A Measurement of the Process P+D → He³ + Photon at Intermediate Energies Citation Kline, Robert Vernon (1974) A Measurement of the Process P+D → He³ + Photon at Intermediate Energies. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XW3E-WX28. https://resolver.caltech.edu/CaltechETD:etd-05202005-085150 Abstract We have measured the process pd → He³γ in the energy region of Δ(1236) nucleon isobar excitation. At an incident proton energy of 462 MeV, data were assembled for center of mass angles of 45°, 60°, 75°, 90°, 105°, 120°, and 135°. We also measured the energy dependence of the 90° cross-section in the center of mass, for incident proton energies of 377, 462 and 576 MeV. We discuss implications for T-invariance in the electromagnetic interaction by a detailed balance comparison with the inverse reaction. In addition, we present an angular distribution for the process pd → He³π° at an incident proton energy of 462, as well as limited angular distributions at 377 and 576 MeV. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Heusch, Clemens A. Thesis Committee: Unknown, Unknown Defense Date: 10 October 1973 Record Number: CaltechETD:etd-05202005-085150 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-05202005-085150 DOI: 10.7907/XW3E-WX28 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1895 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 20 May 2005 Last Modified: 26 Jul 2024 22:19 Thesis Files Preview PDF (Kline_rv_1974.pdf) - Final Version See Usage Policy. 6MB Repository Staff Only: item control page

_ A MEASUREMENT OF THE PROCESS P+D + He? + PHOTON AT INTERMEDIATE ENERGIES Thesis by Robert V. Kline In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1973 (Submitted October 10, 1973) ii ACKNOWLEDGEMENTS ~. A large experiment necessarily draws upon the talents and resources of many people, and often does so for an extended period of time. The help, cooperation, and material support received during the course of this experiment are gratefully acknowledged. Special thanks are extended to the following people for their contributions to this project. First of all, my thanks to my advisor, Clemens A. Heusch. In addition to conceiving the experiment, he was active in all phases of its execution, and in general insured that the project was a valuable and rewarding experience. My thanks to Kirk McDonald for many contributions to all aspects of the experiment, and for an active interest in its progress. Construction and testing of one of the photon detectors owes much to the help and suggestions of Charles Prescott and Steve Yellin, and to the ingenuity and skill of Walter Nilsson. - My thanks to Abe Seiden for encouragement, and for many valuable discussions. To Jim Carroll, Don Fredrickson, Mike Goitein, Burns MacDonald, and Al Stetz go my thanks for a great deal of effort in bringing the experiment through the data collecting phase, and for many helpful suggestions during the subsequent analysis of the data. iii To Barry Lieberman and Karl-Stein for many hours donated to the ' task of collecting data. I am grateful to Victor Perez-Mendez for making available the resources of the Lawrence Berkeley Laboratory, and for a continued interest in the progress of the experiment. Also to James Vale and the crew of the 184-inch cyclotron for keeping the machine running smoothly throughout the several months of data taking. My thanks to Robert Walker and to Caltech for providing continued financial support during the long course of this project. Finally, I would like to thank Jeanne Elliott, Patti Fox, and Judi Laurence for contributing generously of their time and skill toward the production of this document. -iv ABSTRACT _ We have measured the process pd > Hey in the energy region of A(1236) nucleon’ isobar excitation. At an incident proton energy of 462 MeV, data were assembled for center of mass angles of 45°, 60°, 75°, 90°, 105°, 120°, and 135°, We also measured the energy dependence of the 90° cross- section in the center of mass, for incident proton energies of 377, 462 and 576 Mev. We discuss implications for T~invariance in the electromag<- netic interaction by a detailed balance comparison with the inverse reac- tion. In addition, we present an angular distribution for the process pd > He n° at an incident proton energy of 462, as well as limited angular distributions at 377 and 576 MeV. PART Il. iit. TABLE OF CONTENTS TITLE INTRODUCTION EXPERIMENTAL METHOD ‘DATA TAKING - Hourly Checks 4-Hourly and 8-Hourly Checks Preliminary Analysis Calibrations Information Collected DATA ANALYSIS Constants Data Summary Program A. Spark Chamber Efficiencies - Helium B. Spark Chamber Efficiencies -~ Photon Geometry-Kinematics Cuts | Efficiencies A. Geometric Solid Angle Acceptance B. Electronic Efficiencies Cross Section Calculation Background Subtraction Systematic Errors PAGE 21 23 25 27 29 33 35 36 36 38 39 39 AA 5] 52 55 56 57 58 PART V. VI. VIII. vi TITLE RESULTS DISCUSSION APPENDICES A. The Beam ‘B. Target Monitor C. Beam Energy and Stability D. Photon Counters E. Vertex Location - Photon Chambers F. Helium Detector Helium Chamber Local Coordinates H. Geokin I. Data Summary Program Structure J. Efficiency Program K. Chi-Square Fitting i. Pi-Zero Analysis M. Targets N. Beam Integrators 0. current Experimental Status of Symmetries REFERENCES PAGE 63 72 FIGURE | 2.1 2.2 2.3 3.1 3.2 3-3 3.4 AL 4.2 4.3 el 45 4.6 5el 23 5.4 6.1 6.2 vii LIST OF FIGURES TITLE Experimental Setup Helium Lab Angle Versus Helium Center-of-Mass Angle ‘Simplified Schematic of the Electronics Hourly Check _4-Hourly Check 8~-Hourly Check Run Sheet Definition of @ and g Angles Reconstructed Event Origins Differential Pulse Height Counter Spectrum Time-of-Flight ADC Versus Helium Detector ADC Typical Solid Angle Acceptance Typical Chi-Square. Distribution Angular Distribution for pd » He3y at 462 MeV. Energy Dependence of the 90-Degree cm Data. Angular Distribution for pd > He3’at 462 MeV. Energy Dependence of the Pi-Zero Data Structure of the Proton Beam Ray Trace for on Momentum Protons - Horizontal View PAGE | 16 19 22 26 28 | 31 4) 47 49 48 59 59 65 66 6y 70 80 84 FIGURE 6.3 6h 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6,12 6.134 6.138 6.14 6.15 6.16 6.17 6.18 6.19 viii TITLE Ray Trace for on Momentum Protons - Vertical View Ray Trace for off Momentum Protons ~ Horizontal View Kinematic Position of the Target Monitor Telescopes Schematic View of the Target Monitor Telescopes Target Monitor Logic Electronics Typical Bragg Peak Obtained from a Range Measure Numerical Integration Results Range Measuring Apparatus | Relative Ionization Versus Range with Mean Range Noted Basic Components of the Photon Detector Liquid Light Pipe Details of Photon Counter Construction Tagged Photon Beam Experimental Setup Photon Detector Logic Electronics Pulse Height Versus Energy Energy Resolution Versus Photon Energy Individual Component Pulseheight Spectra Conversion Efficiency Versus Energy for a 2X° ead Glass Converter PAGE 85 86 92 93 96 99 101 102 103 105 107 107 108 109 111 113 114 116 FIG 6.20 6.21 6.22 6,23 6,2h 6.25 6.26 6.27 6,28 6.29 6.30 6.31 6.32 6.33 6.34 6.35 6.36 6.37 6.38 . Response of He3 Detector to p, d, He3, He TITLE Typical Electron Pair Shower ‘Relative Positions of Lead Glass Converter and Wire Spark Chambers Resolution for a Single Track _ Assignment of a Vertex Error - Pairs of Tracks Assignment of a Vertex Error When Both Tracks Have the Same Slope Assignment of a Vertex Error - Three Tracks Exploded View of the Helium Detector Helium Detector Construction Details _ Helium Detector Logic Electronics Americium-241 Energy Spectrum Typieal He3 Spectrum - 114.6 MeV Heliums Typical He3 Spectrum - 114.6 MeV Heliums - Log Plot | y Versus Energy Definition of Wire Spark Chamber Coordinates Construction of the Angles Logical Structure of the Program Geokin Logical Structure of the Data Summary Program Logical Structure of the Efficiency Program Definition of the Angles @ and d PAGE 118 119 122 124 125 127 130 131 133 134 142 143 154 147 15] 152 155 158 160 FIGURE 6.39 6.40 6.41 6.42 - 6.43 TITLE Differential Pulse Height Counter Spectrum Reconstructed Event Origins Differential Cross Section for pd » He3° at 462 MeV Differential Cross Section for pd > Herat 377 and 571 MeV Target Construction Details PAGE 171 172 174 175 | 179 5.5 6.1 6.2 6.3 6.4 6.5 6.6 xi LIST OF TABLES ‘TITLE Alpha-63 Output Kinds of Data Collected Kinematic Settings for Which Data Were Collected Background Subtraction Ratios Angular Distribution for pd > Hey at . 462 MeV He? Photodisintegration Data Angular Distribution for pd > He? n° Comparison of 462 MeV Data Comparison of 90° CM Points Amount of Degrader Used in the Proton Beam Elements of the Proton Beam - Horizontal Elements of the Proton Beam - Vertical Beam Energy and Beam Width Degrader Thickness - gm/ cm? Angular Distribution for pd + He*n° PAGE 30 32 33 61 64 68 71 76 77 79 82 83 89 95 176 xii To My Parents INTRODUCTION “We report on a measurement of the process pd + He? .. Q1) At an incident proton energy of 462 meV, we have measured process (1) for seven center-of-mass angles: 45°, 60°, 75°, 90°, 105°, 120° , and 135°. We also assembled data at a center-of-mass angle of 90° for incident proton energies of 377 MeV and 576 MeV. The angles were chosen to overlap as much as possible with existing He? photodisintegration data. The energy region was selected so as to be able to probe the effect of the excitation of a A(1236) nucleon isobar. We also report on a measurement of the process pd > He'n®. | (2) Data were collected over a center-of-mass angle region from 45° to 135°, at an incident proton energy of 462 MeV. Limited angular distributions were obtained in the region of 90° center-of-mass angle for incident | proton energies of 377 MeV and 576 MeV. The interest here again was to see whether nucleon isobar excitation is important in this process. We were motivated to measure process (1) by the observations of earlier investigations showing that nucleon isobar excitation plays an important part in the reaction yd > np. (3) A prominent enhancement, attributed to the A(1236) isobar, appears in the energy dependent cross section of reaction (3) in the energy region of Kk = 290 MeV. Are such excitations important in other light . . . . 3 nuclei? We set out to study this question in He . 2 A second motivation for measuring process (1) was the suggestion of several investigators that the yNA vertex, important in process (3), might be used in experiments investigating T-invariance in the electro- magnetic interaction of hadrons. Berstein , et a1, (26) » after reviewing the experimental evidence, had concluded that existing data were consis- tent with rather large violations of C and T. Subsequently, Barshay (45) (27) _ and Christ and Lee selected a set of experiments involving the yNA vertex to test this conclusion. Our interest in time-reversal invariance (TRI) in the electromagnetic interaction of hadrons has its origin in the now well confirmed CP vio- lation, observed in the weak decay of Ke into two pions. This decay mode occurs about .2% of the time, a possibly meaningful fractional strength of about a/t. This, in turn, led to the suggestion, mentioned above, that the observed CP violation may be the result of an electro- magnetic correction to the weak Hamiltonian. Since existing experiment- al evidence did not preclude a rather large violation in the electro- magnetic interactions of hadrons, it was clear that this might be a fruitful area in which to search. Two techniques exist for investigating T-invariance in the electro- magnetic interaction of hadrons: 1) measurements of expectation values of T-odd operators; 2) detailed balance measurements. The results reported in this thesis employ the second technique. A third technique has been used for systems with zero additive quantum numbers: assuming (with good reason) that P is a good symmetry of the electro- Magnetic interaction, the decay of C-eigenstates (n°, n°,...) must conserve C if T is good. 3 “We review here*briefly some results obtained in earlier measurements, gncluding, for completeness, some made employing weak and strong inter- actions. An‘excellent review of the experimental status of time-reversal invariance through 1969 has been made by Henley ‘22) , The principle of detailed balance is embodied in the following recipro- city relation, which, with A = 0, is valid in the center-of-mass system if the process ab <> cd is invariant under time reversal: 1 +A = (28 +1) (28, + 1) P2do/da| _,/ (28,4 +1) P2do/d0| _ P. and Po are momenta, S$. ae 5a? and Sa are spins, and do/dQ2 is the differential cross section. A is a T violation parameter. This rela- tionship assumes an unpolarized beam and target; one must be careful to insure that these conditions are met when performing experiments in order . . . Oo to avoid confusing effects. If possible, measurements are made near 0° or 180° in order to minimize contributing spin channels. McDonald ‘> has made a survey of possible reciprocity tests for the electro- magnetic interaction of hadrons of the form yA «> BC, where excited states for A, B, and C can be excluded from consideration. Possible targets in- clude p, n, d, He>, w, He’, and 1i°, The possibilities for B and C include all of those for A, plus charged pions. Selection of a pair of reactions for use in a detailed balance test of time-reversal invariance from these possibilities involves such experimental considerations as the number of neutral particles involved, kinetic energies and angles of final states, radioactivity of targets or beams (e.g. H), any existing data suggesting nucleon isobar excitation, among others. 4 ' no violation, with error bars as small as 1.5% (Ref. 66). Lower energy’ measurements look for interferences between competing mul- tipoles to measure the relative phase.’ Usually only M1 and E2 multi- poles are involved. Some of the most accurate measurements have been made using the Méssbauer effect. Using a polarized target, and linearly polarized photons, one looks for a term of the form (k-F x e) (k-4) (4), where k is the photon vector, € is its polarization vector, and j is. the polarization of the absorber. This term is proportional to ¥5 (6,9) sin @. The most accurate result, using a Ml - E2 transition in Ru’, gives sin $ = (1.0 +/- 1.7) x 10°? (Ref. 67). Measurements involving two photon final states have placed limits of comparable magnitude on the relative phase between Ml and E2 multipoles. One recent measurement using the capture of polarized neutrons on 3661 looks for a correlation of the form (k, “k, x 5) &,°k), where Kk, and k, are photon momenta, rf is the polarization vector of the nucleus. (68) 3 Bulgakov reports a value for ¢ of (-1.8 + 2.2) x 10 ~. A weak interaction measurement has been made using the reaction A° > ntp. > A violation would be indicated by a term of the form <0,>* <0 4 >x ko The resulting time reversal phase is given as $6 = 18°.+/- 1.6° (Ref. 70). A strong interaction measurement using pp elastic scattering looks for > > 2 +> 3+ ® > = Pi a a2 a term of the form (9, "4 Oy°K + oy K Sy q) F(k, .ke) with q = k, - Ke» K = k, x ke, places sin $ = .06 +/- .09 (Ref. 71). Finally, we consider measurements of static electric moments, especially the static electric dipole moment of the neutron. Here one looks for an J 5 . - time+reversal invariance. Upon redoing one of these experiments on (reaction 4), and improving the statistical accuracy of the other, the evidence disappeared. The most recent results measure a phase of fe} 4° + 10° . The need to use a neutron beam in reaction (4), as well as the presence of two neutral particles in both reactions (3) and (4), make these experiments very difficult to perform. The statistical accuracy is about 7%. _A similar reciprocity test has been performed on the reactions 7 p+> ny. Again one faces formidable experimental difficulties, owing to a completely neutral final state in one direction, and the necessity of using a deuterium target in the other. Early measurements again claimed (53) a departure from time-reversal invariance, although more recent measurements are compatible with no effect. (4) Some of the most accurate measurements, especially at low energies, have come from experiments testing the strong interaction. The most accurate experiment to date, employing the reaction Mg~4a <> Mg”p, gives 1+As= 0.999 + .003 (Ref. 65), implying that time-reversal is good to at least the .3% level in this strong interaction reaction. As the second basic method to search for T-violation effects, we mention the investigation of correlations among measureable quantities, which would indicate the presence of T-odd amplitudes. Time-reversal invar- iance requires the relative phase of contributing amplitudes to be either 0° or 180°. The results of these experiments are usually expressed as a . fe) . . phase, >, where a phase of 90 represents maximal interference between Py, any existing data suggesting nucleon isobar excitation, etc. Barshay suggested that one measure reaction (3), and the reaction np > dy (4) arguing that since the A(1236) isobar is such a dominant feature of these processes, perhaps they might exhibit a large T-violation. He first assumes that one can associate a phase with yNA vertex, and suggests that the following diagram dominates the resonant amplitude: ig € A Y N | d \ N Using a partial wave analysis in which only S,P and D wave transitions are considered, Barshay argues that the resonant amplitude for the om transition M(1) > Dy contributes about 36% to the cross section. The most likely background amplitudes are taken to correspond to E(1) > 3p, and M(L1) + 1, transitions which Barshay estimates contribute about 60% 0 and 4%, respectively, ‘to the cross section. Parameterizing the resulting angular distribution as Ay + Ay cos*6, the phase ¢ is represented by Ag AQ) 3 sin $6 = | forward ~ —| backward) 0 Ay For maximal T-violation, > = 90°, and one might expect a violation on the order of 30%. cS (68) 36 - Measurement of the capture of polarized neutrons on Cl”, followed . | so by double photon emission, looks for a correlation of the form (k,°k, x —> — —_ _ —_ 5) (ky °k,), where k, and ky are photon momentum vectors, and j is the (68) reports a value polarization vector of the nucleus. P. A. Bulgakov of (1.8.4 2.2) x 10°> for the relative phase, again consistent with no interference of competing multipoles. * (69) A weak interaction measurement has been made using the reaction A° + mp. A violation would be indicated by the presence of a term . _ = > _ seal “4 . ° ; proportional to ad | x a , where oy and o, are the polarization of the ; ; _ final state proton, and the initial A°, respectively, and aa is the momentum vector of the final state proton. The resulting phase is given fe) o : : . fe) re) . as 2.6 + 4.2°, again consistent with 0 or 180 relative phase of the dominant competing S and P partial wave amplitudes. In 1969, when poorly confirmed indications of T-violation effects in the electromagnetic interaction abounded, our group decided to perform a measurement of a pair of reactions as a test of time-reversal invariance. Rather than repeat measurements. of reactions already measured or in pro- gress, we decided to measure reaction (1), and its inverse reaction 3 yHe~ > pd. (5) Reaction (5) was measured in the last experiment performed on the now defunct Cal Tech 1.5 GeV electron synchrotron. The results of the ) measurement has already been reported 2° elsewhere. Although reactions (1) and (5) have cross sections typically one order of magnitude lower than those for np «> yd, they have the advantage of 8 y- _ an additional charged particle. This allows for better constraint on the kinematical definition of the initial and final states. s One difficulty with reaction (1) is the presence of a large background 34° (n° > ¥y ), which is on the order of 20-30 times larger than pd > He reaction (1). A corresponding background was the most serious contami- nation for the reaction np > yd. Another difficulty was due to the low helium kinetic energy encountered for backward helium center-of-mas angles. The double charge makes. energy loss and multiple scattering potentially serious. On the other hand, the double charge enhances the definition of this particle in any Coulomb interaction. . * Another problem could result from processes such as pd >» He? Y, since our experiment would not resolve excited states of the 3 nucleon system. Although there is no consensus on this point, it is generally believed that no excited states of He? exist, either bound or virtua1. 7) Results on reaction (5) 0256) do not indicate the presence of a bump in the total cross section due to the contribution of a A(1236), as is so prominent in the reaction np +> yd. One possible explanation for this is that the contribution of a resonant amplitude is small. But why? Consider isospin: indicated below is a possible diagram for a resonant amplitude. y He _ Isospin keeps tne lower intermediate nucleons from forming a deuteron. Partial wave analysis ©) suggests that the most likely state is "Sy: The two nucleons can possess relative kinetic energy which serves, in part,. to obscure the observation of A production by smearing out the kinematics. In the photodisintegration of the deuteron, we note’ that the deuteron. is a very loosely bound system. The breakup process is described very well _by considering one nucleon to be a spectator. The photon then interacts © with a nucleon on the mass shell. The resultant energy dependent cross section can easily show a dominant influence from A production; the width of the resonant behavior is due largely to the natural width of the A excitation. No analogy to the deuteron breakup process can be made for He” photo- disintegration, since isospin forbids the breakup of He? into an ex- changed nucleon and a spectator deuteron. Instead, the vertex of helium breakup contains a *S, intermediate dinucleon state and a virtual nucleon. It is the interaction of this virtual nucleon with the incident photon combined with the relative kinetic energy of the two nucleons in the *S, intermediate state that serve to obscure any influence of A produc- tion in the process yHe® > pd. The absence of a dramatic $ channel effect obviously does not affect the value of reactions (1) and (5) as a test of time-reversal invariance. It does, however, serve to indicate the complications for interpretation of the results in terms of individual resonant and non-resonant amp1i- 10 particularly promising probe of time reversal invariance independent because it can provide a wholly new set of amplitudes for interference effects; it may exhibit features unobservable in the published work of other reactions. The measurement of process (1) was performed at the Lawrence Berkeley . * ° Laboratory 184" synchrocyclotron. The data will be compared with a measurement of the photodisintegration of He? already completed and re- . ported elsewhere. (27>) *Frormerly the Lawrence Radiation Laboratory. 11) Experimental Method _ Two major points entered into the decision as to what kind of apparatus to use for the detection of the reaction pd 3 Herne First, pdsHe3y7° will contribute a very large background, on the order of 30 times larger than the reaction of primary interest. Second, the absolute cross 3 section for the process pd > He~y is a very small one, on the order of 1073" om”. ‘The apparatus was chosen so as to optimize geometric detection efficiency in order to offset the small cross section. Good resolution of all particle trajectories was the essential feature that helped ‘towards efficient background subtraction. . References are made to the more detailed discussions of the apparatus found in the appendices. The basic features of the experimental setup are as follows: = A proton spectrometer providing about 10° protons/sec with -5% momentum resolution, and a set of ion chambers and integrators for beam monitoring. - Liquid deuterium targets with two flasks of different thickness and a target monitoring systen. - A thick plastic total absorption scintillation detector for energy determination of the He3's, and a set of wire spark chambers for trajectory delineation. - Tio total absorption lead glass photon hodoscopes/spectrometers, and associated wire spark chambers for determining photon vertices. 12 -« A special purpose computer for recording information on magnetic 20: tape. An overall view of the apparatus can be seen in Fig. 2.1. The experiment was performed using the LBL 184~inch synchrocyelotron, which operates at a fixed energy of 735 + 20 MeV. Based on some * Monte Carlo studies made to determine the quality of the proton beam needed to enable us to effectively separate the forward and background reactions, the following requirements resulted: - A momentum bite of < 1% for energies between 300 and 600 MeV; - An angular divergence. of < .5 degrees, at the same energies. In order to obtain useful counting rates we needed a flux of no less 8 than 10 protons/sec at the liquid deuterium target. The resulting beam design is shown schematically in Fig. 6.1. oa The main features of the, beam are as follows. First the 135 MeV -eyelotron beam passes through a copper degrade in order to produce a beam with the desired mean energy. The position where the beam exits from the copper serves ‘as the beam source. The angular acceptance of the beam is determined by slit 1. ‘The momentum acceptance is deter- .. mined by slit 3. Finally a quadrapole double t images slit 3 on the target with a magnification of about 1.8. Steering of the beam is done with the final bending magnet, Atlas. Details of the beam design, and the acceleration of particles other than protons, can be found in Appendix A. 13 ©DEDX counter @ Helium counter @ Anti @Beam dump Proton detector for target 130° a beam monitor 9 4), LD, target | © Split i yy, ' 5° chamber | Hel ao 55 ) WO GY a Ks ORS ~h_ m4 eon” \\ BNO REX I~ 20" Bending magnet Photon counter number 2 Wad 10 xq lead glass absorber @ Veto counters - © Light pipe @ 2 Xxq lead glass converter © Deuteron for target beam monitor - @ Trigger counter -@ lon chamber number 2 @ é Xg lead glass absorber © Split ion chamber - XBL723- 2613 . Figure 2.1 experimental Setup 14 » "The beam intensity was measured with a set of on chambers and current | integrators. Three integrator systems were employed to provide for “relative consistency checks. The current integrators were kept inside of a box constructed of styrofoam in order to thermally insulate them. The local barometric pressure was recorded; from this, corrections to the integrator thickness were made. In order to minimize the effects of multiple scattering of the He , our liquid deuterium targets were as thin as permissible by data rate. requirements. For those settings in which the kinetic energy of the He? was greater than 100 MeV, a half-inch target was used, for (He? ) < 100 MeV, a sixth-inch target. Use of the thinner target was somewhat compensated for by the higher cross-section for those settings in which the He? energy was low. The target, was about four inches high and wide (for construction details, see Appendix M.) te The liquid was obtained by condensing gaseous deuterium. Liquid hydro- gen was circulated around the target flask, and served as the cooling agent for the liquid deuterium. The liquid hydrogen container was in turn surrounded with liquid nitrogen. Bubbling in such thin targets was a potential problem. In order to ” mondtor the condition of the target, a set of range telescopes were placed so as to measure the proton-deuteron elastic scattering rate. The telescopes were placed at a setting kinematically unavailable to proton-proton elastic scattering. Careful adjustment of the ranging material made random triggers negligible, as measured by the full-to- empty ratio of the monitors (cf. Appendix N). 15 We. now turn to the detection apparatus for the final state particles. A total absorption plastic scintillation detector, with an energy resolution of about 3% HWHM, was used to detect the He? particles. Since the velocity of the helium particle is less than that of the 7 velocity of the center of mass,the lab angle has a maximum (see figure 2.2). The helium detector was made large enough to intercept the lab * He? ts from all center of mass angles of interest. Data were in fact collected from two center of mass angles simultaneously defined by two ‘photon detectors. This helped compensate for the low cross section for pd — Hey, The detector was just thick enough (4 inches ) to absorb the highest energy He? 'g encountered in this experiment (430 MeV). This thickness provided a unique pulse height for maximum He” energy. For lesser pulse heights, there is less uniqueness of interpretation, as discussed in Appendix F. Additional discrimination was achieved againgt non- stopping particles by placing a veto counter behind the detector. See Appendix F for construction details. Since the range counter could be "fooled" by protons or deuterons, we built an additional safeguard into the system: a 1/8-inch scintillation ~. eounter covered the entire face of the range counter. We demanded that 3 a He candidate deposit considerably more energy in this counter than a fast proton or other singly charged particle. A clean separation was possible notwithstanding the larger counter size. Helium-3 trajectories were determined with two sets of wire spark chambers. Multiple scattering effects, as well as ionization losses, 16 28.0 T T ) | ! 18.7 — — 42.5 —— : 6.3 — ; G.c | \ 0.0 45.0 90.0 135.0 180.0 Figure 2. 2 Helium Lab Angle Versus Helium Center-of-mass Angle 77 were minimized by placing helium filled bags between the target and the wire chambers, and between the two sets of wire chambers. The ‘same bags also enclosed the proton beam for about 10 feet downstream of the target. The feature reduced the counting rate in the helium detector by minimizing air-induced spray. For photon detection, we used two independent telescope systems. Each shower counter was designed to provide both position and energy infor- mation on incident photons. They consisted basically of a 2x° lead glass converter, a set of wire spark chambers, and lead glass absorber, at least 8X° thick (refer to Fig. 6.12). <A veto counter was placed before the 2x° converter to allow only passing neutrals. A counter was placed directly behind the ex° converter to detect charged products. This counter was part of the event trigger. The output signals from the converter and the absorber were added to give a signal proportional to the photon energy. The energy resolution is important in helping to separate the background, primarily photons, from the decay of x°'s in the process pd + He? a, t > yy. One of the counters was an updated version of one designed and built about fifteen years aac. The glass composing the absorber was quite yellow, and non-uniform, raising the energy resolution to about 10% at 500 MeV. The other counter was designed specifically to detect photons in the energy region .1 to .6 cev’. It employed high quantum efficiency photomultiplier tubes, very clear and wniform lead glass, and a liquid- Filled light pipe between the absorber and the photomultiplier tubes. The energy resolution of this counter is on the order of 7% at 500 MeV. With the 7% to 10% energy resolution, much of the background can be 18 eliminated using energy alone. Construction details appear in Appendix D. | The information from the spark chambers which were located between the converter and total absorber, is used to construct a conversion vertex, to make the angle of photon emission measurable. ‘The counters were mounted on moveable three-legged tables, each leg of which could be independently adjusted in height. These tables were in turn attached -to adjustable radius arms. The whole apparatus could then be moved in circular trajectories, and adjusted between about 28° and 119° with ‘respect to the beam line. Data were taken about every 15° in the -« center of mass system (see Fig. 2.1). A special purpose computer” ° was employed to gather information for each event trigger, and to store the information prior to writing it onto magnetic tape. The device consisted of a 512 twelve-bit-word data buffer, capable of storing enough information for two event triggers, a data bus system used to access information from the experimental apparatus, and a tape unit. Digital information was obtained from event scalers, wire spark | chamber word sealers, and six analog to digital converters. In addi- tion, selected data buffer words were hard wired to specific values. These were later used to check the fidelity of data transmission to magnetic tape. In practice only two runs had to be rejected for errors of this type. A simplified schematic of the electronics is shown in Figure 2.3. 19 He detector Ate Proton beam Photon « detector 2 Photon detector | D= discriminator REDI- C= coincidence Master trigger . XBL737-3279 ’ Figure 2.3 Simplified Schematic of the Electronics 20 - Consider either photon detector. An event trigger consisted of no “signal from the photon detector veto, a signal from either the lead ‘glass converter or the lead block absorber, a "conversion" counter, located behind the converter; a signal from the helium detector, dk appropriate pulse height from the ~— counter, and no signal from the dx helium veto; a ready signal from the data recording apparatus. * Signals from the two photon detectors were orred, making the logic sensitive to the three body process pd > He? 2?, (3° > yy). Not shown are the analog to digital converters (ADC's) used in - recording pulse ‘heights fromthe converter and block of each photon detector, and the helium detector. Time of flight was recorded as ' the difference between the helium flight time and that of the photon. Finally, the amplitude of the differential pulse height counter was recorded. 4 “DATA TAKING Run Procedure - General “Data collecting for the experiment was a fairly dynamic process for the experimenters. Formal equipment checks were made every hour. On every fourth such hourly check, a more extensive equipment check was made, and - on every eighth hourly check, all tube voltages were also measured. At all times the experimenters were expected to keep one eye on such things as spark chamber wand performance, the target liquid level (including periodical visual checks of the target flask for any bubbling), beam _ steering, beam intensity, amount of magnetic tape remaining, shape of beam spill, and other things prone to rather sudden failure or depletion. Between hourly checks, various calculations were performed, and the re- sults tabulated so that any serious drift or equipment malfunction could be detected. At the end of each run and at every hourly check, hard ’ copy was obtained+of all scalers, and of the helium detector pulse height analyzer. 1. Hourly Checks ‘Figure 3.1 is one of the hourly check sheets from the experiment, and illustrates the kinds of information of interest. Most of the informa- tion is directed at trying to detect equipment malfunctions, and involved someone looking at a gauge, liquid level, or oscilloscope, and recording the information. Using scaler information, consistency checks were made by correlating the performance of various pieces of apparatus. If any of the checks were found to be outside of acceptable limits, corrective action was taken. Three separate beam integrators were simultaneously 22 *YouRLt™ CUES: - ~~ . RESET TIMER TO a MINUTES. DON'T RELAX. % . FRIMT CUT 3 | EVENTS. A) Micnus TYPE conTece SvITcH: TO TACTIVE! —£) STCP pun AS SCOt AS EVENT STARTS PPINTINE C) SYITCH TQ "INACTIVE' AND THEN STAPT pur, MAKE “SURE THAT YOU GET ONE FVEIT FPO EACH GAMMA TRIGGER. PEAM CFF. REZERO SPLIT 1.C. ELECTPCVETERS IF NECESS/APY. . WAS: TT S) 7 a -.e —— _ Lo HE BAG FLOW O.K. nie CU. FT. REMAINING IN HE BOTTLE u ice HYDROGEN RESERVOIR LeveL | O° DEUTERIUM RESERVOIR LEVEL A FLASK LEVEL __f)>vGEoO “DEUT. RES, PRESSURE COUTSIDE GUAGE) - ei Seren _SPARK CHAMBER HIGH. VOLTAGE; GAMMAS 2. HELIUM 25 NEON FLOW TO SPK CH 9-4", _FROM SPK.cH His _ Hi: ALCOHOL 23.y<.__ TRAP LAST CHANGED —e HOUPS CAEONS) AGC, = 7 ee ee ae a SNOUT READING CASK CONTROL blxrg © ARE THE STABILISERS STABILISING | —N____ tt DO THE PULSER AND PEDESTAL OCCUR OUTSIDE THE SPILL GATE IS THE SPIKE JUST OUTSIDE THE SPILL GATE __—____ anann on 1S THE SPIKEADEQUATELY MODEST IN MA Ss ; 7 AMOUNT QF MAGNETIC TAPE REMAINING 2622 | reer . oo Te THE FILE PROTECT LIGHT CFF oS > 7 et K- 63 LIGHTS KEATING! re Pipl Ce vaPp 1 severeer >. mm : ARE fITS S, 12, 28 SET PEGULAPLY ..___ (BAD IF $0> EVENT SCALE? TECPEPEDT ING Cot __; : WHAT Is tyre FAP TEL/Y (DECADE CUT OF ‘2€) ye _ ARE ALL JACKSON SCALERS SWITCHED TO ‘cate? 7S - ARE ALL THRESHOLDS CH JACKSONS AT THEIR BLACK DOT VALUES aatnen CHECKS. DERIYED_FROM_3- EVENT. PRINTOUT. ARE FIDUCIALS PRESENT AND CORRECT ON ALL WANDS —>____ ANY DOURLE-COUNTING OF SPARKS/FIOUCIALS ANYTHING ODD ABOUT THE TRACKS ANY *SPSPfsg* ENTRIES IN AMONGST THE JACKSON SCALERS IF So, TRACK THE PROBLEM DCWN RELENTLESSLY. eagecn) BQ) = YS _ COMPUTE CCN STANDARD SHEET) CERTAIN CRITICALIA AS OESERVED BETWEEN THIS CHECK AND THE LAST. "2S THIS THE FOURTH CHECK SINCE THE LAST. 4-HOUR CHECK a a RELAX. Figure 3.1 Hourly Check |. 23 “used in the experiment. Every hour ratios for every pair of integrator outputs were’ computed and recorded. Changes in any of these ratios indi- cated a drift in one of tle integrator systems. A large drift might indicate an anomalously high leakage current for example. The consistency of the triggers per beam integrator unit was a useful check on the general condition of the logic electronics and the liquid level of the target. A change in this quantity outside statistics might indicate some kind of failure in a logic unit, cable, etc. It might also indicate that the target liquid level had changed, or that notice- : able boiling of the liquid led to bubbling. By observing the ratio of integrators, mentioned above, one could insure that the integrator used as a reference was itself stable. The line time of the apparatus is the fraction of time it is able to detect the presence of an event. During the period in which information about an event is being recorded the apparatus gated off, and is unavail- able for further event detection. ‘Te another event trigger occurs during this period, it will not be recorded. In order to correct for the number of event triggers lost in this way, a scaler measured the output of the fast logic at all times. Another recorded the output only when the event recording apparatus was gated on. The ratio of these scalers is a measure of the live time. A small live time might indicate that the beam intensity is too high, producing a large number of spurious triggers, or accidentals. It might also indicate some kind of failure in a counter. Examples include light 24 “leaks, or a failing veto counter. We collected data at the highest beam rate consistent with a live time of at least 95%. There. is a natural tendency for the cyclotron beam to form bunches due to the stability criteria of the frequency modulated mode of operation. As the beam exist from the machine, it is in the form of narrow high in- *. tensity pulses, perhaps 7. nanoseconds wide. In order to perform coin- cidence experiments it is necessary to have a beam with less intensity and greater duration in order to minimize the effects of accidental triggers. In order to achieve this condition, the beam exits the machine a little at a time. With care, the machine operators are able to release about 95% of the beam. The resulting beam spill still contains a spike due to inefficiencies in slow extraction. This spike, containing 5% of the beam, can be gated out. We had two ways of monitoring the ratio of spike to spill, which we at- tempted to maintain at a level of 1/20 or less. One was to use the beam structure display on an oscilloscope; from this a crude measure of the ra- tio was made. More accurately, a separate beam integrator system measured both components of the beam, spike and spill. Comparing this with one of ‘the other. integrator systems, which were gated so as to measure on the spill, enabled us to monitor the fraction contained in the spike. In summary, during each hourly check we derived and tabulated the: 1. relative ion chamber performance; 2. triggers per unit of ion chamber output; 3. live time of the apparatus; 4. relative amount of spike and spill in the bean. © 25 2. 4-Hourly and 8-Hourly Checks Figure 3.2 if a typical 4-hourly check sheet. Four kinds of information are of interest here: 1. checks to insure that equipment settings are at their nominal values; 2. qualitative checks on counter performance; 3. checks on spark chamber performance. Item one entailed a quick check of the logic electronics for misset switches, loose cables, etc. At this time the magnet settings were _ checked, and also the steering of the beam, which was monitored by split fon chambers. Finally, readings of the high voltage power supplies were made and compared to nominal values for consistency. Each counter in the experiment contained a light emitting diode. In addition to its uge as a timing aid, the diode served as a crude refer- ence against which the performance of the phototubes was checked. Every four hours, the diodes, driven by a pulse generator set to a standard voltage, were turned on and the output pulses of specific phototubes were photographed. Typical pulses are shown in Figure 3.2. The pulses were checked against previous photographs for consistency. Substandard pulses were a clue to either power supply drift, phototube fatigue, or perhaps physical damage to the counter. The last item served to monitor the condition of the wire spark chambers. We ran visual checks of the output signals from the spark chamber wands on an oscilloscope. AE HOURLY CHECK LIST 26 SLEc Tle! Baw ore, ADJUST ATLAS TO CENTER BEAM ON BACK SIC . ee NESTOR ADONIS ~49: 8) ACHILLES 27.22 ATLAS __Ro¢s— SPLIT-ICH_CuaArECLY SCALE SETTINGS: MOVE FRONT FROUT VOLTAGES METER READINGS OF H.V. SUPPLIES EVERY OTHER 4&-HOUR CHECK, DO A COMPLETE H.V. CHECK. WAS THE COMPARISON SATISFACTORY. WHAT WAS THE GREATEST DEVIATION. WHICH COUNTER. WAS IT > _ ARE ALL LINEAR GATES, AND is THE 'TAC', AT BLACK-DOT SETTING ——— . . . 5 SCINTILLAIOBS STOP TRE RUN, TURN ON THE DICGDE- DIODE PULSER. TAKE POLAROID PHOTOS CTRIGGERED ON THE DIODE PULSER) OF COUNTERS: Sl, S2, Al, A2, HE-ANTI AND DE/DX, ALL_PHOTOS. TAKEN_AI_THF_ INPUTS TOQ_THE DISCRIMINATOPS. STANDARD *SCOPE SETTINGS: fi.2 VOLT, 198 NS. / CM 25 en ewe er ae ee ee F ~ S.1.C. TILL A MULL If CETAIPES, SHARK DATE AND TIME Of: STRIP CPARTS. . Al pate: 6/ J TIME; ZRBQL WHO YOU! <7 r7 RUN? 3 3c Fer <> ) Nong Offsets . techewcter ow Brew cell APE MHeteRs texo -. | BACK . ——_— FROM THE PROTOTYPE VOLTAGES. fu. ] EXCEPT FOR DE/DX WHICH IS %S =) _f-1 VOLT, 18 NS. / CM, 4 i HAVE YOU NOW TURNED OFF THE DIOD ue PULSER ___._ Bini _ . | Bm 2/2 BECOPD IRE G2e Mae 7 Gi NAL 2 Gr NAs[ G2 NAL TAN ANN A/SumM SETTIUGS rr weed WN Cerca Ros V0 CIMPUT_ATIEN [2x10 VW - 1k 5 NS x_ouTPuT GaIny b_-__@Z1 __ J_ tH _ te _ BS SN —— - CF_ALL /cue Gi WAZ <4 G4 NAZ1G2 NAZ ase Ane NANOAMPLIFIERSs | _— Y arpo Qe bax sm | ee YY VU X70 Z LERS. | ; ‘s Y, Figure 3.2 4-Hourly Check 20d. a/ On the order of ten pulses were observed for each 24 wands. Of interest were missing fiducials, weak or missing signals, and double pulsing. This information, plus a mentally averaged pulse height for each wand, was recorded, and appropriate action taken for troublesome wands. If many wands were weak this indicated that the gas purifying system needed attention. Multiple pulsing suggested either a defect in the wand caus- ing reflections, a missteered beam, or a large beam halo from an over- - intense beam. The 8-hourly checks were performed at every other 4-hourly check, and . added a check of all power supply voltages to the above. Figure 3.3 shows a typical 8-hourly check list. We would be remiss if we did not report that, unaccountably, this procedure did not catch the only power supply failure of the experiment. It occurred during one of the weekend cyclotron shutdowns, a six hour period during which most of the apparatus was left running, with one somewhat sleepy experimenter left to keep watch. The power supply self-annihilated, burning part of the experimental shack, and was observed only accidently, while in flames, by one of the experi- menters making one last check before retiring. 3. Preliminary Analysis After each run, a rough analysis of the data tape generated was made to determine the general quality of the data, and aid in decision making for future data collection. This was especially helpful during the initial phases of the experiment. Quantitative information was obtained for spark chamber efficiencies, and general information about the data, for example, whether any signal was present. PxHoratTuse \VDLTAGES | | Owes, DE ZENER ORANGS =1 | Gray = 2 MISc, T1 = 221s | 4 = 2164 4 = WUSHa.s]| AZ = 236 “+2 = Z22is Z2 = 2 2 = 4SB.A $2 = 2Z2ZZBu% 7T3 = 2548 3 = 2354 3 = SjI2.f [SiM*B2= Zri0S omt= 2496 [NF 2524 Y= ay. ¥ | AL = 2274 DMZ2= 2uge | 5 = 2467 S.= _yus.o}] si = 2yoy4 DMB= 2ZFHO | 6 = 2323 G6 = YUse.3 [siaat = 24ON Dumas 2435 |z = 2344 2 = HH6.% OM Ss - 2548 | dex = 0 DM C= 2694 _F 4 472794 PM 2Z= 226 He Counus, Swre PM B= 2216 jebve 582-34 PMH=E 22\6 2 585.16 PMS = 22796 2 S8t, &S AWT\ L= 2g0} 4 Sou. UG ANTAL 2= 204 jaw 92-48% ANTI 3 = 2644 Le 5S SU.FC exy t= SIE FA ~ OL — =. , _ExY B = Figure 3.3 8-Hourly Check . ate iets 29 “During production running this was not done for every run, but served only as a periodic check on overall system performance. 4. Calibrations During normal shutdowns, accelerator maintenance for example, calibra- tions were made of the integrators and the helium counter. The integra- tors were checked using a standard current source (see Appendix N). The helium counter was checked against an Americium-241 source (see Appendix FY, which served as an absolute standard. Making a straight line fit to a linear portion of the energy spectrum, one could extrapolate this line to a specific channel in a pulse height analyzer. The gain of the sys- - tem now fixed to a known value, one could adjust the pulse height of the argon glow lamp if necessary. 5. Information Collected Table 3.1 summarises the information collected for each event. A data (20) was used to store an event. The buffer, locally known as Alpha-63, buffer stored two events, a total of 512 twelve-bit words, which were subsequently recorded on magnetic tape. _ Some bits in the system were hard wired at various levels to fixed val- ues, During the analysis, these hard wired bits could be used to monitor the efficiency with which data was transmitted to magnetic tape. The time-of-flight, photon converter and absorber pulse heights, and differential pulse height counter information was obtained from 9-bit digitizers. The helium counter pulse height was obtained from the output of a 400 channel pulse height analyzer. 390 Alpha-63 Word (12 bits) 67 - 130 131 - 136 137 139 - 255 Contents Event number, Ridl Latches Photon counter spark chamber wands Helium detector spark chamber wands Six ADC's - Run number Sealers Table 3.1 Alpha-63 Output 3] Figure 3.4 is a typical run sheet used while taking data. Counter posi- tions, times, and the electronics configuration were recorded before the run, and the nominal beam level noted. At the end of a run, the following items were gathered: 1. Time, at the end of a run. « 2. <A paper copy of the helium counter pulse height spectrum, as well as a photograph. 3. Certain scalers were recorded by hand. 4. A fake event was accumulated, and all of the scalers printed out on a typewriter, subsequently fastened to the data sheet. 5.. Barometric and atmospheric conditions. For various checking purposes, we studied larger cross section reactions with our equipment. Table 3.2 mentions them and gives the number of triggers gathered for each type. Table 3.3 shows the center of mass angles at which data were taken, for each beam energy. In particular 90° points were taken at each energy so the energy dependence of the cross— section could be studied; this angle also was easiest to compare with other data. 32 Run Interval Reaction Energy 130-259 260-367 Sum, pd > Hety 383 31,416 31,416 mom 462 592,143 887,542 1,479,685 Hoon 558 115,872 115,872 pp > pp 462 34,406 * 1,500 35,906 pd + Hen? 383 26,009 26,009 moon 462 1,230 1,230 op + He'd 324 9,976 53,070 63,046 dp > He?y 420 | 27,723 27,723 pp > dn’ : 558 ——-&4,005 44,005 TOTAL "1,824,408 Table 3.2 Kinds of Data Collected - 33 HELIUM CENTER OF MASS ANGLE Beam Energy 45 60 75 90 105 120 135 462 x x Xx xX Xx x x 571 x Xx 377 © Xx te. TABLE 3.3 - Kinematic settings for which data were collected. ne mS , | KEACTICN_pd > he oe RUM 29K TAPE? JOG w7tZ4R LO pare 22 Muy . J — START _O%. 3S TIME: STOP COMMERTS : Chevscdencaccecccecccccdcsecsncccescocsesasceecasewcseesase errr errererererrere ry? Serer rTP eee eee eee eee eee DOO Oe HAO HHHOSEH SEE THHHRESOHEHMEOSHESEHRHHETOSH SHE FO TERS ETAS EE Cem ewer ewreeeesesesseraane sees sees woeerecnesareene - COCO E REF ORHSOS MOSH HEHHEERESEHSE ECHO HE HTEBHETERESHAHESELEHSREOe POCO OHHH EES ORES ERE AHESHESESHESERO HEHEHE SHS HHTOOHERSETHE OEE OSS Figure 3.4 Run Sheet sno 16 2:8 xio~ © Tc . mec ScALER SCE wo x ror L02_ pram enecy_ S?-oev - 10 . . x10 _ -G1 THETA (x) © pe)" \ He POSITION: co tira (IV3 PR (un ny! are . DELAY BOX SWITCHES UZ=GAM, rca, So sia" ns a i : TAC; _ : STOP ns Si___. $2@_ w {s G1 G2 BE Goel, ns GIG G2C__ DX ob _ axiia ns Oo CO ALSU BAROAMP 021: G1 G)) W3CES te “G2 E> OxeT Ss V4; 1 2 Oo. uit: ems) On _ Naa: G2 (Hite G1 DD :G1 G2 gid wan, ot G) ED Berets Cow Ce DT ba — Be es ie ACIER Ku event @H744l a) Buell 251 22ST. 291 OW? ve 226th watian ne $8782L 9 6608 5 ©7683. 51 S7olgul s2_18€ 132% _ 181-87 TSI 2420584 Ts1-3/_ 166870 TEI- TTS fl §911578 62 §662146 ‘93 “$gg2371 a4 996172 ee 5 g2 a7 we 3eels a8 sas2poe ag 8733824 16 totter rr sagnon7 fs aguitse 59 24 #934499 25 gp2g257 26 27 1284588 28 1576286 29 gg49f32 39 $222877 31 & P1S4389 41 9918876 42 9683325 43 MA19943 44 Bagese7 45 sug2aug 32 168987 35 DATA ANALYSIS In this section the procedure is described by which the total of about a million triggers were reduced to a set of angular cross section val- ues. “tt was’ convenient, for economic reasons, to separate this process into three categories: | 1. Data formatting, photon vertex reconstruction, helium track reconstruction, spark chamber efficiency determination. 2. Geometrical reconstruction, kinematic fitting. 3. Cross section extraction. We divide this discussion into eight parts: In Part 1 we discuss the method of storing various constants useful in the analysis of a run. Part 2 outlines the structure of the data sun- mary program, which reformats the raw data, calculates chamber efficien- cies, and uses chamber dimensions .to construct coordinates relative to the chamber plane. Part 3 explains the construction of various kinematic and geometric quan- tities, and the procedure for generating a x2 for each event combination. In Part 4 various cuts are examined. In Part 5 we describe the calculation of various efficiencies, and Part 6 outlines the calculation of cross sections. Part 7 gives details on the various background subtraction procedures. Finally, in Part 8 we discuss the errors incurred in the calculation of cross sections. More detailed discussions of various aspects of the analysis can be found in the Appendices. 36 “1. Constants Approximately 70 constants (where by constant we mean a function of run number, but hopefully not of time) were collected for each of about 300 runs. Included were quantities like target thickness, distances from the target to each photon detector, presence or absence of the differential pulse height. counter, reaction type, etc. It was decided that this in- formation would be gathered in one place and stored in the computer dur- . ing the data analysis. During the data analysis one needed only to specify a run number, and all of the information pertaining to the run was automatically retrieved. By reducing the amount of information one had to handle manually for each run, it was hoped the number of errors resulting would be reduced correspondingly. 2. Data Summary Program The first of three stages of analysis performed four functions: te. 1. The raw data were unpacked from 12 bit computer words and reformatted into 60 bit computer words. 2. Spark chamber wand scaler values and survey information were combined to produce coordinates in the spark chamber frame of reference. 3. Photon vertices were derived from shower tracks in the photon counter spark chambers. 4, Spark chamber efficiencies were calculated. The raw data came in the form of 12 bit computer words. The first opera- tion performed by the data summary program (DSP) was to unpack these 12 bit words and from them construct 60 bit words, representing scaler val- ues, ADC's, etc. This was primarily format conversion. 37 ~ The spark chamber wand scaler values and the physical dimensions of the spark chambers themselves, were then combined to produce coordinates relative to the spark chambers. Appendix G describes the procedure for the helium chambers. Appendix E describes the determination of the shower origin in the photon chambers, and the assignment of errors on these positions. The following information was produced event by event, and summarized in tables and graphs for the whole run: 1. Histograms of the number of sparks on each wand, excluding fiducials. A histogram displaying the number of times a specific set of chambers contained sparks, as a percentage of the total number of triggers. Histograms of the distance from any spark to a fitted point or lines in the helium and photon chambers. This was taken as a measure of the goodness of fit. A table of individual wand efficiencies for all wands, based on suitably defined "probe" events for each set of chambers. Histograms of the spark locations for each wand, and of the number lacking fiducials. Plots of scaler ratios, performed every N events, where the user specifies N. Refer to the section on data col- lection for details of these quantities. A grid showing correlations between various fast logics bits. Finally, some of the hard-wired bits were checked. Some bits in the special purpose computer were fixed to be specific values. These were 38 “later used as a check of the fidelity of transmission of the data to magnetic tape. A run was abandoned if too many data transmission errors were found, indicating hardware problems in the data recording systems. In practice only about two runs were lost in this way. Appendix I gives some details of the structure of the data summary program, and a table of its output. Spark Chamber Efficiencies A. Helium Chambers. The procedure for calculating chamber efficiencies involved first obtaining a subset of events called probe events which were used to investigate the efficiencies of individual gaps and wands. A probe event is defined as an event for which at least three of four gaps have sparks, and a track constructed from the sparks extrapolates to the active area of the target. The latter con- straint is to ensure that the probe events are in fact due to particle tracks, and not to spurious sparks. Given a probe event, one makes the following test on an individual gap: 1. If there are sparks in all four gaps, the probe is a probe of any gap. Increment a scaler for each gap. 2. If one, and only one, gap has no spark, the probe is probe of that gap. Increment two scalers, one a scaler indicating a probe event, one indicating a failure for a particular gap. The efficiencies of the individual wands are measured by noting the presence or not of a count of each wand for probe events. 39 The inefficiency for a wand is then: ee Number of test probes with no count of a wand Number of test probes The wand efficiencies are then used to construct the helium cham- ber efficiencies. B. Photon Chambers. The procedure for establishing the wand and gap inefficiency for the photon chambers is identical to that for the helium chambers in all but one respect. The constraint that a track constructed from the sparks project back to the active area of the target can no longer be imposed. Here individual tracks from the photon shower are used to form probes, and these in general do not pro- ject back through the target. Other than that, the procedure is the same as for the helium chambers. The assumptions made for the efficiency calculations are: 1. The efficiency calculated is independent of the kind of particle being used to make the probe, and in the region of interest hére, independent of the energy of the parti- cles. 2. For small numbers of sparks, on the order of three or four, the efficiency is independent of the number of sparks. 3. Geometry-Kinematics Construction of kinematic quantities, using survey information and equip- ment calibrations, was performed in the second stage of the analysis, GEOKIN. Appendix H outlines the program flow of GEOKIN. 40 “In order to calculate the azimuthal and polar angles for each of the final state particles, a trajectory is first constructed using a coordi- nate from each helium chamber. The intersection of the trajectory with the target midplane is taken to be the event origin. A beam direction is constructed through the origin. All coordinates are now corrected for any systematic beam variations. Definitions of the angles are illustrated in Figure4.1. The helium - polar angle is the angle between the trajectory and the corrected beam direction, . The azimuthal angle is the angle between the projection of _the trajectory on the target midplane and the horizontal plane. The azimuthal and polar angles for the photon are similarly constructed, using the event origin and a coordinate from one of the photon detectors. The observed helium energy was calculated using an expression of the we form: T =Ae oO where x is the helium detector pulse height, corrected for any position- al dependence. T, is the helium kinetic energy at the surface of the detector. The kinetic energy at the target origin was obtained by cor- _recting Ty for ionization losses incurred in passing from the target to the detector. The expression used for this was of the form: e “3h¢ qT = Cy + eT, = Co where qT. is the helium kinetic energy at the target origin. Two sets of c 's were used, one set for those runs using, and one set for those 4} p TO ee et om weg |DUILON | dP wipag jonjoy a Oe ey ae ee 42 “runs not using a 1/8" differential pulse height counter. Details of the method of calibration of this counter are found in Appen- dix F. The energy resolution of this counter was on the order to 3% HWHM, or a momentum resolution of 1.5% HWHM. Corrections were made to the nominal beam energy for systematic angle and energy dispersions. Details can be found in Appendix ‘A. Using the cor- . rected beam energy, the helium kinetic energy and the measured angles of the photon and helium particles, a chi-square was generated. Details of the procedure are found in Appendix K. Using momentum and energy balance, we can determine up to four unknown kinematic quantities by knowing the other. twelve for a two body reaction. For example if sufficiently well measured, one could perform this experi- ment by knowing only the properties of the beam and target, and one final state particle, by doing a missing mass experiment. In the language of bubble chamber physics, this is a zero constraint fit, or O-C, meaning that the reaction is not overdetermined, or, equivalently, has no redun- dant information. Essentially one has four kinematic equations and four unknowns to solve. For each additional kinematic quantity measured, one overdetermines the ‘solution by one, increasing the C of the fit by one. One now has more equations than unknowns. The technique for solving the equations is to adjust the unknowns until all of the equations are optimally satisfied. This is the essence of the kinematic fitting procedure. 43 “Procedures for producing both 2 and 3-C fits were used. 2-C fits were employed where the energy of the final state was not known. 2-C fits 3 served to analyze a + p > He’ + D data used to calibrate the helium de- tector. For the pd > Hey data a 3-C fit was employed. We assumed the photon ' energy not to be known. Figure 4.6 shows a typical x2 plot. The missing mass corresponding to the photon side of the experiment was computed in two ways. The first method computes 1) mm” = w2 + 2 (mE - E,E, + m,E,). + 2 P,P cos 8 21 °~«271°3 2°3 1°3 13 . where ye = m7 + M,? + Ma”. Index 1 refers to the beam particle, 2 to the target deuteron, 3 to the helium particle. 813 is the angle between the helium particle and the beam particle direction. The second method uses the final particle angles only. Pas the helium momentum, is calculated as:. P, = P,/sin (8, — 63) 2 Using By = Ps + My’, and substituting into equation 1), we obtain the - desired result. The center-of-mass angle of the helium particle was calculated to facili- tate binning, and was used to calculate the kinematics of an event by an independent method from the x2 procedure described in Appendix K. Since each lab photon angle corresponds to a unique center of mass angle, it was used to compute the center of mass angle. In what follows, primed quantities refer to center-of-mass quantities, B and y are the velocity 44 ‘of the center of mass and 1/7182, respectively. Defining the following quantities: | a ar ee wey Ps tan 6, + P, xe wy PoE, tan’9, y= Beye? tan’6, - py *. the cosine of the helium center of mass angle is calculated by 2) cost; = (-x + sign /,2 — 4wy)/2w, where sign = tand,/|tane, |. 4. Cuts _ Several kinds of cuts were placed on the data, both to enhance the fore- ground-to—background signal, and to make the analysis more efficient. The following cuts were made: 1. coplanarity 2. vertex containment in target volume 3. containment of He? track in. back wire chamber 4, dE/dx in differential pulseheight counter 5. time-of-flight’ and helium pulse height 6. helium angle and energy The two-body reaction pd + Hey is required to be coplanar. A cut of +. 11° was made on the coplanarity angle. Typical coplanarity plots, after applying dE/dx and target cuts, are shown in Figures 4.2, 4.3. Figure 4.2 is a favorable setting, 4.3 a difficult one. Figure 4.2 shows the inter- section of the reconstructed helium trajectories with the target midplane, and indicates where a cut might be placed. Intersections outside of the indicated cut are due to spurious sparks in the helium wire spark chambers. 50 40 10 45, ses eek ea eee ek a | ee ee ee | a ee Lc eae (and ne hate ee eee ae sane a el ce ee eo coovatoselniivintmt Olea bea a pe bape ba Lt ee -40 | -20 0 20 40 DEGREES Figure 4.2 Coplanarity after a target cut, a DE/DX cut and a helium energy cut have been applied. Data is for a 90° cm setting, and is one of the easier settings to sepa- rate background and foreground. 46 sk oe i TRC rrsr Trrrrs 268s ORB OOS eee ee ; bag esr ~ ! 20, . be a 4 4 vl , 155 oop. “ COUNTS so i Si “20 re) Le yd . FTERUREERESEREAEN ERE EROS RES. -15 -10 5 10 15 20 DEGREES Figure 4.3 Coplanarity after a target cut,a DE/DX cut and a helium energy cut have been applied. Data is for a 45° cm setting, and is one of the more difficult runs for back- ground separation. 10 . 7 @) ied id . - . . « . . . -— iaeeamenal ~ nen} . we . . - . - - 100 | -5 O , 5 lO Z-vs -Y TARGET. Figure 4.2 Reconstructed Event Origins 48 “sparks in the helium wire spark chambers. J Local coordinates, for track-associated sparks in the wire chambers in the He? side relative to a chamber-centered coordinate system, corres— ponding to a given photon detector setting are restricted in position. A conservatively placed cut was placed around this region. A differential pulse height counter was employed for those settings where _the helium energy was high. Figure 4.3 is a distribution of pulse heights from this counter; the position of a conservatively placed cut for separating doubly ionizing from singly ionizing particles is indi- cated. This cut alone eliminated almost all triggers not containing a multiply charged particle. For those runs employing the 1/6-inch liquid deuterium target the energy of the helium was too low for the differential pulse height counter to be used. The time-of-flight and helium detector pulse height information is correlated. In the energy region of this experiment, and for the particular experimental configuration used, the data for various reac- tions fall into well separated bands, as illustrated in Figure 4.4, which plots the time-of-flight ADC versus the helium detector ADC. Also indi- cated is the position of a possible cut; the triggers containing multi- ply charged particles lie above the indicated cut. As a check of this, only the upper band remains when a cut is nade on the differential pulse height counter so as to include only multiply charged particles, for those runs employing the counter. Thus the differential pulse height counter and the time-of-flight and helium pulse height information pro- 49 320 -— — t a ieee | 24014 \ a?) Cc —| 160 F- 80 | ee O ‘ep ) @) dE/dx Figure 4.3 Differential Pulse Height Counter Spectrum TIME OF. FLIGHT 59 Figure 4.4 Time-of-Flight ADC Versus Helium Detector ADC 51 “vide equivalent amounts of information. The differential pulse height counter was used where the He? energy was greater than 100 MeV (about 802% of the runs) to reduce the trigger rate From background processes. Finally, a loose cut was placed on the correlated values of the helium lab angle and ft energy. This cut was effective in eliminating the back- ground processes ptd-> Be + o (n° + yy) which, for a given photon detector setting, produced a much broader spectrum of angles and ener- gies because it is a three body final state. 5. Efficiencies In order to calculate crosé sections we must first determine the effi- ciency of the apparatus for detecting an event of interest. Only after this efficiency is known can we transform the raw number of events pro- duced by the data analysis into cross sections. The efficiency is in effect the probability that an event of interest will be detected. The following factors will be considered in determining the overall de- tection efficiency: A. Spark chamber efficiencies B, Photon conversion efficiency C. The geometric solid angle of the apparatus D. He? breakup en route to the helium detector, and subse- quent breakup in the detector Ee Counter and electronic efficiencies * Spark chamber efficiencies (Point A) have already been discussed, and *o.f. Data Summary Program, Part 2 “will not be considered further. Photon conversion efficiencies (Point B) 4 are discussed in Appendix D. Point D is discussed in Appendix F.6. A. Geometric Solid Angle The calculation of the geometric acceptance for this experiment was performed using Monte-Carlo techniques. These techniques . have been discussed in detail elsewhere, and will not be elabor- ated upon here, 829) The apparatus of this experiment was designed so that the geo- metric acceptance was determined solely by the photon counters. Total acceptance by the helium detector for any photon counter setting was one of the useful properties of using a large plastic detector: To be more precise, the solid angle was determined by the conversion counters located behind the 2X, conversion slabs, and by the finite target size. The wire chambers used for photon shower track delineation were made sufficiently larger than the trigger counter to minimize effects due to loss of tracks from the edges of the chambers. Monte-Carlo studies showed this effect to be less than 1%; we therefore ignored it. The center-of-mass geometric acceptance is the quantity of in- terest for computing cross sections, and henceforth is the quan- tity referred to. The calculation proceeds as follows: 1. Using the distance of the trigger counter from the pivot, the target size, and the conversion counter size, we 53 determine a maximum azimuthal angle, and a minimum and maximum center of mass angle, 0, ,85- 2. Within the region 26-|@, - 6 we generate pd > He*y ils events uniformly. 3. For a success, we inquire as to whether the photon con- verted. If it did not, label the trial a failure. . The geometric acceptance, in steredians, is then Q = Naccess * 20° le, ~ 611 /Neeials The relative statistical error is determined by assuming that the successes and failures obey a binomial distribution, and is given by: 1 . : X . Nerials —- Nsuccess Nu. -1 success trials AQ/Q = In order to minimize the amount of computer time used, it is ad- vantageous to narrow down the range of 6, 6 initially in order to maximize the number of successes. For each setting 40,000 trials were made. A typical geometric solid angle acceptance was on the order of .02332 + -00029 stera- dian. Figure 4.5 illustrates a typical differential geometric solid angle. Details of the program structure can be found in Appendix J. An independent check of the geometric acceptance calculations was (58) 3 3 made for the reactions pd > Hey and pd > He n° (n° > yy). ACCEPTANCE .002.f— T 1 r 1 -0020}— | 0 13r— 00Cfre— . He? CM ANGLE Figure 4.5 Typical Solid Angle Acceptance 205.0 55 The results agreed on the one percent level. Additionally, one can compute the lab solid angle for a two-body process rectangular detector using the formula) tan(a) = ab/(c(c2 + a” + b2)%) where a line from the source, of length c, intersects a corner of the detector, of size a,b. Special cases, checked by employ- ing this formula, compare well with the Monte-Carlo calculations. Electronic Efficiencies The electronic efficiency is composed of individual counter effi- ciencies, the beam gate, and the total system dead time. The latter two factors were monitored constantly. The counters used in the event trigger were all more than 99% efficient; their con- tribution to the inefficiency of the system is taken to be negli- oo gible. The spike-to-spill ratio (cf. Section 3.1) of the beam was moni- tored with a set of scalers. If properly tuned, the spike was never more than 5% of the total beam dump, and was typically 22. The system dead time (cf. Section 3.1) was determined by scaling all event signatures, as well as those occurring when a system ready gate was set. The dead time was as large as 20% for some settings, although typically it was less than 52. 56 “6. Cross Section Calculation The differential cross section for a given setting is determined by the relation where: 8: N(0) do (8) /d2 EfE Thus N(8) = do (8) /da x N, x Eff x Ny B center of mass helium angle number of events after background subtraction differential cross section at a center of mass helium angle 6 number of beam particles = 2.85 x 107 x ORTECS solid angle x electronic efficiency x spark cham- ber efficiency x He? breakup x photon conversion efficiency number of target particles = N, x t x o/2 N, = Avogadro's Number = 6.023 x 1073 t = target thickness p = density of liquid deuterium, which was about .165 em/em> do(@)/49 = N(0)/N, x BEf x N, In general each run could have different values of each of the factors making up the differential cross section. McDonald © has shown that, assuming the number of events generated by a given run obeys a Poisson distribution, the value of the differential cross section that maximizes the likelihood function L(x) = TT, e /(W,)! 57 “is given by where n, is all the remaining factors relating X, the differential cross section, and N,. Thus we compute the cross section for a set of runs as the ratio of the average number of events per run divided by the average efficiency. The _ relative error in X is given by 2 2. 2 2, ENG (Ax/x)“ = (Eni“(2 EY .))/(2ni)" + 2 i j 451 (ZNi) where i labels the run, Ei,j is the relative error of the jth quantity, where j includes errors in: target thickness beam total efficiency Pw Ne. Ld t background subtraction 7. Background Subtraction The background subtraction was performed using a method of ratios. Using a center of mass angular distribution derived from analysis of the reac- tion pd > He?n? (37) (the largest background component — see Appendix L), background events were artificially generated using a Monte-Carlo program. These events were subsequently analyzed using a pd > Hey hypothesis, and applying the same cuts used to analyze real data. The resulting chi- square distribution is that for the pd > He n° background only. The method of background subtraction proceeds as follows: 58 1, Determine the ratio of events with 0. <x? <10 to that with 10 <y2 <20, call this R, for the Monte Carlo events. 2. When extracting a cross section, tally the number of events with 10 < x2. <20, call this Nee The number of real p + d+ He? + y events is then: N= (Np - R * Ny)/(1 - k - kR) where N = total real events N; = raw total events - i.e., events with 0. <x2 «10 Nz = number of events with 10 <y2 <20 R = ratio of foreground to background as determined by Monte-Carlo generated events k = fraction of pd > He>y events with x? > 10 The R's depend on the specific geometry of the experimental apparatus, as well as any cuts applied during the analysis to suppress background. Dif- ferent R's were generated for each angular setting. Table 4.1 lists the ratios used. Figure 4.6 illustrates a typical x2 distribution for 90° cm ‘data. The positions of the bins is indicated. Figure 4.7 illustrates a x2 distribution for 45° om data where the separation of the 1° background _is more difficult. 8. Systematic Errors ‘The only systematic error in this experiment known to be larger than a percent was the thickness of the thin (nominally 1/6 inch) liquid deuteri- um target. During the course of data taking an effective change in thick— ness of about 25% was observed, as indicated by the target monitor rates (cf. Appendix B). 59 O02 Ol | Odi | 7 i : lp | i | | | 7. ; a th Td : | to | | | : | [ i} - Botdky, 9 3 sf . $ bd Be yep wo 006 . Ol Od O£ Ov 60 Beg WO (oy LOZ UoTINGTIIASTA azenbs-ty9 TeOTdAL Oz! as aan8tq oz Ol | tl uA Ol Od O£ Ov 61 Beam Energy Lab Angle of cn Angle MeV y-Detector of He Ratio 462 34° 135° .258 + .014 44° 120° | 140 + .007 59° 105° 1184 = 009 71° 90° 384 + 023 86° - 75° .657 4 035 103° 60° - .652 + .034 420° 48° 1.350 + .065 377 . 7° 90° .261 + .014 571 — 71° 90° .372 + .021 Table 4.1 Background Subtraction Ratios, Each term is the ratio of events with 0 < x2 < 20, using Monte Carlo generated data. 62 - Though a change in the effective thickness could be due to bubbles in the liquid, none were observed when visual checks of the target condition were made. Other indications are that.the change was in fact due to a change in the geometry of the target. The thickness of the thin target was measured at liquid nitrogen temperatures subsequent to taking data, and a bulge of about 25% was indeed observed. Data was taken at one photon counter setting using both the thick and thin target. Using the nominal thickness of the thin target yielded cross sections again about 25% discrepant from the thick target data (the moni- tors indicated no more than a percent of less fluctuation of the thick target thickness, again born out by a measurement at liquid nitrogen temperatures). Using data from the monitors, corrections were made to the thin target data on the assumption that the target bulged. The other possibility is that the target was at one point effectively too thin. This, however, is not consistent with the thickness measurement made, or with the discrep- ancy in the cross sections calculated. Additionally, it is hard to imagine how the target could contract. The pressure of the gas buffer surrounding the target was rigorously the same as the liquid deuterium inside the flask. The only additional source of pressure would be due to the head of liquid leading to the flask. This presumably would produce bulging, if anything. s 63 RESULTS In this section we present the results obtained from the data analysis discussed in section 4. Seven data points were obtained at an incident proton energy of 462 MeV. This is the peak energy at which A production might play an important role. This energy is calculated by assuming that the helium can be considered to be made up of a proton and a spec- -tator deuteron. As we will discuss in more detail later, this is almost certainly not the correct picture. One data point was also obtained for \ an incident beam energy of 377 MeV, and one for 57'1MeV. For purposes of comparison, we also present data, appropriately scaled in beam energy to correspond to this experiment, from a hélium-three photodisintegration experiment performed at the now defunct Cal Tech 1.5 GeV electron syn- chrotron. ©9?9©) These are the only data available providing a complete angular distribution in the appropriate energy region. The usual reci- procity relations-are used to invert these data for comparison with our data. The results are shown in Table 5.1, where numerical values of the differential cross section for the reaction pd > He>y are displayed. The helium center-of-mass angle was computed using the photon lab angle and the beam energy. The errors quoted are statistical. Also, systematic corrections have been applied in particular to the two points for the thin target. In Figure 5.1 we plot the corresponding angular distribution. On the (5,56) 64, the inverse process. Data for the same plot we show the data inverse process have been inverted using the detailed balance relation- ship (cf. equation 4, Introduction), in order to facilitate comparison. , Beam Energy ' MeV 462° 462 462 462 462 462 462 462 377 571 Target Thin Thin Thick Thick Thick Thick Thick Thick Thick Thick 64 Photon Helium Lab . . ch Angle Angle 34° 135° 44° 120° 44° 120° 59° ~ 105° 71° 90° 86° 75° 103° 60° 120° 45° 71° 90° 71° 90° TABLE 5.1 Angular Distribution for pd > Hey at 462 MeV. do/dQ 6.80 + .54 5.27 + .60 5.78 + .51 2.50 + .17 2.16 + 212 1.48 + .10 774.11 152 + .06 2.90 + .64° 1.10 + .098 65 a= yHe od ° = pd— yHe® | qo (pd> Hey) x 10°*cm/Ster p 2 | a ; = OO . af = 50- 1 *< 4 s} SC = i O|O ae 4 7.) in . | | mo, o.olL1t itt 30° , 200 se? 150 % p e@ Oy Gp Y Figure 5.1 Angular Distribution for pd» Hey , He? + pd. The latter reaction has been inverted using the detailed balance relationship to facilitate comparison. 66 7 | _ yHe°- pd e (90° om) ae? | . = pd- yHe he ee ee - i : n 6 _ © | = A a 3 4b - x ' | i . é- | @) I | . | j | { — 300. 450 600 T, (MeV) Figure 5.2 Energy Dependence of the 90-Degree cm Data 67 values of the inverted data are displayed in Table 5.2. The center-of- ‘mass angle of the deuteron in the reaction He? + pd corresponds to the He? center-of-mass angle in the reaction pd + Hey. The error bars for the reaction He? + pd include statistical errors, spark chamber effi- ciency errors. Figure 5.2 shows the energy dependence of the differential cross-section ata center-of-mass angle of 90°, again compared with data from the in- verse process. These data would be expected to show some effect of A (1236) production at a proton kinetic energy of ~ 460 Mev, if such isobar excitation plays a significant part in the process studied. Finally, we give here the results of an analysis of our data with regard to the reaction pd > He?n®. While details of this analysis are contained in Appendix L, we include this discussion because this process was the major background, and in fact the only one considered. (The only other ee possibility is pd > He? n n° ,» and this is easily ruled out on kinematical grounds.) Also, for some selected energies and angles, we were able to (34) compare our results with previous data for T° production. This en- abled us to check our analysis programs and provided an additional check on the normalization of our data. Figure 5.3 shows the angular distri- bution for pd > He n°. Figure 5.4 shows the energy dependence of the differential cross section. Values of the cross section are displayed on Table 5.3. A more detailed discussion of the reaction pd > He n° can (64)" be found in another report. BEAM ENERGY MEV 462 462 462. ‘462 462 462 462 377 462 576 TABLE 5.2 pd > Hey data. 68 DEUTERON CM ANGLE _ 45 60 75 90 105 120 150 90 90 90 do do -61 64 1,43 2.16 2.63 4.04 7.63 2.52 2.16 I+ I+ I+ I+ + I+ I+ + He? photodisintegration data used to compare with to correspond to the reverse reaction by assuming detailed bal- ance is valid. 32 12 015 -23 -17 »35 21 -69 -20 ol7 16 The photodisintegration data have been invented X oh: no Re) po Nb wo 69 Ae (pd. He ®) x 102° CM2Ster 7 . 6 a | T _ 4 © Crewe, Ref. 34... ae in @ This Experiment . : “| 3 = Jl ! _ I | L | | 50 70 so. lO 130 150 Gue i Figure 5.3 Angular Distribution for pd > He? f° at 462 MeV. 70 G= (80° CM) x 10° CM7 Ster OG 27 1 , . wo | - ons ; : 300. 400 500 600 Tp- MeV Figure 5.4 ‘Energy Dependence of the Pi-zero Data _ ~ BEAM - "HELIUM ENERGY - ‘ CM _MEV . ANGLE do/da_ 462 i 30.0 35.0 + 2.8 462. | 40.0 35.0 + 2.8 462 53.5 39.1 + 3.2 462 | | 60.5 35.1 + 4.4 462 ; 67.5 34.2 + 2.5 462 74.5 33.3 + 2.7 462 . 76.0 34.54 1.9 462 . 80.0 32.0 + 2.5 462 90.0 28.6 + 2.9 462 104.5 | 30.5 + 3.2 462 105.0 38.0 + 3.8 462 113.5 40.5 + 3.6 462 122.5 “411.2 +. 7.8 462 . 131.5 197.5 + 13.3 462 140.5 344.1 + 27.0 377, 80.0 41.0 + 3.0 576 . 80.0 27.54 2.7 TABLE 5.3 Angular distribution for pd > He>n° 72 ' DISCUSSION The following points stand out in the data: -1. There is no discernible enhancement in the 90° data due to A(1236) production. . 2. The shape of the angular distribution for the process pd + He*y agrees very well with its inverse. es . 3 . 3. The normalization for the reactions pd «> He y agrees with considerable precision. McDonald, ©) on the basis of a study of the energy dependence of angular distribution coefficients, had concluded that A production is greatly suppressed in the photodisintegration of He>. In particular, the role of the Ml] transition in the A production mechanism, so important in the process yd + np, is largely suppressed in the photodisintegration of He®. Our results confirm these conclusions. Note, however, that our argu- ment is compelling only when taken in the context of both our present data and those of the inverse experiment. We note. that A production also 4 (36) seems to be lacking in the process yHe ~* pt, although it is prom- inent in the reactions np <> ya, 9) We also not that an enhancement due to A production is supressed in the reaction pd + He®n? 37) (ce, Appendix L), although it is prominent in the reaction np + nea, (69) ~-Why is A production not observed in the reactions yHe® <+ pd, when it is so evident in the reactions yd «> np? Consider the following diagram for the photodisintegration of the deuteron: y, e A y = N 73 _-The deuteron is a very loosely bound system, and the breakup process proceeds relatively simply. One nucleon acts almost as a spectator, .being. required only to absorb a pion from the decay of the intermediate A. The exchanged nucleon is on the mass shell, and the reaction proceeds like yN + A. Thus the energy dependence of the cross section in this process is almost entirely due to the intrinsic width of the A. « “Now consider a possible diagram for the photodisintegration of He: ig e a Y 2 t P \ \ Hee he d i Se - Isospin conservation keeps the intermediate two nucleon state from forming a deuteron. The most likely two-nucleon state is *S a: Immediately we see that this configuration doeS not behave like a proton plus a spectator deuteron. Instead, we have to consider a vertex at which the Ss) state is formed, with a virtual proton being excited to a A by the incoming photon. The virtual nature of the proton obscures the kinematics of A production, together with the intermediate energy of the *S, scattering length. . Data taken as a function of energy at 90° center-of-mass angle, shown in Figure 5.4, show no discernible evidence of any enhancement due to A production. Similar arguments pertain to the process pd > He n°: in Figure 5.4, the energy dependent cross section for this process is shown, and again one sees no discernible evidence for A production. 74 a Re - No. matter what the precise diagrams are that are used to explain the qualitative aspects of the data and predict relative magnitudes of various features, this is a new and unique test of time-reversal invar- jance;3. it does suggest that models employing the yNA vertex as a source of T-violation may not apply here. A completely different ‘set of amplitudes are called upon in these reactions than those encountered “in tests such as np « yd and tp @ yn, 7) A unique feature of the present test of T-invariance in the electromag- netic interaction is the parameterless comparison of the absolute normal- ization of a pair of reactions in a detailed balance test. There is excellent agreement, as best seen is Figure 5.2, with no parameters adjustable to obtain this agreement. This feature alone adds signifi- cance to this test of T-invariance by suggesting that changes in the magnitude, rather than the relative phase, of various amplitudes does not occur. Such mechanisms have been mentioned in tests of T-invariance such as yn «*.1 p, where total cross sections are measured and where from time to time violations have been reported, 3) and later denied. 4) All tests of time-reversal invariance employing the techique of de- tailed balance, and in particular those measuring total cross sections, are prone to normalization difficulties. During the course of data taking, considerable care was therefore taken to monitor beam and target conditions on both reaction pd > He>y and yHe> > pd, as explained in Appendix N of this thesis. In summary, we find on the basis of comparisons of both shape and normal- ization, that our data are consistent with time-reversal invariance in 75 “in the electromagnetic interaction of hadrons. Any discrepancies be- ~ “tween the reactions pd <> He>y may be due to errors in various efficiency calculations, but do not seem to constitute a violation of the size needed to explain the now well established CP violation. Upon performing a point by point comparison of the 462 MeV data, we find an average discrepancy of .03 + .07,, as illustrated in Table 5.4. Similarly, a point by point comparison of the 90° center-of-mass points gives an average discrepancy of -.09 + .10, as shown in Table 5.5 Within the limits of our errors, we see no evidence for a time reversal violation. $He-cm XyHe? 60 664 + 75 1.43. + 90 2.16 + | . 4 105 2.63 + 120 4.04 + TABLE 5.4 015 23 17 ~35 21 I+ I+ I+ I+ I+ -11 -10 12 ~17 60 (Xpd - XyHe 3) (xpd - .17 0.00 -05 Average = .03 Comparison of the reaction pd + Hey at 462 MeV with data from He? + pd at the same cm energy. The latter reaction was inverted assuming detailed balance is valid. + 224 -17 -10 .16 12 -07 “77 Proton Lo Energy do 3 do do 3_do do Mev dg! YHe dq/ Pd Cg! YHe —z0/pd) /gq/pd 377 2,52 + .20 2.90 + .64 ~.13 + .23 462 | 2.16 + .17 2.16 + .12 0. + .10 576 * (956 + .16 1.10 + .10 -.13 + .17 Average = -,09 + .10 TABLE 5.5 Comparison of the 90° center of mass points for the reactions pd > Hey, He? + pd. The arrow indicates an overlapping point. The He? data was inverted using the de- tailed balance*relationship. 73° VI. APPENDICES Ae The Beam + 1. ‘General Considerations Good resolution, based on some Monte Carlo studies, of signal from background in the reaction pd + Hey require the proton beam to _ satisfy the following requirements: ae A momentum bite of < 1% for energies from 300 to 600 MeV; De An angular divergence of < .5 degrees, at the same energies. . 8 Useful counting rates required a flux of no less than 10 protons/sec at the liquid deuterium target. Finally, practical consideration ‘dictated that the beam be compatible with another experiment already in progress. The 184-inch synchrocyclotron at LBL operates at a fixed energy of 735 + 20° MeV energy, for protons. For other energies, a copper degrader was placed in the beam. Table 6.1 illustrates the amount of copper needed for various energies for a proton beam. The point at which the beam emerged from the degrader was taken as the optical source for the subsequent magnetic spectrometer system. . Figure 6.1 shows the main components of the proton beam. Not shown are the thin window helium bags which were added to reduce angular spread from multiple scattering due to the long air path. The long path (about 80 feet) from the copper degrader to the liquid deuterium target was used to produce the desired characteristics of the beam. Dispersive elements were introduced to provide angular and momentum dispersion, and slits were used to define angular and momentum Tp - Mev 595 500 Lok 400 350 Degrader_— inches of Cu 4 - 1/2 5 - 3/k 6 - 13/16 8 9 9- 15/16 - Table 6.1 Amount of Copper Degrader Used in the Proton Beam gigs - 80 - External ‘proton beam» mm sit | Switching magnet (+18°) "Physics quads” Degrader \ Slit 2 (just outside snout, in physics cave ) Wa _Doublet 1 (Circe) Blend 1 (Nestor) (+ 23°) /siit 2 1/2 (vertical only) | Slit 3 (just inside wall \ of physics cave ) -— ,Doublet 3 ( Diana) / Bend 4 (Atlas) | (- 21°) Blend 2 (Adonis) — | (+ 23°). - Doublet -2 ( Minerva) | | / Bend 3 (Achilles ) Target (+ 21°) | | 0 100 200 Scale (inches : XBL723~2618 Figure 6.1 Structure of the Proton Beam 81 - acceptance. Following are the main features of the beam. Referring to Fig.6.1,s1it 1 determined the effective source size, and slit 2 determined the angular divergence of the beam. Bends 1 and 2 were used to introduce momentum dispersion. The momentum bite of the beam was determined by slit 3. The final quadrapole pair (Diana) produced an image of slit 3 at the target, with a magnification of about 1.8. * Tables 6.2 and 6.3 give brief descriptions of the function of each element, for the horizontal and vertical planes respectively. Starting values for the magnet currents were obtained using both opric™ and Transport.~ These programs were also used to investigate the effects of off-momentum particles. Shown in Figures 6.2 and 6.3 are typical ray traces for on-momentum protons, for the horizontal and vertical planes, respectively. Figure 6.4 shows typical ray traces for one percent off-momentum protons. = Tuning up the beam involved use of beam integrators, split ion chambers , counters and an impressive amount of Polaroid film. The direction of the beam could be determined for each element using split ion chambers. (A split ion chamber is an ion chamber with a slot in the middle. The signals from each half are compared differentially. A null condition locates the position of the beam in one dimension. ) Pictures were taken liberally to measure the shape of the beam, and compared to the calculated shapes obtained from OPTIC and Transport. The attentuation was measured at various points by using two standard beam integrators. Using the above procedures, slit positions and magnet settings were derived for several beam energies. It was then a straightforward matter to interpolate settings for other beam energies. 82 Element _*- “Funetdon Slit 1 ‘ “Determines the horizontal size of the source. " Switching Magnet Steers the beam to the center of me , the physics quads. A-small amount -of dispersion is Incurred. . : Physics Quads These are set to provide parallel - .' to point focusing at slit 2. Slit 2. _ © This determines the angular _ acceptance from the source. - Doublet 1 (Circe) ‘These dare set to produce a parallel beam between the subsequent two bends. : '. Bends 1, 2 (Nester, Adonis) , — > Both bending in the same direction, La ee Lo: “.0. . these elements provide momentum dispersion, Doublet 2 (Minerva) . - 7 Provides a focus at slit 3. Slit 3 ee or - '- (The ‘dispersion provided by Bends aa .1, 2 enables the momentum resolu- Tle — tion of the beam to be determined : Bends 3, 4 (Achilles, Atlas) Are used only for bending and . steering the bean. Doublet.3 (Diana) Provides an image at the target of the dispersed beam at slit 3. Table 6.2 Function of the Elements of-the Proton Beam - Horizontal View * 83° Element slit 1 Phyvefes Quads slit Doublet 1 (Circe) Slit 25 Doublets 2,.3_ .' Function Determines: the vertical size of the source. These are set to provide parallel — to point focusing at slit 2. This determines the vertical angular acceptance from the source, Produces a waste between bends 1 _ and .2,.and has some effect on-the vertical acceptance of the system. This determines the vertical beam size at the target. - Provide point to point focusing — - of the beam between slit 2% and _ the ‘target. *.The bending magnets, in principal, Used only to clean up the bean. Used only to clean up the bean, have no effect in the vertical plane. Teble 6.3 Function of the Elements of the Proton Beam - Vertical Plane 84 | Horizontal CO; SSS == ~— Slit 1. ‘| al LJ Switching magnet — === [] Physics quads Ly — Slit 2 of ESS == [|] Doublet 4 wo Sl s3 7 | TO Bend 1 38 7 oo —| ~~ T] Bend 2 3 > ——— 2 == Doublet 2 a S/T Slit 3 3 | SS ARS i bends L Va : + =— Target L ~—— End of cave on — aL ‘e) + + + + + + + -€ _3 0 Beam stop Horizontal displacement (in.) On - momentum X BL723 — 2619 Figure 6.2 Ray Trace for On-Momentum protons: - Horizontal View — 85, Vertical an a NY /\ WON i CN \ | im Slit { Wi vi \ __| |_ISwitching magnet pooko dS WN) <==] Physics quads SNCS / AA! | — = inv 5 +=i[ | Doublet 1 DN a Bend 1 A ee oe Slit 2 1/2 — ZK {fj Bend 2 Fae ee === | Doublet 2 +} | A = + — —Slit 3 ———____l{f/\i{\\{_ | = Bend 3 ncaa > __, 7 —_ Al __, ___| | Bend 4 4 Target \ i—t- End of cave iL fh, a Beam stop -6 -3 O 3 6 Figure 6.3 Ray Vertical displacement (in) XBL723 -2621 Trace for On-Momentum Protons - Vertical View Jol — WNJUaWOW - {0 (ul) yybuay yyod woag ~ 86 Horizontal °[ RR Slit LF KRKA Switching magnet F inn Tit ue [ = 0 Physics quads oo) ES [] Double O-L-. aa . .@) San EN OA WOU OO —U Bend 1 - To NAAT VL] Bend 2 A Sh SE WS PRES TE A es ! i ee SS =u Doublet 2 ee ei —— — -* onal its 3 | — = = —s =n Deabiet 3 Oy VLE _{] Bend 4 z= +++ ~ Target : —+—+—+_+_+-—4 =¢—— End of cave oa or | QO) F444 +++ +_+_ ++ + — Beam sto 6 -3 0 3 6 ad Horizontal displacement (in) XBL723 -2620 Figure 6.4 Ray Trace for Off-—Momentum Protons - Horizontal View 187 The resulting beam spot size at the target was about two inches in diameter. Pictures taken at the beam stop and at the target showed that the angular divergence was on the order of or less than .5°. ‘The flux at the target for 500 MeV protons was determined to be about . 10°/sec, maximum. Pictures were also taken at various points along the beam line and compared with the beam design. The agreement was * generally quite good when one considers that the design employed only first order optics. The magnet currents were measured using shunts and a potentiometer. The beam energy was measured periodically (see Appendix C) and found to be reproducible to within .3 percent. The magnet currents were ‘ye-measured every four hours during the course of the experiment, and were found to be stable to within about .1%. The cyclotron is capable of accelerating deuterons and alpha particles with no special preparation, since the synchronous frequencies for both are the same, or some harmonic of that for protons. Tritium and Helium-3 beams, however, required some black magic of the kind only the cyclotron crew could provide. Patience and experience enabled them to deftly place delicate tuning devices, for example lead bricks, ~.on the capacitor of the oscillator, thus shifting the frequency enough to produce a useable frequency modulated beam for those runs where perticles other than protons were needed. The magnet settings for those runs were derived by taking into consideration the appropriate particle momenta, particle mass to charge ratios, etc. 88 R ; 34 Helium-four beams were used to produce the reaction Op — Hed. The He? 's were then used to provide further calibration of the thick plastic detector. Details are given in Appendix F. " 2. Beam Energy on an Event-by-Event Basis Several corrections were made on an event-by-event basis in order to _ remove systematic beam effects. ‘The absolute beam energy was measured using a set of variable thickness copper degraders (cf. Appendix C). The measurements were repeated periodically, and the beam energy for a set of runs was referred to the most recent measurement. The energy was related to the range by the function In T (MeV) = 3.2273 + .53471 (1n R) + 016216 (1n R) ~ 0036318 (in R)> + .00043731 (in R)* ' 2 where Ris the range in copper in gm/cm * Using the above energies, the value of the energy corresponding to the actual magnet currents observed during a run was computed using: P aT qT = 7 1+ 0.46 Was Aiy, ) corr meas ( | fT dp | I Table 6.4 indicates the values of Too for various run intervals, rr and also the dispersion ratio, | Pat ° T dP Tt is the beam energy at the center of the target. To this we corr subtracts .24 MeV when the thick (1/2 in.) target was employed, .08 MeV when the thin (1/6 in.) target was used. 89 ‘BEAM ENERGY DATA _ Bun Interval Beam Energy Dispersion Ratio 202 — 203 ‘462.710 1.670 205 — 206. ’ 466.073 © 1.668 207 -— 215 - 466.214 1.668 220 - 224 462..537 1.670 225. - 228 ’ 461.468 1.670 231 - 235 462.250 1.670 236 - 241 462.389 1.670 242 -— 244 460.450 ~ 1.671 245 ~ 258 460.838 1.671 259 -— 266: 467.140 1.668 267 — 269 * 467.724 1.667 270 ~- 291 ' 463..632 1.669 293 — 294 380.122 ~ 1.712 295 - 303 576.385 1.619 304 ~ 307 379.824 1.712 322 - 322 558.516 . ' 1.627 323 ~- 327' 0.000 1.670 328 - 331 462.105 ; 1,670 332 - 367 461.390 1.670 BEAM WIDTH - IN PERCENT Run Interval Beam Width 202 - 215 -590 220 - 224 -470 225 - 235 -490 236 - 244 -440 245 ~ 258 -540 259 - 291 -490 293 -.294 -510 -295 ~ 303 -420 304 - 307 510 308 - 375 -520 Table 6.4 Beam Energy and Beam Width for all Runs 90. | Using the event origin, computed using the intersection of the helium trajectory with the target midplane, the energy, corrected for a systematic horizontal dispersion, is computed using \ P at = 1 + .00. — - event Torr | T ap | (Y YQ) where 5 is the mean position of the event origins, Y the position of “the event origin. 3. Angular Divergence on an Event-by-Event Basis A correction to the beam direction was made using data from the beam design. The corrections were D tH} <O>, + 65 (¥ - Y,) D Ml <O>,+ .4 (Z- Z) where 99 6 are in degrees, < 6 > is the average divergence at the zZ . we target center. ol) : Be “TARGET MONITOR 1. ° Overview a : A set of range telescopes was constructed to measure pd elastic scattering rates at the same time that pd > He? y data were - being collected. The position of these telescopes is shown in Figure 2.1. The rates were used as a check on the deuterium density in the ‘target, as well as the liquid level in the target flask. At one point a set of three counters was placed directly in the proton beam, which was then run at low intensity. Coincidences were taken between the three counters, and the rates compared with the rates for the telescopes. This established a ratio between telescope rates and ‘beam intensity. The telescopes were surveyed into a kinematic setting for pd elastic scattering that was kinematically unavailable to pp elastic scattering, (see Fig..6.5) the biggest possible source of background. Once in place, the telescopes were seldom moved. Surveys were made periodi- eally to check their positions. 2. Design and Construction Figure 6.6. illustrates schematically the construction of the two telescopes and their positions relative to the beam at 462 MeV. 1 Each telescope was mounted on a "uni-strut" stand at target level. Considerations which went into the design of the telescopes include: a. Differences in energy acceptance over the angular acceptance of the telescopes. b. Range straggling. 32 90° 60. | B ee | pd pd aa] 4 Pea E Le B 30° | PP Pp a L S Telescope fe) position | e | Oo rT 5 1. r 1 Ll 2 t of 60° 120° 180° PROTON LAB ANGLE Figure 6.5 Kinematic Position of the Target Monitor Telescopes ; Ee | A AR-Sa Re aaaa Deuteron telescope AR | | W telescope XBL726- 3108 Figure 6.6 Schematic View of the Target Monitor Telescopes 94 x | cs Energy losses of the p and d in the target. ds Seintillator thickness and energy loss. e. Multiple scattering. f. Changes in beam energy. In addition, an overall countion factor was included in order to make the design quite conservative. Table 6.5 shows some typical values of degrader thickness. Refer to Fig. 6.6 for the meaning of R, AR. Shown in Fig. 6.5are the kinematics for both pd and pp elastic scattering. Indicated on the pd curve is the position of the proton and deuteron telescopes. This position eliminates most of the pp scattering still leaving the proton in pd elastic scattering with a useful energy. Copper was used for all of the absorbers. The copper absorber was slightly larger then the active area of the counters to compensate for the effects of multiple scattering. The counters were all one- eighth inch thick. 3. Electronics Shown in Fig. 6.7 is the logic used in the telescopes. For increased efficiency, two counters were used everywhere and the signals added resistively. Majority logic was used with the three counters in the proton tele- scope. The proton energy was sometimes very low for low beam energies, and quite possibly the three counters would be too thick for the “proton to completely penetrate. Thus two counters out of three were 95 Table 6.5 Degrader Thickness ~ gm/cm~ Protons , Deuterons = R AR R AR Beam S71 Mev }2.15 223 68.0 25.5 Lucite degraders | Cu degrader an: LD = limiter/ discriminator C= coincidence _ SC= scalar | = scintillation counter. Le B “yt resistive adder XBL726 -3109 Figure 6.7 Target Monitor Logic Electronics “97 : also accepted. The coincidence labeled "A" is the master coincidence, and gives the pd elastic scattering rate. Another coincidence circuit, with one signal delayed, measured a random rate. The randoms rate was also measured for the deuteron telescope, since it was close to the beam. - Finally, coincidences between the deuteron telescope, and the triple coincidence rate for the proton telescope were collected at "B". If the absorber thicknesses were correct the ratio of A/B should be 1. h, Uses As mentioned, once the monitors were surveyed in place, and the correct amount of absorber put in place, the monitors were not moved while collecting data at a given energy. We collected pd + Hey data at three energies, 377; 462, 576 MeV, finishing all data collecting at a given energy hefore proceeding to the next. The telescope 's function, while collecting data, was to monitor the deuterium density in the target flask. Periodically the telescopes were moved to a position favorable for pp elastic scattering in order to perform an ion chamber calibration. Three direct beam counters _ ‘were placed in a low intensity beam (about 10° protons/sec), and the rates for triple coincidences in these three counters compared to the coincidence rate in the two telescopes. This established a ratio of beam flux to telescope rates. The procedure was to then increase the beam flux to the level used while collecting data, and, with this known beam, calibrate the ion chambers. 98 C. “BEAM ENERGY AND STABILITY _ Range-energy measurements were used to measure the absolute energy, and as a check on the stability, as a function of time, of the de- graded particle spectrometer. These measurements were made each time the spectrometer was turned on after the magnets had stabilized, and occasionally between runs. The method of measurement is based on measuring the relative ionization versus range, using a standard absorber (in this instance copper). Plotting the ratio of the current readings from two ionization chambers versus absorber thickness, one obtains a Bragg curve, as illustrated in Fig. 6.8. The Bragg curve contains the effects of range straggling and beam momentum dispersion, so one must obtain from this curve the mean range. A prescription for obtaining the mean range, independent of the beam momentum dispersion, is described by Mether and Segré>. Let R* be the mean range, and assume that the distribution of ranges due to straggling has a Gaussian form of probability: Nv - -1 2 2 P/R) = (2n) o exp (-(R-R*) Y/2a Let i(t) be the ionization per centimeter in the gas inside of the chamber for a particle at a distance t for the end of its range in the absorbing material (copper ). The measured jonization in the ion chamber will then be of the form I(R) = KJ” exp (-(X-R*)*2,2)i(x-R)ax, where t = X-R, K is a constant. Defining a new set of dimensionless variables t' = t/a, X' = (R+R*)/o, this can be put in the form L19%-€2L18X quoweinseey] eBuBy e WOTs peuTerqg weed B8erg TeoTdA, Q’g east bulpoas 1od abpam 0's 0°6 0°0! 0°9 OrL ee I i T O e LW e ~QO°l e ° . e 0°2 ° e @ e = e e e 4o'¢ -) _-~vr 4 , xD . e | XON 280 © e Jo Cg@ ; ! O's aAL}O]aY UOIJOZIUO! 100 T= Kf? exp(x! + ")i(t" at’. Mether and Segré state that i'(t') is accurately represented by the form . 46 46 it = (const)t' then I = i exp(X' + t')t' «at'. The results of a numerical integration of the quantity ~ 46 £(X) = f exp(X' + t')t! dt', normalized to one at the peak, are shown in Fig. 6.9. “The range is taken to be X' = 0 = R-R*, independent of any beam dispersion. This occurs at .82 of the maximum of the Bragg peak, and is the value used ' 1 -in all of our measurements, as illustrated in Figure 6.11. The apparatus is shown schematically in Fig. 6.10. It consists of two ion chambers, and a variable thickness of copper absorber. The variable thickness“of degrader was measured by a precision potentio- meter. The potentiometer was used to measure the position of the movable wedge. Figure 6.8 illustrates a typical plot of specific relative ioni- zation versus potentiometer setting. The value of the potentiometer . setting at .82 times the peak of the relative ionization curve is indicated. The absolute energy was determined using data from the m range-energy tables compiled by Janni . sqTnsay UOTY BIZ9VUT TROTTOUM -6°9 aIn3ta siIi92-eelL TEx O/(e6uns updaw—abuns) =x ¢ 2 | O f- 2 €- b- \ oe \ | \ : b'0 \ . | 9°0 Vn 0’! - 101 pazijOWsOU- UOIJOZIUO! BAIJOJ[AY co, r= 919¢-222718X = yaquoyo uojA snyereddy Sutanseay esuey OT’9 aaneTaz 4aq JOSqD paXxiy i re J JaqJOSGD ajqoanoy \Y saquioud ag UO] wopeg 193 pa,oy aeSusy ussy] ULTM eFuBy snsze, UCTPeZTUOT eaTzeTsy IT’9 arnt vi92-E2l 18x Ou % S abuoy O C- ,woyw6b 82l_ 9el bel eel Odi t ot 4 81! 1 ON bli } ] l i) ~O pezijOwWw sou — UO!JOZIUO! I Q “BALLDIAY D. . PHOTON COUNTERS We now discuss the photon hodoscope/spectrometer which was designed to have optimal performance in the energy region between .15 and .7 GeV. Two counters were actually used during the experiment after a decision was made to increase the geometric detection efficiency of the apparatus because of the very low cross section for the process .pda + Hey. The two counters differed substantially in design and performance, one being designed and constructed specifically for this experiment, the other being an adaptation of an existing counter. Only the new design will be described in detail. Discussions of the design and performance of the other can be found in the references ?°?” In general, the counter should specify as completely as possible the four vector of the photon, with high efficiency and good time reso- lution. Specifically, it should provide: 1. Good energy resolution, to help separate the process pd ~ Tey from the process pd 3 Hex’, 3 v7. 2. Good spatial location of the photon, in order to enable one to impose angle and coplanarity constraints. 3. Provide the highest possible detection efficiency consistent with good spatial resolution. 1. Construction Figure 6.12 is a schematic representation of the basic components of the detector. The total length of the absorber is 10x" consisting of a 2x° converter, and a main radiator of 8x° thickness. Inserted between the converter and the main radiator were a thin trigger counter and four wire spark chambers. The wire chambers were used to “+195 Wire chamber planes - | (X,Y each) ‘Lead glass converter Liquid light pipe 2Xo ----——— T) | 7 | 8Xo phototubes | Lead RCA 4522, | glass ("0 4, SF-5 ae = Signals _——s Signal to adder XBL724~ 2774 Figure 6.12 Basic Components of the Photon Detector _ 106 delineate charged particle tracks, which were then used to localize the small fiducial volume in which the photon conversion took place. A thin veto counter was placed in front of the converter which served to suppress charged background triggers. In order to obtain maximum energy resolution, the optical coupling between the radiators and the phototubes was optimized. ‘The converter/ “radiator was joined by a folded light pipe to a fast 5-inch phototube, of high quantum efriciency . The main radiator was viewed from the back by seven 5-inch phototubes. The optical coupling was made by a light pipe consisting of a set of interlacing hexagonal cones, .as shown in Fig. 6.13A. ‘The cones consisted of polished aluminum set in ‘epoxy. The phototubes and main radiator were joined to the light pipe - with an adhesive sealant (RTV). The light pipe was then filled with a clear mineral oll with an index of refraction equal to the geo- metric mean of the indices of the glass of the phototube face and the lead glass block. Figure 6.13B shows the main block assembly before it was encased in a 1/4-inch iron box. 2e Counter Calibrations The counter was calibrated in the parasitic electron beam available at the Caltech synchrotron. The beam was obtained from the back side of a quantameter, and emerged through a small hole in the shielding wall. Also used was a magnet/counter setup which provided tagged photons. The test setup is illustrated in Fig. 6.14. The energy resolution. of this setup was, unfortunately, only on the order of p/p & Piaaae This was one of the largest uncertainties in deter- mining the energy resolution of the detector. Figure 6.15 shows the 107 < fon) rm oS a3) 5 o pa ies .) “a es o z © tH Fy 108 dnjes Tequeupredsq weeg uoyoug pessel, Yy1.°9 eunsty YOLVIOVY NS IHVYLSSWNSYS YSLNNOD OLSA i LaNOWW "430 WOLNAWON ‘ . a | tg ‘ . g , . * . . . : vq: 49 x] ~@ : Pt ' a. - 2 x “9 . 4 Sark oe a ty 8 ye lt ee ee) ew i6 et “les le 9 a . YSLAWVLNVNO ) ‘HONAS WOU wvaa 4 109 SOTUOLPOSTY OTSOT Topeyeq uojoud G1°9 amnesty SLV9 ‘V"H'd OL yaWOS BONZQINNIOD — 9 oo . j - ustvos uaxIN-"gaqv -— W uaWWos <—— ] ] W [> agisww ualsIWdnY - Vv | I HOLVNININDSIG = 1 ¥) 3 yaLIWIT — 7 . 5} 5} . fe) — >| wausww [< H3AZATWNV . "H'd OL . 7 . wW Vv - ' otu 1 2- I-DS 4? . <____—_ : ow A [ae 2-Sad I-Sdd i mi / A (X1NO NoLiyearwo 403) S¥3.LNNOS ¥Y3BLNNOD _ SYSLNNOO Noisuaanoo ssv"o avs QL3A = HBLNNOD NINO + 110 electronics used in conducting the calibrations. While the conversion efficiency of the converter/radiator was being determined, a veto ‘counter was positioned in front of the converter. Because they were far more copious, positrons were used rather than tagged photons. As 5. J. Yellin has pointed out®, the calibration is independent of whether one. uses electrons, positrons, or photons. Basically, the energy resolution depends on the total amount of Cherenkov light available. This, in turn, depends to a great extent on the total path length of the charged particles in the shower’, since all the charged particles are electrons or positrons with 68 ~ 1 for high energy incident particles. By actual measurement, the total path length is not sensitive to the kind of incident particle, 12 as long as its energy is high ("high" is about 70 MeV for lead ). 36 Energy Resolution / The counter was tested in three basic configurations: a. Two converter/radiator, each ex® thick, and the 8X° block. De One converter radiator of thickness ox, and the main block. Ce The main block alone. In each configuration, the outputs from each section were added. The . gains of the tubes were then adjusted for each section to optimize une resolution of the counter, for one energy. Then a calibration was done over an energy interval of 150 to 600 MeV. For configuration (3), tne block had to be rotated 90° in order to contain the whole shower at all energies. Figure 6.16 shows the linearity for configuration (1). It was inter- 20; 11] T T . PULSE HEIGHT | (ARBITRARY UNITS) I5- r Iob r 5- e i I 9% J 2 Figure 6.16 Pulse Height Versus Energy Ve * » . , - esting to note that the resolution was as good for configuration (1) as for configurations (2) and (3). In other words, the resolution was not apparently degraded at all by splitting the radiator into sections. Figure 6.17 shows the resolution for configuration (1). The resolution contains a largely unknown beam resolution. We investigated the extent of this contribution as follows. Using a “Light emitting diode, we matched the mean pulse height from the diode to that from 500 MeV electrons. The width of the spectrum using the diode was on the order of 4 to 5%, as compared to 7% using photons! | To put this in perspective, the other counter used in the experiment has a resolution of about 10% at 500 MeV. The 5% figure for the new eounter represents a factor of four improvement in light collection. A better beam is needed to test the lower limit on the resolution of this counter. <= kh. = Detailed Distributions Pulse height distributions were taken of each component of the detector individually in order to investigate the mechanisms of shower detectors a Little more fully. Figure 6.18 shows the pulse heights from each component, and the summed signal for 500 MeV - positrons. Studies of the longitudinal behavoir of showers” i suggest that rather large fluctuations in the pulse heights should occur in each section of the counter . This is seen in the widths of the individual distributions. The summed signal, however, is rather well defined, again, as it is for the block alone, again illustrating there is little 113 207-7 T I a T T ! T T T GAUSSIAN WIDTH o (%) Sr lor 5 = ; yoy E 2 (GeV) % oO L if il L ] iT af i { l 1 fe) { 2 FIGURE 6.17 Energy Resolution Versus Photon Energy 414 PULSE HEIGHT DISTRIBUTIONS FROM DETECTOR ELEMENTS 500 MeV et CONVERTER | (2x°) CONVERTER 2 (2x°) ii SUMMED SIGNAL Figure 6.18 Individual Component Pulseheight Spectra “115 a degradation of the energy resolution due to splitting the radiator into pieces. 5. Conversion Efficiency Knowledge of the overall detection efficiency of the apparatus demanded that we know the conversion efficiency of the 2Xo converters rather well. Using coincidence and anticoincidence requirements, we measured the conversion efficiency as a function of incident photon energy. The results are displayed in Fig. 6.19 for energies between .l and .6 GeV. For completeness, the efficiencies are also shown for the two converter configurations, giving a total converter thickness of 4Xo. Curve 1 is applicable to the configuration used in this experiment, and shows the efficiency being only about 40% at .1 GeV, and becoming about 70% for all energies above .3 GeV. A good fit to this data is me, -ALk obtained by a curve of the form AL +A e 3 2 MeV, A, = . 762558, A= -1.00956, A, = -.0110533. » kK = photon energy in 116 T J T i J t | | CONVERSION IN I CONVERSION 2 CONVERSION IN I EFFICIENCY 3 CONVERSION IN I AND/OR IZ =) (%) 4 CONVERSION IN I AND II 100+ , .80r - 6OF 40h 20 | PHOTON ENERGY ~ GeV ——> 0 1 L ! 1 t ! 0 0.1 0.2 03 0.4 0.5 0.6 Figure 6.19 Conversion Efficiency Versus Energy for 2X° and 4X° Converter Configurations Vay » , E, VERTEX LOCATION - PHOTON CHAMBERS We make the same assumptions for the photon counter spark chambers as for the helium counter chanbers (cf. Appendix G), save that the chambers are not assumed to be in a plane. They were separated by about 1.5 inches. The task of the reconstruction procedure is to provide a set of slopes and intercepts from which the photon vertex -.is constructed. The chambers for the photon counters consisted of four pairs of X-Y gaps for each counter. . When reconstructing both tracks and vertices, the X and Y views were treated independently. Figure 6.20 shovs what the positions of the sparks for an electron-positron pair shower ‘might look like in each view. There are two distinct steps to the vertex finding procedure: ae Track reconstruction. db. Vertex location. Each step is done in both the X and Y view, in both photon counters if necessary. Ll. . Track Reconstruction The procedure involves a least-squares-fit on three and four spark combinations, with the subsequent elimination of sparks used in a fit. Using the known chamber positions (see Fig. 6.21), a matrix M is pre- computed for use in constructing a straight line fit to the component tracks of a shower: al. > |S] = 118 2 zanoug ITeg uot DETR Teopdsy, 02°9 aandta SIIe-92278X | 49} 49AU09 4 uojoud ji \ IN X K Photon converter \ Photon > Z XBL726-3114 ’ Figure 6.21 Relative Positions of Lead Glass Converter and Wire S park chambers - 120 where X is a vector containing the x-coordinates of the sparks in the X-Z plane, ais the line slope, b the intercept with the X-axis. Determining the line involves only the X's; the X's are the fixed chamber positions. This allows the matrix M to be pre-computed. Next, the distance from each spark to the fitted line is calculated and compared to a fitting parameter specified by the user. If all “distances satisfy the comparison, the following information is stored: a. slope; b. intercept; Ce. contributing sparks; d. maximum distance from any spark to the fitted line. The sparks “used up" by a given fit are eliminated from further consideration. The above procedure is repeated until all three ‘and four spark combinations satisfying the constraint imposed by the fitting parameter have been found. 2. Vertex Reconstruction Vertices are also constructed in each view independently. Basically, the procedure is to look for tracks which intersect the midplane of the converter within some specified distance from one another. Each time such a vertex is found, the tracks composing it are subsequently eliminated from further consideration. In practice, the formation of vertices is subject to many complicating factors, especially in the photon energy region of about 150 - 450 MeV, which we find in this experiment. For pair production, one expects the RMS angle between the two electron tracks to be about 121 3 , M/E, where M, is. the mass of the electron, E is the incident photon energy. In practice, both tracks experience some multiple scattering, more or less depending on the depth of conversion inside the - converter. At times, this can be serious enough to make the point of conversion appear to occur outside of the converter. Another potential problem comes from single track events, most probably due to one particle of a pair being absorbed. ‘These tracks can have a substantial slope, increasing the error in the vertex Location. Following is a description of the assignment of a vertex and an associated error under three somewhat different circumstances: single tracks; a pair of tracks; and three or more tracks. There is one major physical assumption made in the assignment of vertex positions an@ errors: due to the complexity of the shower process, nothing can be assumed about the trajectory of the particles' path within the converter. Errors and vertices will be assigned as though the particle's track can be projected in a straight-line fashion into the converter. Be Single Tracks ‘The vertex is taken to be the intersection of the track with the midplane of the photon converter. The error is defined by the condition (see Fig. 6.22) ed =X tan 0. oO yoeRay, e{Zurg e IoZ uotyntossay ege’g eamBTy elite —-92218xX X~— 122 ZY be Pairs of Tracks 123 a Three situations are possible when pairs of tracks are considered; the apparent point of conversion can appear to be: 1) within, 2) beyond, 3) before the converter. Situations two and three arise - because of multiple scattering effects. If the intersection does not lie within the converter, the two points of intersection of the tracks . with one of the surfaces of the converter are required to be within a specified distance. If they are not, each intersection is consi- dered to be a separate vertex. For situation one, the vertex is taken to be the projection on the converter midplane of the point of intersection. Assignment of an -error, on the vertex position is illustrated in Fig. 6.23. In the second and third situation, one computes the points of closest approach of the two tracks on the surface of the converter closest to the point of intersection of the tracks. The vertex is taken to be the midpoint of the two points on the surface. The error is taken to be one-half the maximum distance between points of intersection with the top and bottom surface of the converter. Figure 6.24 illustrates why all four points of intersection must be considered for pairs of tracks. About one half of the time, due to multiple scattering, one expects the tracks to have the same slope. Using the points of intersection on only one surface could clearly cause one to seriously underestimate the error in the vertex position. 124 22 -92271gx syoeiy JO Siteg - 1Olgg xaqte, e@ Jo yueMUsTssy Ce*g saneTZ Q2 — | ak a — Teer wel -—- — — ae Teo -~ + f--- N OMT ———|~ XBL726-3110 igure 6.24 Assignment of a Vertex Error When Both Tracks Have the Same Slope 126 . . “@. Three or more Tracks Showers involving three or more tracks are treated as overlaps of pairs of tracks. Using the vertex assignment described for pairs, one now searches to see whether any vertices due to pairs of tracks - overlap within the fit parameter. If so, one then checks to see whether the pairs have a track in common. If so, the number of tracks ‘contributing to a vertex is reduced by one. The vertex coordinate is taken as the mean of the component vertex’ pairs. An error is assigned as with pairs of tracks. The absolute maximum is. computed for the distance between the intersection of any pair of component tracks with either surface of the converter. The error is ‘one half of this distance. (See fig. 6.25). For each of above situations, and for each vertex located, the following information was recorded: le X and Y coordinates; 26 errors in X and Y coordinates; 3. the number of tracks contributing to a vertex, in each view; h, the distance of closest approach - meaningful only for pairs. 127 Hie -92L718X SHORT], salu, - IOTTg Xaqtea Be JO JueMUaTssy eg eunsTy 128 F.. | HELIUM DETECTOR General Overview In this section we discuss the construction and use of a thick plastic total absorption scintillation counter for the detection and energy determination of He” particles. Counters of this type have 6 15,1 in the energy region < 160 MeV. ‘The been used before for protons ‘momentum resolution obtained by us was on the order of 1.5% with good uniformity across the face of the counter. Two factors motivated the development of such a counter for this experiment: 1. It was desirable to let the photon detectors determine the geometric efficiency. Without moving the counter, it provided total angular acceptance of the lab He's, This enabled us to detect photons at any lab angle without moving the helium counter. Also, we were able to increase the geometric efficiency of the experiment by using two photon detectors, 2. A detector was called for with a dynamic range of about 60 to 340 MeV He?! Se A magnet/wire~chamber spectrometer was considered. The small lab angle of the helium at some settings (as low as 7), loss of solid angle, and prohibitive amounts of absorber, especially for settings with low helium energies, were some of the reasons for not choosing this option. Other points of comparison will be made later. 129 »- - i. Construction Figure 6.26 shows an exploded view of the counter (not necessarily to scale), and Fig. 6.27 shows some construction details. The active area of the detector consisted of a block of pilot y scintillator 60 centimeters wide and high, and 10.65 centimeters | thick. The thickness was chosen so as to just stop 430 MeV He? 's. “The light pipe consisted of two parts: (1) a 45 centimeter high x 60 centimeter wide x 10.65 centimeter thick piece of lucite; (2) 4.5 inch in diameter < 5 inch lucite cylinders. Each eylinder was rounded, on one end, to fit the face of an RCA-4522 phototube. Except for the top and bottom, the whole counter was wrapped with aluminized mylar, and one layer of two mil aluminum. The nonactive area was, additionally, wrapped with black tape. The whole counter was mounted in a 1/4 inch iron frame, which served both to provide mechanical rigidity, and shielding from stray fields. In. addition, each photomultiplier tube had its own H-metal shield. For about two-thirds ofthe runs a differential pulse height counter was placed in front of the helium counter. This consisted of a 1/8 inch scintillation counter, connected by a folded light pipe to an RCA-N522 phototube. Thin mylar sheets were appropriately shaped and placed so as to increase the uniform thickness of this counter. 2. Stability In order to minimize the effects of drifts in the helium counter, the phototubes were closely monitored. As shown in Fig. 6.27, three oe 130 « Intercalibration tube viewing. Am_ source and light pulser 8575 H- Lucite — ——— “| light pipe | 45cm 1/4" iron LL ww L He beam 60cm Pilot -Y scintillator Light pulsers |. . lOcmES a | | . 6 ue U mirror Figure 6.26 Exploded View of the Helium Detector Coon —S~—Front surface Light reducing Ant"! dissolved in scintillator diaphragm Lucite , . ms disc ne Z . g Air | . Z gap ’ Lucite—7~ No N » gs 4 3 ns x? Scintillator SC Pressure Lucite Reflecting collar surface -— Ga Neutral . density Pilot Y Frosted filter glass 1 60cm x 60cm - Yell ow 4" ai I/4 air x 10.65 cm filter gop. | 3 AR-4 Argon glow lamps Figure 6.27 Helium Detector Construction Details ~ tee “AR-K28. éreon glow lamps were mounted on the bottom of the counter. ‘Before the experiment, these lamps were tested and found to have pulse height stabilities of about one percent per week. During the experiment, these lamps were flashed continuously, and served as a reference. Figure 6.28 shows a schematic layout of the electronics associated with the helium counter. The output of the helium counter entered a linear gate, gated for stabilization purposes by an appropriately timed signal from the argon lamp, then through a linear amplifier, a biased amplifier, and finally into a pulse height analyzer (PHA). A signal from the PHA was fed into a Canberra digital stabilizer. - This device continuously adjusted the linear amplifier gain so as to, one the average, keep the argon flash pulses in the appropriate PHA channel. re the phototube voltages drifted too far, the power supplies had to be_adjusted (the voltages of the power supplies were measured with a digital volt meter at least every eight hours ). Periodically, the stability of the argon lamps themselves was checked against an Americium-241 source. Notice in Fig. 6.26 that the 8575 phototube is directed at both the source and the argon flashlamps. Spectra were taken periodically using a PHA of the flashlamps and the source simultaneously. Figure 6.29 shows the part of the spectrum for the Americium-241 source. The procedure was to compute intercept of a straight line fit to the linear portion of spectrum (as indicated in Fig. 6.29) with the channel number. If necessary, the power supply voltage on the 8575 133 ‘ (sl2-(2z18X sopuoTq2eTE OTZOT LoZIa ad UNTTEH .ge°yg aInata ‘3601048 — VHd dwio D ws09 ayo6 oop ‘ a3 ‘| |pasorgy ri) il s0auUly} ol TF aayisisay 2810 Tappo O83Z, | pang h 5 v ] ¥ ~ CEE ford {fa 8 | 5 su , a406 q jeds i Anjaq 4 : Jappo athe (10) . BALISISAY aed wns _, Ee apou ~ 4966124 4 pow ‘ JasSOW # , sasind ayo6 . ot Kojaq Aoreg-L 9 PF} “Av 14617 2000}- a | wet 2 t~Peak—I ". | Ler . Am?*! spectrum w” e r=) ; 8 !000;}- | 4 ere) I50 200 | PHA channel XBL 722-2353 Figure 6.29 Americium-2i,1 Energy Spectrum _ 135 ' phototube was adjusted to make this point fall into the appropriate channel. With new voltage on the phototubes, the voltage bias on the argon lamp in general had to be changed to make it fall in the . appropriate channel. At this point the argon flash lamps themselves were calibrated and acted as a temporary standard while data were being taken. 3. Differential Pulse Height Counter The helium detector presents a large surface for randoms, and during the setup of the experiment it was realized that the trigger rate was prohibitive. A differential pulse height counter (henceforth DEDX counter) was added to the trigger for all runs where the helium ‘energy was greater than 100 MeV. A discriminator level was set on this counter using passing alpha particles. The discriminator level was set conservatively. Installation of this counter reduced the trigger rate by a factor of 50. Figure 4,3 is an example of a PHA distribution of some of the data, showing the helium peak. The voltage on the phototube for this counter was carefully monitored, in anticipation of having to add the DEDX pulse height to that of the main scintillator, for.some runs, to obtain the helium particle's energy. Adding the two pulse heights, rather than considering the DEDX counter to be an ionization energy loss and correcting for this, was to be done only as a last resort, however. Heavy charged particles passing through thin amounts of material obey a Vavilow distribution in the energy lost to the material. Thus the fluctuations in pulse height can be large, especially for high energy heavy charged particles, broadening the resolution accordingly. 136 »- A, Total Absorption Scintillation Counters vs. Magnet/Wire Chamber Spectrometers The biggest advantages of a magnet/wire-chamber spectrometer (MWCS ) is the relative Simplicity of the physics of the device, and the 7 typically -5% momentum resolution obtainable. The primary advantage of a total absorption scintillation counter (TASC) is the large solid angle available. For this experiment, it was a distinct advantage to have the geometric efficiency determined solely by the photon counters. Location of photon vertices to any precision at these energies is difficult, and would have made determination of the solid angle difficult and imprecise had the helium counter not accepted all lab angles available to the photon counters. The TASC is potentially a more compact device, and it is possible to reduce the amount of energy absorbing material in the particle's path more with it than with a MWCS. This was important at some kinematic settings where using a MWCS would have made it impossible to measure the energy of the helium before it was absorbed. As mentioned, the simplicity of the physics involved with a MWCS is a very distinct advantage. The TASC we ultimately used was a compli- cated device when investigated in detail. With a MWCS one needs only insure that the magnet and wire chambers function properly. With a TASC one suffers from all the problems possible with scintillation counter : light leaks; phototube stabilities; the need for mapping ; energy tails which are in general energy dependent ; somewhat inferior resolution ; possible changes in the characteristics of the plastic with age ; radiation exposure ; stress. 137 ‘With a MWCS, problems with particle breakup, and background in general tend to. be less serious, aS one measures the energy of all particles independently. The TASC gives an energy averaged over all particles within. the trigger. In addition, the TASC must be tailored for each ' energy range. If the thickness of the counter is more than that necessary to absorb the highest energy particle of interest, one runs the risk of large pulse heights due to highly penetrating backgrounds. Both devices have their respective energy regions where they are best suited. Simplicity and resolution argue for the MWCS where possible. Cali- ‘pration is simple: magnet currents can quite standardly be kept to within a few tenths of a percent; wire orbiting can be used for the momentum calibration. Calibration of the TASC usually demands accelerator time. This can be expensive. oy One way to improve future designs of TASC's might be to consider a - modular approach. If the detector were constructed of, for example, 3/4-inch sheets of scintillator, each sheet joined to its own photo- tube by a folded light pipe, then the total thickness of the detector could be tailed closely to the kinematic demands of each experimental situation. Ambiguities due to highly penetrating backgrounds would pe greatly reduced by the veto counter situated behind the detector. One would, additionally, have an immediate range measurement by recording the number of modules penetrated. An alternative method to the one reported above would have to be devised for keeping the photo- tubes calibrated. 138 a De Calibration Two sources of data were used in order to calibrate the He? counter: ae Information collected using the 88-inch cyclotron at LBL. A well collimated He° beam, with a Ap/p resolution of about .01% FWHM, at energies of 69 and 130 MeV, provided two points. b. Data collected on the 184-inch eyclotron at LBL. This data was relatively free of a background and yielded He? 's of known energies in the region of 200 - 265 MeV. Thus the calibration data spanned an energy region of about 69 - 265 MeV. Each data point provided two quantities needed for subsequent analysis: Be the energy of the He® particle at the front (i.e., closest to the target) surface of the counter. De the counter pulse height. - Using these quantities a predicted counter response was derived. 15,16 Other workers had determined that the Light output of a piece of scintillator in response to a charge particle is well represented by: -1 dL/dax = g ° dk/dx - (1 + b dE/dx) where dE/dx = ionization loss of the He? in the scintillator b = a saturation parameter g = the gain of the counter ll di/dx = light output of the scintillator 139 The resulting pulse height is assumed to be equal to the total light output, with Bb appropriately adjusted, as Will be discussed. Thus: Pulse height = fw of g d&/(1 + B dE/dx) E = my, dk = mBy-ap V ‘Letting . Pulse height = - 5 &-m* ap o (1-B)3/2 (1+b dE/dx) where < ll 3 He velocity at the front surface of the counter 3 m= He™ mass Using the above definition of the predicted pulse height, the para- meters b,g were determined using a least square minimization technique. Using the observed pulse heights, the parameters b,g were adjusted so as to minimize the Quantity 2 HH - x2 2 z (p , 60s) pH, (pred ) i o i The resultant values of b,g giving the best fit are: -3 i b 9.566 x 10 | g 1.325 Using this empirical form for pulse height as a function of energy, a fit was produced which provided the helium energy, as a function of pulse height, at the point it entered the detector. A function of the form : 5 i+l BA, * Be A, FE) + BA *E eT P ( )* By Aue * By 140° where © E c E iL energy at the surface of the counter pulse height-pedestal was used. The values of the coefficients used are: A = -18.3142 A, = ~-,122678 A, = 22,528 Ay = 1.52817 A,. = -3.04728E-3 A. = 7. 73417E-6 AL = -7.80569E-9 To obtain the value of the kinetic energy at the event origin, taken to be the target midplane, a correction must be made for ionization losses in going from the target to the detector. This is a function of the experimental context of the counter rather than the calibration of ‘the counter itself. Here the functional form used was E = C ‘Exp (E/-c)+C +C *E T 1 of 2 3 4 c Where EF is the energy at the center of the target. The values of the T C's used are: i Cc. = 64.4612 1 C, = 72.6527 c. = 0O.5348 C = .939958 74) » : When using the thin target; the differential pulse height counter was not in place. The values of the C_'s in this situation are: Lo . i c, = ho.7473 C, = 43,2372 c, = 26,283 CC F .939052 h 93905 Shown in Pig. 6.30 is a pulse height spectrum using 114.6 MeV incident He's. Figure 6.31 shows the same plot with a logarithmic scale. ‘The shoulders in the second plot are due to He? breakup, and saturation effects. These effects are energy dependent. As the helium energy inereases the fraction of the distribution within these tails increases, up to about 7% at 250 MeV. These shoulders were studied care- fully, and a correction for them was made for this effect in the data analysis. = Using data on the light output charged particles in plastic scintil- lator as a function of energy, a computer program to simulate the counter response was produced. Figure 6.32 shows the results for incident particles with kinetic energies from 0 to 500 MeV for a four- inch thick counter. The response is seen to be fairly linear above 100 MeV incident energy. The peak occurs at the energy for which the particles pass through the counter. Notice that for a counter of this thickness He? 's with a kinetic energy greater than 210 produces a unique pulse if, as was the case, only protons, deuterons and He? 's are present. - 142 - Typic’al He spectrum 114.6 Mev | . oe 6000P-. 7 . _ bd e < 3 © eo ©O 3000/[- _ = e OL we neccieace® __| . Can 50 60 70 Channel number a Figure 6.30 Typical He3 Spectrum - 114.6 MeV Heliums 80 mie) Figure 6.31 Typical He3 Spectrum - 114.6 MeV Heliums - Log Scale _ 143 »- - J T - T J E . & 4 - ; a . _ e 4 r T= 114.6 MeV 7 he . . ‘ | - : e a a e 4 a . q . . 1 . * a Lee e = r e° 4 T oo ° 4 o e 5 ewer (werner < ate e — —_ tS aes, od ee ° _ E 7 e * 0 ee é .. ; . . r) 8 . ° ° “4 " e eo e@ ; ps L. oe e e 7 - e . e = x ee e e¢ se «J ar) ar) - a ee ose ea aa 2. l ia. “10 40 70 =... Channel number 7144 010) *ABZi0u9 DTJeuTy snszea yndyno 4YysTT ARPW - ADYANS OILANIM ZE°9 eanSTy 9H 0Ol osz 002 os! = iOS 1001 7OS| 00d 10S2 (SLINA AYVYLIGYV) LAdLNO LHOM 145 3 x 6, ‘He Break-up Some of. the He? 's break up in the material preceding the detector, either as He > pta, or as He? > ptptn. In either case, these would be vetoed in general by the differential pulse height counter in those runs where it was used. In runs where it was not, the break up would not in general produce a sufficient pulse height to simulate a He? -Thus these particles are not detected, and some account must be made for the magnitude of the loss. A fit was made to the He? detector inefficiency versus range in CH over the He? kinetic energy region 60-260 MeV. Using this fit, the data could be extrapolated to the amount of material the He? ‘encountered enroute to the detector. With the differential pulse height counter in place, the amount of material is equivalent to 8.21 MeV of CH. Without the counter, the figure is 4.4mm of CH. This corresponds to break up losses of (2.9 + 8)% ana (1.6 + .5)% respectively. Some argument can be made for these losses being independent of the kinetic energy of the He, in the energy region of interest. This was taken, to be the case for this experiment. 146 .G. -Helium Chamber Local Coordinates The following summarizes briefly the procedure for construction of local coordinates, i.e., relative to the chamber frame of reference, in the helium chambers. Each of the two sets of helium chambers (see Fig. 2.1). Assumptions (refer to Fig. 6.33): A. A Z-axis perpendicular to the plane of the chamber is assumed. B. ‘Each plane is defined by a set of coordinates, one on the finish wire, one on the start wire, and a line connecting these two points is perpendicular to the wires composing the plane. | C. Sealar counts are supplied from the start wire to the finish wire, and from the start wire to the sparked wire, F and D respectively. D. All planes have effectively the same Z. F is the fiducial count. The equaption of the sparked wire is derived as follows (see Fig. 6,33): it Xx -X + D/F (X_- X I Ss /F ( F 3) Y + D/F (Y_ - ° . Yy /E (Y,, ¥,) I The equation of the sparked wire is: (y- vy )/(X- xX) = (X,- ¥)/(X - Y) I I F Ss F 8 Inserting x Yo this can be put into the form A X + BY +C.. i i XBL726 ~ 3116 a Figure 6.33 Definition of Wire Spark Chamber Coordinates 148 In the experiment, four planes were used for each chamber. The planes of wires were at angles of 0°, 60°, 90°, and 120°. We demand that at least three of the four planes have a sparked wire, and solve for the intersection of the sparked wires in a least-squares sense. This is defined as a local coordinate. For the case of four sparked wires, we have a matrix equation of the form o> = Mve=e or A B Cc L 1 L B C A, 2 x 2 ’ A B Y C 3 3 3 ~f A B 6 4 h h This overconstrained system of equations is solved to give a best fit to X and Y, of the form v= M 2. At the same time, the matrix RSID = com - I) is computed, and used to compute the distances from a sparked wire to the coordinate via > ~ r = RSID’ ¢c The largest component of r is reported as measure of the goodness of the coordinate determination. Input data for this procedure includes a cutoff parameter. If the distance, Tr, from any spark to a fitted coordinate is greater than the 149 A fit parameter, that coordinate is eliminated from further consideration. One can also specify a parameter to resolve ambiguities should a common set of wires be involved in the formation of two or more different coordinates. The procedure searches for the best fit, defined as the coordinate with all wires being closer to the fitted coordinate than to any other coordinate. . Once a coordinate is found, the wires contributing to that coordinate are eliminated from further consideration. After all permissible fits have been found involving four wires, fits are sought containing three wires only. Finally, if no three or four wire fits are found, inter- sections of two wires will be used. H. GEOKIN The second stage of the analysis, GEOKIN (Geometry-Kinematics ), performed two major functions: i. Lab coordinates were constructed using chamber centered coordinates, survey information, and systematic properties -of the beam. Calibrations involving positional dependence, and functions to transform pulse heights to energies were used to construct initial and final state particle ‘energies. . 2. With the energies and angles constructed as above, a kine- matic least squares fitting routine was used to fit a set of energies and angles to an event hypothesis. A scnematic of the geometric configuration, indicating the construction of the angles used, is shown in Fig. 6.34 . Details of the various device calibrations ean be found in the appendices. The program flow of GEOKIN is shown in Fig.6.35. Data, output from the data summary programwere fetched from chip store. The program naturally divided into three segments: - a2. Initialization. 2. Event processing. 3. Run summarizing. Initialization consisted of fetching constants from the data cell, and frox these constructing other constants useful for the event processing stage. 151° suy J @ 50 worsrurzeq. TE*9 seTsuy p pue ; WS [OU|WON Te ae nee ee | As : : oG/\ Lp wipeg jDnjoy , . ‘ ary . ; ‘ ; . o . : 7 ee ee OT me, 4 152 dSIHOd SUOSN LIAGNT'I OaNI LAOunon VovD dSTHaa woLova aauno INLSNOO noany zunns uny azfpazeumns Cog NIMOND Wetdouy ey} JO amyoniig TeoTZoT. GE°9 eansTy ¢AOVdNA XTANOH WVLIX0S KaLKO BdVLOa zRVO g1L0u THYO PALI OLANIN €ai1y aQNva CHL LIGLAXg TALITY wOUNT aaaa LOG wugauo AV1dS1G _ WHIXIN LOWUIG ' WSHXIN aqudsuo WAWXIN xOou WVHKIN NIUSVE ANILVK AON CULINI NIx0g9 ‘WOFIONAASUOIEA DTIJeM0ayg Suy33;3 VpIeusUTy :dooyT quaag 4STd 0‘z SdWIL NVULT NVULY INTUaH LSNOX -UTIOHI SAWIL IsNoo sheiae dn qos Ssqueqsuod yoqzay tUWOTIEZT LER PUL aroqsdty) 03 Vv ASTd ag] bn nnn epee een eee ene ool WVaD0Ud NIV eee o « Q dnjesy yevI9 noisy uyey + WVUD0Ud (NTHORD) SOTLVWENIN-AWLENOTD Ey a oT: . | / vao3zsdyzug t Q,- - 153 For event processing the concept of a sub-event was introduced. In general, each chamber could have more than one coordinate. Thus each combination of coordinates had. to be investigated separately as a possible event type. Prior to actually fitting the sub-event to an event hypothesis, various cuts could be imposed. Cuts might be placed on the: i. differential pulse height counter output; 26 position of the event origin with respect to the target; 3. coplanarity; hy position of the reconstructed helium angle relative to the reconstructed energy. If a sub-event survived these cuts, the fitting procedure was applied, and information pertinent to the sub-event stored. At the conclusion of a run, various statistics about the run were tabulated. Included were such things as the number of events not surviving the cuts, the number. which could not be fit to the fitting hypothesis, the number of sub-events per trigger. Finally, the resulting data was stored on chip store for subsequent processing by the cross section programs. 154 I. Data Summary Program Structure Figure 6.36 is a highly schematic representation of the logical structure of the first phase of the analysis program. The program was constructed in this fashion in order to make use of the overlay capabilities of the computer used during the analysis, whereby a large program is broken _into functional groups. Only the executive program and one of the function groups “are stored in the computer at any time. The executive program coordinated the execution of the functional groups, and in addition, initialized quantities needed for processing @ run. Event by event processing was done in functional group-A. The following sequence was performed for each event: | 1. Read an event, and unpack its contents. 2. Form normalized wand scalar values, update fiducial values if necessary. 3. Form local coordinates in the helium counter chambers , vertices in the photon counter chambers (see separate appendices). . 4, See whether this event can be used as a probe event for calculating spark chamber wand efficiencies. 5. ‘Tabulate statistical quantities. 6. Pack the output, write on output medium. Ts If no more events are to be processed, return control to the executive program. 8. If no error limits have been exceeded, go to step 1, other- wise return control to the executive routine. names of routines used (enter _) executive routine +t event loop AEVENT CHAMBER DISPLA DISPLAY ELIMIN «= FIDDLE FIT2 FIT34 PACKIT PROBE READ1 SHOWER Figure 6.36 To | J summarize information catalog ASUMRE BIN CONSTNT CURVE FACTOR FETCH FCHISQ GAMMA HISTOC HOUROUT INFO LINEFIT PCHISA (_stop ) CATALOG ACQUIRE ARROW BUFEND DOT GINV2 HISTS HOURLY SINV SET, AT Logical Structure of the Data Summary Program 156 * Next the executive program turns control over to functional group-B. This group is composed primarily of binning and plotting routines for display of the statistical information accumulated during event by event processing. Finally, the executive program turns control over to functional group-C, which summarizes the outcome of the processing. it then directs the data processed to the appropriate medium, either magnetic tape or the photo-digital storage system. 157 »- de “Efficiency Program. A program to generate two body events was written to perform three functions: 1. t° compute the geometric acceptance of the apparatus; 2. to aid in performing the background subtraction; 3. to provide samples of events of various types. Figure 6.37 illustrates the basic flow of the program. Input to the program includes counters sizes and distances from a pivot point, target size, coordinate and energy resolutions, particle masses, incident beam energy. Two event types were available. The first was simple two body. ‘The second assumed that one of the final state particles immediately. decays into two photons, and that the photons are subsequently detected. The relative numbers of the two kinds of processes could be specified, and was used to investigate the problems involved in separating pd > Hey from pd > He? x°, yy. Effects such as multiple scattering, conversion efficiencies of the 31 photons in the converter material, energy loss of the He~'s were all included, as well as any known systematic effects. 158° werdorg LDUETOTIIG ayy Jo sinzondys TeoTFoT LE°9 aansTy 4h + 03993 “ soas1a76OT 4 AOVIBA ¢? aze10us4) Agxoue weaq ‘quyod UCTIIELVZUT 38], 42%d ee . , crea . gndjng Oe A Atdera IFGo13 2 delat Loy sioqv—A~Ay il ee OAq aaRLeue ; ; } 104 P A@ + ob : ’ BOFZEZTTE TIPU] _« dngjag “. ~~ eyeq ezyaeumng ; . . Wvu90ud ANAS 1d9 a K. Chi-Square Fitting The method of ritting used was that of least-square-fitting-with- constraints. Application of the technique as employed in this analysis had its genesis in bubble chamber work. Following is an outline of the method. For more details, several excellent references 17,18,19 exist. The following definitions will be useful in the discussion that follows: m = measured variable vector G = inverse square error matrix form @ (4,3) = ma) Pn) x = fitted values of variables vector f = constraint vector B = constraint derivative matrix " B (i,j) = af, / ax J i Q@ = vector of La Grange multipliers A subscript 1 on a quantity implies the beam particle, 3 implies the particle went into the helium detector, 4 the photon detector. In the analysis m is a vector of dimension eight. The measured variables are the polar and azimuthal angles (see Fig.6.38), 9 and %, for the incident beam particle (proton), the helium particle, and the photon. The other two measured variables are beam energy and the helium energy. For this analysis the matrix G is assumed to be diagonal. 160 —-. = = Higure 6, 38.Definitionof the Variables 6, é 161 The constraint equations are those of momentum and energy. Each event is fit subject to the constraint that. it satisfy energy and momentum conservation. Using the azimuthal and polar angles as defined above, the constraint equations are: Momentum: 1) (x = component) P sinOcos® -P sin® cos? -P sind cos? =.0 ; : 1 1 y 4 y 2) (y - component) P)sin6 sin? +P,sind.sind,+P, sind, sind, =0 3) (z - component ) Pcos0, +P,cos0,+P, cos6), = 0 Energy: 4) ES + M, = E, + By Equations 1, 3, and 4 were used as constraints, giving what is in bubble chamber parlance a 3-C fit. The remaining equation, 2, is used to determine the photon energy for the event. The method of obtaining a fit and the associated measure of fit, chi-square, begins by defining the quantity —_—— 2 > > Boo > x” = (x - m) G(x - m), where (x - m) means transpose. > This quantity is minimized, subject to the condition F(x) = 0. introducing a LaGrange multiplier, 4, define a quantity M given by: —> “a + Xe Hh IR M = 2 The procedure now is to minimize the quantity M with respect to & and —_ x. We have, then, ) a = 2 £ = 0 >) aa = 7. 16z . o> 6) &@ 2 patrcx=o ak The constraint equations, 5, are in general nonlinear, and the solution of equations 5 and 6 is in the general case quite difficult. The problem can be simplified somewhat if the constraints are suffi- ciently linear that an expansion of the constraints can be made. Consider a trial solution ¥. To first order, the constraints become: 7) f(x) — i +——= (X, - = £, (x) ; (x, x5) re) or £(x) + -x)=0 8) f(x) . ~> The method is now to use an iterative procedure to find x and a. Using 6, > -l .. x = -G Ba Using 8: > ~~ -l = f(x) = Bx +G _ Ba) or > a — ~~. -1 ~ <1 a=Q °° [f(x) - Bx], where QQ = BG B, and > el x= -~G Ba > > Using these values of x, the next step is to see whether: Ff =O. Im practice, one specifies a tolerance within which one says the constraints have been satisfied. If the constraint is satisfied,stop. If not, one uses the value of x as the new X, and reiterates. The actual routines for carrying out the method outlined above are embodied in the routines FANDB, and SOKIT2M. For reference, listings of these routines are given on the following pages. AAA NAMAAAAAND aaa aan »- SUBROUTINE FANDE (Fs, ByX,NCON) WRITTEN BY RVK MAY 18, 1972 . a REAL Mly M2e M3, N4 COMMON/MASS/ N1le M2_ M3_ M4& DIMENSION F(3). BlBe3), X08) COMMON/MASSQ/ Sly S22 S39 S4& COMMON /EO8S/E30BS, E408S SET UP QUANTITIES USEFUL FOR DERIVATIVE CALCULATIONS $T = SINE QF A THETA ANGLE SP = SINE OF A PHI ANGLE 1 = PROTON , Lees 3° = HELIUM 4 = PHOTON STB=SINC(XCLD) CT3=COSCXC1)) : . ST4=SIN(X(37) H CT4=COSUX(39) STL=SIN(X(5)) CT1=cOS(X(5)) : SP3=SINUX(29) | ; - be cP3=COs(x(2)) a SP4=STNCX(4)) vs CP4=COS(X(4)) : 7 SPL=SINIX(6)) . ; . : CP1=COS{xXt6)) ; P3=X(7) a : P1L=X (8) { E3=SQRT (P3**24S3) : EL=SQRT(P1**24S1) SO ae : ¥=PL*STI*CP 1L-P3*ST 3#CP3 : ; Z=ST4*CP4 oo P4=Y/Z E4=SQRT(P4¥*2484) E30BS=E3 $ E4NBS=E4 Oe P4ATL=P LECTLSCP1L/Z ce - 1 P4PL=—P1* ST L¥SPL/Z pe P4T32-P3*CT3*CP3/Z P4P3=P 3*ST3* SP3/Z P4T4=-YECT4*CP4/ 2/2 P4P4=Y ¥ST4*SP4/Z/2 P4PP3=—ST3*CP3/Z P4PP1=STL*CPL/Z CALCULATE THE COMPONENTS OF THE CONSTRAINT VECTOR Fe —— ——— FEC LI=PLICTL4+P3*CT3A+P4ECT4 "F(2)=P LEST LSP 14+P3*ST3*SP34P4* ST4*SP4 = F(3)=E14M2-E3-E4 CALCULATE THE COMPONENTS DF THE DERIVATIVE MATRIXs B BOL, 1) =-P3*ST34+CT44P4T3 B(2_ 1) =CT4*P4P3 BU3Be Ld 2-P4*S TSH TE*PSTS Bi 4, LI =CT4*P4P4 BUS¢1)=-PLESTLECT4*P4TL B( 651) =CT4* P4PL 16 4 BU7, L}=CT3+CT4eP4pp3 BCs LP ECTL+CT4*P4pp, BOL,2)=P34CT3*SP3 + «ST4*S5SP4%P4T3 B(2— 2) =P 3eST3CP3 + «ST 4SSP4eP4gp3 B(3s2}=P4*CT4°SP4 + ST4#SP4AXP4TAR .- Bl4e20=P4*ST44CP4 + ST4e5P4RP4p4 BUSe2b=P1SCTIXSPL + ST4*SP4*P4TL Bl6,2)=PL*ST1IHCP] + ST4*SP4eP4P] B(7e2)=ST3*SP3 + ST4*SP4*P4Pp3 B( By 2)=ST1LESP1+ST4*SP4eP4PP) PE4=P47E4 ‘ ~ BG1, 3) =-PE4S*P4T3 B(213)=—-PE4*P4P3 B(393)=-PE4*P4T4 - BC 423) =-PE44*P4P4 BU5,3)=-PE4*P4T1 , - B6.3)=-PE4*P4P] : BU7 4.3) =-PE4 *P4PP3- -P3/E3 - B( 8.3) =-PE4*-P4PP1+P1L/E1 - RETURN END SUBROUTINE KINETCCENOM) REAL Mly M2+ M3y 44 COMMIN/KNC/ Ay Dy Pe E3Cy PBC. ESC, PGC, Ply EINCM2, C COMMGN/MASS/ Mls M2. M3, M4 E1=ENOM+M1 S=SQRT (ML¥M 14M2*M24+2.*M2*EL) W=E14M2 . PL=SQRT(E1L*E1-M14M1) GAM=4/S . BETA=P1/W - E3=(S*S+M3*N3-M44M4)/S/2. E4=S-E3 P=SQRT (E3*E3—M3 £43) A=GAM#P. C=BETA#GAM*F3 D=BETA*GAM* ES - P3C=SORT ( E3¥E3-M3#M3) P4C=SQRT (4% E4-MGe MG) E3C=GAM#E3 E4C=GAM*E4 P3C=8ETASGAM*P3C ~ P4C=G&M* RET AXP4C -- EINCM2=ENOM4+M14+42 RETURN END 165 SUBROUTINE SOKIT2M 200 DO 200 I = LsNVAR VXBAR(I) = VM(T) VCBAR(I) = 0. . SIGTST(1) = EPSI*SQRTIGIUIVT)) GUIs) = Le/GHT.D) “- CALL FAND3( Fy 3, VXBAR,NCON) GO To 710 AMAMRAAAAAAANAAND FOR FIRST ITERATION, GO IMMEDIATELY TO 710 AND TAKE A STEP. FOR SUBSEQUENT. ITERATIONS: CALCULATE CONSTRAINTS AND DERIVATIVES ae ad USING VX FROM THE LAST STEP. IF NO STEP HAD BEEN TAKEN REFORE LAST STEP, CALCULATE THE ASSOLUTE VALUE OF THE CONSTRAINTS AND GO TAKE _—. a c e c . c Cc KINEMATIC LEAST SQUARES FITTING ROUTINE WRITTEN BY BRYCE SCHROCK, Cc OCTOBER, 1971 AT LRL, BERKELEY. THE ROUTINE MINIMIZES CHI-SQUARED Cc SUBJECT T9 THE NON-LINEAR CONSTRAINTS OF MOMENTUM-ENERGY CONSERVATION, Cc . c : - Cc NVAR = NUMBER OF MEASURED VARTABLES Cc NCON = NUMBER OF CONSTRAINING EQUATIONS c VM(D) = VECTOR OF MEASURED VARTABLESCLINPUT) Cc VXOT) = VECTOR OF FITTED VARTABLES(QUTPIIT) c GtIs1) = DIAGONAL WEIGHT MATRIX( GOI,g1) = L/SIGMACT,1)#*2) Cc GY¥(IeI) = DEAGONAL ERROR MATRIX € GICTs1) = SIGMACI,1)**2 ) c ~~ c ~ c c ----= -~- ‘ COMMON/FITBAG/ © CHI2, LFRUCT+NVARsNCONs VM(8) 9 VX08) 2GI(8.8). DIMENSION .G (8,8) VXBAR(8) o VCC 8), SIGTST(S) eVCBAR(8) y VCDIF(8) 9 F (3) © B(8—93) ¢B8DUM (898) 9VR 03) gH1393) eHI (393) eVALEC3) | DATA EPS1,EPS2 /201s201/ DATA ISTPMX, ICUTSEC, ICUTOT/ 505 25, 25 / Cc a oF -€ Cc INITIALIZE PARAMETERS | Cc --- . -_—— : IFRJCT = 0 1sTtP = 0 $ 1CUTS = 0 $ ICUTO =0 OMEGA =.1.F6 $ CHISQA = 0. §$ CHISQB = 0.. CHISQ80 = 5. 8 $ CHI2 = 1.E6 a Od “ —— C SET VXRAR,VCBAR FOR FIRST STEP AND CALCULATE THE WEIGHT MATRIX G '¢ ALSO CALCULATE THE CONSTRAINTS AND DERIVATIVES FOR THE FIRST STEP. .c THE SIGTST(1) ARE THE CONVERGENCE CRITERIA FOR THE DIFFERENCE VECTOR. a c —a — o-ne STEP. IF A PREVIOUS STEP HAN BEEN TAKEN, CALCULATE THE ARSOLUTE VALME OF THE CONSTRAINTS FOR THE LAST STEP AND CHECK IF THE CONSTRAINTS ARE SATISFIED. (4) IF TREY ARE, CHFCK THE CHANGE IN. THE DIFFERENCE VE TF IT HAS STOPPED CHANGING, THE FITTING 1S ALL DONE(GI TO 4000). IF IT 1S STILL CHANGING, TAKE ANOTHER STEP. (8B) IF THE CONSTRAINT ARE NOT YET SATISFIED, COMPARE THE ABSOLUTE VALUE FROM THE LAST STEP THAT FROM THE PREVIGUS STEP. IF IT HAS FMPROVED, GO REDEFINE VXPAR AND VCRBAR AND TAKE ANOTHER STEP. IF YT HAS NOT IMPROVED, CUT THE SIZE AND TRY AGAIN. ‘ “Aaa 166 "300 600 CALL FANDS( Fe Be VX_NCON) OMEGOLD = OMEGA OMEGA = 0. DO 600 I = 1»NCON OMEGA = OMEGA + ARSCF(I)) IFCISTP.LT.2) GO TO 700 640 650 IF (OMEGA.GT.FPS2) GO TO 660 00 650 I = L»NVAR VCOTFUT) = ABS(VC(T I-VCBAR(T)} TF{VCDIF(1).GT.SIGTST(I)) GO TO 700 CONTINUE ; ’ , GO TO 4000 660 6T0 IF (OMEGA.LT.CMEGOLD) GO TO 700 IFCICUTS.GT.ICUTSEC) GO TO 2500 TFCICUTN.GT.ICuTOT) «GO TO 2700. 1CuUTS = ICNTS + 1 $ IcUTO = IcuTO + 1 00 670 I = L»yNVAR . VCUT) = (VCCID+VCBAR(T))/2- VXC(D) = ver) + VMCT) - CHISQA = (CHISQA42 «*PS1+3.¥*CHISQADI/4~ PST = (PSI+CHISQAD)/2. GO TO 300 , DOD 705 I = 1,NVAR VXBAR(I) = VXUT) VCBARL ET) = VCCT) CHISQAD = CHISQA eee IFCISTP.GT.ISTPMX) GO TO 2000 TcuTs = 0 CALCULATE & = BT#CBAR - F _CALL MTX TMMINVAReNCON, 1 By VCBAR » BDUM ) CALL MTX MSMCNCON, 1, 80UH,F,VR)- CALCULATE H AND THEN H INVERSE. Cc ae en ae ae scat re es ae ae ee ee a Se em eR em orm Cc 1 ‘ ‘ : Cc "CALL MTX MMM(NVAR,NVAR, NCON,GI,B, ADUM) CALL MTX TMM(NVYAR »NCON, NCON, By BDUM,H) DD 1 T=1, NCON DO 2 J=l,s NCON HI CTs J)=H( Ted) CONTINUE “7 CONTINVE CALL MATINV(HI, NCON, AAAA) CALCULATE ALPHA. 725 730 DO 730 = 1,NCON VALF(I) = 0. | DO 725. J = 1leNCON VALF(T) = VALFCT) - HI(T,J)*VR(J) CONTINUE it Qo me oe oe tne CALCULATE C AND X. CALL MTX MMM(NVAR NVARYNCONCGI 4B, ROUM) CALL MTX MMM(NVARSNCONG 1, SDUMsVALF OVC) ee ae oe ee ae ee ee ee ee 740. (167 00 740 IT = LsNVAR vetr) = - VCCI) CALL MTX MAMINVARs Le VCe VMeVX) oan aaa an CALCULATE CHI-SQUARED AND CHECK FOR RNUND-OFF ERRORS. 750 760 -CHISQB CHISQA = 0. DO 750 1 = 1sNCON CHISQA = CHISQA - VALFUI)*VRET) 0. DO 760 I = 1»NVAR CHISOB = CHISQB + VC(I)#G(1,T)#VCUL) it CALCULATE PSI, TO BE USED WHEN CUTTING STEP. 780 N0 780 T = 1lsNVAR PSI = PSI + VCCL)*GC 1, TIFVCRAR(T) ISTP = ISTP + 1 GD TO 300 AMAMAAAAAaAN REJECTED EVENTS COME HERE. KEEP TRACK OF THEM. IFRJCT = 1 NO CCNVERGENCE WITHIN-THE ALLOWED NUMBER OF STEPS IFRICT = 2 STEP SIZE CUT THE MAXIMUM NUMBER OF TIMES WITH NO IMPROVEMENT NOTED. 2000 2500 2700 Cc 1 $ GO TG 5000 > 2 $ GO TO 5000 $ GO TO 5000 IFRJCT TFRJICT TFRJICT=2 ~~ ——_ IF GET TO 4000, A SUCCESSFUL FIT HAS BEEN OBTAINED. c 4000 _ $000 CHI2 = CHISQA | RETURN ~ . CONTINUE RETURN $ END 8 168 L. PI-Zero Analysis Kinematically similar, data for the reaction pd > He 2° (1) was perforce collected simultaneously with the reaction of primary interest, pd > Hey, (2) Reaction 1, owing to the strong, rather than electromagnetic, origin is produced about 30 times more copiously than reaction 2, and constituted the dominant background process. ‘The following consider- ations’ motivated the analysis of the data for reaction 1: 1. The angular distribution for this process was needed in order to perform a background subtraction for reaction 2. 2. Other data existed for seattered angles and energies for reaction 137733934 however, until now no complete angular distribution was available. 3. Previous investigators?’ established the normalization of reaction 1 relative to that for pp elastic scattering by measuring both reactions in the same experiment. This enabled us to check the normalization of our data. The threshold energy for multiple pion production is calculated using: [eo] 2 2 tr = [(M + nM - (M +M }/ah, : in 3 © On My) / , where T is the incident proton kinetic energy, n the number of pions. P The threshold energy for single pion production if 198.7 MeV, 415.4 MeV for two pions, and 64.1.0 MeV for three pions. Three pion pro- duction lies outside of the kinematic range of interest for this 169 d- experiment. A separate analysis was performed to see whether 2° contamination of reactions 1 or 2 would be significant. The conelusion is that it contributes at a negligible level, for at least four reasons: 1... 3. . . . fo) The production cross section is lower for 2x because of ' the smaller phase space. The phase space for the resultant photons from the process ray yy is large. For our apparatus the geometric ‘detection efficiency for these photons is small. The maximum helium lab angle is about 7°. This is less than the helium angle for reaction 1 in the kinematic region of interest. The missing mass for two pion production allows for immediate rejection. We will not considex two pion contamination further. The analysis of reaction 1 was similar to that for reaction 2, differing substantially only in the following respects: 1. The photons produced by x 9 yy were used only in the trigger requirements, but not.in the subsequent analysis. A 1-c kinematic fit was made to the data using a ‘pd + He? x hypothesis. The helium center of mass angle used to bin the data was computed using properties of the helium rather than the photon, as with reaction l. The helium detector determined the geometric acceptance of the apparatus, rather than the photon detector. 170° The data was analyzed using only the properties of the target, the proton beam, and the helium. Modifications were implemented in the least-squares-fitting programs to permit use of a one constraint fit 2 (1-c). . Overall energy balance provided the constraint. AX for the fit was produced and used to make cuts in the subsequent analysis. Prior to the kinematic fitting phase of the analysis, cuts were imposed on the data. A cut was placed on the output of the differ- ential pulse height counter, and on the event origin, as determined by extrapolating the helium trajector to the target midplane. Typical distributions, with the positions of conservatively placed cuts indicated, are shown in Figures 6.39 and 6.40. The first cut was very ‘powerful, immediately yielding a reasonably uncontaminated sample of pd -+ He? x° events. The second cut substantially reduced the amount of analysis by eliminating early event combinations due to spurious spark chamber signals. The helium center of mass angle was needed to facilitate cross section calculations. This was obtained in two ways, one using the helium angle, one the helium eriergy. Using the lab energy, the center mass angle of the helium particle is computed using: cos0” = (E /y-E °)/Bp ” He He He He where primed quantities refer to center of mass quantities. Using the helium lab angle, the calculation of the center of mass angle is performed using: o 2 cosO” = {ac + tance. (22457 )(o°-B)I4/(an4B ) 4771 320 240: I60 80 ro ©) rot | kL dE /dx Figure 6.39 Differential Pulse Height Counter Spectrum 10. (172 5 i _ 0 _ -R iL - _ -10 & | ! | Z-vs -Y TARGET | Figure 6.40 Reconstructed Event Origins lO. 173 where © 2 2 A = Pa (l+B 7) e B = yp’ /tan(@ ) He He L He “The choice between the two roots is made by demanding that the lab helium energy calculated using the derived center of mass angle lie closest to the observed lab energy. The method yielding the best resolution was used, and depended on the particular lab angle or energy involved. Near the Jacobian peak of the lab angle versus center-of-mass angle plot the helium energy was used. Here the large * , value of d@ /d@ made use of the angle unfeasible. The geometric acceptance of the apparatus was computed using Monte- Carlo techniques (ef. section 4 and Appendix J). Independent checks of these calculations agreed on the percent level. The remainder of the analysis proceeded as described in section 4 for reaction 1. Each photon detector setting encompassed a center of mass angle range of about 60°. ‘Three counter settings were analyzed to yield a complete angular distribution for an incident proton energy of 462 MeV. In addition, more limited angular distributions were produced for incident proton energies of 377, 576 MeV. Figures 6.41 and 6.42 display the resulting angular distributions. Note in parti- cular the agreement with Crewe, et al., suggesting that our overall normalization is consistent with pp elastic scattering data. 1030 x bia TU A | { | L 174 de (oq He®ar®) x 10° CM2Ster - da | alt TT T_T S ® Crewe, Ref.34 - ar @ This Experiment : — —“ | — 9 — 8 ~ af — 6 — Re) — 4 — Re) — | ! J 50 70 90. HO . 130 150 : x { ‘ | Figure 6.41 Differential Cross Section for pd + He777° at 462 MeV. 175 GS (pd He*) x 10°°cm’/Ster 6 5 377 Mev A | 571 MeV ++ T+ — 50 70 90 No 130 150 Oe ' Figure 6.42 Differential Cross Section for pd > He tf ° at 377 and 571 MeV. ateneee co 176 ” BEAM me HELIUM "ENERGY ~~ ® _ cM MEV _ANGLE Ao/ dao 462 °° 30.0 35.04 2.8 462 40.0 35.0 + 2.8 462 a 53.5 39.1 + 3.2 462 | . 60.5 35.1 + 4.4 462i | 67.5 | 34.2 + 2.5 462 ; 74.5 . 33.34 2.7 462° - | 76.0 34.5 4° 1.9 462 80.0 | 32.0 + 2.5 "462 . 90.0 . 28.6 + 2.9 - 462 104.5 30.54 3.2 462 : 105.0 . 38.0 + 3.8 462 113.5 40.5 + 3.6 462 - 122.5 | “111.2 2° 7.8 462 - 131.5 . 197.5 £ 13.3 462 | 140.5 344.1 + 27.0 377 80.0 41.0 + 3.0 576 — ' 80.0 . 27.54 2.7 TABLE 6.6 Angular distribution for pd > He>n° 177 The resulting angular distributions for the process pd + He>n° were used to perform a background subtraction. In order to do this a fit was made to the pd > He? 1° angular distribution of the form do _ 6 yi-l an = 2 a, i=1 where 6' is the He? center-of-mass angle in radians. The coefficients obtained are: a, = ~58.30 + .83 a, = 497.09 + .62 a, = -1024.91 + .40 a, = 1029.36 + .23 a, = ~501.00 + .13 = 93.67 + .07 “178 M. Targets Two thin liquid deuterium gas buffered targets were employed in this experiment. The nominal thicknesses were: Ul Thick target «5000 + .0005 inches Thin target «1710 + .0002 inches The thin target was employed for settings where the helium kinetic energy was low, and effects due to multiple scattering and ionization energy loss a potential problem. Figure 6.43, illustrates schematically the target construction. The pressure inside the gas buffer and the liquid deuterium were the same, -minjmizing any tendency of the target to bow. The deuterium was condensed using liquid hydrogen. ‘The 20 mil mylar window was required as a safety precaution should the flask break. ‘The active area of the target was about three inches square. The liquid level was monitored with a set of range telescopes posi- tioned to measure pd elastic scattering (cf. Appendix B). The monitor rates for the thick target varied no more than 1% or so during the course of the experiment. Measurements made of the thickness using liquia nitrogen at the same pressure as encountered in actual running conditions indicated that bowing was negligible. The elasticity of mylar is small at room temperature, and indications are that it is not a strong function of temperature (checks were made of this). Thus making the bowing measurement at liquid nitrogen temperatures seems sufficient. osze-2e2i7Ex STTeLeq uoTpONALsUOD yeBreL Cy*g sInsTT MOpPUIM 1D] AW MaIA apis | {iw Og oH Mala juold ¢ Jajyyng so6 <q — 4+ dD woeg | Ne | oe yo610} Ke oY dad ee cee une tly ee et ee ee oe woag jaquous A Bulia}y09S 180 The monitors indicated as much as 25 - 30% variations for the thin target. The source of these variations is imperfectly known. The following points were checked or measured: i. The thickness of the target was measured at liquid nitrogen temperatures. A bowing of about 25% was observed. 2. Scatterplots of the position of the event origin showed no indication of low liquid levels. 3. ‘The target was watched at various times for indications of bubbling. Bubbling was observed for a period after the deuterium was condensed, after which it subsided. The interpretation that has been made is that the thickness of the target increased about 25 ~ 30% due to bowing. Though we cannot prove that this is the direction of the change, the data obtained for those settings waich overlap with the same setting using the thick target are consistent when this interpretation is made. The pressure. of the liquid deuterium was recorded as a possible additional monitor of the liquid density. The typical flask pressure was about l2 in. Hg, with a typical variation of +1 in. Hg, although variations of 20% were observed. However, no correlations of this — pressure variation with monitor rate was observed. pata ‘© shows that the liquid density is not a strong function of pressure. We take the liquid density to be .16770 + .00050 em/om”. 13] . » ; N. Bean Integrators Three helium: filled ion chambers, each with its own integrator, were used “to measure the beam intensity. The integrators were periodically cali- brated using a current source (Keithly 201). The results of the three ion chambers were consistent to better than 1% over the entire duration of the experiment. A set of direct beam counters, each 1/8" thick and 12" in diameter, were used in conjunction with the proton telescopes (cf. Appendix B) in order to determine the absolute ion chamber calibration. Briefly, the tech- nique was to run the beam at a low intensity to establish a relationship between the beam intensity, as measured by the direct beam counters, and the coincidence rate for the proton telescopes for pp elastic scattering from a CH, target, using a 558 MeV proton beam. Removing the direct beam counters, the intensity of the beam was increased until the leakage cur- rent of the ion chambers was negligible compared to the beam current. Com- paring this beam current to the coincidence rate for the proton telescopes yields the absolute calibration. A low beam intensity of about 10° protons per second, instantaneous, was used with the direct beam counters. At this rate reliable corrections could be made for counting losses. The high beam intensity was about 2x 10° protons per second. The 558 MeV energy was chosen because the pp elastic scattering cross section is quite flat in this energy region. This made the measurement quite insensitive to any small changes in beam steering. The target for 182 - pp @lastic scattering consisted of a 4 inch block of CH,, located down- 2°? stream of the ion chamber being calibrated. The largest correction to the measurement was for accidental coincidences in the proton telescopes. The rate due to accidental coincidences was t typically 22%. Per unit of integrator output, the value of the integrator constant ob- 7 tained finally is (2.84 + .05) x 10’ protons. 183 -O... . Current Experimerital Status of Symmetries Here we briefly review the present experimental status of the symme- tries C (charge conjugation), P (parity), T (time reversal), CP, and CPT in the weak and electromagnetic interactions. The symmetries 26,40, 41 9 / » P, and CPT are all known to be invariant in the 3 strong interactions (SI) with a precision of .3% or better, and will . not be considered further as a possible area in which to look for symmetry violations. In particular, CPT is tested by measuring the =o + = mass of K°, K° ?, where | K° > = cpt | K® >. The equality of Cc) a Tro : boyd <0] Hoy + Hiner * Bar | Ke >=<k | Bo bay Big | K’>, which calculates the mass of K°, K° has been established to a precision of An / ~ 107, where A, = | mo - mgs |p m~ te. In the electromagnetic interactions (EMI) an upper limit on CPT vio- lations of about one part in 10% can be established if one assumes that the contribution to any violation in the SI due to EMI has a strength on the order a”, Studies of EMI via interactions of leptons’” places an upper limit on parity violations of one part in 10°, Bernstein, Feinberg, and lee” reviewed the experimental status of C and T conservation in the EMI, and found the evidence to be consistent with a rather large violation. Recent measurements, using the method of detailed balance, of the reactions np @ 7d and np eny claim results consistent with no violation - These experiments are very difficult, however, all suffering to varying degrees from 184 normalization difficulties. Thus, although one rules out a gross violation of the order of 30%, one cannot as yet rule out 5% violations. Teste of C-invariance using decays of B=0 particles and looking at the energy distributions of the charged final states are inconclusive at this time. In the weak interactions (WI) it is well known that P is violated. In 164 it was observed that the product CP is not conserved in weak decays of the kaon. Specifically, the KL, thought to be a CP eigerstate with eigenvalue - 1, was observed to decay into two pions (CP=1). Present values for the magnitude of the violation for the charged and neutral decay modes are 1.98 x 10°73 and 2.09 x 10°73 (ref. 60). It is this CP violation, thus far observed only in the weak decays of kuons, which has motivated the search for a corresponding T violation. Where should one look for the T-violation? One suggestion stems from the suggestive value of 2 x 10°, whichis approximately A/a. If the decay of Ky, into two pions were due to an electromagnetic correction to the weak decay Hamiltonian, then perhaps there might be a large T-violation in the electromagnetic interaction of hadrons. It is these notions which have lead to measurements of the processes 7 peYn, np © yn, and finally to this experiment which measures pd © yie>. 185 24... T. A. Lasinski, et al., RMP 45 ,part II (1973). 25. OW. Pauli, Niels Bohr and the Development of Physics (McGraw- Hill Book Co., New York, 1955). 26. J. Bernstein et al., PR 139, B1650 (1965). 27. N. Christ and T. D. Lee, PR 143, 1310 (1965). 28. T. G. Inis, Constant-Amplitude Light-Flash Generator for Gain Stabilization of Photosensitive Systems, UCRL-10895, 1965 (Un- published). 29. J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods (Methner & Co. LTD, London, 1967). 30. G. D. Badhman, et al., NIM 57, 116 (1957). 31. R. L. Grawn and D. L. Smith, NIM 80, 239 (1970). 32. oS . Harting, et al., PR 119, 1716 (1960). 33. N. L. Booth, PR 132, 2305 (1963). 34. A. V. Crewe, et al., PR 118, 1091 (1960). 35. J. McL. Emmerson, Symmetry Principles in Particle Physics (Oxford University Press, London, 1972). 36. P. Argan, et al., in: Few Particle Problems, I. Slaus, ed. (North Holland Press, 1972). 37. C. A. Heusch, et al., A Measurement of the Reaction pd + He>n® in the Resonance Region, submitted to the International Conference in Elementary Particles, Aix-en-Provence, Sept., 1973. UCSC Preprint 73/008 (1973), to be published. 38. G. C. Wick, Ann. Rev. Nuclear Science 8, 1 (1958). 39. C. E. Friedberg, Ph.D. thesis, Princeton, 1969 (Unpublished). 40. W. Von Witsch, et al., PL 22, 631 (1966). 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 187 “The checks were made by comparing the results of a Monte Carlo program written by R. V. Kline with results from one written by Gary Olsen, a visiting summer student to LBL (1973) from UCLA. The latter program will appear as a UCRL report. R. Trower, et al., High-Energy Particle Data, UCRL-2426, p121 (1965 Rev.). S. S. Wilson, et al., NP B33, 253 (1971). M. H. MacGregor, et al., PR 169, 1128 (1968); 173, 1272 (1965). F. Boehm, et al., PRL 14, 312 (1965). Ibid. Ref. 24. D. H. Fredrickson, Ph.D. thesis, UC Berkeley, 1974 (Unpublished). D. Bodansky, et al., PRL 17, 589 (1966). S. Rock, Ph.D. thesis, UCRL-2004, 1971 (Unpublished). 0. C. Kistner, PRL 19, 872 (1967). P. A. Bulgakov, et al., Yad. Fiz. 18, 12 (1973). 0. E. Overseth and R. F. Roth, PRL 19, 391 (1967). B. A. Jacobson and E. M. Henley, PR 113, 234 (1959). We note that the electromagnetic vertex yNN can yield an effect of the type discussed with respect to yNA as long as the two nucleons are not on the mass shell, or equally far removed from the mass shell. 39. 40. Ai. 42, 43. 44. 45. 46. 47. 48. 49, 50. 51. 52. 53. 54. 55. 56. 57. 188 n+p +d+t y: A Test of Time Reversal Invariance, Ph.D. Thesis, Princeton, 1969. PL 22, 631° (1966). PR 165, 1233 (1968). L. Grodzins and F. Genovese, PR 121, 228 (1961). D. Alburger, et al, Phil. Mag. 6, 171 (1961). B. Aubert, et al, PL 10, 215 (1964). S. Barshay, PRL 17, 49 (1966). E. Whalin, et al, PR 101, 377 (1956). 3.€. Keck and A.V. Tollestrup, PR 101, 360 (1956). D. Bartlett, et al, PRL 23, 893 (1969). B. Schrock, et al, in High Energy Physics and Nuclear Structure, edited by S. Devons (Plenum Press, New York, 1970). M. Schrock, et al, PRL 26, 1659 (1971). D. Bartlett, et al, PRL 27, 881 (1971). C. Richard-Serre, et al, Nuc. Phys. B20 (1970) 413-440. P. Berardo, et al, PRL 26, 201 (1971). Cc. Joseph, et al, Measurement of the mn Radiative Capture Reaction in the First Resonance Region, Paper #22, Contributed to Bonn Conference, Aug. 1973. W. Frazer, PR 150, 1244 (1966). C.A. Heusch, et al, A Measure of the Reaction He? > pd in the Resonance Region, UCSC 73/004, Submitted to International Sympo-— sium on Electron and Photon Interactions at High Energies, Bonn, Aug., 1973. See ref. 36, page 519 for some current (1972) results. The 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. ‘71. 189 experimental situation is reviewed by K.H. Bray, et al, PR C3, 1771. (1970). The checks were made by comparing the results of a Monte Carlo program written by R.V. Kline with results from one written by Gary Olsen, a visiting summer student to LBL (1973) from G. Igo's group at UCLA. The latter program will appear as a UCRL report. Trower, et al, High Energy Particle Data, UCRL-2426, Vol.1I (1965 Rev.), page 121. S.S. Wilson, et. al., Nuc. Phys. B33, p.253 (1971). MacGregor, et al, PR 169, 1128 (1968); 173, 1272 (1965). Boehm, et al, PRL 14, 312 (1965). Rev. Mod. Phys., Vol. 45, No. 2, Part IL, April, 1973. D.H. Fredrickson, Ph.D. thesis, UC, Berkeley, 1973. D. Bodansky, et. al., PRL, 17, 589(1966). S. Rock, Ph.D. thesis, UCRL - 20041. 0.C. Kistner, PRL, 19, 872(1967). Bulgakov, et. al., Yad. Fiz. 18, 12(1973). Overseth, et. al., PRL, 19, 391(1967). Calaprice, et. als, Phys. Rev. 184, 1117(1969). Stein, et. al., PRL, 19, 741(1967).