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OCHOGAN INTI T TE UNIVERSITY LIBRARIES WI!IIIIHHTIIll/”(IIIWHIIIIWWill/Ill!!!“l 3 1293 00785 9246 -1 3 if LIBRARY Michigan State University This is to certify that the dissertation entitled High Energy Photon Production In Nuclear Reactions presented by Chui Ling Tam has been accepted towards fulfillment of the requirements for Ph.D. degree in Physics O .. . , 51(4):“ /1/¢. 11.]. / Major professor Date §//5’/ :76) M5 U i: an Affirmative Action/Equal Opportunity Institution 0- 12771 PLACE ll RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before due due. DATE DUE DATE DUE DATE DUE MSU Is An Al'flrmdive Action/Equal Opponunlty Intuition ammo-9.1 HIGH ENERGY PHOTON PRODUCTION IN NUCLEAR REACTIONS BY Chui Ling Tam A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1989 movuvw: ABSTRACT HIGH ENERGY PHOTON PRODUCTION IN NUCLEAR REACTIONS By Chui Ling Tam The production of high energy game rays (BY) 20 Hell) was studied using three Cherenkov telescopes. Each telescope consists of a Ba!"2 active converter placed in front of the Cherenkov counter stack. The efficiency and the energy response of the detector were calibrated at the University of Illinois tagged photon facility. The efficiency of the telescope ranges from about wt for .20 Hell photons to 20$ for 80 Rev photons. The detector energy resolution varies from 30$ FHHM at 20 MeV to 1151 at 80 HeV. Photon production from the following light-ion induced reactions were studied: ~Hea- C, ~He + Zn and ‘He + Pb at energies E/A = 25 MeV and 53 MeV; and 2H + C, 'H 4- Zn and 'H + Pb at E/A = 53 Hell. The photon double differential cross sections are exponentially decreasing with increased energy. The slope parameters are steeper than those found in heavy-ion induced reactions at similar energies. The angular distributions in the nucleon-nucleon center-of-mass have larger dipole components than in heavy- ion induced reactions. He observed both target and projectile dependence in the slope parameters and angular distributions. Calculations based on first- chance neutron-proton bremsstrahlung model was able to reproduce the projectile dependence of the slope parameters. Photon production from the following 30 MeV/nucleon heavy-ion induced reactions were also studied: symmetric systems ’Li + Li, 2°Ne + Mg arui “°Ar + Ca and the asymmetric systems 71.1 + Pb and ”Ar + Pb. The energy spectra and the angular distributions are quite similar to those observed in earlier experiments. The ratios of total cross section for systems having different masses agree with predictions of the first-chance n-p bremsstrahlung model. To DAPRID iv Acxnowtencensurs I wish to thank the faculty and staff of the National Superconducting Cyclotron Laboratory for their support of the completion of this dissertation. I would like to specially thank my research advisor Professor Ed Kashy for his guidance during my graduate career. Many thanks go to Professor Halter Benenson and Professor John Stevenson, without their help, this dissertation would be all blank pages. I would also like to thank Professor George Bertsch and Professor Wolfgang Bauer for the many helpful discussions. Finally, many hearty thanks go to my fellow graduate students for their friendship which made the endless working hours much more enjoyable. TABLE OF CONTENTS LIST OF FIGURES . ................................... .... ..... ... ........ x LIST OF TABLES ............................... . ......................... xv CMMM1IMWWflmN”. .............. .H ............ ”nun”. ...... 1 CHAPTER 2 DESIGN AND CALIBRATION OF THE CHERENKOV TELESCOPE . . . . . . . . . . . . A. Introduction ...... ..... .................... ......... ... ...... A.1. Detection of High Energy Gamma Rays ..................... A.2. Shower Type Detectors .. ....... ....... ...... . ............ \DO‘U’IU’IU’I A.2.1. Lead Glass Detector .............................. A.2.2. NaI Scintillator Detector ........................ 10 A.2.3. 8aFa Scintillator Detector ............ .......... . 1A A.3. Cherenkov Plastic Telescope Detector ............ ........ 1H 8. The Cherenkov Plastic High Energy Gamma Ray Telescope ........ 17 8.1. The Construction of the Three Cherenkov Telescopes . ..... 17 8.2. Photon Pair Conversion Coefficient . ....... ......... ..... 19 8.3. Determination of the Photon Energy ..... .. 20 8.3.1. Cherenkov Light Output Level ..................... 20 8.3.2. Position Weighted Sum of Light Outputs .......... 26 C. Calibration of the Cherenkov Plastic Telescope Detector ..... 33 C.1. Calibration of the Detector Efficiency .................. 35 6.2. Calibration of the Energy Response of the Detector ...... 36 D. Comparison with Other Detectors .............................. A1 vi D. E. CHAPTER 3 A. Chapter u Comparison with Other Detectors ........... ............ Summary ...................................................... EXPERIMENTAL SET-UPS AND DATA REDUCTION ..... ......... ..... ... Experimental Set-ups ........................................ A.1. Detector Lay-outs ....................... .............. A.2. Electronics 00.0.0000.00.0.00.........OOOOOOOOOOOOOOOOOO . Background Suppression ......... ...... . ......... . ............. 8.1. Suppression Of Energetic Neutrons ....................... 8.2. Suppression of Cosmic Ray Huons . ..... ... ...... ..... ..... Osmry OOOOOOOOOOOOOO 0......00......00.0000000000000000...... HIGH ENERGY GAMMA RAY PRODUCTION FROM LIGHT ION INDUCED REACTIONS .... ............. . .................. ... ............. Introduction ................................................. A.1. History: The Measurements of High Energy Gamma Rays ..... A.2. Theoretical models ................................ ...... A.3. The Light-ion Induced Photon Production Experiment ...... Experiment Results ....... .............................. ...... 8.1. Photon Energy Spectra ............ ..... .................. 8.2. Angular Dependence ..... . ........................... . . . . . .DiSCUSSion 00..........OOOOOOOOOOO...OOOOOOOOOOOOOOOOOO0...... C.1. Moving source model fit ........ ............. ............ C.2. The Moving Source ...... ......... ........................ C.3. Y-ray angular distributions in the source frame ......... C.fl. Target and projectile mass dependence of Y-ray intensity vii “1 H6 “8 “8 #8 5O 53 53 53 56 59 59 59 61 63 63 63 6A 81 81 8A 86 89 D. Conclusion ................................................... 92 CHAPTER 5 HIGH ENERGY GAMMA RAY PRODUCTION FROM NEAR SYMMETRIC SYSTEMS .......... . ........ ............. . ......... 96 A. Introduction ................................................. 96 A.1. The Nucleus-Nucleus Coherent Bremsstrahlung Model ....... 96 A.2. The Goal of the Symmetric System Experiment . ......... ... 98 8. Experiment Results ..... . ..... ................................ 98 C. Discussion ................................................... 108 C.1. Systematic Studies of the Data by the Simple Moving Source Fit Model ... ..... . ..... .......................... 108 C.2. Source Velocity of Symmetric and Asymmetric Systems .... 111 C.3. Mass Dependence of the Photon Angular Distributions in Center-of-Mass Frame ...... .................. ...... . ..... 115 C.“. Mass Dependence of the Photon Energy Spectra ............ 116 0.”.1. Slope Parameters of the Double Differential Ccross Sections ..... .... ................................ 116 C.u.2. Total Cross Section Ratios ................. ...... 117 D. Summary .. ..................... . ......... . ...... ......... ..... 118 Chapter 6 Theorectical Model Calculations and Comparison with Data ..... 121 A. Introduction .......................................... ....... 121 8. BUU Calculation. ...................... . ...... . ....... ........ 123 8.1. Comparison with the Symmetric Systems Data ....... ...... . 123 8.2. Comparison with the Light-Ion Induced Reactions ......... 126 C. Simple Fermi Gas Model First-Chance np Collision viii Bremsstrahlung Calculations for 53 MeV Light-Ion Data ........ 130 6.1. First Chance Bremsstrahlung Model for Light-Ion Induced Reactions ...... ..... . ...... .................... ......... 130 C.2. The Internal Momentum Distribution of ’H and “He ........ 133 0.2.1. Internal Momentum distribution of 'H ............. 133 C.2.2. Internal Momentum Distribution of ~He ...... ..... . 136 C.3. Result of the Calculation and Comparison with Data ...... 137 C.4. Modified Internal Momentum Distribution Function for 2H and ‘He ................. . .......... .... ..... .... ........ 139 D. Conclusion ............. . ............... . ..................... 191 CHAPTER 7 SUMMARY ........................... ............. ..... . ........ 196 LISTWREFERWCES 0.0.0...0.00.000000...O........OOOOOOOOOOOOOOOOOOO... 11‘8 END OF TABLE ix Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure II-1 II-2 II-3 II-u II-5 II-6 II-7 II-8 II-9 II-1O 11-11 II-13 LIST OF FIGURES Relative importance of the three major type of photon interactio as a fUntion of photon energy and the atomic number of the medium [Ev 55]. ...................... ....... The relative probability of Compton scattering vs. pair production in 8aF,. ..... The response functions of lead glass detector fOr energies from 20 MeV to 100 MeV [He 86]. ........................... The response functions of a single NaI crystal detector (a) and that of a NaI telescope with BaFz converter (b) [8e 87]. ... ........... . ....... ................................ Response functions of a BaF, detector at various energies [He 86]. ... .......... . ..... . ...... . ..... .................. A schematic picture of the Cherenkov telescopes. (a): The eight element telescope, (b): The 13 element telescope. ... Pair conversion efficiency of the BaF2 converter as a function of photon energy. ................................ Principle of operation for the Cherenkov plastic telescope Electron energy-range relationship in Lucite. ............. Typical light output from one element (1" thick) of the Cherenkov stack. Electron energy loss in 1" thick Cherenkov plastic as a function of energy. ....... ...... ........ . ..... ... ......... Schematic of the University of Illinois tagged photon facility. .OOOOOOOOOOOOOOO 7 8 11 13 15 16 21 23 2“ 27 3A Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure II-1A Efficiency of the Cherenkov telescope as a function of photon energy. . ........... ...................... ..... .... II-15 Response function of the Cherenkov telescope at 22, 92, 60, and 80 MeV without including light output from the Ban converter. ......OOOOOOOOO......OOOOOOCOOOOOOOOOOO II-16 Energies of the peak of the response function vs. energies of the tagged photon. ...... . ........ ........ ........... ... II-17 Response function of the Cherenkov telescope with the light output from the converter taken into account. ............. II-18 FHHM of the response functions of the Cherenkov telescope with and without taking into account the converter light output. ........ ......... ......................... ......... II-19 Response functions of the Grenoble NaI telescope in comparison with the MSU Cherenkov telescope [Be 87]. ...... II-2O The FHHM of different type of detectors used in high energy photon measurements. III-1 Layout of the experimental area. .......................... III-2 Eletronic schematics of the master trigger logic. ......... III-3 Eletronic schematics of the detector. ... ....... .... ....... 111-u A typical time spectrum of the gamma rays. ................ III-5 Comparison of photon spectra with and without TOF gate. ... III-6 Comparison of photon spectra with and without anti-u shields. .................................................. IV-1 Photon energy spectra for 25 MeV/nucleon ”He + Pb at laboratory angle of 30°, 60°, 90., 120. and 150.. IV-2 Photon energy spectra for 25 MeV/nucleon ”He + Zn at xi 37 39 NO 92 “3 A“ 95 H9 51 52 59 55 57 65 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 0 O 0 0 0 laboratory angle of 30 , 60 , 9O , 120 and 150 . ........ 66 u IV-3 Photon energy spectra for 25 MeV/nucleon He + C at laboratory angle of 30°, 60°, 90., 120. and 150.. . ...... 67 IV-u Photon energy spectra for 53 MeV/nucleon 2H + Pb at laboratory angle of 30., 60., 90., 1200 and 150.. ....... 68 IV-5 Photon energy spectra for 53 MeV/nucleon 2H + Zn at laboratory angle of 30°, 60°, 90., 120. and 150°. ....... 69 IV-6 Photon energy spectra for 53 MeV/nucleon 2H + C at laboratory angle of 30°, 60°, 90°, 120° and 150°. ...... 70. IV-7 Photon energy spectra for 53 MeV/nucleon ”He + Pb at laboratory angle of 30., 60°, 90., 120. and 150°. ........ 71 IV-8 Photon energy spectra for 53 MeV/nucleon “He + Zn at laboratory angle of 30°, 60°, 90', 120' and 150'. ........ 72 IV-9 Photon energy spectra for 53 MeV/nucleon “He + C at laboratory angle of 30°, 60., 90., 120. and 150.. ....... 73 IV-1O Integrated angular distribution for photon energy above 30 MeV in the laboratory frame. ........ . ..................... 75 IV-11 Rapidity distribution for 53 MeV/nucleon 2H + Pb induced high energy gamma ray. .............................. ...... 77 IV—12 Rapidity plot fOr 25 MeV/nucleon ”He beam on three different targets: Pb, Zn and C. ....................... 78 IV-13 Rapidity plot for 53 MeV/nucleon 2H beam on three different targets: Pb, Zn and C. ........................... ........ 79 IV-1u Rapidity plot for 53 MeV/nucleon “He beam on the three dif ferent targets: Pb, Zn and C. ..... ... ................. ... 80 O IV-16 Moving source model fit to the photon energy spectra at 90 xii Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure in the laboratory fer all 9 reactions studied. ........... 87 IV-17 Moving source model fit to the photon integrated angular distributions in the nucleon-nucleon center-of-mass frame. 88 IV-18 Target dependence of the photon cross section. ............ 90 IV-19 Projectile dependence of the photon cross section. ........ 91 V-1 Photon energy spectra f0r 30 MeV/nucleon 7Li + Li at laboratory angle of 30., 60., 90., 120. and 150‘. . ....... 99 V-2 Photon energy spectra for 30 MeV/nucleon zoNe + Mg at 0 0 0 0 laboratory angle of 30 , 60 , 90 , 120 and 150 . ........ 100 V-3 Photon energy spectra f0r 30 MeV/nucleon noAr + Ca at 0 O I O 0 laboratory angle of 30 , 6O , 90 , 120 and 150 . ....... 101 V-u Photon energy spectra f6r 53 MeV/nucleon 7Li + Pb at 0 0 I 0 O laboratory angle of 30 , 60 , 90 , 120 and 150 . . ...... 102 V-S Photon energy spectra fer 53 MeV/nucleon qur + Pb at laboratory angle of 30°, 60., 90., 1200 and 150°. ....... 103 V-6 Integrated angular distribution f6r photon energy above 30 MeV in the laboratory frame. .............................. 105 V-7 Rapidity plot for the three symetric systems. . . . . . . . . . . . . . . 106 v-8 Rapidity plot for 30 MeV/nucleon 7L1 and no Ar beam on Pb target. .................................................. 107 V-10 Moving source model fit to the photon energy spectra at 90. in the laboratory fer all 5 reactions studied. ........... 113 V-11 Moving source model fit to the photon integrated angular distributions in the nucleon-nucleon center-of-mass frame. 11“ VI-1 Comparison of 8UU calculation of the photon energy spectra with experimental data of the symetric systems. .......... 1211 xiii Figure Figure Figure Figure Figure Figure Figure Figure VI-2 Comparison of BUU calculation of the photon angular distributions in the nucleon-nucleon center-of-mass frame with experimental data for the symmetric systems. ......... 127 VI-3 Comparison of 8UU calculation with experimental data of the light-ion induced reactions systems fbr both the photon energy spectra and angular distributions in the nucleon- nucleon center-of-mass frame. ......... ................ .... 128 VI-fl 2H and ~He internal momenta distribution. ................. 137 VI-5 Comparison of the photon energy spectra with calculation from the first chance bremsstrahlung model using non-zero temperature internal momenta distribution functions shown in Figure VI-A. ........................................... 138 VI-6 Zero-degree-temperature Fermi spheres for 'H and ~He. ...... 190 VI-7 Comparison between experimental data and calculation using zero temperature internal momentum distribution shown in Figure VI-6 for 53 MeV/nucleon 2H + Pb. ................... 192 VI-8 First chance np bremsstrahlung model calculations for ’H + Pb and ~He + Pb reactions assuming zero-degree-temperature Fermi gas as internal momentum distribution fUctions (shown in Figure VI-6). ......................................... 143 VI-9 Comparison between experimental data and calculation using zero temperature internal momentum distribution shown in Figure VI-6 fOr 53 MeV/nucleon ~He + Pb. ....... ... ........ 1AM xiv Table Table Table Table Table Table Table Table Table II-1 II-2 IV-1 IV-2 IV-3 IV-4 LIST OF TABLES Electron energy loss in elements of detector 1 and 2. ...... Electron energy loss in elements of detector 3. ............ Comparison of extracted source velocities Bexp to nucleon- nuc1wn ... ....OOOOOOOOOOOOOOOO......IOOOOOOOOO......OOOOOOO Parameters for the moving source model fit............ ....... Comparison of slope parameters for different systems at similar energies per nucleon. ............................... Comparison of slope parameters of 53 MeV/nucleon light-ion data with systems of different projectile masses at similar energies. 0.0.0.0...............OOOOOOOOOOOOOOOOOO.......0... V-1 The source velocity Bexp extracted from the rapidity plot. O..................OOOOOOOOOOOO...COIOOOOOO......0.... V-2 Results of the moving source model fit to all 5 systems ...... V-3 Ratios of total cross section predicted by different models in comparison with experimetnal data. .......................... XV 29 3O 82 85 93 9a 109 112 119 Chapter 1 Introduction Since the production of high energy gamma rays (EY)20 MeV) in inter- mediate energy heavy-ion collisions was discovered in 19811 by two independent groups at 681 [Gr 85l'and MSU [8e 86], there has been a large amount of experimental and theoretical work done in this area. The study of high energy game ray production is quite interesting because, unlike the measurement of subthreshold pion production, the photons are not reabsorbed within the surrounding nuclear matter. So in spite of the difficulty in measuring its small cross-section, the production of high energy gama ray should provide a relatively clean probe of the reaction dynamics in inter- mediate energy heavy ion reactions. (The term high energy indicates a greater energy than expected for nuclear level transitions, including decay of the giant dipole states.) Several theoretical models have been proposed to explain these game rays at such relatively high energy. The majority of these models are based on the nucleon-nucleon or nucleus-nucleus bremsstrahlung during the very early stages of the reaction. One early model suggested by Vasak et. al.[Va 85], attributed the production of the high energy gamma rays to coherent nucleus-nucleus bremsstrahlung. For symetric systems, the destructive interference between bremsstrahlung from the acceleration of the projectile nucleus and from the target nucleus would lead to a quadrupole angular distribution in the cen- ter-of-mass frame. The gamma ray yield depends on Z2 and becomes most significant in heavier systems. Also in an early attempt to reproduce the data from 681 and MSU group, both Nakayama and Bertsch [Na 86] and Bauer et a1. [Ba 86a] arrived at the conclusion that the contribution of the nucleon bremsstrahlung from nuclear potential field is unimportant compared to the contribution of the in- dividual nucleon-nucleon collisions. Most of the more recent models of high energy game ray production sug- gest that game rays come from incoherent neutron-proton bremsstrahlung within the two colliding nuclei. For example, Bauer et a1. [Ba 86b] con- ducted a dynamical study based 0n the Boltzmnn-Uehling-Uhlenbeck equation, which describes the time evolution of the nucleon phase space density during the reaction process. Nakayama and Bertsch [Na 86] did a calculation using infinite matter approximations with a first-chance zero-range n-p interac- tion, and Remington et al. [Re 86] incorporated a semiclassical bremsstrahlung formla into the Boltzmann master equation [Ha 68]. These models all assume that the microscopic mechanism is individual nucleon- nucleon bremsstrahlung and that game rays are produced in the early stage of the reaction. Nifenecker and Bondorf [Ni 85] introduced a different approach, which attributes the photon production to the multiple scattering during the later stages of the collision. In this approach, the gamma rays are produced by incoherent nucleon-nucleon collisions within a recoiling fireball formed by part of the target and projectile nucleons. The kinetic energy of the par- ticipating nucleons is assumed to be converted to thermal energy of the fireball, so that game rays of relatively high energy can be produced, and the predicted angular distribution is expected to be isotropic in the frame of the moving source. Neuhauser and Koonin [Ne 87], combining a fireball model with the elementary nucleon-nucleon bremsstrahlung cross section, also found good agreement with experiment. Shortly after the first high energy gem ray observation by Beard et al. [Be 86] with the NSCL Enge Split-pole spectrograph [Sp 67], it was quite clear that a better detector system was needed for further investigation of this phenomenon. Development of a high energy game ray telescope made of a stack of Cherenkov plastic, conceived by Dr. J.Stevenson, began at Michigan State University. I had since begun participating actively in the detector construction and calibration and several high energy game ray experiments using these telescopes. Using a pair of the high energy gem ray telescopes, we first measured the inclusive high energy game ray production with 111" beam at 20, 30 and 110 MeV/nucleon, and the production of high energy game ray in coincidence with light charged particles. Then a slightly modified third telescope was finished, and two more experiments were carried out, one measuring the light-ion induced game ray production, and the other game rays from inter- mediate energy symmetric systems. Later, two telescopes were taken to the Lawrence Berkeley Laboratories to perform an experiment using 136 Xe beam at 66, 98, and 1211 MeV/nucleon. More experiments are being done here in MSU using these telescopes together with other detectors. He calibrated one of the detectors using the tagged-photon facility at the University of Illinois. This thesis is organized as follows: Chapter 2 of this thesis covers the development of the gamma ray telescope and calibration with tagged photons. Chapter 3 describes the hardware and electronic set-up used in the actual game ray experiments, the method of background suppression and of extraction of experimental data. Chapter A presents the data from the light- ion induced high energy game ray production experiment and a discussion. Chapter 5 deals with the data from the near symetric system experiment and its interpretation. In chapter 6, theorectical model calculations based on the nucleon-nucleon bremsstrahlung are presented and compared to the data. Finally, the sumary and conclusions are in chapter 7. CHAPTER 2 DESIGN AND CALIBRATION OF THE CHERENKOV TELESCOPE A. Introduction The gamma rays which range in energy from 20 MeV to 100 MeV and their small production cross-section present particular problems in the design of the detector system. There is also a large (10‘-10’ times the photon yield) background of fast and slow neutrons, charged particles and low energy gamma rays. A number of different detectors have been used by various other experimental groups to measure these high energy photons. A.1. Detection of High Energy Ga-a Ibys A photon is uncharged and thus creates no direct ionization or excitation of the mterial through which it passes. The detection of game rays therefore depends on causing the photon to undergo an interaction that transfers all or part of its energy to secondary electrons in the absorbing material. These electrons can then be detected by means of the Coulomb interaction. Although there are many possible photon interaction mechanisms known, only three major types of interactions lead to the conversion of a significant part of the photon energy to electron energy. They are: photoelectric absorption, Compton scattering, and pair production. The relative importance of these three processes in different materials for various photon energies is illustrated in Figure II-1 [Ev 55]. In Figure II-1, the line at the left represents the photon energy at which photoelectric absorption and Compton scattering are equally probable as a function of the absorber atomic number. And the line at the right represents the photon energy and absorber atomic number at which Compton scattering and pair production are equally probable. Thus, three areas on the plot are defined within which one of the three processes dominate. It is clear that for E:Y 2 20 MeV, photoelectric absorption is unimportant as the primary initial process. Most of the high energy gamma ray detectors operate in the pair production zone and use mterial with high Z. Figure II-2 shows the relative efficiency of photon undergoing Compton scattering and pair production within BaF. Crystal. It is seen that for gamma rays of energy above 20 MeV, pair production plays a far more important role than Compton scattering. Currently, all detector systems used in the measurement of high energy game rays rely on photon pair production mechanism to convert high energy photons into electron-positron pairs. A.2. Shower Type Detectors Most of the shower type detectors operate on the basis of a formation of a large number of electron-positron pairs ”shower" inside the detector. Shower'type detectors are usually made of materials that have high atomic number 2 to enhance the yield of the e+e' pair. In order to contain the shower, the sizes of these shower detectors are typically several radiation * ‘ 1 11111111 1 11111111 111111111 111111 120 - _. 100 *- _. "' Photoelectric effect Pair prqdumion “ S 80 1" dominant dominant - ° Compton effect , ‘- N 40 dominant ,, _ 20 ... 0 1111111 1 11111111 I llllllll l l 0.01 0.05 0.1 0.5 1 5 10 50 100 hr in MeV Figure II-1 Relative importance of the three major type of photon interactio as a funtion of photon energy and the atomic number of the medium [Ev 55]. 3° . T I I I V r I r t T I I I T I I I I v T U l I T I t I 4 " 1 t Z 25 +- -~ P a 20 r- g . g C .o 16 :- 3 . g . O. 10 — I.’ — D i d D," .1 V : 5 '_'_ Compton sodium _* sex~ / : . ”...... .4 o I.1 1 I L m 1 L L 1 L L L L 1 1 1 1 I i L L 1 i 1 1 1 1 I 20 40 80 80 100 120 E7 Figure II-2 The relative probability of Compton scattering vs. pair produc- tion in BaF,. lengths. Examples of this type of detector include lead glass detectors and large inorganic scintillators such as NaI and BaFZ. A.2.1. Lead Glass Detector One of the shower type detector used by several groups [Gr 86][Al 86] to detect high energy photon is the lead glass detector. In a lead glass detector, a photon is converted into an electron-positron pair either by an external converter or in the detector itself. As they pass through the detector, they emit photons by the Cherenkov mechanism. This is the well known emission of radiation observed when the velocity of a charged particle in a medium exceeds the speed of light in that medium [Ja 75a]. Because of the high atomic number of lead, these secondary electrons and positrons have a high probability of producing bremsstrahlung photons. Then, the secondary photon in turn produces more e'e+ pairs. This Y ... eIe' process repeats itself many times forming a shower of electrons and positrons in the detector. The total Cherenkov light output of all the electrons and positrons is then collected and the sum gives the energy of the original photon. Because of the Cherenkov mechanism in the detector material, lead glass detectors offer the advantage of very low sensitivity to neutrons and low energy charged particles. Lead glass detector, however, have relatively poor energy resolution for photons with energy below 100 MeV, particularly when compared to inorganic scintillator such as NaI and BaF.. Moreover, the energy response function of a lead glass detector shows a pronounced high-energy tail that can cause serious errors in both the slopes and yields of steeply falling exponential spectra. 1O Herrmann et. a1. made a direct comparison between a single block lead glass detector and a BaF, crystal using monoenergetic photons at the Mainz tagged photon facility [He 86]. The response function of the lead glass for various energies are presented in Figure II-3. The full-width at half- maximum (FHHM) of the energy resolution obtained, described by AE/E = 13.21/lm, is poor when compared to BaF, crystal. More comparisons of the energy resolution of lead glass with that of the inorganic scintillators and Cherenkov plastic range detector will be presented later. Therefore, as pointed out by Herrmann et. al., lead glass as a detector for the measurement of bremsstrahlung photons in intermediate energy should be used with great caution. A.2.2. Nal Scintillator Detector Inorganic scintillators are also widely used for the measurement of high energy photons. For example, the thallium-activated sodium iodide (NaI(Tl)) crystal is one of the most commonly used inorganic scintillators. In a scintillator detector, a photon is converted into an electron-positron pair either by a converter or in the detector itself. Then, as the pair passes through the detector, scintillation photons are emitted. Because of the relatively high atomic number of the crystal, these electrons and positrons also produce bremsstrahlung photons. The energetic secondary photons in turn generate more e'e" pairs through the pair production process. This Y n e+e' process repeats itself many times, thus forming a shower of electrons and positrons in the detector. The total scintillator light output, assuming all 11 .'.m-. -~.. Figure II-3 The response functions of lead glass detector for energies from 20 MeV to 100 MeV [He 86]. 12' electrons and positrons stop in the crystal, then gives the energy of the original photon. NaI(Tl) crystal has the advantage of high light output and a close to linear response to gamma ray energy over most of the energy range. Its energy resolution is much better than that of the lead glasses. It is also possible to obtain large volume NaI crystals. The disadvantages of NaI are that it is quite fragile and is also hygroscopic; if exposed to the atmosphere, it will deteriorate due to water absorption. Due to the large thermal neutron capture cross section of Iodine, NaI is also sensitive to neutrons, one of the major sources of background in the measurement of high energy gem rays. The energy resolution of NaI is predominantly limited by the loss of secondary electrons and photons escaping the detector volume. Figure II-Ma) shows the energy response of e 20 cm long and 15 cm diameter cylindrical NaI crystal illuminated by monoenergetic photon beams [Be 87]. The response is significantly better than that of the lead glass. The Dial spectrm has a low energy tail instead of the high energy tail seen in the case of lead glass. Such a low energy tail has a relatively smaller influence on exponential spectra than the high energy tail found on lead glasses. Bertholet et.al. [Be 87] have combined a large inorganic scintillator block NaI(Tl) with a BaF, converter. The converter is ”active", which means the light output from the converter is added to the light output of the detector, making it possible to take into account the energy lost by the e+e' pair in the converter. The resolution obtained for this NaI telescope detector system is a moderate 6.5“! 8 (GeV) (FHHM). The energy response 13 © @ EiNel) EINeHOEuer) ’1 12w .- .l I 1 2‘ | I 3 ”I" 1 E Nb ‘1 1' H” h | I! ELWLWL' E |£3_wcv ‘ Mu ngfit .Mlt 500 1 500 1000 PULSE HEIGHT Figure ”-9 The response functions of a single NaI crystal detector (a) and that of a NaI telescope with BaF, converter (b) [Be 87]. HI curves are shown in Figure II-Mb). At the end of this chapter, we will compare the energy response of the NaI telescope with that of the MSU Cherenkov plastic telescope. A.2.3. BaF. Scintillator Detector BaF, is a relatively new inorganic scintillator that has enjoyed more and more use in the last few years. It offers some advantages over the traditional NaI crystal detector. BaF, crystal, unlike NaI crystal, is not hydroscopic, so it is more stable in the air. It is less sensitive to thermal neutron capture than NaI. And it also has good time resolution (~ '400 ps) that makes for good fast neutron-gem ray discrimination by time- of-flight when a beam with sharp time structure is used. At the present time, however, there are no single BaF, detectors that are large enough to contain the showers from 100 Rev gama rays. So most of the M, detector systems consist of a cluster of several small BaF. whose light outputs are sumed. The energy resolution of BaF, detectors is also much better than that of lead glasses. Figure II-S shows an example of the response function of a 118 X 10 on BaF, crystal [Hi 87]. The resolution of the detector is Bill-E (Gevs (FHHM). A.3. Cherenkov Plastic Telescope Detector In the MSU Cherenkov plastic game ray telescope (Figure II-6), a high energy photon is converted into an electron-positron pair in the active BaF, converter placed in the front of the plastic Cherenkov detector stack. But ‘5 titi .0“ Q: E Comic/000 uev JJ’ f Lij > 1 O 4' so. 5,-03 Nev . 8 2 m . 8 S s. v * U . (unis/.00 kCV Figure II-S Response functions of a BaF, detector at various energies [He 86]. kc“ U)? Figure II-6 A schematic picture of the Cherenkov telescopes. (a): The eight element telescope, (b): The 13 element telescope. A...“ 17 because of the low atomic number of the Cherenkov plastic (Lucite with a wave shifter additive), instead of forming a shower, the electron and positron simply lose all of their energy and stop in the stack. As the electron and positron travel down the stack of Cherenkov plastic, they emit Cherenkov light in the plastic elements they pass through. A waveshifter additive was added to the Cherenkov plastic which absorbs the highly directional, mostly short wave length UV Cherenkov light, and then radiates isotropically at a longer wavelength (IIZSnm), to which the plastic is more transparent. The total energy of the photon was then obtained by the position weighted sum of the light output from each element. Since the measurement of the photon energy does not rely on shower formation, the length of this telescope is only slightly over one radiation length. Due to theCherenkov detection mechanism, this detector has the advantage of being very insensitive to neutrons and to low energy charged particles. Its energy resolution is better than that of the lead glass detectors for energies below 100 MeV. Also, a Cherenkov plastic telescope can usually be built at a fraction of the cost of any inorganic scintillator detector. B. The Cherenkov Plastic High Energy Ga- Ray Telescope B. 1. The Construction of the Three Cherenkov Telescopes The first two gam ray telescopes built consisted of stacks of eight Cherenkov plastics, each with a 1/16 in. thick BaF, converter with an area of “”1“".(Figure II-6(a)) The BaF, crystal gives good time resolution (~ llOOps), adequate light output, and its relatively high atomic number 2 provides high pair conversion probability as described in the next section. 18 In order to collect the light from the crystal, the Bai’. crystal was enclosed in a 118M? tight box made of thin aluminum, painted in the inside with high reflectivity white paint(titanium dioxide) to achieve good light collection. Two 1.5" diameter photomultiplier tubes were mounted on the top and bottom of the box to collect the light. All eight elements of the two telescopes have the same active area of 9"x9", The thickness of the first element of the stack is 0.5", the second 1", and all the rest are 2". The Cherenkov counters are connected by tapered light guides to 2" diameter phototubes (Hamamatsu R329) poaitioned on top and bottom of each element. The phototubes of adjacent elements are staggered so that the detector elements are in contact, leaving only a very small air gap between them. The Cherenkov counter and the light guides are made in one piece using Bicron BC-HBO Cherenkov plastic, which is Lucite with waveshifter additive added. Each plastic element is polished carefully to obtain mximm internal reflection of the Cherenkov light. The third telescope (Figure II-6(b)) uses the same Bal’. converter as the first two. But instead of eight elements in the stack, there are thirteen 1" thick elements in the stack, which makes its total thickness comparable to that of the other two. The area of the elements, made of Bicron BC-HBO Cherenkov plastic, ranges from 6"x6" in the front element to 10"x10" in the back. The tapered light guides are made of ordinary Lucite, then attached to the Cherenkov plastic using optical glue. The same 2" phototubes are used, and they are again staggered to eliminate gaps between elements. To reduce the rate of cosmic ray muons, a major background in these experiments, the telescope is surrounded by anticoincidence shields on the 19 front, top and two sides. The anticoincidence shields used on the sides and top are 1/2" thick scintillator paddles, each connected by a tapered lightguide to a photomultiplier tube. The front anticoincidence shield is made of 1" thick Cherenkov plastic BC-HBO to avoid being overwhelmed by the high flux of low energy charged particles. But because Cherenkov plastic has a relatively lower light output than scintillators, two photo multiplier tubes are used on the front shield to ensure adequate light collection. The combination of these shields reduces the muon background rate to about 21 of the unshielded rate. The front anticoincidence shield also acts as a charged particle veto to eliminate fast charged particles such as fast protons and electrons. Neutron discrimination was done using the time-of-flight measurement. More detailed information on background elimination will be discussed in chapter III. The detectors, including their muon shields, were assembled on a cart, and could be moved easily during the experiments. This enabled us to cover all the angles with our limited number of Cherenkov telescopes. It also allowed cross-checking of the response of all three detectors by placing different detectors at the same position during successive runs. 8.2. Photon Pair Conversion Coefficient In the initial design of the detector and during the first experiment, the light output from the Bat". converter was not added to the total light output, i.e. the energy loss of the electron-positron pair in the converter was not taken into account. Thus, the choice for the thickness of the converter was a result of the compromise between high conversion efficiency 20 and low energy loss. (The energy lost in the converter was taken into account in all later experiments including those presented in this thesis) The conversion efficiency of the BaF, crystal is photon energy dependent. The efficiency was calculated from the pair production cross section [Mo 69]: Efficiency = t pn[oe(zBa+ZzF)+(oBa+oF)] (II-1) where t is the thickness of the converter 2F and 28a are the atomic numbers of F and Ba pn is the number density of the BaF, molecules within the crystal. 0e: 3.11o.log(ZEY/mec')-11.3 = 3.110.log(2k)-11.3 08a: Z§83.11o.log(2k)-8.On1 0F: 25 3.110.log(2k)-8.0fl7 where k is the Boltzman constant The thickness of all our converters are 0.25" (0.635 cm). The curve of the BaF, crystal conversion efficiency as a mnction of the photon energy is plotted in Figure II-7. For the photon energies we are interested in, it ranges from about 101 for photons having energies 20 Nov to over 201 for photons of 100 MeV. F Pair Production Efficiency (2) 21 30 1' I I I I 1 I 1 1 ‘I’ t I r ‘ I I 1 r y I 1 Y’ 1 r I - ~——_‘ IUUU 25 20 15 10 ITUUIUIIIIIIIIIITITIUUIII h lllllIIJIJILIllIIIIlIIII‘IIIA I I I J I I I I I I I I J l I I I I I I I I I l I I I I O 20 4O 60 80 100 120 Photon Energy (MeV) Figure II-7 Pair conversion efficiency of the BaF, converter as a function of photon energy. 22 3.3. Determination of the Photon Energy 8.3.1. Cherenkov Light Output Level Each member of the e+e' pair can have a kinetic energy ranging from O to EY-Zmec'. The electron and positron dissipate their energy mostly through ionization and radiation as they travel through the detector and eventually stop in different depths of the Cherenkov stack (Figure II-8) . Figure II-9 shows the range vs. energy relationship for electrons in the plastic. If we can determine the position where each member of the pair eventually stops, we then know its range and its kinetic energy. And by summing up the energy of the electron and the positron, we can obtain the energy of the original photon. The Cherenkov light generated by a relativistic electron (or positron) is roughly proportional to the distance the particle traveled within the medium. The Cherenkov light output is only about 11 of the typical light output from a NaI scintillator. The number of photons in the visible range generated by a particle of speed 8 in unit path length of a medium having an index of refraction n is given [Pa 86] by: - 9. __1_ a - N - c [1- 8,",121dv ~ 500 sin Gc/cm (II 2) where 9c: cos'1[§%] is the half angle of the Cherenkov cone. For singly charged particles, the Cherenkov light output level does not depend on the type of particle passing through the medium. We use the level of light output in each element produced by cosmic muons that pass through the entire Cherenkov stack from front to back to be the characteristic light “P -... ... - .- . 23 Figure II-B Principle of operation for the Cherenkov plastic telescope. Electron Range (on) an I I r l I Y I r [171 r' I _—“‘ 30— F 20F" )- noi- o I I I I '4 I I I I I I I LLL I.I I l I I I II 0 25 50 75 100 [25 Electron Energy (lieV) Figure 11-9 Electron energy-range relationship in Lucite. Counts 10000 8000 8000 4000 2000 25 . 2 0 m . O 0 g 5 — .... b J v- -1 " 1 o I i J 1 I I L 1 1 I l 1 1 l J I L 1 1 l 1 1 J J L L I 1 1 0 25 50 75 100 125 150 Electron Energy (MeV) Figure II-11 Electron energy loss in 1" thick Cherenkov plastic as a func- tion of energy. 28 the energy lost by an electron in the plastic does depend on the energy of the electron. A higher energy electron loses more energy per unit distance traveled than an electron of lower energy. Figure II-11 shows the energy losses of electrons of different energies when passing through a 1" thick Lucite (Cherenkov‘plastic). A 100 MeV electron, for example, loses about 12.1! MeV in passing through 1" of Cherenkov plastic, while an electron of 55 MeV loses about 9 MeV in traversing the same length. Therefore, a simple un- weighted sum of the light output from each element of the stack would not yield the correct energy of the electron-positron pair. He tried the un- weighted sm scheme and found it did not work as well as the weighted sum scheme. In order to take into account the nonlinearity of the electron energy loss in the stack, we plot in Figure II-12 the electron energy loss as a function of the range of the electron. This range vs. energy loss relationship is used to determine the proper weight for the different elements of the Cherenkov stack. The weight assignment of the individual elements are tabulated in table II-1 (for detector 1 and 2) and II-2 (detector 3). In the first column of the tables, the individual element of each Cherenkov stack are numbered from the front (right after the BaF, converter) to the back (see Figure II-8 for example of the numbering scheme). In the 2nd column, the thickness of the corresponding element (in cm) is listed. In column 3, we list the distance d from the back of that element to the front of the stack (behind the BaF, converter). Note that if an electron stops at the back edge of this element, we then know that the electron has a range equal to the distance d. And by making use of the electron range-energy 29 Table II-1 Electron energy loss in elements of detector 1 and 2. Element I Thickness Distance to Electron AE . Convertor Energy (em) (all) (MeV) (MeV) ' """ 1 127.27 """"" 2;; """"" 23;” 2 2.5“ 3 81 8.67 5.78 3 5.08 8.09 22.02 13.35 u 5.08 13.17 37.62 15.60 5 5.08 18.25 55.70 18.08 6 5.08 23.32 76.78 20.98 7 5.08 28.80 100.9 20.22 8 5.08 33.118 129.0 28.15 30 Table II-2 Electron energy loss in elements of detector 3. Element I Thickness Distance to Electron AE Convertor Energy (cm) (cm) (MeV) (MeV) " """ . """""" Q T; """"""" 2;? """"" £3; """"" .32“ 2 2.5“ 5.08 11.8“ 6.13 3 2.5“ 7.62 18.50 6.68 “ 2.5“ 10.16 25.70 7.20 5 2.5“ 12.70 33.60 7.89 6 2.5“ 15.2“ “1.98 8.38 7 2.5“ 17.78 51.0 9.05 8 2.5“ 20.32 60.75 9.75 9 2.5“ 22.86 71.2 10.23 10 2.5“ 25.“0 82.0 11.0“ 11 2.5“ 27.9“ 9“.28 12.28 12 2.5“ 30.“8 107.5 13.20 13 2.5“ 33.02 121.3 13.75 31 20 V 1 I I I r r T 1 l r f I l r 9 L 1 § 15— — v _ _‘ o g . o 1 2 - o 1 >s - o . a“ o ’5 10"" o -' g: .. o . m b o o a s - . . ‘s o o . 15 ' o 3 5r— .... m " -1 or. I I I I I I I I l l I I I I l L I L J 0 10 20 30 40 Electron Range (cm) , Figure II-12 Electron energy loss in 1” thick Cherenkov plastic vs. the range of the incident electron. 32 relationship (Figure II-9), we can then obtain the energy of the electron, which we put in colum “. In column 5, AB is obtained by subtracting the energy of an electron having a range of dn by the energy of an electron of range dn-1' This additional energy AE required for an electron to go pass element n-1 and reach the far edge of element n is the weight we assign to element n. Following is an example of how the energy of the photon is determined utilizing the tables: suppose a 98.7 MeV photon was converted into an electron of 76.68 MeV and a positron of 22.02 MeV in telescope #1. The 76.68 Hell electron will have a range of 23.32 cm and will stop at the back of Cherenkov element 66. In the ideal case where there is no statistical fluctuation, this electron produces one unit of light output in elements #1 through #6. Therefore, the energy of this electron can be obtained by sunning the AEs (column 6, table II-1) from elements 1 through 6: 3e: 2.89+5.78+13.35+15.60+18.08+20.98 = 76.68 Hell The 22.02 MeV positron has a range of 8.09 cm and stops at element #3. It will produce one unit of light in element #1 through #3. So, the energy of the positron can then be obtained by summing the A123 from elements 1 through 3: Ep: 2e89+5e78+130 35 = 22.02 MeV 33 Therefore, the energy of the original photon is: E + E 9 .2 II P 1(2.89+5.78+13.35+15.60+18.08+20.93)+(2.89+5.78+13.35)I [2 x (2.89+5.78+13.35) + 1 x (15.6+18.08+20.98)l 98.70 HeV This algorithm can also be understood the following way: since the electron and the positron both pass through elements #1 through #3, the pair produces two units of Cherenkov light in elements #1 through #3. But only the electron travels through element “1 through #6, it produces one unit of light in elements “, 5, and 6. In another words, the energy of the photon can be determined from the sum of the light outputs from all the elements L1, (in units of the characteristic light output of one electron passing through the same thickness L01) multiplied by the proper weight A3 of the corresponding elements. That is: 1.. E1 " I:i(LO)iM:i 1:! of elements (11-3) As illustrated in the above example, we obtain the correct energy of the photon using this algorithm. However, due to the small number of Cherenkov photons produced, there is a large statistical fluctuation of the light output level L in each element. The telescope was found to have only moderate energy resolution, i.e. ranging from about 101 FHHH at 20 Hell to 20$ at 80 MeV. 3“ ELECTRON COUNTER MAGETIC ARRAY SPECTROMET - - .e‘ MAIN BEAM .Er’ E. 'E.‘ Figure II-13 Schematic set-up of the University of Illinois tagged photon facility. 35 C. Calibration of the Cherenkov Plastic Telescope Detector The calibration of the Cherenkov plastic telescope was done at the tagged photon facility at the University of Illinois. The schematic setup of the facility is shown in Figure II-13. Bremsstrahlung photons were produced by electron beams bombarding a thin 25 um aluminium foil. The primary electron beam that did not interact in the foil was bent into a beam dump. Electrons which interacted in the foil and generated bremsstrahlung photons were bent through 180' and detected in a 32 element scintillator counter array. The detector energy was determined by the position of the scintillator counter. By requiring a coincidence between the the photon detector and the electron counter, we then know the energy of the "tagged" bremsstrahlung photon by energy conservation. Four electron beam of energies 99. 77, 56 and 35 Hell were used, providing tagged photons ranging in energy from 7“ to 82 Hell, 53 to 61 MeV, 37 to “3 MeV, and 17 to 23 MeV respectively. One of the eight-element Cherenkov telescopes was taken to the calibration site. C.1. Calibration of the Detector Efficiency The absolute efficiency of the Cherenkov telescope was obtained by comparing the efficiency of our detector relative to a large Hal detector provided by the University of Illinois. The Hal crystal, 30 cm diameter and 36 cm deep, was assumed to be close to 100$ efficient when illuminated by a collimated beam to the center. He define R as the ratio of the number of photon detector-tagged electron counter coincidences to the number of times the tagged electron 36 counter fired. The ratio R is also the product of the detector efficiency 6 d et and the efficiency of the magnetic 398°13'00“” 53p“ Y-e - Ne ' Edetespec R: By measuring the ratio R for both the Hal and the Cherenkov telescope under identical geometrical configuration, it is possible to determine the efficiency of the Cherenkov telescope relative to the large HaI detector. ECherenkov _ RCherenkov eHaI ' RHaI The magnetic spectrometer efficiency 2 was found to be dependent on the spec energy of the electron beam, varying from about 30$ for the 35 MeV beam to 60$ for the 99 Hell beam. Therefore, it was necessary to measure R for each beam energy. Since the efficiency of the large HaI detector were assumed to be 100$ efficient, the relative efficiency we obtained were then assumed to be the absolute efficiency. Figure II-l“ shows the efficiency of the Cherenkov telescope as a function of the photon energy. The efficiency varies from about 10$ for 20 MeV photons to about 20$ for photons of 80 MeV. The error bar on the data reflects mainly the uncertainty in the efficiency of the tagged electron counter. Also shown for comparison are the calculated efficiency from pair production discussed in section 8.2. (formula II-1), and a calculation using the Stanford electron-photon shower code EGS“ [He 85]. The two calculations are in agreement with the measurement within the uncertainty. 37 40 r r v . 1 r r I v 1 r . u . 1 . . . . 1 r : 0 Calibration Data 1 30 _ -—- EGS4 Calculation ‘ . --- Original Eff. Calculations 1 Efficiency (7.) no 0 l I I l I I I I 1 1 B—t 1 1 1 1 1 t—-B—-1 1 1 1 1 1 "' 1 10 §’ —1 . 1 3 1 on..1 “1.31 .I....1 o 20 4o 60 so 100 Figure II-l“ Efficiency of the Cherenkov telescope as a energy. function of photon 38 C.2. Calibration of the Energy Response of the Detector By energy conservation, the energy of the photon plus the energy of the secondary electron reaching the electron counter array equals the energy of the incident electron. By requiring a coincidence between the firing of the photon detector and the electron counter, we can then know the energy of the "tagged” bremsstrahlung photon. Each element of the 32 scintillator has a momentum bite of about 1.25$. This corresponds to a energy span of approximately 0.2 Hell at 20 MeV. The response of the photon detector was measured by taking photons corresponding to the firing of 10 adjacent tagged electron counters, which corresponds to a energy span of about 2 MeV. The response of the Cherenkov game ray telescope for the 22, “2, 60 and 80 MeV tagged photons is shown in Figure II-15. The energies corresponding to the peak location of the response functions are found to be systematically lower than the known tagged photon energies EY by about 7 Hell. Figure II-16 shows the peak energy of the detector response function vs. the energy of the tagged photons. The dashed line represents the correct response. The response of the gama ray telescope lies approximately 7 Hell below the dashed line. Before the calibration, only the light outputs from the elements of the Cherenkov plastic stack were sumed to obtain the photon energy, the energy loss of the e‘e' pair within the Bat“, converter were not taken into account. This neglect of the energy loss of the pair within the converter was found to be responsible for the systematic shift of the peak energy in the telescope response function. To include the light output from the converter in the sum, the photon energy is now calculated using a modified formula II-3: lcufcounts Figure II-15 Response function of the Cherenkov telescope at 22, “2, 60, and 3000 2000 1000 1500 1000 500 o 25 5o 75 100 125 25 5 75 100 125 "'r'lf"'l'f*'1f"'I'val ' "IWI 1 fl L. : t,=-22 uev 37:42 wev 4‘ P 1 L 3 :- 3 ; 2,-60 IIeV 2,-30 IfeV 1 I. 71 E 3 ’ 1--..LJI i--1....1..-.|..i.l. ? o 25 5o ‘ 75 100 125 o 25 5o 75 100 125 39 80 MeV without including light output from the BaF, converter. RECONSTRUCTED ENERGY (MEN) 2000 1000 500 1258 1000 750 500 250 “0 loo 1 T T I r T I r I V I I v I r I I V l' I I V V 9 X1 A D No Converter ,” I 3 3° 0 Converter ,I" "j 3 1’ D J v I a h ,I 1 2 60 ’0’ -j a U : j 0’ J .D 40 IIIU ‘ 3 1 .° 20 x; 7.. o{...minglinmwuluu.‘ 0 20 40 60 80 100 E, (MeV) Figure II-16 Energies of the peak of the response function vs. energies of the tagged photon. “1 57 = zi(%-5)1AE1 1:! of elements Here the total number of elements is n+1 in order to take into account the energy losses of the electron and positron in the converter. The peak energies of the new response functions that include the light output from the converter are also plotted in Figure Il-16 (diamonds). He found the peak energies of the new response function now lies on the correct response line. In Figure II-17, the new response functions that include the converter light outputs are plotted (solid line histograms) in comparison with the response function without the converter light outputs (dashed lines). He found that including the converter light output not only shifted the peak of the response function to correct energy, it also improves the energy resolution of the detector at lower energy. He plotted, in Figure lI-18, the full width at half maximum of the response functions of the Cherenkov plastic telescope using the two different algorithm, for all four energies. The improvement at lower gamma ray energy are considerable. D. Caparison with Other Detectors In Figure II-19, we compare the response function of our Cherenkov telescope with that of the Hal telescope used by the Bertholet et. al. He can see that scintillator type detector has a better resolution at higher energy (EY Z 80). He also plotted the FHHH of the MSU Cherenkov telescope in comparison with that of the other type of detectors in Figure II-20. At energies below 60 MeV, the resolution of the lead glass detector are much “2 0 25 50 ‘75 100 120 25 50 7 100125 *"'I""I"" '7' 1 . - I T—7 I r 1 11' i " .. 5:0 4000 1‘ j . -~ 0 1 2,-22 Hell 5 2.,a42 MeV q 2000 3000 1 i 1 i i 1 1 1500 2000 a m m :' 1 3 3 1000 .1 1... {I 1.. _: 500 g I KL 0. ‘s 1 3 2008 . : ° .5 ...: , - 1250 =- 1500 .-" 2‘ 2,-50 mv .3 1000 ' l 3 1000 5' 1 1 750 '1 -: 500 500 j a 3 g g 1 250 l/ “‘ 0 .'. - ill--l-ii-i‘ JUUIUJIIUHI . 0 25 50 75 1001250 25 50 75 100125 RECONSTRUCTED ENERGY (MEV) Figure II-17 Response function of the Cherenkov telescope with the light output from the converter taken into account. n3 IzoftrrTViitlrerTTTvr’Iv I'U‘ 100 :_ C! No Converter _ I 0 Converter 1 R: 30 :" ‘1 2 60 :— D _: :1: : C! U 1 E. = o 4 40 T o o '3. I o 1 20 E- ‘3 0'1.1L1.L¥.L...L1L.LLL. J 0 . 20 40 60 80 10 E,(MeV) Figure “-18 NH)! of the response functions of the Cherenkov telescope with and without taking into account the converter light output. RELATIVE PROBABILITY Mt 0.10 T f 1 V ' 1 T I l 0.00 - 22,-=42 uzv 2,260 usv ; 7 Duh : USU 4 0.08 b ' o : B olet et.al. +- A L 0.04 0.02 0.00 “ ‘ 0 25 50 75 100 125 20 4O 60 80 ENERGYOAEV) Figure II-19 Response functions of the Grenoble NaI telescope in comparison with the MSU Cherenkov telescope [Be 87]. '45 120 I I I I I I I I I I I I l I r11 I I I I I I I 1 - I I I l I . 100 -- e 1130 .L - ° 0 Lead Glass : : D 3‘7: ‘ 80 — 0 N01 telescope _ " 0 «4 E P o 2 60 — _-1 I 0 j P o q -— " o " 40 _ g. a. -1 p 0 a < . g g . I- o 0 q 20 - ... o I. l l 1 l I l L l L I L l l J I I 4 l L I p l l J I l 1 1 I ‘ 0 20 40 60 80 100 120 E, (MeV) Figure II-20 The FHHH of different type of detectors used in high energy photon measurements . '46 worse than all the other types of detector, while the resolution of the scintillator detectors and the Cherenkov telescope are comparable. B. SI—ry Many different detectors have been used to measure the bremsstrahlung photon production cross section in intermediate energy heavy ion reactions. The majority of these detectors are shower type detectors such as NaI, BaF. or lead glass. He have designed and built three non-shower type gamma ray detectors based on the Cherenkov process. The original concept of the Cherenkov telescope was to first convert photons into e‘e' pairs in the BaF, converter. Then by determining the range of the electron and positron, the energies of the e’e' pair would be determined, so would the energy of the original photon. However, due to the small number of photons produced, the statistical fluctuations made the reliable determination of the electron and positron range impossible. Different algorithm were then tried, and the position weighted sum of the light outputs from all the elements of the stack was adopted to calculate the energy of the photon. The Cherenkov telescope was calibrated in the tagged photon facility in the University of Illinois. The absolute efficiency of the telescope was found to range from roughly 10$ for photons of 20 MeV to about 201 at 80 MeV. This is consistent with calculations both from pair production cross section and from the Stanford electron-photon shower code E0311. The energy response of the telescope was first found to have a systematic shift towards lower energy. The cause was due to the neglect of the energy loss within the converter. When the light output of the converter 117 was later included in the summation scheme, the peak location of the response functions agree with the known energy of the tagged photons. The inclusion of the converter light output also improves the energy resolution of the telescope considerably at low energy. He found the energy resolution of the Cherenkov telescope worse than scintillator detectors while better than that of the lead glass. CHAPTER 3 EXPERIMENTAL SET-UPS AND DATA REDUCTION A. Experimental Set-ups A.1. Detector Lay-outs Two high energy gamma ray experiments using the Cherenkov plastic telescopes were carried out at the National Superconducting Cyclotron Lab: 1) the light-ion induced gama ray production using 25 MeV/nucleon ‘He, 53 MeV/nucleon ‘H and ‘He beams on C, Zn and Pb targets; and 2) the symetric system experiment using 30 MeV/nucleon ’Li, “Ne and ”Ar beams on Pb target and targets having similar atomic mass. The experiment layout is shown in Figure III-1. Three telescope detectors were used to cover the angular range from 300 to 150° in 30° intervals. The first detector (01) covers the more forward angles of 30°, 60° and 90°. The second detector (02) was used for the backward angles: 90°, 120° and 150°. The third detector (113) (the 13 element telescope) was positioned on the other side of the beamline covering angles of 60°, 90° and 1200 (Figure III-1). This set-up enables extensive cross-checking of the relative efficiency of the three detectors. All detectors are positioned 50 cm from the target. At this distance, each telescope subtends a solid angle of 110 msr. One graphite absorber of 1" thickness was put between the target and each of the detectors to reduce the rate of charged particles, which would otherwise saturate the front anticoincidence shield of the telescopes. tor 1 Detector 2 ME: .. 00‘ Detector 3 Figure III-1 Layout of the experimental area. 50 At laboratory angles of 60° and 120', there are data from two detectors, while at 90', data from all three detectors are available. This extensive cross-checking of the response of the three detectors indicated the systematic differences in the cross section measurements by the different detectors were less than 101. Therefore, the average of data from different detectors at same laboratory angle were used to gain better statistics. A.2. Electronics Figure III-2 shows the master trigger used in the experiment. A three fold coincidence is required to fire the master trigger: a signal from one the two photomultiplier tubes of the converter, and from the first two elements of the Cherenkov stack. when the the master trigger is fired and the computer "not busy" condition was also satisfied, the pulse height and the time of the pulse from each phototube of all the Cherenkov plastic elements of the stack and the anticoincidence shields of that telescope were then recorded. Figure III-3 shows the general electronic circuitry. In earlier experiments, all six phototubes (two from the converter, two from the first element and two from the second element of the Cherenkov stack) were required to fire together to trigger an event. But we later found that requiring the coincidence firing of only one of the two phototubes from each of the trigger elements achieves a better compromise between noise rejection and detector efficiency. The minimum photon energy the detectors are able to measure at this configuration are determined by the requirement that at least one member of the electron-positron pair reaches the second Cherenkov element. This corresponds to an energy 51 coma comes D can m can on D an ' > “0 #3132- cxs w u" .. b "'" Figure II I-2 Electronic schematic of the master trigger logic. 52 HIGH VOLTAGE pm ”1" r—I fie}??? cro El ...... VA *1... 1 11_ 75° :w... 11:... TDC :H 1—4 Figure III-3 Electronic schematics of the detectors. 53 threshold of approximately 10 MeV. The cyclotron RF timing with respect to the master gate was also recorded. This crucial information was necessary for neutron discrimination. B. Background Suppression 3.1. Suppression 0f Energetic Neutrons One of the major sources of background in the measurement of high energy gamma ray from intermediate energy nuclear reactions is the large number of energetic neutrons produced in the reaction. Unlike charge particles which can be vetoed by the front anticoincidence shield of the telescope, neutron discrimination was done by the time-of-flight (TOP) method. I The spectrum of the timing of the master gate with respect to the RF signal of the cyclotron is shown in Figure III-11. The slower moving neutrons show up as a "bump" at a later time than the sharp time peak of the gamma rays. By gating on the peak of the fast moving gama rays, we were able to greatly reduce the background of slower moving neutrons. Figure III-5 shows the comparison of the energy spectra with and without the time-of-flight gate. In addition to a significant reduction of the background neutrons, the TOP gate also eliminates a large fraction of the random events produced by cosmic ray muons which do not have the correct timing with respect to the RF of the cyclotron. 8.2. Suppression of Cosmic Ray mans Another important background for high energy gama ray measurements is cosmic ray mons. The muon rate can be significantly reduced by applying the 511 250 q q 1 200 Neutrons 1 l of Counts 100 p 1.. P 150 — 1- 1..— L p 50 1—- 1- q d“ m.- 00"] b l L I l l I l I p l l l I L i 50 75 100 Figure III-ll A typical time spectrum of the ganma rays. 55 500-TIIII—fITIrrIIIIYTIIrvlfirvrI—r 100 Without TOE gate 50 5 I. i of Counts ... 100 - 50 1 With TOF gate 10 1 J.,..l....l.... .. .Dknd Figure III-S Comparison of photon spectra with and without TOF gate. 56 TOF gates. However, because of the very small production cross section of germs rays at high energy, the cosmic ray muon rate during the "beam on" period can still be significant. Therefore, it is in general necessary to employ the anticoincidence shields. Each detector is surrounded by anticoincidence shields on the front, top and both sides. The suppression of the cosmic ray muon background was done during off- line analysis. An event is accepted only when no signal was present in any one of the anticoincidence shields. The anticoincidence shields alone were found to be able to reduce the muon background rate to approximately 21 of the unshielded rate. Figure III-5 shows a comparison of the photon energy spectrum with and without the anticoincidence shield. The reduction of muon back ground was most important in the high energy tail of the photon spectrum. The final photon spectra were then obtained by combining both the anticoincidence conditions and the TOF to eliminate the cosmic ray unions and the fast neutrons. C. Su-ary Three Cherenkov plastic telescopes were used to cover laboratory angles of 30", 60“, 90', 120' and 150°. Extensive cross checking on the relative efficiency of the three detectors was done, and the systematic differences were found to be less than 101. Therefore, data collected with different detectors at the same laboratory angles were averaged to obtain better statistics. When an electron or positron from the e+e' pair passed through the BaF. converter and reached the second Cherenkov plastic element, the master gate 57 I I I I I T T I ' l l I I I I I I I I I r T I I I r 1500'l 100 Without anti-p. gate 50 I of Counts 100 With Anti-u gate 50 10 5 1 1....J....J...l.flfl[|‘llq.[llflfifll.. Figure III-6 Comparison of photon spectra with and without anti-u shields. 58 was fired. Signals from all the elements of the Cherenkov plastic stack and from the anticoincidence shields of that detector were recorded. The corresponding minimum photon energy is about 10 MeV. Charge particles from the target area were vetoed by the front Cherenkov plastic anticoincidence shield. The cyclotron RF timing with respect to the master gate was used to discriminate against energetic neutrons. An anticoincidence shield around each telescope was able to reduce cosmic ray muons rate to about 21 of the unshielded rate. The photon energy spectra were obtained by combining the TOF gate and anticoincidence gate to eliminate all the backgrounds. Chapter A HIGH ENERGY GAMMA RAY PRODUCTION FRO! LIGHT ION INDUCED REACTIONS A. Introductim A.1. History: The Measurements of High My 0. Days The production of high energy gama rays in intermediate energy heavy- ion reactions was discovered in 19811 independently by groups at 081 and 1480. Here at MSU, Beard et al. [Be 85], while studying subthreshold charged pion production, encountered a large background of quite energetic electrons and positrons, which they later attributed to the pair conversion of high energy gamma rays. At about the same time, Grosse et al. [Gr 85] were studying neutral pion production by detecting the two photons coming from the I. in coincidence using lead-glass detector when they, too, observed large yields of single photons. Since then, a large nunber of experiments has been done to study the characteristics of these high energy gamma rays. These experiments can be categorized as either inclusive or exclusive high energy gamma ray measurements. A large amount of work had been done to measure the inclusive photon production cross section. For example, Kwoto et al. [Kw 86] measured gama 110 rays produced in 30 MeV/nucleon Ar + Au reaction, as well as from 1111 60 MeV/nucleon 86Kr beam on C, Ag, and Au targets. Our MSU group also conducted a systematic study [St 86] using “’11 beam of 20, 30 and ‘10 MeV/nucleon on C, Zn and Pb targets. Host of the measurements found the following major characteristics of the high energy photons from heavy-ion induced reactions: exponentially decreasing energy spectra with slope parameters which depend only weakly on projectile and target size; and slightly forward peaked angular distributions in the laboratory frame which can readily be transformed into a near isotropic or slightly dipolar angular distribution in the nucleon-nucleon center-of-mass frame. A few exclusive measurements have also been carried out by several groups to obtain a more detailed understanding of the production mechanism. Hingmann et al. [Hi 87], for example, studied photons produced in the 110 158 reaction Ar + Gd at E/A=|1|1 MeV in coincidence with reaction products that carry impact parameter information. Lampis et al. of the MSU group [La 88] studied the production of the high energy photons in coincidence with light charged particles in the reaction of 30 MeV/nucleon ”N + Pb. More coincidence measurements have been done recently to investigate the relationship between gamma multiplicity and the degree of violence of the reactions [Kw 88b], [He 87]. The mjority of the high energy gama ray experiments involve heavy-ion projectiles (A Z 12) to study photons coming from nucleus-nucleus P collisions. Few studies have been done on light-ion induced photon productions. Recently, results have become available [Kw 88a] [P1 88] for proton beams of 72, 168 and 200 MeV bombarding various targets. The characteristics of the high energy photons produced in proton induced reactions share the basic features of the heavy-ion reactions, though there 61 are some differences. One such difference is that, in heavy ion induced reactions, although it is possible to observe photons having energies up to 2 to 3 time the beam energy/nucleon, the photon energy accounts for only a small fraction of the total available energy. In proton induced reactions, photons are observed to have energies up to all of the total energy available. This difference is attributed to the absence of Fermi motion and Pauli blocking in the proton projectile, which also makes detailed comparison with nucleus-nucleus results difficult. Therefore, light-ion induced photon production is interesting in order to bridge the gap between heavy-ion and proton induced high energy photon production. As in the proton case, the photon energies are comparable to the total energy available in the system. On the other hand, it also resembles the heavy-ion reactions in that the Fermi motion in the projectile can also be important in determining the spectrum. A.2. Theoretical models thny theoretical models have been proposed for the high energy photon production mechanism. Most of the models are based on one of the three basic approaches: nucleus-nucleus bremsstrahlung, nucleon-nucleon bremsstrahlung, and statistical emission. In an early model, Vasak et al. [Va 85] assume a collective nucleus- nucleus bremsstrahlung production mechanism, in which the gem rays are thought to be produced early in the collision by the coherent bremsstrahlung of the projectile and the target nucleus. The model predicts a quadrupolar angular distribution in the center-of-mass frame, and a 22 dependence of the photon cross section. Most of the experimental data, as mentioned before, 62 points to the direction of a more isotropic angular distribution in the center-of-mass frame. However, as Herrmann et al. [He 811] point out, the angular distribution, when integrated over impact parameter, can be quite different from purely quadrupolar. Thus the angular distribution alone is not sufficient to judge the validity of this approach. In the next chapter, measurements of gamma rays produced in near symmetric systems of progressively larger masses will be compared with the z dependence of the photon yield predicted by the model. Most of the recent theoretical models of high-energy gamma ray production are based on a microscopic production mechanin, i.e. incoherent bremsstrahlung from individual nucleon-nucleon collisions within the colliding nuclei [Ba 86a] [Ba 86b] [Na 86] [Ne 87] [Ni 85] [Re 87]. The proton-proton bremsstrahlung is a quadrupole like process and its contribution are an order of magnitude smaller than the dipole like neutron- proton bremsstrahlung process[Ni 85]. Therefore, many nucleon-nucleon bremsstrahlung models attribute the production of the high energy photons to bremsstrahlung from first chance neutron-proton collisions early in the reaction. These models all predict the angular distribution in the nucleon- nucleon center-of-mass frame to be nearly isotropic or slightly dipolar, which is in good agreement with experimental observations. In a third approach, the high energy photons are believed to come from the recoiling hot compound system in the later stage of the reaction. In this approach, the photons are produced by the bremsstrahlung of individual neutron-proton collisions within the hot zone [Ni 85] [Ne 87], or by the statistical emission from the hot zone [Pr 86] [Bo 88]. Since the photons are emitted from an equilibrated stage and the temperature of the hot zone 63 is governed by the total energy injected into the system, the relevant parameter in this model should be the total beam energy. In the light-ion induced reactions I will describe in the remaining of this chapter, we hope to be able to distinguish the first-chance n-p bremsstrahlung from the thermal approaches . A.3. The Light-ion Induced Photon Production Experiment In this experiment, we studied the reactions induced by three light-ion beams: 53 MeV/nucleon ”He and 2H, and “He at E/A=25 MeV. This combination not only enables us to study gama ray productions from "He and 2H at the same energy/nucleon, but the 25 MeV/nucleon “He and the 53 MeV/nucleon 2H beams also allows us to compare their high energy gama ray productions at about the same total energy ”Total" 100 MeV). These comparisons should give us some insight regarding whether the photon production mechanism is first chance nucleon-nucleon collision. In that case the spectrum from the 53 MeV/nucleonZH and “He beam at same energy/nucleon would be similar and differ by only a constant factor in yield. If the photons are produced by the multiple scattering within a recoiling 'fireball' whose characteristic only depends on the total energy of the hot zone, photons produced by 53 MeV/nucleon 2H and 25 MeV/nucleon “He would have the same characteristic. The same three targets: 0.25m thick 0, 0.05m Zn and 0.025m Pb were used for all three beams. B. Experiment Results 3.1. Photon Energy Spectra 611 Energy spectra of high energy gama rays taken at 30°, 60°, 90°, 120° and 150° for the three beams on three targets are shown in Figure IV-1 to IV-9. The spectra can be separated into two regions, EY< 25 MeV and BY) 25 MeV. In the low energy region of EY( 25 MeV, the spectra are exponentially decreasing, with slopes typically ranging between 2-3 MeV. This region includes photons coming from the giant dipole resonance, from statistical decay of excited target fragments, as well as from bremsstrahlung photons [St 86]. The energy spectra in the high energy region (E7) 25 MeV) are also exponentially decreasing with increasing energy, but with much flatter slopes, ranging from 8 to 13 MeV. Photons in this energy region are believed to be predominately products of nucleon-nucleon bremsstrahlung, and are the primary interest in this thesis. For the 53 MeV/nucleon °H induced reactions, the photon energy spectra from the three targets all extend to almost 100 MeV, which is close to the total energy available. In the case of °He induced reactions, the endpoint of gama ray energy spectra are approximately 70 MeV for the 25 MeV/nucleon beam or nearly 3/11 of the total energy available, while it is 110 MeV for the 53 MeV/nucleon beam, which is slightly over half the available energy from the projectile. So the light-ion induced reactions share one of the features of proton induced reactions in that photons of energies up to a large fraction of the available energy were observed in all the systems we studied . 8.2. Angular Dependence As can be seen from the Figures IV—1 to IV-9, energy spectra observed at different laboratory angles have slightly different slope parameters. The da/dOdE (mb/MeV-sr) I I I I r l I I r r r r l— l I _ t; 111/11:25 MeV : :3: 11130 . o X ’e‘lr + e 90' IO0 "' . ‘5‘. ‘H. Pb * 120° 2 .l '— _ 0 150' x .01 (lab frame) 10"3 — __ .. _ 1 10-9 L L l L I JLL L L I L L l l I L L L l L l L L LL ; O 20 4O 60 80 100 E7 (MeV) Figure IV-I Photon energy spectra for 25 MeV/nucleon I‘l-ie + Pb at laboratory I O I I O anglesof 30,60,90,120 and150. da/dfldE (mb/MeV-sr) 66 3 10 I I I I I I I I I I I I I I I r I I 1 [fi— I I _ . E/A=25 MeV . 33° x180 . O O ‘ x . 90. 100 "’ 5“. ‘He-an : 120° x .1" _ .. " ° 150' x .01‘ e \ 32,: (lab frame) .. ‘3; 0.. ‘13: 10-3 ‘2; er“... I!!! I I I O.%\‘...... I!!! n b \x"-. ’ I . .. 8331‘ I I I E 8 £21- 10‘6 - ‘1 II — Iiif 10-9 ,4 ,1 L. I L I 11 1 I. 20 4O 60 80 l-< E7 (MeV) Figure 111-2 Photon energy spectra for 25 HeV/nucleon O l O O 0 anglesof30,60,90,120 and150. II He 4- Zn at laboratory da/deE (mb/MeV-sr) 61 P I I I I I I I I I I I I I I I I I I l I l I I d P E/A=25 MeV - 30' 2100 . 0 60' :10 ‘ 100 _ .. ‘He-I-C - 909 \ * 120' x .1— . ... .. . 150° x .oxq . 0‘. 1‘ (lab frame) 10":3 '— *"*\\.‘.:zgutx —: e; .....‘ II ' ’o.“.. Co... .333 I I I I q . ‘1‘“.5". 00.. ' I I . 6 .. . ’e. .1... ‘21, - 10- _ x- 8‘32- I I' I fl 3:3 all ‘ i . I I. .. .. - 1111“,! .t i z I I I ‘ _ “ _ J __9 ._ I I I :. - 10 “..,.IL.L1..11..L.I.. “ O 20 4O 60 80 1‘ J E, (MeV) Figure IV-3 Photon energy spectra for 25 MeV/nucleon ”He + c at laboratory 0 l I O I angleeof 30.60.90.120and150. da/dfldE (mb/MeV—sr) 68 3 10 r I I I I T ‘ I I I r I r l I I r I I I I I r {—1 I T I c ‘z. E: A=53 MeV - 30' 100 ’ .‘E. / 2H Pb . 60':10 o + ' 90. 100 _ “\‘- * 120° 3: .1 d . .\ “-5-... - 150- x .01 j . 45%; ...”. ”‘32:: t x x (lab frame) ‘0 _3 ‘ a .. ... C i I I 10 — ‘3» " "o ' l ‘ O. \ .... I . x -~ "' ' I i I i ...- 3 I i 1 _ x‘n *‘5' ' 1 I 4 911.1! t :- 2 : I If 10-6 _ - .2! I - - I I — . 11: f I 10..9 J l l g. 1 l L; ' ' O 20 4O 60 80 100 - EL, (MeV) Figure 1V4 Photon energy spectra for 53 MeV/nucleon 2!! + Pb at laboratory 0 O I O I anglooo! 30.60.90.120 3116150. da/deE (mb/MeV—sr) P r u I I I r 1 fl r I I . T I r I If[ I I V VI 1 T ' ' d _ ... . E/A=53 MeV . so- at 100 - 2H ' Z : 63: x 10 100 L- H\ 1. n ' lZO'x.1 ‘1 _ .... ' 150' x .01 j . }.§.~::~8,‘ ‘ (lob frame) * T: o... 3 z 10-3 -— \' .... . . I x I _‘ ..O\. ......” . t 3 i if e ' \.."'- "... £1; 2- ‘ .. ... ....“ . I g i 1 .8 ' n I 10-6 L. .‘h'l! '31: I! “'3'-..“ In! E E i :1 |- ? O . 2' .. " " - 1 I - .. Id- " .. I T 10_9 _ ;. .... I L | i . - - O 20 40 60 80 100 o E7 (MeV) Figure “-5 Photon energy spectra for 53 MeV/nucleon 2!! + Zn at laboratory 0 O 0 angle: or 30 , 60 . 9o , 120' and 150'. dU/deE (mb/MeV—sr) .ffI I I I I I I I I I I I I l I I rl I I I I i " _ B/A=53 MeV ; 33: x {30 3 O __ 2H-I-C ' 0.2: 10 K5. r120'x.1 "" . K e lSO'X-Ol J - (lab frame) 3 ”WM 8' 4 10 — \ .....:3xx _ _ \E mm... ’..f’-Zz_- ' 'J _ - a‘-.. "xii . 10-6 -- ‘5”... ‘5.-- .‘I' If _ . I - '3‘— '1 II! '3' :Z_ I‘- - p I]! 12:? ' 3 - ‘_ 3 10"9 - fin - I l .3 -l I o 20 4O 60 80 100 - E37 (MeV) Figure “-6 Photon energy spectra for 53 MeV/nucleon 2!! + C at laboratory 0 O O l 0 angle: of 30 , 60 , 90 , 120 and 150 . do/dOdE (mb/MeV-sr) 71 3 10 r I r I ‘ I F I I [ ' ‘ ' ‘ I r r i I I II 3 ' '2. E A=53MV J: .. ...: / e . SO‘xIOO 5 0, .=_ ‘He-I-Pb 0 60'x10 7 ‘3 _- 1; II 90’ 10 ‘t K... I120°x.1 “ _ .. “an,“ . Iso°xm 3:. ~ :8: (hbftme) .- A ...... tilt}? .. O .8 ‘5 ...- 10-3 _ 33‘ “a." '3 ‘IIII “'4 .- ' ”I _ 5 .' I I - - .fi'; -' "11' If: . 3‘: 11" -§E-- -- 1 10-6 I—— -.EII;:; 111,1: _ ..+.- 1. ....l . . . I , I - : O 25 50 75 100 E37 (MeV) Figure III-1 Photon energy spectra for 53 HsV/nuoleon I'l-le + Pb at laboratory I I O O O anglesot 30.60.90.120 andISO. da/deE (mb/MeV-sr) 72 3 10 r I I I I I I I I I I I I I I I I I I I I I I . . E/A=53 MeV . 30. x 100 ' 7&- 'HeI-Zn 0 60' x10 . ‘3 - so- 100 "' ’. ‘X I iZO'x.1 “ ‘ 150° 2: .01 ' ‘t “as... (lab frame) ' ‘3;:\‘¢~.- :8 ‘3: :- ~o. I I 10-3 _ k. ”k ...3' i! _ K "I. ......o ‘1 ‘ I b ‘ . .X- .. 3 g I I E ‘ '.""- '3 l I. ‘l" ...8': IIIIEE 10"6 - 1315111“! 1’32_£2 :5— EIZEI ‘ 3“ L 1 1 L i A l I ' L l ’ ' 1 4L ' 0 25 50 75 100 2'3 13., (MeV) Figure III-8 Photon energy spectra for 53 MeV/nucleon I'fle + 2n at laboratory 0 O O I O angles of 30.60.90.120 and 150. da/dOdE '(mb/MeV-sr) 3 lo I I I I I I I r I [ I l I I l I I I I I I l I [I _ E/A=53 MeV . 30°: 100 4 " ‘H c 33310 100 “- ‘92-; 3+ I 120'x.1 "* _ o 1:. '150'x.Ol 1 \\ (labframe) 10-3 __ %\\-~...3xxtxxx . _ . ‘0. ."'¢ I .I x ‘5- “ ...: v ‘. .- \.\~ ...... II;;;; ‘ -6 _ . .....- ..'l' -::_ 10 I . '3 I. _ 't' 1:! 2 ll!:. ; .. 1111: 2.. -:£- . IIIIII ff1-_: 10‘9—1...I..1.l.;.l LII. 4 0 25 50 75 100 1:: E7 (MeV) Figure III-9 Photon energy spectra for 53 MeV/nucleon angles or 30', 60'; 90', 120' and 150'. ”He + C at laboratory 7n larger the angle, the steeper the slopes. The angular distributions for a photon energy above 30 MeV (Figure IV-10) are typically forward peaked in the laboratory frame. These can be indications of photon emission from a recoiling source. The relationship between spectra at an angle 98 in a source frame moving with velocity 8 with respect to the lab (‘1 dgdg B Is ) d’oge,82 and the observed laboratory spectra at angle elab ( dEdO llab) is as follows [Gr 85]: - , -1/2 Es - ElabY(1 - B cosGlab), where Y - ( 1-8 ) ”ines‘ Sinelab Y(1-B;ose S lab d 'o§9,Ez _ d'oge,82 _ _ d'oge,az _ dEdO s' dEdO lab Y“ em“) " dEdO lab (33’ slab) (1" 1) The velocities of the moving source can be extracted from the two dimensional contour rapidity plots [Gr 85]. The rapidity y, of a particle moving with velocity 8 in direction 0 in 1_+___BcosG]:%1+B] a certain reference frame, is defined as y = g- In [1'T""'— Boos 6 1 _ B I! ln[ in that frame. If, in the laboratory frame, the rapidity of a particle with velocity 8" is y", then viewed in a frame moving with velocity 8 with respect to the lab frame, the same particle will have a different velocity 8' and rapidity y' . The relation between the parallel components of the II I , three velocities B, B', and 8" is known [Ja 00] as B = H57. Then the additive property of the rapidity can be shown in the following: da/dw (mb/sr) 10“ 10'? 10'3 10“ 75 Angular distribution in lab frame for E,>30 MeV E a (25 MeV/A) " I 1» - X Pb x 2 x I "‘ x 3 P 'I' 211 X " . ‘ X .41 . ’ C .p I -Ir y l i- Ei 1' " e “j I x x 'l' + + 3 h- ? - .. * X +. * ‘ _ ' '1' -l- + + , ‘ 'l' + . . :- a (53 MeV IA) ‘1 E , x PbicE 3 : . d (25 MeV/A) .. ; ..+ " ‘ Pb X 2 . C _ . + {- Zn ‘ + + C 30 60 90 120 150 30 60 90 120 150 30 60 90 120 EC 9'1“ Figure Ill-10 Integrated angular distributions for photon energies above 30 MeV in the laboratory frame. 76 1 + §_Z_§L 1 + B 1 1 + 88' y": 21n(1—) = 2 ln( 1 _ B + B' ) 1 + 88' I —ln( 1 + 3) 18+ 8' ) =_1M1 + B _) —1n(1 + B _) i.e. y": y + y' To utilize the rapidity plot to determine the source velocity, we have to express the photon double differential cross section in a Lorentz invariant form. The relationship between the photon invariant cross section and the experimental cross section is [83 65]: do do do _d_o d‘p = (1/E)d’p ' (1/E)p’dpd0 p d-—Ed0 Figure IV-11 is a typical example of a contour plot of the photon invariant cross section versus the rapidity and the transverse energy (stuns: BY sin 9), for the reaction d + Pb, one of the systems we studied. The rapidity distribution appears to be nearly symmetric about a centroid with rapidity y it 0.16. By taking advantage of the additive property of the rapidity parameter, the source velocity 8 can be easily extracted from the centroid of the rapidity distribution, assuming Y-ray emission from a single moving source. In the case of d + Pb, it is close to the half-rapidity of the beam ynn=0.166. Figure IV-12 through IV-1fl shows all the rapidity plots for the 9 systems studied, also the nucleon—nucleon center-of-mass rapidities (Ynn) of each beam projectile are indicated on the corresponding graphs as well. All the rapidity plots are nearly symmetric with respect to the nucleon-nucleon 71 d+Pb. I F — q u «lifiull—W «114] 4 q .— — «Id « — 4 + Q. \\e\ 33. \e \ \\\\\ L I. O 8 60 O O O Ynn Rapidity Figure IV-H Rapidity distributions for 53 MeV/nucleon 23 + Pb induced high energy gal-a ray . 78 25 MeV/A He + Pb 100 I I r I I I 1 I I I I I I , r I, I .. I I . 50" : Xd+Pb -- : I 0d+Zn : _ | -1 60— | Dd+C — k _, 9 - I ‘ 0 ~ - 5 _ I s 4 40— I .... a: _ s : l _ .- l a " E . . . . LL. 1 1 1 l L 0 . RapidityY Figure IV-12 Rapidity plot for 25 MeV/nucleon I“He beam on three different targets: Pb, Zn and C. 79 53 MeV/A d + Pb 100 I ' ' ' I l l I I I I [I l I i I I d I I a 80-— I ~ _ l xd-t-Pb -— : °d+Zn - 60. l Odd-C : ,. - ' ‘3 3 I ' -§ 5 - I j I l 7’ 20— g __i I I j 3 | - O i I 1 i 1 1 J I, 1 i I. -1 OYnn 1 2 Rapidity Y Figure IV-13 Rapidity plot for 53 MeV/nucleon 2H beam on three different targets: Pb, Zn and C. 80 (53 MeV/A) a + Pb 100- I I I r T T I I'T—I I I I l I I I 4 ’ I Xa+Pb j b I .-: 80— 0a+Zn q 1.. P I Ia+C ‘ : . _1 SOL—- I 4‘ e : 1 . 2 L _ .. 40- | ii a - 4 r- I 1 20?— l —: - 1 fl .. | : " i .. .11. .i . L Rapidity Y n a Figure IV-m Rapidity plot for 53 MeV/nucleon He beam on the three dl. - ferent targets: Pb, Zn and C. 81 center-of-mass rapidity line. Quantitative values of the source velocity Bexp can also be extracted using a cubic spline fit to the rapidity plots, and are shown in table Ill-1 in comparison with the nucleon-nucleon center- of-mass velocity ann' It was found that the source velocities sex are quite P close to the nucleon-nucleon center-of—mass velocity Bnn’ with a slight systematic shift to lower velocity. Figure IV-15 shows the photon angular distributions transformed into the nucleon-nucleon center-of—mass frame. They are roughly symmetrical with respect to 90° in this frame. One of the interesting features is a quite pronounced dipole component in all three of the carbon target data. The data from the heavier targets of Zn and Pb is minly isotropic, but it also shows a small dipole comonent. C. Discussion C.1. loving source model fit Many of the interesting features of the data, such as the strength of the dipole component, the differences between Bex and BM, as well as the P slope parameter and overall strength of the energy spectra, could be better understood using a more systematic approach. A simple moving source model by Tekashi Murakami was employed to fit the data. The model assumes a forward- backward symetric Y-ray emission from a moving source frame recoiling with a velocity 8, and a photon production cross section energy dependence in that frame of the form d’o ~E/‘l‘ m a: A (1-8 cos‘es) e Table IV-1 Comparison of extracted source velocities Bex center-of-mass velocities an“ and nucleus-nucleus center-of-mass velocities BNN' 82 P BEAM TARGET E/A(HeV) sexp an" eNN “as c 25 0.08 0.115 0.019 "He Zn 25 0.07 0.115 0.013 "He Pb 25 0.10 0.115 0.00u an c 53 0.16 0.166 0.0u0 2a Zn 53 0.17 0.166 0.010 2H Pb 53 0.12 0.166 0.003 ”He c 53 0.16 0.166 0.070 "He Zn 53 0.15 0.166 0.019 "He Pb 53 0.13 0.166 0.006 to nucleon-nucleon g-a O I F. da/dfl (mb/sr) S A. 10‘3 Figure IV—15 Integrated angular distributions for photon energies above 30 83 71 [TIT 1r. - I :E/A825 MeV ‘He rTlIIIIrFII B/A-sa MeV '11 IIIIIII[III EVA-.53 MeV ‘He . X Pb :10 x Pb x Pb :— 0 z“ ‘5 a Zn 0 Zn —- ; 00:5 4 . 0 C 0 C ‘ . x x I 'x X x x ‘ .. x X x x_ . X ‘ x I I >< x ll 1| a l I I . . - . I z" I l ‘3 - 1 P 4 1- 1 O a . O I - 0' <0 e . . 1. e . O . 0 . L l l i i L L14 1 L 1 i 1 i L ' L I l i l i l 1 x 60 120 60 120 60 -2“ 9:210:98). MeV in the nucleon-nucleon center-of-mass frame. when transformed into the laboratory frame (using eq. IV-1), it takes the form of d'o _ A sin‘e -EC/T dOdE lab' 0 “'3“ ' c' ) 9 -1/2 where C=Y (1 - B 0089 ), Y = (1-8) lab Using this model, we carried out a global fit to the five energy spectra from the five laboratory angles and obtained the best fit values of the following parameters: overall strength A, dipole strength B, slope parameter T and extracted source velocity Bexp' C.2. The lbving Source Table IV-2 shows the results of the fits to all 9 systems. The values of the nucleon-nucleon center-of-mass velocities Bnn are also shown in the . It was P extracted from the experimental data Table next to the extracted values of the source velocities Bex found that the source velocities Bexp set, although very close to their corresponding nucleon-nucleon center-of- mass velocities Bnn' appear to be systematically slightly smaller, confirming the previous result using the rapidity plot method. This slight shift may be understood, by assuming target nucleons with higher Fermi momentum opposite to the beam direction have a larger contribution in the production of bremsstrahlung photons, thus resulting a lower effective nucleon-nucleon center-of-mass velocity. Or, it could also be attributed to bremsstrahlung photons coming from multiple scattering. Only the bremsstrahlung photons from the first chance nucleon-nucleon collision would be symetric in the nucleon-nucleon center-of-mass frame, while gamma rays from subsequent scattering could appear to lower the velocity of the source. 85 Table IV-Z Parameters for the loving source model fit. BEAM macs-r E/MheV) new 3m mm) A B (mb/HeV-sr) ”we c 25 0.0810.01 0.115 “110.2 0.003u10.001 0.11810. 10 "116 2:1 25 0.0810.01 0.115 6.510.2 0.0119 10.01 03510.15 “116 Pb 25 0.1110.01 0.115 6.3.10.2 0.080 10.02 03610.19 211 c 53 0.1510.01 0.166 10.610.2 0.00n210.001 0.6010.05 211 2:1 53 0.1111001 0.166 9.010.: 0.0311 10.01 0.5510.06 2" Pb 53 0.1u10.01 0.166 9.010.2 0.066 10.02 03610.08 ”we c 53 0.1610.01 0.166 13.3102 0.002010.0006 05210.05 “we Zn 53 01310.01 0.166 12110.2 0.018 10.006 0.39:0.08 "we Pb 53 0.1510.01 0.166 11.310.2 0.0113 10.01 03610.09 86 A second fit which assumes the source velocity to be the nucleon- nucleon center-of-mass velocity are shown in Figure IV-16 and IV-17. They appear to be rather good fits. The parameters A, B and T given in table IV-Z as well, are obtained using the second fit, in which the fixed source velocities Bnn of the corresponding beam energy were used as the source velocity. C.3. Y-ray angular distributions in the source frame Although most of the heavy ion induced high-energy photon experiments have reported mainly isotropic angular distributions in the nucleon-nucleon center-of-mass frame, the existence of a dipole component has also been reported both by Grosse et al [Gr 85] and by Bertholet et al [Be 87]. As shown on Figure IV-17, though most pronounced in the carbon target data, all of the systems we studied exhibit some dipole component. The relative strength of the dipole component (table IV-Z) for the reactions we studied ranges from approximately 351 for most of the heavier systems up to nearly 601 for the lighter system, while values ranging from 161 to 31$ were found by Bertholet et all [Be 81] using heavy-ion beam of M MeV/nucleonaéxr on various targets . The carbon target data in particular, have rather strongly enhanced dipole components. The values of B of 0.118, 0.52 and 0.60, are significantly larger than those of Bertholet [Be 87] from heavy-ion reactions. However, our light ions on lead target data, which show a dipole strength of about 351, are comparable to the the Bertholet [Be 87] data. Notice [Ja 75b] that the angular distribution for the nonrelativistic bremsstrahlung process pn+pnY takes the form of (1 - £66320) in the long wave length expansion, 87 Ix! r I I I I r I I T IXI Ff] I I r r l—I lxI r .I l r I I r 100 E/A=25 MeV x E/A=53 MeV x E/A=53 MeV X . 2 —: e H ‘He 0 e 9 A .— . o O . ‘ia °. -2 _ > 10 a fi g a ’5‘ E I. E E < d E 10'4 —- 3 \— ca . “U .. g 0‘3 1:: "\\\ 1 q“ 0 . X Pb x100 '° ‘ f 3 En x10 10-8 LL 1 I I L l ILL l L 1 l i I '.' l I I 1 I l l I l ' ‘ o 50 100 o 50 100 0 50 10:3 ' E!7 (MeV) Figure 1V716 Moving source model fit to the photon energy spectra at 90 the laboratory for all 9 reactions studied. 88 O ;- I r I I r I I I I I r FI I I I I r I r I r I fl I T T I Fr I T. ;E/A=25 MeV ‘He E/A-sa MeV 2H E/A=53 MeV ‘He: 10-1 :._ 0 Zn X5 0 Zn 0 Zn 1 : 0 C x5 1 f: - 0 C 0 C .. m 0 X _ \ W a '0 m \ E : b _ _ “U _ .1 10-3 I I I I I ' LI I l I I I LI I I I I I ' I I I I I I L I ' I 60 120 60 120 60 120 ®cm(deg) Figure IV-17 Moving source model fit to the photon integrated angular dis- tributions in the nucleon-nucleon center-of-mass frame. 89 i.e. B=O.6. The dipole component in the carbon target data is close to that expected for the free np bremsstrahlung process, while that of the lead targets is only a little over half of the free np bremsstrahlung value. This target mass dependence of the dipole component may be qualitatively explained by assuming that the dipole component comes from first chance np collisions while the subsequent multiple scatterings are isotropic in nature. Thus the lighter targets like carbon, having relatively smaller contribution from second or third scatterings than the heavier targets such as lead, can appear to have a substantially larger dipole component than heavier targets. C.3. Target and projectile nss dependence of Y-ray intensity The increased contribution of multiple scattering in heavier targets may also be responsible for the target mass dependence in the slope parameters of the photon energy spectra. Figure III-18 shows the photon energy spectrum at 90. angle induced by the 53 MeV/nucleon “He beam bombarding three different targets. Unlike most of the heavy-ion data where the slope parameters are largely independent of the target mass, the slope parameters of the light-ion induced Y-ray spectra decrease slightly with increasing target mass. If one assumes that photons produced in the first collisions are more likely to have higher energy than photons from subsequent collisions, then as the contribution of multiple scattering increases with target mass, the slope parameters would decrease. One of the interesting features in the energy spectra of the high energy photons coming from light-ion reaction is the projectile mass dependence. To illustrate this, the energy spectra of the three different 9O 10"1 . . . , I I r I I I r 10-2 E/A=53 MeV I: ‘He X Pb x 5 T _3 ° Zn 1: 2 3 10 a c 5 .o 10‘4 5 Ci} '255 _c 10 c. I a .6 : E 10"5 _" “U 10‘7 l 1 t ‘ 0 50 100 Figure IVe18 Target dependence of the photon cross section. . da/dOdE (mb/MeV-sr) 10‘“1 10'2 10'3 10'4 10‘5 10"6 91 I Figure IV-19 Projectile dependence . . . . I . ° E/A853 MeV ‘He-e-Pb X E/A=53 MeV 2H-I-Pb n E/A=25 MeV ‘He-I-Pb IIZII )(l. I! II It IIII III! 01 D. 50 100 of the photon cross section. 92 beams on the Pb target are plotted in Figure III-19. The slope parameters of the three beams are 11.3 MeV, 9.0 MeV and 6.3 MeV respectively. While the slope parameters of high energy photon spectra in most heavy- ion induced reactions with the same energy/nucleon were found to be the same, the 53 MeV/nucleonlight-ion induced reactions produced slope parameters ranging from 9.0 - 10.6 MeV for 2H beam and 11.3-13.3 MeV for “He beam of the same energy/nucleon (table III-2). These values not only depend on projectile (as well as target) mass, but they are also substantially smaller than those obtained in heavy-ion induced reactions at similar beam energy/nucleon. By comparison, for example, Grosse et al.[Gr 86] studied the react ion 12 C + C at 118 MeV/nucleon and observed a slope parameter of 19 MeV. Table 111-3 and IV-‘I show our results together with results from other groups for heavier systems at similar energies. D. Conclusion According to the statistical model which assumes the photons are produced within a hot compound system, the 53 HeV/nucleonzfl and 25 HeV/nucleonufle projectiles would produce nearly the same excitation energy, hence the same compound nucleus temperature. So, the photon energy spectra from the two reactions should have the same slope parameter according to the model. Therefore, the observed significant difference in their slope parameters indicates that high energy photons do not come from a hot compound nuclear system. On the other hand, the difference in the spectra of 53 HeV/nucleonzfl and ”He induced reactions contradicts also the naive first collision model, which predicts the same slope parameter for the two reactions and only a factor of two difference in yield. Part of the 93 Table IV-3 Comparison of slope parameters for different systems at similar energies per nucleon. BEAM TARGET E/A(HeV) T(HeV) References 325 Al 22 10.8 [311 87] 323 Ni 22 10.0 [31:1 87] 323 Au 22 9.1 [Stl 87] ”He 0 25 7.11102 ”he Zn 25 6.5:0.2 "He Pb 25 6.310.2 9“ Table IV-u Comparison of slope parameters of 53 MeV/nucleon light-ion data with systems of different projectile masses at similar energies. BEAM TARGET E/A(MeV) T(MeV) References "°Ar Gd nu 12.6 [Hi 87] 86Kr c an 11.7 [Be 87] 86Kr Ag 11 12.5 [Be 87] 86Kr Au an 12.1 [Be 87] 12c c 18 19 [Gr 86] 2 H c 53 10.610.2 2a Zn 53 9.u10.2 2H Pb 53 9.010.2 ”He 0 53 13.310.2 ”He Zn 53 12.110.2 11 He Pb 53 11.310.2 95 difference could come from the different internal momentum distribution between the two projectiles. As discussed above, the mass dependence of the photon energy spectra slope parameters may also suggest that the high energy photons do not come entirely from the first collision of nucleons. To summarize, high energy gamma rays produced in light-ion induced reactions are observed in the energy range similar to that of the heavy-ion reactions. Also, photon energies up to a large fraction of the total energy available were observed, as in the proton case. In the light-ion reactions, the slope of the photon energy spectra are mch steeper than those found in the heavy-ion induced reactions of similar beam energy/nucleon, and have some weak dependence on both the target and projectile masses as well. The dipole component of the photon angular distribution in the nucleon-nucleon center-of-mass frame are larger than in reactions with heavy-ions and become more pronounced as the masses of the systems decrease. CHAPTER 5 HIGH ENERGY GAMMA RAY PRODUCTION FROM NEAR SYMMETRIC SYSTEMS A.1ntroduction A.1. The Inacleus-Ilucleus Coherent Bremsstrahlung Model In the introduction of the last chapter, an overview of the current theories of the production of high energy game rays in nuclear reactions was outlined. Most of these theoretical models fit in one of three categories: nucleus-nucleus bremsstrahlung, nucleon—nucleon bremsstrahlung, and statistical or thermal emission. The nucleus-nucleus bremsstrahlung model by Vasak et. al.[Va 85] is one of the early models proposed to explain the production mechanism of high energy photons. This approach distinguishes itself from the majority of the more recent models, which assume a microscopic production mechanism of incoherent nucleon-nucleon bremsstrahlung between individual nucleons. The nucleus-nucleus bremsstrahlung model makes the assumption that the microscopic production mechanism is collective nucleus-nucleus bremsstrahlung. In that model, both the projectile and target nucleus, or a substantial parts of them, act as a whole when they are scattered off one another. That is, all nucleons within the colliding nuclei experience the acceleration field simultaneously. The high energy photons are therefore 97 produced by the coherent contribution of the bremsstrahlung of the projectile and target nucleus. For symetric systems or systems having the same charge-to-mass ratio, the model predicts a quadrupolar angular distribution in the half beam velocity frame. However, later analysis [He 811][Va 86] found that only the coherent bremsstrahlung gama rays produced out of the reaction plane would be purely quadrupolar, and that the angular distribution averaged over impact parameter would instead be dipolar in nature. Hhile experimental data point to a photon angular distribution containing both isotropic and dipolar components, it is not in strong disagreement with the theory. So the absence of a quadrupolar angular distribution alone is not sufficient to rule out collective bremsstrahlung as the production mechanism. The coherent model predicts that the magnitude of the gamma ray cross section for symmetric systems to should have a strong 2' dependence. The majority of the experiments, consisted of mostly asymmetric systems, agree instead with a differnt scaling law which predicts a mass dependence of roughly (11911023. These observations, while inconsistent with the coherent bremsstrahlung model, are in qualitative agreement with the prediction of models base on incoherent bremsstrahlung mechanism. Ko et. al. [Ko 85] calculated bremsstrahlung within a cascade calculation. They found that, while incoherent bremsstrahlung dominates in systems having projectile and target mass less than 20, coherent bremsstrahlung should become observable at lower photon energy (EY( 110 MeV) for heavier (Ap,At>u0), symmetric systems. Therefore, a change of the angular distribution in the center-of-mass frame from isotropic and dipolar 98 to one with a quadrupole component would be the experimental signature of the onset of the coherent bremsstrahlung. A.2. The Goal of the Sy-etric System Experiment Re have studied in this experiment a series of symmetric or near symmetric systems ranging from light (71.1 4- 7Li) to heavy (qur + 110 Ca) at the same (30 MeV/nucleon) projectile energy. According to the simple first collision bremsstrahlung model [Na86], symmetric systems of different mass A would produce gama ray spectra of identical characteristics except for different magnitudes. Using the same experimental set-up and the same incident energy, it was possible for us to look for subtle changes, both in angular distributions and in cross sections that may indicate any changes in the gem ray production mechanism. Three beams of the same incident energy per nucleon were used for this 71.1, ”we and "our. The following 5 reactions °Ar+Ca, "00r+Pb. For the study of experiment: 30 MeV/nucleon were studied: 7Li+Li, 7L1+Pb, 20Ne+Mg, u the symmetric systems, a 0.21 mm thick Li, a 0.11 mm Hg and a 0.096 mm Ca target were used, respectively. And for comparison, a 0.02511 m thick lead 7 20 target was used for both the Li+Pb and Ar+Pb reaction. Energy spectra of photons with energies from 20 to 100 MeV were measured at laboratory angle 0 of 300, 60°, 90°, 120 and 1500 using three Cherenkov plastic range telescopes. B. Experiment Results Figure V-1 to Figure V-5 show the energy spectra of high energy photons I 0 0 O 0 at laboratory angles of 30 , 60 , 90 , 120 and 150 for the three symetric do/dfldE (mb/MeV-sr) 99 3» lo I I I I I r I I I I I r I I I I I I I I I I I I I I _ E/A=30 uev - 30- :100 7 _ . 0 60' x10 ‘ 100 _ Li+Li 0 90' _ \ * 120' x .1 _ 0 150' x .01 q \‘ (lab frame) 10"3 m 1 1 e I “I ‘ 10- I ‘ If I q 10-9 1 I I l I I l l I 100 120 Figure V-1 Photon energy spectra for 30 MeV/nucleon 7Li 4- Li at laboratory 0 0 0 C 0 angles of 30 , 60 , 90 , 120 and 150 . do/deE (mb/MeV-sr) 100 _ E/A=30 MeV 0 10° — ‘°:\ ”Nam“ I 9° 30' 1:100 60‘ x10 " 120' x .1 "‘ _ 0 150’ x .01 q (lab frame) 10"3 — - ' III: ‘ I I 3 - I I ' 3 1 I I 10 5 — 111 II I I I I I - 10-9 L L I I I I I I L I I L l L I I I I l I I I I I L L L L 1 O 20 4O 60 80 100 120 E7 (MeV) 20 Figure V-2 Photon energy spectra fer 30 MeV/nucleon O O O 0 0 angles of 30 , 60 , 90 , 120 and 150 . Ne 4- Mg at laboratory 101 103 W s...” I r r r r "t I I T l q _ s. E/A=30 MeV - 30' x100 q 9. 4° . 60' x10 7.? 100 _. ’ Ar+Ca . 90° _ m \ ”a... a 120° 1: .1 I _ \ ”an . 150- x .01 . % t‘\°"0~. ‘3 x x t (lab frame) :3 . g; '5... -.g..'l.txt I I I . E 10‘3 — "a . *~,__ ' u. _ 5 \%~. . c 3 I I I I I v . .3 I .1 .51: t ' I I I m - "-5. . ' ‘ x I 1 I 1 1 "U I 1! I I I f g 1’ I I \ . I Ii - b 13 _ . 10-9 I I L I 14 L I I I I I L L I L I I I I I L I l I L I I J O 20 4O 60 80 100 120 E7 (MeV) Figure V-3 Photon energy spectra for 30 MeV/nucleon qur + Ca at laboratory 0 O O O angles of 30 , 60 , 90 , 120 and 150 . da/deE (mb/MeV-sr) 102 3 10 T T I T T ' I T I I—T f l I l I T I 1* 1 r l’ T T I E/A=30 MeV ' 30‘ 2100 q 7L'+Pb : :3: :10 10° 1 * 120° 2 .1 ‘ - 150° 2 .01 . (lob frame) I 1 I " ‘ 10-3 11. I; 1 .— I I! t I I . I I I I I i If “ 10‘6 I I ‘- b 1 10—9 1 l l l l l l #1 l L l L I l l l l l I l I I I l l l l O 20 4O 60 80 100 120 Figure ‘14 Photon energy spectra for 53 MeV/nucleon 71.1 + Pb at laboratory angles or 30', 60°, 90 , 120' and 150°. da/deE (mb/MeV-sr) 103 I I I I I I I I I I I I I I l’ I I I I l l I I I E/A=30 MeV .... O (J H O O l . e. ..n. I 10-3 .. \ . a” "'11:; l I ' 30° 2100 0 60° :10 _ a “AH-Pb - 90 * 120‘ x .1 ‘ .... . 150- x .01 __ a . ‘8'": :3 (lab frame) ‘3. . I r . 1'! I . “.13 Iziizf;!111 1 -5 _ I! 10 IIIII '— 10-9 1 I l l l l l l l I l I l l I l l l l l l l 1 ll 1 l I O 20 4O 60 80 100 120 Figure V-S Photon energy spectra for 53 MeV/nucleon O O I O 0 angle: of 30 , 60 , 90 , 120 and 150 . 40 Ar + Pb at laboratory 1014 systems and the two lead target systems. All of the spectra can be seen to have two regions. The low energy region (EYS 25 MeV), where the spectra are exponentially decreasing with a slope of typically between 2-3 MeV, are thought to be photons coming from statistical decay, giant dipole resonance, as well as bremsstrahlung photons. In the high energy region, BY) 25 MeV, the spectra are also exponential but with a much flatter slope. We will again concentrate on the "high energy region" of the spectra. The slopes of the photon energy spectra in the laboratory frame depend on the angles of observation in the lab. The slopes are ‘flatter' in the forward angles than those observed in the backward angles. The integrated angular distributions for photon energies above 30 MeV for all five systems are shown in Figure V-6. They are typically forward peaked in the laboratory frame. Therefore, the high energy gamma rays could be coming from a recoiling source. (The relationship between photon energy spectra in the laboratory frame and a source frame moving with velocity 8 was discussed in chapter u) To study better the photon angular dependence, the two dimensional contour rapidity plots discussed in the last chapter were employed to extract the velocity of the recoiling source. The rapidities of a particle moving with velocity 8 = We in direction 9 in the laboratory frame, ylab= % 1+Bcos 6 1n [1-Bcos 9 ] = -;- ln [H‘] are plotted both for the symetric systems and n for the lead targets in Figure V—7 and V-8. Here the nearly symmetric nature of the rapidity distributions is again observed. The centroids of the symmetry also appear to be near the rapidity of the nucleon-nucleon center- of-mass frame Y“ in all cases. The quantitative values of fitted centroids, da/dfl (mb/sr) 105 O 10 I f I I I 1 I F] I l f F T I I r 1 I l [ I I : : E/A-SO MeV x wAr+Pb Z - xx “awe. x 7mm: . ' it ”Nu-Mg ‘ 10-1 .__ X 711+“. X ... E x ‘ 4‘ x i D ‘ x ‘ . x ' . x ,‘ x _ it x to a; E" " x -= I II: I 1 : I! 1 F * " x I .. 3 q 10'3 :- x -— : I I I I I I L I I I I I L I I I I l I I I I I1 60 120 60 120 GLab(deg) Figure V-6 Integrated angular distributions for photon energies above 30 MeV in the laboratory frame. 100 I I I I I I I I II I [I I v 1 i t | q 60;- ' ‘ _ l XLi+Li .— : ' °Ne+Mg j ’ l DAr+ I 80*— ] Ca _ 9 ' I I o . 5 - ‘ ca“ 4°:— l _— I I ~ 20— l _: .. l a I I . O 1 1 l1 1 11 I]; 1 11 1 J '1 Gym: 1 2 Rapidity Y Figure V-7 Rapidity plot for the three symmetric systems. 107 _ l ' ' ' ' I,’ T ' ' l ' ' ' ' 80:—- : 0 Ar + pb _— : l xLi+Pb - .- ’ q eo— ' I 9 ~ I : 3‘: : . d a; 40-- ‘ - . 7 : ' ‘ .. l ‘ 20— ' - . . T - 1 . l . 1 . 1 ll. . , . , , . 1 -l O 1 2 RapidityY Ynn 1; Figure V-8 Rapidity plot for 30 MeV/nucleon 7L1 and OAr beam on Pb target. 108 which due to the additive property of the rapidity parameter are the rapidity of the moving source frames assuming Y-ray emission from a single moving source, were obtained by using a cubic spline fit to the rapidity plot. The extracted quantitative values of the emission source rapidities are tabulated in table V-1, together with the nucleon-nucleon center-of-mass velocity for comparison. It is evident that the source velocities extracted from the measured spectra are rather close to the nucleon-nucleon center-of-mass velocity. Further study of the photon angular dependence can be carried out by transforming the experimental spectra from the laboratory frame to the nucleon-nucleon center-of-mass frame. Figure V-9 contains the Y ray angular distributions in the nucleon-nucleon center-of-mss frame. 0. Discussion C.1. Systematic Studies of the Data by the Simle Moving Source Pit Model The photon angular distributions in the center-of-mss frame appear to be fairly symmetric about 90°. All data of the symetric systems show some evidence of a dipole component superimposed on an isotropic angular distribution. The anisotropy is most pronounced in the lightest system, 7 Li + Li. And the ’Li + Pb data also show a rather pronounced dipole component. There is no evidence of any quadrupole component which would otherwise signal the onset of the coherent nucleus-nucleus bremsstrahlung. But as we discussed in the introduction, the absence of quadrupolar angular distributions alone is not sufficient to rule out coherent bremsstrahlung as a possible production mechanism. 109 Table V-1 The source velocity Bex extracted from the rapidity plot. P BEAM TARGET E/A(MeV) Bexp cm 7L1 L1 30 0.10 0.126 20m». Mg 30 0.09 0.126 qur Ca 30 0.12 0.126 71.1 Pb 30 0.10 0.126 “0 Ar Pb 30 0.16 0.126 110 O 10 b T y—l r j t r l’ t r if I r T I I I—r I r r 3 E E/A-3O MeV X ‘%U+Pb 3 ‘ 1: ”AH-Ca " 714+?!) ‘ u- i. ”Ne...“ 4 7 . . A 10-1 :— X LH'LI —-: 33 E I ‘ “ x 2 ‘\\ t ‘ I '2 :x " " * x : \" r a x ‘ c: " I § 3 10‘2 H I o t " -1 s e 3 . _ x x q + " x 4 - " J 10-3 L l l l l J l i J. l l l 1 L L l 1 L L l [i l L 60 120 .60 120 @cm(deg) Figure V-9 Integrated angular distributions for photon energies above 30 MeV in the nucleon-nucleon center-of-mass frame. 111 To study systematically the many interesting features of the measurements, such as the relative strength of the dipole component, the simple moving source model discussed in the last chapter is again used to fit the data. The model assumes that the photon cross section takes the form dad 2 -E of ail—dB“ A (1-B cos 6) e fits to the five energy spectra for each system were made. The best fit IT in the moving source frame, and simultaneously values of the following parameters: overall strength A, the relative dipole strength 8, slope parameter T and the source frame velocity Bexp are shown in Table V-2. The fitted curves for the energy spectra and angular distributions in the nucleon-nucleon center-of-mass are shown in Figure V-10 and V-11. 0.2. Source Velocity of Sy-etric and Asy-etric Systems In table V-2, the nucleon-nucleon center-of-mass velocity BNN is given for comparison with the experimentally extracted source velocities sex for P all the systems studied. The extracted source velocities B for the . exp symmetric systems are in good agreement with the nucleon-nucleon center-of- mass velocity BNN within the limit of uncertainty. The source velocities for the lead target data, however, shows a small systematic shift to lower velocities by approximately 0.026c. This small shift may be due to multiple scattering within the colliding nuclei. For the two asymmetric systems, both involving lighter projectiles bombarding on heavier lead target, only the incoherent sum of the bremsstrahlung photons coming from the first chance individual nucleon- nucleon collision would be symetric in the nucleon-nucleon center-of-mass 112 Table V-2 Results of the moving source model fit to all 5 systems BEAM TARGET E/A(MeV) sexp ann T(MeV) A a (mb/MeV-sr) 71.1 L1 30 0.12:0.01 0.126 9.010.2 0.01u10.0011 . 0.08:0.09 2011a Hg 30 0.13:0.01 0.126 8.810.2 0.00110.012 0.32:0.07 “°Ar Ca 30 0.11:0.01 0.126 8.310.2 0.1810.05 0.29:0.05 7L1 Pb 30 0.10:0.01 0.126 7.910.2 0.10:0.03 0.19:0.10 ”OAr Pb 30 0.10:0.01 0.126 ~7.u:0.2 0.66:0.20 0.36:0.06 da/deE (mb/MeV-sr) 0 Figure V-10 Moving source model fit to the photon energy spectra at 90 in p... O O p—s O I O) ... O I Q 113 l I f r r l x “mph x10 0 ’u+1=b r I r I I I I fiT I l’ I x x ‘°Ar+Ca x100 x 0 ”Ne-rug x10 . c1 ’LH-Li O I — o ‘1‘ ‘PI‘ *1 l l J l l L l LTI l l 50 100 0 E7 (MeV) ‘xx imp; 1....1 50 100 the laboratory for all 5 reactions studied. 11“ O 10 : fit I I f I T I I I I I I I I I I I I [fl I I: E E/A=30 MeV xx “AH-Pb 3 r x “Ar-1C3 1: 7mm: ~ _ 1% 2°Ne+Mg ‘ 7: 10‘1 :- x 11H“ - .o I 1 E m v i- d s A b '- I “U I i A 1 10-3 1 l l l i l l l l l l l I l l l J l l l l l l 60 120 60 120 @cm(deg) Figure V-11 Moving source model fit to the photon integrated angular dis- tributions in the nucleon-nucleon center-of-mass frame. 115 frame. Subsequent scatterings, on the other hand, would contribute to this slight lowering of the source velocities. For the symetric systems, the nucleon-nucleon center-of-mass and the nucleus-nucleus center-of-mass are identical. Therefore, bremsstrahlung photons from both the first chance nucleon-nucleon collision and subsequent scatterings are expected to be symetric in this comon frame. C.3. lhss Dependence of the Photon Angular Distributions in Center-of-Mass Frale There have been reports [Gr 86][Be 87] of small dipole components present in the angular distribution of the high energy bremsstrahlung photons. The relative strength of the dipole component reported by Bertholet et al. [Be 87] ranges from 161 to 31$ for NI MeV/n 86Kr induced reactions. The values for our symmetric systems range from about 29$ for qur + Ca to 1&8} for 7l..i 4- Li, and 361 to “91 for qur + Pb and 7Li + Pb respectively (table V-2). The dipole component appears to decrease with increased system size. The values obtained here are also consistent with our finding from the light-ion induced reactions (discussed in chapter it) and the finding by Bertholet et a1. [Be 87]. For comparison, a relative dipole strength of 3:605 for the elementary np bremsstrahlung is predicted in the nonrelativistic long wavelength approximation; the values of B found here range from 501 to 80$ of that of the free up bremsstrahlung. The dependence of the dipole components on target masses may be associated with the multiple scattering between individual nucleons within the colliding nuclei. Only the nucleon-nucleon bremsstrahlung from the first collision can have dipolar angular distribution in the center-of-mass frame; 116 bremsstrahlung photons produced in subsequent collision no longer bear any clear signature of the initial beam direction, and would therefore be isotropic in the center-of-mass frame. Thus, the increased contribution of multiple scattering in larger systems can lead to a more isotropic angular distribution. CJI. Mass Dependence of the Photon Energy Spectra 0.11.1 . Slope Parameters of the Double Differential Cross Sections Table V-2 also shows other parameters of the photon energy spectra extracted using the simple moving source model for all the systems studied. They are in general in good agreement with other published data of similar systems. Kwato et al. [Kw 86] had studied high energy gamm ray production 180 197 from Ar + Au at the same incident energy of 30 MeV/nucleon. They reported a slope parameter of around 7.5 MeV, while the slope parameter for our similar system of qur + 208 Pb was found to be 7.11:0.2 MeV. The magnitude of the cross section are in rather good agreement as well. The slope parameters of the energy spectra of the two lead target data are both smaller than that of the corresponding symmetric target data by about 1 MeV, as can be seen in table V-2. Although the slope parameters of the energy spectra of symmetric systems are quite similar, they also decrease slightly as the size of the system increases. A qualitative explanation of this size dependence can be that bremsstrahlung photons produced during first collisions are more likely to be of higher energy than those produced in subsequent collisions. Therefore, larger systems which would have higher probabilities of mltiple collisions produce a slightly larger portion of the bremsstrahlung photons from multiple scattering; there 117 are more photons in the low energy end of the spectra making the spectrum steeper. c.t1.2. Total Cross Section Ratios An interesting feature of the data is the mass dependence of the total cross sections. Different theories predicted different mass or charge dependences of systems having the same projectile energy/nucleon. The coherent bremsstrahlung model by Vasak et al. [Va 86] predicted a nuclei charge dependence of roughly 2'. Most of the experimental data, however, did not show such charge dependence. Instead, a phenomenological scaling law assuming photon cross sections proportional to the product of the projectile and target geometrical cross sections, i.e. °Y~ (AtAp)2/3 was found quite successful. A scaling scheme based on first collision incoherent nucleon-nucleon bremsstrahlung was proposed by Nifenecker and Bondorf [Ni 85], which suggests the game ray total cross section following the relation: °y= PY' By assuming uniform density nuclei of radii 11:1.2 111/3 fm, both quantities aR and = A ‘---—JE-- =-——-— (z N + z w ) np p 5(A;/3+ A‘1/3) ApAt p t t p where (AF) is the average mass of the participant zone (the projectile and target overlap area, assuming A p5 At ). The experimental total cross sections are obtained by integrating over 11: for photons above 30 MeV energy using the fit parameters. The ratio of 20 1[0 total cross section for the symmetric systems are_7Li+Li: flea-Mg: Ar+Ca = 1:2.8:9.6 (Table V-3). Also listed in table V-3 for comparison are the prediction of the coherent model, prediction of the simple (ApAt)2/3 scaling rule, and the prediction base on first collision nucleon-nucleon model by Nifenecker and Bondorf [Ni 85]. One can see clearly from the table that the experimental ratios deviate substantially from the prediction of the coherent bremsstrahlung model. And it appears the simple (ApAt)2/3 scaling is in better agreement with the experimentally observed ratio than the prediction of the first collision model . D. My The high energy gama rays produced in 30 MeV/nucleon heavy ion induced reactions have angular distributions symmetric about 90‘ in the nucleon- nucleon center-of-mass frame. There is no evidence of quadrupole components in their angular distributions. Instead, all of the reactions we studied show a dipole component superimposed on an isotropic component. The relative 119 Table V-3 Ratios of total cross section predicted by different models in comparison with experimetnal data. SYSTEM RATIO ex p RATIOooh RATIO RATIO , 2/3 (2 ) (AtAp) PYOR 7Li+Li 1 1 1 1 ZONe+Mg 2.8 11 14.6 6.6 “0 Ar+Ca 9.6 4H 10.2 19.0 120 strength of the dipole component range from 291 to #91, and we fbund a trend of increased dipole components with decreasing masses of the systems. The mass dependence of the relative dipole strength my be due to the increased contribution of multiple scattering within the colliding nuclei. He were also able to extract the velocity of the recoiling photon emission source. They are in general in agreement with the nucleon-nucleon center-of-mass frame. While the source velocity of the two reactions with lead targets are slightly shifted to the lower side, it may be due to the increased probability of second or third chance collisions from the relatively large mass of the lead target. The slope parameters obtained for all our systems studied are in general agreement with data at the same energy measured by other groups with similar systems. we have also observed some weak mass dependence of the slope parameter, which may again be due to the contribution of the multiple scattering. with the increased mass of the systems, there appears to be an increased contribution from the later stage of the collision process. The integrated photon cross sections for game ray energy above 30 MeV are in better agreement with the simple (ApAt)2/3 scaling scheme than with the first collision bremsstrahlung model. The ratios of the bremsstrahlung photon total cross section provide no evidence to support the 22 charge dependence predicted by the coherent bremsstrahlung model. Chapter 6 Theoretical Model Calculations and Comparison with Data A. Introduction Many different theoretical models have been advocated to explain the high. energy gamma ray production in nucleus-nucleus reactions. Most of the models can be categorized into three different basic approaches: 1) The nucleus-nucleus coherent bremsstrahlung approach: ii) 111) In this approach, the photons are thought to be produced at the early stage of the collision by the coherent bremsstrahlung of the projectile and target nucleus acting as a whole. This model predicts quadrupolar photon angular distributions and a 2' charge dependence of cross section magnitudes. The nucleon-nucleon incoherent bremsstrahlung approach: These models assume a production mechanism of incoherent bremsstrahlung from individual neutron-proton collisions within the colliding nucleus at the early stage of the reaction. They predict a superposition of isotropic and dipolar angular distributions and an A”3 mass dependence for the magnitude of the cross section. Thermal model: 122 In this approach, a 'fireball' or hot zone is formed from the colliding projectile and target nucleus, and photons are emitted from this recoiling hot system at the later stage of the reaction. These models predict isotropic angular distributions and cross sections that depend on the total energy of the projectile. In the two experiments described in the previous chapters, we measured high energy gamma rays coming from light-ion induced reactions and reactions involving symmetric systems. In our data, we did not observe any evidence of quadrupolar angular distribution. We found that the high energy photon angular distributions consisted of a dipole component on top of an isotropic distribution. In the light-ion induced experiment, the very different features observed for systems having similar total energy indicates that the thermal model is unlikely to be the main origin of the high energy photons. In the experiments with symmetric systems, the ratio of the gamma ray yield, which follows the simple scaling rule of 112/3 , also suggests first chance np collisions is a major source of high energy gamma rays. Experimental results covering a wide range of systems (from p+d to "‘Xe+Sn) and projectile energies (10 - 125 MeV/nucleon) are available. Most of these show isotropic or dipolar angular distributions in the nucleon- nucleon center-of—mass frame. The success of the A2,3 dependence of the cross section indicates that the incoherent neutron-proton collisions in the early stage of the reaction are the main source of these high energy ganIna rays. A variety of incoherent nucleon-nucleon collision models have had some success in explaining the major trends of the experimental results. Many of 123 them were able to reproduce some of the data sets. In this chapter, we will compare some of the model calculations with the data we obtained. B. BUU Calculation. Bauer et al.[Ba 86] introduced an incoherent nucleon-nucleon collision model that contains a complete nucleon-nucleon collisional history of the system. Using the BOD (Boltzmann-Uehling-Uhlenbeck) equation, which describes the time evolution of the nucleon phase space density distribution during the nucleus-nucleus reaction, the model enables a dynamical study of the reaction process in both momentum and coordinate space. The elementary process for game ray production is assumed to be the classical individual neutron-proton bremsstrahlung, modified to take into account the energy loss of the nucleons after the production of the high energy photon. They found, by following the time evolution of the gamma emission process, that game rays are produced in the early stage of the collision process. Photon production cross sections and angular distributions of a wide range of experiments were satisfactorily reproduced. B.1. Comarison with the Sy-etric Systems Data Figure VI-1 shows the results of the BOD calculation of the photon energy spectra at 90° laboratory angle for the symmetric systems and systems of Pb targets in comparison with the data. The spectra of the ”Ne 4- Mg and 'Li + Li were obtained by summing over the results of BUU calculations performed at 1 fin interval of the impact parameter. To calculate the other heavier systems requires significantly more computer time, so a slightly different scheme was employed. The calculation da/dfldE (mb/IleV-sr) 10'3 10" 1211 I r . I I I I F W I I x 0 ”NC‘I'I‘ X10 x “me. 11100 n x o 'u+u -- 0 711+» 1 L l l J 1 q _ 50 E27 (MeV) 100 10'3 10‘”6 Figure VI-1 Comparison of B00 calculation of the photon energy spectra witrI experimental data of the symmetric systems. 125 was done at zero impact parameter to obtain the probability for gama ray production, then the probability at other non—zero impact parameters were assumed to be nearly proportional to the geometrical overlap area of the two circles having the same radii of the colliding nuclei. For near symmetric systems (Ap~ At)’ the maximum overlap area of two circles of radius R ~ Agl3~ Allgt impact parameter b is [Ba 86]: S(b)=[ZR'cos-1(b/2R) - b(R=- b=/u)"2]/IR= (v1-1) 1/3 1/3 . And for asymetric systems of R=At and r=Ap , the overlap area will be. b‘+ R‘- r2 bz‘.‘ R1- P1)1/2 2bR , -1 S(b)=[R cos ( ZbR ) - §E(b=+ 32- r=)(1- a -1 b1+ [‘2' R2 P 1 b2... r1- R: 1/2 + r cos ( 2br ) - Eb + r'- R’)(1- 2br ) l/IIRa The agreement between the model and data for ”Ar + Ca and “Ne 4- Mg are quite good, but the calculation underestimates the magnitude of cross section for the 'Li + Li spectra by approximately a factor of 3. For the Pb target cases, the calculation overestimates the cross section of ’Li + Pb and ”Ar + Pb by a factor of 3 to 11. Some of the discrepancy in reproducing the Pb targets data may come from the use of the zero impact parameter and the scaling of the non-zero impact parameters. The scaling (formula VI-1) of production cross section in proportion to overlap area was found valid by Bauer et al. [Ba 86] for relatively light projectile and target nuclei (A~12). It may not necessarily be the appropriate scaling rule for the heavy-target nuclei systems studied here. 126 Figure VI-Z shows the angular distribution in the nucleon-nucleon center-of-mass frame for the symetric systems and the Pb targets data in comparison with the prediction of the model. Probably due to the poor agreement in the energy spectra, the magnitudes of the integrated cross sections for the ’Li 4- Li and the two Pb targets are not very well reproduced. To bring the curves into the similar scale for ease of comparison, the 800 curve for the 'Li + Li data has been shifted by a factor of 3, and the curves for the two Pb target data by a factor of 0.25. The calculation reproduces reasonably well the shapes of the high energy photon angular distribution for the symmetric systems, but it underestimates the dipole component in the 'Li + Li reaction. This may be due to an overestimation of photons originated from multiple scattering. For the Pb target reaction data, however, the model failed to reproduce the shape of the photon angular distribution. The results of the calculation were noticeably backward peaked in the nucleon-nucleon center-of-mass frame. This may originate from an overestimation of gamma ray production in the later stage of the reaction which come, on the average, from a slower moving "source" than the nucleon-nucleon center-of-mass frame. However, some of the discrepancy may have come from the breaking down of the simple geometrical scaling of the zero impact parameter calculations. 8.2. Comarison with the Light-Ion Induced Reactions Figure VI-3 shows the results of B00 calculation for photon energy spectra at laboratory angle of 90° fbr carbon target data and the integrated cross sections for photons having energies over 30 MeV. The calculation reproduces the energy spectrum for 53 MeV/nucleon “He + C reasonably well. 127 IITITIIIIIIIIIIIIIIIITIITIIIIITIIIIrII P X “AHCa X “AH-Pb T ’ 0 ”New; 0 ’mpb ‘ -i _ 7 - _ 10 : 0 Li-I-Ll x x x : b x 1 +- __ .. ~ _ x . X x \ ‘ da/dfl (mb/sr) 10-3 L 1 l l l l l 1 i 1 l l l l L l l l J L l l 1 l l l l l l l l 1 L L l I l l l -l -0.5 0 0.5 1—1 -0.5 0 0.5 1 005w“) Figure VI-Z Comparison of 300 calculation of the photon angular distribu- tions in the nucleon-nucleon center-of-mass frame with experimental data for the symmetric systems. o I I I U r U I I I I Ij I I I I rTrjr -1 10 I I I I I I I I I 10 -1 X x x/a-es MeV ‘3»: mice a ”g.” I.“ ,3 10 X 0 was: 80' 'n+c x10 . x 0 l/A-OS 'u+c 10-2 0 ”‘Cu '0' M X I/A-lfl ”*6 ’1: 10-2 A. '1' 10"3 "’ ' " ‘ ~ 1 a E 10“ . ’3; a ’ \ ‘3’ 10‘5 N -3 3.. 5: l0 8 10"6 " x- “ x- - .x ‘ 10"7 " ‘ 10-8 1 1 1 1 l 1 L 1 1 l 1 1 114 l 1 1 1 1 I 1 1 1 1 I 1 1 1 10-4 50 100 -l -0.5 0 0.5 1 E, (MeV) 605w“) 128 Figure 111-3 Comparison of 800 calculation with experimental data of the light-ion induced reactions systems for both the photon energy spectra and angular distributions in the nucleon-nucleon center- of-mass frame . 129 However, the predicted slope for the 53 MeV/nucleon ’H + C data is flatter than the experimental result, while the prediction fbr the cross section fbr the 25 MeV/nucleon ~He + C is a factor of 2 to 3 too large. Part of the discrepancies may come from the use of a uniform density distribution with radii of a=1.1211/3 , which is appropriate for large nuclei, for the light projectile nucleus. Also, the Fermi momentum may not describe the internal momentum distribution of light-ion projectile properly. In addition, the treatment of the Pauli blocking of the final state phase space is adequate only for photon energies up to about 801 of the total available energy. Therefore, results for photons having energy near the kinemtical threshold would not be expected to be valid. The agreement between the B00 calculation and experimental data for the magnitude of the 53 MeV/nucleon ~He + C reaction cross section is reasonably good. But the model under-predicts the 53 MeV/nucleon 2H + C data and over- predicts in the case of 25 MeV/nucleon 2H + C, probably due to the discrepancy in the energy spectra calculations. The calculated curves for the 53 MeV/nucleon ‘H + C and ‘He + C in Figure VI-3 have been scaled by factors of .33 and 2 respectively for ease of comparison. However, the model predicts a backward peak for the angular distribution in the nucleon-nucleon center-of—mass frame. This may again, as mentioned in the previous section, be due to an overestimation, particularly for light-ion induced reactions, of gamma rays coming from multiple scattering. The model also underestimates the relative strength of the dipole components in the angular distribution, especially in the BIA = 53 MeV ‘11 + C case. This is consistent with the overestimation of gamma ray yields from subsequent collisions. So, the use of parameters appropriate for 130 large nuclei in the calculation may be an important contributing factor to the discrepancy between the prediction and data on the light-ion induced reaction. C. Simple Fer-i Gas Model First-Chance np Collision Bremsstrahlung Calculations for 53 MeV Light-Ion Data C.1. First Chance Bremstrahlung Model for Light-Ion Induced Reactions Due to the limitation of the BUU model discussed in the previous section, the calculation did not reproduce the slope and the magnitude of the photon energy spectra for the light-ion induced reactions. As we mentioned in chapter IV, one interesting feature of light-ion induced bremsstrahlung photon spectra is the projectile dependence. Unlike the heavy-ion induced reaction where projectiles having similar E/A have rather similar behavior except in overall magnitude of the photon yield which follows a simple (AtAp)1/3 rule, the slope parameters of ‘H and ‘He induced bremsstrahlung photon production cross section are substantially steeper than heavy-ion induced reactions at similar energy (shown previously in Chapter IV, Table IV-ll). Also, the slope parameters of the photon energy spectra for the 53 MeV/nucleon 2H + Pb and ‘He + Pb, too, are noticably different. Part of the difference may be coming from their unique internal momentum distribution, which is clearly different from the Fermi sphere distribution commonly used to describe that of the heavy-ions. In this section, we will investigate the role of internal momentum distribution within light-ion projectiles in the production cross section of high energy gamma rays using a simple first collision np bremsstrahlung model developed by K. Nakayama and G. Bertsch. 131 In this model, the target nucleus is characterized as a sphere both in configuration and momentum space. The elementary cross section for photon production is assumed to be the semi-classical bremsstrahlung cross section. The bremsstrahlung rate is given by the second order formula of perturbation theory: [Na 86] d" an E -H. 1 1 2 = 2: <0 Olj-A —-—V + V ——-j0A|¢ q) (dn dn /dE) ij 1 81-HO fj f q Here V is the residual interaction between two particles. The interaction was assumed to be only a function of the spacial separation between the neutron and proton, independent of the energy and momentum transfer, i.e. - a _ V-v.5 (rp rn) In this calculation, v0 = 50 MeV. Momentum conservation reduces the sum over intermediate states j to a single term in the plane wave representation. The subscripts 1, 2, 3, and 11 denote the enersy (or momentum) of the initial proton, initial neutron and that of the final proton and final neutron. d‘H _ av’ d’ d’p, t-v Gov 2 dme ' 223 3L (21113 [(2:13 °5(“*‘=“"‘~‘“” 1-2-v, ' 1-2-1], Q is the Pauli blocking operator. For single nucleon projectile, Q simply takes into account the target Fermi sphere: 132 Q=9(P:-PF)9(P~-PF) The total collision rate is given by 3 3 Hpn=211lz fir = ZuvfiglaFg—z-EfiI-‘(i—z-gh 08(e,+e,-e,-e.) If we assume pp collisions are just as likely as pn collisions, the differential cross section for up bremsstrahlung is: d'P _ 1 d‘H dme ’ 2111pn mm In the simplest approach, only the first collisions are considered. After the first collision, the projectile nucleon loses some of the energy, and its probability of making high energy photon in subsequent collisions is thus reduced drastically. The model was able to reproduce satisfactorily the p + Be data of Edgington and Rose [Ed 66]. In the light-ion induced bremsstrahlung, photons can be produced when the protons in the projectile interact with the neutrons in the target, or when the neutrons in the projectile collide with the protons in the target. So, to make use of this proton-nucleus model to calculate photon production cross section in ’H induced reaction, we considered the 'H nucleus a collection of 1 proton and 1 neutron, each of them have a probability fH(p) of having a particular internal momentum p. Then the photon production cross section is obtained by integrating over all the possible values of the 133 internal momentum distribution fbr the proton (or the neutron) inside the 2H nucleus: d'P d’P d'P m H: Zld’pffl(p)méflan = ZIGIPH’HIPHa $21an And for ~He, the cross section is: d‘P _ , d’P _ , , d'P (1me He" ”I“ ""11e(")-dfii(ie)"’pY ' “I“ ””1149” @1021an Where the distribution of fHe(p,) is different from the distribution inside the ‘H, fH(p,), and is the relevant parameter whose role we hope to investigate using this model. C.2. The Internal Maentum Distribution of 'H and ~He C.2.1. Internal Muentum distribution of 1'H A simple analytical ferm of the 'H wave function in coordinate space is given by the Hulthen wave function [De 67]: e-r/R -r/p - e r ) I1?) = [u(r>l“’2< where N(r), is the normalization factor 21(R+p-VRp/Rp) Here R(: u.31 fm), the "radius" of deuteron, is a real quantity, and p ~ R/7 as indicated by experiment[De 67]. The wave function falls off exponentially at large r. 1311 Tb express the wave function in momentum space, we make a Fourier transform of the wave function from coordinate space to momentum space: 1(5) (2:)‘3’2 d’r 0(r) e'ik" 4/221 2[k’+1/R' kii1/p11 (2IN(r)) The ’1! induced bremsstrahlung probability is then calculated by integrating over the momentum space: _d_”.i’. 2111““ (p, 11mm dmdfl H dmdfl _ 1 1 _ ,d =me " Zld’k 211N(r) [Ra'I-I/R: k‘+1/p’ _] dwdfl 1 1 d Ppgpz ' 21°91“ “2 21mm [k'+1/R‘-k‘—:—1/p’]zdwd9 dwdfl Zldflldk k’ fH(k)‘--$Rlan Figure VI-ll is the plot of the momentum density distribution lluk‘ffl(k). It has the value zero at k=0, goes through a maximum and drops off again at large k as can be seen from the graph. 411k2f(k) 135 Figure VI-V ’H and ~He internal momentum distributions. 2.0 136 C.2.2. Internal Momentu- Distribution of ~He For ~He projectile, we use the spherical harmonic oscillator wave function to approximate the behavior of the individual nucleons within the nucleus. In coordinate space, the wave function is: -vr’/2 -vx'/2e-vy’/Ze-vz'/2 6(3) = N e = n e Here, v ~ 0.99. To find the proper normalization constant, we make 10(F)1= N‘ Ie'vxadx [e-vy‘dy [fl d2 = "2 ((- “)1/2)3 1 p. (D 2 N I _ 313/2 (1) Therefore, we obtain: + _ g 3/2 -vr’/2 I1r> -/<,) e Its Fourier transfbrm is: 9 ik-r 1(2) (2:1'3’2 d'r 1(r) e“ "(v)'3/2e-k2/2V _ 2 137 This is then the wave function for “He in momentum space. The bremsstrahlung probability is then obtained by integrating over all possible momenta of the individual nucleons in the ‘He nucleus. d'P d=P - d=P 3635' He: “[d’pfuem w" ’ "ld’pwuem" #102le Vld’k(-3)3/2e'kz/v 41111230 pY 1Ildflldk k’(-3-)3/2e’kz/V _Jflndl’Pm pY uIdoldk k‘ rflem d4359-1in dde The momentum density distribution unwrflem is also plotted (in dash line) in Figure v1-11. He can clearly see from the graph that the maximum of the momentum density peaks at a much higher momentum compared to that of the 'H nucleus. That is, the nucleons within the *He nucleus have a larger probability of having a higher internal momentum. C.3. Result of the Calculation and Comarison with Data The bremsstrahlung photon cross sections were obtained by multiplying the bremsstrahlung probability by the geometrical cross section 1IR' (R = 1.2All3) of the target. Figure VI-5 shows the result of our calculation for 53 MeV/nucleon ’H + Pb and ‘He + Pb at 90° angle. Both the data and the calculated spectra for the 1H + Pb case are shifted down by a factor of 10 for clarity. The calculation reproduces the slope of the spectrum for the 1H 10"2 10" , da/dfldE (mb/MeV—sr) 10'6 138 90 degree lab I aura I l ff I T I I I I I I I I I I l I I I I an E/A ' 53 “0V 0 ‘He + Pb date . fil1:1 ' Calculation (x .5) ”’13.,“ ah‘. '"d:f‘- . ~-~-—::-~-.e I ' m s m a — 0 Figure VI—S Comparison of the photon energy spectra with calculation from the first chance bremsstrahlung model using non-zero temperature internal momenta distribution functions shown in Figure VI-u. 139 + Pb, but the overall strength is a factor of 2 larger than the data (in the Figure, the calculated spectra has been shifted down by a factor of 2 for comparison of the slope with the data). However, the predicted slope parameter for the ~He + Pb was too flat when compared with data, and the magnitude of the calculated spectrum is also too large. This failure may come from our use of the harmonic oscillator wave function, which were known to have a high momentum tail, as a model to describe the internal momentum of the .'He nucleus. Therefbre, we were not able to establish evidence on the effect of the internal momentum distribution on the bremsstrahlung photon spectra. CA. Modified Internal Ila-enti- Distribution Function for 'H and ~He The difficulty of finding a simple yet realistic analytical expression for the momentum distribution of the light-ion projectiles, particularly for ~He in this case, presents a major obstacle. A different approach to this probl- has to be made to investigate the role the proton (or neutron) internal momentum plays in the production of high energy photon. Figure VI-6 shows the deuteron internal momentum distribution function fH(p) we obtained in the last section. Employing this distribution function, we were able to predict the the shape of the bremsstrahlung photon cross section induced by 2H at 53 MeV/nucleon as shown in the previous section. we decided to replace this distribution with a simpler zero temperature Fermi gas distribution, shown as the solid line in the figure. Conserving the total population, we arrived at a Fermi sphere of radius p1,: 0.15 fm'1. Using this new distribution function as the internal momentum distribution of the 2H nucleus, we again calculated the energy spectrum of the 53 MeV/nucleon 2H + 1&0 15-0 - I I I I T I I I I I T r I I I I I I I l I I I I 1 12.5 — p'3.15 p'3.3 O f‘(k) 0mm“ '1 - $ $ Fermi sphere for 'H .. ...... Fermi sphere for ‘He ‘ 10.0 ...: A Z . 5, 7.5 — _ g- n 5.0 '— 2.5 *—" 0.0 1 1 l 0.0 Figure VI-6 Zero-degree-temperature Fermi spheres for ’H and “He. 1‘41 Pb at 90° laboratory angle. The resulting spectrum is shown on Figure VI-7, also plotted on the same graph is the experimental data for comparison. The calculated photon yields fall off sharply at energies above 50 MeV because of the sharp cut-off in the deuteron internal momentum distribution. Nevertheless, the calculation was able to predict the slope of the spectrum in spite of the simple minded approximation in the momentum distribution. Alpha particles not only have one more neutron plus one more proton than deuteron, the individual nucleons within alpha particle also have higher internal momenta. Therefore, the Fermi sphere for “He nucleus must contain higher momentum, i.e. a larger Fermi radius. He chose the Fermi sphere having twice the radius of the 2H, p5,: 0.3, shown in Figure VI-6 by the dashed line. The energy spectrum of 53 MeV/nucleon ~H + Pb at the 90° laboratory angle was calculated. Figure VI-8 shows the comparison between the energy spectra of 2H + Pb and ‘He + Pb both at 53 MeV/nucleon incident energy. The spectrum of “He + Pb has a larger yield and a flatter slope than the spectrum of ‘H + Pb. The predicted spectrum is compared with the data for the 53 MeV/nucleon ~He + Pb reaction at the 90° laboratory angle (Figure VI-9). We find the predicted yield is a factor of 2 larger than the data, while the agreement in slope parameter is quite satisfactory. Therefore, the difference in the internal momentum distribution of both systems having the same energy/nucleon can be responsible for the different slope parameter we observed. D. Conclusion We have calculated in this chapter, using the BUU model by Bauer et al., both the reactions of symmetric systems and the light-ion induced 1‘42 da/deE (mb/MeV—sr) caI I I r I I r I T I I T l—I I I I G 10‘1 °o 53 MeV/nucleon “a + Pb 0 data 10"2 x Model 10‘3 10“ m a 4' 41 10‘5 10-6 1 1 1 1 L 1 1 1 i l 1 1 1 1 l L 1 1 111 o 20 40 so so 100 E7 (MeV) Figure VI-9 Comparison between experimental data and calculations using the zero temperature internal momentum distribution shown in Figure VI-6 for 53 MeV/nucleon ~He + Pb. 1‘43 da/deE (mb/MeV—sr) I I T7 I r j I T I r I I r I l I I r I : 10-1 -7 D p,-.4 in" (Alpha) 3 1 10‘2 x p,-.2 m" (d) a 10‘3 —§ 10" _: 10'5 3 10-6 1 1 g I 1 1 1 1 l 1 1 g 1 1 L 1 1 1 1 o 20 4o 60 80 Figure VI-8 First chance np bremsstrahlung model calculations for 2H + Pb and “He + Pb reactions assuming the zero-degree-temperature Fermi gas as internal momentum distribution fuctions (shown in Figure VI-6). da/deE (mb/MeV-sr) 10‘1 10'2 10‘3 10" 10-5 10"6 1M an I ' I , I ' y I 1 T 1 I I T I : o . “a 53 MeV/nucleon ‘He + Pb 1 1% 5 m 0 data : ‘% mm x Model (x 0.5) 2° 4° 5° 80 100 E7 (MeV) Figure VI-7 Comparison between experimental data and calculations using the zero temperature internal momentum distribution shown in Figure VI-6 fer 53 MeV/nucleon 2H + Pb. 1'45 reactions. The 800 model was able to reproduce most of the energy spectra of the symmetric system data reasonably well. But it failed to predict the correct slope and overall strength of the light-ion data, probably due to its use of some of the parameters that are more suitable for heavy-ion systems. The predicted angular distributions in the nucleon-nucleon center- of-mass frame, which are backward peaked, disagree with the data. The discrepancy may be due to an overestimation of multiple scattering within the colliding nucleus. He adapted the first-chance collision Fermi gas model, proposed by Nakayama and Bertsch, to study the effects of internal momentum of the light-ions on the production probability of bremsstrahlung photons. The calculation was in good agreement with the data from 53 MeV/nucleon “H + Pb reaction. But the agreement with the 53 MeV/nucleon “He + Pb data was poor, due to the poor approximation of the internal momentum distribution we have chosen. In order to investigate the projectile dependence of the photon cross section, a simplified internal momentum distribution, zero temperature Fermi gas, was used. Using this new approximtion of the internal momentum distribution, the model was able to reproduce the data of 2H + Pb. Then by varying the size of the Fermi sphere, we found that pp: 0.3 fm'1 - 2 ' ZPF( H) gives the best agreement with the slope parameter of the 53 MeV/nucleon “He + Pb data. This calculation shows, for the light-ion case, the increased internal momentum within the “He projectile could be an important contributing factor for the flatter slopes in the “He induced bremsstrahlung photon energy spectra. Chapter 7 Summry The high energy gamma rays produced in both the light-ion induced reactions and the symmetric systems have exponentially decreasing energy spectra. The double differential cross sections in the nucleon-nucleon center-of—mass frame can be characterized by a function of the form A(1-Bcos’9)e'E/T. The angular distributions are symmetric about 90° in the nucleon- nucleon center-of—mass frame. All of the reactions we studied show a dipole component superimposed on an isotropic component. The relative strength of the dipole component ranges from 29% to #91 for the heavy-ion induced reactions and up to 60% in light-ion on carbon target reactions. He also detected a trend of increased dipole components with the decrease in the masses of the systems. He observed no evidence of quadrupolar angular distribution in the center-of-mass frame. The slope parameters obtained for all of the heavy-ion induced systems we studied are in general agreement with data at the same energy measured by other groups with similar systems. The slope parameters in the light-ion induced reactions are substantially smaller than those found in heavy-ion induced reactions at similar systems. The projectile dependence in light-ion induced reactions may be due to the difference in the projectile internal momentum distribution. A calculation based on first-chance n-p bremsstrahlung model was able to reproduce the different slopes of “He and 1117 2H at the same energy. He also observed target mass dependence in the slope parameter T for both the light-ion and heavy-ion induced reactions. For the three symmetric systems at E/A = 30 MeV, the integrated photon cross sections for ganma ray energy above 30 MeV are in good agreement with the incoherent bremsstrahlung (ApAt)2/3 scaling scheme. The ratios of the bremsstrahlung photon total cross section provide no evidence to support the 22 charge dependence predicted by the coherent bremsstrahlung model. A1 86 Ba 86a Ba 86b Ba 87 Be 85 List of References N. Alamanos, P. Braun-Hunzinger, R. F. Freifelder, P. Paul, J. Stachel, T.C. Awes, R. L. Ferguson, F. E. Obenshain, F. Plasil, and G. R. Young, Phys. Lett. 173B, 392 (1986). H. 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