MSU LIBRARIES ”- RETURNING MATERIALS: P1ace in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. MEASUREMENT OF LIGHT PARTICLE~COMPLEX FRAGMENT COINCIDENCE CROSS SECTIONS BY Bruce Earl Hasselquist A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 198D ABSTRACT MEASUREMENT OF LIGHT PARTICLE-COMPLEX FRAGMENT COINCIDENCE CROSS SECTIONS BY Bruce Earl Hasselquist Light particle (ZSZ) inclusive and coincidence spectra have been measured for the reactions 92 MeV/A “°Ar+Au and 30 MeV/A 12C+A1,Au at angles from MS to 90 degrees. Coincidence triggers for the light particle spectra were intermediate mass fragments (35257) at -30 degrees, near projectile velocity fragments (352518) at -13 degrees, and light particles (252) at -MS and -90 degrees. The Ar+Au inclusive spectra are compared to hydrodynamics and firestreak model calculations. A coalescence model calculation is used to extract coalescence radii for d,t,3He, and “He from the Ar+Au spectra. Triple differential cross sections predicted by hydrodynamics are compared to the intermediate mass fragment triggered light particle spectra. A single moving source parameterization is employed throughout to depict the relevant trends in the data. Simple conservation laws are considered for the coincidence spectra in the context of a thermal moving source . ACKNOWLEDGMENTS I would like to thank Dr. Gary Crawley for.taking me on as a graduate student and providing invaluable guidance throughout my graduate career. The freedom afforded me by -Dr. Crawley made my time as a graduate student both enjoyable and profitable. I am deeply indebted to Dr. Gary Westfall for his assistance in all aspects of this dissertation. He provided the motivation and the means for the experiments on which this dissertation is based. His assistance during the analysis of the data and his many insights into their physical meaning will always be appreciated. I I would like to recognize the staffs of the Michigan State University Cyclotron Laboratory and the Lawrence Berkeley Laboratory for their efforts at various stages of this dissertation. The physics faculty at the University of Wisconsin - River Falls are thanked for their role in encouraging me to continue in physics. Special thanks go to Dr. Neal Prochnow who advised me in my undergraduate studies and continues to be a source of advise and encouragement for me. I would like to thank fellow graduate students Barb Jacak and Zach Koenig for their innumerable contributions to 11 this dissertation. Technical assistance by John Yurkon during the detector development stages is greatly appreciated. All of my fellow graduate students are thanked for their friendship during my graduate career. Special thanks go to Joe Finck who helped me to get through prelims and both Joe and Jim Duffy who were most enjoyable officemates. Barb Jacak and Zach Koenig proved to be very special friends whose friendship and dedication will never be forgotten. My parents, Earl and Joyce Hasselquist, and my wife's parents, Earl and Helen Woodbury, have been constant sources of support and inspiration throughout my undergraduate arm! graduate careers. Their many prayers on my behalf are appreciated. Above all, I would like to thank my wife, Jan, for her love and devotion over the last eight years. Her confidence in me has helped me to persevere through the hardest of trials. My son, Erik Earl, born during the first experiment at NSCL and whose second birthday coincided with my Ph. D. oral defense, is recognized for the joy which he has brought into our lives and the hOpe for the future which he represents. 111 TABLE OF CONTENTS PAGE List of Tables . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . viii CHAPTER I. INTRODUCTION . . . . . . . . . . . . . . . . . 1 II. DETECTOR DEVELOPMENT . . . . . . . . . . . . . 12 A. Scintillator Telescope Array . . . . . . 12 B. Plastic Scintillator Energy Calibration at IUCF o o o o o o o o o o o o o o o 19 C. Can Thickness . . . . . . . . . . . . . 25 D. Multiwire Proportional Chamber . . . . . 28 III. EXPERIMENTAL SETUP . . . . . . . . . . . . . . 36 A. LBL Experimental Setup . . . . . . . . . 36 B. NSCL Experimental Setup . . . . . . . . . uu IV. DATA REDUCTION AND ANALYSIS . . . . . . . . . . “8 A. Energy Calibrations of Detectors Used in LBL Experiment . . . . . . . . . . . . H8 B. Energy Calibrations of Detectors Used in NSCL Experiment . . . . . . . . . . . 56 C. Normalizations . . . . . . . . . . . . . 59 D. Target Thickness Correction . . . . . . . 60 E. Reaction Loss Correction . . . . . . . . 60 F. Scattering Out Correction . . . . . . . . 69 iv V. VI. RESULTS AND DISCUSSION . . . . . . . . . . A. 92 1. SUMMARY MeV/A “°Ar+Au Inclusive Spectra Light Particle Inclusive Spectra Moving Source Parameterization Coalescence Model . . . . . IRF Trigger Inclusive Spectra PLF Trigger Inclusive Spectra LP Trigger Inclusive Spectra MeV/A “°Ar+Au Coincidence Spectra Momentum Conservation Model Light Particle - IRE Spectra Light Particle - PLP Spectra Light Particle - LP Spectra . . . MeV/A 12C+A1,Au Inclusive spectra Light Particle Inclusive Spectra IRF Trigger Inclusive Spectra PLF Trigger Inclusive Spectra . LP Trigger Inclusive Spectra MeV/A "C+Al Coincidence Spectra . Light Particle - IRF Spectra . . . Light Particle - PLF Spectra Light Particle — LP Spectra . . . MeV/A "C+Au Coincidence Spectra . Light Particle - IRF Spectra . Light Particle - PLF Spectra . . . 73 73 73 77 81 89 9M 97 152 152 152 162 170 170 17“ APPENDIX APPENDIX A. Momentum Conservation Model . . . . 181 REFERENCES 0 O O O O O O O O O O O O O D C O O 189 vi LIST OF TABLES Calcium Fluoride Punch Through Energies (MeV/n) . . . . . Detector Angles for the Bevalac Setup Detector Angles for the NSCL Setup Moving Source Parameters for 92 MeV/A Ar+Au (Inclusive) Coalescence Model Parameters Moving 92 Moving 92 Moving 92 Moving 30 Moving 30 Moving 30 Moving 30 Source Parameters for MeV/A Ar+Au (IRF Trigger) Source Parameters for MeV/A Ar+Au (PLF Trigger) Source Parameters for MeV/A Ar+Au (LP Trigger) Source Parameters for MeV/A C+A1,Au (Inclusive) Source Parameters for MeV/A C+A1,Au (IRF Trigger) Source Parameters for MeV/A C+A1,Au (PLF Trigger) Source Parameters for MeV/A C+A1 (LP Trigger) vii PAGE 30 38 “5 an 88 132 137 1H3 160 167 171 FIGURE II—1. II-2. II-3. II’N. II’S. 11-6. 11—7. II-8. II’9. III-1. LIST OF FIGURES Seven telescope scintillator array used at LBL and NSCL. I.OOOOOOOOOOOOOOOOIIOOOOOO Timing diagram for scintillator array telescopes. The anode signal is a sum of the fast plastic scintillator component and the slow CaF2 component. ............ Schematic for active PMT base design used with scintillator array telescopes [Em 79]. 0.00.0.00...OOIOOOOOOOOOOOOOOOO Coincidence p-p spectrum from CH2 target during IUCF plastic scintillator calibration. 00.0.0.0.0000000000000000000 Singles proton spectrum from CH2 target during IUCE plastic scintillator calibration. ............................ Proton energy calibration of a plastic scintillator detector from IUCF calibration. The line is a least squares fit. 00......00....OOOOOOOOOOOOOOOOIOOOOO ..... Plastic scintillator resolution in percent for protons from IUCF calibration. The solid curve is the inverse of the square root of the proton range normalized to 2 percent at 100 MeV. ..................... Calculated AE-E isotope separation for p, d, t, ’He, and “He for a CaE‘2 AE thickness szmm. 0....I.OOOOOOOOOOOO0.00.00.00.00 .............................. MWPC position resolution obtained with a 8- source placed at 5 locations along the center of both the X and Y planes. ...... Chamber setup during the LBL and NSCL experiments. .00...OOOOOOOOOOOOOOOOOOOOOO viii PAGE 1“ 15 18 20 22 2Q 26 27 33 37 III*2. III-3. IV-1. IV*2. IV-3. IV~U. IV'S. IV-6. IV’7. IV—8. IV-9. IV*10. Electronics schematic for the LBL and NSCL experiments. 0.0.0.0...IDIOOOOOOOOOOOOOOO Ion chamber count rate calibration for the second weekend at LBL. The solid line is a least squares fit. ‘.................... Energy calibration for protons (circles) and alphas (triangles) in the plastic scintillator E element of a scintillator array telescope. The lines are least squares fits. ........................... NE102 plastic scintillator. Calculated ‘scintillation response to protons, deuterons, tritons and a-particles. [Go 60] ................................. Uncorrected energy calibration for protons (circles) and alphas (triangles) in the CaF, AE element of a scintillator array telescope. ............................. Plot of AE vs. E for a scintillator array telescope.‘ Note prominent band at the bottom is caused by neutrons and gammas stopping in the plastic. ................ Corrected energy calibration for protons (circles) and alphas (triangles) in the CaF2 AE element of a scintillator array telescope. The line is to guide the eye. Separate calibrations were used for protons and alphas. ..................... Energy calibration for protons and alphas in the NaI E element of a Silicon- NaI telescope. The line is to guide the eye. Separate calibrations were used for protons and alphas. ..................... Parameterized fit to measured total reaction cross section for protons on carbon. Data is from Measday [Me 69]. ........... Calculated tail—to-peak ratio for reaction losses of protons in NaI with data compiled by Measday [Me 69]. ............ Same as FIGURE IV— -8 for NE102 plastic seintillator. 0.0...OOOIIOOOOOOOOOOOOOOOO Calculated tail-to-peak ratios for reaction losses of p, d, t, ’He and “He in the ix In 43 50 51 53 5A 55 57 6A 65 66 Silicon—Mal telescope. IV—11. Same as FIGURE IV-1O for the scintillator " array telescopes. ... IV-12. Calcuated tail-to-peak ratios for scattering ‘ ' out losses of p, d, t, scintillator array telescopes. .......... ’He and ‘’He in the V—1. Energy spectra of (a) p,d,t, and (b) ’He,“He ‘ from the reaction 92 MeV/A “°Ar+Au. The angles measured are “5° (circles), 67.5° (squares), and 90° the laboratory. statistical. (double triangles) in The errors depicted are The solid lines correspond to a hydrodynamics model calculation and the dot-dashed lines correspond to a firestreak calculation as described in the text. ............................... ....... ..... V-2. Schematic representation of the energy ' spectrum of particles emitted from a thermally equilibrated source (a) in the source's rest frame and (b) in the lab frame with the source moving in the forward direction. .. ...... V-3. Energy spectra of p,d,t,’He, and “He from the reaction 92 MeV/A I"’Ar+Au. The solid lines correspond to moving source fits as described in the text. The dot-dashed lines correspond to coalescence model calculations. V—A. The variation with incident energy above the ‘ barrier of:(a) the p,d,t,“He cross sections associated with a mid-rapidity source (the solid lines are to guide the eye, and the dashed line is the fireball model prediction for protons);(b) the extracted temperatures from the moving source compared with fireball description (dashed) and a Fermi gas model (solid) for equal participation from projectile and target nucleus;(c) the moving source velocities compared with the fireball (dashed) and equal participation models (solid). ................................ V-S. Invariant cross ' momentum for fragments in the reaction are to guide ......... section plots versus total intermediate rapidity the IRF trigger at -30° from 92 MeV/A “°Ar+Au. The lines the eye. X 67 68 72 75 80 83 86 91 V-6. V—7. V-8. V-1N. V-15 Projectile-like fragment cross sections for the PLF trigger at —13° plotted versus the fragment velocity over the projectile velocity from the reaction 92 MeV/A “°Ar+Au. ............................... 93 .............. Invariant cross section plots versus total momentum for p,d,t, and “He in the LP trigger at -90° from the reaction 92 MeV/A “°Ar+Au. The lines are to guide the eye. ................................ 99 .......................... (a)Proton inclusive energy spectra and proton coincidence spectra for IRE trigger fragments (b)lithium, (c)beryllium, (d)boron, (e)carbon, and (f)nitrogen from the reaction 92 MeV/A “°Ar+Au. The trigger fragment angle was -30°. The solid and dotted lines are moving source fits and momentum conservation calculations, respectively, as described in the text. ............... 10” Same as FIGURE V—8 for deuterons. .......... 106 ..... Same as FIGURE V-8 for tritons. ............ 108 ......... Same as FIGURE V-8 for 'He. ................ 110 Same as FIGURE V-8 for “He. ................ 112 ............. [(a) and (c)] Coincidence spectra moving source fit temperatures and velocities- for the LP and IRF triggers and [(b) and (d)] the PLF trigger from the reaction 92 MeV “°Ar+Au. The parameters for protons (circles), deuterons (squares), tritons (double triangles), 'He (crosses). and I'l-Ie (pluses) are plotted as ratios of the coincident spectrum value over the inclusive spectrum value as a function of coincident particle mass. ............... 118 .............. Coincidence energy spectra from 92 MeV/A Ar+Au for (a) p.d,t and (b) ’He,“He triggered by a Li fragment in the IRE trigger. The solid (dot-dashed) lines correspond to an impact parameter averaged hydrodynamics calculation for an azimuthal angle of 0° (180°). ........... 121 ...... (a)Proton inclusive energy spectra and proton coincidence spectra for PLF trigger fragments (b)lithium, xi V-16. V’17. V-18. V*19. V-20. V—21. V-22. (c)beryllium, (d)boron, (e)carbon, (f)nitrogen. (8)0xygen, and (h)fluorine through phosphorus from the reaction 92 MeV/A “°Ar+Au. The trigger fragment angle was -13°. The solid and dotted lines are moving source fits and momentum conservation calculations, respectively, as described in the text. ............... ............... Same as FIGURE V—15 for deuterons. ......... Same as FIGURE V-15 for tritons. ........... Light particle coincidence spectra for (a)protons in coincidence with p, (b)protons in coincidence with d, and (c)deuterons, (d)tritons, (e)3Heliums, and (f)“Heliums in.coincidence with protons in the LP trigger from the reaction 92 MeV/A “°Ar+Au. The LP trigger was at -90°. The solid and dotted lines are mov1ng source fits and momentum conservation calculations, respectively, as described in the text. . Inclusive energy spectra for p,d, and t from the reactions (a) 30 MeV/A "C+Au and (b) 30 MeV/A "C+Al . The angles measured are A7° (”5° for the A1 target) (circles). 56° (squares). 71° '(triangles). and 90° (diamonds). The errors depicted are statistical. The solid lines correspond to moving source fits as described in the text. .......... Inclusive energy spectra for d and t from the reaction 30 MeV/A 12C+Au at angles of 15° (pluses). “5° (circles). 75° (squares). 90° (double triangles). and 105° (crosses). The spectra were measured in a separate experiment using a Si-NaI(T1) telescope. ................... Inclusive energy spectra for fragments in the IRF trigger at —25° with 35256 from the reactions (a) 30 MeV/A 12C+Al and (b) 30 MeV/A lzc+AuO ......OOOIIOOOOOOOOOOOOO ........... Inclusive cross sections for fragments in the PLF trigger at an angle of -13° with 35256 from the reactions (a) 30 MeV/A 12C+Al and (b) 30 MeV/A “C+Au (b) plotted versus the ratio of the fragment velocity over the projectile velocity. . xii 125 127 129 136 139 142 146 149 V-23. V-ZN. V-25. V-26. V—27. V-28. v-29. Unnormalized inclusive distributions for intermediate mass fragments with 35236 from the reaction 25 MeV/A 12C+Au at an angle of 15° plotted versus the ratio of the fragment velocity over the projectile velocity [Ja 8A]. ....................... Invariant cross section plots versus total momentum for p (circles), d (squares), t (triangles), ’He (diamonds). and “He (double triangles) in the LP trigger at —95° from the reaction 30 MeV/A HC+Al. The lines are to guide the eye. ......... Proton coincidence energy spectra for IRF trigger fragments (a)lithium, (b)beryllium, (c)boron, and (d)carbon from the reaction 30 MeV/A 12C+Al. The trigger fragment angle was -25°. ‘The solid and dot-dashed lines are moving source fits and momentum conservation calculations, respectively, as described in the text. ............................ Same as FIGURE V-25 for deuterons. ......... [(a) and (0)] Coincidence spectra moving source fit temperatures and velocities for the LP and IRF triggers and [(b) and (d)] for the PLF trigger from the reaction 30 MeV/A 12C+Al. The parameters for protons (circles), and deuterons (squares) are plotted as ratios of the coincident spectrum value over the inclusive spectrum value as a function of trigger particle mass. .................. Proton coincidence energy spectra for PLF trigger fragments (a)lithium, (b)beryllium, (c)boron, and (d)carbon from the reaction 30 MeV/A “C+Al. The trigger fragment angle was *13°. 'The solid and dot-dashed lines are moving source fits and momentum conservation calculations, respectively, as described in the text. ............................ Proton coincidence energy spectra for LP trigger particles (a)p. (b)d, (c)t, and (d)“He from the reaction 30 MeV/A 12C+Al. The trigger particle angle was -A5°. The solid and dot—dashed lines are moving source fits and momentum conservation calculations, respectively, as described xiii 151 15” 156 158 162 165 in the text. O.......OOOOOOOOOOOOOO0.0... 169 V-30. [(a) and (c)] Proton, deuteron coincidence ' energy spectra for the IRF trigger summed fragments Li, Be, B, and C at -25° from the reaction 30 MeV/A l2C+Au. [(b) and (d)] Proton, deuteron coincidence energy spectra for the PLF trigger summed fragments Li, Be, and B at -13° from the reaction 30 MeV/A 12C+Au. The solid and dot-dashed lines are moving source fits and momentum conservation calculations, respectively, as described in the text. . 173 A—1. Sample conservation of momentum model ‘ calculations for source sizes of (a) A-30 and (b) A=82. The trigger particle angle is -95 degrees. The spectra are shown for angles from +10° to +90° (solid lines) and —10° to -90° (dotted lines) in 20° steps. ;............................. 187 xiv CHAPTER I INTRODUCTION Much work has been done in the field of heavy ion nuclear physics, both experimental and theoretical. In the past decade, the interest has been concentrated in the projectile energy regimes below 20 MeV/nucleon and above 200 MeV/nucleon. As a result of studies in the lower energy regime, theories of compound nucleus production and mean field theories of the nucleus such as the Time Dependent Hartree-Fock theory (TDHF) have been developed. Theories such as hydrodynamics, cascade, and fireball/firestreak have been developed as a result of studies in the higher, relativistic energy regime. Theories developed for a( particular energy regime tend to give agreement with the experimental data in that energy regime. But because of the differences in their underlying assumptions,1unmaof them can be extrapolated into the other regime. It would seem that the projectile energy range from 20 to 200 MeV/nucleon should provide a transition region in which these disparate theories can be joined. Only recently, with the inauguration of the K500 superconducting cyclotron at NSCL and the availability of beams from the low energy beam line au.Lawrence Berkeley Laboratory (LBL), has this transition region been open to experimental exploration. Other new 2 facilities such as the GANIL national facility at Caen, France, the SARA accelerator in Grenoble, France, and the HHIRF at Oak Ridge are also beginning to produce results in this energy regime. The present study is a preliminary look at two energies in this region. Most of the experimental work that has been done at intermediate energies with heavy ions has involved the measurement of inclusive double differential cross sections from carbon, oxygen, and argon induced reactions on Au or other heavy targets [Ab 83, F1 8“, Ja 81, Ja 83, We 82, and We 8“]. Some work has also been done using more symmetric systems [Ab 83, Ja 81, and Jo 8A]. In general, it has been found that, the resulting double differential cross sections for light particles with 15252 and for intermediate mass fragments with 352510 give indications of the existence of a thermalized region in the combined projectile-target system moving at a velocity near the velocity of the center of mass. Other reaction mechanisms are known to exist as shown, for example, by the results of projectile fragmentation experiments [Bo 83, Cu 8A, Moéfl, Ra 8A, Va 79, and Vi'HXL Borrel, et al. observed fragments of the projectile with 352516 at laboratory angles less than 12 degrees from “°Ar induced reactions on Au and Ni at AA MeV/nucleon. The velocity distributions for these fragments were found to be gaussian in shape with centroids near the projectile velocity. The reaction mechanism is thought to be a fragmentation process whereby the projectile nucleus is 3 eaaccited by the target nucleus and subsequently breaks up :Llnto smaller fragments. Whether the breakup occurs almost :Lrnmediately after the collision or only after a partial ‘tlnermal equilibrium of the projectile is established, is a ‘t<3pic of current research. In order to better understand a tgiven reaction mechanism, it is necessary to constrain the <1ynamics of the reaction under investigation. To this end, a number of investigators have undertaken complex coincidence measurements, each concentrating on a particular aspect of the reaction. A typical coincidence measurement is the detection of light charged particles with 252 in coincidence with slow, heavy target-like fragments [Br 83, Me 80, Na 83]. Examination of the fragment yields as a function of the light particle multiplicity indicates that the lighter fragments are associated with high multiplicity, while the heavier fragments are associated with low multiplicity. The high multiplicity events have in turn been identified as indicators of central collisions. The most ambitious coincidence experiments are the work of the "Plastic Ball" group at LBL . The "Plastic Ball" An detector allows detection of light charged particles with nearly a full Aw acceptance. Analysis of events based on a calculated energy flow tensor as a function of light particle multiplicity by Gustafsson, et al. [Cu 8“] has given indications of what are termed non-trivial collective nuclear flow effects, namely, the bounceoff of the projectile fragments for peripheral collisions, and the u £3.1de-splash of fragments from the disintegration of the p>t~ojectile and target nuclei for central collisions. The r~<3actions studied were Ca+Ca and Nb+Nb at A00 MeV/nucleon. 1?11e present work seeks to observe the dependence of the 1.1ght particle spectra (252) on fragment production. C)bserved fragments are projectile-like fragments with 352518 at.forward angles and intermediate mass fragments with 35257 at angles away from the projectile direction. An estimate of the direct knock out contribution to the light particle Spectra, proposed for the higher energy regime,is also sought in coincidence measurements with other light particles (252). Four models are widely accepted today-cascade, hydrodynamics, fireball/firestreak, and coalescence. These models all have their origins in the relativistic regime and have been applied in the intermediate energy regime with varying degrees of success. The cascade model [Cu 81, Cu 82, Ki 8A, 10" 8A, Ya 79] assumes that high energy heavy ion collisions proceed via individual nucleon-nucleon collisions within the overlap zone of the two nuclei. The nucleons follow straight-line trajectories between collisions. As the collisions continue, particles whose energy exceeds the binding energy are considered to be emitted, until a minimum collisional density is achieved or until a predetermined collision time is reached. Effects due to the Pauli principle and pion production have more recently been included [Ki 8A, Kr 8A]. A cascade 5 calculation was unavailable for inclusion in this work. Most applications of the cascade model have been restricted to energies above 900 MeV/nucleon. Comparisons of the early cascade models with experimental data at these relativistic energies [Bc 8A, Gu 8A, St 68, St 82] show that the cascade model fails to reproduce the trends in the lufllldeV/A Nb+Nb data of Gustafsson, et al. [Gu 8A]. A more recent cascade calculation by Kitazoe et al. [Ki 8A], has had more success in describing the Nb+Nb data by including the effects due to Pauli blocking and pion production. It remains to be seen whether or not the cascade formulation can be successfully extended down into the intermediate energy region. The hydrodynamic or nuclear fluid dynamic model [Bu 81, 80 8A, St 68, St 79, St 80, St 81, St 82, St 83] requires the assumption of a short mean free path relative to the size of the interaction region. This is in contrast to the necessary assumption of a long mean free path used in the cascade model. For peripheral collisions involving only a few interacting nucleons, the mean free path is likely to be long. Since inclusive measurements contain contributions from all impact parameters, it is likely that inclusive measurements are not a good test of hydrodynamics. Although hydrodynamics predicts regions of extreme temperature and density during the reaction, at later times in the reaction the density becomes so small that the nucleons rarely collide. At this point hydrodynamics no longer applies because of the requirement of a short mean free path and an 6 evaporative model is employed in order to give cross sections directly comparable to experiment. Comparisons with the recently obtained results of Gustafsson et al. [80 8h, Gu 8A] show that hydrodynamics is capable of reproducing the trends in the high multiplicity selected Nb+Nb data at A00 MeV/A. A hydrodynamic calculation was available for this work and will be compared with the data for both inclusive and central impact parameter selected events. The nuclear fireball model has been compared with heavy ion reaction data at relativistic energies greater than 200 MeV/nucleon [Go 77, Go 78, We 76, My 78] and also with data from 2°Ne induced reactions on Au at 100 and 150 MeV/nucleon [We 82]. The fireball model assumes that a highly excited interaction region is created by the projectile sweeping out the portion of the target which is in the overlap region of the two nuclei. This region, called the fireball or participant zone, moves forward in the laboratory frame with a velocity near half the projectile velocity. The fireball is treated as an equilibrated nonrotating ideal gas of nucleons characterized by a temperature. The fireball then expands isotropically in its center of mass frame with a Maxwellian distribution in energy. The laboratory distributions are obtained by transforming the fireball frame momentum distributions relativistically. The model incorporates the specific geometry for the colliding nuclei, the binding energy of the nucleons in the fireball, and composite particle production. 7 (Of more importance for extreme relativistic collisions, the model also considers the creation of baryonic resonances in order to obtain a more accurate estimate of the temperature from the available energy in the center of mass of the fireball. The firestreak model is an extension of the fireball model, in which it is now assumed that chemical equilibrium is reached between the various hadronic species. This is described by a chemical potential. A critical "freeze out" density is introduced, below which the fragment momentum distributions no longer change. The other modification to the fireball is the use of a nuclear density distribution with a diffuse surface. The use of a diffuse surface leads to a temperature gradient across the participant zone according to the relative amounts of material coming from the target and the projectile. The firestreak has had its greatest success at energies above 1 GeV/nucleon [Go 78], although it seems to agree with the data at least as well as the fireball at energies down to 100 MeV/nucleon [We 82]. A firestreak calculation was available for the inclusive light particle spectra from 92 MeV/nucleon “°Ar+Au and will be presented in Chapter V. The models which have been discussed so far have all incorporated aspects of the dynamics of the collision process in heavy ion reactions to calculate proton cross sections as well as composite particle cross sections. The coalescence model [Aw 80, Cu 76, Le 79, Sa 81] uses a primary nucleon distribution, usually the experimental 8 iriclusive proton spectra, to determine the cross sections f<3r composite fragments in the reaction. The model assumes that if a subset of the primary distribution of nucleons corresponding to a bound nucleus is localized in a region of phase space with a radius less than a "coalescence radius", the subset will coalesce and form a nucleus. The cross section:h1nmmentum space for the emission of a composite with A nucleons is then related to the Ath power of the single nucleon cross section at the same momentum per nucleon. A single free parameter, the coalescence radius, is used in the calculation of the composite cross section. The coalescence radius has been determined for a number of systems over a large range of projectile energies by fitting measured composite cross sections with spectra calculated from the measured proton cross sections [Ab 83, Aw 80, Aw 81, Go 78, Le 79, Sa 81]. In general, this radius is constant in magnitude from 20 MeV/nucleon to over 2000 MeV/nucleon. A coalescence model fit has been done for the Ar+Au reaction of the present work and coalescence radii have been extracted for d, t, 3He, and “He. A more detailed discussion of the actual coalescence calculation performed will be presented in Chapter V. 0f the four models discussed, hydrodynamics and the fireball/firestreak models require the assumption of short mean free paths for the interacting nucleons. They also require the thermalization of at least a localized region of the interaction zone. The cascade model requires the 9 assumption of long mean free paths compared to the length of the nuclear interaction. The nucleons are assumed to undergo only two body interactions. The coalescence model makes no assumptions as to the dynamics of the collision, but instead, uses a primary nucleon distribution to predict the cross sections of the heavier composite particles. All of these models have been shown to work at incident energies above 200 MeV/nucleon. Only the coalescence model has been shown to work at energies much below 100 MeV/nucleon. Theoretical models developed for the energy regime below 20 MeV/nucleon have not been successfully extended up into the intermediate energy regime. Attempts to apply TDHF theory at energies of 30 and 85 MeV/nucleon [St 81, So 80] have shown that TDHF predicts too great a transparency for the colliding nuclei. Calculations directly comparable to experimental data could not be found in the literature for TDHF. Further discussions of these models, as well as a wealth of references to the literature, can be found in the excellent review articles of Scott and Boal [Sc 79, Sc 81, Bo 8“]. Results from two experiments will be presented in this thesis. In the first, the “°Ar+Au reaction was studied at 92 MeV/nucleon. Various inclusive or "singles" and coincidence measurements were made. Light particle, 2525 inclusive spectra were measured at angles from A5 to 90 degrees in the laboratory. Energy spectra were also measured for light particles (252) in coincidence with intermediate 10 mass fragments with 35257 at -30 degrees in the laboratory (180 degrees in azithmuth from the light particles) and with projectile velocity fragments with 352518 at ~13 degrees. Energy spectra were also measured for light particles in coincidence with other light particles at -90 degrees. In the second experiment carried out using the K-500 cyclotron at the National Superconducting Cyclotron Laboratory, a 30 MeV/nucleon 12C beam was used to bombard targets of Al and Au. Light particle inclusive spectra were measured at a number of angles from A5 to 90 degrees in the laboratory. Light particle coincidence spectra were measured for the intermediate mass fragment (35256), projectile velocity fragment (35256), and light particle triggers at -25, -13, and ~A5 degrees respectively. The thesis is organized as follows. Chapter II deals with the development of the plastic scintillator array and multi-wire counter that were used in the two experiments. The setup of the experiments is presented in Chapter III. Chapter IV outlines some of tuna specifics of the data analysis performed. In particular, the methods used to make the corrections to the light particle spectra for reaction losses and scattering out of the detectors will be given. The data, along with a discussion of the observable trends will be presented in Chapter V. Fits to the available models will be shown and discussed. A summary of the findings of this thesis will be given in Chapter VI along with some possible avenues of future research. The 11 Appendix contains a detailed description of the momentum conservation calculation which is used for most of the coincidence data. CHAPTER II DETECTOR DEVELOPMENT In order to accomplish the goals set forth in Chapter I, it was necessary to undertake the development of a detector array capable of detection of high multiplicity light particle events. The design of this detection system can be separated into two separate subsystems; an array of light particle telescopes capable of determining the energy and identity of light isotopes (p, d, t, ’He, and “He), and a multiwire proportional counter capable of providing more precise position information on these same light isotopes positioned in front of the telescope array. We will discuss the telescope array first. A. Telescope Array The design of the telescope array is in many respects similar to the design employed by the Plastic Ball group at Lawrence Berkeley Laboratory [Ma 80, Ba 82]. There are, however, several aspects of our design that warrant its discussion here. The array consists of seven NE102 [Nu 80] plastic scintillator - CaF2 "Phoswich" telescopes each of which uses a single photomultiplier tube to collect both the plastic scintillator and the CaF2 signals. The two signals 12 13 are distinguished by means of their extremely different decay times. The decay time for plastic scintillator is less than 10 nsec compared to 1 nsec for the Can. Integration of the photomultiplier output in a charge integrating ADC for the first 80 nsec gives most of the plastic scintillator signal. A separate integration in another charge integrating ADC over a period of 2 usec delayed by 2A0 nsec relative to the beginning of the first integration gives the CaF2 signal (Figure II-1). There is a certain amount of each signal which is either lost or contained within the wrong integration due to the overlap of the two signals. ,This is, however, a fairly small effect in most instances and can be corrected offline. Discussion of the corrections will be deferred to Chapter IV. In our design the plastic scintillator is 17 cm thick and functions as the stopping detector thus giving the E informatUNL The CaF2 is 2 mm thick and functions as the energy loss detector thus giving the AE information and enabling particle identification (Figure II-2) to be carried out. The telescopes were designed to close pack in a spherical geometry as six tapered hexagonal shaped detectors surrounding a seventh tapered hexagonal shaped detector. The design is in fact not correct for a An geometry 1J1 that a perfect design would be based on a truncated icosahedron, ie. a pentagonal detector surrounded by five hexagonal detectors. The discrepancies in the geometry at this scale were however outweighed by the advantages of having 1H MSUX-82-366 Photomdltiplier Tube NE 102 Plastic E Detector Co F2 AE detector Figure II-1. Seven telescope scintillator array used at LBL and NSCL 15 ‘*‘ RNODE SIGNRL PLRSTIC SCINTILLRTOR J-_______ .. E 900 GATE .L__J I I l I ' I c F I | O 2 I I 235 noc GATE I I I I I . I I I I I I l l I I l I I : I. I I I t=0 80 2‘10 nsec 2.29 usec Figure II-2. Timing diagram for scintillator array telescopes. The anode signal is a sum of the fast plastic scintillator component and the slow CaF2 component. 16 identical solid angles for the seven telescopes and a single geometry to machine. Due to the low melting point of the plastic scintillator and its tendency to craze near regions exposed to high temperatures, care had to be taken in its machining and polishing. The finish cuts on the plastic were done with a fly cutter running at a 1000 RPM, removing a 10 mils of material per cut. The cutter was cooled using a continuous flow of a water soluble oil. The plastic scintillator was then sanded with #600 grade silicon carbide waterproof polishing paper immersed in water and finally polished with optical polishing alumina (particle size below 9 pm) slightly moistened with water on a cotton cloth. This procedure produced a highly polished surface on the plastic with no noticeable machining marks and no evidence of crazing. A clear lucite lightpipe was also machined to match the plastic scintillator to the photomultiplier tube. In order to achieve optimum light collection efficiency and resolution, the plastic scintillator was painted with a T102 water based reflective paint [Bi 67]. In addition, the light guide was also painted with T102 paint but in a striped pattern loosely based on a Monte Carlo simulation of light collection efficiency and resolution by SchOlermann and Klein [Kl 79, Se 80]. This was predicted to give better energy resolution by more uniformly distributing the emitted light over the surface of the photomultiplier photocathode. 17 The photomultiplier tube used for the telescope array was an EMI model 9872, 3.81 cm diameter, 10 stage compact focused tube with beryllium copper secondary emitting dynode surfaces [Em 79]. The tube was chosen based on its compact size, a fast response time of 2.2 nsec risetime comparable to the 2.u nsec decay time of the plastic scintillator, and its relatively low cost. The base containing the divider chains for the photomultiplier tube was an EMI active base design (Figure II-3) which incorporated high voltage transistors in the last four stages of the divider chain to maintain a constant voltage drOp during periods of high count rate. The design also current limited above a certain maximum current to prevent destruction of the photomultiplier tube should the tube be exposed to excessive light accidentally [Hi 77, Ke 77]. The light particle teleSCOpe was completed by the addition of the CaF2 element which was machined from a 5.1 cm diameter by 2 mm thick disk of CaF,(Eu) using a 1/16 inch wide diamond wheel on a vertical grinder with a constant spray of water soluble coolant directed onto the material. The mounting procedure for the CaF2 was similar to a procedure used in mounting Si wafers to be cut for solid state detectors using a wax substrate between the material and an aluminum mount. This procedure worked well and produced only one partially fractured crystal out of eight which were cut. It should be noted, however, that for crystals 12.5 cm in diameter, this procedure does not 18 .fiow 3mg mmqoomoaou xmccm Loumaaflpcflom nu“: com: cmwmmc ommn HZm m>Huom Lou ofipmamnom .mIHH mgsmfim . _ - . ( ( ( ( 1‘""""" """‘.‘D‘ I‘""’ ."‘ "" ’ ’ D‘ I b"""‘b‘ P 9‘. D "" . v.8. goo. x8. x8. x I q A car H cam. _ _ . I I I I I N N N I . I _ _ M. h h h M 4M - 2 m. Re: ma: 5A ......b u f xRfi _ a III..o ....II... -II 1w IIIIo -I Ilo IIIIm Ila Sm II: zco- >2. H NW|I|$$>11 Ea. .... x8. >RF >x. >E >5 _. a. _. m8. I v.3.._.Tli.l [011. sq. as as. a...“ a... as was é. o “v zo—Av >§K5 .. 1w Q. I n mm.— o. 0. 9w mm m _ W EM mooza 8 E as 3 as E as O a... S R. 19 produce satisfactory results as the material tends to fracture severely. The entire assembly of CaF,, plastic scintillator, light guide, and photomultiplier tube was joined with a thin layer of optical epoxy at each interface and wrapped in a layer of aluminum foil to prevent light leakage into the detector. The entrance window to the detector was a 13 pm aluminum foil. B. Plastic Scintillator Energy Calibration at IUCF Before the CaF, elements were ready, six of the seven plastic elements were taken to IUCF to be calibrated for proton energy response from Ep-15 Mev to 120 Mev [Ha 82]. Protons of various energies were selected by the angular positioning of the detectors in the chamber and the use of the elastic scattering of 1A8.9 Mev protons from a 20 mg/cm2 CH, target. A simple coincidence between the scattered proton and its recoil 1H target provided a clean spectrum in the detectors (data in two detectors at a time). Because of the large dE/de a slit was fixed to the front of each detector. The slit was 0.25 cm x 1.27 cm slot in the center of a 0.890 cm thick copper disk. This gave an angular opening of o.u1°. The COpper disk was sufficiently thick to stop up to ~80 Mev protons. The coincidence spectrum, shown in Figure II-A, consisted of a peak for protons which passed through the slit and also a lower energy peak for protons which were degraded by penetration of the COpper disk. 'The 20 P" 8 . 37.5. lH1p,p] I. noose > _ £ 8 S > 300-— §§ :5 m g] 5 '— - a 2 ' é a c.) | :3 d 35‘ as 200:— Ice _ J 1 L L MIMI. - ' III .-.-... 100 200 300 uog CHANNEL NUMBER FigmweII-h. Coincidence p—p spectrum from CH, target during IUCF plastic scintillator calibration. 21 proton beam energy of Ep=1u8.9 Mev was too low to allow both the incident and the recoil proton to penetrate the copper disks in front of the detectors. The energy of a proton penetrating the COpper disk was determined ffiwnn its energy loss in the disk using an initial energy given by kinematics and the angular position of the slit through which its coincident proton passed. Singles data was also taken using the CH, target (Figure II-5). Peaks were found for the 12C elastic and first (u.uu MeV) and third (9.69 MeV) excited states [Aj 75] for protons which were degraded by penetration of the copper disk. Protons passing through the slit did not appear in the spectrum because the amplifier gains were set too high. Elastic peaks for protons scattered from a Au target and from deuterium in the CH, target were also seen. Again, only the peaks for the scattered protons which were degraded in the copper disk appeared in the spectrum. The detector angles were checked by comparing the position of a dip in the degraded singles p-p elastic scattering peak at angles of i 30 degrees (Figure II-5). The dip was caused by the removal from the degraded peak of the elastically scattered protons which passed undegraded through the slit opening. The large magnitude of dE/de for p-p scattering gave a large spread of energies across the 7 degree width of the detector. -This spread in energies, which can be seen in the large width of the dominant peak in Figure II-5, combined with the relatively small spread 22 >2 5 855m: . a... 8 325895535 IUIIIIR 8 = -29.5° I- 1HIp,pI ...... 12CIM'I >2. 9: 925%-? 3.3: 3.. x: .8935? as? 2.: .3 38589253..." --lIIIIIIII 5353253.... L 300‘ 200" fl$238 100P 200 300 400 CHANNEL NUMBER 100 Singles proton spectrum from CH, target during IUCF plastic scintillator calibration. Figure II-5. 23 across the slit Opening gave a well defined minimum in the spectra. From this it was found that there was a misalignment of the zero angle of 1.28 degrees. The misalignment was verified by the observation that Opposite curvatures of the calibrations for detectors on the two mounting arms in the chamber were eliminated when the correction of 1.28 degrees was applied. Four of the six detectors calibrated at IUCF were found to have essentially the same calibration, the slopes being very nearly linear and the intercepts being close to zero. A representative calibration curve is shown in Figure II-6. A fifth detector experienced a gain shift throughout the calibration, which was later found to be due to the separation of the phototube from the lightguide. The sixth detector had a somewhat different slope but about the same intercept as the other detectors indicating a different gain characteristic of the base. The resolution of the plastic scintillator detector was also determined during the IUCF calibration run. The intrinsic resolution of the detector was unfolded from the fwhm of the coincident calibration peaks and the effect of dE/de on the proton energy across the slit opening. The effects of energy straggling for coincident protons which penetrated the Cu slit material and the 13 um Al foil entrance window, the finite beam spot size, and straggling in the CH, target were not taken into account. These are relatively small contributions to the overall resolution and 400. CHANNEL. NUMBER (10 Figure II—6. 2“ MSUX-BZ-SGT 300. 200. 100. I T I T — a — 1 — a h- '1 _ q p q _ a h a J L I l 25 SO 75 IOO PROTON ENERGY Proton energy calibration of a plastic scintillator detector from IUCF calibration. The line is a least squares fit. 25 would only serve to slightly decrease the calculated intrinsic resolution. The calculated intrinsic resolution for five Of the plastic scintillator detectors is shown in Figure II-7 along with a plot Of the root inverse range in the plastic as a function of the particle energy. The curve has been arbitrarily normalized to 2 percent at 100 MeV. The resolution is seen to vary smoothly from greater than 10 percent below 20 MeV to approximately 2 percent above 100 MeV. From the statistics of photon counting and the range energy relationship, the intrinsic detector resolution should be proportional to (Range)-'25 . This can be considered as a lower limit to the resolution. The departure from the lower limit at low energies is seen as an indication of less efficient light collection for particles which stop farthest from the photomultiplier tube. The proton beam energy at IUCF was determined from the beam Optics and an NMR reading and is estimated to be correct to better than 1%. C. CaF, Thickness The choice of thickness for the CaF, element of the light particle telescope was based on a calculation of the energy loss in the two elements Of the telescope. Figure II-8 shows the calculation for a CaF, thickness Of 2 mm. Assuming that the resolution obtainable with the combined elements of the telescope would not be much different from that Obtained in the IUCF calibration run for the plastic 26 .>62 00! um pcmocma N O» ummfiamenoc mmcmn :OOOLQ on» «0 Soon mgmscm on» no omcm>cfi on» ma O>L:O cfiaom one .cofiumcnfiamo mozH EOLO m:O»OLO Lou ucoocma :H :Oflusaommg Loumaafiucfiom Owummém 13V onbnqommm zebombmo Gm; @QH am sm ®: am .NIHH mLzmfim . 1 q q 1 I TO. -I CU CD 00 “D :r CU III-I0 v—O (A914) AOEIEINEI NOIOEId 27 30._— . . _ ~25... ° ° I E . ' 2%, o 20... ° . ' . .. N . ' '11-'10 LI. 0-154— 0 . ."‘ 9 o . 3H. In ‘<:113. -. T .7. ‘ S; F. o .. "0,..":0 .. . - ..0000. ..."d..t O 190 200 EIPLASTIC SCINTILLATOR (MeV) Figure II-8. Calculated AE-E isotope separation for p, d, t, 3He, and “He for a CaF, AE thickness of 2 mm. 28 scintillator, it was apparent that a 2 mm thickness would give both sufficient energy loss and isotOpe separation for the range of particles and energies anticipated. Another important consideration was the low energy cutoff imposed by the relatively thick CaF, front element. Calculated cutoffs are given in Table II-1 for the hydrogen and helium isotopes for CaF, thickness of 2, 3, and A mm. The cutoffs imposed by the 2 mm thickness were considered to be sufficiently low for the beam energies at MSU and quite sufficient for LBL Low Energy Beam Line energies. D. Multiwire Proportional Chamber Small angle light particle correlations have been shown to yield information about the size Of the emitting system in nucleus-nucleus collisions [Ly 83, Cu 89]. In order to extract this information one needs to be able to determine the relative momenta Of two coincident light particles to better than - 2 MeV/c. For two protons Of 50 MeV this translates into an angle resolution of the order of 1 degree. One way to achieve this level Of spatial resolution is through the use Of a Multiwire Proportional Chamber or MWPC [Ch 70]. The principal behind the Operation of an MWPC is that the electrons liberated by ions traversing the chamber drift (typically 20-N0 nsec/mm) to the positively charged anode wire. Close to the wire (within a few diameters), the electric field is very strong. Here the electrons experience inelastic ionizing collisions, 29 giving rise to a multiplicative avalanche. The positive ions produced in the avalanche drift toward the cathodes. An important point is that the pulses detected on the anode are mainly produced by the motion Of positive ions. Negative signals are induced on the central anode wire while positive signals appear on the adjacent anode wires. In this design [Ti 81, Ti 82], the MWPC contains 3 anode planes, two of which provide horizontal and vertical position information, while the third plane is positioned at “5° with respect to the first two planes and is used to resolve the position ambiguity which arises when several ions traverse the chamber simultaneously. The sensitive area of the detector is 15.5 cm x 15.5 cm, the anode-cathode spacing is 6 mm, and the anode wire spacing is 2.5“ mm. Each anode plane consists of 6“ sense wires (gold plated tungsten with a diameter Of 20 pm) which are paired electrically into 32 channels giving an angular resolution cn'0.8° when the detector is 35 cm from the target. This resolution satisfies the requirement imposed by the small angle correlation measurement. To reduce the material thickness of the detector, some of the cathodes are common to two anodes. The design consists of three contiguous cells having a total of four cathode planes made Of sheets Of 6.“ pm aluminized mylar (both sides aluminized) and the three anodes giving a material thickness of 10 mg/cmz. The resulting signals from each pair of anode wires are processed using an electronic Proportional Chamber 30 TABLE II-1 CALCIUM FLUORIDE PUNCH THROUGH ENERGIES (MeV/n) THICKNESS 2 mm 3 mm “ mm Proton 21.5 27.0 31.5 Deuteron 1“.5 18.2 21.“ Triton 11.5 1“.5 17.1 3Helium 25.2 31.5 37.0 I'Helium 21.5 27.0 31.5 31 Operating System (PCOS III) developed by LeCroy [Le 81]. LeCroy 2735 16 channel integrated circuit boards placed directly on the anode wire plane board first amplify the anode signals from each plane using four quad amplifier chips, one for each set of four wires. Each set of four amplifier outputs is then passed through a quad discriminator chip and then bussed out Of the detector to a slave CAMAC crate containing LeCroy 2731 Delay and Latch modules each capable of processing up tO 32 channels or one entire MWPC plane. The information in the latches is controlled via the backplane of the CAMAC crate by a LeCroy 2738 MWPC Digital Readout Controller. The controller is strobed with a valid event gate and read via a single 50 conductor ribbon cable by a LeCroy “299 Databus Interface. The interface resides in a CAMAC crate which is under the control Of the data acquisition routine. Only "hit" information is available from this system. Linear (prOportional) signals are not provided. This is not a limitation, however, since there is insufficient energy loss in the detector to obtain a good energy signal for light particles. The energy information is obtained from the telescope array which is behind the MWPC. Operating conditions for the MWPC were determined to be a gas mixture of Argon-Ethane (50%) at 500 Torr and a cathode high voltage of -3000 volts. Early bench tests Of the MWPC system using a 1”Ru 8- source with an endpoint energy Of 3.5“ MeV revealed that the detector was extremely 32 sensitive to RF noise. The detector vacuum box was therefore designed to provide adequate RF shielding as well as good ground plane connections between the enclosed amplifier-discriminator cards and the vacuum box. In addition, the entrance and exit windows of the detector were required to withstand an internal/external pressure differential of 500 Torr when the detector was placed in the vacuum chamber. This necessitated the development of a wire mesh (0.6 mm dia. piano wire) which held a 75 um Kapton window in place. The spacing of the crossed wire wire mesh was approximately 1.5 cm and was pressure tested up to a pressure differential of 760 Torr without failure. Tests Of the completed MWPC with the B- source show that single wire resolution is achievable and that the efficiency Of the detector is reasonable, although highly dependent on the threshold settings Of the amplifier- discriminator cards. Figure II-9 shows a representative test Of the MWPC using the 1”Ru 3- source with a small (approximately one wire pair wide) start scintillator behind the detector. The chamber was Operated at an atmosphere Of Ar-Ethane (50%) with Vcath-2.7 kv. Note that the source was placed in five different locations along the center Of both the X and Y planes. The source was left in each position fxw'varying amounts Of time. Figures II-9;a,b,c show the projecions of each wire plane for the different source positions. Figure II-9;d is a two dimensional plot of coincidences between the X and Y planes Of the detector with 33 (b) 3.. I- (a) 3.2 3.6 1.. . a (d) X-Y Figure II-9. MWPC position resolution obtained with a 8- source placed at 5 locations along the center of both the X and Y planes. 3“ the additional requirement that only one wire fired in each of the two'planes. Overall, the position resolution of the detector is quite good, especially considering the amount of angle scattering for an electron in an atmosphere of Ar- Ethane. The MWPC was used in two experiments, one at Lawrence Berkeley Laboratories, and the other at NSCL. Tuning the former experiment, the MWPC functioned properly during the setup runs and for the first few minutes of the first data run, however, a sudden increase in the beam intensity caused the MWPC to are internally. Attempts to restore the cathode voltage caused further arcing before a useful working voltage could be reached. Later examination of the anode and cathode planes revealed no Obvious cause for the arcing. It has been assumed that the large instantaneous secondary electron flux at the time of the beam current surge created a high electric field point somewhere in the detector (perhaps a whisker on an anode wire), which limited the current. NO useful data were obtained with the MWPC at LBL because of this problem. During the NSCL experiment, the MWPC appeared to be functioning properly during the on-line analysis, however, subsequent scanning of the data showed that the MWPC was being gated properly for singles events only. The coincidence events, for which the detector was designed, had MWPC wires in the events a substantial amount of the time, however, the wires seldom corresponded to the array plastics which had fired in the event. 35 The MWPC has since been used in another experiment at NSCL. This time the detector functioned as originally expected. It is expected that some interesting results will be forthcoming from the use of the MWPC in this latest experiment. CHAPTER III EXPERIMENTAL SETUP The experimental setups for the data to be presented can be divided into two distinct parts. Data was taken over two weekends at the Low Energy Beam Line (LEBL) at the Lawrence Berkeley Laboratory Bevalac using the same beam and target combination, 100 MeV/n “°Ar+Au, and with similar detector combinations and experimental goals each weekend. Another experiment, which was performed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University, used a single beam with two different targets, 30 MeV/n 12C+Au,Al, and a single setup. We will discuss the experiment at LBL first. A. LBL Experimental Setup The experimental setup for the 60 inch Maryland chamber is shown in Figure III-1. The positions and solid angles for the detectors are given in Table III-1. All Of the detectors to be described here were not in the chamber for both weekends. Differences will be pointed out in the discussion for each detector. The plastic scintillator telescope array (See Chapter II) was positioned in the chamber with the center three telescopes at the beam height (Figure II-2). This array was the only detector which was 36 37 CHAMBER SCINTILLATOR ARRAY [45°‘90°) MWPC \ I LAYOUT MSU-83-483 PLF {-13°} IRF (80°) LP (-45°) LP [-QO°) Chamber experiments. Figure III—1. setup during the LBL and NSCL 38 TABLE III-1 DETECTOR ANGLES FOR THE BEVALAC SETUP DETECTOR THETA (DEG) PHI (DEG) SOLID ANGLE (use) PLF(a) -13.0 0.0 2“.7 IRF(b) -30.0 +10.0 16.0 IRF(C) -30.0 -10.0 1u.0 LP(d) -u5.0 0.0 u.5 LP(e) -90.0 0.0 10.9 (f) “5.67.5.90 0.0 12.0 ARRAY (a) Projectile-like fragment telescope first weekend. (b) Intermediate Rapidity fragment telesc0pe second )High energy stack. (0) Intermediate Rapidity fragment telescope second Low energy stack. weekend. weekend. ) Light Particle telescope first weekend. e) Light Particle telescope second weekend. ) Angles are for the central element Scintillator Array. Of the array. 39 moved during the experiment and three runs were taken with the center telescope at “5.0, 67.5, and 90.0 degrees, respectively. This allowed essentially a full coverage of the in-plane angles from 38 to 97 degrees for light particles. The plastic scintillator telescopes functioned properly throughout the experiment, although, due to an unforeseen timing problem with the scaledown modules for the singles events during the first weekend, the ADC gates for the plastic scintillator singles data were Off by about 50 nsec. This was enough to prevent useful recovery Of the first weekend singles data. The scaledown modules were not used during the second weekend. The energy calibrations will be discussed in Chapter IV. In order to improve the coincidence counting rate the singles gate was removed from the electronics logic at the Master "OR" for most Of the runs. These runs will be referred to as "coincidence" runs as Opposed to the runs in which the singles gate was not removed which will be referred to as "singles" runs. A high energy fragment detector was placed at ~13 degrees as a Projectile-Like Fragment (PLF) trigger for the plastic array during the first weekend. This detector consisted of a five element silicon stack (800 pm, 5 mm, 5 mm, 5 mm, and 5 mm) which measured spectra for near beam rapidity fragments from L1 through Ar. During the second weekend a fragment detector was placed at -30 degrees as an Intermediate Rapidity Fragment trigger for the plastic array.‘ This trigger consisted Of “0 two separate silicon stacks placed at the same in-plane angle but at out Of plane angles of :10 degrees. The low energy stack (100 pm, 300 um, and 5 mm) measured spectra for particles 35258, while the high energy stack (800 um, 800 um, 5 mm, 5 mm, and 5 mm) measured spectra for particles from L1 through Mg. During the first weekend, a Light Particle telescOpe (LP) was placed at -“5 degrees as a light particle trigger for the plastic array. The LP detector was placed at -90 degrees during the second weekend. This detector was a silicon (1 mm) - NaI(Tl) (10 cm) telescopes and measured spectra for light particles (p, d, t, ’He, and l‘He). Unfortunately, the p, d, and t spectra for the -“5 degree setting were restricted to low energies due to a high threshold setting for the LP Si constant fraction discriminator. Data acquisition at the Low Energy Beam Line was controlled by a PDP 11/3“ computer through an M80 CAMAC interface. Experiment control and on-line data sampling and histogramming were done using the programs QDA and MULTI running on the PDP. Figure III-2 shows the electronics diagram for the LBL and NSCL experiments. Note that the scaledowns were removed from the electronics for the second weekend. In order to improve the coincidence counting rate the singles gate was removed from the electronics logic at the Master "OR" for most of the runs. These runs will be referred to as "coincidence" runs as Opposed to the runs in “1 m¢084¢mzuu wuko Un< .mucme~coaxm Jumz cam am; on» son ofiumamcom moficogpomam .NIHHH answfim 3me- UQ< OF m 3m¢- uo< 09 m4 mmq_s “MW“:VOMW esmazza IJMHL m.ame mmem<¢m< mmoummqme mozmoaoz_oo . 2:5 mmzeo moeaa “mu“ :5: m.sme 2320 and a u 5525. mmmmuOmm 1 mmxeo emazo gas. as .mmH .maa em200 L- + J 2 Ma ._4*_. >_].So )— d g + LU -1Ir- le. _ - LIJ 4- 50 I- ++ .1 1' 0 50 100 150 200 250 CHQNNELS Figure IV-3. IJncorrected energy calibration for protons (circles) and alphas (triangles) in the CaF, AE element of a scintillator array telescope. 5“ MSU-83-485 (SEI3CHJFEZ V'V'V—v'r' mac-obit. mD-- 00000000000 ...... o ooooooooo .00‘... .0 ooooooooooooo ’ODO. .000 a... ..... o 0000. .00. ............... o oooo o ........ 0.00.00... 0 o ooooooo o oooooooo 000000 0000000000000 00 O a... 00000 o ooooooo o ooooooooooo o o o OOOOOO . “...-b; ooooooooo 0 o O... b oooooooooooooooooo ... 'Iooho ...... va 'fik ’ H... :t'lbbb. fi oooooooooo o o IIIIIblIb: Obtb ooooooooo o OOOOOOOOOOOOOOOOOO . Figure IV E PLASTIC SCINTILLATOR Plot of AE vs. E for a scintillator array telescope. Note prominent band at the botton is caused by neutrons and gammas stopping in the plastic. I—s I—s m m ® 01 G U! ENERGY (MeV) 01 Figure IVvS. 55 —+ . J . PROTONS A ALPHAS ' SO [190131501 260‘ 260 CHANNELS Corrected energy calibration for protons (circles) and alphas (triangles) in the CaF, AE element Of a scintillator array telescope. The line is to guide the eye. Separate calibrations were used for protons and alphas. 56 timing problem with the scaledowns, the calibrations for the first weekend were further restricted to fits to coincidence spectra. The CaF, AE spectra and the plastic scintillator E spectra were matched to spectra from the second weekend using a least squares fitting routine which determined the prOper calibration for each telescope. The correcton to the AE response for charge from the E signal in the AE gate, which was made for the beam calibration, was also made for the fitted calibration. Values of the reduced chi-squared for the fits were typically less than 5 and a comparison of the final normalized coincidence spectra indicated that a satisfactory calibration was obtained. The Si AE element of the Si-NaI telescope at the -90 degree setting was calibrated with a calibrated pulser. A calibration using the direct proton and alpha beams gave similar results. The NaI E element was calibrated using the direct proton and alpha beams, as shown in Figure IV-6. The Si-NaI telescope at the -“5 degree setting was calibrated using only the direct alpha particle beam for the NaI E element and a pulser calibration for the Si AE element. The various fragment detectors, which all consisted of stacks of silicon detectors, were calibrated with the calibrated pulser. B. Energy Calibrations of Detectors used in NSCL Experiment The calibration of the scintillator array telescopes at NSCL presented a special challenge in that at the time of 600 . ENERGY (MeV) 00 4: L” Q Q Q 69 59 69 n) 69 CD 100. Figure IV-6. 57 L ‘4 A' o PROTONS " 1| RLPHRS - I I— -I L 5 0 160 1 250 ‘ 360 ' L160 ' 500 CHQNNELS Energy calibration for protons and alphas in the NaI E element Of a Silicon—Nal telescope. The line is to guide the eye. Separate calibrations were used for protons and alphas. 58 the experiment, the best beam available for energy calibrations was a 25 MeV/n alpha particle beam. An attempt was made to calibrate using 25 MeV/n alphas elastically scattered from a Au target. However, since the minimum energy for an alpha particle which penetrates the CaF, is 22 MeV/n, and since the proton and alpha particle calibrations are not the same, as shown in Figure IV-1, this calibration proved to be inadequate. Approximately one year after the original data was taken a 53 MeV/n alpha beam became available, at which time inclusive p, d, t, ’He, and “He spectra were measured for the original reactions Of 30 MeV/n 12C+Au,Al using a Si-NaI telescope. Calibration points were obtained for 53 MeV/n alpha particles elastically scattered from a Au target and for 70 and 100 MeV recoil protons from alpha elastic scattering on a mylar target. The recoil protons were measured in coincidence with the elastically' scattered alphas, giving well separated proton calibration peaks. These calibrated spectra were then used to calibrate the original spectra using a fitting technique similar to that used to calibrate the first weekend Spectra from LBL. The AE calibration was retained from the 25 MeV/n alpha calibration and was used for both protons and alphas. NO correction was made in the AE channel number for the contribution from the E signal since the measured particle energies did not extend to high enougm.energies to Show a significant contribution. 59 The Si-NaI telescope was calibrated using a calibrated pulser for the silicon AE element and the 25 MeV/n alpha calibration for the NaI E element. The NaI inclusive data were compared to the “5 degree data taken in the more recent calibration run with 53 MeV/n alphas and found to be in good agreement. The fragment detector telescopes were again calibrated with a calibrated pulser. C. Normalizations The method for monitoring the beam currents in the two experiments has been discussed in Chapter III. All runs with the same detector settings were summed for the coincidence events. The singles events were summed only for singles runs, ie. the runs in which the singles event trigger was present in the electronics logic. Pseudo singles events were present in the coincidence runs due tO coincident neutrons and gamma rays and other unidentifiable coincident particles, but, these events were biased by the coincidence trigger requirements and therefore, did not constitute true singles events. The NSCL spectra originally had only a relative normalization because Of a problem with the current integrator which was discussed in Chapter III. It was possible, however, to provide an absolute normalization for the spectra by normalizing to the spectra measured in the recalibration run. It is believed that the normalization 60 for the NSCL spectra is known tO approximately 20 percent based on errors incurred in the cross normalization of the coincidence spectra discussed in Chapter III and the absolute normalization method, which is believed to be known to 10 percent. The LBL normalizations are believed to be good to 10 percent. 0. Target Thickness Correction Because of the 213 mg/cmz Au target thickness at LBL, the fragment spectra (PLF and IRF) were corrected for energy losses in the target. The corrections were based on the energy lost by a given particle at a given energy in the full thickness of the target, including the added thickness encountered by the particle due to the target angle relative to the detector. Corrections were typically less than 20 MeV. The bin sizes for the inclusive fragment histograms were 100 Mev for the PLF and 30 MeV for the IRF and a factor Of two larger for the coincidence histograms. This was therefore, a relatively small correction to the spectra. This correction was not applied to the NSCL spectra due to the small thickness of the 2.0 mg/cm2 Au and 3.0 mg/cm2 Al targets. E. Reaction Loss Correction The scintillator array and Si-NaI telescope spectra were corrected for reaction losses of the light particles stopping in the detectors. Charged particles traversing a 61 scintillation counter or solid state counter may undergo nuclear interactions as well as interactions with the atomic electrons. The latter type of interaction gives rise to the full energy peak in the detector. The nuclear interactions, on the other hand, tend to broaden the full energy peak on the low energy side. Inelastic collisions in the detector typically have neutrons, gammas, deuterons, and alphas as the reaction products. Due to the nonlinearity Of the response of scintillation materials to more highly ionizing particles, the light output in the detector is less for these reaction products than it would have been for the original projectile. This results in the loss Of the particle from the full energy peak. In the case of neutrons and gammas, light output is less because Of the reduced probability of any further interaction in the detector by the reaction products. Other effects can also lead to losses in the detector. We will discuss one of them, scattering out Of the detector, later on in the chapter. A number Of authors have presented data and calculations for reaction losses in detector materials such as silicon [Ja 66, Ma 68 and Me 69] and NaI(Tl) and plastic scintillator [Ja 66 and Me 69]. We have patterned our calculation after that of Measday and Richard-Serre [Me 69]. The calculation requires the integration of the total inelastic reaction cross section of the incident particle as it stops in the detector. The range Of the particle is divided up into cells of about 0.1 mgfcm2 in length. At 62 each cell the particle has a different energy and since the reaction cross section is energy dependent, the reaction cross section must be determined for the average energy of each cell. The average energy in each cell was calculated from a range-energy table generated by the code DONNA. The reaction cross section was then calculated using a parameterization obtained by fitting a modified form of the standard reaction cross section aRsnAZI1-vc/E)x(1+(K/E)‘) (IV-1) to measured cross sections tabulated by Measday and Richard- Serre [Me 69]. The parameters in Equation IV-1 are the nuclear interaction radius R given by /3 1/3 R-r°(A,1 +A, -1) (fm), (IV-2) where r,-1.2 fm, the coulomb potential at the interaction radius, Vc’ given by vc-z,z,e=/R (MeV), (Iv-3) and K and A which were adjustable parameters. An adjustable overall normalization factor was also included in the fit. The calculation Of the reaction cross section was repeated for each cell with the total fraction of interactions being given by f-1-exp(-£nioi), (IV-“) i 63 where n1 is the number of atoms/cm2 in the 1th cell and a1 is the calculated cross section in each cell. The data and the parameterized fit for protons in carbon are shown in Figure IV-7. Although plastic scintillator also contains hydrogen, its contribution to the reaction loss is negligible since the scattered proton is likely to remain in the detector volume. The quality of the fit in Figure IV-7 was limited by the use Of the standard reaction cross section formula as the basis for the fit“ 'This parameterization was necessary in order to extend the cross sections to particles other than protons. Another limitation on the quality Of the fit was the attempt to determine a single consistent set Of parameters for all relevant materials. The values found for x and A were K=20 MeV and A=1.2, with the normalization constants being 1.1 for silicon, 2.0 for NaI, 2.7 for CaF,, and 1.“5 for plastic scintillator. The resulting corrections for protons in NaI and plastic scintillator are shown in Figures IV-8 and 9 respectively, plotted as the ratio "tail-to-peak", i.e. f/(1-f), along with the data tabulated in [Me 69]. The agreement is good for both detector materials. The tail-to- peak ratios for p, d, t, 3He, and “He in a silicon-NaI telescope and a scintillator array telescope are shown in Figures IV-10 and 11 respectively. The fit to the reaction cross section and the calculation of the correction factors 6“ U1 Q Q .4: Q G (A) Q Q R) (a .3 I l I 0 510 160 ISO PROTON ENERGY (MeV) TOTFIL REQCTION CROSS SECTION (mb) Figure IV‘7. Parameterized fit to measured total reaction cross section for protons on carbon. Data is from Measday [Me 69]. 65 20.- 15.- TRIL-TO-PEQK RRTIO (%) ISO 200 160 PROTON ENERGY (MeV) 0 S0 Figureinh8. Calculated tail-to-peak ratio for reaction losses of protons in NaI with data compiled by Measday [Me 69]- 66 20.~ . $3 0 EISOI- -I 05 NC 0: LLJ 0'- c310.. . ’— _'1 CE '— S or- ..I 0 50 100 J ISO 1 200 PROTON ENERGY (MeV) Figure IV-9. Same as Figure IV--8 for NE102 plastic scintillator. 67 HO.— - x c: H E“ F- c30‘ L. g § 1 CK «v 6% E a GI ¢ a. 3' ,§ <520" $3 4 H. .§ Q I «0 .4 .5 4§ a: }—. IO.— - 0 SC 106 150 ENERGY (MeV/Q) Figure IV-IO. Calculated tail-tO—peak ratios for reaction losses Of p, d, t, ’He and “He in the Silicon— NaI telescope. 68 I46. I— "‘ .\° Q -~ 1— .1 t 5 G30. I- Q s 05 g z- r» E K as é a: 3 <3 “’ S 0- ‘41 '29 . —’ Q a O 1.. 1 $63 ..J ... as CE 1-— 10.L I l L l 4 l 1 l 0 SO 10% 158 288 ENERGY (MeV/Q) Figure IV-11. Same as Figure IV—IO for the scintillator " array telescopes. 69 was also performed for the silicon AE element. NO data or independent calculations were available for CaF,, so parameters similar to NaI were used instead. The silicon and CaF, corrections had little effect on the overall correction because Of their limited thickness. The actual correction to the spectra was made by dividing each bin by the appropriate value Of 1-f F. Scattering Out Correction In order to achieve the high packing density Of the scintillator array, the individual telescopes were not collimated. Particles incident near the edge Of a detector were likely to scatter out and not be identified as valid events. This is the other important mode of particle loss in the array detectors. Particles scattering into the detectors from neighboring telescopes would not be identified as valid events since there would be no AE signal for such events. NO correction is required for these events. To correct for the scattering out, a Monte Carlo calculation was developed to simulate the effects Of transverse straggling of the particles and to correct for the slight geometrical error incurred by placing the telescopes closer than their design distance. The code calculated the range of a given energy particle in the plastic and then calculated its transverse straggling based on a gaussian distribution with a root mean square projected angle given by the formula [Pa 8“] 7O 2~1“(t+m,) 1/2 1 Am Oproj. A-t(t+2m,) (L/LR) [1 + 9 Log,°(L/LR)][1 TETEITKS] (IV-5) where tsIncident kinetic energy per nucleon, mo-931.5. LaThickness Of material traversed (g/cmz), LfisRadiation length, A,AS=Mass number of particle, medium, 2=Atomic number of particle. Radiation lengths for a variety Of materials are tabulated in the literature [Pa 8“]. Radiation lengths for unmeasured compounds were calculated based on a formulation given by Tsai [Ts 7“]. The calculated trajectory of the particle was checked against the actual geometry Of the detector to ascertain if the particle would have scattered out. The effect Of transverse scattering in the CaF, was included in the calculation of the trajectory. The entrance point for each particle at each energy was also found uSing a Monte Carlo technique such that the geometry of the front face Of the telescope was treated exactly with a constant probability at each point. The fraction scattered out, R, was calculated as the number of simulated events for which the particle scattered out divided by the total number Of events. The correction factor with which each bin Of the measured spectra was multiplied is then 1/(1-R).. The 71 fraction scattered out of a scintillator array telescope for p, d, t, 3He, and ~He are shown in Figure IV-12 plotted as tail-to-peak ratios. 72 8.- _ $3 C3 gen- . QC &5 CE LU or 04“ 7 '— l .J C: F- 2... _ O SO IOO ISO 7 2OO ENERGY (MeV/O) Figure IV-12. Calcuated tail-to—peak ratios for scattering ' out losses of p, d, t, 3He and “He in the scintillator array telescopes. CHAPTER V RESULTS AND DISCUSSION The data presented in this chapter are primarily light particle energy spectra derived from the scintillator array telescopes discussed earlier. Exceptions will be figures showing the inclusive spectra for the trigger telescopes. Of primary interest here are the effects of the various coincidence conditions imposed on the light particle spectra measured with the scintillator array. All telescopes in the array have been summed together in order to obtain the best possible statistics. The errors depicted in the energy spectra are statistical. Positive detector angles imply the side of the reaction plane on which the scintillator array was placed. Negative angles imply the Opposite side of the reaction plane. A. 92 MeV/A “°Ar+Au Inclusive Spectra 1. Light Particle (Scintillator Array) Inclusive Spectra Light particle inclusive spectra (2:1,2) have been measured for the reaction 92 MeV/A “°Ar+Au at angles Of “5, 67.5, and 90 degrees in the laboratory. Energy spectra for D. d, t and ’He, “Re are shown in Figures V-1;a&b, respectively. The solid curves in the figure correspond to 73 7“ Figure V-I. Energy spectra of (a) p,d,t, and (b) ’He,“He from the reaction 92 MeV/A “°Ar+Au. The angles measured are “5° (circles), 67.5° (squares), and 90° (double triangles) in the laboratory. The errors depicted are statistical. The solid lines correspond to a hydrodynamics model calculation and the dot-dashed lines correspond to a firestreak calculation as described in the text. 75 _-> ogzmaa Ao<$ roamZm em .oa a. on o oo. oo o .»b_ ..b. .79 . 9 O O on 09 on O . 23535.2-.- - o. mo_§<2>88>: 1 N- x +=<+~< <\>02Nm hfln-¢..81 I JS'AOW/qu-I) up 39/9 ,p 76 hydrodynamics (HD) calculations by Buchwald [Bu 8“] with arbitrary normalizations for each light particle as follows: protons x10; deuterons x3.3; tritons x.13; ’He x1; and “He x.33 . The HD results are azimuth and impact parameter averaged for impact parameters from 0 to 7 fm. The dot- dashed curves are firestreak (FS) calculations for the same system using the impact parameter with the maximum weight giving a firestreak with 82 nucleons and 3“ protons at an impact parameter of 5 fm [We 8“]. It is interesting to note that while neither calculation fits the proton spectra, both fit the deuteron spectra. The HD calculation tends to give a more realistic fit to the other spectra. This is especially true at the low energy end of the Spectra where the FS calculation tends to overpredict the cross sections. The firestreak model assumes that the surfaces of the colliding nuclei are diffuse. The surface of each nucleus is divided into infinitesimal streaks parallel to the projectile direction. The projectile streaks follow straightline trajectories and interact with the target streaks only through completely inelastic collisions. The streaks are not allowed to broaden during the collision. The simplifying assumptions for the trajectories and interaction mechanism are valid at the relativistic energies for which the firestreak model was first proposed. At intermediate energies, ie. between 20 and 200 MeV/nucleon, these assumptions break down, causing the model to overpredict the 77 low energy part of the Spectra, particularly for particles Of mass A>2. 2. Moving Source Parameterization When considering a large volume of data it becomes useful to find a way to parameterize the whole set in terms of a few meaningful parameters. To that end, we have chosen to fit the light particle scintillator array spectra with what is commonly known as a single moving source parameterization. It has been shown that the high energy tails of light particle inclusive spectra can be explained in terms of emission from an excited source Of light particles in thermal equilibrium [Go 77]. This source emits particles isotropically in its rest frame which is moving at approximately half the beam velocity. The energy spectra are also assumed to be isotropic in the source rest frame with a relativistic Maxwell-Boltzmann energy distribution in the rest frame [La 69] given by dag . o exp(-E/T) pzdpdn “11m3 2(T/m)2 K,(m/T)+(T/m)K,(m/T) ' where p and E are the momentum and total energy, (V-I) respectively, Of a particle in the source rest frame. K, and K, are MacDonald functions, also known as modified Bessel functions Of the second kind. The double- differential cross sections are transformed into the laboratory frame using dag _ dag ' _ dEdn pg p'zdp'dfl' ’ (V 2) 78 where dza/p'zdp'dn' is the moving source rest frame momentum distribution, p(p') is the particle lab (source rest frame) momentum, and E' is the source rest frame total energycn? the particle expressed as I . .. .. E Ym.s.(E Bm.s.p coselab). (V 3) where a _ 2 1/2 _ Yan. 1/(1 3111.3.) . (v II) Here E and e are the total energy and angle in the lab, lab respectively. The moving source spectra are fit to the data using the method Of least squares with three free parameters. The three fit parameters are a, the total cross section, Bm.s.’ the velocity Of the moving source (usually expressed as the ratio to the beam velocity), and T, the SIOpe parameter, which is Often referred to as the temperature CH? the source. The effect Of the velocity parameter can be understood by considering that if the source velocity is zero, then the Spectra at all angles will be identical, ie., isotropic emission as in Figure V-2;aq If the source is moving along the beam direction, the spectra will no longer appear isotropic, but will have the general appearance Of Figure V-2;b. The source velocity is then a measure of the change in the cross section as a function of angle, ie. the source velocity is related to the slope Of the angular distribution da/dn. The inverse temperature reflects the slope Of the spectra in the high energy tails. A negative energy shift is applied to the Ciata before fitting to take into account the boost acquired Figure V-2. 79 Schematic representation Of the energy spectrum of particles emitted from a thermally equilibrated source (a) in the source's rest frame and (b) in the lab frame with the source moving in the forward direction. 80 Mfi+84£flfi ISOTROPIC EMISSION ' “NI SLOPE=T" logq dK (a) FORWARD ANGLES BACKWARD ANGLES K9 // ‘ (b) Figure V-2 81 by the particle in the coulomb field Of the target. The resulting moving source fit spectra are then shifted up in energy by the same amount for cmmparison with the measured spectra. The coulomb shifts used in the analysis Of the Au target data were 10 and 18 Mev for 221 and 2, respectively. For the Al target data, shifts of “ and 8 Mev were used for 2-1 and 2, respectively. The inclusive spectra for p, d, t, and ’He,“He are shown with single moving source fits (solid curves) in Figures V-3;a&b, respectively. The Spectra were not fit for energies below 50 MeV/nucleon to eliminate contributions from target emission. All angles were included in the fits. The values of the parameters extracted from the inclusive spectra are given in Table V-I and agree with the systematics of the moving source parameterization as shown in Figure V-“ [We 82]. 3. Coalescence Model The dot-dashed curves in Figure V-3 are the results Of coalescence model calculations for the light composite fragment cross sections. A coalescence relation given by 2 10(ZSN9EA) a C [d20(1101E)]A (V-S) dEAdflA 939“ where N + N N _1 3 A-I C ‘ E t A 1 [ )4an /3 ] (v-6) [zp+ zt ATE? 3: [p/(p=+m=)1 Figure V-3. 82 Energy spectra of p,d,t,’He, and “He from the reaction 92 MeV/A “°Ar+Au. The solid lines correspond to moving source fits as described in the text. The dot-dashed lines correspond to coalescence model calculations. 83 3. 8v m1> mezmfle .>o!. >o¢uzu 8n SN 8 8N8. 8. On SEER . x0 3+2 22~m 858348 . I . - mum-40m 02392 I CI. ()5 .Aaw/qw) 159 39/939 'av.'013ml 8“ TABLE V-I MOVING SOURCE PARAMETERS FOR 92 MeV/A Ar+Au (INCLUSIVE) “Particle Temperature Cross section Velocity T 00 8 (MeV) (mb) (C) PROTON ' 21.u:0.2 22600.:2u6. 0.205:0.002 DEUTERON 21.6:0.2 13600.:223. 0.181:0.003 TRITON 19.5:0.3 7827.:217. 0.152:0.002 3He 29.“:0.2 25“O.i 35. 0.218:0.002 “He 25.9:O.3 3960.:111. O.19“i0.002 Figure V-“. 85 The variation with incident energy above the barrier of:(a) the p,d,t,“He cross sections associated with a mid-rapidity source (the solid lines are to guide the eye, and the dashed line is the fireball model prediction for protons);(b) the extracted temperatures from the moving source compared with fireball description (dashed) and a Fermi gas model (solid) for equal participation from projectile and target nucleus;(c) the moving source velocities compared with the fireball (dashed) and equal participation models (solid). 86 m) I l0 ’1’, ,a” 9 “Y ‘3 C 2 1» / 6° 3.; 16» . E I- .4 T I k) / .3I- // -‘ ‘ I 2- + . / Q a/‘ * / v I- / .. / s ’5’ Io Eb (Evpmumw Figure V-“ 1000 87 was used to extract the coalescence radii ownn fits Of the proton inclusive spectra to the composite fragment spectra. In Eqn.V-EScI’o(Z,N,EA)/dEAdnA is the double differential cross section Of nuclei composed of 2 protons and NsA-Z neutrons. Np'Nt are the number of neutrons in the projectile and target nuclei, respectively, and 2p,2t are the number of protons in the projectile and target nuclei, respectively. The value Of 00 is taken to be the total reaction cross section. PO is the coalescence radius and p and m are the relativistic momenta and mass for the protons. The coalescence radius in momentum space, was the single free parameter used in the fits. The deuteron and alpha spectra are well described by the coalescence model. The model does not fit the triton and 3He spectra very well, although, the coalescence radii are still reasonable. The coalescence radii are summarized in Table V-2. It is possible to relate the coalescence radii to the size Of the fireball at tune freeze-out density V through the parameter 0, given as [Me 78] A-1 3 23+1 A-1 (P03) ”A 2A (p03) (II-7) This parameterization removes explicitly the spin alignment and phase factors from the coalescence radius. With the freeze-out density given by [Le 79] 1/(A-1) v -(N!Z!) (3h3/“np,°) (v-8) and the volume Of the equivalent Sphere taken to be 88 TABLE V-2 COALESCENCE MODEL PARAMETERS Po D, V R (MeV/fm) (MeV/fm) (fm’) (fm) 92 MeV/A “°Ar+Au (a) 2H 165 90 615 5.28 3H 139 101 629 5.32 3He 155 113 “50 “.76 “Re 171 1“7 229 3.80 100 MeV/A 16O+Au (b) 2H 87 5.5 3H 111 3.8 3He 115 3.8 “He ’ 1“2 2.9 (a) Present work. (b) Parameters from Auble, et al. [Ab 83] 89 V=H/3(NR3) (V-9) the radii at freeze-out were obtained and are presented in Table V-2. Included in Table V-2 are the coalescence model parameters obtained by Auble, et al. [Ab 83] for the reaction 100 MeV/A 1°O+Au. The parameters Obtained in the present experiment are in fair agreement with the 160 induced results. “. Intermediate Rapidity Fragment Inclusive Spectra The inclusive fragment spectra (35257) for the Intermediate Rapidity Fragment (IRF) trigger at -30 degrees are shown in Figure V-5. The data have been plotted as invariant cross sections as a function of the total fragment momentum. The lines are to guide the eye. The similarity Of the shapes Of the cross sections is an indication that a Single reaction mechanism is responsible for the production Of the various fragments. This phenomenon has been examined in detail by Jacak, et al. [Ja 83]. It was shown that the inclusive fragment spectra from 30 to 90 degrees in the laboratory frame could be explained with the assumption Of fragment emission from a single intermediate rapidity thermal source. Temperatures and velocities extracted from the intermediate mass fragment spectra using the single moving source parameterization were similar to parameters found for inclusive light particle spectra measured in the same experiment. 9O FWgureIPB. Invariant cross section plots versus total momentum for intermediate rapidity fragments in the IRF trigger at -30° from the reaction 92 MeV/A “°Ar+Au. The lines are to guide the eye. 5. 01 Up dzo/dE d0. [mb/(MeV/C)- MeV° SI] 10'4 10"5 91 MSU-84-447 T T‘ITIIIIr’ I I [III I ‘1 I III!!! I I TFIIIII— r I Illilll r T I I I I I I fi 92 MeV/A 4°Ar+Au+IRF+x i NIXIO4) BIRF=30 C(XI03) J 1 1 1 L1 11111 B(x102) 1 11111 Be(><|0) 1 1.1111111 __1‘1 1 1 11111111 _L 1_1 111111 ll__l llLLkLll I J I l 1 I000 2000 3000 4000 MOMENTUM (MeV/c) Figure V-5 92 Figure V-6. Projectile-like fragment cross sections for the PLF trigger at -13° plotted versus the fragment velocity over the projectile velocity from the reaction 92 MeV/A “°Ar+Au. “30'04'307 fiwvnrnr .rv YIWfi firrn,,..,lv ., 4000? WWW J 3 . SODIUM + 1 3000» 6. 2000- ' i 4- + i 1000» « 2f +*# 4 “11.111. AWLILU .1‘..1A..11.0ni-i“1”. fl ,...,. .,,V,TH.‘,W fiwlfllnvlmwhe 750 L BERYLLIUM . ‘ 3 p MAGNESIUM + 1 O 6" 500' . w 4,. +* 4 250}- ‘ 2- +* ‘*+1‘ “‘ A‘ 1.1:); WI flow WNW [hp 400% BORON o . . 8 - ALUMINUM * 300- ' ' 5» ‘ 200+ 4- fl 4 100+ . * 2~ fig .111: JUAI. .91 ..‘1...L. 11.,9..!H?A-l ll fowl. W” V Y" Wormr .., .0, A CARBON . a. SlL|CON ;200' . 0. . 6" #+ E chr . 4 n 2_ 3; 4 3 .. IA 41111.11“ 1... H L; -1 All.”3911.~4 fi'l 'I "I’ 'I" " fi‘l' 'l‘ 'II"1""f" m h- ; 75L NITROGEN 'o, ‘ 8 PHOSPHORUS * E 50% ‘ , . J 6’ 1 Nb . 4r w .1..11. 1-1.11.2 .1‘ A1. .1.01§1..LL "l"'l' I‘ l fi'I' Ifi l' 'l' " """" 40- OXYGEN i 8 - SULFUR J * 30r 1 6* + no ++ 20+ 9. 4r fi++ ] +- O 1 I- + IO . 2 W . ll. .1 1 L111 1 1.1.1 1.; 11111.; 1...: i ff 1' I I I‘ '7 I I" "I'I ]"II' 'I"'I" |5— FLUORINE + 20_ CHLORINE § 4 IO“ §1+ v *1 5 , , ‘ l0- *. .u +r} § *4;e{42a—¥—--‘x t;§;; :: § ¥¥:‘-1 I5 0 NEON * + 75 _ ARGON \ |O+ 50L 4 +N ’ 5* 3 25r . 4 Q ..-1.1A1..-1L..”.°1U-m.- ..gl...1...l11:a.°_‘_._b_ .20 :40 .60 .80 LOO .20 .40 .60 .80 IDO Vfrog/fooi Figure V-6 9H 5. Projectile-Like Fragment Inclusive Spectra The inclusive double differential cross sections for the Projectile-Like Fragment (PLF) trigger at -13 degrees are shown in Figure V-6. Cross sections are shown for fragments with (352318) as a function of the ratio of the fragment velocity to the incident projectile velocity. It is possible to observe evidence of three distinct reaction mechanisms in the PLF fragment Spectra - projectile fragmentation, thermal emission, and few nucleon transfer. Projectile fragmentation has been described as an interaction occurring for large impact parameters in which the incoming projectile nucleus becomes excited upon contact with the target nucleus. The projectile velocity is not appreciably reduced by the collision as it would be for a collision at a smaller impact parameter. The excited projectile either breaks up near the target nucleus before equilibration of the excitation energy or decays in flight after thermal equilibrium is established. The momentum distribution for a fragment emitted from a decaying projectile has been described by Goldhaber [Go 7H] using a gaussian distribution exp(-p’/202), where a is the momentum width of the distribution. For a fragment with K nucleons emitted from a projectile with A nucleons the momentum width is given as a2 - o,’K(A-K)/(A-1), (V-9) where 00- 100 MeV/c. The value of 00 can be related to the fermi momentum of the nucleons in the projectile nucleus by 95 oo-pf//S . Projectile fragmentation has been observed in Ar induced reactions on Au at 213 MeV/nucleon by Viyogi, et al. [V1 79] as well as at energies below 100 MeV/nucleon in Ar, C, and N induced reactions [Mo 81, Bo 83, Cu 83, Ba 83]. The velocity distributions in Figure V-6 which most clearly show projectile fragmentation are those for the oxygen through phosphorus fragments. The observed peaks appear gaussian in shape with centroids between 85 and 90 percent of the projectile velocity. The shift in velocity down from the projectile velocity can in part be accounted for by the loss in kinetic energy of the emitting system due to the binding energy associated with the emitted fragment. The L1 and Be fragment velocity distributions are primarily exponential in shape with only slight shoulders to indicate the possible presence of projectile fragmentation. phenomena. The exponential fall-off of the distributions is consistent with the assumption of emission from a thermal source, as discussed in section A.N. The B,Ch.and N velocity distributions show evidence of both fragmentaticnl and thermal emission. The few nucleon transfer reaction mechanism involves the exchange between the target and projectile nuclei of one or several nucleons. The fragment velocity distributions for the transfer process are characterized by narrow peaks centered at the beam velocity. The narrow peak widths can be attributed to the limited range of energies of the 96 available excited states into which the exchanged nucleons can be transferred. The sulfur, chlorine, and argon fragment velocity distributions of Figure V-6 appear to be dominated by the few nucleon transfer mechanism as shown by the markedly narrower widths and higher velocities relative to the oxygen through phosphorus distributions. The apparent sudden change from fragmentation to transfer reactions at sulfur has been examined more closely by Borrel, et al. [Bo 83] and Rami, et al. [Ra BM] in Ar induced reactions at an and 27.6 MeV/A, respectively. They find that the mechanism changes from fragmentation to few nucleon transfer between 35S and "S. Interestingly, formation of a fragment smaller than "S from l”Ar would require the transfer to the target of a fragment larger than an alpha particle. The argon velocity distribution undoubtedly contains a large component from elastic scattering. The grazing angle for the 92 MeV/nucleon “°Ar+Au reaction is approximately 3 degrees. These three reaction mechanisms need to be taken into account when attempting to understand the light particle coincidence data. For coincidences with fragments with 237, the contributions from thermal sources are non-negligible. A picture which includes both fragmentation and thermal emission is necessary. For coincidences with fragments with 852515, a fragmentation picture should suffice. There will undoubtedly still be contributions to the light particle spectra from emission from a moving thermal source as well 97 as target evaporation. Coincidence events with the highest three Z fragments might be expected to yield light particles originating primarily from target evaporation. 6. Light Particle (90°) Inclusive Spectra The inclusive light particle spectra (Z=1,2) for the Light Particle (LP) trigger at -90 degrees are shown in Figure V-7. The spectra are plotted as invariant cross sections as a function of the total particle momentum. The lines are to guide the eye. The slightly steeper slopes at the low energy end of the d and t spectra are associated with evaporation from the colder target remnant. For the LP triggered light particle coincidence spectra, the target evaporation portion of the LP Spectra has been discarded. A lower cut at an energy of 20 MeV/nucleon was imposed on the LP spectra, corresponding to a momentum of approximately 200 MeV/c/nucleon. Inclusive spectralmeasured at 90 degrees if! the scintillator array were in good agreement with the LP spectra. B. 92 MeV/A “°Ar+Au Coincidence Spectra 1. Momentum Conservation Model The interpretation of coincidence spectra has as an inherent hazard the possibility of assigning special significance to phenomena which had their origins in simple conservation laws. It is, of course, not possible to 98 Edgure\hfl. Invariant cross section plots versus total momentum for p,d,t, and “He in the LP trigger at -90° from the reaction 92 MeV/A “°Ar+Au. The lines are to guide the eye. 99 MSU-84-454 ltfrr E p 92 MeV/A 40m + Au a. LP+X§ r-! b :59 ° d {5 - 9”: O a '0": d 2 : x A I ‘1 1 e ' \ > § |O.2E \ \ P- \ a E I \ "" - \ g IO’3: : “J E : '° - : \ D -4 Nb ' . . 'o " . - E 1 10-5 l ' ‘ l ‘ ' ‘ I 1 1 l 1 1 I I 1 1+1 1 O 200 400 600 800 MOMENTUM (MeV/c) Figure V-7 100 perfectly model a nuclear reaction, even for conservation of momentum, because of the simplifying assumptions which must be made. It is, however, useful to attempt to understand the coincidence results from the perspective of the current level of understanding of the inclusive results, and do so within the framework of the conservation laws. The calculation which has been performed assumes that two coincident particles are emitted sequentially from a single moving source as described in section A.1. In reality, more than two particles are emitted from any collision violent enough to create an excited thermal source. The assumption of two particle emission is a minimal requirement. Emission of a third particle would be likely to reduce the correlations seen in the two particle calculation due to the increased number of degrees of freedom. From a knowledge of the momentum of the first particle, it is possible to calculate the reduction in excitation energy of the source and its recoil momentum. The second particle is then emitted from the cooled, recoiling source. Since it is not possible to know which particle was emitted first, both time sequences are combined to give the final coincidence cross section. The initial source parameters used in the calculations were those parameters extracted from the inclusive light particle spectra for the particle of interest. The size of the emitting source was chosen to correspond to the size of the fireball formed at the most probable impact parameter. This gave source sizes of N-82 101 for the Ar+Au reaction and N-18 and 38 for the C+Al and C+Au reactions, respectively. The normalizations of the final calculated coincidence cross sections were obtained using cross sections from moving source fits to the inclusive spectra of both emitted particles. The intermediate mass fragment cross sections were provided by Jacak [Ja 8A]. The spectra were further normalized by dividing by the reaction cross section. There were no other free parameters in the Ar+Au normalizations. Fragment cross sections were not available for the 30 MeV/A reactions. The calculated spectra for the 30 MeV/A reactions were arbitrarily normalized in order to compare the shapes of the distributions. A detailed presentation of the calculation is given in Appendix A. All of the coincidence spectra to be presented here have been divided by the solid angle of the trigger detector. The limits imposed on the integration of the trigger particle spectra are those imposed by the lower and upper energy cutoffs of the detector, except where noted. The solid curves in the figures are moving source fits to the data with energy and angle cuts as given in the presentations of the inclusive results. Exceptions will be pointed out when they occur. The dotted curves in the figures are momentum conservation calculations as outlined above. 102 2. Light Particle - IRF Coincidence Spectra Light particle spectra for coincidences between p, d, t, 3He and “He at us, 67.5, and 90 degrees and intermediate rapidity fragments (35257) at -30 degrees are shown in Figures V-8-12. The inclusive light particle spectra have been included in the figures for comparison with the coincidence spectra. The coincidence spectra have the same general features as the inclusive spectra for all measured light particle - intermediate rapidity fragment combinations. the momentum conservation calculation (dotted lines) for the proton spectra of Figure V-8 are in overall agreement with the data. Differences between the calculation and the data are seen to occur for low proton energies and for the normalizations of the Be and B triggered spectra. Excessive emphasis should not be placed on the normalizations of the calculation. The discrepancies at low energies can be understood as an overestimate of the calculated recoil velocity of the source. The trigger fragment is assumed to be emitted to -30 degrees causing the source to recoil. The perpendicular component of the recoil velocity makes the calculated light particle spectra between +u5 and +90 degrees slightly less steep because the source now has a velocity component directed toward that side of the reaction plane. The parallel component of the recoil momentum reduces the original velocity of the source and causes the calculated spectra to become more isotropic. The effect of the source recoil on the calculated spectra is Figure V-8. 103 (a)Proton inclusive energy spectra and proton coincidence spectra for IRF trigger fragments (b)lithium, (c)beryllium, (d)boron, (e)carbon, and (f)nitrogen from the reaction 92 MeV/A “°Ar+Au. The trigger fragment angle was -30°. The solid and dotted lines are moving source fits and momentum conservation calculations, respectively, as described in the text. 1011 “““‘ ‘ 1 1', V 92 MeV/A “Ar+Au-t 9mm, 1 V ’D’b’b D ‘ 14‘401 1‘. .1 11““ 4 ‘ ‘ 1114144 1 1131141 ‘ 4 1 1 r T V I INCLUSIVE PROTONS V '— IPDPPF P I III-Pb b p P .P’b Pb P F Inbhh h h P htbbPh - h hilt!) D P > P urn-hr p b up-pbrb - b hppbh- P n b r»»»- n p r O 0 o I". z Er» p F m m .m $3,223.... “a. do an we 3% m .m 40 150 0 ENERGYHMN) I00 50 Figure V-8 105 Figure V-9. Same as Figure V-8 for deuterons. 106 “30‘ 64“” INCLUSIVE DEUTERONS 92mm “maximum. : 4 1 4n XIRF ‘ Li 5. N d3a'ldE an an n; (mb/MeV-srz) 5. ._ 0. "fir 1' A . . .... v vvrvv' 2.0.40 eo‘eo 0 20.40.60 80 ENERGYWW/A) Figure V-9 107 Figure V-10. Same as Figure V-8 for tritons. «Pox dE d a an” (mb/McV-sr 2) 108 - . l M INCLUSIVE TRITONS _ 92 McV/A 4°Ar+AuN+XmF : 1, 10' E 1% xIRF ’ U 3 E 3. ‘ P 4} 10°L 3 I 1 '0": I0°s a IO“ 5' 3 1 1 . '. 1 Ida: 3 t I E |d'5 162:- i .3 10 g o 20 40 so so 0 20 ENERGY (Mch) Figure V‘10 109 Figure V-11. Same as Figure V-8 for ’He. d3cr/ dE an. an. m; (mb/MeV'srz) 110 MSU-34-449 Idl 2 INCLUSIVE 3HELIUMS -_ ...... XIRF= Li E 92 MeV/A 4°Ar+Au2He + W A 1111.“ O, 5. XmF‘Be I03:— XmF=c XMF=N 50 I 100 ENERGY(MeV/A) 0 So ' 100 Figure V-11 50 Figure V-12. Same as Figure V-8 for “He. 112 3“ 1 :14‘14‘ 4 :411‘1‘ .1 :11111‘ 4 I801“. 4 92mm “Ar+Au-u He +x .3, v T v INCLUSIVE ALPHAS' v V DIDIPD P P DDDDPDP P I nun-lb. h I 1 v ““1 ‘ I :“‘4.‘ 1 ‘ 33‘ ‘ ‘ 1‘4‘41 ‘ Ii““4 1‘ ‘ ‘I““I‘ ‘ I1 4414141 1 J 20 0 It. - D I nbbPPb- I D hip-Pp b b D nib-hp» P DIIPFP D I huh-b h PI, P nib-bp- b - pnnhbb - h 60 80 40 20 o ' 0v 5.0 A0 AU AU $3.33.... .25.. an 2.8% 2 .m 3 . ENERGY (MW/A) Figure V-12 113 quite small. Any effect in the data is apparently even smaller. The extracted moving source fit parameters for the IRF triggered light particle coincidence spectra are tabulated in Table V-3. the temperatures and velocities are plotted in Figures V-13;a&c, respectively, as ratios to the inclusive values. Note, the points plotted for fragment masses of 1 and 2 correspond to coincidences with the LP trigger and will be discussed later in the chapter. Figure v-13;a shows that the extracted coincidence spectra temperatures tend to be slightly higher than the inclusive temperatures (about 5 percent). There does not appear to be any significant variation in this parameter over the range of trigger fragments measured. Figure V-13;c shows that the extracted coincidence Spectra velocities tend to be lower than the inclusive velocities by about 10 percent. There may be some indication of a decrease in the velocity parameter with increased trigger fragment mass. There seems to be no significant dependence of the temperature and velocity parameters on the particular type of light particle measured. The apparent differences between the 3He parameters and those of the other light isotopes may be due to the lower statistics of the ’He spectra. The slightly lower apparent velocities for the coincidence Spectra relative to the inclusive spectra may be due to the fact that the MS degree angle was included in all 11H woo.o«mm_.o .o— H.=Nw >.Ffiw.mm zmoomHHz woo.0Homp.o .mm H.mzm w.ouo.:w zomm_.o .o: H.2wm >.0Hw.=m zomom :oo.onpop.o .30 “.mm:— o.owm.mm zquqwmmm o—o.OH—>_.o .szH.P>Nm N.OH©.MN ZDHIHHA zommesma moo.oamop.o .zm «.mo: :.—H>.—m zmoomHHz woo.oumw—.o .m: «.mmo m.ouo.mm zommozv amH m on p >uHoon> :oHuoom mmoLo ogsumnoqsop Lommfige oHoHume Ammuonb mmHv :<+L< <\>oz mm mom mmmemzOZ MI> mqm<9 115 mmo.owmmp.o .N— M.ooF m.©Hm.mm zomm—.o .NN M.o>— m.zHo.Nm zomom Fmo.oumwm.o .m: H.0wm w.mam.—m stqummm z—o.0Hwom.o .mm H.0—o m.—Hm.zm stthq 0:» w—0.0Mmmp.o .zm H.:op m.—Hm.mm zmoomsz mmo.owwmp.o .mm “.mom m.ouo.=m zomm H.2mw o.—H=.om stqgwmmm :oo.ow>m—.o .mm—H.>mzm m.oaw.op zszth zoeHmh on Apes A>mzv amH m on v 15:00:; :ofipoom mmogu ogzumgmaeoa Lommze macaugmm AmmazHHzoov mI> mqm<9 116 mmo.oammF.o .>_ «.0m m.mab.mm zmoompaz m_o.oum¢_.o .mm «.mpm =.mum.>m zommm zomom ooo.oammF.o .om w.o:m m.Fam.om 23H44»mmm soo.oam>_.o .mm.«.mmwp o.F«m.mm zathHq 0:. on Anew A>ozv .mmH a on p zufiooHo> coapoom mmoco onzumnoosww Lommfigw oaowugmm AamszHezoov m-> mamas Figure V-13. [(a) and (c)] Coincidence Spectra moving source fit temperatures and velocities for the LP and IRF triggers and [(b) and (d)] the PLF trigger from the reaction 92 Mev “°Ar+Au. The parameters for protons (circles), deuterons (squares), tritons (double triangles), ’He (crosses), and “He (pluses) are plotted as ratios of the coincident spectrum value over the inclusive Spectrum value as a function of coincident particle mass. 118 m~I> mLsmwm mmSz ...zwzwdm... mnmI¢mIDm2 0.0 md N._ v._ md md N._ v._ em 0. m o N. o 1 _ + I 1 a I - . L - . I. umH as - AB is - H “31¢ v N “H H . a...» x n u I - - _ + I. _ _ _ m I I - ... * a. + * - . mom I. um“ as - .3. 37:4 «322 mm is .. uj/2181 ll/le 119 of the moving source fits. The Size of the scintillator array gave an angular acceptance at the MS degree setting forward to ~35 degrees. It is well known that forward angle inclusive light particle Spectra show contributions from projectile evaporation at energies corresponding to the beam velocity. It is likely that detection of intermediate mass fragments at -30 degrees selects events in which the projectile either disintegrates or is appreciably slowed. The IRF triggered light particle spectra would therefore not be as likely to have contributions from projectile evaporation. Figure V-1H shows the results of the hydrodynamics (HD) calculation of Buchwald [Bu 8“] for the reaction 92 MeV/A “°Ar+Au. The solid.1ines are the predicted p, d, t, 3He, and “He spectra for in-plane angles of AS, 70, and 90 degrees and an azimuthal angle of ¢-O°.Iulazimuthal angle of ¢-0° corresponds to the side of the reaction plane on which the projectile nucleus is incident in the calculation. the dot-dashed lines Show the prediction for an azimuthal angle of ¢-180°, ie. the opposite side of the reaction plane. The calculation is impact parameter averaged for impact parameters from 0 to 7 fermi. The calculation is not azimuthally averaged as was the HD calculation used in comparison to the inclusive light particle spectra. The normalizations used for the HD predictions of Figure V-1u were the same as those used for the azimuthally averaged predictions of Figure V-I. The hydrodynamics prediction can Figure V-1u. 120 Coincidence energy spectra from 92 MeV/A Ar+Au for (a) p,d,t and (b) ’He,“He triggered by a Li fragment in the IRF trigger. The solid (dot- dashed) lines correspond to an impact parameter averaged hydrodynamics calculation for an azimuthal angle of 0° (180°) 121 MSUABd-SSS fl v r —1 92 MeV/A AH AU! 9X + Li (IRF) (a) d’a/dE an an," (mb/MeV-sr 2) 50 I00 A o A 20 A 40 60 ‘ so A ENERGY (MW/A) Figure V~1H 122 be characterized by the enhancement of the forward angle ¢-0° spectra. The 0-180° prediction is almost isotropic. This azimuthal angle dependence is due to what is called the "highly inelastic bounce-off" effect. Hydrodynamics predicts that for collisions which are not head-on, the incident projectile is inelastically scattered from the target nucleus into the ¢-0° side of the reaction plane and then decays by emission of light particles. The light particles are focussed in the direction of the scattered projectile due to its relatively high velocity. The target nucleus is also excited and decays by emission of light particles while slowly recoiling into the ¢-180° side of the reation plane. The predicted ¢-0° spectra subsequently show an enhancement in the high energy tails at forward angles. The ¢-180° Spectra are characteristic of emission from a stationery source. The symbols in Figure v-IH are light particle coincidence spectra for a Li fragment in the IRF trigger. The light particle spectra, while not in agreement with the prediction at either azimuthal angle, are qualitively more like the ¢=0° prediction. The disagreement with the data may be a result of the experimental determination of the reaction plane. The intermediate mass fragments measured in the IRF trigger detector may be from central and head-on collsions in which the projectile explodes into a number of lighter fragments. An individual fragment would carry no information about the reaction plane. The disagreement may also be due to an 123 overprediction of the reaction dynamics bytflm model. It appears that an event trigger which more completely measures the multiplicity of charged particles created in heavy ion collisions, ie. a Mn array, is needed. 3. Light Particle - PLF Coincidence Spectra Light particle spectra for coincidences between p, d and t at MS, 67.5, and 90 degrees and projectile-like fragments (352515) at -13 degrees are shown in Figures V-15- 17. It was shown in section A.5. that the observed fragmentation process was the same for fragments in the PLF trigger with 852515. The spectra for coincident fragments with 952515 have therefore, been summed together in order to obtain reasonable statistics. The inclusive light particle spectra have been included in the figures for comparison with the coincidence spectra. The light particle coincidence spectra for the Li through N PLF triggers appear to be very similar to the inclusive Spectra. As was pointed out in section A.5. of this chapter, the inclusive PLF spectra for fragments with 257 exhibit substantial contributions from thermal source emission associated with central collisions. It is therefore, not surprising that the light particle coincidence spectra associated with these fragments are Similar to the inclusive Spectra and the IRF triggered spectra. The conservation of momentum calculations (dotted lines) are shown for the Li through N PLF triggers. Comparison of the calculation with 12“ Figure V-15 (a)Proton inclusive energy spectra and proton coincidence spectra for PLF trigger fragments (b)lithium, (c)beryllium, (d)boron, (e)carbon, (f)nitrogen, (g)oxygen, and (h)fluorine through phosphorus from the reaction 92 MeV/A ”°Ar+Au. The trigger fragment angle was -13°. The solid and dotted lines are moving source fits and momentum conservaticni calculations, respectively, as described in the text. 125 ISU'IO-SO! SE 92 MeV/A Ar+Au . 9..an INCLUSIVE PROTONS xPLF =Li if Io’" v rvvwn' 102g .. I I0 : 5' Ms") f "PLF 0 50 I00 I50 50 10° '50 ENERGY (MoV/A) Figure V-15 126 Figure V-16. Same as Figure v-15 for deuterons. a3a/dE an anPLF Imb/MeV-sr2 ) INCLUSIVE OEUTERONS 35 92MeV/A Ar+Au +cI+xPLF MSU 'OQ'SOI 0 20 4‘0‘6‘0 80‘ 0‘20 40 so‘ao ENERGY ( MeV/A I Figure V-16 128 Figure V-17. Same as Figure V-IS for tritons. d’c/IIE an on” (WW-"2 I 129 tGJ-OO' 4” 1 v Y V v V r ' Vi SZW/A AI+M . '9’an 4 - - "VV‘V‘ V 'm TY“ - O v vanvq V 11"" 5 .1. v vvvvn‘ T vvvww 5k xPLF' F'P Go‘o 20 40 so ENENWIMGVAI Figure V-17 130 the data shows that there is little effect due to conservation of momentum for emission to -13 degrees. It can be seen from Figure V-15 that the proton coincidence cross sections for the oxygen and the fluorine through phosphorus PLF triggers have much flatter angular distributions than the inclusive cross sections. A flatter angular distribution is characteristic of a lower source velocity. A similar trend is seen for the deuteron spectra. For fragments at -13 degrees with 852515, the inclusive PLF spectra are dominated by the projectile fragmentation process. Collisions leading to projectile fragmentation must necessarily be peripheral and therefore, less likely to create an excited moving source. There would be two primary sources of emission for this type of collision -Iunission from the fragmenting projectile which would be focussed in the direction of the projectile, and emission from the excited target which would be isotropic in the laboratory frame. The light particle spectra measured in this experiment are well away from the measured fragment direction. The observation of lower apparent source velocities for the proton and deuteron Spectra is therefore consistent with emission from the excited target. There is still a contribution from an intermediate source, although it appears to be greatly diminished. Light particle - fragment coincidence spectra for fragments with 2216 had insufficient statistics to study the reaction mechanisms involved. If the mechanism for these 131 fragments is few nucleon transfer, then it is likely that the associated light particle coincidence rate is low. The low statistics are consistent with this assumption, as well as with the observed trend toward decreasing fragmentation cross sections with increasing fragment mass. The extracted moving source fit parameters are given in Table V-h. The temperatures and velocities are plotted in Figures V-13;b,d as ratios of the coincident values to the inclusive values. Note that the parameters for spectra summed over coincidences with fluorine through phosphorous fragments are plotted at an approximate average mass of 2“. As was true for the light particle - IRF spectra, the temperature parameter shows no variation with the PLF trigger fragment mass. In addition, the PLF triggered spectra source temperatures are the same as the inclusive temperature. The velocities Show a clear trend toward decreasing velocities with increasing trigger fragment mass for the proton and deuteron Spectra. An apparent velocity 30 percent below the inclusive result is obtained for the average projectile mass of A-2fl. The triton spectra velocities do not decrease with trigger coincident fragment mass and in fact, are very nearly constant. One might speculate, that since composite emission is suppressed for a less excited system, the triton spectra which are observed between us and 90 degrees are dominated by the contributions from more central collisions and or alternately by emission from whatever intermediate source might be created in the 132 omo.oaomp.o .Fp «.wm m.mwo.zm mommlmoaqm opo.oupop.o .mm “.mmp N.NHm.om zmomxo o—o.ouoop.o .Nm “.mum N.F«m.om zmoomHHz opo.oammp.o .ma H._mm m._am.lm zommao moo.o«>>—.o .om M.>oo— ¢.owm.—N zomom moo.onm>—.o .m:_n.omzm >.ono.PN Equqwmmm ooo.oumm_.o .NNNH.mP—m u.o«z.mm zathHq ZOmMHDMQ fooamzfio .3 “.2: ..mum.mm mommumosqm 30.03.26 .3 «.mmm 93.1mm zmowxo moo.o«NaF.o .om H.wmm m.0HN.—m zmoothz woo.owmwp.o .wo H.0om_ 0.0Ho._m zommozv mam u so p xufiooao> cofiuoom mmogo ogsumLoQEoe Lommfigh odouunmm AmmoonH mqmv s<+g< <\>mz No mom mmmemzoz zI> m4m¢e 133 omo.owom—.o .w— H.=o o.m«m.=m mommImosdm NNO.OH©:F.O .mN H.0mF m.NHm.mF zmowxo opo.0H©>P.o .om H.>m— 0.9Hm.om zmoomeHz m_o.oazop.o .om H.acm m.FHm.mF zommao moo.oamep.o .mo—H.©om o.—Hm.mF zomom moo.oumm_.o .mzpn.mo:— N.FHo.mF ZDHJJMmmm moo.owmcp.o .zomfl.ompm m.oum.mp ZDHIHHA ZOHHmH on Ansv A>mzv baa m on p >uaooHo> cofiuoom mmoco ogsumLUQEom LommHLWI oHoHuLNWI AQMDZHHZOUV :I> mgm:> o.mao.mm 2090mm 0:. opo.owomm.o .mo H.0mm m.NHo.Nm 2090mm or" moo.oawzp.o .om H.3m:~ F._Hm.om 2090mm zoeHmF Fpo.oapop.o .m: H.>Nm w.oao.zm zommesma zommhama w_o.o«:mp.o .om H.o_—m >.oum.mm zoeomm zommhsmo mFo.oumom.o .o: «.mho m.—HN.mN zommeamo zOHOmm coo.onmmp.o .s@ “.mon m.owo.mm 2090mm 2090mm on Apes A>m2v as m on P mufiooam> :oHpoom mmoLo mmsumcoaeomI Lowmwnm mHoHume Ammoone may mI> mqmmz No mom mmmemzoz Figure V-19. I38 Inclusive energy spectra for p,d, and t from the reactions (3) 3O MeV/A 12C+Au and (b) 30 MeV/A 12C+Al . The angles measured are u7° (u5° for the Al target) (circles), 56° (Squares), 71° (triangles), and 90° (diamonds). The errors depicted are statistical. The solid lines correspond to moving source fits as described in the text. 139 mFI> mesmfim 256:. 655 9 8 I Q x1 34.09 5%: cm “I '1’ '9 9 (15 -AaIN/qw) 09 39/029 . TO. M OO— .o.vo-3m3 1&0 Au target have been combined because of low statistics at the H5 degree setting. An average angle of A7 degrees will be used for the combined spectra. Energy spectra for the hydrogen isotopes are shown in Figure V-19. The solid curves in the figure are moving source fits to the data. The lower energy cuts for the fits were 30, 2M), and 20 MeV/nucleon for p, d, and t, respectively. These cuts were selected in order to eliminate contributions from-target evaporation. The most forward angle data were not included in the fits in order to eliminate contributions from projectile evaporation. The contributions from projectile evaporation can be more clearly seen in the d and t spectra shown in Figure V-20. These inclusive spectra were measured in a separate experiment for the reaction 30 MeV/A 12C+Al at angles of 15, H5, 75. 90, and 105 degrees in the laboratory. The peaks in the 15 degree cross sections at energies of approximately 30 MeV/A are evidence of projectile evaporation. It can be seen that there is still a contribution from projectile evaporation at 45 degrees. A coulomb shift of 4 MeV was used for light particles with the aluminum target and 10 Mev with the gold target. The samecnns and shifts will be used for the coincidence spectra. The moving source fit parameters are given in Table V-6. The temperatures and velocities are in agreement with the systematics of Figure V-fl. Spectra for the helium isotOpes were also measured. However, it was found that there was an insufficient amount of data to warrant further Figure v-20. IIII Inclusive energy spectra for d and t from the reaction 30 MeV/A 12C+Au at angles of 15° (pluses), M5° (circles), 75° (squares), 90° (double triangles), and 105° (crosses). The spectra were measured in a separate experiment using a Si-NaI(Tl) telescope. 1’42 MSU-84- 532 xx' 0 i I 4' .. )3!" ... I d : X I X X I. I +4. I0" XXI! I .. + g x x ' ' Jr+ 5 X x ' . +1, 4 " x ‘- 0 ‘ IO-z x x . I a I X x ., ‘t :1: A X I ’+ ? f d ?’ [0'3 I. * + I . > #1 .3. § “ II fl 3 D - q S l . c: + ' . I ‘o ++++ g :. ++++++++ ++ +++ I .4 0.. + Nb I00 :- .... ’4. O x- ”o. + xx.- 0. ,_ X! I . .5 1 . .I ... I I0" x2... .0. + xxxx I.. . I1, 1 . -I Xx xx .. .. +++ q -2 . IO 1: xx ~ 0 i X 3 fl 1 3 3*; I0. l * + ”III II 0 50 I00 I50 200 ENERGY (MeV) Figure V-20 1U3 TABLE V-6 MOVING SOURCE PARAMETERS 30 MeV/A C+A1,Au (INCLUSIVE) Particle Temperature Cross section Velocity 1 00 8 (MeV) (mb) (0) 30 MeV/A C+Al PROTON 9.5:0.2 77“.: 38. 0.13910.0H7 DEUTERON 8.”:O.N 510.: 75. 0.130i0.007 TRITON 7.0:0.2 760.i1u3. 0.1N0t0.003 30 MeV/A C+Au PROTON 9.3:0.1 1200.: 32. 0.12110.003 DEUTERON 9.3:O.3 697.: S9. 0.10010.005 TRITON 9.2:O.6 600.:131. 0.092:0.005 1H“ analysis. The extracted source temperatures for the two targets are quite similar. The source velocities for the Al target spectra are ~30 percent higher than for the Au target. The fireball model and the systematics of the moving source parameterization predict that the source velocity should scale as the velocity of the center of mass of the colliding system. For C+Al,Au, the ratio of the center of mass velocities is about 1.35 in agreement with the observed velocities. 2. Intermediate Rapidity Fragment Inclusive Spectra The inclusive fragment spectra (35256) for the IRF trigger at -25 degrees are shown in Figures V-21;a&b for the Al and Au targets, respectively. The shapes of the Spectra are quite similar and again indicate, that as was true at higher energies [Ja 83], these fragments are created by similar mechanisms. Further evidence for a single mechanism has been seen in the reaction 30 MeV/A ‘ZC+Au by Fields et.al. [Fi 8M]. Using a single set of initial parameters for all fragments, Fields performed a model calculation which assumed emission from an excited region of the combined target and projectile. The excitation region then spread into the colder surrounding material giving rise to a continuous progression of temperatures for the apparent source. It was concluded from the intermediate mass fragment spectra that the lighter fragments were more favorably emitted from the highly excited, early stages of 1U5 Figure V-21. Inclusive energy spectra for fragments in the IRF trigger at -25° with 35256 from the reactions (a) 30 MeV/A 12C+Al and (b) 30 MeV/A 12C+Au. MSU'84'5l9 1146 I *1 D l d r- E " “ a . I O a: + ~ * I . d U . I N «I "'- . d I I- . ‘ d I I O .. I I J 4 I A I O ”I A N I I O " I '0 o I 8‘ o q I Q ; I _ 4 .I x v I X 4 I: m V r- _l m m 0 '4 p .1 I p- "I" I d .. 4 O .. I . 4 O F LI. I I o ‘ .- m I I I O _‘ - I I 4 O L I I I I o .1 I I 4 O J " a I I I o + I I I o ' O I I 4 o .9 a. u . . I A I d O b S I A N I I o _ % .IO 0 I A I o 2 I 2 i I 0‘ . I X ~__,I — v 8 I ._ a, 5 U " .1 CD a: llllLl 1 L 1111111 1 1 1111111 1 4 1111111 1 1 l11111 1 1 1 411111 1 1 1 N .. o T 0,1 Q Q 9. 9. Q (IS-Am law) 09 39/039 200 300 ICC 200 300 |00 Figure V-21 1A7 the reaction, whereas the heavier fragments were more favorably emitted from the cooler, later stages of the reaction. These trends may be evident hithe cohumdence spectra. 3. Projectile-Rapidity Fragment Inclusive Spectra The inclusive fragment spectra (35256) for the PLF trigger at -13 degrees are shown in Figures V-22;a&b for the Al and Au targets, respectively. The spectra have been plotted as a function of the ratio of the detected fragment velocity over the incident projectile velocity. The fragment Spectra at 30 MeV/A do not show the different reaction mechanisms described in section A.5. of this chapter as clearly as the 92 MeV/A spectra. The statistics of the coincidence data limited the fragment analysis to separation by Z leaving four fragment types with which to study three phenomena. The range of measured fragment energies shown in Figure V-22 have low energy experimental cuts which make it difficult to determine if fragmentation peaks exist in the spectra. This limited range is especially a problem for the Li and Be fragment spectra. Figure V-23 shows a more complete range of energies for the same fragments at 15 degrees in the reaction 25 MeV/A ‘2C+Au [Ja 8A]. The existence of a gaussian shaped peak in the boron fragment spectrum of Figure v-23 may be an indication of projectile fragmentation. The carbon spectrum appears to be dominated by elastic scattering. The laboratory grazing Figure V-22. 1&8 Inclusive cross sections for fragments in the PLF trigger at an angle of -13° with 35256 from the reactions (a) 30 MeV/A 12C+Al and (b) 30 MeV/A 12C+Au (b) plotted versus the ratio of the fragment velocity over the projectile velocity. 1u9 “80"04'527 "I"'I"'1**v ‘VIr"‘rrr'1rfi 5” 0'.(0) 1 5‘}. 0. (b) 4 _ LITHIUM . 4_ LITHIUM .. 3 - . 3.}- 2.- 2.- I.” . i I.“ ' * rH-I-+—I—+—I+v-I—I-+-I-I-I‘ —+—+—1—-}—+—+—1—I—H—+—H—+4-< I a. BERYLLIUM 0 I 2.-BERYLLIUM .... - ° . _ 00 I O , c? | I '. Ix . > o '- . F . 4 g . H—H—I—rI—H—I—H—I—I—o—FH~ WW .5. _ J . I I g 2 BORON . l 3 - soaow o 4 DJ " P . . E I I 2... .4 b - 1 » “v _ ° 1 I.- L O . L+-o—¢+o—+—++1—H—I4-+-+- 1111II11111L1111 0.60 0.80 LOO _ CARBON ~ V V - 3. . . 4 Incl pro; 2 ._ I I. ‘ 44 1 l 1 1 1 l 1 1 1 1 0.60 0.80 LOO Vfraq/Vproj Figure V-22 Figure V-23. 150 Unnormalized inclusive distributions for intermediate mass fragments with 35256 from the reaction 25 MeV/A ‘2C+Au at an angle of 15° plotted versus the ratio of the fragment velocity over the projectile velocity [Ja 8H]. COUNTS 200 I00 200 I00 300 - 200 IOO 300 - 200 IOO 151 MSU‘ 84'528 I V U I I T U I I I T I 1 V V r- ... r LITHIUM I liilllllljlllll; IV IWT'UU'YfU T T 1 m o :n 2 8 jrrrl I _1 F I I W, 0.60 0.80 |.00 ' Vfrat) / Vproj Figure V-23 152 angle for the C+A1,(Au) reaction is approximately 2.u,(1o.u) degreesl Projectile fragmentation may be more easily observed for the Al target carbon spectrum, since the projectile velocity fragments were detected well outside the grazing angle where the contributions to the spectra from elastic scattering are greatly reduced. u. Light Particle (LP) Inclusive Spectra The inclusive light particle spectra (Z=1,2) for the LP trigger at -us degrees are shown in Figure v-2u. The LP trigger data were available only for the A1 target. The spectra are plotted as invariant cross sections as a function of the total particle momentum. The lines are to guide the eye. For the light particle - LP coincidence spectra, a cut at an energy of 20 MeV/A was imposed on the LP trigger spectra to eliminate contributions from target evaporation. D. 30 MeV/A 12C+Al Coincidence Spectra 1. Light Particle - IRF Coincidence Spectra Light particle spectra for coincidences between protons and deuterons at 45, 56, 71, and 90 degrees and intermediate rapidity fragments (35256) at -25 degrees are shown in Figures v-25 and V-26. It is interesting to note that, although the MS degree angle was not included in the fits, the moving source does not underestimate the forward Figure V-ZN. 153 Invariant cross section plots versus total momentum for p (circles), d (squares), t (triangles), 3He (diamonds), and “He (double triangles) in the LP trigger at —u5° from the reaction 30 MeV/A 12C+Al. The lines are to guide the eye. 154 MSU-84-448 p 30MeV/A '2c+AI +.LP+X ; _ d GLP : 45° .. IO'ZE I I I0‘3 I* I I I11nI| I I’I’IIIII[ l/p dza'ldE d9. [mb /(MeV/c)-MeV-sr] 5 I5. I I I IIIIIr’ ‘. l #1 lllLll I0"6 . . I . . L J . . . I . . . l I . . 200 400 600 800 MOMENTUM (MeV/c) 0 Figure v-2u Figure V-ZS. 155 Proton coincidence energy spectra for IRF trigger fragments (a)lithium, (b)beryllium, (c)boron, and (d)carbon from the reaction 30 MeV/A 12C+Al. The trigger fragment angle was - 25°. The solid and dot-dashed lines are moving source fits and momentum conservation calculations, respectively, as described in the text. 156 MSU-84~495 5. N 5. b . so MeV/A '2<:+AI—»p+xIRF dsa/dE d0 dQIRF (mb/MeV-srz) 0 0 40 ENERGY (MeV/A) Figure V-25 157 Figure V-26. Same as Figure V-25 for deuterons. MSU—34-493 so MeV/A IZ‘LC+Al->d+XIRF 5. N 5. (N lO-4s d3cr/dEdfldQIRF (mb/MeV-srz) 5. Ln IO-S: Io”6 M 0 4O 80 O 40 80 ENERGY (MeV/A) Figure V-26 159 angle as it did for the inclusive spectra (Figure V-19). This is another indication that the enhancements observed in the inclusive spectra are due to projectile evaporation. For the 12C+Al reaction, the fireball formalism predicts a source size of 18 nucleons for the impact parameter with the maximum weight. A preliminary calculation with N-18 gave spectra with slopes much flatter than the experimental results. Because of the relatively small source size compared to the emitted fragment, there is a large transverse velocity imparted to the source upon emission of the fragment. This recoil shows up in the light particle spectra as an enhancement of the higher energy cross sections. The effect becomes more pronounced for the heavier fragments as would be expected. The poor agreement with the experimental results for a source size of N-18 indicates that a larger source size is needed to take up the recoil momentum. If one considers that the source is probably not spatially separated from the remainder of the target, then the recoil momentum would be taken up by the 'entire projectile-target system, minus the emitted fragment. For example, for a coincident fragment with A-12, the source size becomes N-27 nucleons instead of 18. Calculations with a source size of N-27 nucleons are shown in Figures V-25 and 26 (dot-dashed lines). This calculation is in fair agreement with the data, although, there is still a flatter slope for the proton spectra with heavier IRF trigger fragments and for the deuteron spectra. 160 moo.oawww.o .o H.>m w.OH 0.0— mmmz om moo.o«oo—.o .— “.2 :.0H —.m zommF N.OH z.m zszqu zoyomm I H<+o <\>oz om on Anev A>ozv mmH m so e hufiooHo> :ofiuomm mmOLo mgsumcoaswe memfigm mHodume AmmouHmH mmHV :<.H<+o <\>mz om mom mmmemzoz >I> mqm ogsmfim mmg h2u29.0H:.NF zomomuzth zomMHDMQ woo.ouoop.o .w H.3m z.os~.m 20momuzeH4 2090mm s<+o ¢\>mz om ooo.owom—.o .N w.zm o.oww.o~ zommmz pm on Anav A>ozv mqm u so w auaooam> cofiuomm mmogo mgsumgmqemh memfice mHoHume Ammoone mqmv :<.H<+o <\>mz om mom mmmhmzOz wI> mqmp +pr MSU-84-515 . -4 l . . . . . :- _4 ‘_ XLP- He 1. T A .40. ' so 0 E40 ENERGY (MeV/A) Figure V-29 ‘ so 170 general agreement with the data. Little effect was seen due to the recoil momentum of the source for the light trigger particles. The extracted moving source fit parameters are given in Table V-9. The temperatures and velocities are shown in Figures V-27;a&c along with the IRF parameters as ratios to the inclusive values. The proton temperature ratios increase smoothly with increasing coincident light particle mass from about 10 percent below the inclusive temperature for A-1 coincidences to about 10 percent above for A-u coincidences. The ratios for A-3 and H are similar to those for the light particle - intermediate rapidity fragment coincidences. The velocities do not show any significant variation as a function of the coincident light particle mass and are approximately equal to the inclusive value. E. 30 MeV/A l2C+Au Coincidence Spectra 1. Light Particle - IRF Coincidence Spectra Light particle spectra for coincidences between protons and deuterons at “7. 56, 71, and 90 degrees and intermediate rapidity fragments (35256) at -25 degrees are .shown.in Figures V—30;a&c. The spectra for all trigger fragments have been summed together to obtain satisfactory statistics. The dot-dashed lines in Figure V-28 are the momentum (Hanservation calculations based on a source size of 38 171 moo.OHoN—.o .m H.om c.0Hm.> zomMHDMQ omo.ome—.o .m M.N: m.o«o.> 2090mm zommhsma moo.o«~=—.o .P H.> m.oa:.o_ mm: o_o.o«mm_.o .F “.2 m.ow>.o mm" N—o.owmmw.o .o “.2 m.owm.o zoeHmH :oo.ow:=~.o ._ H.m_ m.o«o.w zommpamo moo.owzap.o .m «.mm m.on.w zoeomm 2090mm on Anev A>mzv mg m on v aufiooam> cofipomm mmOLo mgsumgoaeoe memfige mHoHume AmmoonH adv H<+o <\>mz om mom mmmemzoz mI> m4m33. W [Wa 83] A. I. Warwick, H. H. Wieman, H. H. Gutbrod, M. R. Maier, J. Peter, H. G. Ritter, H. Stelzer, F. Weik, M. Freedman, D. J. Henderson, S. B. Kaufman, E. P. Steinberg, and B. D. Wilkins, Phys. Rev. C§l(1983)1083. [We 76] G. D. Westfall, J. Gosset, P. J. Johansen, A. M. Poskanzer, W. 0. Meyer, H. H. Gutbrod, A. Sandoval, and R. Stock, Phys. Rev. Lett 31(1976)1202. [We 82] G. D. Westfall, B. V. Jacak, N. Anantaraman, M. W. CIirtmin, G. M; CI~aleey¢, C. K. (Sellake, B. Hasselquist, W. G. Lynch, D. K. Scott, B. M Tsang, M. J. Murphy, T. J. M. Symons, R. Legrain T. J. Majors, Phys. Lett. 116B(1982)118. 195 [We 8“] G. D. Westfall, Z. M. Koenig, B. V. Jacak. L. H. Harwood, G. M. Crawley, M. W. Curtin, C. K. -Gelbke, B. Hasselquist, W. G. Lynch, A. D. Panagiotou, D. K. Scott, H. Stacker, and M. B Tsang, Phys. Rev. C 32(198A)861. [Ws 8A] 0. D. Westfall, private communication. Y [Ya 79] Y. Yariv and Z. Fraenkel, Phys. Rev. C39(1979)2227.