transfer  of small quanta  as an adiabatic of energy  process or  to v i b r a t i o n a l and  r o t a t i o n a l molecular states. There has been much discussion about the competition between the slowing down and atomic capture processes, and i n p a r t i c u l a r the energy of the pion when the t r a n s i t i o n occurs. Korenman and Rogovaya believe 6  the energy that  i s i n the order of hundreds of eV whereas Leon  the t r a n s i t i o n  implications,  occurs  especially  closer  to 20 eV. This  f o r isotopic  mixtures,  7  predicts  has interesting  as with  energies of  10's of eV, v i b r a t i o n a l and r o t a t i o n a l differences could be s i g n i f i c a n t i n the stopping powers and cause an isotopic asymmetry i n the i n i t i a l capture rate. We  do  know  that  when  the pions  have  low enough  energy,  (10eV<E<10keV), most of them are captured into excited mesomolecular or mesoatomic  states.  The most  likely  process  f o r this  capture  i s the  - 7 -  emission  of  an  Auger  electron as  than that of radiative capture. the  capture  process  the  dimensions of the f i e l d  this  We  cross-section  i s much larger  also know that throughout most of  pionic wavelength  i s short  through which i t travels and  relative  to  the  that the entire  process time i s short compared to the natural decay time. This process has  been of interest for quite some time and  so many models have been  developed with somewhat limited success. The  Fermi-Teller model  8  was  the f i r s t  the energy loss of a meson i s considered to  conduction electrons  such model developed. Here  to be the transfer of energy  i n a degenerate electron gas.  l i n e of thought, a Z dependence for the  Following  capture process i s  this  obtained.  This Z dependence i s derived by assuming to a f i r s t approximation that the  p r o b a b i l i t y of  capture on  an  atom i s proportional to the  energy  loss of the p a r t i c l e to that atom. If one  defines by W(Z)  the probability that the pion w i l l end  on an atom of atomic number Z,  then one  up  can define the atomic capture  r a t i o by;  A ( z z ) = WCZ^/WCZ^ . 1 5  Fermi and T e l l e r  8  derive;  -l 3/2 + 4,rZ e b (l-.8/X ) N-lw^ + 4 rZ e b^ (l-.8/X° ) 3  ACZ^Z^  where  b  is  proportional  N =  (2.4)  2  w  3/2  1  2  1  a  constant  to  the  Bohr  ni  3  from  (2.5)  2  2  2  the  radius  and  statistical X-  is  model  determined  of by  the  atom  boundary  - 8 -  conditions. In the approximation that the pion energy w i s small, gets, neglecting any Z dependence of X  ;  Q  A(Z ,Z ) * Z /Z . 1  2  1  (2.6)  2  Numerous experiments followed which showed that the "Z law", good description of the measurements. Zinov et a l . mesic X-rays  i n metal  alloys and  one  1  was  not a  studied the K-shell  metallic halides  and  determined  a  capture r a t i o ;  A ( Z Z ) = 0.66 1 5  It was  Z /Z  2  1  noted by B a i j a l et a l .  be described  .  2  (2.7)  that a l l the experimental ratios could  9  by;  A(Z ,Z ) = ( Z / Z ) X  Vogel et a l .  2  1  n  2  developed a new  1 0  ,  0.5  < n < 1.5  (2.8)  theory. They calculated the number  of stops on each atom (N^) by integrating;  N 1  where P(E) atoms  of  extracted  was  = /" n 0  the  P(E) a (E) i  dE ,  (2.9)  1  flux of mesons of energy E, n^ was  species  i  the values  and  a*  was  the  capture  cross  the number of section.  They  of a* by assuming a linear dependence on energy  of the form;  a  1  =  C  x  -  CE 2  (2.10)  - 9 -  where  and  C  were  2  determined  from  the  potential  used  in  the  Thomas-Fermi model of the atom. Their calculations predicted a capture r a t i o of the form; A(Z ,Z ) = X  (Z /Z ) . 1  2  1  (2.11)  1 5  2  consistent with other models, but s t i l l not very useful. A  d i f f e r e n t approach  energy  loss AW  was  taken  by D a n i e l . 1 1  He  determined  the  of a p a r t i c l e moving inside a screened spherical well  and found;  (2.12)  where V  Q  i s the average electron v e l o c i t y and i s proportional to  and T i s the pion k i n e t i c  X  which f i t s  2  Z Z  1 / 3  U  i  2  2 / 3  ,  energy. The i n t e g r a l i s over the trajectory  of the pion. This formulation  A(Z ,Z )  Z  yields;  ln(.57Z ) ln(.57Z )  (2.13)  2  rather n i c e l y with the metal halides, but otherwise does a  poor job, mainly because  i t i s so sensitive to the atomic r a d i i which  are somewhat i l l - d e f i n e d  for atoms bound i n molecules by ionic  and/or  covalent bonds. The importance of atomic structure has been c l e a r l y i l l u s t r a t e d by Evseev et a l . They point 2  protons  and  oscillations-  alpha This  out that the stopping powers of low energy  particles has  been  are known  characterized for  quite  by  some  Z time  dependent and  the  - 10 -  o s c i l l a t i o n s have been explained by examining  the idiosyncrasies of the  e l e c t r o n i c s h e l l structure. These same periodic o s c i l l a t i o n s have been observed i n negative muon capture i n oxides and other compounds and i t was shown by Evseev et a l . that there was a strong c o r r e l a t i o n between the two. Figure 2.1 displays the p e r i o d i c i t y of the muon capture r a t i o i n oxides as a function of Z. The large points are predictions of an empirical formula developed by Stanislaus et a l The most  successful model u n t i l  f i t to a l l d a t a (S.P.P.). and  n  1  2  .  recently, as determined  was developed by Schneuwly, Pokrovsky  1 3  They  considered  be the e f f e c t i v e  molecules  numbers of core  and Ponomarev  of the form electrons,  respective valencies, Then the t o t a l number of electrons  N  = k(n + v) + £(n*+v*)  T  The probability  by a x  2  14  Z^Z£. Let n v and v  the  i s just;  (2.14)  of capture into mesoatomic and mesomolecular o r b i t a l s  can then be given by;  cr = kn/Nx  a  m  ,  = (kv + £v*)/N  (2.15a)  (2.15b)  T  From these one can write the atomic capture r a t i o as;  I (a +o_w ) A(Z,Z ) =  *—™~rr  k (a +a w ) m  as kv = t v . Here w and w  n + 2vw * * * n + 2v w  are the p r o b a b i l i t i e s  (2.16)  that the pion w i l l  FIGURE 2.1  Periodicity of the muon capture ratio in oxides.  - 12 -  de-excite into of  electrons  orbitals  of Z or Z  i n a sub-shell  respectively.  j can be  The  effectiveness  given by a function p(Ej) so  that;  n = Z p(E ) n  with  Ej  model,  the  binding  assuming  (2.17)  energy  that  only  of  the  the  less  j t h sub-shell. tightly  bound  In  the  S.P.P.  electrons  important i n the capture process, two p ( E j ) functions were t r i e d .  are The  "sharp boundary",  P  (  E  j  )  i0  =  llS ? Otherwise.  (2.18a)  E  and the "smooth boundary", 1 E. < E ^ e x p ( ( E - E°M,v2s ) / E ) otherwise  =  P(E.)  J  2  j  where E the  Q  and E  data  c  have  0  ;  are adjustable parameters shown  the  (2.18b)  2  smooth  boundary  of the model. F i t s approximation  to  to a l l be  more  successful. The S.P.P. model, and the large mesic molecule model are based on the b e l i e f  that  the pion i s f i r s t  captured into  large  mesomolecular  o r b i t a l s rather than direct capture into atomic o r b i t a l s . Experimental evidence for this i s strong. If one defines by F(x) the probability a pion w i l l end up on a hydrogen atom i n some mixture x, then we have, for example * ; 15  3  - 13 -  F(N +2N ) F(N H ) 2  Here we  30  2  2  k  see  that  the  F( 2HD  1.23.  )  chemical bond has  (2.19)  played  an  Important  role  In  determining the ultimate fate of the pion. In  recent  work by  further  developed. The  quantum  mechanical  von  Egidy et a l .  muon capture  approach.  The  1 6  the  S.P.P  model has  ratios were calculated using  interaction  cross  sections  calculated i n terms of Z, the atomic binding energies, and numbers n and  increased  a  were  the quantum  I. Their results reproduced the data quite well, except  for low Z values where the S.P.P separately,  been  did role  a  better  of  the  job.  model, treating the valence electrons This  chemical  was  believed  bond  in  to  be  distorting  due  the  to  the  electron  distribution.  =7 FIG  r» H  2.2  HZir" Potential  Thus the idea i s that the pion i s f i r s t captured molecular states. In p a r t i c u l a r , i f we form H Z , for  then an exotic H Z T T  the H Z T T  -  of the o r b i t a l s  electrons.  Adiabatic  The  examine binary molecules of the  molecule would be formed. The potential  system i s shown i n figure 2.2.  occupy one  process.  -  transfer  i t must give up  capture of  i n highly excited  has  small  been  In order  i t s energy to one  proposed  amounts of  for a pion  as  energy  the  most  implies  of  to the  likely  that  the  - 14 -  r e s u l t i n g o r b i t of the pion must be very similar i n geometry to that of the  electron  electron into  knocked  the only hydrogen  i s locked up i n the chemical bond, the pion must be captured  a mesomolecular  capture.  out. In the H Z system, since  state  first  unless  one allows  The entire rate diagram for the H Z T T  -  f o r radiative  i s shown i n figure 2.3.  FIGURE 2.3. Rate Diagram for HZir" System.  The radiative capture probability i s given by D, and the molecular capture p r o b a b i l i t y by P. The transitions from the mesomolecular are  state  given by Q and E as shown i n the diagram. R i s the probability of  retention on the hydrogen. Let the cross-sections  for atomic capture be  given  radiative  by o  and o , where  r  z  hydrogen. Let the molecular the N  n  number  densities  a  i s the purely  r  cross-section  of Z and H  be given  i n a compound  capture on  by o . Then, i f m  Z^H^ are N  z  and  one can write for P and D; ON, P  =  o~N"+o"N~+o N m h r h z z  However,  we  expect  ON. * that  a"N.+o~N,+a~N " m h r h z z a  r  «  o  m  as Auger  K  capture  '  dominates  - 15 -  radiative capture i n the energy region of i n t e r e s t , so D i s expected to be n e g l i g i b l e . Only i n the very  low  lying states of de-excitation are  radiative processes thought to play a role as w i l l be seen i n section 2.3. Now Cohen et  we  must consider  al.  predict  1 7  mesons stopping  possible  that  there  i s o t o p i c e f f e c t s . Calculations i s an  asymmetry  i n the  by  number of  on the various isotopes. Their calculations were done  only for atoms, and reduced masses and  the asymmetry i s a manifestation  of the d i f f e r e n t  i o n i z a t i o n potentials. For muons on H and D atoms  they predict the p r o b a b i l i t y of capture on the proton to be about greater  than  that  for  the  deuteron. To  make this  a more  3%  realistic  treatment molecular effects w i l l have to be included as there w i l l  be  dipole moments which w i l l tend to l o c a l i z e the pions about one atom.  did  Now  whilst predicting an i n i t i a l isotopic asymmetry, Cohen et a l .  not  calculate any  non-linearity i n the  concentration  This i s i n t e r e s t i n g to note as i n the work by Petrukhin i t was  and  found that the capture p r o b a b i l i t y could be described  F(Z H£) = (1+SC)  • (l+SC^ )""  -1  3  k  S = 7.1(Z  Here C i s the r e l a t i v e Petrukhin belonged believe  dependence.  to that  and  18  by;  (2.21a)  1  - 1)  (2.21b)  concentration.  Suvorov believed  another their  1/3  Suvorov  process,  treatment  the could  that  the  transfer add  second, non-linear process.  credence to the  Cohen  et  19  who  al.  statement  Petrukhin and Suvorov, which i s i n contradiction to other opinions that of Korenman and Rogovaya,  term  of  like  predict a large non-linearity i n  - 16 -  the i n i t i a l capture rate.  §2.3  De-excitation. When the pion i s captured i n excited mesoatomic or mesomolecular  o r b i t a l s i t w i l l de-excite to the lower energy levels and eventually be captured into the nucleus. The radiative de-excitation of energy to Auger electrons  and the transfer  are the two competing processes of this  mechanism. The probability f o r a t r a n s i t i o n from an excited with  angular momentum SL" and projection  m' to the state  state n'  n,£,m i s a  function of the t r a n s i t i o n energy AE. For radiative t r a n s i t i o n s , the probability W  R  = W  R  4 3  is,  <d> (AE)3 h* c? 2  with the dipole matrix element being given by,  <d>  2  = < n',£',m*|r|n ,1 ,m >  Atomic selection rules require  that  2  = Z  - 2  (2.23)  A£ = ±1 and Am = ±1,0 which  l i m i t the cascade and hence slow the radiative rate. The radiative rate for pionic hydrogen can be shown  20  to be related to the radiative rate  of hydrogen by i t s reduced mass p. We can write;  r'P = y rH . rad irp rad  The  p r o b a b i l i t y of an Auger process i s given by;  (2.24)  - 17 -  °  where  and  electron (2.25)  <  *  *  f  K  f  I  e  <J> are the pion and  separation yields  a  is  r^g.  (AE)~  *  ^  i  >  electron wave functions, and A  calculation  dependence  1 / 2  (2.25)  2  for  of  the  W^.  the pion  matrix  Leon  element  and  Bethe  20  calculate the Auger rate to be;  Aug  a  u~  2  AE"  I  /  .  2  (2.26)  In the mesic atom the orbits are much smaller due to the increased mass of the meson. In hydrogen, the n = 16 pionic o r b i t a l i s already smaller than  that  of  the  vacated  K-shell  electron  o r b i t a l s , AE i s very small between adjacent  orbital.  In  the  higher  states, and since AE a  Z, 2  for the l i g h t e r elements the Auger process w i l l dominate. Only i n the low  valued  n o r b i t a l s with  large AE w i l l  radiative transitions be of  significance. Experimental al.  2 1  evidence  seems  to  support  this,  as  Goldanskii  et  could not see the X-rays i n carbon or oxygen for n values greater  than Z. This implies that the probability of radiative capture, by D i n figure 2.3 In  systems  resulting  pit  penetrate  other  excited  -  state,  given  i s very small.  like  HZ,  i f the  atom w i l l  be  atoms and i t can  pion  small  and  ends up  neutral. It  approach the nucleus.  give  up  large  on  amounts  the can  hydrogen then  the  easily  If the pw  i s i n an  of  to  -  energy  Auger  electrons of the host atom and de-excite. In mesic molecules the cascade time i s shorter as we are no longer  - 18 -  working i n a central f i e l d , and hence the selection rules are somewhat weakened. In of  the  our  standard  p r o b a b i l i t i e s of  compound  Z^Ify  one  transitions to the  can  predict  the  atoms from the  ratio  molecular  states N.  This  implies  Z~ .  %n*  that  the Q p r o b a b i l i t y of figure 2.3  F i t s to d a t a  2  Z  W  which  -3  "  "  Z  ( - >  2  2  27  i s proportional to  i n compounds of the above type have shown that F a  22  agrees  well  Fermi-Teller Z law and  with  Q o Z  the  naive  picture  from above. We  -2  of  P  note that we  from are  the still  ignoring possible transfers between the atoms. However, controversy  is  present  Z~  again  as Jackson et a l .  dependence when they measured  2 3  the  could find no evidence of a Q a X-ray spectra  of pion  2  cascades i n  compounds of hydrogen, carbon and oxygen. An it  interesting  gives us  There w i l l the  feature  a probe into the i n general  atoms. The  form  be of  of  the  mesomolecular  system  is  that  electronic composition of the molecule.  some asymmetric electron d i s t r i b u t i o n about this  distribution will  e l e c t r o n e g a t i v i t i e s of the i n d i v i d u a l atoms.  be  determined  by  the  Electronegativity i s the  c a p a b i l i t y of an atom to a t t r a c t electrons to i t s e l f . There w i l l be a weighting of the electronic d i s t r i b u t i o n about the more electronegative  constituent. In purely  covalent  bonds there  will  be no asymmetry r e l a t i v e to the single atoms but a dramatic effect i n polar  covalent  resulting  and  ionic  bonds. Hence the e f f e c t of the bond and  p o l a r i t y i s to reduce the  electronegative  atom and  to increase  capture p r o b a b i l i t y on i t for the more  the  the less  electronegative  - 19 -  atom. In the model of the large mesic molecule, the i o n i c i t y i s included in  the form of a constant a^ where L stands f o r a particular  in  the periodic  table.  Then  one  can define  p r o b a b i l i t y P to be the p r o b a b i l i t y that  the i n i t i a l  period capture  the pion stops i n an o r b i t a l  l o c a l i z e d near the hydrogen atom. In equation (2.16) of the S.P.P. model there were p r o b a b i l i t i e s w and be  w  of de-excitation  to atoms Z and Z .  These p r o b a b i l i t i e s can  determined from a knowledge of the valence electron  density  about  each atom which i s given by the i o n i c i t y . The i o n i c i t y i s related to a^ and can be calculated localization density  parameters  p and p  of the respective  p = (l-a)/2  from the e l e c t r o n e g a t i v i t i e s . One can define which  are equal  to the  electron  atom.  ,  p* = (l+a)/2 ,  (2.28)  where a i s the i o n i c i t y . One can also define r e d i s t r i b u t i o n terms q and q* which correspond to the Q and 1-Q-E i n figure 2.3 In the S.P.P. model the r e d i s t r i b u t i o n factors were taken to have a Z  2  dependence and  w i s given by;  w =  §2.4  z -*-* pq + p*q* 9  •  (2.29)  Transfer. The  p o s s i b i l i t y of transfer  can play  an important  role  i n the  - 20 -  stopping schedule of mesons i n matter. The  transfer process i s of the  form;  Z  In  7T  +  the example of H  effect which was unity. One which pir-  1 ~  is  also  Z  2  >  + D  2  different > p + dir .  In  experiments *  Z  2 ~  (2.30)  1T  we  saw  that there was  i n the fact  a molecular  that F(H +D )/F(2HD) was 2  not  2  that the absolute value of F(H +D ) i s 0.417, 2  from  + d  +  vs HD  2  manifested finds  l  Z  0.5  showing  a  net  2  transfer  of  the  form  gas,  this  -  21  transfer has  with  H  2  +  Z,  where Z  been seen very c l e a r l y . The  i s an  inert  probability R that the pion  w i l l not be transferred to the heavier Z atom has been the subject of much debate *.  The  21  transfer  process  i s generally considered  to  be  c o l l i s i o n a l l y induced by the fast moving neutral piT - atom. In general the process i s i r r e v e r s i b l e as the new de-excited state i s more t i g h t l y  bound and  nuclear capture can proceed  quickly. Since  the transfer i s a Coulombic a t t r a c t i o n to the higher Z valued atom, i t tends  to  suppress  experiments measured  the  the  pion  capture  Petrukhin et a l . * 2 1  on  hydrogen.  established this  concentration dependence.  In  the  H  2  suppression and  They found  that the  +  Z  also  capture  p r o b a b i l i t y was only a function of r e l a t i v e concentration. The transfer process  i s evident  i n gases and  mixtures,  but  not  so noticeable i n  bound systems l i k e CH^ + Z [Ref 26] so for most complex molecules R i s taken to be 1 to a f i r s t In place  most cases from  excited  approximation.  27  transfer i s not a large e f f e c t , and can only take states  where  the  probability  of  transfer  is  - 21 -  comparable transfer  with  those  for de-excitation  i n the pir systems probably -  and  nuclear  takes place from  capture.  The  the n =  5-10  levels. To develop a phenomenological must include a l l p o s s i b i l i t i e s . competing  6  B  r  In terms of the cross sections 6  X  one for  reactions we have;  pion capture on proton due to radiative transitions i n the pir" atom.  =  Z(H)  =  pion capture on proton due to a c o l l i s i o n with atom Z (or H). transfer from pir to a Z atom v i a a tunneling through the H-Z bond.  X t  x  model for the transfer process  z  c o l l i s i o n a l y induced transfer to Z atom.  -  Thus the R p r o b a b i l i t y can be written as;  B  D  =  + 6 »N + 8,»N,_ E h__2 8 + 8 -N + B «N +X + X «N r z z h h t z z  v  (2  11 •>  J  U  U  which can be written i n the following form;  R =  Since  6 /N + B C + 3, r h z h 3 /N + 8 C + B, + X /N. + X C r h z h t h z  experimental  evidence  (2.32)  shows only a r e l a t i v e concentration  - 22 -  dependence X  and  hence  no  direct  dependence  on  the  terms  £  r  and  must be n e g l i g i b l e . We can then write R i n the standard form;  R =  where B  z  It  = B /B z  h  1 + B C  z + A )C z z  and A  i s very  complex  molecules  effects  like  hydrogen  (2.33)  1 + (B  = X /6 -  z  Z  Z  difficult because  to  extrapolate  there  are  so  the structure of the Z-Z'  and  deuterium  the  transfer  this  formulation  many interrelated  to more competing  and  Z-H  bonds. In the case of  can  go  in  either  direction,  although the net transfer w i l l s t i l l be to the deuteron.  §2.5 Nuclear Capture. When the pion has de-excited to the lower l y i n g levels of an atom, i t s wavefunction w i l l overlap with the nucleus and there w i l l be a high probability  for nuclear  probe the interactions If t|» £ (r) n  m  we  we  It i s during  between nuclei and  describe  then  capture.  the  can  pion  calculate  that we  can  pions.  wavefunction the  this stage  overlap  in  an by  orbit  n,£,m  integrating  by over  the volume of the nucleus. This w i l l then give us the probability w of finding the pion i n the nucleus.  w This  can  primarily  be  =  J  v  solved,  I  (2.34)  *<r) P dx  and  in particular  for pions  which get  captured  from the spherical £=0 states for low Z values, one obtains;  - 23 -  w = 4(yr ) zV3n 3  (2.35)  3  0  In nuclei of low Z value, -for a given n, the p-state capture rate has been shown  28  to be several orders of magnitude smaller than the s-state  capture rate. Also we see from equation (2.35) that the very strong n dependence w i l l suppress any capture from the higher excited o r b i t a l s . There capture  has been  widths.  some  confusion i n the calculations  In pionic  X-ray  experiments  these  of nuclear  calculations are  v i t a l f o r the pion cascade codes. Most calculations are consistent f o r I > 2 but vary depending are  considered and what form of potential  Recent for  on how many terms of the pionic wavefunction  calculations by Turner and J a c k s o n  the p and s states  determined  parameters  by using  29  i s used  have improved  a potential  and by expanding  f o r 1=1 and 1=0. the formulas  with experimentally  the wavefunctions  to higher  order. In the case of hydrogen, the nuclear capture i s easy to detect as the two main channels are;  p + ir p + IT"  —> —>  n +y n + IT  (2.36)  0  > 2  and  Y  the charge exchange reaction i s strongly suppressed on a l l other  nuclei except He. Since the p7T~ atom i s so small and neutral i t can 3  e a s i l y penetrate other atoms electronic s h e l l s and approach the nucleus and  i n the presence of this external coulomb f i e l d  i t s energy  may get mixed. The t r a n s i t i o n times between o s c i l l a t i n g extremely  fast.  For  example,  30  f o r n=6,  levels  1 states are  T(6£-»-6(£-l))  is  about  - 24 -  lxl0  - 1 6  sec.  This allows the populated 1*0 states to spend some time i n  £=0 states and enhance nuclear capture. This i s known as Stark mixing. There  i s also  the p o s s i b i l i t y  f o r direct  nuclear  capture  from  mesomolecular states. This i s represented by probability E i n figure 2.2.  From  figure 2.2 we see that the probability  of capture  on the  proton i s given by;  F(H +Z) = DR + PQR +PE  (2.37)  2  and using equations (2.20,2.31), and neglecting a , one gets; r  1 + B C  1 Q  F = 1 + SC where S = a / a . z  m  Since  r+(B"+X")C z z  for H  2  +  (2.38)  E  + Z there  i s no chemical  bond, one  must have Q = 1-E. The only way that (2.38) w i l l f i t the data, which i s fitted B  z  just  by (2.21a),  i s for B  z  and E to be small. A small value f o r  implies that i n a c o l l i s i o n  with a Z atom the pion i s l i k e l y  to be transferred. The smallness of E implies that direct capture from mesomolecular states i s not a large contribution to the o v e r a l l rate. It i s interesting to note that none of the available gas data have shown a pressure dependence of the atomic  capture or transfer rates  over a range of about 10 to 100 atmospheres. I t appears that the Stark enhancement of nuclear capture just offsets the increased probability of c o l l i s i o n a l l y  induced transfer.  The nuclear capture reactions that we need to understand experiment  for this  are the ir-p and n-d reactions. These w i l l be discussed i n  - 25 -  some d e t a i l i n chapter 3. The primary source of background  comes from  pion stops i n the target which are e s s e n t i a l l y just stops on carbon or aluminum. In these reactions the pion couples to a nucleon-nucleon pair and the reaction becomes (ir-,2N).  S p e c i f i c a l l y we have;  ir" + " d " •»• n + n,  (2.39a)  and the much less l i k e l y ; ir~ + p + p * p From  this  we  could  + n.  (2.39b)  anticipate  that  most of our background  would  be  neutrons.  §2.6  The H2D2 and HD  Systems.  The f u l l rate diagram for a pion stopping i n a mixture of H D  2  gases  i s shown i n figure 2.4  where the X's and B's refer  following; ^mol _ p,d  direct nuclear capture from mesomolecular states of hydrogen,deuterium.  ^dir _ direct atomic capture of pion on atom of irp,ird hydrogen, deuterium. ^at _ t r a n s i t i o n from mesomolecular irp,ird atomic o r b i t a l . ^ pd,dp B  PP  state to  _ transfer from p to d,(d to p) i n c o l l i s i o n with d,p.  C = irp + p -»• (n+ir° or n+y) P  B ,C, pd a  = irp + d +  (n+ir° or n+y)  3. C dp p  = ird + p •»• (n+n or n+n+y)  2  and  to the  - 26  FIGURE 2.5  Rate diagram for HD.  - 27 -  In  BJJC, da a  = ird + d >  k  , = I n i t i a l capture rate on H„,D.. * 2» 2  .C  P,d p,d  Cp ^  the above,  deuterons.  (n+n or n+n+y)  are the atomic  If we assume  that  molar  direct  fractions of protons and  capture  from  the mesomolecular  state i s small so that; x  mol p  <  K  x  at up  a  n  d  x  mol ^ d  at ird  x  ^  A  Q  )  and from equation (2.19) we ignore the direct atomic capture rates then FJI j) can be written as; 2 2 F  k C = _E_E H,D, T 1  B C +3 ,C , k C EE_E__El_d + _2_p_ B C +B .C.+X , C , T pp p  pd d  X, C d2_E 6, C +B J J C,+X, C  pd d  dp p  dd d  (  dp p  ^-  , . H L  '  where T = k p C p + k d C d . Then i f we define; z  A  6  =A  =- 2  B  p  pp  X _ A = - -  8  K = ——E  E  pp  dp  B,  r  = _4d  dp  C, c = -p  we can write;  HD 2  2  1 + EC  1+BC+AC  1 + EC  1+K+rC  The  parameter E i s expected to be very nearly 1 as i t i s a measure of  the  asymmetry In the i n i t i a l  some concentration  capture rates of H  2  and D . It may have 2  dependence i f the pion does get captured  so that the difference i n r e l a t i v e stopping  near 20 ev  powers between H  2  and D  2  has a s i g n i f i c a n t e f f e c t . We note that i n the above formulation we have assumed that only one transfer can take place. From the experimental results ' 3  3 1  i t appears that  approximate F J J n by; 2 2  the reverse  transfer i s small so we can  - 28 -  HD 2  "  2  1+C  1 + BC + AC  Now we can examine the HD rate diagram, shown i n figure 2.5 where the parameters here have the same meaning as for H D 2  definition C  p  = C  Xm0^  except  that by  and;  d  =  molecular capture of pion on HD.  ^mol _ p,d  Again,  2  direct nuclear capture on p,d from HD mesomolecular states.  i f we assume  that direct  capture  from  the mesomolecular  state i s small so that; Xmo1 p  «  X up  and  X™51 « X . d ird  (2.44)  and from equation (2.19) we ignore the direct atomic capture rates then F^n can be written as;  F  HD  X  = X  *P +X  irp  8 +6 , PP pd  . .  B  +8 .+X  X ,  ird .  +  ,  ird pp pd pd  X  +X ,  X  dp  (2.45)  Bj +B..+X,  irp ird dp  dd dp  which can be reduced i n the same fashion as equation (2.39) to; X  F  n n  =  n  molecular  break  •  X +X J irp ird  By combining  X ,  1+ B p  + 1+B+A  1 * • X +X , 1+K+r irp ird d  (2.46)  the experimental data from Ref (1) and Ref (31), the up r a t i o  X^j/X^p  f o r HD can be shown  to l i e i n  the i n t e r v a l (1.46,1.54). From equation (2.25) we see that the r a t i o of r a d i a t i v e t r a n s i t i o n rates i s just;  - 29 -  r  nd rad  f  r  =  Trp  rad  / u nd  u  Trp  =  1.07.  (2.47)  The Auger contribution i s given from (2.26) as;  Aug  Aug  irp T r d  where we have used the fact that AE ~ y. Neither of the above processes explains the high r a t i o seen. Another  possibility  preferential transitions  capture  to  that  may  final  explain  states  about  the  effect  deuterium  i s the  in  direct  from the mesomolecular state. This would require that the  d i r e c t nuclear capture for deuterium be greater than that for hydrogen, and  of the same order  However  as we  have  of magnitude as the molecular breakup rates.  already  pointed  out there  i s no  experimental  evidence to support this hypothesis.  §2.7  Summary of Previous Hydrogen Measurements. There have only  been two measurements  which concentrated  their  e f f o r t s on just hydrogen isotopes. Aniol et a l .  3  examined H  and D  2  2  i n a 50%-50% mixture and compared  i t to HD. They determined;  F  H  F  independent  of  =  D  2 H D  0.417±0.004  2  =  0.338±0.008  pressure  Petrukhin and Prokoshkin  over 31  the  range  6  to  90  atm.  measured a range concentrations of H  2  - 30 -  and  D„ ,  and  to F J J Q  f i t them  as  given  i n equation  (2.43).  A x  2  2 2  f i t to their data yielded;  Similar Results  from  B  =  1.3 ± 0.4  A  =  0.4 ± 0.1  data has these  been measured i n the form  by  Petrukhin  et  al.  in  2 3  of an  + Z mixtures. early  experiment  observed the transfer e f f e c t . They found;  Here the low  A  =  B  «  ( 0.7 ± 0.2  )Z  A  value of B just  implies that i n a c o l l i s i o n of pionic  hydrogen with a Z atom the pion w i l l  have a very high probability of  transfer. Later experiments  where  S  is  the  by Petrukhin and Suvorov  S  =  A  =  7.1( SC ' 1  initial  comparable to E i n the  H  2  Z  1 / 3  2  determined that;  -l)  3  asymmetry D  18  term  of  equation  (2.21) and  is  system.  The bulk of the rest of the experiments  done i n this f i e l d involve  much more complicated molecules which can not e a s i l y be compared to the above data.  - 31 -  Chapter 3  The  The Experiment.  probability  of  transfer  from hydrogen  measured experimentaly i n mixtures of the two  to deuterium can be gases by counting the  number of negative pions which stop on either a proton or a deuteron. The signal f o r nuclear capture on hydrogen i s quite clean. From §2.5 we saw  there were two main reactions, the charge exchange  the  radiative  given b y ;  32  >  capture reaction.  The  branching ratios  reaction, and f o r these are  33  I T - + p -»• n + T T °  ( 60.7 % ),  (3.1)  Tr- + p  ( 39.0 % ).  (3.2)  n +  y  In deuterium there are again two main reactions *, namely; 31  T T - + d •*• n + n Tf-  + d->-n  + n + Y  ( 73.7 % )  (3.3)  ( 26.1 % )  (3.4)  Although the pionic atoms ir-p and ir-d are small and neutral and as such are free to wander through the gas, for the purpose of kinematical calculations i t i s s u f f i c i e n t  to consider them to be at rest. In Tr-p  radiative  photon  whilst  capture the  single  i s monoenergetic  the neutron has an energy of 8.9 MeV.  almost instantly  MeV  The neutral pion decays  ( x = .83E-16 sec ) to two photons.  photons has a center of mass energy of 67.5 MeV  at 129.44  Each of these  and are emitted back to  back. Since the n° i s s e m i - r e l a t i v i s t i c with a v e l o c i t y of .2c, the lab photons range from 54.8 to 83.1 MeV.  This energy range i s referred to  - 32 -  as  the pi-zero  box. The neutron energy i n this reaction i s small at  0.42 MeV. The  two neutrons of reaction (3.3) carry away 68.1 MeV back to  back.  Because  of the strong  final  state  i n t e r a c t i o n between the  neutrons i n reaction (3.4) the photon y i e l d i s peaked at about 130 MeV. [See Ref 35] .  §3.1  Overview of Experimental Setup. The  experiment was conducted at the T r i - U n i v e r s i t y Meson Factory  ( TRIUMF ) i n May 1985. The high pressure  gas target was positioned at  the focus of the Ml3 pion beam l i n e . The experimental setup i s shown i n figure 3.1. The beam d e f i n i t i o n was formed by requiring a coincidence i n s c i n t i l l a t o r s S1,S2 and S3 with s c i n t i l l a t o r S4 i n anti-coincidence. A degrader was positioned appropriate  between SI and S2 to slow the pions to the  energy. SI was positioned  41cm x 8cm x  .65cm p l a s t i c  near the beam snout and was a  scintillator.  The degrader was a 2.75cm  thick aluminum block and was positioned as close as possible to S2 and the  target.  S2 was a 3.8cm x 3.8cm x .16cm p l a s t i c s c i n t i l l a t o r and  was positioned as near as the geometry would allow to the target. The  photon  detectors  used  were  two  large  cylindrical  sodium  iodide c r y s t a l s known as the TRIUMF Iodide of Natrium ( TINA ) and the Montreal Iodide of Natrium ( MINA ). TINA i s the larger at 51cm x 46cm<(> and was located at right angles to the beam at the focus 98 cm from the target  center.  through selected  MINA measures 36cm x 36cm<J> and was at 180° to TINA  the target  at a distance  of 72 cm.  These distances  to maximize the s o l i d angle acceptance while s t i l l  were  having a  good time separation between photons and neutrons from the target. Both  - 33 -  TINA and MINA were shrouded by large Iron walls with opening of  30ci»J>.  In  addition because of MINA's smaller diameter  install  a  This was  15cmJ>  orifices  done i n an attempt to reduce background problems.  lead  collimator. In  order  to  i t was veto  necessary  charged  to  events  s c i n t i l l a t o r s were placed before the front faces of the crystals inside the iron boxes.  FIGURE 3.1  §3.2  Experimental setup, viewed from above.  Target Design. In order to have an appreciable number of pions stop i n the target  it  i s desirable to have the gas as thick as possible which requires  high gas pressures. However one would also l i k e to have the gamma rays traverse through a minimal amount of material, so a compromise must be  - 34 -  made between wall thickness and density. The target vessel i t s e l f was turned from 7075-T6 aluminum which i s the alloy  commonly used i n a i r c r a f t  strength-to-weight r a t i o . seal  against the vessel  applications due to i t s excellent  The brass flanges, see figure 3.2, formed a and the l i g h t  guides. External  fastened to the l i g h t guides i n an attempt  clamps were  to prevent inward movement  when the target was under vacuum.  BRASS  FLANGES ALUMINUM  TARGET  VESSEL  S3 ,  S3  LIGHT  \  \>'\  \  V  /  \  \  \  \  GUIDE  \  \  S4  LIGHT  \  SEALING  GUIDE  S I /  A  O-RINGS  FIGURE 3.2  Target design.  The l i g h t guides collected the l i g h t from the defining counter S3 and  the veto counter S4 and transported i t to their  multipliers. minimize  In an attempt  respective photo  to to reduce the hydrogenous background and  the number of stops i n the s c i n t i l l a t o r i t s e l f ,  S3 was made  - 35 -  of a very  thin  ordinary p l a s t i c  ( 0.5mm ) deuterated scintillator  plastic  (CD) .  S4 was a 0.32cm  n  of closed cylinder shape with one face  open. S c i n t i l l a t o r d e t a i l i s shown i n figure 3.3.  FIGURE 3.3  To prevent  Scintillator detail.  cross talk between the two s c i n t i l l a t o r s an aluminum  r e f l e c t o r was affixed  to the end of S3. Tests were conducted  beam to measure the cross t a l k . The Compton edges of C o and 6 0  with no 1 3 7  Cs  were used to calibrate the two counters. Then using S3 as a trigger we examined  the signal i n S4.  It was believed that the cross talk, i f  present, occurred less than 5 percent of the time.  §3.3  Selection of Beam Parameters. The TRIUMF cyclotron accelerates H~ ions which can be extracted by  stripping  o f f the electrons  direction  of curvature  proton  beam  i s then  causing  and leave steered  the protons  to reverse  the machine. The 500 MeV  down  a beam  line  their primary  and impinges  upon  production target T l creating a copious supply of pions, neutrons and  - 36 -  secondary  protons. The  charged pions decay  quickly  to muons and  the  TT°+2Y decay generates electron pairs i n any material. The  Ml3  pion and muon beam l i n e  i s shown i n figure 3.4.  It i s  tunable over a momentum range of 20 to 130 MeV/c. The pion f l u x , Y(E) 3 6  goes approximatly as,  Y(E) « E 2  at  (3.5)  5  least up to energies of about 40 MeV.  However above this energy i t  f l a t t e n s out reaching a maximum somewhere around 50 From  a  Monte  Carlo  analysis  of  the  MeV.  target  as  a  sequence  of  degrading materials the f r a c t i o n of pions stopping i n the gas S(E) was seen to approximate to a function of the form,  S(E) « E ( A E / E ) _ 1  where  the  AE/E  i s the  (3.6)  _ 1  full  width  half  maximum  ( FWHM  ) of  the  d i s t r i b u t i o n entering the gas. Hence the combined d i s t r i b u t i o n took the form,  S(E)Y(E) °= E  _ 1  • (AE/E) 5  (3.7)  -1  which indicated that a high energy i n i t i a l beam was favourable. Energy  straggling  in  the  degrader  was  a  significant  factor.  Predictions f o r straggling due to large energy losses are d i f f i c u l t to make. percent.  Tschalar » 37  38  determined  that  AE/E  could  range  from 5 to 15  Taking 10 percent as a guide, and adding the variances, i t  - 37 -  FIGURE 3.4  TRIUMF M13 beam l i n e .  - 38 -  appeared  that the energy variance due to the beam momentum bite could  go quite high without appreciably affecting the t o t a l energy spread. Another scattering  worry  was the divergence of the beam due to multiple  i n the degrader. Ideally  at the focus the beam has 2.1cm  FWHM horizontal and 1.3cm FWHM v e r t i c a l p r o f i l e s . Calculations of the standard would  deviation  i n the scattering  not converge,  but that  this  angle  would  indicated  that  the beam  not be a problem  if  the  degrader was close to the target. Based  on the above analysis we planned to run with a pion energy  of 40 MeV with s l i t s wide open and a 2.75cm thick aluminum degrader. It turned  out that  the s l i t s  had been removed  from  the channel  for a  previous experiment so they were not replaced. The beam flux was about 60kHz through the defining counter S3. We then varied the momentum to maximize the I T  0  y i e l d i n hydrogen at 100 atm and the entire experiment  was conducted using this single tune.  §3.4  Gas Preparation, Handling and Mixing. The  and  gases we used were isotopes of hydrogen,  HD. The gases  were bought  i n the case  of H  s p e c i f i c a l l y H ,D 2  2  2  and D , with the 2  manufacturers claiming purity levels of 99.9% and 99.5% respectively. The balance of the D was HD. The HD gas we manufactured ourselves. The 2  apparatus for this i s shown i n figure 3.5. The HD i s formed through the reaction , 3 9  4D 0 + LiAlH^ •»• LiOD + A1(0D) 2  3  + 4HD  with tetrahydrafuran ( THF ) being used as a c a t a l y s t .  (3.8)  - 39 Hg MANOMETER  FIGURE 3.5  The frozen  lithium  Apparatus f o r HD manufacture.  aluminum  by immersion  hydride was mixed  in a liquid  manifold was then brought  nitrogen  with  ( LN  2  the THF and then ) bath. The entire  to vacuum by pumping and using an a u x i l i a r y  pump i n the form of a desiccant at LN  2  temperature. This removed a l l  undesirable gases. The mixture was then allowed to warm slowly and the D 0 added i n drops. The r e s u l t i n g gas was passed through the f i r s t 2  trap and stored pressure  could  cold  i n the balloon reservoir. As the balloon f i l l e d the be read  on the mercury  manometer.  As the pressure  approached atmospheric the reaction mixture was again immersed i n a LN  2  bath and the gas transferred v i a a glass cold trap and a s i l i c a g e l cold trap into the reservoir. Mixing  of  gases  and  transfer  to and  from  the target  was  accomplished using the gas manifold system i l l u s t r a t e d i n figure  3.6.  After evacuating the lines a gas was transferred to the mixing vessel using  either  the natural  bottle  pressure  or the compressor.  The  compressor was a single stage diaphragm compressor capable of pressures  Q  T/C  ION  GAUGE  GAUGE  VACUUM ^  u  GAS  T  6  T/C  T1  : <: <: *\'<: f , u  VENT  COMPRESSOR  INLETS  - 41 -  to 1300 atm. It pumped at lcm /sec and so to make e f f i c i e n t use of time 3  a reasonable  back pressure was  required. At any  rate at least  3 atm  backing pressure was required to operate the valves. After one gas was i n the mixing vessel the lines were again pumped out  and  the second  relative error  gas  added to the lines with a positive  to that i n the mixing  vessel. This was  i n concentration determination due  narrow  lines.  The  second  gas was  pressure  done to reduce  to uncertain mixing  then added and  the  two  the  i n the  allowed  to  mix. The  pressure  i n the mixing  vessel was  measured using  s t r a i n gauge transducer, accurate to better than  a Varian  .05 percent. It  was  noted that the pressure dropped gradually as a result of gas cooling, so presumably the gas was make  consistent  readings  heated  by the compressor. The  represented  the  largest  i n a b i l i t y to  error  in  the  determination of r e l a t i v e gas concentration. After evacuating a l l the l i n e s again the mixed gas was to  the  target v i a the compressor and  the s i l i c a  gel cold  transferred trap. The  f i n a l pressure i n the target was read on a standard diaphragm gauge. We f i l l e d the target to 100 atm f o r a l l mixtures. In some cases, where the a v a i l a b i l i t y of gas dictated i t , upon completion of a run the mixture was  returned to the vessel and further gas added.  were taken and  their  contents analysed  Samples of each gas  on a mass spectrometer  as an  additional check of r e l a t i v e gas concentration. We measured a range of gas concentrations from pure D If  we  denote by C the molar f r a c t i o n of deuterium  2  to pure  H. 2  then values of C  measured were from 0.0 to 1.0 i n steps of 0.1 with additional checks at 0.25,  0.45,  0.55  and 0.75. We also measured the HD gas. For pure HD the  - 42 -  molar f r a c t i o n i s just 0.5. A l l measurements were made at 100 atm gas pressure at room  §3.5  temperature.  Electronics and data A c q u i s i t i o n . A schematic  of the electronics  i s shown  i n figure 3.7. In this  diagram the squares labeled D or CFD represent discriminators. They are used to convert  linear  signals above a user set threshold into  logic  signals. The CFD's are constant f r a c t i o n discriminators f o r which the timing of the output pulse i s r e l a t i v e l y independent of the size of the pulse, The  so these  are used where the timing information i s important.  triangles represent linear or logic fan-in/fan-out units. They are  essentially  OR  gates  with  many  outputs.  The  small  triangles  with  variable arrows drawn through them represent amplifiers or attenuators. The  circles  computer,  indicate  into  locations where  scalers,  b i t registers,  items  are to be read  by the  ADC's or TDC's. The  logical  coincidence units are represented by the AND gates. The  primary  coincidence was the beam counters S1,S2 and S3.  The  veto S4 was not hard wired. In order to determine the t o t a l number of stops we sampled with a pulser the S1«S2«S3 coincidence. This became a strobe, known as the 'pulser' strobe, where by strobe we mean that an event has been tagged and a l l information about that event i s read into TDCs  and ADCs. Two  requirements  other  strobes were the 'singles' where the only  were that either TINA or MINA f i r e d and there was a stop  S1»S2'S3. The fourth type of strobe was a 'coincidence' which required that both TINA and MINA f i r e d with the stop. The vetoes MINA were not hard wired, C212 f o r each event.  but rather just  registered  for TINA and  as b i t s  i n the  - 43 -  FIGURE 3.7  Electronics diagram.  - 44 -  There  were  two  types  of  data  read  onto  tape.  The  type  1  corresponded to strobe events. Whenever a strobe f i r e d the ADC and TDC gates were set and the time and energy read  i n . What follows  information f o r each counter  i s a summary of the information collected f o r  each strobe. 1) ETINA(l-7)  energies of the 7 TINA tubes,  2) EMINA(l-7)  energies of the 7 MINA tubes,  3) ES(4)  energies of the beam counters SI....  4) ETINA  summed TINA energy,  5) EMINA  summed MINA energy,  6) C212  event b i t pattern,  7) TOFT  time of f l i g h t to TINA,  8) TOFM  time of f l i g h t to MINA.  9) RF(2)  time of RF strobe, two time delays,  10) CP  time of capacitive probe signal.  Associated with each beam burst from the cyclotron i s a signal. This signal i s the 'RF' and has a period of 43ns. Also, i n the beam l i n e there i s a capacitive probe which detects the presence of beam and issues a signal, called  'CP'. These signals are used to determine the  beam content. The timing i s determined by the S2 signal, so a l l times are r e l a t i v e to i t . The RF or CP spectra c l e a r l y show the difference i n time taken f o r p a r t i c l e s  leaving  the production target. In this way  pions, muons and electrons can be separated by their time of f l i g h t . For a number of coincidences we set a b i t i n a b i t r e g i s t e r , the C212,  whenever a strobe f i r e d . By examining  the b i t pattern we could  then reconstruct the event. The b i t s that were collected into C212 are  - 45 -  l i s t e d below. 1) PULSER«S1»S2»S3  Pulser sample of beam.  2) TINA*MINA*SI«S2»S3  Coincidence i n TINA and MINA.  3) TINA*S1*S2*S3  TINA singles event.  4) MINA*S1*S2*S3  MINA singles event.  5) S4  Signal i n S4.  6) TINCH  TINA charged signal.  7) MINCH  MINA charged signal.  The type 2 events were just the scalers. They counted continuously only being written to tape when a register overflowed or at the end of a  run. The  interest.  The  scalers  counted  the number of signals  for each item of  The following scalers were kept; 1) S1*S2*S3  5) TINA*Sl*S2*S3  2) S1*S2  6) MINA*S1*S2*S3  3) TINA  7) TINA*MINA*S1*S2*S3  4) MINA  8) PULSER*S1*S2*S3  data  acquisition  was  controled  by  a  PDP  11/34  computer  connected to a Camac logic controller, 2 disk drives and 2 tape drives. The data a c q u i s i t i o n had p r i o r i t y  over a l l other computer processes.  Whenever a buffer was f u l l the buffer was transferred to tape. Only one event was  handled  at a time. If the computer was busy processing an  event an i n h i b i t was sent to the coincidence units to stop more events from  piling  up.  When  the  computer  was  not  busy,  on-line  analysis  monitored the progress of the experiment. During the experiment we collected data i n two d i f f e r e n t modes. In  - 46 -  one case we used a l l four strobes and gathered a l l information. This was known as the singles mode. In singles mode the data taking rate was very  fast  and contained  few r e a l  events.  Since  we were  primarily  interested  i n coincidences from the ir° decay and wanted to get good  statistics  on their number we limited  the data  taking by physically  removing and terminating the two singles strobes from the electronics. This was known as coincidence mode. For each mixture we collected data i n singles and coincidence mode.  - 47 -  Chapter 4  The  Analysis.  data  computers. supplied  was  We  analysed  used  using  standard  subroutines. The  data  goal was  the  TRIUMF VAX  manipulation to determine  8600 and programs  VAX  with  780 user  the hydrogen capture  r a t i o F, the number of captures on a hydrogen i n the target per stop i n the gas. The  number of stops was  to have been calculated by counting the  number of SI*S2«S3'N0T(S4) events. This turned out to be impossible as upon dismantling the number of slipped  target assembly at the end  things were observed.  i n when the target was  pressure against S4. guide. However, due  First, evacuated  of the experiment  the l i g h t as S3 was  The veto counter S4 was  guides  a  must have  badly warped from  not fixed to i t s l i g h t  to the c o n s t r i c t i v e nature of the target geometry  i t could not have moved far and so must have always been resting on the light  guide  with  some  optical  coupling.  s c i n t i l l a t o r s had two major repercussions.  The  movement  of  For one, with each new  the degree of o p t i c a l coupling between S4 and  the mix  i t s l i g h t guide varied  and thus so did the signal l e v e l . For another the two l i g h t guides were now  i n contact  certain  and  depending  on  the  level  of  contact  there was  amount of cross talk between the two. This implied that S4  a was  no longer a perfect veto. The second strange effect noticed was that while S3 was warped, i t was  still  of good o p t i c a l quality, whereas S4 was  severely discolored  on the surface. Presumably there was some reaction on the surface of S4 s p e c i f i c to this p l a s t i c rather than that of S3. It was not clear what caused  the discolouration  or when i t occurred as the target was  not  - 48 -  disassembled u n t i l  after  a second experiment had been completed. The  only gases that should have come into contact with the s c i n t i l l a t o r s were Hj , D , HD, 2  Ar, He and Xe. Also we used methanol  to search f o r  vacuum leaks and a brand name, "SNOOP", soap mixture to look for high pressure  leaks.  Both  of  these  s c i n t i l l a t o r with n u l l r e s u l t s . from  the compressor  even  products  were  tested  on  fresh  Another p o s s i b i l i t y considered was o i l  though  with such a low vapour pressure i t  could only pass into the target i n parts per m i l l i o n . Tests showed that o i l was not the c u l p r i t . F i n a l l y we wondered i f the hydrogen gases could be converting on the surface and causing the e f f e c t , but further tests showed that there was  no conversion or discolouration i n H /D 2  2  mixtures. The p o s s i b i l i t y  of a contaminant i n the HD gas was ruled out as HD from the same batch had been used i n an e a r l i e r muon catalyzed fusion experiment. In that experiment any Z > 1 contaminant would have led to rapid muon transfer to the Z. This was not observed.  §4.1  Determination of Gas Concentration. O r i g i n a l l y we planned to determine the r e l a t i v e gas concentrations  using both the measured pressures and a mass spectrometer analysis of the  gas  samples.  Unfortunately  the mass spectrometer was  working  poorly and the results were l a t e r found to be useless. In addition to i o n i z i n g the gases the molecules were being dissociated so that a l l the mass channels were being mixed. The only r e a l problem this presented was  that we could not determine the condition of the HD gas.  not possible with our setup to manufacture pure HD.  It was  In the past our  samples have had 93±2% HD with the remainder being two parts H  2  to one  - 49 -  part T>2 • the  Since the experiment which continued on after this consumed  remainder  determined.  of the HD  We surmised  gas the exact  concentration could  not be  that the same conditions applied here and used  these figures i n our calculations. When measuring the gas concentration from the r e l a t i v e there  were  two sources  of uncertainty. F i r s t  i t was  pressures  important  to  r e a l i z e that the readings had to made after the gases came to thermal equilibrium. When the gases were introduced  to the mixing  took  to s t a b i l i z e .  some  time  f o r the transducer  reading  vessel i t This  was  attributed to the gas being heated as i t passed through the compressor. Since i n the early going we did not recognize this effect and, i n an attempt to optimize beam time, the mixing procedure was done as quickly as possible, there i s an unavoidable uncertainty i n the r e s u l t s . The itself.  other source of uncertainty comes from the transducer reading Throughout  fluctuating  the run we  noticed  the c a l i b r a t i o n  was  i n an unpredictable manner. This was seen because, after  every mix, the target was evacuated not agree.  that  and the zero pressure readings did  I t was l a t e r discovered that this was due to problems with  the power supply. We discovered ( too late ) that there must have been some strange  ground  loops  i n the l o c a l AC lines  extension cord and an outlet  as when we used an  f a r from the experimental  apparatus the  problem was cured.  §4.1.1 It  V i r i a l Corrections. i s important  to recognize  concentration from the pressures;  that  the determination  of gas  - 50 -  c  d  «--h- '  •  d  is  only  an  p  D  approximation  2  < -!> 4  2  based  on  the  ideal  gas  law  PV  = nRT.  At  pressures of 100 atm this i s not such a good approximation. The  correct  treatment  i s to use  the f u l l  expansion observed for  non-ideal gases;  Pv  =  RT( 1 + § + ^- + ... ) v v  (4.2)  2  where B and C are the second and  third v i r i a l  coefficients  and v i s  the molar volume. It i s s u f f i c i e n t to neglect the t h i r d c o e f f i c i e n t  and  so we can write;  Pv  where  now  B'  = RT( 1 + B'P  is  the  )  (4.3)  reduced  coefficient  B/RT.  In  theory  we  calculate B' f o r a given mixture at a temperature T. Then i f we with a mixture given by n  P (n ,n )V i  d  p  =  ( n  d  d  and n  + n  p  p  n )  _±__d__E_  P (n,,n +An ) f d' p p jr v  n +n =  5__E  n,+n +An d p p  start  we can write;  )RT Q+B' ( n ^ n ^ P ^ n ^ ) )  and upon adding a small amount of hydrogen, An  P (n  can  p  (4.4)  we get;  (1+B'(n ,n )P (n  n ))  2__E__±__a__E  (1+B*(n,,n +An )P^(n.,n +An )) d' p p' f d' p p v  v  (A  5\  ' '  - 51 -  In  order  to determine  the concentration  i t i s necessary to  calculate the two second order v i r i a l c o e f f i c i e n t s . I t i s s u f f i c i e n t to estimate  of B (n ,np+An )  the parameters  by using  1  d  Q  the i d e a l gas  law approximation. c a l c u l a t i o n of B  The used  to represent  i s somewhat d i f f i c u l t . Various models are  1  the molecular interactions.  Among the best  is  the  Leonard-Jones p o t e n t i a l . A s p e c i a l form of this potential i s often used to make the mathematics manageable. It i s given by;  r  * ( r ) = 4e •  a 2  1 2  _  r j  a 1. 2g. 6  a  repulsive  term  f o r r < a. Attacking  mechanically gives the following  B '  where first is  B '  C  =  B '  C  £  ±  A  3  B '  S  £ i s the c l a s s i c a l  correction  which  6 )  this  problem  quantum  expansion for B ' .  +  A  B * Q  2  limit  +  1  and  and second order quantum corrections.  an added  .  and an a t t r a c t i v e term f o r r > a  This i s a potential with a depth e and  ( 4  takes  into  A  1  * B ' Q  B'QJ^  2  +  . . .  and 'Q2 B  (4.7)  a  The s t a t i s t i c a l account  p a r t i c l e s . It i s p o s i t i v e f o r fermions. A i s related  the spin  r  e  t  term  n  e  B'  of the  to the molecular  parameters e and a. For mixtures we calculate;  B '  =  B  '  ^  2  +  B '  2  X  2  2  + B  '  ^  X  ^  S  (4.8)  where the X's are the molar fractions and B '  12  i s estimated using the  empirical mixing rules;  a  and A  1 2  1 2  = ( a a )/2 1  2  , e  1 2  = (c^)*'  2  (4.9)  i s calculated using an average mass term.  Table 4.1 V i r i a l l y corrected deuterium gas concentration. Run #'s  Pressure ( p s i )  Concentration.  Error  166,167  1500  0.995  ±0.005  62,63  1500  0.900  ±0.026  27,28,29  1500  0.811  ±0.032  168,169  1500  0.755  ±0.022  30,31  1500  0.713  ±0.034  32,33  1500  0.606  ±0.034  170,171  1500  0.559  ±0.016  35,36,37  1500  0.520  ±0.033  172,173  1500  0.460  ±0.014  38,39  1500  0.400  ±0.013  40,41  1500  0.316  ±0.011  174,175  1500  0.258  ±0.009  42,43  1500  0.216  ±0.009  44,45,46  1500  0.116  ±0.008  47,111,112,113  1500  0.000  ±0.005  The B' terms have been shown to be a converging  series of gamma  - 53 -  functions multiplied by a power series i n temperature with c o e f f i c i e n t s which have been using the f i r s t  tabulated * • We 1  calculated the  0  the B'  15 to 20 terms of the series depending on the rate of  convergence. The v i r i a l c o e f f i c i e n t for each mixture was the  coefficients  concentrations  adjusted  accordingly.  The  calculated and  virially  corrected  concentrations and their associated errors are l i s t e d i n table 4.1.  §4.1.2  Concentration Error Analysis.  The pressure was  determined as a function of the transducer  output  voltage V and was given by;  P  Then, since we  = mV + b  are  .  (4.10)  interested i n the  ratio  C of  initial  and  final  pressures, we write:  C = ( mV  + b )/( mV  ±  + b ).  f  (4.11)  Then the absolute error i n C, AC i s just given by;  (AC)  2  = (Am) (6c) 6m 2  2  + (AV ) ( 6 C ) 6V 2  ±  2  + (AV )(6C) + (Ab) («C) 6V <Sb 2  2  2  . (4.12)  f  where we have neglected the covariance terms. This i s j u s t i f i e d major error i n the intercept was  a result of the DC  output  power supply wandering whereas the error i n the slope just the uncertainty i n i t s measurement.  as the  from the  represented  - 54 -  When  the mixture  was  not a  fresh  mixture,  but had been  r e c i r c u l a t e d and additions made, the errors compounded. In these cases there was f i r s t an addition of D , followed by an addition of H . If we 2  label  the intermediate  concentration  r c  2  pressure  of this  process  P  then  m  the f i n a l  i s just;  P  _  + ( C i  m  v  - 1 ) P. ' i _  mV +b + (C.-l)(mV +b) m i i ' v  J  / v  ,,  ( 4  i.r»\  1 3 )  and the error becomes the obvious extension of (4.11);  (AC)  = (Am) 6C^, + ( A b ) 6 C ^ -6m 6b  2  2  2  2  r  r  l  J  l  J  2  + £(AV) 6C^ UvJ 2  r  2  + (AC ) ,6C >, 1 ^ c J 2  2  (4.14)  where AC^ i s the error determined for the previous mixture.  §4.2  Analysis of the Data. We had to determine the number of pions which were captured  proton i n the gas. To do this we looked  on a  i n TINA and MINA f o r the T T °  decay photons. To qualify as an event we required several things. F i r s t both p a r t i c l e s reaching also required  the Nal crystals were i d e n t i f i e d as photons. We  that the event be neutral. This was done i n software by  requiring that neither of the veto counters of TINA or MINA f i r e d . Then neutrons could the  target  particle determined  be eliminated  on the basis of the time of f l i g h t from  to the detector.  entering by  the target  examining  p a r t i c l e s were discarded  Secondly was  the RF  we demanded  a pion. time  that  The beam  spectra  and  the i n i t i a l content  the  was  non-pionic  from the data set. A t h i r d condition imposed  - 55 -  was  that the photons  carry the correct amount of energy based on the  kinematics outlined i n chapter 3. In order to compare the number of captures on hydrogen between gas mixtures  i t was necessary to normalize them to a common value. The  normalization that we used was the t o t a l number of pions which stopped in  the target.  We  then defined  the probability  of capture on pure  hydrogen to be 1.0. In this way when we compared capture p r o b a b i l i t i e s a l l s o l i d angle and e f f i c i e n c y e f f e c t s canceled.  §4.2.1  Time Cuts.  The  start  of the time gate was based  on the a r r i v a l  time of a  strobe signal at the gate generator. The leading edge of the signal from the constant f r a c t i o n discriminator of S2 determined the timing so a l l times were measured r e l a t i v e to the time a p a r t i c l e passed through S2. The timing stop was based on the a r r i v a l time of signals from the constant  fraction  time of f l i g h t  discriminators  of TINA and MINA. By examining the  from S2 to the detector, neutrons and photons could be  isolated from one another. A photon  typical peak  time  spectrum  i s easily  f o r TINA  distinquished  i s shown i n figure from  4.1. The  the neutrons. A  clearer  separation could be made at the expense of s o l i d angle and thus rate, by moving the crystals  further from the target. The cuts Imposed are  shown on the figure as v e r t i c a l arrows. The problem with the timing was that  the strobes were not timed  together so i t was necessary to have a different time window for each strobe. It was also a curious fact that the timing for the singles and coincidence runs were shifted by 1.5 ns. It appears that the number of  - 56 -  o o o  FIGURE 4.1  TINA time spectrum. The first peak is the photon peak, whilst the second is the neutron peak.  - 57 -  strobes into the event fan-in unit affected the stagetime The  time of 1.5  of the unit.  ns i s much longer than the manufacturers claimed  time.  In TINA the possible strobes were; TINA'MINA*SI*S2•S3 i n both singles and  coincidence  singles  mode  modes,  whenever  TINA*S1*S2«S3  strobe  and  TINA«S1*S2*S3  there  as  was  a  w e l l . Since  in  singles mode only.  coincidence the  there  coincidence  had  strobe  to  In be  arrived  early i t dictated the timing i n these cases. The same effect was  seen  with the MINA strobes, only here the TINA*MINA*SI*S2*S3 strobe was well timed to the MINA*S1*S2*S3 strobe, so i t was time windows. To all  the  centroid. The figure 4.1  §4.2.2 As  to have two  One for singles mode, and one for coincidence mode.  try and  had  only necessary  make these  same  width  cuts have the same e f f i c i e n c y the windows and  were  centered  about  the  photon  peak  number of photons lost with the window size as shown i n  i s almost zero.  RF Cuts. described  earlier  the  RF  discriminate between pions, muons and primarily of concern  CP  spectra  allow  us  to  electrons i n the beam. This i s  for the analysis of the randomly selected events  which were sampled with the pulser. We pulser events. Cuts were made on the RF as well although  and  i t was  very  s h a l l refer to these events  as  spectra for the other strobes  rare that a non  pion could trigger  an  event which s a t i s f i e d the other conditions i n TINA and MINA. A  typical  RF  spectrum  is  shown  in  figure  4.2.  Most  of  the  electrons have already been eliminated from the spectrum. This was done by r a i s i n g the threshold of S2 so that only large non-electron pulses triggered the discriminator. The main peak i n figure 4.2  contains  the  - 58 -  FIGURE 4.2  RF time spectrum. Pions, muons and electrons are present.  59 -  -  pions, followed by a small muon peak. At the far edge some electrons appear. The  pulser strobe was very early r e l a t i v e  to the event  strobes.  This meant that we had to keep separate RF spectra for pulser strobes and  event  strobes  strobes. We recorded on tape the RF and CP times for pulser  and, with  a different  delay,  the RF time f o r event  strobes.  The problem with the RF signal was that i t tended to wander quite a b i t so each run had to be examined i n d i v i d u a l l y to determine the RF cuts. On several runs the RF peak shifted mid run and so portions of the data corresponding entire  to the t r a n s i t i o n time had to be ignored. In some cases  runs were useless. As we s h a l l  electrons i s c r u c i a l to determining The  first  see the removal of muons and  the number of stops i n the target.  pass at the data was to determine the RF cuts to be applied  i n the subsequent treatments, and to eliminate useless data.  §4.2.3 The  Energy Cuts. energy cuts were based on a knowledge of the kinematics and  the spectra themselves. The kinematics were used to calibrate TINA and MINA. Using pure hydrogen we could c l e a r l y see the pi-zero box and the monoenergetic peak at 129.44 MeV. Because of the r e s t r i c t e d geometry, only i f i t were in  approaching  the coincidence  mode.  either TINA or MINA would a it" be detected This  i s because neutral pions  emitted at  other angles would not have the correct photon opening angles to allow detection i n both TINA and MINA. This means that only the lowest and highest  energy  photons  are  detected  giving  the  characteristic  coincidence spectrum shown i n figure 4.3. In singles mode this i s not the  case  and the entire  spectrum  i s seen. A t y p i c a l  singles energy  - 61 -  FIGURE 4.4  TINA singles spectrum.  - 62 -  spectrum  i s shown  contaminated  with  i n figure  4.4. The singles  radiative  capture  from  events  are however  the deuterium  or the  containment vessel, so the cleanest i d e n t i f i c a t i o n of ir-p capture i s a coincidence event. The TINA and MINA energy resolution functions can be described by a  gaussian  distribution  about  the mean  energy  multiplied  by an  exponential drop-off at low energies. The gaussian term represents the natural  line  broadening  and  apparent  lowering of energy  escaping  from  the c r y s t a l  the exponential term due to bremsstrahlung  without  represents the from  the shower  being detected. The un-normalized  TINA resolution function i s given by;  F(E) =  A exp((E-E )/B)( 1 - ERF((E-E )/C) (J  where A i s an amplitude  (4.15)  0  term and B and C are representative of the  widths of the peak on the low and high energy sides of the mean Ey. The energy spectra of TINA and MINA for pure hydrogen runs were f i t t e d with  this  function  to calibrate,  the energy.  repeated a number of times throughout  The  calibration  was  the experiment and found to be  consistent. The f i t s to the energy spectra were done by f i t t i n g the end points of the TT° box i n coincidence mode to 54.83 and 83.06 MeV and the single photon peak to 129.44 MeV. F i t s to the single radiative capture peaks  are shown i n figure 4.5. From these we can see that the energy  resolutions  of TINA and MINA were 9 MeV and 8 MeV FWHM at 129 MeV  respectively. The figure  cuts which were applied to the pi-zero box are indicated i n 4.3. As an additional  energy  cut we required  that  i n each  -  FIGURE 4.5a  63 -  F i t to TINA radiative capture peak.  - 65 -  coincidence one of the photons had to have low energy and the other had to have high energy.  §4.2.4  The Stop D e f i n i t i o n .  Because  the damage  scintillators that  S4  occurred  into  could i n S3  no  i n the t a r g e t  contact, longer  also  a c t as  appeared  Tab! .e 4.2 Description of event.  they  were a  to S3 and S4 optically  simple  Stopping  coupled.  veto  i n S4. L i k e w i s e  brought  as  any  there  was  the two  This  meant  signal  significant  p r o f i ..e of target.  Raw energy ES3 ES4  With cross talk ES3 ES4  Approx. prob.  TT-  stops i n S3 on carbon.  med ium  zero  medium  small  TT-  stops i n S3 on hydrogen.  small  zero  small  v. small  <1%  TT-  stops i n gas  small  zero  small  v. small  9%  TT-  stops i n S4 on carbon.  small  large  large  large  80%  Tf-  stops i n S4 on hydrogen.  small  medium  large  medium  <2%  Tf-  stops i n rear wall  small  small  small  small  <1%  9%  non pions that escape cuts.  ?  ?  ?  ?  -0%  stops i n front A l scat, into S3  ?  1  ?  ?  -0%  stops i n S2 scat, or random i n S3,S4  ?  ?  1  ?  ~0%  ?  ?  ?  ?  -0%  stops i n rear A l random or scat into S3, S4.  that  - 66 -  crosstalk from S4 into S3. In table 4.2 we l i s t the possible conditions i n the target and estimate the  the r e l a t i v e contribution each w i l l make to  observed energy spectra  of S3 and  S4.  In the following we  refer to the energies i n S3 and S4 as ES3 and The directly  first  thing  compare the  to  point  pulser  This as we s h a l l see was  out  strobes  was  ES4.  that  with  shall  any  i t was of  the  impossible event  to  strobes.  due to the fact that the pulser strobe created  a timing s i t u a t i o n so different  that the ADC  gate sampled a different  part of the pulses for S3 and  S4 and hence the apparent energies were  different.  the  In  S4  particularly  gain  shift  was  on  the  order  of a  factor of 2. The  best  way  to examine the  scatterplots of the energies ES3  vs ES4  i n S3 and  was  by  making  S4. These we  two-dimensional  s h a l l refer to as  s c a t t e r p l o t s . A raw spectrum for the pulser type strobes i s  shown In figure 4.6. we  data  The  same scatterplot i s shown i n figure 4.7 where  have required that at least one  of the non-pulser strobes f i r e d i n  anti-coincidence with the pulser strobe. For the purpose of discussion these  scatterplots w i l l  be  referred  to  as  the  pulser  and  event  scatterplots. The and  second pass through  electrons  outlined  and  noticeable  from  energy  spectra.  labeled 3 and  effect  removed the two the  the  the data allowed  i n the  This  removed  us to remove the muons the  troublesome peaks  4 i n the pulser s c a t t e r p l o t . There was event  s c a t t e r p l o t . With the  peaks 3 and  no 4  scatterplots have much the same appearance, except for  s c a l i n g . It  energy scaling was  due  was  not  at  a l l apparent  that  the  different  to a timing effect so we conducted a systematic  - 67 -  FIGURE 4.6  Scatterplot of ES3 and ES4 for pulser strobe. Peaks 1,2,3 and 4 are discussed in the text.  If)  FIGURE 4 . 7  . 10  s 3  Scatterplot of E S 3 and E S 4 for non-pulser strobe. Peaks 5 and 6 are discussed in the text.  -  69 -  search of the data to determine the nature of the peaks. The best source of information came from the data collected while doing the range could  curves.  approximate  corresponded  Since these runs varied i n pion momentum we  the l o c a t i o n  i n the t a r g e t  to. Referring to the schematic  there were approximately 8 peaks observed  that  each  depicted i n figure  peak 4.8  i n a l l . These peaks had the  following properties.  ES3"  —  ES4 FIGURE 4.8  Schematic of ES3 vs. ES4.  F i r s t peaks B and C were eliminated when the RF cut was imposed. In addition they were only observed with the pulser and were favoured at low momenta. This led to the obvious interpretation that these peaks represented the beam contamination. These peaks were analogous to peaks  - 70 -  3 and 4 of figure 4.6. The appeared  exact  origin  of peaks  A and E was not clear.  They  both  only i n the very low momenta runs and also were recorded as  rejected  events.  The most  likely  neutrons  i n TINA and MINA from  explanation  pions  stopping  was  that  they  were  i n S2 and the front  aluminum with some scattering or randoms i n S3. The randoms rate was much higher since few of the pions were making i t to the gas. Peak D was only  seen  with  an event  and was maximized  at the  optimum momentum. This peak was thus i d e n t i f i e d as representing pions stopping i n the gas or i n S3. It turned out that since S3 was so thin there was not enough energy resolution to discriminate between stops i n S3  and stops i n the gas. This peak was analogous  4.7.  to peak 6 of figure  Peak F was very similar to D, having similar  energy  ranges and  maximized at medium momenta. However i t was only seen with the pulser. It was given the same i d e n t i f i c a t i o n as peak D and corresponded  to peak  2 of figure 4.6 Peaks G and H were also very similar to each other except f o r the large  energy  shift  and the fact  that G only occurred with a pulser  strobe whereas H was associated with  event  strobes.  Both of these  peaks dominated at high momenta indicating stops i n the veto counter. They  are represented  by  peaks  1 and 5  i n the pulser  and  event  scatterplots respectively. Referring back to table 4.2, we reemphasize that the resolution of S3  prevented  us from  distinguishing between stops i n S3 and stops i n  the gas. Also s t a t i s t i c s d i d not allow us to observe different peaks for  stops on carbon  and hydrogen as the capture on carbon dominates  that on hydrogen, and the energy resolution was probably not s u f f i c i e n t  - 71 -  anyway. Further  tests  supported  the above conclusions. When looking at  the background vacuum runs peaks D and F were greatly reduced to  relative  G and H i n d i c a t i n g a loss of stops due to missing gas. In addition  when searching events  occurred  corresponded  f o r neutral pion i n an energy  to stops  events  band  i n pure  similar  on the hydrogen  deuterium  to H. These  i n the veto  the only must  counter.  have  When we  examined the data from the second experiment where pure Xe was used, i t was  seen that the peaks G and H v i r t u a l l y disappeared,  the  increased stopping  indicating that  power of the xenon was preventing  pions  from  reaching S4. We f e l t  that  the above analysis was correct and that the only  difference between figures 4.6 and 4.7 was due to the s h i f t i n energy caused by d i f f e r e n t strobes.  We  reasonably  also  a r r i v a l times believe  that  of the ADC gate from the different with  the RF  cuts  the spectra are  clean and only a very small f r a c t i o n of the data could be  attributable  to the random events  indicated i n the last  few rows of  table 4.2.  §4.2.5  F i t t i n g the Stop Region.  In the second pass through the data using the RF cuts determined from the f i r s t pass we collected into histograms and scatterplots a l l the  available information  about  the energies  deposited  i n the two  s c i n t i l l a t o r s S3 and S4. We also output the bin values of the histogram and scatterplot arrays so that they could be input into various  fitting  routines. We defined the stop region as the e l l i p t i c a l area i n an ES3 vs ES4  - 72 -  scatterplot  corresponding  to stops  i n S3 or the gas. The biggest  problem with setting cuts on the stop region was that the cuts had to be d i f f e r e n t  f o r each new gas mixture. This was because when gas was  moved i n and out of the target, the position of the veto counter S4 was altered, and so the degree of crosstalk between the two s c i n t i l l a t o r s varied.  In some cases the two peaks, representing the stop region and  stops i n S4, were reasonably well separated, the case.  but this was not always  Often the two peaks were very close together, making i t very  d i f f i c u l t to f i t them. The f i r s t cuts made to the scatterplot and histogram arrays of the pulser  and event  approximately to  strobes were rather broad  isolate  two dimensional  cuts to  the region of i n t e r e s t . These cuts are referred  as the box cuts. Figures 4.9 and 4.10 are t y p i c a l  spectra of the  energies ES3 and ES4 before the box cuts were made. The cuts applied are indicated by the box i n figure 4.7. The results of the cuts to the data  i n figures 4.9 and 4.10 are shown i n figures 4.11 and 4.12. The  stop peak i s now quite w e l l defined. The fitting  data  from the region to be f i t t e d  routine. The data  was  was input to a Minuit * 1  f i t to a function composed  1  of two  gaussians plus a linear background. The f i r s t gaussian approximated the stop peak whilst the second was constrained to represent the t a i l of the S4 stopping peak.  This was used as i t f i t the data well and was  quite straightforward. the  The second gaussian  told us what f r a c t i o n of  stop peak was due to stops i n S4. Other methods of f i t t i n g were  tried.  A three gaussian  separation  f i t where the additional gaussian  to be made between stops  i n the gas and stops  allowed a i n S3 was  unsuccessful as there were too many parameters, so that almost any f i t  - 73 -  ENERGY I 6000  S3  D I S T R I B U T I O N  _L  Run  3D  20 0 0  200  ENERGY FIGURE 4.9  T  400  600  (  T"  800  C h a n n e l s  Energy d i s t r i b u t i o n o f S3 b e f o r e  1  ) cuts,  Run  4000  300 0  H  20 00  H  ooo  3D  t ooo H  1000 ENERGY  Channels  FIGURE 4.10 Energy d i s t r i b u t i o n o f S4 b e f o r e  cuts.  - 74 -  6000  ES3.  AFTER J  SLASH 1  Ru n 30  CUTS. i _  5000 H  Aooo  H  3000 —{  20 0 0 —\  1000 —\  200  400  ENERGY  600  (  800  Channels  FIGURE 4.11 Energy d i s t r i b u t i o n o f S3 a f t e r  2500  ES4.  AFTER J  SLASH _J  CUTS. L  1000  ) cuts,  Run  30  2 0 0 0 —\  1 50 0  1000 —\  500  200  ENERGY  1000  60 0  (  Channels  FIGURE 4.12 Energy d i s t r i b u t i o n o f S4 a f t e r  ) cuts.  - 75 -  could  be  had.  by f i t t i n g  Another method  a parabola  tried  was  to the contours  to remove the c r o s s t a l k , e f f e c t of an ES3  vs ES4  scatterplot  p r o j e c t i n g the data down to t h a t l i n e . Then the converted fit  using  two  gaussians  as  b e f o r e . T h i s method was  data c o u l d be  aesthetically  p l e a s i n g but s i n c e the same r e s u l t s were o b t a i n e d i n e i t h e r case not  important  standard ES4,  i t was  parameters d e r i v e d from these f i t s were the mean and  deviation, E  were  f i t and  w i t h e n e r g i e s ES3  a  and  Q  a stop and ES4  respectively.  d e f i n e d by  Both  requiring  standard  located  at  with  0  d e v i a t i o n s . For each mixture  event  that f o r a given  s t r o b e s . Then these  and event  met;  (4.16)  c o n s t r a i n e d to l i e w i t h i n the area of  (E 4,E 3) Q  ES3  < 9.0  With t h i s c o n d i t i o n the data was ellipse  histograms,  the f o l l o w i n g c o n d i t i o n be  +  and  more  employed. The  an  and  major  and  minor  the data was  axis  of  three  f i t f o r both p u l s e r  c u t s were a p p l i e d i n a t h i r d pass to the  data. To the  determine the  number  obtained  o n l y sampled  t o t a l number of stops i n the gas we by  fitting  the beam w i t h  for  each beam p a r t i c l e . The  the  sum  of  the  generated  event  scalers,  Sc(l)/  by;  scaled  data.  T h i s was  d i d not  collect  t o t a l number of stops NS  pulser  (see  pulser  the p u l s e r , and  s t r o b e s . The Sc(8)  the  stops  was  plus  the  number  scale factor  was  given  §3.5).  Then  had  the  number  of  to s c a l e  because  we  information  then g i v e n by  of by  stops the  stops  which  ratio  of  i s given  - 76 -  "  N S  where  NS ^  f-fH Sc(8)  and  pu  NS  ey  NS pul .  are  the  +  NS ev  (4.17)  number  of  stops  each  for  pulser  or event strobes.  §4.2.6  Comment on Error Analysis and Combination of Data.  For a given concentration the number of pions stopping i n the gas plus S3 region should have been a constant  independent of whether we  were running i n singles or coincidence mode. This gave us a method to average the data. If NTT- was  the number of incident pions coincident  with the pulser then the r a t i o R;  NS  ,  should have been a constant. Since the ES3 different  data  and ES4  acquisition  spectra were quite d i s s i m i l a r f o r the modes the  fits  varied s l i g h t l y  two  f o r what  should have been equivalent data. In an attempt to average these runs we  took a weighted average of the r a t i o  (4.18) for runs of the same  concentration. Then the weighted average <R>  <R> < R >  =  i s given by;  ( 19)  l-LUL**lll  4  I (1/(AR)*)  where AR i s the error i n R. With t h i s , the error i n <R>  C 4  i s just;  -  i y j  - 77 -  ( A < R > )  2  =  r  Then f o r a g i v e n run  ?  f  i - -  7  j , the  J  I  (4.20)  T  t o t a l number of p u l s e r  stops i s j u s t g i v e n  by;  <NS^p u l>  = <R> NTT-  n  and  (4.17);  i n analogy w i t h  NS  J  = §£lU^ Sc(8)  (4.18)  From e q u a t i o n  A D  A  --  as  the  NSp ^. U  in  Then  w i t h the The  N  the  the  minimization  was  and  p u l  as;  varying the  either  was the x  2  side  pass  determine  the  the  to  the  error  error  free  at  to  the  of  associated  some  had  the  value The  increased  mean  where  and  1.0.  this  was  errors.  the  i t was  necessary  a  error the  routine  by  negative data  data u s i n g  associated  parameters.  value of  best f i t to the  calculate  fixed  l o c a t i o n s were the p o s i t i v e and third  compared  4.23)  e v  To  the  approximated  NS «  technique.  by  During  to  calculated  which  be  negligible  routine  minimized  on  was  problem  question  location  can  (  NIT-  in  at  P U L  1  parameter  location  (4.22)  NS  S  2«i pul  f i t values N S Minuit  <N J > + J  J  e r r o r AR  S  =  error  (4.21)  x  2  the  function  sought  the  found  the  It  true.  to  These  determine  - 78 -  what e f f e c t  these e r r o r s would have on  do t h i s the a n a l y s i s program used the  t r u e number of stops and  windows  of  simply  different  set  to  the  EQ  the b r u t e f o r c e method by  Then  the  errors  possible error  stops  NS  i n the  (MPE)  g r e a t e s t d e v i a t i o n between the t r u e value and The  To  calculating  the number f o r each of the o t h e r p o s s i b l e  or a.  maximum  the number of stops counted.  as  values  determined  were  by  the  any of the o t h e r windows.  t o t a l e r r o r i n v o l v e d f o r a s i n g l e measurement of the number of  could  now  be  calculated.  A l l the  errors  e q u a t i o n (4.21) were added i n q u a d r a t u r e . We when d e t e r m i n i n g  for  each  variable  assumed P o i s s o n  the e r r o r s o f the s c a l e r v a l u e s , and  in  statistics  as b e f o r e i g n o r e d  the e r r o r i n NTV- so t h a t ;  A<NS  §4.3  ,> pul  =  <NS  -> pul  .  <R>  (4.24)  C a l c u l a t i o n of the Hydrogen Capture R a t i o . In  order  mixture  we  to  counted  normalized  them  events  full  the  calculate  to  the  the  hydrogen  number of  the  energy,  number time  events  of  and  stops.  RF  capture stemming To  ratio from  The  yield  background c o n t r i b u t i o n was of  events  per  stop  given  the  and  number  of  c u t s were a p p l i e d to the d a t a .  We  determined  ( Y(x)  a  a ir° decay  determine  a l s o r e q u i r e d t h a t t o be q u a l i f i e d as an event, i t had The  for  to be a s t o p .  from empty t a r g e t runs.  ) f o r some mix  x  could  then  be  g i v e n as;  Y(x) =  N T T ° ( X ) / NS(x)  (4.25)  - 79 -  where Nir° was the number of ir° events counted. If we define the capture rate  on hydrogen to be i d e n t i c a l l y  1.0, then  the normalized  capture  r a t i o i s given by;  = ILZI-Z-ILP-I-  F(x) n  3  Y(H ) - Y(0)  U  (4  .26)  2  where Y(0) i s the background contribution. The y i e l d f o r the background runs and f o r pure deuterium was zero within the experimental errors, and so presented no problem to the data analysis. In  addition  f o r runs of the same concentration the y i e l d s Y(x)  were calculated by taking the error weighted  <v  (x)  >  =  <YQX)>  average.  0_X^)/iAY(x))£) £  (  i/(A. (x))Z) Y  ^-tn  and;  (A<Y(x)»  2  = l / ( I ( 1/(AY(X))2 )  The error AY(x) has been determined  (4.28)  by adding the errors of NTT° and NS  i n quadrature with the error i n Nir° just given by Poisson s t a t i s t i c s . Table 4.3 shows the f i n a l results f o r the capture ratios for each mixture and their associated errors. The  value of F f o r the HD mix i n table 4.3 has had an additional  correction made to i t . The o r i g i n a l uncorrected value Fyn was;  - 80 -  =  F° HD  .371 ± .011  Table 4.3 Run #'s  (4.29)  Hydrogen capture r a t i o s . F(H D ),F(HD)  Concentration.  2  Error  2  166,167  0.995  0.000  ±0.002  62,63  0.900  0.064  ±0.004  27,28,29  0.811  0.192  ±0.008  168,169  0.755  0.207  ±0.011  30,31  . 0.713  0.242  ±0.010  32,33  0.606  0.336  ±0.015  170,171  0.559  0.362  ±0.018  35,36,37  0.520  0.411  ±0.016  172,173  0.460  0.474  ±0.021  38,39  0.400  0.623  ±0.029  40,41  0.316  0.693  ±0.026  174,175  0.258  0.726  ±0.040  42,43  0.216  0.707  ±0.024  44,45,46  0.116  0.888  ±0.032  47,111,112,113  0.000  1.000  ±0.017  0.355  ±0.021  HD  58,59  This was corrected f o r the hydrogen and deuterium impurities. Since the impurity  concentrations  contributions  to FHD  were small from  HD, H  i t was 2  and  safe  D  2  to assume that the  could  be  weighted  t h e i r r e l a t i v e concentrations. Then r e f e r r i n g to figure 2.4 and  by  -  81  -  equation (2.42) we see that one can write;  F  HD  ' pd HD C  F  +  C  p  A  +  C  d  B  ( 4  -  3 0 )  where A and B are given by;  xmo1  .  A  x  mol P  2 +  x  at  x  mol P  +  B =  where XT  1  Xp  now  and X T  2  xat  +  x  1  and X d  X  _2  at  +  »P  »  E_„  (  4  .  3  1  )  x  ^  P  —  (4.32)  are u-p and i r - d nuclear  capture  rates and  are the forward and reverse transfer rates.  Using  the p r e d i c t e d  approximation  that  F  values  n (C=l)  H  2  C  =  =  p  ( A+B  2C  d  and  )/2 where  making C  =  the Cd/C  p  2  we can write;  F  HD  = pd HD C  F  +  2  C  i \ l > ™  +  C  d  A  ( 4  '  3 3 )  Averaging our result from chapter 5 with those from §2.7 y i e l d s ;  F _ (1) = H D u  2  0.430 ± .015  2  Term A i s given by equation (2.43) as;  (4.34)  - 82 -  A  =  _ _ i j: 5 _ B  1 + " ( § " + A)C  (4.35)  which from our data from chapter 5 must l i e i n the range 0.78 to 1.0. I f we use the value C p d = 0.93 ± .02 t h i s gives the f i n a l r e s u l t ;  F„_ nu  =  0.355 ± 0.021  where the errors have been added i n quadrature.  (4.36)  -  Chapter 5.  -  83  Results and Discussion.  The hydrogen capture r a t i o s that we measured as a function of gas concentration graphically  have in  been  figure  listed  5.1.  We  in  table  see  that  expected, a monotonia increase i n capture content of  increases. The  data  for  transfer.  the  We  from this l i n e .  the  and  are  general  presented  trend  is  as  probability as the hydrogen  s o l i d l i n e represents the expected d i s t r i b u t i o n  case  can  4.3  of  clearly  no  preferential  see  that  initial  capture  plus  no  there i s a s i g n i f i c a n t deviation  Since we believe that the i n i t i a l capture asymmetries  are small we conclude that there i s s i g n i f i c a n t transfer occurring. We  can calculate the probability of transfer given that the pion  has been caught i n an orbit about the proton. From the rate diagram of figure 2.4 we see that the above probability  P  T  =  6  C  E2_2  i)  C5  6 ,C, + X .C, pd d pd d  +  pp p  i s given by;  v  J  which using the same notation as before i s just;  p  _  AC  T  This  can  be  /c  1 + BC + AC  expressed  in  v  terms  of  our  measured  quantity  o} ' '  Ffl JJ 2  and using equation 2.43  P  T  "  1  "  2  as;  ( 1 + C ) F  H D 2  (5.3) 2  - 84  -  FIGURE 5.1 Hydrogen capture r a t i o in mixtures of H 2 and D 2 .  - 86 -  In  figure  5.2 we have  plotted  the transfer  probability  as a  function of the r e l a t i v e concentration. The asymptotic behavior of the data i s parameterized by the r a t i o A/(B+A) and i s the probability that the pion w i l l  be transferred to a deuteron  in a collision  of pionic  hydrogen with deuterium. In fit  both figures 5.1 and 5.2 the dotted curve represents the best  to the data  function  was  a  as determined f i t of  by a x against  n  2  2  minimization routine. The  concentration based  on the  2  model developed i n §2.6. The data was f i t with free parameters  B' and  A' to the function of equation (2.43). _ 1 + BJC  HD 2  In  1+ C  2  .  r+"B C +~A C T  ^  7  order to relate B' and A' to the model parameters  we must  that the reverse transfer i s small, that there i s no i n i t i a l asymmetry,  and that  terms l i k e  the direct  nuclear capture  }  assume capture  from the  mesomolecular state and direct atomic capture contribute l i t t l e . Attempts  were made to have more free parameters  but these  fits  were not successful due to the scatter of the data. If we assume our model i s correct  then the values of B and A determined  from the f i t  are;  B A  = =  0.77 ± 0.14 0.21 ± 0.04  The errors here were determined by the f i t t i n g routine Minuit i n the same manner as outlined e a r l i e r .  - 87 -  §5.1  A Comparison of the Results to the L i t e r a t u r e . We  compare  Prokoshkin  our results  with  those  obtained  by Petrukhin and  and Aniol et a l . Table 5.1 summarizes a l l the r e s u l t s .  31  3  Table 5.1  Comparison of Results with Previous Measurements.  Author  B 1.3  Petrukhin  0.4  ±0.4  A  F(H D ) (a)  ± 0.1  .43  2  Aniol Current work  0.77 ± 0.14  0.21 ± 0.04  F(HD)  2  ± .02  .417 ± .004  .338 ± .008  .45  .355 ± .021  ± .01  (a) Taken at (C=l); measured by Aniol et a l , otherwise calculated.  From the above table we see that our values for the parameters B and A are not i n very good agreement with Petrukhin and Prokoshkin, but our errors are smaller. More importantly we limit  point out that we  calculate  the asymptotic  of the transfer probability to be P(C->-<») = .21 ± .04 which i s T  i n very good agreement with the value from Petrukhin and Prokoshkin who calculate  P (C-»"») =  .24  T  ±  .07. Hence we  are confident  that  this  represents the true probability of transfer of a pion i n the c o l l i s i o n w-p •*• d. Our capture  ratio  for H D 2  2  i n equal parts i s i n agreement with  that of Petrukhin et a l but the error bars are very large. Our result i s not i n very good agreement with the d i r e c t l y measured value of Aniol et a l , but a l l the results are c l e a r l y less than 0.5. The agreement i s better  i n the  case  of  the HD  capture  ratio,  although  again  the  - 88 -  uncertainty  is  large.  We  also  note  that  our  ratio  n /FHJJ i s i n good agreement with that of A n i o l 2 2 We obtain 1.26 ± 0.13 compared to their value of 1.23 ± 0.03. FJJ  §5.2  Limits on the Molecular  of  et a l .  Breakup Rates i n HD.  If we make the usual assumptions that direct atomic capture rates and direct nuclear capture from the mesomolecular states are small, but do include the p o s s i b i l i t y of reverse transfer we can write;  H D  F  2  F  2  "  2  HD -  1"+ B + A  rH-h  x  +  +  1 +~l +~T '  2  (1  -  x)  (  C  =  1  )  (  i-+-r+-f  5  (5  ,  5  -  )  6)  where X i s the HD molecular breakup rate;  Trp  ird  Then i f we c a l l the common terms i n the above equations A we can write;  F F  HD  =  (A X  A  l  + A ^  2  1_X  )/2 > 2 A  we can solve for X and eliminate the term A  1  to get;  1  and A  2  then  - 89 -  FIGURE 5.3  Limit of molecular breakup rate.  - 90 -  x - i  A  plot  of  this  .  curve  i s shown i n figure  reasonable value of about 40%.  (5.9)  5.3.  We  see  that for any  the probability of breakup to a ir-p system i s  Since we  expect  the reverse transfer  to be small, i n the  range;  A  we  e [0.0,0.2] ,  2  find X  This  e [0.314,0.397] .  implies that given a  deuteron  between 60  transfer  that  and  system the pion w i l l  ir-HD  transfer  to the  70%  of  the time. It i s this intermolecular  i s attributed  to  the  suppression  of  pion  capture  on  hydrogen i n HD r e l a t i v e to H 2 D 2 . It small  i s possible of course terms  earlier,  actually  play  a  significant  a theory where our assumed role,  but  as  there are experimental data on other molecules  that these terms play a minimal  §5.3  to develop  pointed  out  that indicate  role.  The Future of these Measurements. Since  field,  we  i t appears would  like  likely to  that experiments  conclude  with  some  will  continue  comments  i n this  on possible  improvements which ought to be made to ensure better r e s u l t s . First  in  the  experimental  setup  there  must  be  a  good  stop  - 91 -  definition,  so the operation of the internal s c i n t i l l a t o r s i s c r u c i a l .  Preferably they should be aluminized to prevent any cross t a l k . Since we have seen that our background i s e f f e c t i v e l y zero, the addition of a very  thin  layer  of aluminum  problem. There  should  without  to break the vacuum i n the rest  having  also  to the s c i n t i l l a t o r s  be a convenient  should  not be a  way of drawing a sample of the system. This  would be to allow f o r a quick analysis of the gas concentration. Also since i t appears that aluminum dissociates hydrogen the least i t would be a good idea to ensure that a l l mixing vessels and storage tanks are aluminum. It would also be useful to have a thermo-couple In the mixing chamber  to ensure  thermal  equilibrium  has been  established before  measuring the pressure. In less  the electronics  to tape,  the s t a t i s t i c s  so charged  events  could be improved by writing  should  be hard  wired  and the 14  i n d i v i d u a l signals from TINA and MINA eliminated. This i s mostly true for the singles rates as i f there had been enough r e a l events on tape from  the these  runs  the data  could have been  analyzed  fashion. This method would have been to f i t the H , D 2  spectra  individually  relative  amplitude  branching  ratios  and then of each  do f i t s  of these  f o r the radiative  to the data components.  2  i n another  and background  to determine the Then  knowing the  capture rates the capture  ratios  could be calculated. Also with respect to the electronics i t would be nice to include timing information on both S3 and S4.  §5.4  Summary• We measured  the pion capture rate i n mixtures  of H  2  and D  2  and  determined how the rate varied with concentration. We f i t the data to a  - 92 -  phenomenological information  model and  determined  the parameters. These  gave us  about the transfer mechanism whereby the pion was observed  to be p r e f e r e n t i a l l y  captured on the deuterium. We  also measured the  capture rate i n HD and probed the difference between i t s value and that of a mechanical mixture of equal parts H  2  and D . We surmised that the 2  difference must have been due to the molecular breakup rate asymmetry. In conclusion  we observed that the experiment was  successful although  the errors were necessarily large due to the damage i n the target. The experiment  should  probably  be  repeated  to  reduce  the  errors  and  establish the true capture r a t i o s . Means of improving the results i n a subsequent experiment have been outlined.  -  93  -  References. 1.  Zinov,V.G., Konin,A.D. and Mukhin,A.I. Sov. J . Nucl. Phys. 2, 613 (1966).  2.  Evseev,V.S.,Mamedov,T.N.,Roganov,V.S. and Kholodov.N.I., Sov. J . 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