A STUDY or ‘pd INTERACTIONS FROM 1.09 To; ' ' 1.43 GeV/c‘ ' " " Dissertation for :the Degree of Phg D ‘. . MICHIGAN STATE UNIVERSITY ' PAUL DANIEL ZEMANY, Jr. ' 1975 ‘ ‘4 —V ‘—_ Lynn usv‘ km. 13.3..- 1 1 .17 4;" z'. Univvm'ry ' I" V ‘ ABSTRACT A STUDY OF pd INTERACTIONS FROM 1.09 TO 1.43 GeV/C By Paul Daniel Zemany, Jr. The reaction and topological cross sections for pn interaction producing 3 or 5 charged particles are measured. This is done using data from the Brookhaven National Laboratory 3l-inch deuterium filled bubble chamber. The s-channel behavior of intermediate states of the reaction 5n + 2N+3n', in particular the p°p°n' state, are examined for possible structure at a center of mass energy of 2l90 MeV. With a 90% confidence, no enhancement is found at a level of 0.7 mb if the width is assumed to be :50 MeV. In addition, the complications involved in using a deuterium target as a source of neutrons are inves- tigated using pn annihilations. The results indicate dis- crepancies with the assumption that deuterons can be used as a source of quasi-free neutrons. In this work, double scattering effect accounts for approximately 30% of the apparent pn annihilation events. An examination of the properties of protons emerging from the 5d annihilations Paul Daniel Zemany, Jr. indicates that the data can be properly described if and only if effects of double scattering are considered. A STUDY OF pd INTERACTIONS FROM 1.09 TO 1.43 GeV/c By Paul Daniel Zemany, Jr. A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1975 ACKNOWLEDGMENTS I would like to express my thanks to Dr. Z. Ming Ma, my major professor, for many comments and suggestions involving this work. Also the advice of Professor G. A. Smith is greatly appreciated. Many thanks go to the MSU scanning and measuring staff and the Brookhaven National Laboratory bubble chamber staff. Finally, I would like to thank my wife, Hye Son, for encouragement and assis— tance during the preparation of this dissertation. ii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES CHAPTER I. II. III. IV. INTRODUCTION EVENT AND FIT SELECTION 2. 2 2.3 .4 2 1 .2 Introduction Selection of the Events to be Measured . . Processing the Measured SampIe. Fit Selection ANTIPROTON NEUTRON TOPOLOGICAL AND REACTION CROSS SECTIONS . DOUBLE RHO PRODUCTION IN 5n + 3D-2fl+ woo Q) woo an» £>¢hh 01-h (QM-d 01-h no N--' Introduction . Cross Section Equivalent for an Event Scanning, Measuring, and. Systematic Losses Screening Corrections Topological and Reaction Cross Sections Introduction . The Reaction pn + p 3n 2n+ The Intermediate States in pn + 3n 2TT+ . . . . . Analysis Procedure Conclusions DOUBLE SCATTERING EFFECTS IN THE DEUTERON . . . . . . iii Page viii —IKO-b «b h 17 17 18 20 22 23 35 35 36 37 50 62 CHAPTER Page 5.l Introduction . . . . . 62 5.2 Evidence for Double Scattering . . . 66 5.3 Final State Interaction . . . . . . 75 5.4 Initial State Interaction . . . . . 92 5.5 Fits to the Data . . . . . . . . 94 5.6 Considerations of Possible AA States in the Deuteron . . . . 103 5.7 Conclusions . . . . . . . . . . . . 109 VI. CONCLUSIONS . . . . . . . . . . . . . . . 112 APPENDIX A. SUMMARY OF FIT SELECTION PROCEDURES . . . ll5 SCANNING EFFICIENCY . . . . . . . . . . . 123 C. MEASURING EFFICIENCY . . . . . . . . . . l32 D. BEAM COUNT. . . . . . . . . . . . . . . . l35 E. SCANNING BIAS FOR SPECTATOR PROTONS . . . l42 E.l Slow Protons . . . . . . . . . . . . l42 E.2 Fast Protons . . . . . . . . . . . . l46 F. UNSEEN ELASTIC SCATTERING . . . . . . . . 149 LIST OF REFERENCES. . . . . . . . . . . . . . . . 153 iv Table CON (Ilka-b Awwwwwwm \lOfiU‘l-hwm boom—a 01 .la .1b LIST OF TABLES Total Events Measured . Reaction Hypotheses Events on the Final Tape Cross Section Equivalent for an Event . Scanning Efficiencies Measuring Efficiencies Screening Correction pd + pS + ... Topological Cross Sections pn Reaction Cross Sections Mass and Width of Pion Resonances and Bumps Charge and Number of Combinations Events Used in Fit Fractional Rho Signal Relative Importance of Elastic and Inelastic nN FSI 3-4 Prong Terms 5-6 Prong Terms FSI Model Predictions p = 1.09 GeV/c FSI Model Predictions p = 1.19 GeV/c FSI Model Predictions p = 1.31 GeV/c FSI Model Predictions p = 1.43 GeV/c Page 10 11 19 21 21 22 23 24 38 38 51 58 82 84 85 88 89 90 91 Table >>>UT¢II wa UDUUU 0'1wa pp and En Cross Section Summary of Fits Effects of FSI Events in Measuring Categories A and B Events in Measuring Category C pd + p + ... Events in Measuring Categories A and B pd + p + ... Events in Measuring Category C Events in Categories A and B Events in Category C (4 Prong) Events in Category C (6 Prong) Classification of the Code 4 Events in Measuring Categories A and B Classification of the Code 4 Events in Measuring Category C. Scanning Efficiencies Measuring Efficiencies C.1a Uncorrected Measuring Efficiencies C.1b Corrected Measuring Efficiencies Beam Count p = 1.09 GeV/c . Beam Count p = 1.19 GeV/c . Beam Count p = 1.31 GeV/c . Beam Count p = 1.43 GeV/c . Summary of Beam Count . Scanning Loss Corrections for Slow Spectator Protons vi Page 93 102 111 116 118 120 122 125 126 127 128 129 131 133 133 133 136 137 138 139 141 146 Table E.2 F. F. 1 2 Scanning Losses for Events with Fast Spectator Protons . . . . . . Estimate of Unseen Elastic Scattering Total and Observable pd Cross Section vii Page 148 151 151 Figure “MOON _..| LIST OF FIGURES Page Typical Bubble Chamber Photograph . . . . . 6 Missing Mass Squared Distributions . . . . 14 Topological Cross Sections . . . . . . . . 25 5n + ppn' Cross Section . . . . . . . . . . 27 Cross Sections for 6n + 2n’n+ and fin + 3U 2U . . . . . I . . . . . . . . . 29 5n + 2n'n+n° Cross Section . . . . . . . . 31 5n + 3n'2n+n° Cross Section . . . . . . . . 33 Momentum Distributions of Protons from the Reaction pd + pS3TT'21T+ . . . . . . . 39 Invariant Mass Distributions of Pion Systems . . . . . . . . . . . . . . . . . 42 Nonresonant and Double Rho Background Invariant Mass Distributions . . . . . . 47 Fractional Amounts of p°21r'Tr+ and p°p°n' Production at Each Beam Momentum Setting . . . . . . . . . . . . . . . . . 52 Fractional Amounts of p°21T'TT+ and p°p°n' Production at Each ECM Band . . . . . . . 55 Fractional Amount of n+n' pairs in the p° Signal . . . . . . . . . . . . . . . . 59 Spectator Momentum Distributions . . . . . 63 Final State Interaction Process and Initial State Interaction Process . . . . 53 viii Figure 5.3 U1 uooowm Invariant Mass Distributions of n+ p5 and n pS Systems . . . Cosine Distribution of Protons Invariant Mass Distributions of n+p and n'p Systems . Cross Sections for n+p(A) and n'p(B) Four Prong Double Scattering Fits Six Prong Double Scattering Fits Invariant Mass Distributions of n+ pS and n' pS Systems . . Cosine between the Beam Direction and the TT"'ps Momentum Direction Spectator Proton ¢ Distribution ix Page 71 73 78 8O 97 99 105 107 143 CHAPTER I INTRODUCTION The study of 6d interaction can be used to obtain information about the pn system. In the first approxima- tion, one can regard the deuteron as two separate parti- cles. Therefore, information about pn reactions can be obtained in a direct manner. This approximation is, in fact, not valid when more detailed examinations of the deuteron are made. First of all, the proton and the neu- tron in the deuteron are not stationary and are known to have an expected Fermi momentum of about 45 MeV/c. There- fore, the total available energy in the collision center of mass varies according to the initial momentum of the target neutron. In addition, the presence of a spectator proton may affect the dynamics of the collision process. The proton may screen the neutron from the incident anti- proton, thus reducing the probability for a pn interaction. Furthermore, the presence of two nucleons at close range may cause the antiproton to double scatter in traversing the deuteron. This may happen in two ways: First, the antiproton may interact with one of the nucleons before it does with the other. Second, particles produced by the first collision may interact with the spectator nucleon. These double scattering processes will be shown to account for an excess of high momentum protons observed in the re- action Dd + pS + mesons. Since there has been no complete description of double scattering in absorptive type reac- tions, one of the objectives of this dissertation is to develop a comprehensive model for double scattering that is applicable to 6d annihilation reactions. Such a model is of great importance for studies involving a deuteron target because the presence of a spectator nucleon is often used to identify the type of reaction. As it will be shown in Chapter V, double scattering modifies the expected charac- teristics of a spectator nucleon. Therefore, it is impor- tant to understand the nature of such a modification. For example, one must take account of the fact that double scattering causes an excess of high momentum spectators. Therefore, to measure reaction cross sections based on a sample of events with a spectator momentum cut becomes con- siderably more complicated than just a simple correction using a deuteron wave function. Also, double scattering can modify the characteristics of the initial or final states of the reaction. These modifications are important in considering s-channel resonances, resonance production and reaction cross sections. The double scattering model developed here will be shown to be in excellent agreement with the data. Some of the considerations discussed above were not 1 applied by Abrams t 1. in determining the total nucleon antinucleon cross sections for pure isospin one and isospin zero states. Using an impulse approximation, Abrams gt 11. reported the existence of two isospin one and one isospin zero enhancements between 1 and 3 GeV/c incident antiproton momentum. The observation of a narrow bump near 2190 MeV was 2 reported by Kalbfleisch gt 1. in the reaction pp + p°p°n°. These authors suggested that it might provide a partial ex- planation for one of the I=1 enhancements (called A: (2190)) observed in the total cross section measurement. However, Donald __t_ _I.3 and Handler gt 531.4 failed to confirm this effect in similar experiments. Since the pn system is a pure I=1 state, the effect should be twice as prevalent as that in a 5p system. In this work, the reaction 5n + 2n+3n' is investigated for a possible s-channel enhancement near 2190 MeV. As a by-product of this work, the pn reaction and topological cross sections involving 3 and 5 charged secon- daries are measured and presented here. CHAPTER II EVENT AND FIT SELECTIONS 2.1 Introduction The major fraction of the sample used in this work came from 150,000 triad exposure taken at the Brookhaven National Laboratory 31-inch deuterium filled bubble chamber. The incident antiproton momenta were 1.09, 1.19, 1.31, and 1.43 GeV/c. The film was divided into 72 sets with three views per set. Twenty-four of these sets were taken at 1.31 GeV/c and the remaining sets were evenly divided among the other momentum values. Only a certain subset of the interactions visible on the film was used in this study. This subset consisted of any event in which the antiproton appears to interact with the neutron and result in 3 or 5 charged secondaries. First, a set of events satisfying the scanning criteria was measured. Then, the relevant events were obtained by a kinematic analysis of these events. 2.2 Selection of the Events to be Measured The desired sample consists of events in which the antiproton appears to interact with the neutron and produce 3 or 5 visible charged particles. Depending on its momen- tum, the spectator proton may or may not produce a visible track in the bubble chamber. Therefore, events of interest will have 3, 4, 5 or 6 outgoing tracks. These events will be referred to as 3, 4, 5 or 6 prong events. In the even prong events, one of the positive tracks is assumed to be the spectator proton. Using the above considerations, a set of rules was set up to determine if an event is to be measured. These rules were devised to select all the desired events with as little contaminations as possible. The events satisfying any of the following criteria were measured: A) Any three or five prong event. B) Any four or six prong event with a stopping proton. (A stopping proton is defined by a heavily ionizing track with three or less gaps. It must not resemble the characteristic manner, of hue decay.) C) Any four or six prong event if the ionization density of one of the positive tracks is equal to or greater than that of the beam in all three views. This track must not decay in the manner of Rue. (See Figure 2.1 for the defini- tion of a positive track.) In addition, only the events due to a beam track interacting Figure 2.1 Typical Bubble Chamber Photograph The fiducial volume is defined between the two lines. The antiprotons enter the chamber at the bottom of the Figure. Three events are shown: A) B) C) Four Prong Event with a Stopping Proton. The stopping proton is at the 8 o'clock position. A track produced by a n+ is at the 4 o'clock position. Two remaining tracks were produced by n”. . Four Prong Event with a Fast Proton. The fast proton is the positive track at the 2 o'clock position. This track has a greater ionization than the other tracks in the event. Five Prong Event. The positive track at the 9 o'clock position is not a proton, despite its high ionization, because it is observed to decay. (Note the light track which is produced as a result of the decay.) within the fiducial volume of the chamber (see Figure 2.1) were measured. Events with the vertex obscured by other tracks were not measured but were recorded for correction purposes. Category A contains events in which the proton is moving too slow to produce a visible track. The momentum of these protons is usually less than 100 MeV/c. A proton having a momentum greater than 100 MeV/c will usually pro- duce a visible track in the chamber. Category 3 contains events with a visible stopping proton. Most of the remain- ing desired events are contained in category C. These events usually have protons with a momentum greater than about 200 MeV/c. Table 2.1 summarizes the measured sample of events. Table 2.1 Total Events Measured Momentum 3 Prong 4 Prong 5 Prong 6 Prong GeV/c 1.09 5418 7495 2519 2341 1.19 7943 10164 3670 3398 1.31 14457 1853 7053 6578 1.43 9898 12868 4566 4528 2.3 Processing the Measured Sample The events selected in Section 2.2 were then measured using an image plane digitizer (IPD). This machine projects the film onto a surface. The x and y coordinates of several points on the image of each track were recorded on a magnetic tape for three stereo views. Then, the data on the tape were processed through the PANAL9 ‘0 1‘ - TVGP - SQUAN chain of programs. The PANAL program converts the data from the IPD machine to a form suitable for TVGP. TVGP uses the PANAL output to recon- struct the tracks in a three dimensional space from the optical properties of the chamber and the known value of the magnetic field in the chamber. The particles that produced outgoing tracks were assumed to have a mass of a n, k, or p. The reconstructed track information for a given event was then used by SQUAN to perform kinematic fits. The reaction hypotheses are listed in Table 2.2 A summary of the number of fitted events on the final tape written by SQUAN is presented in Table 2.3. 10 Table 2.2 Reaction Hypotheses 3 or 4 Prong_Events Reaction Number of Constraints Mark Number Pd'+ PSPPU' 4 3 13d + psn+21r 4 3 5d1+ pska'n' 4 30 5d +~psn'2n'n° 1 9 5d + psntzn- + m o 10 pa + psk+ T + mm o 31 fid'+ pspin- + mm 0 5 5d + n52n+21r' I 15 Ed +-n52n+2n"+ mm 0 17 5 or 6 Prong Events Reaction 5d + p52n+3n' 4 8 5d + psk+k-R+2R- 4 30 5d + p52n+3n'w° 1 9 13d + pszntw + m o 10 5d + psk+k‘n+2n’ + m o 31 5d + n53A+3Ir 1 15 [3d + ns3n+3n' + mm 0 17 11 Table 2.3 Events on the Final Tape Momentum 3 Prong 4 Prong 5 Prong 6 Prong GeV/c 1.09 5063 6937 2285 2060 1.19 7567 9411 3347 2945 1.31 13634 17274 6379 5791 1.43 9427 12062 4164 3970 2.4 Fit Selection The SQUAN program often gives acceptable fits to several kinematic hypotheses for each event. Therefore, a procedure to select the correct fit was devised. This procedure was to compare the projected ionization density of the outgoing tracks predicted by mass interpretation of a given fit to the projected ionization of the data. It was often necessary to examine the event in all three views in order to determine the mass of the particle that produced the track. The chosen fit was required to be consistent with the results of the ionization scan. The comparison indicated that fits involving the four con- straint reactions 6d + psppn', pd + psn+2n', and 5d + p52n+3n' could be reliably selected using kinematic criteria. This was done by requiring the missing mass squared (the square of the magnitude of the missing four 12 momentum) to be within two standard deviations of zero. If the event had a multiple fit involving these reactions, the fit with the highest confidence level was chosen. For the remainder of the events, the fit ambi- guities could not be resolved on an event by event basis by using the missing mass squared and confidence level. A large fraction of these events were contained in cate— gory C (see Section 2.2). Therefore, an ionization scan was performed on all events in category C, which contains about 40,000 events, to settle the ambiguities involving the mass interpretations of tracks. In addition, events with either pd + psk+k"n' or 5d + psk+k'2n'n+ fits were checked in the ionization scan. These fits were assigned to an event only if the ionization density predicted by the fit agrees with the observed ionization density. In addition to producing charged particles, anni- hilation reactions may also produce neutral particles. The fit hypotheses involving neutral particles are zero constraint or one constraint fits (see Table 2.2). Non- strange neutral particles are often not observable in a bubble chamber. Therefore, the total four momentum of the neutral particles cannot be directly measured. How- .ever, it can be inferred using conservation of four momen- tum for a given reaction. If only one neutral particle is produced, the square of the "missing" four momentum, which is called the missing mass squared, is equal to the 13 mass squared of the particle. In the case of two or more neutral particles, the missing mass squared is equal to the center of mass energy squared of the neutral particle sys- tem. If no neutral particles are produced, the missing mass squared is zero. Since the resolution of the measur- ing system is folded into the missing mass squared distri- bution, the peaks due to the one constraint or four con- straint type reactions acquire a characteristic width. The missing mass squared distribution can be used to determine the number of events involving single n° pro- duction. This is done by examining the missing mass squared distribution for events having track ionization consistent with a fit hypothesis of the type pd + pS + charged pions + neutral particles. Since the events pro- ducing only charged particles have already been assigned fits, these are not included in the distributions. The resulting missing mass squared distributions are shown in Figure 2.2. In each plot, a prominent peak at the n° mass squared is seen. The sum of the shaded area and unshaded area represent the total missing mass squared distribution for single n° events and multi-neutral events. The events in the unshaded area, which represent candidates for single n° production, were obtained by requiring the missing mass squared of events with a fit hypothesis involving a single n° to be within two standard deviation of the mass squared 14 Figure 2.2 Missing Mass Squared Distributions Zero constraint fits - shaded area One constraint fits - unshaded area EVENTS PER .01 DEVI-2 EVENTS PER .01 GEV-IZ EVENTS PER .01 GEV-IZ EVENTS PER .01 DEVI-2 210 . 140.1 250 . 200 . 1 5 S-H PRUNG P=1.09 GEV/C § '2' 1”,:1 . K" I“) ‘r 32" 2 / 71:, / '1' I 4 I ,.' / ' , , (1 . ‘/24//r///’.,)/2 “/h' I I [I V VI‘ ’ ' .HVWI/U ““2”, -.3 0.0 0.3 0.6 MISSING MOSS SOURRED (GEVIIQI S-U PRONG P=l.19 GEV/C 0.3 MISSING MESS SOURREO (GEVIJ21 -.3 0.0 0.6 0.9 U00 - 3-u PRUNG P=I.3l DEV/C 300 . 200 . Ioo . 1 _ _ (Il’! /~-SI/, ‘/ ‘ /, /’%/ (I -/::7’ 0 .1 flI/I/jfif/Cfllj ”.3 0.0 0.3 0.5 0.9 MISSING NRSS SOUBRED (GEVIIQl 3-H PRONG P=I.U3 GEV/C 150+ .I)172.,, .I,A'» I. .1.‘ ,JII",'v/'// , IN)" ’I [)1 ’(If‘l ‘ . ‘ ”In” '/1"“- '2" “(UH/ " I ,"‘I"", ’ Y/D‘r TAU OIHASFJ 445; -.3 0.0 0.3 0.6 0.9 MISSING M955 SOURRED (GEM-n21 EVENTS PER .01 GEV-IZ EVENTS PER .01 GEVII2 EVENTS PER .01 GEVII2 EVENTS PER .01 GEVIIZ 5-6 PRONG P: l. 09 GEV/C 0.0 0.3 -03 0.6 0.9 MISSING MESS SQURRED IGEVII21 210 1 SP8 PRONG P=l.19 GEV/C 140 . 70 . 0 1 -03 0.0 0.3 0.6 0.9 MISSING MHSS SUUPRED (GEVII21 H00 - 5-3 PRUNG P=I.31 GCV/C 300 I 200 . 100 . o . ~ ir~ “.3 000 0.3 0.6 0.9 MISSING M955 SQURREO (GEVIIQI 250 . 200 1 5-5 PRUNG P=l.u3 GEV/C 150 4 100 I 50 a 0 . '.3 0.0 0.3 0.5 0.9 MISSING H955 SOURRED (DEVI-21 16 of a n°. The shaded area represents events producing two or more neutral particles. The n° peaks, particularly the three and four prong topologies, appear to be asymmetric with respect to the known n° mass squared value. Therefore, the number of events for single n° production channels must be corrected. The correct number of events is found by splitting the n° peak at the n° mass squared. Unlike the high mass side of the n° peak, the low mass side is not contaminated by multi- neutral type events. Therefore, the number of single n° production events is found by doubling the number of events in the low mass side of the n° peak. CHAPTER III ANTIPROTON NEUTRON TOPOLOGICAL AND REACTION CROSS SECTIONS 3.1 Introduction The cross section, 0, is related to the probabi- lity that an incident particle will interact with a par- ticle in the target. If the beam intensity is initially I then the cross section can be defined by: o, I = I e'“Gx (3.1) Here, I is the intensity of the beam after it has tra- veled a distance x into the target and n is the number of target particles per unit volume. In 5d interaction, several different final states result when the antiproton interacts with the deuteron. Therefore, the total cross section is a sum of partial cross sections representing each final state. This chap- ter presents the cross sections due to antiproton neutron interactions resulting in final states with 3 or 5 charged particles and zero or more neutral particles. The fin reactions are assumed to be characterized by the presence of a spectator proton. The fact that the proton may screen 17 18 the neutron from the antiproton is taken into consideration. 3.2 Cross Section Equivalent for an Event The cross section equivalent for an event, R, can be used to determine the cross section for a given topology if the number of events corresponding to the given reaction or topology is known. The value of R can be found from the total pd cross section, at, by defining a reaction volume and counting the number of beam particles, Nb’ entering the reaction volume. These numbers can be used to determine the total number of interactions in the reaction volume by: -£/£o Nt = Nb (1 - e ). (3-2) Here, 2 is the effective length of the reaction volume and 20 is given by: 20 = 2/(0tpAo). (3.3) The quantities A0 and p are the Avagodro number and the density of liquid deuterium respectively. The reaction volume was defined by: IA 10.0 cm, (3.4a) 17.6 cm, (3.4b) IA -10.0 x IA IA and -24.0 y where x and y are coordinates measured from the center of the bubble chamber. Values for at were taken from refer- ence l and the effective length of the reaction volume was 19 12 calculated by Mountz. A detailed discussion of Nb is pre- sented in Appendix B. Then, R can be found by: R = ot/Nt. (3.5) However, in a bubble chamber, not all the interactions are visible. The invisible or missing interactions are due to low t elastic scattering. In Appendix E, the amount of missing cross section, cm, is estimated. To account for the effects of this missing cross section, at was replaced by the observable part of the cross section ot—om. The value of R, however, is not very sensitive to this change. The change in R due to this correction is less than 1%. Table 3.1 summarizes the numbers used in the calculation of R. Table 3.1' Cross Section Equivalent for an Event Number of Momentum Beams R(cm) ot(mb) ot-om(mb) R(pb/event) 1.09 168924 41.96 200.31 200.31 3.880 1.19 258789 41.94 195.56 166.66 2.523 1.31 498757 41.68 191.50 162.60 1.312 1.43 331612 41.79 184.56 155.66 1.957 20 3.3 Scanning, Measuring, and Systematic Losses To calculate the cross section from R, the true number of events involving the desired reaction must be known. The final sample does not contain all the pn events because of scanning, measuring, and systematic losses. These losses must be determined before the cross sections can be obtained. To determine the scanning efficiency, cs, a sample of film was rescanned and the resulting event sample was compared to the original event sample. Since the loss of events is assumed to be random, the scanning efficiency can be calculated using the number of events in common between the two scans and the number of events contained in one scan but not the other. The resulting values of as are listed below. Scanning efficiencies in category C have no signifi- cant difference, within statistical uncertainty, for differ- ent beam momenta. Therefore, scanning efficiencies for the combined four or combined six prong samples are used. Appendix B gives the details of the calculation. Measured events that do not appear on the final data tape are due to measuring losses. These losses are taken into account by the measuring efficiency, cm, which is calculated in Appendix C. The resulting measuring efficien- cies are presented in Table 3.3. 21 Table 3.2 Scanning Efficiencies Categories A & B Events Category C Events p(GeV/c) es Event 5 Type 1.09 .901i.007 4 Prong .836i.004 1.19 .87l:.006 6 Prong .857:.007 1.31 .872:.006 1.43 .883:.005 Table 3.3 Measuring Efficiencies p(GeV/c) 3 Prong 4 Prong 5 Prong 6 Prong 1.09 .938:.0034 .930i.0030 .9ll:.0050 .884:.0067 1.19 .957:.0024 .930i.0026 .916:.0047 .871:.0058 1.31 .947:.0019 .938i.0018 .908:.0035 .884i.0040 1.43 .956i.0021 .941:.0021 .916:.0042 .881t.0049 In addition to the scanning and measuring ineffi- ciencies, events with apparent proton ionization higher than that of the beam track were rejected by scanners due to criterion C (see Section 2.2). This was due to a judg- ment error of the scanner and caused a loss of some events having high momentum protons. Since these events were not 22 lost at random, this effect cannot be accounted for by the scanning efficiency. The losses due to this effect are calculated in Appendix E. The true number of events can be found from the number of measured events, No’ and the number of unmeasured events, "1055 by: Ne = (N0 + Nloss)/(€s Hm)‘ (3'6) The values of No and N1 are presented in Appendices 055 A and E. 3.4 Screening Corrections To obtain the pn reaction cross sections, a correc- tion must be made to account for the screening of the neu- tron by the proton. The screening correction factor is defined by: S E pno_ p (3-7) pd The values of 5, calculated from cross sections in refer- ence 1, are shown below. Table 3.4 Screening Correction Momentum (GeV/c) Screening Correction S 1.09 1.10 1.19 1.10 1.31 1.10 1.43 1.11 23 The fin reaction cross sections are corrected for the screening effect by assuming that screening applies equally to all the reactions. 3.5 Topplogjcal and Reaction Cross Sections By using the numbers discussed in Sections 3.2-3.4, the measured cross sections are given by: G = R(N + o Nloss x E) (3.8) )/(e:m S The reaction cross sections for 6n interaction are cor- rected for screening by multiplying by S. The results are summarized in Tables 3.5 and 3.6 and Figures 3.1-3.5. The higher momentum data of Eastman £3 11.13 are shown for comparisons. Table 3.5 pd + pS + ... Topological Cross Sections Momentum (GeV/c) 3 Prong 4 Prong 5 Prong 6 Prong 1.09 17.73i.50 17.09:.65 8.41:.28 5.95:.29 1.19 17.65:.41 15.91:.54 8.34:.25 5.82:.23 1.31 16.99:.47 15.23:.46 8.26:.23 5.97:.23 1.43 16.93:.44 15.82:.51 7.94:.23 5.60:.23 24» Table 3.6 6n Reaction Cross Sections 3-4 Prong Events Momentum _ Multi- GeV/c ppn' n+2n' n+2n'n° KTK‘n' neutral Total 1.09 .261.05 2.16:.17 11.38:.53 .24:.05 24.32:.88 38.36:l.45 1.19 .681.07 1.80:.13 10.91:.45 .251.06 23.28:.74 36.92:1.11 1.31 1.40:.08 1.61:.09 9.36:.33 .22:.04 22.86:.65 35.44: .98 1.43 2.59:.14 1.43:.10 8.93:.35 .26:.05 23.14:.70 36.35:1.04 5-6 Prong Events Momentum 0 Multi- GeV/c 2n+3n' 2n+3n'n K+K‘n+2n' neutral Total 1.09 4.08:.26 6.82:.37 .09t.03 4.82:.28 15.81:.62 1.19 4.01:.22 6.43:.29 .16:.03 4.99:.24 15.59:.50 1.31 3.68:.17 6.70:.24 .16:.03 5.121.21 15.66:.45 1.43 3.40:.17 6.27:.27 .16:.03 5.19:.24 15.02:.48 25 cowgumm compumm :o_uumm :o_¢umm mmOLU mmOLU mmOLU mmOLU FmUPmo—oaop ... pmowmopoaop ... PmmeoFoaou ... Pmuwmo—oaou ... mg + an mcoga 0 ma 1 um mcoga m ma 1 cm mcoga ¢ ma.. cm mecca m mcowpumm mmogu quwmopoaoh _.m aczmwa D X 26 HQ\>muH zzpzmzoz m¢4 m.m m.m :.m m.m o.m m.H m.H _ F _ _ _ _ _ monHumm mmamu quHwoqomoh NDIIDES 88033 (SH) 27 cowpomm mmogo Team I an N.m aczmpu 28 o.m m.N w.N :.N HU\>on zshzmzoz mag N.N o.N m.~ _ _ _ m gum: m.H NDIIOQS 88033 (SH) 29 + +: FIFN + : +=Nupm + cm x +pu=N + cm : Nuum + cm was n so» mcowuomm mmogo m.m «gnaw; __ __I ...—I1 30 o.m m.N HU\>on zshzmzoz mm; m mum: NDIIOES 38033 (SH) 31 cowuumm mmogu o: :-:N + cm 1.: ¢.m mgzmvu 32 o.m m.m _ m.m _ :.N _ Hu\>mog zabzmzaz mag N.N o.N m.H F b _ m 1mm: wzomm 31m m.H _ :4 _ m.“ _ o.fi .NH NDIlOBS 88033 (SH) 33 cowuumm mmogu op+=mupm + an m.m mgsmvm 34 o.m m.w _ Hu\>mug zshzmzoz mag m.N :.N w.m o.N m.H _ g _ L _ m gum: mzomm mum m.H _ d.H _ N.H o.fi .NH NOIIDES 88033 (SH) CHAPTER IV DOUBLE RHO PRODUCTION IN 5n + 3n‘2n+ 4.1 Introduction In a high statistics counter experiment by Abrams t 1.,1 an enhancement near the center of mass energy of 2190 i 10 MeV was observed in the total 5d and 5p cross sections. By assuming an impulse approximation for inter- actions on the deuteron and that the enhancement has a Breit-wigner line shape, these authors deduced that this structure is an I=l state with a width of 85 MeV. The re- ported height of this enhancement was 5.5 mb. Since this enhancement may be due to a resonance, a threshold effect or both, there have been several attempts to uncover its source.2'8’ 15 In studying the reaction 5p + 2n+2n'n°, Kalbfleisch t 1.2’ 15 reported observation of a s-channel structure in the reaction pp + p°p°n°. These authors sug- gested that this structure, having a mass of 2190 MeV and a width between 20 and 80 MeV, may be partially responsible for the 2190 MeV enhancement in the total pp cross section. 3 However, Donald at l. and Handler gt 31.4 failed to con- ——————— firm the Kalbfleisch result in similar experiments. 35 36 Since the pn system is a pure I=l state and the pp system is an equal admixture of I=1 and I=0 states, an I=l s-channel resonance should be twice as prevalent in the pn system. In particular, the reaction fin + 3n'21r+ should have an enhancement twice as large as the 0.5 i .1 mb en- hancement reported by Kalbfleisch in 5p + 2n'2n+n° if the amplitude for producing the pp system in an I=0 state is dominant. Kalbfleisch15 suggested that the pp sub-system + show no is I=0 because their cross sections for p°pifl bump while the p+p'n° cross section shows a "probable" bump. It is of interest to see if this enhancement is pre- sent in the reaction 5n + 3n'2n+. Therefore, the interme- diate states of the reaction 5n + 3n'2n+, in particular the p°p°fl- state, have been examined for possible s-channel structure. 4.2 The Reactionpn + 31r'21r+ The reaction 5n + 3fl-Zfl+ has been examined at thir- teen different beam momenta values: l.09, 1.19, 1.31, l.43, l.60, 1.75, 1.85, 2.00, 2.15, 2.30, 2.45, 2.60 and 2.90 GeV/c. The data were collected in three different bubble chamber experiments. The four lowest momentum values were from data described in Chapter II. The higher momentum values were taken in two different experimental runs in the Argonne National Laboratory 30-inch deuterium filled bubble 37 chamber. The details of these data are described elsewhere.13 To be included in this analysis, an event must have a fit to the reaction pd + pSBn'Zn+ satisfying the criteria described in Section 2.4. In addition, the spectator proton momentum was required to be less than 190 MeV/c. The pur- pose of this cut is to remove events in which both nucleons participate in the scattering processes. The momentum dis- tribution of protons from the reaction 5d + p531r'21r+ shows evidence for this double scattering process (see Figure 4.1). The solid curves represent predictions of the deuteron wave function. As can be seen in the figure, there is a definite excess above 200 MeV/c. This excess is attributable to the double scattering effect and will be discussed in detail in Chapter V. All the data satisfying the above conditions are used to examine s-channel structure of the intermediate states of 5n + 31r'2n+ for possible resonances. 4.3 The Intermediate States inpn + 31r'21r+ There are several possible intermediate states in the reaction 5n + 31r'2n+ involving the production of Zn, 3n, or 4n resonances. Table 4.1a lists the masses and widths of the well-known resonances and bumps which might be involved. To decide which of these resonances are produced in this re- action, the invariant mass distributions for each possible Resonance System 2n 2n 2n 3n 3n 3n 4n 4n 38 Table 4.1a Mass and Width of Pion Resonances and Bumps Mass (Me!) Width (MeV) Decay Mode 745 135 2n 1269 156 2n 1310 100 pn + 3n 1640 Broad fn + 3n 1070 Broad on + 3n 1680 160 4n Table 4.1b Charge and Number of Combinations Chargg_ Number of combinations/event -2 3 0 6 +2 1 -3 l -l 6 +1 3 -2 2 0 3 39 Figure 4.1 Momentum Distributions of Protons from the Reaction pd + pS 3n'2n A) Events from the data with beam momenta of 1.09, 1.19, 1.31, and 1.43 GeV/c. B) Events from the data with beam momenta of 1.60, 1.75, 1.85, and 2.00 GeV/c. Also shown is the expectation distribution of the internal Fermi momentum of the deuteron. This distribution has been normalized to the data below 190 MeV/c. EVENTS EVENTS 800 — 40 .2 R) 500 - 000 a 200 -v 0 I 1’ 1 71‘ 1 ‘ I I 0.0 0.2 0.0 0.6 0.8 1.0 ] SPECTRTUR MOMENTUM (GEV/Cl 300 — B) 1 0.2 0.0 0.6 SPECTRTUR MOMENTUM 0.8 1.0 [GEV/C) 1 .2 41 Zn, 3n, and 4n charge states were examined. These distri- butions, which are shown in Figure 4.2, contain events from the four lowest incident beam momentum settings. Table 4.1b shows the possible charge states and the corresponding number of pion combinations. Inspection of the invariant mass distributions show that the p° is the only resonance that is obviously present. Similarly, the higher momentum 54 Therefore, for the data also involve only p° production. purpose of this work, it will be assumed that the fin anni- hilation into five charged pions can only proceed by the following reactions: 5n + 3-n'2n+ (4.1a) 5n + QOZW-N+ (4.1b) 5n + p°p°n- (4.1c) These reactions will be referred to as nonresonant, single rho, and double rho production respectively. To determine the fractional amounts of each type of production, distinguishing characteristics must be found. There are six possible n+n’ pairs in the 3n'21r+ final state which could be a p° candidate. For single rho or double rho production, only one or two of these pairs are in the p° signal. The remaining n+n' pairs comprise the background distribution. Both the shape of the background distribution and the fractional amount of n+n' pairs in the p° signal 42 Figure 4.2 Invariant Mass Distribution of Pion Systems (1666 Events) (A) n+n" Invariant Mass (B) n'n' Invariant Mass (C) n+n+ Invariant Mass (D) n'n+n+ Invariant Mass (E) n'n'n+ Invariant Mass (F) n n'n' Invariant Mass NUMBER OF COMBINRTIONS 43 500...1 (R1 250.- 0' I 1 I F 250. 500. 750. 1000. 1250. 1500. 1750. 2000. 200.- (B1 100.- 0' I I I I I ‘D ‘ I I 250. 500. 750. 1000. 1250. 1500. 1750. 2000. 80. - (C) ”U. u 0' I I I I “$11.... 1L! I 250. 500. 750. 1000. 1250. 1500. 1750. 2000. INVRRIRNT MRSS (MEV) NUMBER OF CUMBINRTIUNS 44 200.- 10] 100.- 0' ‘ I I I r T I 250. 500. 750. 1000. 1250. 1500. 1750. 2000. 000.- 1E1 200.- 0' I I T W F I —1 250. 500. 750. 1000. 1250. 1500. 1750. 2000. so. 7 (F1 40. - 0' l r I T f T 1 250. 500. 750. 1000. 1250. 1500. 1750. 2000. INVRRIRNT MRSS (MEV) NUMBER OF COMBINRTIUNS 45 150.- [G] 75. 1 0’ " I I I I r I 500. 750. 1000. 1250. 1500. 1750. 2000. 2250. 200'.1 1H1 100.4 0' I 44' I I I I I 500. 750. 1000. 1250. 1500. 1750. 2000. 2250. INVRRIRNT MRSS (MEVI 46 depend on amounts of each type of production. The features of each type of production were simulated using the Monte 16 In each case, a Carlo event generating program SAGE. simple statistical model type mechanism is assumed. The results show that the n+n' invariant mass distributions in- volving nonresonant production, single rho background and double rho background are similar in shape. This is shown in Figure 4.3. The main difference between single rho and double rho production appears to be in the fractional amounts of n+n' pairs in the p° signal. For single rho production 1/6 of the n+n’ pairs are contained in the p° signal. The corresponding number for double rho production is 1/3. Because of the similarities in the invariant mass distributions, it is possible for a combination of nonreso- nant production and double rho production to look like single rho production. Therefore, an anticorrelation between the amount of p°p°n' and p°2n'ir+ is expected in fitting the n+n' mass distributions to the data. 4.4 Analysis Procedures The n+n' invariant mass distribution of the data is assumed to be the sum of the Monte Carlo generated n+n' in- . . . . - + variant mass distributions for nonresonant, p°2n n and O O n' channels. Fitting was done using the following pp expression: 47 Figure 4.3 Nonresonant and Double Rho Background n+n' Invariant Mass Distributions The dashed curve is the nonresonant invariant mass distribution. The solid curve is the double rho background invariant mass distribution. 48 l- , .' - -— i’=1.09 1% I ‘13 3 'L g . a. I 1‘ U) "i .... I. z 0 :3 I- o u I t... "T r I I I ' ‘ 250. 500. 750. 1000. 1250. 1500. M953 0F PI+ PI- SYSTEM , ," -. . 922.90 u: Z P ‘13 at w L I .9 s 1%,,“ o u 5‘1, I r T r i 250. 500 750 1000. 1250. 1500. Bass or fiI+ PI- srsren 49 M = (l - A - B) Mn + AMs + BM (4.2) d n’ Ms’ and Md are the n+n' invariant mass distribu- Here, M tions of the nonresonant, p°2n'n+, and p°p°n' Monte Carlo events respectively. The sums of each of these Monte Carlo distributions are normalized to the sum of the data sample. The quantities A and B are fit parameters corresponding to the fractional amounts of p°21r'ir+ and p°p°n' production. The center of mass energy (ECM) for each beam momen- tum setting is not well defined. This is caused by the re- solution in beam momentum, energy loss of the beam as it passes through the chamber, and the Fermi momentum of the nucleons in the deuteron. A spread of :17 MeV in the center of mass energy is caused by the Fermi momentum of the target. The energy resolution of the beam and energy loss in the chamber each cause a :2 MeV spread in ECM. In addition, ex- perimental measurement errors cause a :10 MeV resolution error in ECM. Combining these errors in quadrature gives a ECM resolution of :20 MeV. Since this spread could inhibit the observation of s-channel structure, least squares fits were made to determine parameters in Equation 4.2 for each beam momentum setting as well as for data grouped in 40 MeV center of mass energy (ECM) bands. The fitted results for each ECM band were used in the next section to calculate the probability of having an enhancement in p°p°n' produc- tion. The numbers of events corresponding to each momentum 50 setting or ECM band are shown in Table 4.2. Figure 4.4 and 4.5 show the results of these fits. The contours, which correspond to one standard deviation, show that there is a strong anticorrelation between A.and B. Since the only distinguishing feature between p°21r'1r+ and p°p°n' production appears to be in the strength of the p signal, it is possible for a combination of p°p°n' and nonresonant 5n production to appear to be p°21r'1r+ production. Therefore, the only meaningful information that can be ob- tained from the invariant mass distribution is the fractional amount of n+n' pairs in the p signal. To find this fraction, the following expression was used to fit the data: M = (1-f) Mn + er (4.3) Here, Mn is the Sn phase space distribution and Mr is given by Mn times a Breit-Wigner function having the mass and width of the p°. The sums of Mn and Mr are each normalized to the data. Therefore, f gives the fraction of n+n' pairs in the data resulting from the decay of a p°. The resulting values of f are presented in Table 4.3 and Figure 4.6. 4.5 Interpretation of the Fit Results As seen in Figure 4.6, the fractional amount of signal shows no obvious s-channel structure. In particular, assuming that the amounts of p°21r'II+ and p°p°n' production 51 Tab1e 4.2 Events Used in Fit P(GeV[c) Event§_ ECM Band (Gey)‘ Egggugi 1.09 680 2.09 - 2.13 633 1.19 997 2.13 - 2.17 1171 1.31 1852 2.17 - 2.21 1494 1.43 1123 2.21 - 2.25 920 1.60 679 2.27 - 2.31 381 1.75 381 2.32 - 2.36 352 1.85 383 2.36 - 2.40 336 2.00 380 2.41 - 2.45 241 2.15 277 2.46 - 2.50 135 2.30 252 2.52 - 2.56 222 2.45 248 2.57 - 2.61 180 2.60 266 2.62 - 2.66 191 2.90 217 2.72 - 2.76 90 52 Figure 4.4 Fractional Amounts of p°21r'1i+ and p°p°n' Production at Each Beam Momentum The contours correspond to one standard deviation. 53 I. 1 9 3 S «I. u. 7 ..... .m. ._.-.. DI P D... f I ...... . fl ' q A «I 4 1.1 d - q 9 1.. 0 O 3 6 .... . L T .... 2 2 Z DI P DI I 1 r . I TI ' q u d u q 4 u q 11 4:1 u 0 8 6 u. 2 0 8 2 0 8 6 u. 2 1. o 0 0 0 0 0 0 0 .0 O 0 0 0 0 arm era mo zo~hu¢mm Dru era mo zomhucmm Dru arm mo zonpucmm 0.0 FRRCTION 0F RHU FRRCTION 0F RHU 54 no no no nu Q. .6 «2 I n2 n2 : : : P. D. P. T T- a J 1 4 d - I s .. s 5 av 11 u. I. r «2 n2 : : : P. p. P. T TI - u 3 - _ - I. - q I- 0 8 6 u. 2 0 8 6 Us 2 6 D C D . l D I D I O I 1. 0 0 U 0 0 o 0 O 0 0 arm Dru no zo—hucmu arm Dru mo zonhummu Dru arm mo zoapummm .0 0.2 0.0 0.6 0.8 1 0.0 FRRCTION 0F RHO FRRCTION 0F RHO 55 Figure 4.5 Fractional Amounts of p°31r'1r+ and p°p°n Production at Each ECM Band The contours correspond to one standard deviation. fl 1 1 9 3 S «J u. 7 I. .. L T L . : : : P DI ' r I r r r o O. .- fi- 1 no ...... H H 1 fi 1 d u1 a (1% «I 6 9 cl. 0 cl. 1 .la r- 1“ l : = .- P. D. P. r r r r T- I- o o o -D T 5 fi- ..... ~ ' — u ( I- 1 u a — qi 0 8 6 u. 2 0 8 O 8 0 1. nu nu nm nu nu nm nu nm nu era era mo zonhummm Dru ora no zomhucau 91m era mo zonhummm 1.0 0.0 0.2 0.9 0.6 0.8 FRRCTJON 0F RHO 0.8 0.9 0.6 FRRCTJON 0F RHO 0.2 0.0 57 i 1 0 0 0 0 3 6 2 2 2 I _. = : DI 9- Di 0 1. q 1 11 A a 1 a u 1 q 4 4 b s 5 S 8 1.. u. I. a: r n4 I = : : DI P. D: I 5 rl I: F I 7 A I a .I . I. d 1 I . I a - 0 8 6 u. 2 0 8 6 U. 2 0 8 6 u. 2 0 la 0 0 0 0 0 o o 0 U 0 0 0 0 0 0 arm Dru mo zonhucam era etc we zoqhucam era era mo zo—hucum 0.6 0.8 0.0 0.2 0.9 0.6 0.8 1.0 FRHCTJUN 0F RHU 0.9 0.2 0.0 ERECTION OF RHO 58 Tab1e 4.3 Fractional Rho Signal P(GeV[c) Fraction ECM Band (GeV), Fraction 1.09 .201 i .029 2.09 - 2.13 .202 i .027 1.19 .169 i .025 2.13 - 2.17 .197 i .021 1.31 .200 i .019 2.17 - 2.21 .181 i .024 1.43 .191 t .024 2.21 - 2.25 .221 i .033 1.60 .198 i .029 2.27 - 2.31 .209 i .052 1.75 .197 i .042 2.32 - 2.36 .235 i .046 1.85 .197 i .043 2.36 - 2.40 .209 i .044 2.00 .217 i .042 2.41 - 2.45 .190 i .043 2.15 .165 i .046 2.46 - 2.50 .195 i .068 2.30 .203 i .050 2.52 - 2.56 .185 i .056 2.45 .161 i .052 2.57 - 2.61 .188 i .059 2.60 .182 i .046 2.62 - 2.66 .187 i .054 2.90 .178 i .049 2.72 - 2.76 .193 i .060 59 Figure 4.6 Fractional Amount of n+n' Pairs in the p° Signal FRRCTIONRL QMUUNT FRRCT 1 ONRL RMOUNT .140 - .30 - .20 .10 ‘- .00 r .90 n .30 - .20 .10 n .00 I 60 ECM BRND --II- EWIIIIIII c-IL— I I 2.00 2.15 2.30 2.115 2.60 2.75 ECM (GEV) ' MOMENTUM SETTING 1111111111111 —1 I I I 1.00 1.110 1.80 2.20 2.60 3.00 LRB MOMENTUM (GEV/C] 61 do not change in such a way to keep the fractional p signal constant, no obvious s-channel structure is observed. Assuming that the behavior of the p°20'n+ channel is smooth in this energy range, a 1 mb enhancement in p°p°n' at 1.31 GeV/c (ECM = 2190 MeV) corresponds to an enhancement of 0.09 in the fractional p signal. This follows from the fact that if the reaction 5n + 30'20' proceeded purely via the p°p°fl- intermediate state, two out of six n+n' combinations would have been in the p° signal therefore, f must be approximately 1/3. To determine the probability of an enhancement of a given height, one must first assume a possible width. Then, the ECM resolution is folded in and the resulting distribution plus a background term is fitted to the data. The four values of fractional p° signal from 1.09 to 1.43 GeV/c were fitted using a flat background plus an ECM resolved Breit-wigner function. Different widths and heights for the enhancement were assumed in the fits. The probability of having a 1 mb enhancement in p°p°n' pro- duction, which is expected from the Kalbfleisch result, depends on the width of the enhancement. Using the lower limit of :20 MeV, given by Kalbfleisch, gives a probability of 0.03 (x2 = 6.7/2 degrees of freedom). For a :80 MeV I wide enhancement, the probability is 0.14 (x2 = 3.4/2 degrees of freedom). CHAPTER V DOUBLE SCATTERING EFFECTS IN THE DEUTERON 5.1 Introduction Since there exist no sources of free neutrons, the deuteron is often used to provide a quasi-free neutron target. In the impulse approximation, one assumes that the deuteron break-up occurs spontaneously upon impact by the projectile particle. Each of the constituent nucleons . carries away a momentum which can be predicted by the deu- teron wave functions. The constituent nucleon that did not participate in the reaction with the beam particle is called a spectator. The momentum distribution of the spec- tators may be found from the deuteron wave function, ¢(p), by ¢Z(p)p2. Figure 5.1A shows such a distribution. The probability of finding a spectator proton with a given momentum value peaks sharply at 45 MeV/c and declines to zero at about 300 MeV/c. However, numerous investigations have shown that there is an excess, over the dueteron wave function prediction, of spectator protons with momentum 13,17, 18 19 greater than 200 MeV/c. ‘Dean explains this 62 63 Figure 5.1 Spectator Momentum Distributions (A) Reid soft core deuteron wave function (B) Four prong data (C) Six prong data EVENTS BRBITRRRT UNITS EVENTS 64 300 a 200 - 100 - 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1800a 1200- 600 — 0.0 0.2 0.4 0.6 0.8 1.0 1.2 600 a 400 ~ 200 — 0 I I T I ‘I7 I 0.0 0.2 0.0 0.6 0.8 1.0 1.2 MOMENTUM (DEV/C) 65 excess of high momentum spectator protons by calculating the multiple scattering correction using Glauber multiple 20, 21 diffraction theory. Glauber theory, which considers the involvement of both nucleons in the scattering, has 22 been used by Ma t al. to describe pd elastic scattering between 1.6 and 2.0 GeV/c. In En annihilation reactions using a deuteron tar- get, a similar excess was also found. In this work, a de- finitive study of the double scattering processes in 5n- 1ike annihilation reactions will be presented. Two types of double scattering mehcanisms will be discussed. One type, which is called final state interaction (FSI), re- sults from scattering with the spectator nucleon by one of the particles from the BN annihilation. The other double scattering process results when the antiproton elastically scatters from the proton before it annihilates with the neutron. This is called initial state interaction (ISI). Since pn annihilation reactions at the beam mo- menta used in this study, 1.09-1.43 GeV/c, produce mostly pions,(see Chapter III), the following reactions will be discussed: 6d + p520-0+jn° j 3 0 (5.1) Ba + ps3n‘2n+jn° j - 0 (5.2) 66 The set of reactions given by Equation 5.1 appears in the data as three or four prong events. Five or six prong type events are described by Equation 5.2. These two sets of reactions will be considered separately. However, the individual reactions of each set will not be considered separately because it is observed in Chapter II that an event separation of the individual reactions is not possi- ble for j > 1. In addition, all four beam momenta, 1.09, 1.19, 1.31, and 1.43 GeV/c, will be combined when comparing the data to the model. 5.2 Evidence for Double Scattering The momentum distributions of protons emerging from apparent 5n annihilations in a deuterium target are shown in Figure 5.1 B-C. Also shown is the deuteron wave func- tion prediction of the internal Fermi momentum distribution of the deuteron. The prediction was made from the Reid 23 If the idea that the deuteron soft core wave function. break-up occurs spontaneously when the incident particle interacts with one of the nucleons is indeed correct, the momentum distribution of the spectator nucleon should follow the curve in Figure 5.1A. (This process will be referred to as single scattering.) To compare the momentum distri- butions of protons emerging from 5n annihilations to the impulse'approximation prediction, the fact that low momentum 67 protons are not always observable in the bubble chamber must be considered. In Appendix E, it is shown that pro- tons having a momentum between 70 and 130 MeV/c are syste- matically lost. Protons having a momentum less than 70 MeV are not able to produce observable tracks in the bubble chamber. By comparing the data to impulse approxi- mation prediction above 130 MeV/c, one can see that there is a region of excess above 200 MeV/c. This excess appears to be in the form of a broad peak or bump centered at 300 MeV/c. Similarly, this excess is present when the data are compared with other deuteron wave functions.“-28 The probability of finding the deuteron with a neutron-proton separation of r is greatest for r 2 2 fm. This probability is given by ¢2(r)r2 where ¢(r) is the deuteron radial wave function. Since the nucleon dimen- sions are of the order of one fermi, both nucleons may be involved in a scattering process. Two possible ways the proton could be involved are depicted in Figure 5.2. The first diagram (called final state interaction or FSI) describes a pion, from the fin annihilation, interacting with the proton. The second is called initial state in- teraction or 131. Here, the antiproton scatters from the proton before 5n annihilation takes place. To determine the presence of F51 and ISI, one must look for features characteristic of these processes. 68 Figure 5.2 Final State Interaction Process and Initial State Interaction Process (See text for detailed description.) ‘DI ‘01 69 (FSI) (ISI) 70 Since FSI results when a pion scatters from the spectator nucleon, production of the A(1236) resonance is expected. Figure 5.3 shows the n+ps and n'ps invariant mass distributions. For comparison, the n'ps distribution is normalized to the n+ps distributioh. Only events with spectator momenta above 190 MeV/c were used in the plot. By comparison, one observes a peak in the n+p mass distri- bution characteristic of the A(1236) resonance. Both 0' and 0+ may scatter from the proton. However, since the n'p cross section is smaller than the n+p cross section in the A(1236) mass range, the peak in the n'p mass distribu- tion will not be as apparent as the n+p peak. In addition, there is one more 0' than 0+ in an event, therefore assum- ing only one pion scatters from the proton, the peak in the n'p mass distribution will have more background than the peak in the n+p mass distribution. 131 results when the antiproton elastically scatters from one constituent nucleon before annihilation by the other. This elastic scattering imparts a transverse momen- tum to the spectator nucleon. Therefore, the distribution of the cosine of the angle between the beam and spectator nucleon should show a bump characteristic of elastic scat- tering. Figure 5.4 shows the cosine distribution for the spectator for three spectator momentum ranges. The first range pS < 190 MeV/c appears to be smooth. A peak at 71 Figure 5.3 + Invariant Mass Distributions of 0 pS (unshaded) and n'ps (shaded) Systems (A) Four prong events (B) Six prong events The n;p distribution has been normalized to the n p distribution. The momentum of the spectat3r proton is greater than 190 MeV/c. :1 000000 : U __ ////////////////////I/Y///Wmmu. - .. ~ I), 73 Figure 5.4 Cosine Distribution of Protons (A) p S 190 MeV/c (B) 190 < p 5 350 MeV/c (C) p > 350 MeV/c ' EVENTS EVENTS EVENTS 300 7 74 81 200- 100 _WWM O I I T I -1.0 —.B -.2 0.2 0.6 1. 300— B] 200— 1001 0 1 1 1 0 -1.0 -.6 -.2 0.2 0.6 1. 3005 C1 2004 IOU-— 0 I I I I ~1.U -.6 -.2 0.2 0.5 1 CBS [THETR] 0 .0 75 cos (0) between 0.2 and 0.4 is seen for spectator momenta in the range 190-350 MeV/c. This peak is also observed for spectator momentum greater than 350 MeV/c. In summary, properties of protons emerging from apparent pn-like annihilation cannot be described by a sim- ple impulse model. The discrepancies can be seen in the spectator momentum distribution, the invariant mass of the n+p and n'p systems, and the cosine of the angle between the spectator proton and the beam. These distributions show features characteristic of double scattering. 5.3 Final State Interaction The products of antiproton-neutron annihilation pro- cesses are mainly pions. An estimate of the extent of final state interaction can be made from the pion nucleon cross section, OnN’ and the mean inverse square proton neutron separation in the deuteron <1/r2>. The probability that a pion from the annihilation will interact with the spectator nucleon can be estimated by: 0 ~_ 0N 1 Using values of ~.25 anZ for and ~60 mb for CNN gives a value of ~.12 for P. Effects which are attributable 29, 30 to FSI have been observed in other data. However, a complete and detailed description of the FSI process has not 76 been attempted. In this section, a model describing FSI in the reaction pd + pS + pions is developed. The probability that a pion from the annihilation will interact with the spectator depends on the neutron- proton separation. This probability is greater for smaller values of n-p separation. Large values at internal Fermi momentum of the deuteron can be related to smaller values of the neutron-proton separation by the Fourier transform. Therefore, FSI will have a greater probability to occur if the internal Fermi momentum of the deutron is large. To incorporate this feature in the model, the following ampli- tude for FSI was assumed: F(r) = Cf $451 (5.4) Here, ¢(r) is the radial deuteron wave function and fTIN is the 0N scattering amplitude. C is a normalization constant. The factor l/r, which can be thought of as the amplitude for spherical waves of pions, takes account of the fact that FSI was a greater chance to occur if r is small. To obtain the momentum space representation of F(r), the Fourier transform was used. -' . 3 f(p) = C'fflN [ $§£l e 1p rd r (5 5) C'fflN 9(0) (5 6) 77 In performing the integral over r, it was assumed that f1TN could be taken outside the integration. This assumption is valid because f1TN does not explicitly depend on the value of r. Then, the probability for FSI, expressed in momentum space, is given by: P(p) = 4 C'ZGWN 92(p)p2 (5 7) To calculate CnN’ which depends on the pion nucleon invariant mass, elastic scattering was assumed to be domi- nant. The validity of this assumption is based on the fact that much of the invariant phase space of the pion nucleon system is in a region where pion production is unimportant. (See Figure 5.5) In this region, most of the cross section is due to elastic or charge exchange scattering. If the invariant mass of the pion nucleon system is less than 1400 MeV/c, less than 17% of the total n+p or n'p cross section is due to inelastic scattering. This is shown in 32’ 33 One sees that inelastic scattering is Figure 5.6. important above 1500 MeV. However, Figure 5.5 shows that pion nucleon systems above 1500 MeV represent a small fraction of the total sample. This small fraction, along with the high cross section in the A(1236) mass region causes the elastic scattering processes to dominate. An estimate of the relative importance of inelastic processes compared to elastic processes can be made by considering 78 Figure 5.5 Invariant Mass Distributions of n+p and n‘p Systems NUMBER OF P PI SYSTEMS 900- 600-“ 300—1. 79 4 PRUNG MTP,P1+] H PRUNG MTPIPI—l 500- 250—‘ 6 PRUNG MIP,P1+1 G PRUNG MIPIPI-l INVRRIRNT MRSS (GEV) 80 Figure 5.6 Cross Sections for n+p(A) and n'p(B) The total cross section is denoted by + and the elastic plus charge exchange cross section is denoted by D . The difference between the two curves represents pion production processes. CROSS SECTION (MB) CROSS SECTION (MB) 225. 150. 75. 225. 150. 75. 81 _ R1 + +Tllmaflgag3365335533000055 1 1.1 1.U 1.7 2.0 PIUN-NUCLEUN M955 (GEV1 _ B1 .3 ++°n0006333333e°°°++3333;; :3; I 1 1 1.1 1.” 1.7 2.0 PIUN-NUCLEUN M953 (GEV1 82 the following integrals: 3 1e] =10“ (TINS) 51; , (5.8a) 3 I1." = [01." (nus) 9;. (5.8b) Here oe](nNs) and oin(0Ns) are the elastic and inelastic parts of the total pion nucleon cross section. The factor 9%: is the invariant phase space of the pion nucleon sys- tems in the double scattering process,and was obtained by assuming that the Fermi momentum distribution of the con- stituent nucleon is given by 02(p)p2 and the momentum dis- tribution of the pions is given by a statistical model for annihilation. The values of Iel and Iin’ whose sum has been normalized to unity, are shown below: Tab1e 5.1 Relative Importance of Elastic and Inelastic nN FSI 4 prong 4 prong 6 prong 6 prong n‘p n p N'p n p elastic or charge exchange .85 .94 .91 .97 inelastic .15 .06 .09 .03 83 The table shows that the fraction of W+p inelastic FSI is smaller than the fraction of n'p inelastic FSI. This is caused by the fact that the n+p cross section is higher than the n'p cross section in A(1236) mass region. This fact also causes the 0+ to be involved in FSI more often than the 0'. Since inelastic scattering plays a minor role in FSI, it will not be considered here. Only elastic and charge exchange scattering will be included. Characteristics of elastic and charge exchange scattering are taken from phase shift analysis by Donnachie, 34 These results were used to calcu- Kirsopp and Lovelace. late both the total pion nucleon cross section, on", and the differential elastic scattering cross section doflN/da. The total cross section is needed to calculate the probabi- lity for double scattering. If double scattering occurs, doflN/dQ was used to obtain the momentum transfer between the pion and the spectator nucleon. Tables 5.2 and 5.3 list the BN reactions and the types of scattering involved in FSI. pN annihilations pro- ducing up to seven pions were considered. The cross sec- tions for producing more than seven pions are small in our momentum range. A total of fourteen reactions were consi- dered for three or four prong topologies and nine reactions were considered for five or six prong topologies. Each type of FSI was assigned a code depending on its effect on 84 Table 5.2 3-4 Prong Terms Reaction Type of Scattering Code 5d + Psn+20730° n+p +'n+P 1 j = 0.1.2.3,4 n'P +~n'P 1 n‘pt+ n°n 2 n°p + n°p I n°P + 0+0 2 Ed +.n52n+2n'jn° n'n-+ n'n 3 .1 = 0.1.2.3 n+0 + n+n 3 0+" +-I°P 4 n°n-+ n°n 3 n°n +-n’p 5 fid.+ nsn+n'3n° n+n'+ 0+0 3 3 = 1.2.3.4,5 n‘n«+ n‘n 3 1r°n + n°n 3 n+n +-n°p 5 n°n-+ n‘p 4 Code 1 5n annihilation counted as a 6n type event. Code 2 5n annihilation leaving 6n tapology. Code 3 6p annihilation counted as a pp type event. Code 4 5p annihilation leaving pp topology into 5n 3-4 prong topology Code 5 pp annihilation leaving pp topology into a in topology which is not 3 or 4 prong. 85 Tab1e 5.3 5-6 Prong Terms Reaction Type of Scattering gggg_ Pd'+ P520+30‘Jn° 0+P + W+P 1 1 = 0,1,2 n'p + n'p 1 n'p + n°n 2 n°p + n°p 1 n°p + n+n 2 5d +-n530+3n-jn° n'n + n-n 3 J = 0,1 n+n + n+n 3 n+n + n°p 4 w°n + n°n 3 n°n + n p 5 6d +'n52n+2n-jn° n+n + n+n 3 j = 1,2,3 n°n + n°n 3 n°n + n°n 3 0+0 + n°p 5 n°n + n-p 4 Code 1 6n annihilation counted as a 6n type event Code 2 pn annihilation leaving 6n topology Code 3 pp annihilation counted as a pp type event Code 4 pp annihilation leaving pp topology into pn 5-6 prong topology Code 5 6p annihilation leaving 6p topology into a 6n topology which is not 5 or 6 prong. 86 the topology of the event. These codes are listed on Tables 5.2 and 5.3. The events with codes 1 or 4, which have a pn type topology, are present in the measured sample of the data. The code 1 events are 5n annihilations in which a pion interacts with the spectator proton. The code 4 events are 5p annihilations which have a 5n type topology. These events have a proton because a pion from the 5p anni- hilation scatters on the spectator neutron by a charge ex- change process. Charge exchange scattering also causes some 5n annihilations to have a topology characteristic of 5p annihilations. These events, which have been assigned code 2, do not appear in the measured sample. To describe the effects of FSI, fin and 5p annihi- lation events were generated using the Monte Carlo event 16 The proton and neutron were generating program SAGE. assumed to have equal but opposite momentum values given by the momentum distribution 02(p)p2. The generated event was weighted by the flux factor to account for the Fermi motion of the target. The probability that one of the pions re- sulting from the annihilation will scatter from the remain- ing nucleon depends on the pion-nucleon invariant mass. The cross-section, on“, and angular distribution of the pions, doflN/dQ, in the double scattering process are given 11 by Donnachie, Kirsopp and Lovelace. Monte Carlo events were generated for each of the 23 reactions listed on 87 Tables 5.2 and 5.3. For each of these reactions, the frac- tional amount of different types of FSI was determined. These fractions, which are summarized in Tables 5.4-5.7, are determined for the following three categories of events: 1) 5p FSI events having a pn topology due to charge exchange scattering 2) 5n FSI events having a 5p topology due to charge exchange scattering 3) 6n FSI events having a 5n topology To compare the model to the data, only the Monte Carlo events in categories 1 or 3 were used. The category 2 events are not present in the measured sample. The Monte Carlo events were used to predict the spectator momentum distribu- tion, the n+ps invariant mass distribution, and the cos (0) distribution. These three distributions were generated for the three or four prong and five or six prong topologies by combining the Monte Carlo events of the appropriate reac- tions. To combine the Monte Carlo events, the number of_ events in the distribution from the ith reaction is given by: Ni a g Pj(p)°i (5.9) Here, 0i is the cross section for the ith pN reaction. In addition, the cos (0) and invariant mass distributions con- tain only the events with proton momentum greater than or equal to 190 MeV/c. 88 Table 5.4 FSI Model Predictions p = 1.09 GeV/c _ fin FSI Leaving pp FSI Entering Reaction pn_f§l_ pn Tapology_ 6n Topology Topology_ PP + 24"2.‘ - - .041 4 PP + Mar-4° - - .046 4 PP + 2 +2 '2 ° - - .067 4 [3p + 2.32.1.8 - - .062 4 50 + "In? - - .014 4 I59 + IRE-24° - - .040 4 6p + 11+1r‘311° - - .073 4 59 + «*n'4w° - - .122 4 6p + Inn-54° - - .134 4 (In + .124' .090 .030 - 4 im + «VII-4° .151 .059 - 4 5n + «Wu-24° .207 .095 - 4 5n + n+20'3n° .280 .172 - 4 5n + .+2.-4.° .340 .165 - 4 6p + 34"34' - - .085 6 5p + 3n+3nnr° - - .086 6 [3p + 2n+211'ii° - - .027 6 6p + 2..”‘24‘24" - - .055 6 6p + 21324-319 - - .079 6 5n + 24"34- .239 .075 - 6 5n + 21334-18 .306 .125 - 6 I'm + Zn+31r'21I° .375 .149 - 6 89 Table 5.5 FSI Model Predictions p = 1.19 GeV/c fin FSI Leaving pp FSI Entering pn Reaction pn FSI pppTopology Topology Topology 5p + 24"24' - - .039 4 50 + 21321:? - - .045 4 pp +-2.I+21r2.° - - .051 4 5p 4 2.+2.I'3..° - - .061 4 5P'+ n+n-n° - - .014 4 5p + «+4721? - - .040 4 6p + “+439 - - .074 4 50 + 4"..‘4n° - - .123 4 5p + «fin-54° - - .133 4 6n + n+211- .089 .031 - 4 5n + "+2.? .149 .059 - 4 6n + "Wu-24° .205 .095 - 4 5n + n+2n‘3.° .285 .151 - 4 En + .*2.'4.° .356 .160 - 4 Tip + 3n+3n' - - .083 6 5p + 34+3.‘n° - - .086 6 I30 + 216124-19 - - .026 6 PP + 2.12521." - - _.055 6 5p + 24+2n'3n° - - .080 6 6n 4 2..”‘34' .240 .076 - 6 in + 24+3-u'n° .307 .120 - 6 5n + 24+3n'2.° .372 .146 - 6 90 Table 5.6 FSI Model Prediction p = 1.31 GeV/c 5n FSI Leaving pp FSI Entering Reaction §n_f§l_ 6n Topology pn Topology Topology PP + 26121:" - - .039 4 50 + 21324? - - .044 4 I39 + 2..“‘2..'2.° - - .058 4 5p + 24+2n-3n° - - .058 4 110 + n+n'1r° - - .013 4 5p + "hr-24° - - .037 4 I30 + n+n'3n° - — .073 4 PP + n+4'4n° - - .100 4 5p + VII-54° - - .140 4 5n + n+211' .087 .028 - 4 5n + «+2.? .142 .058 - 4 5n + n+21r'211° .206 .098 - 4 5n + "VII-3.9 .270 .150 - 4 (3n + n+24-4.° .371 .172 - 4 5p + 34'34- - - .080 6 |5p + awn-4° - - .081 6 5p + 24+2474° - - .025 6 5p + 24+2n'2-n” - - .054 6 5p + 24+2n-3n° - - .078 6 in + 2H3.“ .237 .074 - 6 5n + 24+3u'n° .302 .115 - 6 6n + 20+3n'2'rr° .380 .145 . - 6 Reaction 5p + 21r+21r- 5P + 20+21r-ir° [3p + 21r+21r-21r° [5p + 21r+21r-31I° .. +_ pp+1rnir° 5P + n+ir'21I° 5p + n+ir-3ir° 5P + fl+fl-41T° 5P + n+ii'5'II° pn + n+21I' pn -> n+ZiI'n° pn-+ n+Zn-ZnO 6n + n+21I'3iI° pn-+ n+2n-4no 0p + 31r+3ir- 5p + 31T+31T-‘ll'° 5p + 21T+211-TT° 5p + 20+Zn'20° 5p + 21r+21r'3ir° 5n + 24"34‘ [3n + 2n+31r-n° [3n + 211+311-2‘n'o 91 Table 5.7 FSI Model Predictions p = 1.43 GeV/c fin FSI .085 .135 .204 .266 .365 .231 .295 .372 6n FSI Leaving pp FSI Entering pn Topology pn Topolpgy_ Topology - .039 4 - .044 4 - .065 4 - .057 4 - .011 4 - .034 4 - .071 4 - .096 4 - .143 4 .026 - 4 .058 - 4 .096 - 4 .128 - 4 .181 - 4 - .077 6 - .077 6 - .026 6 - .052 6 - .075 6 .069 - 6 .109 - 6 J45 - 6 92 The values of Oi for the fin reactions were obtained in Chapter III. The cross sections for the pp annihilations 3, 13, 35-39 were obtained elsewhere. However, the cross sections for the reactions involving two or more 0° in the final state were not directly measured. To calculate these 140 cross sections, the Fermi statistical mode was used. The model has been shown to be in good agreement with antiproton- 41 nucleon annihilations. Neglecting pion mass difference, the model relates the cross sections for pion production as follows: n1! n1! nl! o = 0 " o. (5.10a) r nr, nr. nr' 1 o' _. +. r r r _ i i i no + n_ + n+ - n0 + n_ + n+ . (5.10b) Here or is the cross section for producing ngn°, nrn', and + . . . . . nrn . Similarly, Oi is the cross section for produc1ng i o i i + non , n n", and n The values of 0 used in the FSI 11 - + model are presented in Table 5.8. Multi-0° cross sections found by Equation 5.10 are denoted in the table with an *. 5.4 Initial State Interaction It is possible for the incident antiproton to elasti- cally scatter from the proton before the fin annihilation 913 Table 5.8 5p and En Cross Sections Reaction 1.09 1.19 1.31 1.43 in + 2.-.* 2.17 . .17 1.81 . .13 1.61. .09 1.42. .10 pp + 2.-.+.° 11.43 . .53 10.96 . .45 9.41. .33 8.89. .35 in +2.-.+2.° 12.3 . .9* 12.1 . .7* 11.1 . .6* 10.1 : .6* in + 2.-.+3u° 6.9 . .4* 6.5 . '.3* 6.7 . .3* 6.2 : .3* 5n + zu-r‘w 2.4* 2.5* 2.6* 2.6* {in + an.“ 4.10 . .26 4.02 . .22 3.70. .17 3.38: .17 pp + 3.-2.+.° 6.85 : .37 6.46 . .29 6.74: .24 6.24: .27 pp + 3II+211'11+ mm 4.84 . .28 5.01 . .24 5.14. .21 5.18: .24 pp + 21120“ 3.6 . .2° 3.3 : .2° 3.0 : .2° 2.8 : .2° pp +2u+2m° 13.5 :1.5° 12.9 .i.3° 12.0 :i.2° 11.1 : 1.0° pp + 21824-2." 4.5* 5.0* 5.4* 5.4* 6p + 2.+2u-3.° 3.3* 3.3* 3.3* 3.3* pp + 2a+2u- + m 11.4 . .5° 11.2 . .5° 11.0 . .5° 10.9 : .5° pp + 3.+3.- _ 1.0° l.l° .i.2° l.2° 5p + 34%.? 2.2° 2.2° . 2.2° 2.2° pp + 3.*3.‘ + an .3 . .2° .3 . .2° ' .4 : .2° .5 : .3° 5p + I+I'fi° 2.2" 1.8° 1.6° 1.4° 6p + .flrzr 7.2* 6.6* 6.0* 5.6* [1p + 11??!" 9.05 . 8.6* 8.0* 7.4* pp + six-44° 1.5* 1.7* 1.8* 1.8* pp + firs." .7* .7* .7* .7* pp + .+.- + m 18.8 : .7° 18.0 : .1° 16.8 : .6° 15.8° : .6° *Calculated from Eq 5-9. °Taken from References (see text) 94 takes place. This process will be referred to as initial state interaction or ISI. ISI will tend to give the proton a momentum in a direction transverse to the beam direction. The momentum transfer between the antiproton and the proton is given by do/dO = (do/d0)oeAt. In the momentum range used here, A = 17.5 (GeV)'2 and the total elastic cross section is 42 mb.38’ 39 Monte carlo events for ISI were generated for 5n annihilations producing up to seven pions. The Fermi momen- tum distribution of the deuteron was given by 62(p)p2 and the double scattering probability was assumed to be propor- tional to gz(p)p2. This distribution was used to account for the fact that small p-n separations have a greater chance to result in a double scattering. The ISI Monte Carlo events for each reaction were combined into three or four and five or six prong groups. This was done by re- quiring the number of Monte Carlo events in the group to be proportional to the cross section for that reaction. Then, the events in each group were used to produce distri- butions of spectator momentum, M(n+ps) and cos (6). 5.5 Fits to the Data To determine how much of the data can be described by FSI and 151, fits were made to the data using the spec- + tator distribution, the invariant mass distribution M(n p5), 95 and the cos (6) distribution. The Monte Carlo events for FSI and ISI were used to produce these distributions. Only the events with spectator momentum greater than or equal to 190 MeV/c were included in the cos (0) and invariant mass distributions. In this region, the data are dominated by the F51 and ISI processes. This region is used so the A(1236) signal in the 0+ps invariant mass distribution can be enhanced. Since the 0+ps scattering is assumed to be elastic, the 0+ps invariant mass is not modified by the scattering. Only by a sample of events in which the W+ scatters from the spectator proton, can the 4(1236) signal in the invariant mass distribution be observed. The spectator momentum, cos (0), and invariant mass distributions were calculated for single scattering events. However, because FSI and ISI are more probable when inter- nal Fermi momentum of the deuteron is high, the shape of the single scattering spectator distribution is modified from the usual ¢Z(p)p2. To determine the shape of the modi- fied single scattering proton distribution, the deuteron wave function, ¢(p), was used. Spectator protons with a momentum distribution given by ¢2(p)p2 were generated and then randomly selected, using a probability proportional to 92(p)p2, to be involved in double scattering. The frac- tional amount of double scattering was required to be con- sistent with the amount of double scattering in the data. 96 The modified single scattering spectator proton momentum distribution is given by the momentum distribution of the protons not involved in double scattering. These distri- butions are shown in Figures 5.70 and 5.80. These figures show that there is no single scattering above 190 MeV/c. Figures 5.7E-F and 5.8E-F show how the invariant mass and cosine distributions for single scattering events with spectator momentum greater than 190 MeV/c would look if there were no double scattering. Fits were made to the data using the double scat- tering distributions. The fits were made by assuming that the data distributions are sums of the Monte Carlo distri- butions, shown in Figures 5.7G-I and 5.8G-I, for the FSI and ISI contributions. That is, the data distributions were assumed to be given by: F(p) = BFFSI(p) + DFISI(p). (5.11) C(cos 6) = BCFSI(cos 6) + DCISI(cos e), (5.12) M(n+ps) = BMFSI(n+pS) + DMISI(n+pS). (5.13) The subscripts FSI and 151 stand for final state interaction and initial state interaction resepectively. To perform the fits, the integrals of the Monte Carlo events in the fitted region were required to be unity. Then, the values of B and 97 mucw>m opcmo mucoz HmH mpcm>m o_gmu mucoz Hm; mpcm>m o_gmu mucoz m=_cmpumom mpmcwm mm>gzu umuupm use mama --.:v --.:V EA: Ao-m opgmu mucoz HmH mpcw>m opgmo mucoz Hm; mucw>m oFLmu mace: mcwgwppmum mchvm mw>gsu cwupwm use mama AA-qv AH-uv Au-ov Ao-uou Bunny» L as L. 00:: «on 9.“ 0.“ Con o.a «ca Goa 8118“ 188811888 «.0 9.“ o.« Don o.u “on Goa a.“ boa o.u Don 0.“ «on Gun 8118“ 188811888 N.“ Don Don P 8 .1 h o.— v.« Non Don 8118“ 188811888 818813 auxin-o cahlucuc nuhcbuusn «an on 9.9 0.70 0.... «we 9.: a 1 an u an 1 up .5 r can N.— can 0.9 0.0 Cob “.0 0.0 . P‘ p I can 0.0 “.0 boo - . N.u Don Goo . . . .1 1'6 u." Don Goo DMD cub «.9 0.0 8118“ 188811888 8118“ 188811888 8118“ 188811888 818318 101 D are equal to the numbers of F51 and ISI events in the fitted region. To determine the values of B and D, the x2 of the fit was minimized by adjusting the values of B and D. The uncertainty for B and D was determined by varying these parameters one at a time until the X2 increases by one unit. This was done to take account of any correla- tion between B and D. To determine the total amounts of FSI and ISI, the number of events in the fitted region was used to find the number of events below l90 MeV/c. This can be done for FSI and ISI because the fractional amounts of the spectator distributions above l90 MeV/c are deter- mined. The results of the fits are summarized in Table 5.9 and Figures 5.7A-C and 5.8A-C. Since there are no single scattering events above l90 MeV/c, the amount of single scattering can not be found by using these fits. However, since there are events in I the data having visible spectators with momenta values below 190 MeV/c, it is of interest to see how well these events can be described. Therefore, the number of events in the modified single scattering momentum distribution, N , plus $5 the total number of FSI and ISI events, NFSI + NISI was required to be equal to the total number of events in the data, Nd. The resulting normalization gives excellent agreement with the data in the 130-l90 MeV/c regions of the spectator momentum distribution (see Figure 5.7A and 5.8A). 102 Table 5.9 Summary of Fits 3-4 prong 5-6 prong Events in fit region l5891 6l88 FSI Events in fit l2395 i 758 4383 i 307 ISI Events in fit 3072 i 240 l629 i l84 Total FSI Events l5474 i 946 5504 i 385 Total ISI Events 4376 i 34l 23l7 i 262 Total Events 58l67 25398 Fractional Amount of FSI .266 i .0l8 .217: .015 Fractional Amount of ISI .053 i .004 .064: .007 103 Below 130 MeV/c, spectator protons are not always seen in the bubble chamber. 5.6 Considerations of Possible AA State in the Deuteron In most cases, the deuteron can be thought of as a bound neutron-proton system. However, it is possible for the deuteron to exist as a virtual AA state for a fraction of the time. This virtual state must have the same quantum numbers of the deuteron. Two possible states, which have been the subject of both theoretical and experimental 44-53, are the A++A' and A+A° states. This conjecture 44,45 work was used to describe the magnetic moment of the deuteron. Previous experimental works attempt to detect the AA state by observing spectator A(As) produced in deuteron break-up 49'53 To establish the existence of the AA state reactions. in such a direct manner, one must be certain that the ob- served A signal corresponds to spectator As because these are other mechanisms, such as FSI, which can produce a A. This is done by examining kinematic regions which have as little background as possible. Since the existence of AA states implies the existence of spectator A, one expects to observe AS in the backward direction. Previous experimental studies49'53 make use of this fact since the background from other processes is expected to be smaller in the backward 104 direction. In this section, the double scattering model is used to predict the angular distribution of A. An-increase over this background would require the existence of AA states. Since the deuteron is an I=0 state, an equal admix- ture of the A++A' and A+A° states is expected. Both n+ps and n'ps invariant mass distributions should show the pre- sence of a spectator A. Figure 5.3(see section 5.2) com- pares the n+ps and n'ps mass distribution for events having protons greater than l90 MeV/c. A comparison shows that n+ps distribution has a signal at the A mass. However, this signal appears to be well described by double scattering. To detect possible A spectators, one must examine for an excess over the background. The distribution which will be examined is the cosine beam direction and the n+ps momentum direction. To observe possible As++, a set of AS++ candidates is defined. This set is defined so the background from other processes will be small. The AS++ candidates were selected by requiring the n+ps to be in a range 1180-l300 MeV. In addition, since the n+p mass distribution for events having visible spectator with a momentum less than l90 MeV/c shows no A++ signal (see Figure 5.9), these events were not used. The same cut was applied to the double scattering model. Figure 5.l0 shows the distribution of the 105 Figure 5.9 + Invariant Mass Distributions of n pS (unshaded) and n‘ps (shaded) Systems (A) Four prong events (B) Six prong events The n'ps distribution has been normalized to the n+p distribution. The momentum of the spectatar proton is less than l90 MeV/c. '1 0 1.0 [1.2.0 2.; 107 Figure 5.10 Cosine between the Beam Direction and the n+ps Momentum Direction (A) Four prong events (B) Six prong events The curve is the double scattering prediction. EVENTS EVENTS 160 120 80 no 160 120 80 00 108 -1.0 - 6 -.2 0.2 0.6 1. CUSINE 0F (PI+ P) SYSTEM 8) 1 TT T l -1.0 -.B —.2 0.2 0.8 1. CUSINE 0F (PI+ P] STSTEM 0 109 laboratory cosine between beam and the n+p system. The data appears to be well described by the double scattering models. In particular, no excess of backward n+p systems is observed. The AA state is not needed to describe the data here. 5.7 Conclusions It has been shown that a substantial fraction of the reaction pd + ps + pions involves final state interac- tions or initial state interactions. Final state interac- tion can sometimes change the topology of the event. The work here shows that only 74% of the FSI events having the topology characteristic of the reaction pd + pS + 3 charged pions are due to En annihilations. The remaining fraction, 26%, are pp annihilation events which have the "pn" topo- logy because of charge exchange scattering. The five and six prong events having the 5d + pS + 5 charged pion topo- logy are 81% pn annihilations and l9% pp annihilations. This effect causes an increase in the number of events having the "pn" topology. This increase is offset by the loss of fin events into the 5d + nS + pions topology. About 33% of the total 5n annihilations involving FSI which pro- duce three charged pions and zero or more neutral pions leave the "fin" topology. This number is 27% for 5n annihi- lation producing five charged pions and zero or more neutral 110 pions leave the "in“ topology. This number is 27% for flu annihilation producing five charged pions and zero or more neutral pions involved in FSI. The effects of this topolo- gical interchange are summarized, for pn annihilations, on Table 5.l0. In addition to topological interchange, FSI will modify other characteristics of the final state pro- duced by the annihilation. This modification is of interest when examining resonance production. The effects of ISI are not as striking as those of FSI. First of all, only 5.3-6.4% of the total sample in- volves ISI. This is to be compared with the percentage of the data, 22-27%, involved in FSI. ISI does not affect the final state as FSI does. Therefore, it does not change the topology of the event. However, ISI does change the center of mass energy of the BN system. This change might impair the observation of a narrow s-channel resonance. The two double scattering models give an excellent description of the distributions involving the spectator proton in the reaction pd + pS + pions. No evidence which can uniquely establish the existence of a AA state in the deuteron was found in this work. 111 Table 5.10 Effects of FSI 3-4 prong Fractional amount of FSI with pn topology in the data (fitted) .266 i .018 Fractional amount of fake fin events in all the data .069 Fraction of fin annihilation events lost .095 5-6 prong .217 i .015 .041 .062 CHAPTER VI CONCLUSIONS The reaction and t0pological cross sections for pn interactions producing three or five charged particles and zero or more neutral particles have been determined by using a deuterium target. The effects of unseen elastic scattering were considered. Also, a screening correction factor was used in obtaining the pn reaction cross sections. The resulting cross section values are in good agreement with the result at the higher momenta values found by Eastman t 1.13 A study of the s-channel dependence of the p°p°n' intermediate state produced in the reaction 5n + 31r'21r+ was made. This was done using individual beam momentum setting as well as 40 MeV wide bands in the center of mass energy. In particular, the bump in the p°p°n° state at 2190 MeV ob- 2 served by Kalbfleisch t l. in the reaction pp + 2n'2n+n° was sought for. Kalbfleisch suggests that this bump might be a possible source of the I=1 enhancement observed by Abrams t al.1 ment in the p°p°n' state was found at 2190 MeV even though in the total EN cross sections. No enhance- 112 113 the pn system is a pure I=1 state. However, the similari- ties in the distributions produced by the p°p°n' and p°n'n'n+ intermediate states limit how well the fractional amount of p°p°n' production can be determined. If there were to be any s-channel structure in the p°p°fl- state, then the p°p°n' and p°n'n'n+ states must change simultaneously in such a manner that the fractional amount of p signal is constant. Using the cross section values for the reaction 5n + 31r'21r+ and the fractional amounts of n+n' pairs in the p signal, it was concluded that there is no enhancement, having an assumed width of :50 MeV, greater than 0.7 mb at 2190 MeV with a 90% confidence level. Finally, a model which describes the double scatter- ing processes in the reaction pd + pS + pions was developed. Two types of double scattering were considered. The first type involves an interaction between a final state particle and the spectator nucleon. The other type involves an in- teraction between the incoming antiproton and the spectator nucleon. Evidence for both these models is shown in dis- tributions involving the spectator proton. The model dev- eloped for the two types of double scattering give an ex- cellent description of the data. The double scattering model was used to study the characteristics of A production in the deuteron. The angu- lar distribution of n+p systems in the A mass are well 114 described by the double scattering model. Therefore, the existence of the AA state is not warranted here. APPENDICES APPENDIX A SUMMARY OF FIT SELECTION PROCEDURES Using the fit selection procedure discussed in Chapter II and a cut on the vertex position with the reac- tion colume defined in Chapter III, the numbers of events corresponding to each type of fit may be estimated. These are summarized in Tables A.1 and A.2. The events contained in measuring categories A and B are summarized in Table A.1. At this stage, there are three groups of events that have not been assigned fits. They are "Bad Mark 30", "No Missing Mass Fit", and “Ambig- uous". The events in the "Bad Mark 30" group had Mark 30 type fits, pd + psk+k'n' or pd + psk+k'2n'n+, but were not Mark 30 events. This was determined by the ionization scan made on events with Mark 30 type fits. These events in the "Bad Mark 30" group were then assigned a fit that agrees with the ionization scan. The results are listed in Table A.3. The "No Missing Mass Fit" group contains events which lost a constraint due to improper measuring or missing information. A possible cause of this type of event could be due to very short or obscured tracks. Such events were assigned fits with the same ratio of the already assigned 115 116 4_ mm N m mom 4 mmm -_ o o m mop mm o _Fm mp «No. _me o m “_F Nu m m” kmpp F_ owe mm mm 4 e_ mm_ 4N o mmmm we oem_ m_m mm_ m msoamwas< “we mum: om xtmz NPJmF gem: _mepamc om x1e: m x1e: w xemz m x1e: acoea mcpmmwe oz cam -wp_=z U\>au m_._ u e m «N m o 441 N 8mm em_ 0 o m mm m_ 0 New 4_ men one o m mm mm _F o_ m_w e woe mu m_ e 8 cm mm o _mem NN omop NmN Rm m msoamwne< eve mum: om xx“: “P-8F sew: _mepzac om eta: m eta: m xemz m x25: meat; mcwmmwz oz uam -Pp_=z U\>mw mo._ u a m ecu < mmmgommumu newcamomz cw mucw>m ~.< mpnoh 117 mm _m n m mom m mwm mom 0 m P QNF om o emoy mm Nomp awn o m mmp mm mp mm mmmp w New um mNF v Pp mop mm o moee mm mpmp Nam oFN m mzosmwae< awe mam: om Jen: NP-o_ x1e: _mepsme om x28: m eta: m xemz m ecu: mecca mewmmws oz cum -Pp_=z o\>mw me.~ u 8 m_ we FF op «Ne w mum mom o o e mop mm o 0mm, Ne comp ¢m__ o m em— mop mm mm mFNN vp New Fmp mnp e om omm mm o ammo me «New mpm omm m mzoamwas< pr; mmmz om x18: spun. xgmz _msuam: om xgmz a 31m: w xgmz m x18: .mcoga mcpmmwz oz tam -Pstz U\>mo pm._ u a A.u.=ouv _.< «_nmp 1'18 oq NN NN eN NNN NN _NN «Ne NNN o N NN NN. Ne, FNN NN_N NN NNNN NNN NNF NN N Necmmwz Naoamcae< . “_N.NNNz -N+N+N= N_-NN _N-oN o_ xcaz N Nch N chz N 3cm: Neocc asymmwx oz chz chz U\>8N N¢._ r A NN NN NNF NN_ NNN NN FNN NNN NNN o N ON NPN PNN .Ne FNNN pp, NNNN NNNN NNF Ne N Nc_mmcz Naoamcns< “cc NNNz -x ¥+N= NP-N_ PN-NN o, chz N Nch N chz N Nch Neocc uchNNz oz + chz chz N\>NN NN._ u a NP NN NN _N NNN PN NNN FNN NNN o N NN NN NN_ NPN NNNN NN FONP NNN Noc NN e Nccmmcz Naoamcne< ave NNNz -¥+x+N= NP-N_ _N-NN o, xcmz N chz N chz N Nch Neocc mchNwz oz xcaz chz uc>mN N_.P n c NN NP NN NN CNN _ PN_ NNN NNF o N NN NN NNN NNF NNNP NN NFF_ NNN NN o N NcNmmcz NNONNNNEN ANN NNNz -x+¥+mc N_-NN _N-NN o_ chz N Nch N chz N Nch Neocc mammmmz oz xcuz xcmz 0\>mo mo.~ u a u anamoumulmcrcammmz er Nucm>m N.< mpamh 119 fits and are listed in Table A.3. Finally, the events in the "Ambiguous" group could not be assigned fits using the missing mass or confidence level. These events had multi- ple one constraint fits or multiple zero constraint hypo- theses involving pd + pS + ... and/or pd + nS + ... type of reactions. The odd prong ambiguous events were either Mark 9 or Mark 10 type events. The even prong events were shown, by an ionization scan, to be half pp type events and half 5n type events. Therefore, half of this even prong sample was assumed to be pp type events. The remaining half of the ambiguous even prong events and all of the ambiguous odd prong events were assumed to be either Mark 9 or Mark 10 type events. They were assigned to either the Mark 10 or Mark 9 group using the ratio of the previously assigned events. The resulting numbers of Ed + pS + ... type events in measuring categories A and B are summarized in Table A.3. Table A.2 summarizes the events contained in meas- uring category C. There are three groups of events in Table A.2 which must be asSigned fits. The events in the group called "No Missing Mass Fit", which is defined in the same way as the events in measuring category A and B, in- clude only those that were determined to be the 5d + pS + reaction by the ionization scan. Therefore, all of these were assigned either Mark 9 or Mark 10 fits using the ratio of the already assigned events. The ionization scan did 121) Table A.3 pd + ps + ... Events in Measuring Categories A and B P = 1.09 GeV/c Multi- Prong Mark 8 Mark 9 Mark 30 neutral Total 3 1057 2507 3861 4 429 867 1388 5 713 603 1780 6 250 155 547 P = 1.19 GeV/c Multi- Prong Mark 8 Mark 9 Mark 30 neutral Total 3 1620 3707 5836 4 517 1289 1940 5 1083 860 2658 6 345 216 748 P = 1.31 GeV/c Multi- Prong Mark 8 Mark 9 Mark 30 neutral Total 3 2603 6937 10696 4 920 2363 3643 5 2057 1653 4989 6 659 444 1419 P = 1.43 GeV/c Multi- Prong Mark 9 Mark 30 neutral Total 3 1680 4556 7303 4 642 1471 2402 5 1340 1162 3282 6 415 283 917 ' n .- _"H~‘Hr '. 121 not provide any information about the events in the "Ambiguous" or "Missing" groups. The "Ambiguous" group of events had positive tracks pointing almost directly toward or away from the camera. Therefbre, the projected ionization density was too g, high to provide information on the proper mass interpreta- 41 tion of the track. The events in the "Missing" group simply could not be found in the ionization scan. This could have been caused by a mislabeled frame or tracks observing the p event. Therefore, the events in the "Ambiguous" or "Missing" group were assigned to other groups in the ratios of the already assigned events. Tab1e A.4 summarizes the measuring category C pd + pS + ... type events. 122 Table A.4 pd pS + . Events in Measuring Category C P = 1.09 GeV/c Prong, Mark 3 Mark Mark 9 Mark 10 Mark 30 Mark 31 Total 4 0 106 674 1237 19 30 2066 6 0 176 309 151 1 0 637 P = 1.19 GeV/c Prong Mark 3 Mark Mark 9 Mark 10 Mark 30 Mark 31 Total 4 28 117 995 1758 12 47 2957 6 0 262 376 325 23 0 986 P = 1.31 GeV/c Prong Mark 3 Mark Mark 9 Mark 10 Mark 30 Mark 31 Total 4 53 211 1665 3431 40 82 5464 6 0 436 885 658 37 O 2016 P = 1.43 GeV/c Prong Mark 3 Mark Mark 9 Mark 10 Mark 30 Mark 31 Total 4 86 145 997 2586 30 68 3922 6 0 258 519 437 30 0 1244 APPENDIX B SCANNING EFFICIENCY There is a finite probability that a scanner will 1 miss an event at random. Therefore, the number of events must be corrected for this loss. To determine the correc- tion factor, three rolls of film at each momentum were in- ’1 dependently rescanned. Then, a conflict scan was performed on the rescanned rolls of film. This was done by examining and comparing the sample of events obtained in the original scan, scan 1, to the sample of events obtained in the se- cond scan. This comparison involved examining the event on the scan table to decide if it was correctly located and identified in scan 1 and/or scan 2. One of the following codes was assigned to each event: 21?. 1 good event in scan 1; major error in scan 2 2 good event in scan 2; major error in scan 1 4 junk event 5 good event in scan 1; minor error in scan 2 6 good event in scan 2; minor error in scan 1 7 good event in both scans 8 duplicate event 123 124 (1) A major error is defined as follows: (a) The event was not found. (b) The event had the wrong prong assignment which was not caused by missing a short spectator proton track. (2) A minor error is defined as follows: (a) The event had a wrong prong assignment because a spectator proton track was not seen. (b) The wrong frame number was recorded. The conflict scan results are presented in the Tables Bl-B5. The true number of events, N, can be found from the number of events found in scan 1 or scan 2, N1 or N2, if the scanning efficiencies for scan 1 or scan 2, S1 or 52, are known. The true number of events is given by: N = Nl/Sl (8.1) or N N2/S2 (8.2) The number of events common to both scans is given by: N (8.3) Equations B.l, 3.2, and 3.3 give the following scanning efficiencies: N (1 N S = ———.__..—_II 2 (3.4) 1 N2 125 Table B.1 Events in Categories A and B c 0 D E P(GeV/c) Roll/Scan 1 2 4 5 6 7 1.09 R011 61 $1 43 0 30 5 25 627 52 0 75 77 5 25 627 1.09 R011 65 $1 65 0 11 3 2 683 $2 0 74 70 3 2 683 1.09 R011 69 $1 44 0 19 3 5 541 $2 0 59 44 3 5 541 1.19 R011 44 51 67 0 43 6 13 748 $2 0 53 52 6 13 748 1.19 R011 49 $1 120 0 53 1 10 920 ~ 52 0 169 103 1 10 920 1.19 R011 53 $1 70 0 48 0 0 967 $2 0 173 97 0 0 967 1.31 R011 24 51 85 0 29 11 2 786 $2 0 120 73 11 2 786 1.31 R011 28 $1 68 0 44 4 3 981 52 0 119 63 4 3 981 1.31 R011 34 $1 128 0 47 3 20 1008 $2 0 173 59 3 20 1008 1.43 R011 5 51 106 0 47 6 13 1118 $2 0 124 81 6 13 1118 1.43 R011 10 51 201 0 74 4 11 1466 $2 0 233 94 4 11 1466 1.43 R011 14 $1 209 0 78 6 3 1377 52 0 175 116 6 3 1377 126 Table B.2 Events in Category C (4 prong) c 0 0 E P(GeV/c) Roll/Scan 1 2 4 5 6 7 8 1.09 R011 61 $1 62 0 19 2 0 355 4 $2 0 61 84 2 0 355 0 1.09 Roll 65 $1 68 0 76 1 2 369 4 52 0 67 97 1 2 369 0 1.09 R011 69 $1 64 0 32 0 3 334 7 52 0 66 42 0 3 334 0 1.19 Roll 44 51 81 0 38 1 0 450 9 $2 0 46 95 1 0 450 0 1.19 Roll 49 51 79 0 40 0 1 499 8 52 0 133 64 0 1 499 0 1.19 R011 53 51 143 0 48 3 2 509 7 s2 0 81 84 3 2 509 0 1.31 R011 24 $1 74 0 36 1 2 413 5 s2 0 89 86 1 2 413 0 1.31 R011 28 51 91 0 20 0 467 2 52 0 112 96 0 467 0 1.31 Roll 34 51 182 0 49 2 5 614 9 $2 0 113 66 2 5 614 o 1.43 R011 5 $1 186 0 46 3 4 679 9 $2 0 95 127 3 4 679 0 1.43 Roll 10 $1 158 0 48 2 2 867 19 $2 0 193 125 2 2 867 0 1.43 Roll 14 $1 216 0 51 1 6 718 16 52 0 180 65 1 6 718 0 127 Table 8.3 Events in Category C (6 prong) C O D E P(GeV/c) Roll/Scan 1 2 4 5 6 7 8 1.09 R011 61 $1 12 0 6 2 1 120 2 $2 0 23 15 2 1 120 O 1.09 R011 65 51 6 O 9 O O 127 4 $2 0 18 14 O 0 127 O 1.09 R011 69 S1 16 0 5 2 2 132 3 $2 0 21 20 2 2 132 O 1.19 R011 44 S1 18 0 9 2 1 144 0 $2 0 22 26 2 1 144 0 1.19 R011 49 $1 30 0 15 l 1 209 1 $2 0 49 40 1 1 209 0 1.19 R011 53 $1 36 O 10 O 3 197 2 $2 0 25 34 O 3 197 O 1.31 R011 24 S1 28 O 5 0 O 153 1 $2 0 24 27 0 0 153 0 1.31 Roll 28 $1 23 0 10 0 ' 1 189 2 $2 0 36 45 0 1 189 O 1.31 R011 34 S1 34 O 6 3 2 256 3 $2 0 42 53 3 2 256 O 1.43 R011 5 S1 23 0 14 l 0 272 3 $2 0 39 28 1 0 272 0 1.43 R011 10 S1 58 O 16 1 3 307 5 $2 0 75 37 1 3 307 0 1.43 R011 14 S1 55 O 14 3 3 274 1 52 O 27 33 3 3 274 O 128 Table B.4 Classification of the Code 4 Events in Measuring Categories A and B P(GeV/c) Scan a b c d e f 1.09 1 24 10 1 17 7 1 1.09 2 77 18 24 49 14 9 1.19 1 70 26 10 28 9 1 1.19 2 104 16 34 76 12 10 1.31 1 71 21 5 10 7 2 1.31 2 91 16 22 58 6 2 1.43 1 114 18 14 45 6 2 1.43 2 111 27 48 88 8 9 a) Event does not belong in measuring category A or B. b) Event is out of measurement region. c) Event is a result of a secondary interaction.’ d) Event assigned wrong event type. e) Event is unmeasurable because of obscured vertex or tracks. f) Event cannot be located. sits-£5 (\J " '3. 1' l ‘ “an F’s-n.3- “WON-A ._‘-. Classification of the Code 4 Events in Measuring Category C 1239 Table 8.5 P(GeV/c) Scan Prong a b c d e f g 1.09 1 4 85 2 5 2 3 6 5 1.09 2 4 139 8 20 25 3' 4 24 1.09. 1 6 9 0 3 7 O O 1 1.09 2 6 19 3 5 14 0 O 8 1.19 1 4 79 6 9 20 5 1 6 1.19 2 4 141 13 24 33 8 1 23 1.19 1 6 8 5 6 11 2 O 2 1.19 2 6 36 8 12 12 5 0 27 1.31 1 4 55 7 13 16 7 7 0 1.31 2 4 145 15 28 19 9 2 30 1.31 1 6 7 2 3 5 2 1 1 1.31 2 6 53 3 18 18 5 1 27 1.43 1 4 93 9 15 14 3 6 11 1.43 2 4 180 13 37 44 7 8 28 1.43 1 6 18 4 9 6 0 2 5 ' 1.43 2 6 38 6 12 18 3 2 19 a) Event does not belong in measuring category C. b) Event out of measurement region. c) Event is a result of a secondary interaction. d) Event was assigned wrong event type. e) Event is unmeasurable because of obscured vertex or tracks. f) Event can not be located in conflict scan. 9) Event type misidentified because of short spectator. - rum-...:— zmeA—‘uo‘h‘l. _ _ . ' . . 1° : uva‘- . 1 ~.- 50‘ 130 The number N111 N2 is equal to the total number of events with codes 5, 6, or 7. N1 is the number of events with codes 1, 5, 6, 7. Similarly, N2 is the number of events with codes 2, 5, 6, or 7. S1 is the scanning efficiency of the original scan. The scanning efficiencies were calcula- ted for the events contained in measuring categories A and B. Also scanning efficiencies were found for both the 4 prong and 6 prong events in measuring category C. The re- sultant scanning efficiencies are shown in Table B.6. Scanninngfficiencies 131 Table 3.6 Events in Categories A and B P S] 1.09 .901 .007 1.19 .871 .006 1.31 .872 _ .006 1.43 .883 .005 Events in Category C P 4 Prong 6 Prong 1.09 .846 i .010 .862 i .016 1.19 .849 i .009 .853 i .014 1.31 .830 i .009 .856 i .013 1.43 .831 i .007 .860 i .011 Weighted average .836 i .004 .857 i .007 APPENDIX C MEASURING EFFICIENCY Only the events which successfully pass through the- PANAL-TVGP-SQUAN chain of programs appear on the final data tape. However, the events that failed include some 5n type events. To take account of the events which failed, the measuring efficiency must be determined. The measuring ef- ficiency is defined as: em. = Np/Nm (C.1) where Np is the number of events on the final tape and Nm is the number of measured events. Table C.1a presents the measuring efficiencies found by using equation C.l and the numbers on Tables 2.1 and 2.2 in Chapter 11. However, in Appendix B, it was shown that there is_a class of events in the data which should not have been measured. These events were assigned a code 4 in Appendix B. Certain types of these code 4 events have a particularly high fail rate. In particular, there are 285 events listed in subcategories d, e, and f on Tables B.5 and B.6. This group of events has a measuring efficiency of em" = .59. 132 :- ”W ..L - 133 Table C.1 Measuring Efficiencies C.1a Uncorrected Measuring Efficiencies Momentum 3 prong 4 prong 5 prong 6 prong (GeV/c) 1.09 .934 i .0034 .926 i .0030 .907 i .0058 .880 1 .0067 1.19 .953 i .0024 .926 i .0026 .912 i .0047 .867 i .0058 1.31 .943 i .0019 .934 i .0018 .904 i .0035 .880 z .0040 1.43 .952 i .0021 .937 i .0021 .912 i .0042 .877 i .0049 C.1b Corrected Measuring Efficiencies Momentum 3 prong 4 prong 5 prong 6 prong (GeV/c) 1.09 .938 i .0034 .930 i .0030 .911 i .0050 .884 i .0067 1.19 .957 i .0024 .930 i .0026 .916 i .0047 .871 t .0058 1.31 .947 i .0019 .938 i .0018 .908 i .0035 .884 i .0040 1.43 .956 i .0021 .941 i .0021 .916 i .0042 .881 i .0049 'nmwv*“““‘““*faéfiv 134 The measuring efficiency of the sample excluding these events, em, is given by: 3m = N , (C.2) where the total number of events in scan 1 is Nt and the number of high fail rate events in scan 1 is Nf. The values of N = 22224 and Nf = 285 are obtained from Tables B.2-8.6 t in Appendix B. Table C.1b presents the values of em. These values, which are .004 higher than the values in Table C.1a, are the measuring efficiencies used for the cross section calculations. 1mg: 2 APPENDIX D BEAM COUNT To calculate the cross sections, the number of beam % particles entering a defined reaction volume must be deter- : mined. A track was counted as a beam particle if it crossed L the first fiducial cut-off line (see Figure 2.1 in Chapter E 1 11) without any obvious interaction before that point. The counting was done using every 50th frame on each of the 72 rolls. The total number of beam tracks was calculated by: N N = N —£3 (0.1) Here, Nb is the total number of beam tracks; Nbc is the number of beam tracks counted; th is the total number of frames; and Nfs is the number of frames used in the counting. The results are summarized in Tables D.1-D.4. The reaction volume, which was defined in Chapter III, is downstream of the fiducial cut-off lines used for beam count purpose. The number of beams entering this volume may be obtained from the beam count. The geometrical pro- perties of the bubble chamber require the beam particle to travel an average of 7.2 cm from the first fiducial cut-off line to reach the defined reaction volume. Therefore, number 135 136 Table D.l Beam Count P = 1.09 GeV/c 5911_ Number of beams Number of frames scanned Total frames 57 186 41 2092 58 169 41 2098 59 239 41 2093 60 210 41 2094 61 235 41 2092 62 210 41 2096 63 171 41 2088 64 238 41 2093 65 250 42 2112 66 196 42 2107 67 230 42 2131 68 232 41 2091 69 236 41 2087 70 ' 199 41 2088 71 194 41 2082 72 203 41 2079 TOTAL 3499 659 33514 Total number of beams = 178,000 i 3000 _136_1_1_ 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 TOTAL 137 Table D.2 Beam Count P = 1.19 GeV/c Number of beams Number of frames scanned 251 270 272 275 210 183 307 334 422 432 413 462 443 386 382 309 5351 41 41 41 41 41 41 42 41 41 41 42 39 41 41 41 42 657 Total number of beams = 272,200 1 3700 Total frames 2089 2090 2098 2095 2089 2088 2102 2095 2094 2090 2109 1999 2087 2098 2090 2110 33423 :22} ‘ I; l ...9_. 1n: . Murry—mm . 1138 Table D.3 Beam Count P = 1.31 GeV/c 3211 Number of beams Number of frames scanned Total frames 17 592 41. 2093 18 549 42 2102 19 431 41 2092 20 382 41 2090 21 386 41 2095 22 417 41 2098 23 365 42 2100 24 291 41 2198 25 575 42 2107 26 392 41 2081 27 393 42 2112 28 378‘ 42 2106 29 364 41 2097 30 549 41 2096 31 p 593 42 2104 32 500 42 2101 33 512 42 2106 34' ' 400 41 2096 35 462 41 2066 36 321 42 2099 37 400 42 2099 38 366 41 2091 39 300 41 2089 40 411 41 2088 TOTAL 10333 994 50406 Total number of beams = 524,000 1 5200 139 Table D.4 Beam Count P = 1.43 GeV/c 3911. Number of beams Number of frames scanned Total frames 1 187 24 1224 2 452 42 2087 3 447 ‘ 42 2099 4 514 41 2092 5 417 41 2096 6 250 41 2086 7 301 41 2073 8 392 41 2055 9 298 41 2085 10 567 41 2093 11 649 42 2099 12 578 41 2076 13 396 42 2108 14 635 42 2102 15 518 42 2102 16 284 41 2092 TOTAL 6885 645 32569 Total number of beams = 347,700 i 4200 140 of beams entering the reaction volume is given by: -eA 20 /2 _ o obs Nbr - Nb e (0.2) Here e = .14 gm/cc is the density of liquid deuterium; 8 = 7.2 cm is the path length before entering the reaction volume; and Cob , see Appendix F, is the total 5d cross s section less the unobservable part of the elastic scatter- ing. The numbers of beam tracks entering the reaction volume for each momentum value are summarized in Table 0.5. were : 141 Table D.5 Summary of Beam Count "69"“) Beam "b 32231152113314” 32231152531314?) 1.09 178000 1 3000 167400 168700 1.19 272200 i 3700 256500 258400 1.31 524000 3 5200 494400 498000 1.43 347700 1 4200 328700 331100 (1) No elastic correction (2) 28.9 mb elastic correction APPENDIX E SCANNING BIAS FOR SPECTATOR PROTONS E.l Slow Protons The spectator distribution about an axis defined by the direction of the beam, the y axis, should be symmetric. arc tan (z/x) is not Therefore, if the distribution for 0 isotropic, it would be indicative of a scanning bias. Figure E.la shows such a distribution. It is apparent that there are dips in the 0 distribution at 0 near 0° and 180°. These values of 0 correspond to spectator protons moving toward or away from the scanner and the projection of the track on the film becomes short. Since a low momentum track has a shorter track length in a bubble chamber, it is expected that some low momentum tracks will be missed. This loss can be determined by fitting the following ex- pression to the data: N (0) =A+B|Sin 0| (15.1) obs Ncorr (¢) = A + B (E.2) 142 ‘Ef*“‘”" 143 Figure E.1 Spectator Proton 0 Distribution (A) Slow protons (p < 100 MeV/c) (B) Fast protons (p > 400 MeV/c) EVENTS EVENTS 50 25 100 50 144 1 R) 1 1 1 1 O 90 180 270 360 PHI (DEGREES) B) 1 1 1 0 90 180 270 360 PHI (DEGREES) 145 Here A and B are the fit parameters; Nobs (0) is the fitted 0 distribution; and Ncorr tion. The values of A and B are found by fitting expression (0) is the expected 0 distribu- E.1 to the data. Then the number of events in the data is given by: Zn Mobs = g (A + BlSln ¢1)d¢ (E. = 20A + 48 (E. The actual number of events is given by: Zn Mcorr = g (A + B)d¢ (E. = 2N(A + B) (E. The correction factor is then given by: C = Mcorr/Mobs ('5 II The values of C are presented in Table E.l. (E. (A + B)/(A + ZB/n) (E. 3) 4) 5) 6) 7) 8) 146 Table E.l Scanning Loss Corrections for Slow Spectator Protons Spectator Momentum C(4 Prong) C(6 Prong) MeV/c 50-90 1.57 1.57 70-110 1.39 i .02 1.50 i .03 90-130 1.14 i .02 1.22 i .04 > 130 1.00 1.00 This loss causes events to change topology. Even prong events with a low momentum spectator proton will be meas- ured as odd prong events. Since in the conflict scan, this type of mislabeling was considered a minor error, this loss will not change the total cross sections. How- ever, this loss must be considered when studying the spec- tator distribution of the data. E.2 Fast Protons. The 0 angle distribution of fast spectator protons also shows a scanning bias. This bias appears as a loss of events with fast spectator protons moving perpendicular to the line of sight. This corresponds to 0 equal to 90° or 270°. The reason for this loss is the way an event was selected to be measured. When a track is perpendicular to 147 the line of sight, it appears lighter than a similar track in any other orientations. Therefore, an event with a fast proton with 0 equal to 90° or 270° might not be meas- ured because it looks like a 5p type event. Figure E.lb shows such a distribution. To determine how many events are not measured, expression E.l was fitted to the 0 angle distribution of events whose proton has a momentum greater than 250 MeV/c. In this case, the values of B were negative. The corrected number of events is given by: Zn Mcorr = of A d0 (5.9) Mcorr 20A (E.10) Table E.2 presents the numbers of events that were lost for different reactions. 148 Table E.2 Scanning Losses for Events with Fast Spectator Protons Reaction Type 4 Prong Mark 8 4 Prong Mark 9 4 Prong Mark 10 6 Prong Mark 8 6 Prong Mark 9 6 Prong Mark 10 1.09 GeV/c 1.19 Gel/c O 0 28 55 42 27 O O 5 O O O 1.31 GeV/c 1.43 GeV/c O O 69 64 74 100 9 8 20 8 12 8 APPENDIX F UNSEEN ELASTIC SCATTERING The cross section measurements involve the use of the total 0d cross sections. However, in this experiment some of the 5d interactions are not observed. These unseen interactions are low t elastic scattering. There are three types of elastic scattering in deuterium: (a) 5d elastic scattering; (b) quasi-elastic pp scattering; and (c) quasi- elastic 5n scattering. To determine the amount of unseen elastic events, one must estimate the minimum momentum transfer that can be detected. In a bubble chamber, an elastic scattering event is detected in two ways. First, if the recoil particle is charged and has a large enough momentum, it will produce a visible track. If the recoil particle is a neutron the only way to detect the interaction is to observe the deflection of the incident particle. In the case of charged recoil particles, either a proton or a deuteron, one can estimate the smallest detectable t if the lower limit of momentum for detecting protons is known. The sample of 4 and 6 prong events shows that there are very few protons with momentum less than 80 MeV/c. From a study of the azimuthal angle 149 150 distribution (see Appendix E), it was known that the detec- tion efficiency of proton with momentum between 80 MeV/c and 100 MeV/c is low. Therefore, the momentum values of 100 MeV/c for protons will be used for the lower limits of /:E. The corresponding value for a deuteron with the same range is 80 MeV/c. If the neutron is the recoil particle, the event can only be seen by observing the deflection of the incident particle. If the deflection angle is less than 6°, the event is difficult to observe. At a beam mo- mentum of 1.3 GeV/c, a 6° deflection angle corresponds to a t transfer of -.0185 (GeV/c)2. This will be considered the minimum t transfer for fin elastic scattering. The differential elastic cross section can be written as: 99 = Aebt (F.l) Then the missing cross section is given by: min e1 b g ebt dt (F.2) 0' Q 11 missing bt . gel (1 - e min) (F.3) In equations F.2 and F.3, Gel is the total elastic cross sections. The values of o and b were determined else- e1 where.22’ 42’ 43 Table F.l shows the results of the 151 Table F.l Estimate of Unseen Elastic Scattering . . 2 -2 . b b Elastic Scattering tm1n(GeV/c) °EL(m ) b(GeV/c) Omissing(m ) 5d .0064 38 44 9.1 50 .0100 43 18 7.8 En .0185 43 18 12.0 Total missing cross section is 28.9 mb. 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