IV1ESI_J RETURNING MATERIALS: P1ace in book drop to LlaaAmEs remove this checkout from .4“. your record. FINES will be charged if‘book is returned after the date stamped below. HIGH ENERGY GAMMA RAYS IN INTERMEDIATE ENERGY NUCLEUS‘NUCLEUS COLLISIONS BY Kevin Breckenridge Beard A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1986 ABSTRACT HIGH ENERGY GAMMA RAYS IN INTERMEDIATE ENERGY NUCLEUS-NUCLEUS COLLISIONS BY Kevin Breckenridge Beard During an experiment to measure charged pion production for 1“N + Cu collisions at E/A - uo Mev using an Enge split-pole magnetic scectrograph, a much larger than expected background of high energy electrons and positrons was observed. By comparison of the target-in to targetqout spectra, it was deduced that most of the leptons were produced by gamma rays which were converted to electronspositron pairs in the material of the entrance aperture of the spectrograph. An experiment was constructed and carried out to determine the photon, electron, and positron yield. The method for the detection of the high energy gamma rays was to convert the photons to electron-positron pairs immediately at a stopping Cu target. The energy spectrum of the electrons and positrons was measured using a magnetic spectrograph with specially constructed multiwire proportional counter plus Cherenkov detectors. The beam was Kevin Breckenridge Beard 1"N accelerated by the National Superconducting Cyclotron Laboratory K500 cyclotron to an energy E/A - NO MeV. Use of three converter elements with very different conversion efficiencies permitted the separation of the yield of electrons and positrons due to the pair conversion of gamma rays from that originating in the collision. The direct yield of e+e- pairs is less than 2% of the gamma yield. An improved experiment using a telescope of active converter backed by a stack of Cherenkov counters was then used to measure the high energy gamma rays for 1"N+Pb, Zn, and C at E/A-NO MeV, and ‘“N+Pb at E/A-30 Mev. The cross sections are nearly isotropic. For gamma rays of energy EY)20 MeV, 0‘“N+Pb'0‘3 mb. The gamma ray cross section is compared to the neutral pion cross section allowing for the difference in mass and phase space; the two appear quite similar. Several theoretical models are compared to the data. DEDICATION To my wife, Jan. 11 I-“ ‘— ACKNOWLEDGEMENTS This work has been supported through the efforts of the staff of the National Superconducting Cyclotron Laboratory, especially Drs. W.Benenson, J.Stevenson, J.van der Plicht, and J.Yurkon. Additional support from my parents, Dr. and Mrs. G.B.Beard, grandparents, Mr. and Mrs. W.Roehling, and my wife Janet M. Hodgson~Beard is greatfully acknowledged. iii TABLE OF CONTENTS LIST OF TABLESOOOOOOOOOOOOOOOO0.000000000000000000.0000. V11 LIST OF FIGURES.........................................viii Chapter 1 - Introduction................................ 1 Chapter 2 - The Pion Experiment and the Observation of High Energy Electrons and Positrons......... 7 2.1 Pion Production in Nucleus-Nucleus Collisions.. 7 2.2 Experimental Technique for the Pion Measurement 9 2.3 Results of the Pion Experiment................. 16 2.h The First Electron and Positron Experiment..... 18 Chapter 3 - The Positron Experiment.. ............ ....... 21 3.1 The Converter Concept.......................... 21 3.2 Modifications to the Spectrograph and Scattering Chamber............................. 2“ 3.3 Changes in the Detector........................ 26 3.“ verification TestSOOOOOOOOOOIOO ..... 00.00.00... 29 3.5 Results...OOOOOOOOOOOOOOOOOOOOOO0.0000000000000 29 Chapter A - Analysis of the ei Experiment ..... .......... 39 u.1 Introduction and an Example of a Monte Carlo Calculation....................... ....... ...... 39 U.2 Modelling the Detector Efficiency. ..... ........ NS u.2.1 Verification Tests... ........... ......... 53 N.3 The Pair Production Cross Section.............. 53 A.“ Other Processes.. ....... ................ ..... .. 59 u.5 Modeling of the Target and Converter........... 61 iv Chapter 5 - Gamma Ray Telescope Experiment ...... ........ 68 5.1 Introduction....................... ........ .... 68 5.2 The Design of the High Energy Gamma Ray TelescopeOOOOOOOOI...IOOOIOOOOOOOOOOOOOOO ..... O 70 5.3 The Experiment........ ....... .................. 7h 5.A The Results.......... ..... .............. ...... . 76 Chapter 6 - Theoretical Models.. ....... ................. 83 6.1 Comparison of Photons and Pions................ 83 6.2 Coherent Bremsstrahlung........................ 87 6.3 Hard Sphere Bremsstrahlung..... ............... . 93 6.N Fireball........................ ...... ......... 93 6.5 Incoherent Bremsstrahlung From the Fireball.... 101 Chapter 7 ~ Conclusions....... ...... . ...... .. ........... 107 Appendix A r Theoretical Calculations. ................. . 109 A.1 Bremsstrahlung. ................................ 109 A.2 Hard Sphere Bremsstrahlung ...... ............... 116 A03 F1reba1100000000 ........ .00.... ....... O 00000000 118 A.u Incoherent Fireball Bremsstrahlung ............. 121 Appendix B - Experimental Hardware. ..................... 127 8.1 The Enge Split-Pole Spectrograph......... ...... 127 8.1.1 General Relationships.................... 127 8.1.2 Nonrelativistic Kinematic Corrections.... 131 801.3 EXit Windowcooooooooooooocoo-cocoon. ..... 133 8.1.“ New Scattering Chamber and Aperture...... 133 8.2 General Design of the wt experiment............ B.3 Experimentai Electronics............... ........ 8.3.1 The n Experiment E1ectronics............ 8.3.2 The 62 Experiment Electronics............ 8.3." The Y Telescope Electronics.............. B.u PCOS III Electronics... ..... . ........... ....... B.5 Delay Cards......... ...... . ........ ............ Appendix C - Detector Development and Design............ C.1 MIW Counter.... ...... .......................... C.1.1 Introduction............................. C.1.2 MIW Prototypes..... ...... ................ C.1.3 MIN IV................................... C.2 The ‘2C(a,p)‘5N* Test of the MIW........... C.3 Scintillators.......... ...... .................. C.3.1 Introduction....... ....... ............... C.3.2 Scintillator Design...................... Co“ Cherenkov DetectorSOOOOOOOOOO...OOOOOOOOOOOOOOO Appendix D - Computer Codes............................. D01Acqu181t10nCOdeOOOOOOI.OOOOOOOIOOOOOOOOOOOOOOO D.2 MIN Detector Simulation SCATTER and SUbroutineSoooococoon.one.ooooooooooooooooooooo D.3 Pair Production Simulation GAMMATEE and SUbroutineSOOOO0.0.0.0....OOUOOOOOOOOOOOOO0.0.. LIST OF REFERENCES............................. ..... .... vi 135 1N1 1N3 1N6 1N8 1N9 152 15” 15N 15A 157 16“ 168 171 171 172 176 180 180 182 198 206 LIST OF TABLES Page 2.1 Results of the first search for high energy electronSOOOOO0.0.0.0....OOOOOOOOOOOOOOOOOOOOOOO 19 A.1 Steps for the example Monte Carlo simulation.... uu A.2 Initial limits of the e+ and e_ distribution for the COde SCATTER.OOOOOOOOOOOOOOOOOOOIO000.0. “8 A.3 Parameter T values taken from a fit to the difference in positron results between the Pb and Be converters............................ 66 6.1 ,The angle between the original direction and the direction at impact for two nuclei Just tOUChinBOOOOO.I0.00000IOOOOOOOOOOOOOO0.0.0.00... 92 6.2 Fireball parameters for l"N+Pb at NO MeV/u...... 97 6.3 Temperature of the fireball used in the incoherent bremsstrahlung model................. 102 8.1 General Specification of the Enge SpectrographOOOOOOOOOO. ..... OOIIOOOOOOOOOOOOOOOO 128 C.1 MIN III Specifications.......................... 161 C.2. MIN connectors.. ................. . ..... ......... 161 C.3 MIN IV specifications. ........ . ...... . ......... . 166 C.“ Dimensions of the active region of the scintillators...................... ....... ...... 173 vii 3.6 3.7 3.8 3.9 OF FIGURES The original charged pion experiment......... The original charged pion detector.......... Idealized particle identification plot; the dark regions represent the range of momenta selected by the magnetic spectrograph......... Pion detector modified to identify energetic electrons and positrons...................... Particle identification plot from the first electron experiment........................ Particle identification plot with the requirement that the Cherenkov counter produce a signal in coincidence with the event. Positron experiment concept; stopping target backed by photon converter.................. 1 Configuration of the e Experiment.......... Configuration of the et Detector............. Typical e:t positron spectrum................. Pulse height in Cherenkov#1 vs. pulse height in the E scintillator detector.............. The same as in 3.5. but with the requirement of a good angle in the MIN counter.......... The same as in 3.5. but with the additional requirement that Cherenkov#2 produced a pulse. Electron yield as a function of electron energy for the three converters at 17°......... Positron yield as a function of positron energy for the three converters at 17°......... Positron yield as a function of positron energy for the three converters at 0°....... viii Page 10 11 1“ 15 17 17 22 25 27 3O 32 32 32 33 3H 35 wt...- T wfla 3.11 3.12 Positron yield as a function of positron energy for the three converters at uoo.......... Angular dependence of the high energy positron (70 - 105 MeV) yield for the three converters................................ A particle scattering through N thin identical SlabSOOOOOOOOOOOOOOOOOOOOOOOOO0.0.0.00 Example probability distribution P(G)........... Integrated probability distribution F(0)........ Inverse of the_integrated probability distributionF (X).IOOOOOOOOOOOOOOOIOOOIOOOOOOO Co-ordinate system used in the Monte Carlo calcu1at1°n000000000OOOOIOOOOOOOOOOOOOOOO0 000000 Calculated efficiency of the detector for electrons penetrating the scintillator and the first Cherenkov counter, and for electrons then penetrating the second Cherenkov counter............................... The calculated and measured effect of inserting a 1" aluminum plate between the Cherenkov counter‘SOOOOOIOOOOOOOOOO000......0.... Differential pair production cross section in Pb for 20, 50, and 100 MeV photons.. ...... ... Total pair production cross section in Pb as a function of photon energy............ ...... Superposition of the difference in yield from the Pb and Be converter for electrons at 17°, positrons at 0°, 17°, and ”0°. The solid lines are an assumed gamma ray spectrum with a slope parameter of 18 MeV and the resulting positron spectrum from the calculation..................................... Typical plot of x2 vs. slope parameter.......... The data points give the e1 yield as a function of energy for ‘“N + Cu at E/A-AO MeV for three different converters at 0 - 17°. The dashed curve shows an assumed ggmma-ray yield based upon a thermal source and the solid curves show results of the Monte Carlo calculation for the conversion positrons........ ix 36 "37 no “3 "3 “3 “7 51 52 56 58 60 6A 65 5.8 Concept of the High Energy Gamma-Ray Telescope.. Efficiency of the CsI converter as a function or gamma-ray energy...0.0...OOOOOOOOOOOOOOOOOOOO The High Energy Gamma-Ray Telescope............. Output of the top phototube vs. output of the bottom phototube for a single element....... Output of one element gated by a higher elementOOOOOOOIOOOOOOOOOIOOOOOOOOOOOOOI.00...... Gamma-ray cross section as a function of gamma-ray energy at eLab-90° for ‘“N on Pb, zn, andcat no MeV/UOOOOIOOOO0.00000IOOOOOOOOOO Gamma-ray cross section as a function of gamma-ray energy for HN+Pb at no MeV/u at I o 0 O eLab 30’ 90 ,and 150 coo-00000000000000 ..... o Gamma-ray cross section as a function of gamma-ray energy for l"N+C at NO MeV/u at eLab. 30°, 90°, and 1500.0...OOOOOOOOOOOOOOOO.O. Integrated gamma-ray cross section for 'E > 20 MeV as a function of angle for 1"n+0, Zn, and Pb at no MeV/u................... Gamma-ray cross section as a function of gamma-ray energy for l"N+Pb at “0 and C o OOOOOOOOOOOOOIOOOOO 30 MeV/U at eLab 90 .0000... Comparison of the high energy gammaqray cross section and the neutral pion cross section multiplied by the relative phase space as a function of the total energy of the photon or pionOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO System used in the coherent bremsstrahlung caICUIationO0.0.00.00.00.00.00000000000IOO. ..... Cross section for the coherent bremsstrahlung model as a function of gamma-ray energy for 1'°N+Pb at NO MeV/u and e . 90° with stopping times of 10, 15, and 20 P3 c.................... Cross section for l‘°N+Pb at A0 MeV/u as a function of lab angle for E - “0 MeV using the coherent bremsstrahlung model with t-15 fm/c....................................... X 71 73 75 75 77 78 79 8O 81 8h 88 9O 91 Ill“ ‘ aha u\i ' 6.7 6.8 Cross section for HN+Pb at NO MeV/u and E - 50 MeV using the hard sphere blemsstrahlung model for various maximum impact parameters.............................. Cross section for HN+Pb at NO MeV/u and 0 - 30° using the hard sphere bremsstrahlung m8881 with the maximum impact parameter 37% Of the rad1100000OO...0.0.0.0...OOOOOOOOCOOOOOO Cross section for l"N+Pb at NO MeV/u and eLab' 30° using the fireball model............. Cross section for HN+Pb at NO MeV/u and EY- N0 MeV using the fireball model............ Cross section for ll’N+C, Pb at 0L - 90° using the incoherent bremsstrahlugg model....... Cross section for ll'N+Pb at no, 30 MeV/u using the incoherent bremsstrahlung model....... The Enge split-pole magnetic spectrograph...... i The n experimental configuration... ..... ...... The n: experiment detector...... ....... ........ The n: experiment electronics ........ .......... The e1 experiment electronics... ....... . ..... .. The High Energy Gamma-Ray Telescope electronicSIOOOOOOOOOOOOOOOOOOOOOOOOOOO00...... Design of the delay cards....................... The Multi-Inclined Nire concept.... ............ The MIW counterocoooooooOOOOOOOOOOOOOOOOOOOOOOO Operating voltages of the MIN III prototype using 1 atm 50-50 argon-ethane................. Assembly view of the MIN IV counter............ Spectrum of alpha particles from 12C(a,a')”C at Bus 80 MeV.......... ...... .... xi 9“ 95 99 100 10“ 105 129 136 138 1N2 1N5 1“? 153 156 158 163 165 169 111“ | Protons measured simultaneously using the reaction "C(a,p)"N ........................... 169 Scintillator and Cherenkov detector used in thee experimentOOOOOOOOOOOOOOOOOOOOO0.00.0.0.0 175 Cherenkov element of the High Energy 178 Gamma-Ray Telescope............................. xii Us“ ' Chapter 1 Introduction This dissertation deals with the observation of high energy photons from intermediate energy nucleusnnucleus collisions. It includes the third and fourth in a series of experiments I participated in while a graduate student in Physics at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The first experiment in which I was heavily involved with at NSCL was my original thesis project, the use of the (d,‘He) reaction to study certain transitions in nucleiEJa76],[Be82]. The 2He system is unbound, but can be detected as a "diproton", two protons closely correlated in energy and direction- To use this reaction to examine a variety of nuclei, it was necessary to build a detector compatible with the NSCL Enge SplitnPode spectrograph and capable of identifying and measuring the position of two protons simultaneously. This need led to my development of the Multi-Inclined Nire detector, which is described in detail in Appendix C. Ne carried out an experiment using the reaction 12(:(c1,°He)”13 with Ed: 99.2 Mev at the Indiana University In“ ‘ . 1 <\ I I a h .3 a a. .- Q~ VI. ax :4 Ow 7'. .J. .n. .3 n. 5.. nu .: e an a. . w“ n. 6» Mn 2 Cyclotron Facility (IUCF). To measure the diprotons, we used two solid state detector telescopes mounted as close as possible to each other within the IUCF 60" scattering chamber.. ‘The goal of the experiment was to see if the (d,‘He) reaction would be a useful probe of AT-AITzl-AS-AJ-1, AL-O transitions at the higher energies available with the NSCL cyclotrons. The results indicated that (d,2He) would be of limited usefulness as a probe at these higher energies, primarily because random proton pairs created by deuteron breakup into protons and neutrons obscures the diprotons. I then participated in two very different experiments involving the production and detection of pions. 'The first; was the measurement of the mass of ”Zn using the (par-1 reaction, and the second a measurement of the yield of energetic: protons Ehld pions from "’La on 139La at 2A6 MeV/u. The s"Ni(p,-rr-‘)“"Zn experiment used a 200 MeV proton beam at IUCF, and the QQSP spectrometerESh83].[Gr82]. The Quadrupolesguadrupole Split-Pole spectrometer had been especially constructed to measure pions, and used a track reconstruction technique to obtain a large solid angle. Energetic electrons were a source of a large background, but by using an aluminum wedge to slow the pions, some of the pions stopped in the plastic scintillator. Those that stopped were absorbed into nuclei, causing the nucleus to receive 1A0 MeV of excitation, which then is released in a 1““ . 3 variety of ways, forming a pion "star". 'nuelarge energy released in the star was used as a signature of a pion. The "’La pion experiment used the one arm of the TASS (Two Arm Spectrometer System) spectrometer at Lawrence Berkeley LaboratoryEKr86]. In our configuration, the track through the spectrometer was determined by three plastic scintillator hOdOSCOpeS. Separation of the pions, electrons, and protons was by virtual mass calculated from the momentum and timesofsflight through the spectrometer and by use of a water filled Cherenkov counter beyond the last hodoscope.. .Again, a large background of electrons and positrons was observed with the same momenta as the pions. In the course of these experiments, I became curious as to the origin of these high energy electrons and positrons. The coincidence of both experiments having an electron rate comparable to the pion rate was remarkable, and I had no good idea of their source. As third series of experiments began, my thesis project had become a measurement of the pion yield for s°Ni(”N,ni) at A0 MeV/u. Production of pions with the beam energy per nucleon below that necessary for nucleonnnucleon pion creation (~290 MeV/u) is referred to as "subthreshold pion production", and is of interest as a measure of collective nuclear effects, where the energy of many nucleons is pooled to create a pion. Although first measurements in this energy range were made using neutral pionsEBr8A], the project was still interesting as a way of measuring the Han ' [/11 0.. Ad 4.— H v :4 9a a: n» I In L \ ad. 1* «v «1 s v I; .0. 1». AC 7v .5 ‘ c A O Q s a e p . U 1 a 7- up.» D» at . .1; a . n 8 $ A“ ...I ‘~ Q» u n-/n+ ratio. Previous work at high energy had discovered that the n-hr+ ratio became very large for pions with velocity near the beam velocity, and had shown it to be due to a Coulomb effectEBe79]. Part of the motivation for this experiment was to determine if this effect persisted at much lower energy. Because of the small cross section, it was necessary to construct the system in such a way that background would be minimized. The experiment used the NSCL Enge Split~Pole spectrographESp67]. The beam entered the 1A" scattering chamber, passed through a relatively thin target, and stopped in a water filled Faraday cup at the back of the chamber. The path for the pions passed through the slits, through the spectrograph, through a window and air, the MIN position sensitive detector, the AE scintillator, and stopped in the E scintillator. Only pions and lighter particles would have sufficient range to reach the MIN for the field settings for 20-N0 MeV pions. Nhile running the experiment in this configuration, a number of events were observed which were apparently electrons and positrons. To test this, a plexiglas Cherenkov counter was placed behind the AEsE telescope. The signals from the Cherenkov counter confirmed that the events were indeed electrons and positrons of about 100 MeV, similar to the background I had observed in the other pion experiments. 0 MIN" 5 Encouraged by recent theoretical modelsEVaSH], we then attempted to measure the electron and positron yield as a function of their energy, but we found the rate to be nearly independent of whether the target was in or out of the beam. As discussed later, the electrons and positrons we saw were shown to have been created by pair conversion of very hiya energy gammasrays from the Faraday cup. To measure the photon, positron, and electron flux from the target it was necessary to limit pair conversion to a well defined, calculable geometry. The final experiment in this series used "converters" placed directly behind the target and demonstrated a relatively large cross section for the formation of very high energy pmctons, whose subsequent conversions in matter give rise to high energy electrons and positrons. This surprising result, which indicates some cooperative process is taking place, has generated much theoretical interest, and further experiments are in progress at GSI in EuropeENoSS] and at NSCL. The results of this experiment immediately led to the development of the fourth series of experiments, in which a specially constructed telescope, made of a stack of Cherenkov counters, was used to measure the high energy gamma spectrum for a variety of beam energies, targets, and anglesCStBSc]. The first of these experiments has been completed, and similar experiments looking for high energy Y - charged particle coincidences have been proposed. .10“ ‘ 6 At much higher beam energiesEBu81], energetic photons from the decay for the prolifically produced neutral pions mask these photons. At much lower energies, the production of high energy photons decreases rapidly, and can be hidden by neutron interactions in conventional detectorsEMoBS]. TWm fortuitous choice of detector and system led to their observation. 3““ ' Chapter 2 The Pion Experiment and the Observation of High Energy Electrons and Positrons 2.1 Pion Production in Nucleus-Nucleus Collisions The production of pions in nuclear collisions when the energy per nucleon is below the nucleon-nucleon threshold, usually referred to as subthreshold pion production, is the subject of recent experimental and theoretical study after a gap of thirty years since it was first proposedERiSO]. The first manmade pions were produced at BerkeleyEGaAB] in 19N8, but until 1978 there was little data available. When the incident nuclei have energy mn°rumleon well above the nucleon-nucleon threshold of 290 MeV (the nucleonnnucleon threshold), the production of pions by heavy ion collisions is well explained by tune sum of the production by the individual nucleon-nucleon collisions. A class of calculations known as the cascade model use a Monte-Carlo technique to follow each nucleon throughout the collision,anuirms been successful describing many of the characteristics of these collisions. Nucleons within a nucleus are not at rest, but have a momentum distribution. Production of pions at energies per nucleon less than the mu ' 8 nucleon‘nucleon threshold is energetically possible due to the additional energy available from the other nucleons. It was found, however, that as the beam energy decreased, the pion production cross section did not fall as predicted. At energies of 25-50 MeV/u, the cascade model underpredicts pion production by many orders of magnitudeESh8Aa]. Pion production has been observed near the absolute limitEStBSa], the point at which there is Just sufficient energy in the entire system to produce a pion. Several theories have been advanced to explain this phenomenon, but all require the nucleus to show collective behavior. This collective behavior may give insight into the nuclear equation of state, and into the nature of nuclear matter far from equilibrium. Several models are discussed in Chapter 6. At these "subthreshold" energies the collisions giving rise to the pions are of great interest, since the collective behavior is manifest. Moving somnnefits to a variety of emitted particles suggest that the region has about ‘/2 the beam velocity, and about 2x the beam massEGo77]. An additional discovery, made by Benenson et al., that the ratio of n—ln+ becomes very large near 0° and the beam velocity, was explained as being due to Coulomb repulsion between the interacting region and the n+[Be79]. The motivation for our pion experiment was to measure i the n production cross section at a beam energy lower than had been done before, measure the angular distribution, and .11“ ‘ a g:1 inVé e:h« 2.2 pl. .v . a: :— o . n I. r . Lrs n . May. > . V. a: :3 a a A. . :5 a C I. -D. . . 3. «A w an .. x p a 0 a. n. cc ; w 2. a» at r e. ”V. a} a; a at a u. 24 AJ 01. .l 0. .r u .1 a... Q; L)» -« D» n. nu. ac to a 81. ml P. T . «J. 9 investigate the n-/1r+ ratio to determine whether the enhancement effect persisted at much lower energies. 2.2 Experimental Technique for the Pion Measurement Charged pions are produced at low beam energies with a very small cross section. The pion has a mean lifetimecn’ 26 nS and a mass of 1N0 MeV. Because of its small mass, for a given energy it has a small g;, a large range, and a large charge-to-mass ratio relative to a proton. In addition, the stopping 1r- is absorbed by a nucleus, exciting the nucleus by the pion rest mass. Subsequent de-excitation takes place many ways forming a pion "star", the most common being the emission of several neutrons. The n1 experiment used the fact that pions have a large range and charge-to-mass ratio relative to the more commonly produced hadrons such as p, d, t, and a. A magnetic spectrometer separated the charged particles coming from the target according to their momentumstoficharge ratio, and absorbing matter in front of the detector on the focal plane of the spectrometer prevented protons and heavier particles with the same momentum but lesser range than the pions from reaching the detector. The experimental configuration is shown in Figure 2.1. The beam of ”N6 ions enters from the bottom of the figure, passes through the target, and stops in the Faraday cup. The spectrograph is connected to the target with a sliding seal, so the dipole is also under vacuum. Pions produced by HI“ ' Figure 2.1. .10 ‘ PARADAY CUP TARGET , BEAM ’ 1 M The original charged pion experiment. ll MIN—- Figure 2.2. The original charged pion detector. “In ‘ II- {D m (U in “I 12 reactions in the target and which enter the spectrograph are bent by the magnetic field, exit the dipole and enter the camera box through a thin window. The camera box is at atmospheric pressure. The pions pass through the position sensitive counter, through the AE plastic scintillator, through an aluminum wedge, and stop in the E plastic scintillator. The spectrograph and the experimental configuration are discussed in detail in Appendix B. The detector consists of several components, the detail of which are in Appendix C. The Multi-Inclined Nire (MIN) detector measures a location on and the angle to the focal plane for each particle, and the AE-E plastic scintillator telescope behind the focal plane detector provides an energy loss and energy signal for each particle (Figure 2.2). The MIN detector is a multiwire proportional counter, designed and built specifically for the Enge spectrograph. It has two planes of 96 active wires which serve to determine both the position and angle of a particle. A particle passes through the thin front plastic window, through an active region filled with a gas, and out though the thin rear plastic window. The active region has an electric field, with a cathode on the bottom, and anode \wires above.. .Free electrons created in the gas by the ionization caused by the passage of the particle drift up to the anode wires. The small diameter of the anode wires creates a very large electric field, where the number of free electrons is multiplied through collisions with the .11“ ’ 13 gas. Each anode wire is electrically connected to its own amplifier outside the detector. In addition, a signal is induced on the cathodes. The energy loss resolution is poor; the small amount of energy depositmdimithe detector is not used for particle identification. Behind the MIN are two plastic scintillators forming the particle identification telescope. The scintillator plastic converts a fraction of the energy deposited by the charged particles into light. Some of this light is contained by total internal reflection until it strikes photomultiplier tubes at either end of the scintillator, where it is converted into an electronic pulse. The front scintillator, called AB, is thin enough for the particle to pass through. The next scintillator, called E, stops the particle. A plot of AE against E is used to identify the particles. Empirically (very similar to the Bethe equation), the energy loss of a nonrelativistic particle (heavier than the electron) in material is: 9.13. a. E--- E- E03 0. so that when particles enter the telescope, the plot appears as curved bands, but the limited range of momentumsto-charge ratio which reaches the detector breaks the bands into islands in the AE-E plot, as illustrated in Figure 2.3. Ha“ ' 14 111“" AE t E Figure 2.3. Idealized particle identification plot; the dark regions represent the range of momenta selected by the magnetic spectrograph. 15 BASE / PHOTOTUBE _‘—-INNER SHIELD —--- OUTER SHIELD 0’. --——— PLEXIGAS E \\ CHERENKOV MIN—— : DETECTOR Figure 2.11. Pion detector modified to identify energetic electrons and positrons. 16 In the later runs, a Cherenkov detector was placed behind the AE-E telescope (Figure 2.”). (Sherenkov detectors, discussed in detail in Appendix C, use the light created in a material when the speed of a charged particle exceeds the speed of light in that medium. For the plexiglas used (n-1.5). the speed of a particle needs to exceed c/n-.67c before any light is produced. The Cherenkov light is produced in a cone around the particle's path; in the Enge the path runs around 115° to the detector, so most of the internally reflecting light ends tuaeat the high radius end of the detector, hence only one phototube was used. For particles that follow a proper orbit through the spectrograph, only e1 have sufficient velocity to produce a pulse in the Cherenkov detector. 2.3 Results of the Pion Experiment Figure 2.5 shows a particle ID plot made during a pion run. Figure 2.6 shows the same data, but has the added requirement that there be a good track in the MIN position sensitive counter. These figures show that particles with low specific ionization were exiting the spectrograph, that these partdwxies have a range of greater than ”.5 cm of plastic, and that these particles have a speed greater than .67c in the Cherenkov detector. A typical yield of 50 per hour for a beam current of 30 pnA was observed, and zero with no beam. The only particles compatible with these .HU ' 17 AE .:' Particle identification plot from the first Figure 2.5. electron experiment. AE Figure 2.6. Particle identification plot with the in requirement that the Cherenkov counter produce a signal coincidence with the event. 18 conditions and the momentum selected by the spectrograph are electrons and positrons of around 100 MeV. These results were obtained in June, 198A. In other pion experiments in which I had participatedEKr86],[Sh83], electrons and positrons have also been observed, but had been treated as uncharacterized background. Nhile I had been curious as to their source, I failed to find an explanation which seemed plausible. At the same time, Nalter Greiner, the well known nuclear theorist, came to NSCH. and gave 23 talk on his theory of picnic bremsstrahlungEVaBA]. His model made subthreshold pions through a process analogous to classical electromagnetic bremsstrahlung. When asked if these high energy electrons and positrons could also be produced by the acceleration, Dr. Greiner responded positively, and suggested an immediate measurement of these electrons and positrons. 2.N The First Electron and Positron Experiment The experimental configuration previously used in the pion experiment remained unchanged, except for the target which was 60 mg/cm2 natural nickel (67.95% s'Ni, 26.10% ‘°Ni, 1.13% HNi, 3.59% 62Ni, and 0.91% ‘“Ni)[Ne81]. The polarity and field of the spectrograph were varied so electrons and positrons of 20-1110 MeV could be measured. The lower limit of 20 MeV was chosen since multiple i scattering of the e in the scintillator would drastically reduce the efficiency of these particles to reach the mu ‘ 19 Table 2.1. Results of the first search an~ high enaergy electrons. HAM ‘ polarity TeLMgll relative yield (cts/uC) target in out + 80 -111 8.9 9.“ + 38 - 52 9.0 9.9 + 22 " 31 9.5 10.1 - 22 -' 31 11.5 12.5 ‘ 38 r 52 11.6 12.8 - 80 -111 13.N - 20 Cherenkov counter. The results cM’ this run appear 1!! 'Table 2.1. The number of e+ and e‘ observed were about the same for a given momentum setting, but surprisingly were produced at nearly the same rate whether or not the target was in the beam. The explanation for this strange result is that most high energy photons were being produced in the Faraday cup *used to stopithe beam. These photons then were interacting with the nearby aperture slits of the spectrograph entrance and were being converted into electron-positron pairs. The tantalum slits were about 65% of a radiation length, and acted as a fairly efficient converter of high energy gamma rays. It was then clear that a different technique was needed to measure and separate the high energy electrons, positrons, and gamma rays. HIM ‘ 21 Chapter 3 The Positron Experiment 3.1 The Converter Concept The previous experiment proved unable to separate electrons and positrons produced directly by the nucleus—nucleus collision and those produced by subsequent pair conversions of photons. To solve this problem, the rnain change was to use a stopping target. In addition, a converter was placed directly behirui the target (Figure 3.1).. The converter is a piece of metal whose function is to convert high energy photons to electrons positron pairs. The converter was a known photon energy dependent conversion efficiencyEMo69]. Three different converters were used. A comparison of the positron yield for the same target with two different converters allows the determination of the high energy photon flux as well as the direct positron yield from the target. The emerging positrons include those directly created by the nucleuSQnucleus collision (direct positrons) and those created by a pair conversion of a photon into an electron and a positron within the target cn' converter (conversion positrons). Because of the small yield of the 22 HM ‘ BEAM PARTICLE CO\NVERTER 6+ 6... C— TAéET Figure 3.1. Positron experiment concept; stopping target backed by photon converter. 23 direct positrons, only an upper limit could be obtained from this data. The target was changed from nickel to copper for convenience. The atomic number Z and mass A of copper are close to those of nickel, and subthreshold pion experiments had shown only a slow dependence on target massEBr8N]. The range of the ”N 140 MeV/u in copper is .77 g/cm2,[Li80] so the target was made that thickness. Three converters, rather than the minimum of two, were selected so that the consistency of the model could be (mecked. Since the cross section for pair production goes as the square of the atomic numberCMa69], three metals available in pure form were chosen, beryllium, copper, and lead with atomic numbers A, 26, and 82 respectively. The three converters were made the same area density so that the contribution from processes which depend on the atomic electrons rather than the nuclei would be approximately the same for all converters. The choice of thickness was a compromise between.lnigh conversicni efficiency and low multiple scattering and energy loss, so all three were made with area density 3 g/cm’. This made the conversion efficiency of the beryllium comparable to that of the target. The conversion efficiency for 50 MeV gamma rays for the target and converter were A, 13, and 2A% respectively for the beryllium, copper, and lead (as calculated in Chapter A). HIM" l'\ (I) (3 () (f 2A The angle between the original photon and the electron or positron is small for the high energy photonsEMa69]. Multiple scattering of the electron and positron within the converter deflects the electrons and positrons from their original direction. Better angular resolution could have been obtained by placing the converter at the entrance of the spectrograph at the expense of efficiency for detecting the electronnpositron pairs. Since the previous experiment had not shown a marked angular dependence, it was decided to place the converter in contact with the target. The efficiency would be maximized, since the number of electrons and positrons scattered out of the entrance direction would approximately equal the number scattered in. Angular resoluticniivould be sacrificed, being limited to about the mean scattering angle within the converter. The energy lost by the electron and positron was approximately the same in all the converters. 3.2 Modifications to the Spectrograph and Scattering Chamber In order to minimize the presence of electron-positron pairs produced by interactions outside the target and converter, as much mass as possible was removed from the entrance of the spectrograph (Appendix B). The 1N" scattering chamber was removed and replaced with a A" chamber with 0.60" thick aluminum walls and an exit hole covered with .003" Kapton to maintain vacuum. The aperture slits were far too thin to limit the acceptance of energetic mu ‘ 25 TONVERTER NINDONS TARGET BEAM 1 M + Figure 3.2. Configuration of the e‘ experiment. mu ‘ 26 electrons and positrons; they only served as a source of multiple scattering and conversion. The entire slit mechanism was removed and a large thin window placed across the spectrograph entrance. Electrons and positrons from the target and converter were required to go through the scattering chamber window, air, the entrance window, through the spectrograph, through the exit window, through air to the detector (Figure 3.2). Multiple scattering in the converter was much larger than that due to the windows and air, so the latter was ignored in subsequent calculations. The effective aperture was determined by the steel pole tips of the spectrograph vertically, and by the angular acceptance based on the horizontal angle measured at the de t act or . 3.3 Changes in the Detector The detector was modified to improve electron identification (Figure 3.3). The MIN counter was unaltered, but the telescope was replaced with a 1" thick plastic E scintillator and two 1" thick Cherenkov counters. These Cherenkov counters were a.substantial improvement over the simple plexiglas Cherenkov counter used in the pion experiment (Appendix C). A wavelength shifting plastic developed by Bicron Corp. specifically for Cherenkov counting was used. This plastic absorbs the Cherenkov light and re-emits it isotropicly and at a longer wavelength more suited to the photomultiplier tubesEHu8A]. This plastic mu ‘ 27 ,Fy. .fivnmm sn-urnwo ‘ /‘ cram PLASTIC MIW\ MTM + Figure 3.3. Configuration of the e‘ detector. 28 allowed the Cherenkov counters to have a phototube at either end, so that a coincidence between the two ends reduced random noise. In addition, the Cherenkov counters were made much larger than the previous one to allow for the greater multiple scattering of lower energy electrons in the scintillator. The scintillator's increased thickness provided a much stronger signal for the near minimum ionizing electrons or positrons. The multiple scatteringiof the positrons or electrons in the plastic increases rapidly with decreasing energy; the size of the Cherenkov counters is a compromise between being able to detect low energy positrons and electrons with good efficiency and keeping the background low. Details of the design of the telescope are in the Appendix. Nhile the plastic scintillator is sensitive to neutrons and gamma rays in the room background, the Cherenkov counter is sensitive only to the gamma rays, which produce relativistic electrons within the counter by Compton scattering, and to cosmic rays, primarily relativistic muons. In addition, the two Cherenkov counters were made identical to simplify design and minimize cost. Nith the final design, the telescope had nearly unit efficiency for electrons and positrons of energies of greater than A0 MeV. An event of interest required a signal in both phototubes of the scintillator and first Cherenkov counter. The firing pattern of the MIN, as well as the time and height of each pulse from the scintillator, Cherenkov |Hu ' 29 counters, and MIN cathode was recorded by the acquisition system. In the process of data analysis the requirement that the MIN pattern correspond to a particle withintflw correct solid angle, and that the scintillator and both Cherenkov counters produce proper pulses, eliminated the events due to cosmic rays and room background. 3.A Verification Tests The interpretation of these data depended strongly on the calculations of the efficiency of the converter and detector. Since high energy electrons can be created not only by pair production, but also by Compton scattering of high energy photons, most of the data was taken with positrons. During the course of the experiment, several tests were carried out to check that the high energy positrons being observed were of an energy consistent with the energy deduced from the spectrograph magnetic field setting. These tests were based on the range and multiple scattering of the positrons, and consisted of placing absorber between the Cherenkov counters. The calculations and results of the tests are described in detail in the next chapter. 3.5 Results 'The highest energy l"N beam available, N0 MeV/u, was used since it was assumed that the yield of these high energy photons, electrons, and positrons would increase with mu ' 30 20 15 —- HUI-l“ counts 8 ,_:£E;:: 1—3 J—r—‘g 1 J a 71 O i l L I l I l I L l L I I I l L I I I I I I I o 20 40 so so 100 T wire number T 20 c Te (MeV) > 27.2 Figure 3.” Typical e+ position spectrum. 31 energy. The target was copper, and the laboratory angles measured 0°, 17°, and ”0°. Greater angles could not be reached with this system, since target and converter needed to stay fixed normal to the spectrograph entrance, and the beam spot size increased as the angle was increased. The details of the data acquisition are in Appendix B and D. A typical ungated positron position spectrum in the MIN counter is shown in Figure 3.“. Figure 3.5 is a plot of Cherenkov#1 pulse height vs. the E scintillator pulse height signal. The same plot is shown in Figure 3.6 but has in addition the requirement of a good angle from the MIN counter. Finally, Figure 3.7 has the additional requirement of a valid signal from Cherenkov#2. Nith these requirements, the counts remaining in Figure 3.7 represent positrons which are within the aperture of the spectrograph and penetrate the scintillator and both Cherenkov counters. Figure 3.8 is a plot of the electron yield vs. the electron energy at 17° for the three converters. Figures 3.9, 3.10, and 3.11 are plots of the positron yield at 17°, 0°, and “0° respectively for the three converters. Multiple scattering in the converter smooths the angular distribution; 20 MeV positrons have a mean scattering angle of 27° in the Pb converter, whereas 70 MeV positrons have a mean scattering angle of 8°. Thus, the angular distribution of the high energy positrons reflects the angular distribution of the gamma rays (shown in Figure 3.12). 32 Ckl (Mu ‘ vs. pulse Pulse height in Cherenkov counter #1 Figure 3.5. height in the E scintillator. Ck 1 . 3:5";- .. : . Figure 3.6. The same as in Figure 3.5. but with the requirement of a good angle in the MIN counter. Ckl . but with the The same as in Figure 3.6. Figur'e 3.7 additional requirement that Cherenkov#2 produced a pulse. 33 e- Yield 0: 17° 2 ’3: 1° , r'n 1 .. 10 ‘3 a 2 10° ' a I " . ‘é 10"1 "x x Pb :1 n 9‘ 2 0 x1 x m -' “.XL \ar 10 Cu. X 4-: . 0 3‘ 0 10"3 Be x01° o v ° 0’ ‘0 'U 10'4 9 3 I _i 1 1 1 '5" 10"5 - 20 40 so so 100 120 Te (MeV) Figure 3.8. Electron yield as a function of electron energy for the three converters at 17°. 34 e+ Yield 0: 17° A Lo 7’ 1 10 ‘3 10° ' 8 =3 I'll U -1 a a 10 X x Pb :1 u a. x" m m h 10‘”2 Cu 2.1 x +2 °° ° x ‘ v Be 1.01 g g. “U 10“ 9 f '63 '9. 10"5 — i l i l 4—1— 20 40 60 80 100 120 Te (MeV) Figure 3.9. Positron yield as a function of positron energy for the three converters at 17° 0 mu ‘ 35 e+ Yield O=0° 2 17 1° ? 1 lilu‘ 10 > ‘D o 2 1° ' u I I 1 l' a Lé 10 x x Pb 11 a Q. __2 xx :1: \ 10 Cu 1.1 1‘ .8 , " -3 0 x 3 1° 99 Be 1.01 Y 9 'o 10“ l p... .9. --5 _ J J l l I h 10 20 4O 60 80 100 120 Te (MeV) Figure 3.1CL Positron yield as a function of positron energy for the three converters at 0°. 36 e+ Yield O=40° 2 2: 1° T’ 1 10 > “’ o 2 10 I a ' ll -1 ‘3 10 xx x Pb :1 a ‘1. XIX: II E 10'”2 Cu 1.1x +2 0" x 0 10-3 0 e ! V Be 1.019 9 9 "U 10-4 9 F‘ .210_5_11111 bx 20 40 60 80 100 120 Te (MeV) Figure 3.11. Positron yield as a function of positron energy for the three converters at AO°. MSU-85-143 l I I 1 t t T T’ 1 I I A Pb x Cu 0 47- Be «- mu“ YIELD (arbitrary units) - N .—A"__ + —e— + ;— + -o- L L l l 1 0 10 L ab so 40 91. (deg) Figure 3.12. Angular dependence of the high energy positron (70 - 105 MeV) yield for the three converters. 38 The Monte-Carlo simulation of the detector used in the analysis of the data reflected that a positron scattered in the first Cherenkov counter sometimes misses the second counter. This is discussed in the next chapter. mu ' 39 Chapter A Analysis of the ei Experiment A.1 Introduction and an Example of a Monte Carlo Calculation The results of this experiment depend strongly on efficiency of the converter and detector. Two separate calculations were done; one to simulate the conversion of the photons into positrons, the other to simulate the response of the detector to those positrons. Both used Monte-Carlo techniques and were run on the NSCL VAX-780 computer. As an overview cM’ the technique, consider the two-dimensional example of a particle passing through N identical thin slabs (Figure A.1). In each slab of thickness t, the particle loses no energy, but scatters into a new direction A0 from the entrance angle with a mean angle of on. To find the exit angle distribution for the entire stack, one could find the distribution for exiting the first slab, solve for the distribution after the second slab as a function of its entrance angle, combine these to get the net Iliu * 40 III“ ' Figure 11.1. A particle scattering through N thin identical slabs. A1 distribution after the second slab, and repeat this for all the slabs. If the scattering angle is small: t 9 << 1 308 G t the slab 1 distibution is 1 . -——- ’AOi/O: Thu" and for N identical slabs P(0) - f P(AO1)...P(AON) 6(O-ZA01) dAO ...dAG 1 N __ 2 2 9(0) . —fi1:fi 1 e £(Aei) ’¢° 6(O—ZAGi) dAG1...dAON ¢o/" Using 6(x) - 5% Je-ikxdk [Re65] _ ._ 2 2 9(a) . --%—:fi I e ike [ f e [(Aei) /¢° + iRAGinAoiJN dk 2noo/n completing the square in the exponential and integrating, 1 f -ik0 -k=¢§/u N "TN‘IR J 9 ] 2noo/n [ col; e dk E 2 :dx AZ The exact integral could be attacked numerically, but an alternative is available. The alternative is to start with one particle and follow it through the system, providing the scattering angle (and corresponding energy loss) from a random number generator whose output provides the correct probability distribution of scattering angle. The process is repeated for many particles so that an exit angle distribution is made. In this example, a random number generator with the apprcun~iate distribution must first be made. Starting with the probability distribution P(AO) (Figure A.2): 1 sAezcos’( A0 )/¢§ P(AOi) - /; e i J§i J a new function F must be defined such that A9 I P(a) do HAG) . -.. +0 I P(a) dd -Q and the inverse function F—1(x) must be found for 0 s x S 1. Here (Figure 1.3) COS(J§1AOJ) [AG <1». J_,, F(AO) - f; e-[cos’(J§iA0J)/¢§]ozda u _ 2 recall erf(u) - /% j t 1111‘ ‘ 43 Figure A.2. Figure A. P(AO) 1 A0 Figure “.2. Exam Le probability distribution P(O). figure 9.3. Integrated probability distribution F ". F'RX) AC9 Figure A.U. Inverse of tme integrated probability' —1 distribution F (X). 111M ' NH Table “.1. Steps for the example Monte Carlo simulation. .1. th 111M ‘ set 0 - 0 choose 0 S x S 1 using a random number generator choose 0 S y S 1 using a random number generator get |A0 Ifrom x using F‘1(x) for the current value of 0 if y S 1/2, set 0 - 0 n ADJ, otherwise 0 - 0 + 130j repeat steps 2-5 for each of the N elements record 9N and repeat entire sequence 1-6 many times “5 1/2 + erf(+Ae)/2 Ae>0 hence F(AO) ' 1 1,2 _ erf(-Ae)/2 AG. g 60 -— .3 E+Ck1+Ck2 3:3: 40 -— «q o b\° 20 l I o J l o 20 40 so so 100 To (MeV) Figure “.6. Calculated efficiency of the detector for electrons penetrating the scintillator and the first Cherenkov counter, and for electrons then penetrating the second Cherenkov counter. HIM" 52 10"2 I INIIIF 1 counts / ,u.C l 1 l 80 100 120 Te (MEV) Figure “.7. The calculated and measured effect of inserting a 1" aluminum plate between the Cherenkov counters. i HIM“ (D 53 A MeV in the E, C1, and 62 elements as a function of electron energy. The breaks in.trm line are due to edge effects in the detector; the detector is more efficient for an electron of given energy at the low radius end than at the high radius end. An important feature to note is that the efficiency reaches about 100% by a positron energy of 25 MeV. The program EFFTAB produces a smooth description of efficiency as a function of positron energy from the tabulated results. “.2.1 Verification Tests To check experimentally the validity of this calculation, extra elements were inserted into the detector during the experiment. First a 1 inch, then a 2 inch thick aluminum plate was placed between the first;anid second Cherenkov detectors and the measurement repeated. Figure “.7 shows the measurement with no aluminum plate and a 1" alumirnun plate. Superimposed are solid lines representing the calculations, and the dashed line is the fit to the original positron spectra without the aluminum plate. “.3 The Pair Production Cross Section The technique used to detect high energy photons in this experiment is based on the reaction: 4. Y+e+e 11m ' 5“ which occurs in the strong electric field of a nucleus or electron. The difference in the momentum and energy of the pair'anid the photon is transferred as recoil to the nucleus or electron. If the particle is heavy, like a nucleus, virtually all the energy of the photon appears in the electron-positron pair, and the process is called pair production. If the particle is an electron, the momentmn and energy is distributed over a positron and two indistinguishable electrons, and is called trident production. For high energy gamma rays, pair production is the dominant mode of conversion. Nhile measurement of both members of the pair gives the [Huston's energy, measurement of one member provides only a lower limit on the photon's energy. This experiment was limited to detection of only one half of the pair at a time, requiring a calculation based on the measurement of many positrons to determine the original photon distribution. The differential cross section for a photon producing a positron of energy E; is known and can be used to determine the approximate original photon spectrum given the cross section for positron production. Information about details in the photon spectrum is lost, but the magnitude and trend of the spectrum can be determined using a Monte«Carlo simulation of the experiment. Due to the high momentum of the photon, the electron- pmsitron pair created through interaction with the nucleus has a large momentum in the direction of the photon. The mu” 55 angle between the original photon and the positron is about mec’IEY radiansEMa69], but the kinetic energy of the positron may have any value between 0 and (EY- 2 mec’). The differential cross section for a given photon energy has been calculated, and a simple form good to about 10% is formula 30-1003 of referenceEMo69], used in the earlier work of BudianskyEBu81]. The formula for differential cross section for pair conversion is found by taking: if Y<2 then 1.1 35+- 2§1_2 {(E:+EE)[¢,(Y)- % 1n 2] . % E+E_[¢2(Y) _ § 1n 2]} and if 2 S Y S 15 15+. ieégni (2:.55. g E+E_)[1n(§E+E-) _ % _ C(Y)] where k . EY/mecz + 2 2 E+ . (T(e ) + mec )/me° . T 2 2 E“ (T(e ) + mec )/mec Y - 100 k/(E+E_Z1/3) G . 1.36 Y Hill" 56 111“" .mCOuocq >mz oop new .om .om Low mm :H cofiuoom mmoco compozcoca Lfimq Hmfipcoeocufio $2: .2. cc" on on 0* cm .a.e oeaaai _ _ g A In G! >o2 Sanka at: emuam >22 omuam C) K) g. :2 (new/atm) °.LP/0P ll mm." 57 The T(ei) denotes the kinetic energy of the ei. For all practical purposes k - E++ E“. Fitting a curve in referenceEMo69]: -o,u980655 Y + 0.01528705 C(Y) - .52“9857 e If G S 1, then o,(T) - 20.868 — 3.2u2 0 + 0.625 0° o,(v) - 20.209 - 1.930 0 + 0.086 02 if G > 1 then o,(Y) - 02(7) - 21.12 - “.186 ln(G + 0.952) The FORTRAN function SIG(x) calculates the differential cross section in units of fmz/MeV for x - E+/(EY-2mec’). A plot of the differential cross section for Pb and EY- 20, 50, and 100 MeV is shown in Figure “.8. The region Y>15 represents positrons with momentum either close to zero or near the momentum of the original photon. iIn particular, if Y>15, Zc“, k-100 (~50 MeV Y) the positron has either less than “% or more than 96% of the photon's energy. For the purposes of the calculation, two above form was also assumed to be valid for Y>15. The error introduced is less than the fraction of the positrons whose energy range is outside the region Y>15 for all photon 111M" 58 Ill“ ‘ .zmgwcw cowocq mo :ofioocsu m mm on :H cowuomm mmogo cofipozooca LHmQ Hmooe .o.: mgzmfim $25 as com on” and on o fl _ _ coca coon coon ooo¢ coco (gun) (__a+e+-L)o energi array for p? tract: Of em of the energy .— (love POSitr PemGVe in :5. 59 energies of interest. Subroutine ISIG generates with the array "sigT(EY)"; the total pair production cross section for photons of energy EY' the array "er(Ey,E+/EY)"; the fraction of the cross section for production of a positron of energy 3+, and the array Xinthe(Ey,E+/EY); the fraction of the cross section for the production of positrons of energy equal to or less than E+. The output consists of a table of the positron energy (lower edge of a positron energy bin) and the number of positrons in the bin per 10‘ photons. The normalization removes the tables' dependence on the number of photons used in the calculation, which was typically 10’ for each spectrograph setting. The total cross section is found by numerical integration of tune differential cross section. The total cross section as a function of energy for Pb is plotted in Figure “.9. u.u Other Processes Both trident production and Compton scattering depends only on the electrons in a material. Both contribute to the number of high energy electrons, but only trident production gives rise to positrons. Positrons from trident production ruave lower energy and a more rapidly decreasing energy sspectrum than positrons created by pair production. In axidition, the cross section for pair production goes as Z’, mun 1 1 1 A>02|On\muov 1|- Ummw> 60 10"1 - ’r; —2 g 10 7 I O (,3, 10"3 — I .. \ ' . 1. .3 3 10“ e+ @=0° <>e" 17° ! :3 10’5 e+ 17° 52' 3‘8e‘“ 40° " 10—6 _ J l I 20 40 60 80 100 120 T 6 (MeV) Figure 14.10. Superposition of the difference in yield from the Pb and Be converter for electrons at 17°, positrons at 0°, 17°, and “0°. The solid lines are an assumed gamma-ray spectrum with a slope parameter of 18 MeV and the resulting positron spectrum from the calculation. and s; nucle; of Z r 61 and since there are 2 times as many atomic electrons as nuclei, trident production is suppressed by about a factor of Z relative to pair production. Since the number of electrons in the converters is approximately constant for all three converters, taking the difference between the lead and the beryllium converters' yield reflects the nuclear pair production contribution. The ratio of the electron to positron yield in the data is about 3:2. Usingiflw above procedure, the electron and positron data give very similar results (Figure ”.10). h.5 Modeling of the Target and Converter It is necessary to assume some form of the Y ray energy distribution in order to run a simulation. Two simple distributions were chosen. The exponential distribution with the form: 95 _ K e-E/T in which T is called the 310pe parameter, and the Planck distribution used to describe black body radiation: 2 2.! . 513%“ dE e - 1 where T is the temperature. The exponential humiLmed in the code GAMMAEE is particularly easy to use to produce an IIIMJ 62 appropriate random number generator, and is widely used to characterize distributions of fragments in heavy ion collisionsEBeBll]. The Planck form used in the similar code GAMMATEE would yield the temperature if the source were thermal, but requires numeric integrations to be performed to generate the random photon distribution using the subroutine PLANKGEN. The photon energy is chosen using a random number generator according to the appropriate distribution. The full thickness of the copper target was assumed to be available for conversion. The photon interaction depth in the target is chosen such that the probability of the photon converting at a depth less than x is: P(03. . NJU_.PK o D 211,01 o g 10“3 -— ,, x Cx.01 S Q \ 4? 11: PE 10"4 —' s E § § § D v _5 H m m m i f i i i G 3 I? 1? 1> "U x x 8 Q ?~ 10"6 - x \ 10—7 ~— g 3 $ $ 1:: .P 1 1 1‘ 10—9 11 11 IJILI L4 lLJll 11 1111 IIL 0 20 40 60 80 100 E7 (MeV) Figure 5.6. Gamma-ray cross section as a function of gamma-ray energy at OLab-90° for UN on Pb, Zn, and C at “0 MeV/u. 78 10 ’1 ”C e o 0 x1 'I” 10‘"2 —— o L“ CD 10—{3 __ B e 2 e x 8,»)«01 \\\ a G c ._4_ ___ R a m o ”a 10 mm o X \_/ m m § § § § 10—5 1..— Xx m § § f? c. ‘5 z 6‘ M £11 3 7 1i 1” 10'” '— b 01 10.... 1 1 1 L 1 1 1 1 a 1 O 20 4O 60 80 100 E7 (MeV) Figure 5.7. Gamma-ray cross section as a function of gamma-ray energy for l"N+Pb at “0 MeV/u at O - 30°, 90°, Lab and 150°. 8 I'luisl 79 10“1 o 8 x1 10"2 ~— 1“” 9 D 8“,be 10_3 ”" 9 X 81.9001 o a 10"4 -- ° 1: o a a a a Q Q 10“5 —— i x ”’m i f x ”’mqu f §i€fl.1 10"6 1— x *x M 0 1 1 i 111 v 10 3 826/815:de (mb/MeV--sr) 10'"8 1— % 1- i 1 1111. 10—9 1 L l l l l 0 20 40 60 f 80 100 E7 (MeV) Figure 5.8. Gamma-ray cross section as a function of gamma-ray energy for HN+C at “0 MeV/u.at eLab' 30°, 90°, and 150°. ‘ 1nu-1’ 80 0.100 _ A - 5-1 1- U] r- \0.050 - '“W‘ .0 L- E: — c '- \\ "c . Pb >0010 a -‘- ‘ 2 I Zn 0.005 - o " L N '5' .1. A .- 5 12:1 _ ‘6 '8 1 1 1 C 0001 1 1 1 1 1 1 1 1 1 1 1 1 1 i 0 60 100 150 ®Lab (deg) Figure 5.9. Integrated gamma—ray cross section for E > 20 MeV as a function of angle for 1"N+C, Zn, and Pb at £13 MeV/u. 81 10"1 z ’1: E m 5 e 0 E/u=40 MeV x1 1 10—2 5— % E 9 D E/UZBO MeV X.1 mu.- ' 2 10‘3 =— 8 ° \ E <0 .0 3 a <1 Q ,2 E 10—4 E— g i § § _ C 10—5 __ ID if "U E :0 _ B : m 1 131—1 I [D Pd “6 1;] <> 10 E— \ E 0111 b. E f If] N 7 E. T T: 10 E—. m E 10_8 liLillllillilllLllLlll 11 0 20 40 60 80 100 E7 (MeV) Figure 5.10. Gamma-ray cross section as a function of gamma-ray energy for HN+Pb at “O and 30 MeV/u at 0 - 90°. Lab 82 electromagnetic showers. The energy of the photons was extracted from the ranges of the electron and positron in the telescope. Figure 5.6 shows the photon cross sections at 90° for three targets, C, Zn and Pb, and Figures 5.7. 5.8, and 5.9 show the effect of laboratory angle for three targets. The yield is nearly independent of angle for the heavier targets, but the decrease in the yield with lab angle is most pronounced for the lightest target. Figure 5.10 shows the photon data on the Pb target at “O MeV/u and at 30 MeV/u. While the spectra for photons below -20 MeV are very similar, the spectra above that energy show quite different slopes. I 1116.11 ‘ 83 Chapter 6 Theoretical Models 6.1 Comparison of Photons and Pions Subthreshold pion production has been used for years as a probe in nucleus-nucleus collisions. Since pions are the lowest mass strongly interacting particle not originally present at the start of the collision, they are an important probe of the collision. Numerous theories have been advanced to explain the production of these pions far below the free nucleon-nucleon limit. A natural comparison to make is between the pion cross ssection and the photon cross section. Figure 6.1 compares the photon cross section for HN on Pb at “0 MeV/u and the n° cross section for the same system at 35 MeV/u [Br8“] times the ratio of phase space for w°'s and Y's. The ratio of the phase space can be found by: 2 2 %Y . -512722y . §§T%§T . E$--.— 0 __ 2 2 _ .. w 3x4wpfldp" p1r p: dET 3/(ET m“) The slope of the cross sections and the extrapolated overlap ”jun" 8“ 10‘“1 10“2 0 ’i? —3 m 10 cm)! i; m m 10-4 (“pm 2 3 181 E 10"5 T I? “f 1 D to 1 ~_/ [:3 10—6 x TT'Vy/V." U ' ‘L “Ed. .11. .1. X \ x b x '0 10—7 X 10..., _ 1 1 1 1 0 50 100 150 200 250 Total Energy (MeV) Figure 6.1. Comparison of the high energy gamma-ray cross section and the neutral pion cross section multiplied by the redative phase space as a function of the total energy of the photon or pion. 1uu--‘ 85 for the same total energy of photons and pions appears to be very similar. This would suggest that the pions and photons are due to nearly identical processes, thus the measurements of photons would yield similar information to difficult subthreshold pion measurements at low beam energies. Another piece of evidence linking the high energy photons and pions is the similarity of their angular distributions. Both are nearly isotropic, the pions having been measured by Braun-Munzinger et al[Br8“] from 0 to 180°, and photons from O to “0° in the first experiment with 1“N + Cu, and from 30° to 150° with HN + Pb, Zn, and C in the second experiment. The departure from isotropy in the ‘“N + C data can be explained as an isotropic distribution in the center-of-mass frame distorted by the large velocity of the center of mass for the light system. When the high energy photons were found, several pion theories were quickly extended to include photons. The first of these was the picnic bremsstrahlung model of 11.0reiner [Va8“]. Since the picnic bremsstrahlung was the analog to classical bremsstrahlung, it seemed an ideal test of the model. H.St6cker and D.Hahn produced a modified form of their hydrodynamic modelEHa85a,Ha85b], and shortly later .J.Aichlein and G.Bertsch produced a calculationEAi85]. The cascade models, which describe nucleus-nucleus collisions in terms of the sum of the individual nucleon- nucleon collisions, have been successful in describing 11mm 1 86 particle production at higher energies. RichmanERiSO] suggested using the pion yield to determine the number of nucleonsnucleon pairs having sufficient energy to create a pion, and hence the Fermi distribution of the original nucleus. As the beam energy is decreased, the cascade model predicts a pion yield that is too small. Pion production has been measured as low as 25 MeV/uEStBSa]. A new microscopic approach by W.Bauer using a large time dependent Hartree-Fock model corrects some of the deficiencies, but has not yet been calculated for the systems studied here[Ba86]. The thermal models also have problems at the low beam energies with the pion cross section; the pion represents a large share of the available energy in the collision, but why this energy is not rapidly dissipated among the nucleons is difficult to explain. These problems led to a third class of theories, all using the concept of bremsstrahlung. Electromagnetic bremsstrahlung’is a well understood classical phenomenon; Greiner et al.[Va8“] introduced pionic bremsstrahlung, where the virtual photons of the electromagnetic field are replaced by the virtual pions of the strong nuclear field. The important free parameter in this theory is the stopping time of the nucleus in the collision. If picnic bremsstrahlung occurs, then electromagnetic bremsstrahlung should also occur. Experiments have been done at higher energiesEBu82] to look for this, but nothing Hit... 87 had been published for searches in the intermediate energy range. The observation that high energy e+ and e‘ were being detected, discussed in Chapter 2, strongly suggested that electromagnetic bremsstrahlung was indeed taking place. If this were the case two entirely different probes, pions and photons, should yield the same stopping time. Ko suggested that electromagnetic bremsstrahlung may be observed, and have two components; a coherent part due to the net motion of the nuclei, and an incoherent part due to nucleonsnucleon collisionsEKoBS]. 6.2 Coherent Bremsstrahlung 'The uncertainties in the calculation of bremsstrahlung from the nucleussnucleus collision lie entirely with the collision process itself; electromagnetic bremsstrahlung is well described. A question remains, however, whether the photons add coherently or incoherently. The photons of interest are from 20-100 MeV, with a wavelength of about 62- 12 fm. The radius of-the HN nucleus is about 2.9 fm, using the relation [Pr75] R . ”111/3 ro - 1.2 fm so the wavelength of the photons is larger than the size of the interacting region, suggesting that coherent emission is likely. Innul g £0 88 v Iliuhi v2 R1 It Figure 6.2. System used in the coherent bremsstrahlung calculation. 89 A simple model of coherent bremsstrahlung was made using a classical model by BudianskyEBu82]. Starting with the familiar equation from Jackson [Ja75]. the intensity of radiation emitted during the collision can be expressed (in esu units) as: 2 dt J dax annxJ(x,t)]e1w(t_n°X/°) To convert this expression into a form expressing the number of photons N per photon energy interval BY per solixianigle Y just divide by haw. dN2 1 dzI a§;16 ' R73 3386 The collieukn1 can be modeled as two spheres of uniform charge colliding along the 2 axis. 'The spheres interpenetrate without distortion, exponentially slowing to a stop. This model is described in detail in [Bu82], but is restricted to impact parameter b-O. A straight forward extension is to consider b¢0 (Figure 6.2), which is calculated by the program BREMIW and its subroutines. The details of the calculation appear in Appendix A. The results of the code BREMIW for UN + Pb are shown in Figures 6.3 and 6.“. Hugh . fl 90 p O I p " II‘HHIV H O I N H O 1 GI dza/dE1d0 (mb/MeV- sr) Figure 6.3. Cross section for the coherent bremsstrahlung model as a function of gamma-ray energy for 1"N+Pb at “O MeV/u and 0 - 90° with stopping times of 10, 15, and Lab 20 fm/c. 91 dzo/dEde (,ub/MeV—sr) 9 o l f: T I Figure 6.“. Cross section for function of lab angle for E - ®Lab (deg) bremsstrahlung model with 1-15 fm/c. HN+Pb at “O MeV/u as a “0 MeV using the coherent I 1111..“ ‘ 92 Table 6.1. The angle between the original direction and the direction at impact for two nuclei just touching. [IIu1I (‘- systgm_ lab deflection angle “0 MeV/u 1"N + Pb 3.87° “0 MeV/u 1"N + C 0.52° 30 MeV/u 1"N + Pb 5.29° 93 The Coulomb force deflects the trajectory of the two nuclei. so that for impact parameters not equal to zero, the axis of motion is rotated. The maximum amount of the rotation occurs when the two nuclei just touch, and is about one half the grazing angleENb76]. For the systems under consideration, this rotation is insignificant (Table 6.1). 6.3 Hard Sphere Bremsstrahlung Another estimate of the coherent bremsstrahlung, suggested by Stevenson [St85a], is to use a model of two hard spheres bouncing off each other to model the collision. The center-of-mass scattering angle of the nuclei is entirely dependent on the impact parameter b. The size of the maximum impact parameter taken has an effect on the shape of the angular distribution. Taking the maximum impact parameter to be that of a glancing collision, b-R,+R,, completely removes the minimum near 90° (Figure 6.5 and 6.6). Although this is not a very realistic model of the collision and greatly overpredicts the photon yield, it represents the other extreme to the interpenetrating spheres model. 6.“ Fireball A sucessful model used to explain the particle spectra Observed in intermediate energy nucleus-nucleus collisions $18 the fireball model or hotspotEGo77]. In this model, the , .. HahnH dad/dEydfl (pb/MeV—sr) 9“ 10 bmu= RN+ RPb bung: .72' (Ru'1‘pr) hm“: . 37' (RN+RPU) TII[1TIIIITTTIIITI]erTIII @011 (deg) Figure 6.5. Cross section for l"N'er at “0 MeV/u and E - 50 MeV using the hard sphere bremsstrahlung model for vgrious maximum impact parameters. '. '11u‘1 95 l |1lu11|‘ H O H 1... O 0 ll H D l H E! I! E! m@@@@@@ T9? 1 1 dog/dEde (pb/MeV—sr) °1 10-3 10"4 10—5 ‘ L 1 L 1 l 1 1 L 1 I 4 1 1 1 l 0 50 100 150 E7 (MeV) Figure 6.6. Cross section for l"N+Pb at “O MeV/u and 19 ab. 30° using the hard sphere bremsstrahlung model with the maximum impact parameter 37% of the radii. 96 overlapping region of the colliding nuclei forms a hot region which evaporates particles. By applying the black body equation to the hot spot and knowing the size and temperature of the hot spot, the approximate photon yield can be calculated. 1 As a simple model of a fireball (function FIREBALL), '“u“‘ the number of participant nucleons and the volume of the hot region is set equal to the overlap of the two spherical nuclei passing through each other. The volume swept out is calculated in Appendix A. The temperature is found by assuming all the thermal energy comes from the kinetic energy per nucleon of the participants in the center-of-mass frame of the fireball. Calculated size and temperature of the fireball as a function of impact parameter for “’N + Pb is shown in Table 6.2. In a black body of temperature T, the energy density with angular frequency w is [Be70]: 1 Mm“ “ 9’ _ E 4 ,0 10 —- é _ % _ 9 ' 1 ~12 1:11 -8 __ E - . \ NFU 10—10 I I I 1 LI I I L LL I I l I I I I I I L I I I I L 0 20 40 60 80 100 E7 (MeV) Figure 6.9. Cross section for HN+C, Pb at 0 the incoherent bremsstrahlung model. . 0 Lab 90 using AL m 1 >0 2\£ 2C \,\ yfl.h p. 7.. 105 1. CD1 00 I 2 d U/dEde (mb/MeV—sr) ‘1 I 10—9 __ _ (Ebeam=30 MeV/u)><.01 \ \ \ I I I I I LII I I I I I I I I4 I I I I I I I I I 0 20 40 60 80 100 E7 (MeV) Figure 6.10. Cross section for l"N+Pb at “0, 30 MeV/u using the incoherent bremsstrahlung model. “uhl 106 weighted fireball. The results of the calculation and the data are shown in Figure 6.9. The general trend of the high energy component of the data is reproduced, as is the angular distribution, the beam energy dependence, and the target dependence (Figure 6.10). Similar calculations have been done by Nifenecker and BondorfENi85], where both the coherent part and the incoherent part of the bremsstrahlung are calculated analytically. ““11 ‘I 107 Chapter 7 Conclusions The high energy gamma rays discussed in the preceeding chapters are an active area of research. Many groups have become involved in measurements and models, and new data and calculations are continually being published. The first experiment demonstrated the existence of gamma rays of up to 100 MeV in HN+Cu at “0 MeV/u using pair production and a magnetic spectrograph. The second used an entirely different technique, a Cherenkov telescope, and studied three targets, one at two beam energies. Subsequent experiments with other systems and beam energies, indicate that these high energy gamma rays may prove a powerful tool in probing heavy ion collisions, especially at decreasing beam energies where n° experiments prove very difficult. Simple calculations, as in the previous chapter, have been used to try to understand this phenomenon. Coherent bremsstrahlung, where the current is provided by the net nuclear motion, fails to produce the nearly isotropic angular distribution measured, but provides roughly the correct photon energy dependence. The thermal model, where the photons are emitted as black body radiation from the ““41 b 1111 b 108 nuclear fireball, provides the isotropic angular dependence, but fails to predict the photon energy dependences. The incoherent fireball model, in which the photons are bremsstrahlung from nucleussnucleus collisions within the hot fireball produced in the collisions, gives roughly the angular, beam energy, and photon energy dependence. This is a region of current interest in intermediate energy heavy ion physics. Theorists W.Bauer, D.Hahn, R.Stdcker, G.Bertsch, J.Aichelin, and W.Greiner are currently working on this problem. R.Shyam and J.Knoll have recently published a paper on the co-operative model, in which both pion and photon production is due to virtual clusters of nucleons pooling their enerSYESh86]. Similar experimental work using a different techniques is in progress at GSIEHe8“,No85]. In summary, these high energy gamma rays are of great interest in heavy ion reactions, may be closely related to the pions which have been the subject of experiments in recent years, and may prove a valuable probe in intermediate energy collisions. 11n..-‘ 109 Appendix A Theoretical Calculations A.1 Bremsstrahlung The current J is written as: J(x.t) = 81(t)p,(X.t)02 - 82(t)p,(x.t)cz and since J = J2: In x [n x J]| - J sinOcm so the integral becomes: ————— s --- ——— 3 - 0 dB 00 unzl°c° J at I d x [819°C 329°C] iw(t-n-x/c) 2 sinO e where 1 I. .In.” " and 1 $1.: (“f ’1‘ (I) I.) 11) ( J 110 I I I! ' J at J 93* 081(t)p.(x.t) eiw(t-“'x/°) and I: ' I dt I d’x 082(t)pz(x.t) ei“(t‘“'x’°) .IHHI " and if the center of the first nucleus is at X the second 1 l at X then: 2! x - X1(t) + r = X2(t) + r 1 2 SO I, . I dt 081(t) ei‘“t x I d’x, e-nox1(t)/c p,(X1(t)+r1)e-n°r‘/c rearranging, and assuming that the nucleus does not change shape during the collision: I I1 . J dt c81(t) e '1“"°’/c 16: e-n-X1(t) I d,x 91(r1)e 1‘ . 11time x I‘space The time independent part is the integral over the space iaround the nucleus: I w . szrzdr icr cose Jd(cose) p,(r) e 1space flu Q» f' s n , Qg 111 the charge density is taken to be a uniform sphere: Ze 01(P) ' F?fif PAt using this to determine Z1(t) and 22(t): Z1(t) - -R, + 8°1tc tAt .Breaking the time integral into two pieces, Itime ' ItAt {At (x-O) - Jdt c8°1e (LI imt -i-(-R +8 ct)cosO I 1 o 1tAt(x'O) , Ii: CB°1e e _ 2 q ‘(t‘AtI/T x e 10[ R,+B,1cAt+8°101(1se 19(R -cB At)cos0 8 s 1 0 I‘t>At(x 0) Bo1ce c 1 x Jdt e(iw1‘1)t/t e-iw801ICOSO(I-e At . (.0 I‘t>At(x'O) g 8°101e1cR‘ cBO1At)cosO e aAt/t w -x x de e ax ek(1 e ) 0 Where X = (t-At)/I a - 1-iw1 k - -iw8°1t cose ‘(t‘At)/T ,9 “11' Replacing e"x with v, (I) i—(R,-c8° At)cosO I‘t>At(x 0) 8,101 e c 1 1 x e aAt/t ek 5 va 1 e kvdv O -|~l!1|“ The integral is the incomplete complex gamma function, (A) I,t>0(x-0) . 30101 eic(R‘ CB°1AUCOSG e aAt/T k'a ek r(a,1) similarly, (x.0) . {at cBoZeut/Teimt At Izt>At ‘(t‘AtI/T)] -i%[R,-ce,21t-e,2c:(1-e cosO X e (A) 13(R2 cBoZAt)cosO e aAt/r 5a k (x-O) . 80201 e k e 1: t>At x F(a,1) Where a s 1‘in k = iw8011 0080 These calculations are found in subroutine BREMANYB, listed in Appendix D. >1 ifag. 115 The calculation of the cross section in the laboratory frame is straight forward (program BREMIW). First, the angle in the laboratory'frame is transformed into an angle in the center-of-mass frame: sinOL — NIII Y(cosOcm B) tanOcm where 8,7rwfier to the nucleus-nucleus system relative to the laboratory frame. The ratio of the solid angles can be found: (1 - BcosOLl Y(cos0t-B)2 cosze d0 d9 cm L The relation between the photon energy in the laboratory frame and the center-ofsmass frame is: E a EYLY(1-Bcos0L) ch so the cross section in the laboratory frame is just b 2n do2 I ° I dzN -——_———( E ’ O ) 8 d ¢ bad b ------- (E ’ ¢) dEYLdnL YL L J0 J0 dEchdncm ch 1.2 Hard Sphere Bremsstrahlung The center-ofsmass scattering angle of the nuclei is related to the impact parameter b by: 08 - n - 2 Asin[§:%§:] where R, and R2 are the radii of the nuclei. The only change in the evaluation of the previous calculation is a change in the time integral after the collision, and in the value of the quantity [nx(nxJ)] which becomes: IID‘IDXJ) 3| 2' Si“2(9-68)+Sinzesinzessinz¢ + 2(1-cos¢)sinOcosOsinOscos0S After the collision, the position becomes X,(t) . 1[§ + c8,sines] + 8[-R,+c8,At + cB,c0s08(t-At)] the time integral becomes: -81 _ e-iwe. ei§<1«s.q11t I‘tlme . iwII‘qu) with 8: ' g31n980080 + 0030 ('R,+c8,(1-cos08)At “Eu"‘l and q - sinOcos¢sines + cosOcosOS and -81 6-10.182 eiw(1+82q)At - .1- 12121018 iw(1+82q) as...” with 32 - -%sin0cos¢ + cosO(R,-B,(1-cosOS)At L3 ’3 LL 118 A.3 Fireball The overlap of the two spherical nuclei passing through each other is equivalent to the intersection of a cylinder of radius R, intersecting a sphere of radius R1 for the contribution of the first nucleus, and a cylinder cM’ radius 11, intersecting a sphere of radius R, for the second. The volume intersected is (function OVERLAP): +111 . I Area(R,,r,) dz, where r, - /R",’-z2 HS LR I muiArea(R,nqu) is the area of intersection of circular regions of radii R, and r1 whose centers are separated My distance (impact parameter) d (function AREA) R = larger of R,,rl and R a smaller of R, and r1 L S R2 + d’--R2 W = -S L 2de if w 5 -1 Area . 0 if w a +1 Area - "R; if -1 s w S +1 0 - Acos(w) The The 801 DEF $1; «xv I”. H; Area - R The number of nucleons from nucleus #1 is . -4HS- A 1 1 HS ”HR: Iwu" The temperature is found by assuming all the thermal energy comes from the kinetic energy per nucleon of the participants in the center~of~mass frame of the fireball (Table 6.2): TLcm AlHSLElcm T - 54HS' AIHS + A 2HS In a black body of temperature T, the energy density with angular frequency w is [Be70]: 1 Mm’ ”(9) ' 775‘ um/T d“ e 1 So the number of photons in volume V is u(w) hm 2 1 V d" '16“ V0 [KB] .116 ehm/T ; d‘"°’ The hotspot is taken to be normal nuclear density containing A nucleons, so V - -nR3 , R - rS-A r, - 1.2 fm 120 Allowing all the photons to leave isotropically, lam 1“" 121 A.“ Incoherent Fireball Bremsstrahlung To estimate the yield of nucleon-nucleon bremsstrahlung within the fireball, consider a fireball of temperature'r and A nucleons. Assuming the energies of the nucleons in the fireball to have a Boltzmann distribution of velocity u: The energy of one nucleon in the center of mass of the nucleon-nucleon collision is: . a 21:2: 2 . e - 2 e 2 ( 2 1 8(u, u,) SO u, - u, + /8E7m n mu2 __9 -“-‘ 2 P(e) s (5%T13 I e 2T 9 2T(u + /8e/m n) 93“ 2 2 -_-“ 1 -22 -12 -25 -eeiésiecose - (5%?)3 2n I e 2T e 2T e T e T uzdu dcosO .In“- mu ———- mu ———— [e fi/Be/m __ e+-§;i:v/8€/m] u’du -5 2- "“ 2 f —_ J e T(u u/ZE/m)u2du _ " /§em . (_m )3 “HT e-He/T { f .. E 2 "“ f e T(u +u/28/m)uzdu } completing the square in the exponent, - 2.. -2 2-1 ——-— 2 3 (5%?)3 yggg e He/T e+2T [ I e T(u 2/2€/m)uzd em ‘ -m zi----2 f (u +2/25/m)uzdu } J e T Taking c s /E7T§mj P(e) ' Egg??? e-ZE/T {Imquy2(y+C)2dY ‘ Jae—%y2(Y‘C)2dY} “C C ”4“”fl 123 C m 2 C m 2 m ‘ZE/T r- -- - 5:7??? e {f e Ty y’dy - 2;} e Ty ydy “C “C C _E z + :2} e Ty dy} “C the unnormalized distribution is m -2€/T 1 3/2 2 _ :2 P(e) Engfc e {(m) [ 1rerf(c) ce ] + c2(§)‘/2[,gerr1} For the case of interest, e< mscnmmron {>0 LmlCfl. 1mm E::]ane~ooawrunmnat fi=7 aw“ . t . . Tigure 8.“. The n experiment electronics. H“. 1“3 and scalars. In addition, a module called the a databus allows the PCOS information to be read into the LSI. The program SARA [Sh85] samples the information gathered by the [.81 and performs analysis while the LSI is running, allowing continuous monitoring of the experiment. 8.3.1 The wt Experiment Electronics While the electronic setup was modified many times throughout the deve10pment of the experiment, the initial scheme was straight forward. This setup is shown schematically in Figure 8.“ and used liming Dilter Amplifiers (TFA) to amplify the direct anode pulses from the photomultiplier tubes. The TFAs proved very nonlinear with such fast pulses. The TFAs provided signals to both an ADC and to a Donstant Draction Discriaunator (CFD). 'Nu3CFD provides a logic pulse, the timing of which is independent of the pulse height. This pulse is delayed and used to stop the TDC as well as being used in the coincidence logic. The TFAs were later replaced by fast amplifiers. The dynode of the photomultiplier was connected to a preamp, which shaped and stretched the pulse. A slow amplifier was used to send the pulse to the ADC. The anode pulse went to a fast amplifier, which in turn fed a CFD, providingtflw signal for the logic and timing circuits. The coincidence gate, defining when an event of interest had occurred, was varied to reflect the 1H“ 1““ experimental configuration. In Figure 8.“, the requirement is AE+E+EU§Y, whereas later it was made AE+E+C2+8-fi-S-Y. The signal 88S"!- is provided by the LSI and means that the computer is not busy. The signal C is taken from the 2 secondary cathode of the MIW chamber; it is generated late:n than the photomultiplier signals due to the electron drift time within the MIW. The drift time was measured using a lime to Amplitude Donverter (TAC). The start for the TAC was the AE+E coincidence; the stop was the MIW (primary cathode) C pulse. The output was proportional to the time 1 between them and was put into an ADC channel. The use of the 02 signal in the gate suppresses spurious events due to (n.p). (n,n'), and (Y,Y') background by about a factor of “0. The fact that the C2 signal may be delayed from 0 to ~300 nS required the using a wide gate, delaying the scintillator signals, and using the maximum internal (“fliay of the PCOS system (682.5 nS). The coincidence output goes to Date and Delay Denerators (000), which provide adjustable width pulses for the ADCs and for the PCOS E1 gate. The widths of the inputs to the coincidence gate were made wider that the RF period of the cyclotron (~50 nS). This allows an event to be defined even if the pulses from the counters were made by particles from different beam pulses. This provide a way of determining the random coincidence rate. The information from the TDCs determines 1" 1“5 vmsnm umcnm: mus: «nun: uxnmu 1m wuch+D>—13E_ ED-“C rm m! cz-D-D' an: 5- mmo nun up [) gunman D comm mum onscnmuman prurnun. {>oimmuimuna Dianna» tz-cum E::] munouuwammml B "E TO "LIT!“ WEI . + Figure 8.5. The e‘ experiment electronics. "‘0 1“6 whether the event was due to a single beam pulse, and a TDC channel recorded the relative time between the RF pulse and the event. This technique determined that the majority of the events with the gate AE+E was due to correlated background as described above. When the presence of high energy electrons and positrons was suspected, the electronics was again changed to include the plexiglas Cherenkov counter. The coincidence was not changed, but another ADC and TDC channel were added. 8.3.2 The at Experiment Electronics In this experiment, the Cherenkov counters (61 and 62) were much less sensitive (~100X) to background and were further apart, reducing the spurious event rate to a low level, so the MIW 02 requirement in the event gate could be omitted. All the time and amplitude information was recorded and available during playback, so the 02 requirement could be added offline. The definition of an A event was EI+C1 (Figure 8.5). An additional change was made as a response to the suggestion that the observed "particles" in the previous experiment had been the result of pileup in the electronics. The anode of each photomultiplier was connected to a fast amplifier with two outputs; one went to a CFD, the other to a QDC. The QDC functions similarly to an ADC, but uses a much faster pulse and a smaller time window, greatly reducing the likelihood of pileup. The dynode of each 1"“ O) 0.... .4 g 511111 5511111 5. 51 Figure 8.6. The electronics. 1“? D SLOW PREAMP D‘ TIMING FILTER AMP -I> FAST AMP CD CONSTANT FRACTION DISCRIMINATOR " DELAY High Energy Gamma-Ray Telescope H" 1“8 photomultiplier went to a preamp, spectroscopy amplifier, and then to an ADC. Two entirely separate numbers representing the pulse height were obtained for each event and each phototube. When the ADC value was plotted against the QDC value for a single phototube, the effects of pileup appear as an increase of the ADC signal relative to the QDC. 8.3.“ The Y Telescope Electronics The plastic scintillators and Cherenkov counters, produce fast (~10 nS) signals, and the CsI converter produces somewhat slower signals (~100 nS). The anode of each of the tubes on the plastic elements has its anode connected to a fast amplifier with two outputs. One output goes to a QDC, and the other to a GED, and from there to scalers and to the'TDC. The outputs of the phototubes on the CsI converter are preamplified and sent into a slow amplifier and then to an ADC. The coincidence gate defining an event is 61L+61R+EZL+EZR+§U§Y (Figure 8.6). M" 1“9 8.“ PCOS III Electronics The LeCroy Research Systems Corporation introduced the PCOS III (Droportional Dhamber Dperating System, third generation) system in 1981. This system is designed for the readout of large multi-gire proportional ghambers (MWPC) quickly at a low cost per wire. To meet these constraints, the PCOS system can only determine if the signal on the MWPC wire exceeded a threshold within a specified gate; it does not record any other pulse height or time information. The front end of the system is the 2735 amplifixnn/discriminator card. This 16 channel printed circuit board resides on the detector. Fast amplifiers send the signefl. from each wire to fast discriminators. The output of the discriminators is a differential ECL (Emitter ‘Doupled Dogic) pulse whose width is equal to the time that the input signal exceeds the thresholxi. All 16 discriminators share the same threshold, which comes from a digital to analog converter in the 2731 Latch&Delay module. The MIW detector uses 12 cards, 6 for each plane. The differential ECL outputs of two front end cards are connected to a 2731 Latch&Delay module. When this module receives a strobe from its controller, it records which wires produced a pulse above threshold duringtflmestrobe. These modules include a unique feature, a programable delay, 1"" 150 where the signals from the front end'cards may be delayed from 300 to 682.5 nS according to instructions received by the controller. The programable delay proved not to be a useful feature; the delay was always set to the maximum (to allow time to decide if an event had taken place) and the system was very prone to oscillating and "locking up" in the "on" state. Only one threshold and delay could be set for each Latch&Delay module, corresponding to 32 wires. The 6 modules sit in a CAMAC crate near the detector and are controlled by a 2738 Readout Controller in the same crate. The 2738 Controller can control up to 23 latches (736 wires). The controller receives the strobe to gate the Latch&Delay modules and generates the busy signal. It also arranges the sequence in which to read the wires out. It receives its instructions from the LSI computer via the “299 Databus. The databus resides in the same crate as the QDCs, TDCs, and ADCs. Its sole purpose is to interface the Controller and the rest of the acquisition system, and communicates with the Controller via a 50 conductor ribbon cable. Great care must be used when cabling the PCOS system together. None of the connectors (except one) used throughout the system are polarized. This includes the power connectors. The 20 conductor ribbon cable specified to carry power to the 2735 cards allows too much voltage drop when used with more than two cards; hence the MIW s'” 151 detector used 1/“" copper bus bars to distribute the power and the 20 conductor ribbon ran only from the bus bars to each card. During the course of the experiment, five generations of 2735 cards were issued by the manufacturer in attempts to eliminate the tendency of the cards to oscillate. The final version, the 27358, proved quite stable, but has 10x less gain tTEUl the original cards. Several versions of the 2731 modules were released, but a tendency to lock in the "on" state remained, increasing in probability with the number of modules used. In the configuration used, the PCOS would send a header word of how many words to follow, one word per wire fired, followed a delimiter word marking the end of the string. Occasionally, the acquisition system would receive bad data from the PCOS system, in the form of string with header followed by a long list of nonexistent wires. This bad data Twould continue till the buffer of the LSI filled, then the LSI reset the PCOS and the problem disappeared temporarily. In retrospect, the PCOS III system proved to be a poor choice for a small detector. A similar but simpler system made by Nanometrics of Chicago has become available, and appears to lack the problems of the LeCroy PCOS III system[8r8“]. 152 8.5 Delay Cards In light of the difficulties with the PCOS III system, and in order to provide a simpler way of testing the MIW detectcn', as well as a backup to the entire LeCroy PCOS III system, delay cards were made (Figure 8.7). Each delay card connects 16 wires to a delay line (Rhombus Industries Inc. 9821 TY8 36-5), and each of the delay line to a coaxial (LEMO RPL 00.250) connector. The difference in delay of each tap on the line is 5 n3, easily resolved using the TDCs. Although the delay lines were tested, they were never used to take data during an experiment. They are described here primarily as a testing device for detectors designed to use the PCOS III system. The delay cards have, in addition to the delays and connectors, a 10 KO resistor to ground in the middle, a pair of fast clamping diodes at each end to protect external preamps from sparks, and a 50 O resistor termination at each end. 1*" 153 15“ Appendix C Detector Deve10pment and Design C.1 MIW Counter C.1.1 Introduction A magnetic spectrograph distributes particles on its focal plane according to their charge to mass ratio. While a variety of detectors have been built to measure the positions of these particles and to identify them, none of the existing designs was suitable to measure diprotons [8e82]. Three special problems are associated with measuring diprotons in the Enge split-pole spectrograph: the focal plane position of each proton crossing the focal plane must be determined simultaneously, the counter must be able to function in a very high background rate, and the counter must cOpe with the “5° incidence angle of the protons relative to the focal plane. A simple design for a focal plane detector is a gas filled proportional chamber with a single resistive anode wire running parallel to the focal planeERoTTJ. The wire is IN". 155 kept at positive high voltage; the free electrons from the ionization of the gas by the passing particle are drawn to the wire where they are accelerated.tw the electric field and undergo collisions with the gas, freeing more electrons [Sa77]. The position X of the particle is determined frmn the relative amount of charge collected at each end of the length Lo wire: Q x . ——— -—- Lo QL¥QR If two particles are present, however, this simple scheme does not work. Another way is to subdivide the cathode into strips, and connect each strip to a tap on a delay lineEMa79]. The position is then determined from the time delay in the signal reaching the end of the delay. This pmesents problems if the count rate is high; there may be many pulses present on the delay line simultaneously. A high count rate limits the usefulness of a counter with a single wire, since all the ionization collects on that wire, and pileup can occur. In addition, the ionization tends to spread out along the wire, reducing the position resolution of that counter. The Dulti-Dire Droportional Dhamber (MWPC) overcomes these difficulties by using many wires instead of a single wire. In the conventional MWPC, the anode wires are vertical and lie in the focal plane, and are about 5x as far from the cathodes as each otherESa77]. A particle “5° to the focal ’1‘1’ IRES ANODE W CONVENTIONAL MIW MWPC 157 plane, as is the case for the split-pole spectrograph, will divide its ionization among 9 wires (Figure C.1). By placing the wires above and parallel to the “5° path, the ionization would be collected by a single wire. This configuration is used in the the Dulti-Dnclined Wire (MIW) counter. The MWPC configuration lends itself to a readout system in which each wire is treated as a separate counter, and connected to its own amplifier and discriminator. The LeCroy PCOS III (Droportional Dhamber Dperating System) was chosen since it was already to be used in the HIT detector then being built by R. Tickle and collaborators[T181]. C.1.2 MIW Prototypes 'The MIW detector was designed to be used with the PCOS III electronics. It would be used in air rather than vacuum to provide the cooling requirements of the amplifier/discriminator cards, each of which produced more than 5 W of heat [Le80]. The change of the goal from measuring diprotons to pions to electrons and positrons made 1 ittle difference to the detector since increasing the <3perating voltage increases the gain substantially. The general MIW design calls for a printed circuit boardq called the anode board, to support the anode wires. 'The center region of the board is removed, so the anode Ivires are stretched across open space. 0n the other side of the anode board is the secondary cathode, separated from the 158 msux-sz-sss CATHODE 2 / SECONDARY CATHODE I 4" a) 77' PRIMARY CATHODE CAT HODE 1 Figure C.2. The MIW counter. 159 wires by the thickness of the anode board. The secondary cathode is essential to the operation of the counter since a reasonably uniform electric field is required near the wires for good multiplication to take place. On the same side of the anode board as the wires, but separated by a much greater distance, is the primary cathode. The region defined by the open space in the anode board and the cathodes is the active region (Figure C.2). The anode wires remain near ground potential and the voltages on the cathodes are negative high voltage. The approximate ratio of the voltages can be found by solving Laplace's equation for cylindrical geometry. Free electrons created by ionization in the active region drift in the electric field to the anode wires, where the signal is generated. Free electrons produced outside tine active region are drawn to the anode board, but do not undergo multiplication. The first prototype, MIW I, consisted of 32 wires with a .100" (edge) spacing, an active area ~1" deep, mounted in 21 large vacuum chamber, with the wires connected via small coaxial cables to the PCOS card in air. This design failed to provide any discernable signals, but several important lessons about the PCOS system and detector design were learned. First, the detector chamber case must be well grounded to the PCOS cards immediately at the differential inputs. IJnless this is done, extraneous signals completely bury the 1", s l 2 {TH 160 ones from the detector. Second, the path from the wire to the PCOS card must be minimized. Last, the runners on the anode printed circuit board must be recessed from the edge of the active region, or considerable arcing will take place between the runners and the secondary cathode. These ideas were incorporated into the next prototype, MIW II, which used the same anode board and cathodes, but mounted them in a metal box. The anode board had wires and runners extending beyond the active wires in order to provide as uniform an electric field as possible over the active region. The connection between the anode board and the connectors for the PCOS cards mounted on the lid was made by a piece of flexible flat multiconductor cable. Windows in the box allowed testing using a 8- source. As an aid in testing the counter, a card was made to replace the PCOS 2735 amplifier/discriminator card. This card shorted all the wires save one to ground, and connected this wire to a 509 resistor and a coaxial cable leading to an Ortec 109A preamplifier, whose output ran to an oscilloscope. The MIW II prototype (Table C.1) was tested using a ‘°‘Ru source producing B- of up to 3.5“ MeV and a scintillator placed behind the counter as a trigger, and produced current pulses at the wire of about 10 uA. The width of the position distribution was due to the large multiple scattering of the 3" particles. .‘.- ‘. .4“ a...“ -7" “Ha—r. . .e 161 Table C.1. MIW III Specifications Number of active wires 32 Wires 12.7 um gold plated tungsten Primary Cathode-Anode Gap 10 mm Secondary Cathode-Anode Gap 1.57 mm Gas 1 atm 50-50 argon-ethane Typical Operating Voltages Primary Cathode -“.53 KV Secondary Cathode -1.51 KV Anode 0 V Table C.2. MIW connectors. anode board Samtec TS-132-G-A (modified) adaptor board Samtec SS-132-G-2 (modified) gas box lid Viking 3VH18/1JND12 162 The next prototype, MIW III, used a similar gas box, but had several important improvements. The spacing of the wires as measured along the edge was doubled to 0.200" (5.08 mm) and the primary cathode-anode gap increased to 20 mm. Testing with this prototype indicated that increasing the gap beyond this limit reduced the position resolution of the countxn'. The anode board was subdivided into two separate counters, each with 16 anode wires, lying in the same horizontal plane, one ahead of another; this provides better rejection of spurious events and a measurement of the angle followed by the ionizing particle. The connections between the wires and the PCOS cards outsick: the gas box was made using mating SamtecESa85] male connectors on the anode board with every other pin removed (to provide .20" spacing) and an adapter printed circuit board with similarly modified female connectors (Table C.2). The adapter board runners connected the pins of the Samtec connectors to the pins of the wire-wrap style VikingEVi79] 36 grin card edge connectors epoxied to the lid of the gas box. In this way, a large number of reliable, gas tight cornuections were made to the PCOS card. This consideration Twas important, since the final detector would have nearly 200 wires to feed through a gas tight seal. This version was tested extensively, and deliberately allowed to spark in order to determine its region of operation. The final version, MIW IV, would be too diffVicult to repair after this distructive testing. A plot -*" b ' 11-?" n '. .k‘i'h .J plug" 163 400 cc CD CD anode output (mV) (9 8 I rII II II I II I I1 II I rI .4 1.6 1.8 2 V2 voltage (KV) Figure C.3. Operating voltages of the MIW III prototype usirqg 1 atm 50-50 argon-ethane. 16“ of the pulse height out vs. secondary cathode voltage is displayed in Figure C.3. C.1.3 MIW IV The final detector design, MIW IV, (Figure C.“) is very similar in principle to that the prototype MIW III (Table C.3). The gas box is made of aluminum alloy and uses O-ring seals for all removable parts. The Viking card edge connectors were potted into the lid with epoxy to form a gas tight connection. The secondary cathode is epoxied to the anode board to prevent the wire tension from bendingtflw anode board, and polycarbonate supports for the male Samtec (nannectors on the anode board are used to prevent damage to the connectors. The adapter board is rigidly attached to tru3.lid by screws and .25" phenolic spacers to prevent flexing when the 196 electrical connections (192 wires and “ grounds) are made or broken. Polycarbonate supports hold the secondary cathode-anode assembly and the primary cathode rigidly, and are not prone to damaging the wires when they .are removed, as was a problem in MIW II and III. The 1M9 resistors used for current limiting to each cathode in the case of a spark were moved to a box external to the detector. A .01 uF capacitor within the box was (nonnected from the cathode side to a 8NC connector so that a si.gnal could be picked off the cathode and run into a preamp. The detector used gas tight MHV connectors rather 165 |“. Al .Lmucsoo >H 3H: 93 uo 36H> >Beomm< 5.0 mczw; xom mew zosaom som.11\\\ \\\ \\\ n mQOIFqu he MW >m¢ZHmQ E952. $93228 23511111111111.1111 $93228 2E me 83:1 1 is}!!! mQQIIQQ , ..1 , MM meiu>mqazoomm mmuLGOm 26x1: 11% ; 1. 1 . 1 I ; , , meoaemzzoe zse me -Isczui To: . 11:11:11111111||i>/quom mmaeeee 32: 025.43% 5&8 111.1 mNlekmlwhlmwNVlwkwlw wnIICQnImb ,: .IOZIIIrI flaz%1|w\z/ 1 we segues QR S11 e. I macesmzzoe some gees AN meosemzzou muesso> :oI: >1: 166 Table C.3 MIW IV specifications Active wires in each plane: 96 Primary Cathode-Anode gap: .787" Secondary Cathode-Anode gap: .062" Wire spacing (normal to the wires): 0.1“1“" Wire spacing (along the focal plane): .200" Size of each active region: 19.2" x .7" Distance between Planes (center to center perpendicular to focal plane): 1.125" Wire: Wire Tension: Electronics requirements: Typical operating conditions: gas: Voltages- Cathode 1: Cathode 2: .0005" gold plated tungsten 58 12 PCOS 2735 Amplifier/Discriminator Cards requiring +5V€5.“A and ‘5VDCQ7.0A 1 atm. CF“ ”5.5 KV ‘1.96 KV 167 than SHV since SHV to solder lug gas tight connectors were not available. 168 i c.2 The uc(a.p)”N Test of the MIW A test was need to determine how well the MIW counter actually worked. The pions it was designed to measured would have a production rate of only ~1/hour, a rate far to low to use to test or adjust the detector. Any useful test needed to meet several conditicnua; the particles must be penetrating enough to penetrate the exit window, air, MIW counter, AE scintillator and stop in the E scintillator, they must have a rigidity low enough for the Enge spectrograph to bend them to the MIW's focal plane position, and the particles should represent a discrete spectrum with the levels separated by several wires to test the MIW position resolution. The wires in the MIW are .200" apart along the focal plane, corresponding to roughly 17 KeV/channel for 80 MeV protons. A good choice was the reacticnI ‘N3(c,p)"N* at Ea-=:20 MeV/u. The first excited state of 15N is about 5.3 MeV above the ground stateELe67] and the cross section fcn‘ the formation of the ground state should not be very :unallEGl71]. With the maximum field, the protons from the ground state would fall well on the detector, and the range of’ the protons was greater than the thickness of the AE scintillator. 169 50W1t-' (I) ch) :1 ‘3 L o o *‘ L ’ 01" . O 25 50 75 100 wire number .32 (3.5. Spectrum of alpha particles from ‘2C(a,c')‘2, It’s = 80 MeV. '1 icoo - 1A .1 500 —- X10 counts , I 1 III 0 25 50 75 100 wire number Figure C.6. Protons measured simultaneously using the reaction 12C(a,p)”N . 170 The elastically scattered alphas, however, have nearly the same momentum to charge ratio as the ground state protons. These alphas were numerous enough that reactions taking place within the AE scintillator were triggering the E scintillator approximately as often as protons were. Using the particle ID plot, however, allowed the complete elimination of the alpha particle background (Figure C.5) and produced a very clean ‘5N spectrum (Figure 0.6) despite the large number of alphas passing through the MIW, giving justification to its claim of being able to function in high background. I" " . .n _ mun thin—1 171 C.3 Scintillators C.3.1 Introduction As charged particles penetrate matter, they loose kinetic energy. Scintillators are materials which convert some of this energy into light. By measuring the amount of light produced, the energy loss of the charge particle can be determined. Many scintillators are commercially available. Inorganic scintillators, such as NaI(Th), BGO, CsI, CaF, produce a relatively large amount of light (~1Y/25 eV), with a relatively long decay time (~200 nS)[A382]. Plastic scintillators, such as the Bicron 8C-“00 and Nuclear Enterprises NE-100 series, are not as efficient (~1Y/100 eV), but produce all the light within a short time (~10 nS)[Ag’82,8183,Nu72]. Recently, slow plastic scintillator has been developed, with a decay time similar to that of inorganic scintillatorEHuSS]. Plastic scintillators are easily and cheaply machined cn~ cast into large shapes, have a low 2 and density, and can be polished for total internal reflection. Low atomic ninnber Z means that plastic is less sensitive to gamma-rays, but the presence of hydrogen makes it more sensitive to neutrons than inorganic scintillator. 172 C.3.2 Scintillator Design All the plastic scintillators used in these experiments were made of Bicron 8C-“08, plexiglas UVT (Dltraeliolet Transmitting) light pipes, and 2" photomultipliers (both the RCA 8575 and its equivalent the Hamumatsu 329 were used). The size of each scintillator was dictated by the energy loss and multiple scattering of the particle, the solid angle of the spectrograph, and the size of the MIW position sensitive counter. Since the original experiment was to have measured 20- 100 MeV pions, the [38-8 scintillator telescope needed to be able to stop all the pions within the E scintillator. An absorbing wedge behind the MIW and ahead of the telescope could be used to slow the pions above “0 MeV, but left the problem of the pion's stopping position due to the angle of the pion's entry. A pion could enter anywhere between 36° and 5“° to the normal of the telescope, meaning the E scintillator needed to be at least 6 cm thick. Multiple scattering of the pion increases the required size somewhat, so the E ,(later called E3) scintillator was made 3.0" (7.6 cm) thick. The A8 scintillator was chosen so that a “0 MeV pion passing through it (at “5° to the normal) would loose about 5 MeV. This made the AE scintillator .25" (.63 cm) thick. The other dimensions of the scintillators were determined by 173 Tane<3J1 Dimensions of the active region of the scintillators. Dimensions (in.) DE D3 D1 thickness .25 3.0 1.0 height 2.0 3.0 2.0 length 2“.0 26.0 2“.0 _l" .5 Am ““1 17“ the spectrograph and the MIW (Figure 2.2), the final scintillator dimensions are shown in Table C.“.‘ Due to the unavailability of high energy beams to make pions, the experiment was later limited to 20-“0 MeV pions. A new 8 scintillator was made with this in mind, called E1 (Figure C.7). The decreased size of the E scintillator decreased background by roughly the ratio of the volumes without sacrificing any solid angle. The light pipes needed to be reasonably efficient. They also needed tOIreduce the position dependence of the signal as much as possible, and to allow placement of the magnetic shielding around the phototubes. The A8 scintillator light pipes were made of .25" x 2.0" x 1OJT'pflexiglas UVT, heated, bent, and polished to rnate the flat scintillator to a.pmrtial circle on the photomultiplier. This provides light more uniformly diiatributed on the photocathode of the photomultiplier tube and a much stronger joint. The light pipes of the E3 susintillator were made of a single large piece of plexiglas UVT about 1“" long tapering from a square to a 2" diameter cyl inder. The 81 light pipes were plexiglas UVT pieces 1"x2"x3.5" and 1"x2"x“.5". All these designs satisfied the requirements. The A8, and E scintillators have positibn dependence of the 1 signals of only about 10%. All three used double magnetic E3, shields, so that there was no measured shift in gain of the tubes ewen with the spectrograph at its maximum field. 175 2- PHOTOTUBE 80-409 OUTER SHIELD V l 1 l _[ I \ BASE 1" E SCINTILLATDRW“ 5'1“” 2- PHOTOTUBE ec-4eo OUTER SHIELD 1 A a. INNER SHIELD 9‘5": 2' ' ’6 CHERENKOV 1 ll 1 i' F as experiment. gure 0.7. Scintillator and Cherenkov detector used in the I. 1’ J 'I—r: 176 C.“ Cherenkov Detectors As a charged particle moves through a medium at a speed greater than the speed Of light in that medium, light is produced at an angle depending on the speed of the particle and the index of refraction of the medium. This light is walled Cherenkov light, and is primarily produced at short wavelenghtsEMa69]. The blue glow surrounding the core of a water cooled nuclear reactor is a manifestation of this effect, as large numbers of 8 particles are ejected by the .fission fragments into the water, in turn producing photons of Cherenkov light. The advantage of a Cherenkov detector is that it is completely insensitive to particles with a velocity less than C/FL. ‘This makes it a powerful tool in discriminating against slower particles. The difficulty is that Cherenkov chetectors produce much less light than a scintillator, (typically, for a high energy electron, ~500¥sinOg/cm, or ~1Y/“ KeV in plastic)[A382]. A drawback, however, is that various gamma ray interactions in the plastic produce r~elativistic electrons seen by Cherenkov detectors. The first Cherenkov counter used in these experiments Iwas a single piece of 2“"x2"x1" plexiglas UVT (so as to ti~ansmit as much light to the tube as possible) with a single phototube glued to the high radius end. Since the eluectrons (Y>>1) were entering at “5° to the counter, most ”I! 1.: ' I... Jinn-n1 177 10f the internally reflected light would be expected to arrive at that end. The critical angle is (n ~ 1.5)[Ag82]: 1 OC- Acos{§fi} - 66° so that the light on the low radius end would strike the surface near 2“° to the surface, and little would be internally reflected. While this counter was simple, it had two drawbacks. The thermal noise from the tube overlapped the size of the signals, and the counter was not uniformly responsive along its length. The coincidence requirement eliminated most of the thermal noise, but it made determining the efficiency of the counter difficult. A recent development, Bicron Corp. introduced a plastic wavelength shifter specifically designed for Cherenkov detectorsEHu8“]. This plastic, 8C-“80, shifted the Cherenkov light into longer wavelengths suited to common phototubes and simultaneously re-emits the light isotropically. This greatly decreases the position dependence of the signal. The ei experiment essentially eliminated the background from ‘r-ray interactions and thermal noise by using two separated identical telescopes on 8C-“80 with phototubes on either end (Figure C.7). The size Of the Cherenkov counters was increased to allow for \multiple scattering Of lower (~20 MeV) electrons, and the ends tapered to allow the use I"" 178 [:3/ BASE ’,MAGNETIC SHEILD /:/\PLEXIGLAS UVT l M —— 80-480 / —— PHOTOMULT I PL I ER ] Figure C.8. Cherenkov element Of the High Energy Gamma-Ray Telescope. 179 Of magnetic shields. The light pipe was integral with the Cherenkov counter to maximize efficiency. The same idea was carried over into the High Energy Gamma-Ray Telescope (Figure 5.2). Each Cherenkov element (Figure 0.8) would measure the passage of 0, 1, or 2 electrons (or a cosmic ray muon) (Figure 5.5). TWm muons provided the normalization between the elements. The first element was .5", the next 1", so that low energy e+e- pairs could be better measured. The next 8 elements were 2" thick. Due to their increased thickness, a plexiglas UVT "cookie" was used to adapt the 2" phototubes (RCA, Hamumatsu, and EMI RCA 8575 equivalents) to the elements. The phototubes were offset to allow for clearance of the phototube bases. .8 180 Appendix 0 Computer Codes D.1 Acquisition Code The code SARAESh85] was used for all aquisition and playback of the data for all the experiments. Generally, this code is flexible enough to handle most experiments, with all the user defined parameters and pseudo parameters placed in the subroutine DATA68K called by the main program. The PCOS III system used in the spectrometer experiments anoduces a variable number of words; two plus the number of wires which fired. This means special care must be taken in decoding the data buffer; it is not listed here since the routine used has been made obsolete by subsequent revisions of ESARA. Modifications were also to the histogram updating section of SARA in order to allow multiple updates of a Itistogram during a single event. This was necessary to Inonitor the detector for "dead" or "hot" wires; ones which either never or always fired. The PCOS system was connected to the MIW counter such that; each of the latches had channels 0-15 connected left to 4h. 181 right to the front plane and 16-31 right to left to the rear plane behind the front plane. The latch numbers ran 0 to 5 left to right. This was done so that the failure of a single latch would disable only one sixth of the detectmc rather than a third. The wire numbers run 0-95 left to right on the front plane and 96-191 right to left on the rear plane. This special version Of the subroutine, DATAQZ, assigned the average of the front wire numbers to variable "FrontAv", and 191 minus the average of rear wire numbers to "BackAv". ‘ The routine used to decipher the PCOS words taken from the data buffer "I8UF(IPOINT)" is taken from DATAQ2. D.2 MIW Detector Simulation SCATTER and Subroutines 00000000 0 86 87 0000 0 123 122 182 SCATTER .......................... K.Beard 12/6/84 calculates multiple scattering trajectories thrOugh MIW and extracts efficiencies for varies energies and angles real pot character‘ZO INNAME(40),HNAME(40) character*5 ENAME(0:10) dimension Npart(10).Iw(-10:lO0.0:5).Eloss(-10:100.5) dimension Rpot(40).Rstep(40).1wsum(0:40) common/particle/X,V,Z.angXZ,angV,xMO,T.step,MIW_e1 common/element/extent(0:10.0:10.0:3) common/statistics/reSultz(0:10.6),Tke,Nthpart.Iel common/randM/ISEED ISEED=99999 xMO=.511 type ‘ type * type *. program MIWscat ................ K.Beard 12/84’ type * type *. running instructions come from SCATT:, logical‘ type *.’ name assignment of file generated by program ROSTER' open(unit=4,name='SCATT:’.status=‘old’) icyc=0 icyc=icyc+1 read(4.87) Npart(icyc).Rpot(icyc),Rstep(icyc). 11NNAME(icyC).HNAME(icyc) format(1x.IS.F8.3.F10.5.5x.A20.5x.AZD) if(Npart(icyc).ge.1) go to 86 TCyc=icyc-l close(unit=4) Cycle throutn the list from ROSTER.DAT DO kCyC31.1CyC pOt=aDS(PpOt(kCyC)) step=Rstep(kCyc) read in description of MIW open(unit=2.file=INNAME(kCyc).status='old’) read(2.123) kzl.(extent(0.0,j).j=0.3) format(15.4FlS.5) read(2.122) (ENAME(n),n=0,10) format(1x.11A5) 0 00 0000 0 000000 0 183 if(kzl.ne.0) then type *. stop endif Last=extent(0.0.0) do kz=l,Last read(2.123) kzl,(extent(kz,0,j),j=0,3) if(kzl.ne.kz) then type ‘. stop endif do i=l,extent(kz.0.0) read(2,123) kzl,(extent(kz,i,j).j=0,3) if(kzl.ne.kz) then ' #1 error in ’.INNAME(kcyc) ’ #2 error in ‘,INNAME(kCyC) ’ :3 error in '.INNAME(kcyC) type ‘. stop endif enddo enddo close(unit=2) 8kg=BFIELD(pot) open(unit=1.tile='TEMPORARV.DAT'.status=’NEW') do Nthpart=l,Npart(kcyC) first generate the incoming particle uniformly illuminate detector to 1" beyond last active wire focal_loc= 1.+ 40.025 ‘ 21.‘RAN(ISEED) xMOM=xMOMENT(8kg.focal_loc) T=sqrt(xMOM**2+xMO“2)-XMO Tke=T ent_ang=9.0*2.*(RAN(ISEED)-.S)+4S. Vneight=.787*2.S4*(RAN(ISEED)-.S) vertang=1.2*(RAN(ISEED)-.S) initial conditions x=(40.0ZS-focal_loc)*2.54 V=Vheight Z=O angxz=ent_ang‘3.14159/180. angv=vertang*3.14159/180. Last=extent(0.0.0) MIw_el=O 00000 00 0 00 0000 C1 18“ Iel=MIw_el runs till particle leaves the detector or stops do while (T.ge.0. .and. MIw_el.le.Last) if(INSIDE(MIw_el,X,V,Z)) then call NEWDIRECT call NEWCOORD Tke=T else call STATZ call FILEZ MIw_el=MIw_el+l Iel=MIw_el call NEXT if(Iel.le.Last) then call STATZ call FILEZ endif endif enddo Iel<0 signal the end of the particle's track Iel=-Iel call STATZ call FILEZ enddo finished Npart particles ose(unit=l) set him width iwide # wires/bin 1w106=16 wide=1wide 101n=96/1wlde threshold to c0unt as a ”hit” on an element (MeV) thrsh=l.O Zero all aCCumulators do i1=-10.1OO do j1=O.S Iw(11.j1)=0 enddo enddo 185 open(unit=l,File='TEMPORARV.DAT',status='old') Ielast=-l Lpart=-l Nthpart=0 Iel=0 do k=0.5 do j=1.ibin Iw(j.k)=0 enddo enddo do while (Npart(kcyc).gt.Nthpart .or. (Npart(kcyc).eq.Nthpart .and. Iel.ge.0)) read(l.33) Nthpart,X,V.Z,T.angXZ.angV,Iel format(I10.6FlS.5.13) if(Nthpart.ne.Lpart) then iwr=(X/2.54)/(.2*wide)+1 deg=angXZ°180./3.14159 Iw(iwr,0)=1w(iwr,0)+l endif if(Iel.eq.Ielast) then Eloss(iwr,Iel)=Tlast-T endif Iel<0 ends the particle track it(Iel.lt.D) then do ik=l.5 if(E10$S(iwr,ik).99.thrsh) Iw(iwr.ik)=Iw(iwr,ik)+1 Eloss(iwr,ik)=0. enddo endif Lpart=Nthpart Ielast=Iel Tlast=T enddo C1ose(unit=1,DISPOSE='DELETE’) Open(unit=3,file=HNAME(kcyc).status=’new’) name of fi1e.... write(3.676) HNAME(kCyc).INNAME(kcyc) format(10x.A20.le.’....with detector configuration '.A20) scurces for this caICulation write(3.666) INNAME(kCyc).Rpot(kcyc).Rstep(kcyc) format(’ MIW descriptionz',A20.' pot=',F7.2.‘ step size=’ I .51 677 678 679 680 600 186 1 F6.4.’cm’) lables write(3.677) (ENAME(l).l=O.10) Format(/.3x,'bin’3x,A5,1x,A5,1x,A5,1x,AS,1x,A5,1x,AS,1x,AS,1x.AS, 1 1x,A5.1x.A5.1x.A5) do j=0.5 stum(j)=0 enddo do it=1,ibin write(3.678) it.(Iw(it.k),k=0,5) format(716) do k=0.5 IwSum(k)=Iw(it.k)+IWsum(k) enddo enddo write(3.679) format(6x,' -------------------------------- ') write(3.680) (IwSum(1),1=O,5) format(6x.616) type 600.HNAME(kcyc) format(5x.A20.’ written') close(unit=3) ENDDO end 0 0 187 subroutine NEXT common/particle/X.V.Z.angxz,angv.xM0.T.step.MIw_el common/element/extent(0:10.0:10.0:3) proceed to the next detector element Zedge=extent(MIw_el.l.3) deltaZ=Zedge-Z Z=Zedge X=X+deltaZ/tan(angXZ) V=Y+sin(angV)'deltaZ/sin(angXZ) return end SuprOutine STATZ puts re5ults into array ”resultz” common/particle/X,V,Z.angXZ.angY,xMO.T,step.MIw_el common/statistics/resultz(0:10.6).Tke,Nthpart.Iel entraning & exiting coords resultz(MIw_el.6)=angV reSultz(MIw_el.5)=angXZ re5u1tz(MIW_el,4)=Tke resultz(MIw_el.3)=Z resultz(MIW_e1.2)=V resultz(MIw_el,1)=X return end 0 188 Subroutine FILEZ(num_part) puts results of a particle into a file common/particle/X.Y,Z.angXZ.angV,xMO.T.step.MIw_el common/statistics/resultz(O:10.6),Tke.Nthpart.Iel write(1.33) Nthpart.(re5ultz(MIw_el.k).k=l.6).lel format(IlO.6F15.5.13) return end 1.— 0000000 0000000000000000000000 00 00000 0 0 0 189 SUBROUTINE SCATEL(theta.phi) real m0.step_scat.LLr,Mom common/particle/X.Y.Z.angXZ.angV,xMO.T.step.MIw_el common/element/extent(0:10.0:10,0:3) common/randM/ISEED this routine calculates the multiple scattering taking place for particles within an element of the MIW detector II:" kpts=extent(MIw_el,0.0) radLEN=extent(MIw_el,kpts.0) density=extent(MIw_el.O.1) Zthick=extent(MIw_el.kpts.3) 4 MIw_el ........... number of the MIW element under consideration radLEN ........... radiation legnth of detector element (g/cm**2) density .......... density in g/cm**2 of detector element m0 ............... mass in MeV of scattered particle T ................ kinetic energy in MeV of scattered particle this coordinate system uses a rectagular system. with X along focal plane. zero at lowest active wire V vertical, zero on median plane Z normal to YSZ. zero at front wire plane ><)<>><><>><><>><><>><><>><><>)<><>><><>><><>><><>><><>><><>><><>><><>><><>> radiation legnths of atomic element LLr=step*density/radLEN Mom=sqrt(T*T+2*T*MO) beta=Mom/(M0+T) rms angle due to scattering AO=14.l/(beta*Mom)*sqrt(LLr)*(l+log(lO.)*log(LLr)/9.) randoml=RAN(ISEED) random2=RAN(ISEED) inverse guassion function from IMSL library call MDNRIS(randoml.txv,ierr) tprob=(1./sqrt(3.14159))*exp(-t*t/2.) ers=sig*sqrt(sqrt(3.14159)/2) sig=AO/(sqrt(sqrt(3.14159)/2.)) theta=tXV*sig phi=2.*3.14159‘random2 return end 0 lOO 190 function 8field(ypot) f0=(ypot+.9205)/11.476 f=f0 do 100 k=l,25 z=XPOT(f) if(z.gt.ypot) f=f-fO/2*°k if(z.lt.ypot) f=f+fO/2*‘k continue freq=f 8field=freq/4.2577 end function XPOT(freq) xpot=-.9205+ll.476'freq+4.9023e-10‘freq*'6 xpot=xpot-l.9262e-13‘freq**8+4.5274e-l7*freq**10 end function xMOMENT(Bkg,DX) 8kg in Kg. OK in inches rho: (89.557-DX)/2.48306 xMOMENT= Bkg*rho/l.3132465 end 00 000000000000 0000 0000 1 191 Subr0utine NEWDIRECT finds the new direction of the particle real p.phi fl" common/particle/X.V,Z.angx2.angv,xMO.T.step.MIw_el f5 angXZ .................. angle (in rad.) to X axis in XZ plane 55 angv ................... angle (in rad.) to XZ plane I theta .................. angle (in rad.) particle scattered relative ' to origional direction of travel phi .................... azimuthal angle of scatter (with respect to x axis) 5 first get the theta,phi due to a scattering call SCATEL(theta.phi) find the new angles of the particle a=angXZ p=angv th=theta p=phi sa=sih(a) ca=cos(a) sb=sin(b) cp=cos(p) st=sin(th) ct=cos(th) sp=sin(p) cp=cos(p) these transformations convert the old direction8theta.phi into the new direction ' aprime=Atan2(ct*satcb-ca*cp*st-sa*cb*sp*st. sa*cp*st-ca*sb*spfst+ct*ca*cb) 1 i bprimezAsin(-cb*sp°st+sb°ct) angxz=aprime angV=bprime return end 0 000000000000 192 Subroutine NEWCOORD finds new XVZ coords given direction & old coords X ..................... parallel to focal plane (cm) zero at lowest active wire,+ toward greater radii v ..................... vertical (cm) zero on median plane.+ up Z ..................... horizontal perpendicular to focal plane (cm). & away from Split-Pole common/particle/X.Y.Z.angXZ.angV,xMO,T.step.MIw_el common/element/extent(0:10.0:10.0:3) X=X+step*cos(angV)‘cos(angXZ) V=V+step°sih(angV) Z=Z+step*cos(angV)*sin(angXZ) T=T-dEdX(MIw_el,T)*step return end function dde(Ielement.xKE) common/element/extent(0:l0.0:10.0:3) dde in MeV. step in cm, density in g/cm*‘2 density=extent(lelement,0.1) dEdX=l.9*density end a 00 0000 0000000000000 0000 0 193 function inside(MIw_el,x.v.Z) returns a true or false depending whether XVZ lies within or without detector element #MIw_el common/element/extent(0:10,0:10.0:3) there are coords for each corner of the element in extent extent .................... gives the physical extent of the element (MIw_el.pointt.X or Y or 2 (1.2.3)) pointJO= I of points to describe a quadrant (MIw_el.O.3)...Z coord of front edge (MIw_el.1,3)...Z coord of back edge test to see if within 2 extent of element kpts=extent(MIW_el.0.0) Zedge=extent(MIw_el.1,3) Zthick=extent(MIw_el.kpts.3) implicit 45 deg offset of detector elements included in definition of "Xa" xa=abs(X*Zedge) Va=abs(v) Za=Z if(Za.lt.Zedge) then inside=.false. return endif if(Za.ge.Zedge+Ztnick) then inside=.false. return endif if within 2 extent. check XV plane dir=Atan2(Va.Xa) do k=extent(MIw_el.0.0).2.-l XC=extent(MIw_el,k,l) Vc=extent(MIw_el, .2) if(Atan2(Vc.XC).ge.dir) kpair=k enddo Xl=XC V1=YC x2=extent(MIw_el.k-1.l) v2=extent(MIw_el,k-1,2) 0 0 19“ front_edge=extent(MIw_el.l.3) set center ZO=front_edge XO=O. VO=O. slope & intercept of line connecting corners a=(Vl-V2)/(Xl-X2) b=(V1*X2-X1*V2)/(XZ-Xl) point on line closest to X,V Xl=(x+a*V+a*b)/(1.+a‘a) Vl=a*Xl+b distances to center dEdge2=(Xl-x0)**2+(V1-V0)**2 dxv2=(Xa-x0)**2+(Va-VO)**2 if(dXV2.lt.dEdge2) then inside=.true. else inside=.false. endif end . A... LIL-1"!” 0000000000000000000000000000 76 195 descriMIW ........................ K.Beard 12/7/84 requests critical MIW detector parameters and puts them into a file called “descriMIw.dat” using the proper format for program "MIWscat" to read the form of the data file: 0(focal plane),# elements.0.0,0 name element,name element. ........ #element.# of description pts.density.Z atomic.A atomic telement. 0. x.v. front edge location telement. O, X.V. O zelement. O, X,V, O selement, radiation legnth,X,V, thickness character*5 ENAME(O:10) dimension extent(0:10.0:10.0:3) open(unit=1.file='descriMIw.dat'.status=’new’) do l=1,lO ENAME(l)=’ enddo zeroth element is the MIW mwpc ENAME(O)='MIW’ type *.'h0w many elements to this configuration ’ type f.‘ not including the MIW gas detector?‘ accept *.Last extent(0.0.0)=Last type ‘ do k=1,Last type *.' element:'.k type *,' front edge to focal plane distance (cm)’ accept *.Zedge extent(k.1,3)=Zedge type * type *.‘ description of element ............ ' type *.' name of element (A5)’ read(5.76) ENAME(k) format(A5) type *.' how many points for a Quadrant description' type *,' including axis?’ accept *.kpts extent(k.0.0)=kpts type * m=1 type *.' points',m,’ rotating from horizontal' 196 type ‘.‘x.y=0’ accept *,xc.yoid extent(k,1,1)=xc extent(k.l.2)=0. ~‘ do m=2.kpts-1 type ‘ type f,’ pointt’.m.' rotating from horizontal' type *,’x.y' accept *.xc.yc extent1k,m,l)=xc extent(k.m.2)=yc enddo type * type f.’ pointt’,kpts.‘ rotating from horizontal' type *,'x=0.y’ accept f.xiod.yc extent(k.kpts.l)=0. extent(k.kpts.2)=yc type f.‘ how thick (cm) is this element?' accept *.Zthick extent(k,kpts.3)=Zthick type ’,' radiation legnth (g/cmf‘Z)’ accept *.radlegnth extent(k.kpts.0)=radlegnth type f.‘ density (g/cm*f2)’ accept *.density extent(k.0,l)=density type *.‘ effective Z.A‘ accept *.Zel.Ael extent(k.0.2)=Zel extent(k.0.3)=Ael enddo type * type " . ' ><><><><><><><><><><><><><><><><><><><><><><><><><><>< ' c kOutz=O write(l.123) koutz.(extent(koutz.0.j).j=0.3) write(1.122) (ENAME(n).n=O.lO) 122 format(1x,11A5) C 1 do kOutz=1,Last ; do i=0.extent(koutz.0.0) write(l,123) kOutz,(extent(koutz.i.j).j=0.3) 123 format(IS.4F15.5) enddo enddo c type * type t.‘ Output placed in descriMIw.dat‘ stop €00 197 III-1‘ _1 c . c C program ROSTER ‘ c c makes list of combinations to run in MIWSCAT C and puts them in ROSTER.OAT c c Character*20 INNAME,OUTNAME.HNAME.blk ' open(unit=l.file='ROSTER.DAT'.status=‘new’) blk=' ' type ‘ type *.' program ROSTER .................. K.8eard 12/84' type * type *.‘ first run descriMIw then rename the output file' type *.‘ (origionally named descrile.dat)' type * type *.’ end inputs with a 0.0.0’ 889 type ‘.’ input the number of particles to be run. pot setting, 1 and step size (cm)' accept *.Npart.xpot.step if(Npart*xpot*step.le.O) then Npart=0 write(1,2) Npart,xpot.step.blk,blk I stop endif type *.' name of the file containing the description of the MIW' read(5.3) INNAME type f.’ name to hold histogram information' read(5.3) HNAME 3 format1A20) write(1.2) Npart.xpot.step.INNAME.HNAME 1 2 format(1x.IS.F8.3.F10.5.5x,A20.5x,A20) , go to 889 ' end - I 198 D.3 Pair Production Simulation GAMMATEE and Subroutines c c GammaTee ............................. K.Beard 1/9/85 c modified to read instructions from file 1/10/85 c modified to include target and energy loss 1/14/85 c modified to give Output in counts/1M gamma 2/12/85 c modified to use Plank distribution 3/5/85 c c takes a distribution of gamma rays and converts c to an electron/positron distribution using the c correct cross sections c common/Plank/ Xplank,Vplank,Temp common/lookup/ sigT,er.Xinthe.Egamma common hv.Ze.Z dimension Xplank(0:500),Vplank(0:500) dimension sigT(2,lOO).fze(2,100.0:lOO),Xinthe(2.100.0:100) dimension 2(2).A(2).Den(2).thick(2) dimension Pmom(0:200).Igam(0:200),iEbin(0:200).sigTOTAL(2),Xprob(2) cnaracter*30 GammaFile.PositronFile real hv.k,NA,mc2 iseed=9999 type *.' program GammaEE ................... by K.Beard‘ type *,' instructions from file ”GEF:”' type * type *.’ files written:’ c c c 1: target c 2: converter c units: NA=6.023E+23 !atoms/mole c A=g/mole c Den= g/cm**3 c Thick: cm mc2=.511 iMeV dde= 1.9 lMeV/(g/cm*‘2) c c open{unit=5.file=lGEF:’.status='01d’) 9 read(5.8) 2(1).A(I).Den(1).thick(1) 8 tormat(lx.4F8.3) if(Z(l).eq.O) stop read(5.10) Z(2).A(2).Den(2).thick(2).scl,Mgamma.GammaFile.Positronfile 10 format(1x,5F8.3.I10.1x.A30.1x,A30) c c c generate the normalized functions giving kinetic energy of positron call ISIS c Temp=scl lMev c c generate normalized Plank distribution generating function call PLAngen do izi=1,2 do m=0,100 type *,izi,m.FZE(izi.10.m).Xinthe(izi,10.m) enddo enddo 0000000 0 0 199 do m=O.1OO Igam(m)=0 iEbin(m)=O Pmom(m)=0 enddo cl=1/scl ll/MeV Emin=lO. lMeV do icyc=l.Mgamma Gamma distribution Egamma = Eplank(RAN(iseed)) k=Egamma/mc2 iE=Egamma/lO. m=Egamma/5. if( m.gt.lOO) go to 44 Igam(m)=Igam(m)+1 if(iE.gt.99) iE=99 interpolate total Cross section sigTOTAL(1)=(sigT(1,iE+1)-sigT(1,iE))‘(Egamma/lO.-iE)+sigT(1,iE) fm‘Z/atom convl=NA/A(l)*Den(1)‘sigTOTAL(1) ‘ l.E-26 lprob/cm Xprob(1)= -log(l-RAN(iseed))/conv1 sigTOTAL(2)=(sigT(2,iE+l)-sigT(2.iE))‘(Egamma/lO.-iE)+sigT(2.iE) fm‘Z/atom conv2=NA/A(2)‘Den(2)'sigTOTAL(2) ' l.E-26 fprob/cm Xproo(2)= -log(1-RAN(iseed))/conv2 if(Xprob(l).le.thick(1)) then ep=Xeff(1,iE)‘(k-2)+1 !mc2 units Epos=ep*mc2 lMeV energy loss passing thrOugh target Epos=Epos-dde*Den(l)*(thick(l)-Xprob(1)) energy loss passing thrOugh converter Epos=Epos-dde‘Den(2)*thick(2) if(Epos.lt.mc2) Epos=mc2 Xmsm=sqrt(Epos‘PZ-mc2ff2) !MeV/c Xke=Epos-mc2 fMeV m=Xmom/5. Pmom(m)=Pmom(m)+1 m=Xke/5. iEbin(m)=iEbin(m)tl 200 c else c if(Xprob(2).le.thick(2)) then c ep=Xeff(2.iE)°(k-2)+1 !mc2 units Epos=ep*mc2 lMeV c c energy loss due to converter Epos=Epos-dde'Den(2)'(thick(2)-Xprob(2)) c if(Epos.lt.mc2) Epos=mc2 Xmom=sqrt(Epos**2-mc2"2) !MeV/c Xke=Epos-mc2 lMeV c m=Xmom/5. if(m.lt.0 .or. m.gt.100) type f.‘ mmmmmm=’,m Pmom(m)=Pmom(m)+l m=Xke/5. iEbin(m)=iEbin(m)+1 c endif endif c enddo c c open(unit=ll.file=GammaFi1e.status=’new') open(unit=12,file=PositronFile.status=’new‘) c do i=2.30 E=i*5 il=Igam(i)+1 fil=i1*l./(Mgamma‘l.E-6) i2=iEbin(i)tl f12=i2‘l./(Mgamma*1.E-6) «F1te(11,7) E,f11 write(12.7) E,f12 7 format(3x.F15.7.’.’,E15.7) enddo c write(6.88) GammaFile.PositronFile 88 format(5x,A30.Sx,A30) Close(unit=ll) close(unit=12) go to 9 end FunctTOn Xeff(iel,iEx) c c randomly generated Xeff from extrapolated positron yield tables c common/lockup/ sigT,er.Xinthe.Egamma dimension sigT(2,lOO),fze(2.100.0:100).Xinthe(2,100.0:100) c iE=Egamma/10. y=QAN(iseed) i=100/2 201 i=' id=i do 1:1,7 if(Xinthe(iel.iEx.i).gt.y) then i=i-(id+1)/2 else i=i+(id+1)/2 endif if(Xinthe(iel,iEx+l.j).gt.y) then j=j-(id+l)/2 else j=j+(id+1)/2 endif id=id/2 enddo Xeff=( (j-i)*(Egamma/lO.-iE) + i )/100. return and 0000 00000 202 Subroutine PLANngn generates integral of Plank distribution from EgamO toward infinity common/Plank/ Xplank,Vplank,Temp dimension Xplank(0:500).Yplank(0:500) dimension sto(0:500) Egam0=10. lMeV Emax=500. !Mev Estep=l. !Mev SUth=O do ihv=Egam0.Emax.Estep lMeV hv=ihv sto(ihv)=SUth SUth=SUth + fhv(hv/Temp)*Estep/Temp enddo do ihv=Egam0.Emax.Estep EMeV hv=ihv Xplank(ihv)= hv Vplank(ihv)= sto(ihv)/SUth enddo return and function fhv(x) plank distribution (unnormalized) for dN/dEgamma = (dEinterval/dw) ‘ l/w hw = Egamma dEinterval = N * hw if(x.lt. 88.) then _ fhv=(x**2)/(exp(x)-1.) else fhv=0 endif return end 0000 0 203 Function Eplank(y) looks in Xplank,Vplank table made by PLANngn and finds Egamma for O