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Iran! .1... . ‘ .:$0 Seven telescope scintillator array used in the Hit detector, i.e. the Hit plastics (HP) ..................... vi PAGE 12 15 17 18 19 21 23 2H 26 27 3O II“12 III‘1 III"2 IV-1 IV-2 IV-3 IV-H IV‘5 IV-6 IV-7 IV-8 IV-9 IV-1O IV-11 Contour plot of the AE (vertical) Vs. E (horizontal) for a CaFZ/ plastic scintillator telescope in the Hit detector 0.....00.0000..0.0.0.0 Chamber setup during the expiment ..... Electronics schematic for the experiment Light particle inclusive energy spectra f‘Or‘15MeV/AC*.AlJ0.0.0.00..00.00000... Light particle inclusive energy spectra for 15 MeV/A C+C ...................... Light particle inclusive energy spectra for 30 MeV/A C+Au 00.....0....00...00.. Light particle inclusive energy spectra for. 30 MeV/A C+C .00....00.0.00..0..000 Inclusive energy spectra for Be, B and C from the 30 MeV/A C+C reaction, as measured with the BCS ........ ...... ... Projectile~like fragment inclusive energy spectra for the PLF detector at 15° for 15 MeV/A C+Au .............. Projectile-like fragment inclusive energy spectra for the PLF detector at 15° for 15 MeV/A C+C ............... Projectile-like fragment inclusive energy spectra for the PLF detector at 15° for 30 MeV/A C+Au ..... ......... Projectile-like fragment inclusive energy spectra for the PLF detector at 15° for 30 MeV/A C+C ...... ......... The weighted distribution of source sizes for the momentum conservation calculation based on 2nbN(b) for C+Au.. The weighted distribution of source sizes for the momentum conservation calculation based on 2wa(b) for C+C. vii 31 35 38 A6 “7 us A9 57 58 59 6O 61 66 67 IV-12 IV‘13 IV-1M IV-15 IV-16 IV~17 IV-18 IV-19 IV-ZO Energy spectra for protons at A5° in the Hit plastics in coincidence with the BCS for 30 MeV/A C+Au. Solid lines correspond to a moving source fit. .... Energy spectra for protons at “5° in the Hit plastics in coincidence with the BCS for 30 MeV/A C+C. Solid lines correspond to a moving source fit. Ratio of coincident to inclusive temperatures from the moving source fits of protons for the quasi-elastic (QE), deep-inelastic (DI) and the bragg curve (BC) as a function of fragment mass from 30 MeV/A C+Au. Ratio of coincident to inclusive temperatures from the moving source fits of protons for the quasi-elastic (QE), deep-inelastic (DI) and the bragg curve (BC) as a function of fragment mass from 30 MeV/A C+C. ..... Energy spectra for protons at “5° in the Hit plastics in coincidence with the QE for 30 MeV/A C+Au. Solid lines correspond to a moving source fit. .. Energy spectra for protons at 45° in the Hit plastics in coincidence with the DI for 30 MeV/A C+Au. Solid lines correspond to a moving source fit. Energy spectra for protons at A5° in the Hit plastics in coincidence with the QE for 30 MeV/A C+C. Solid lines correspond to a moving source fit. .... Energy spectra for protons at “5° in the Hit plastics in coincidence with the DI for 30 MeV/A C+C. Solid lines correspond to a moving source fit. Proton energy spectra for the HP (opp. side) and the BP (same side) in coin- cidence with a lithium in the BCS for 30 MeV/A C+C. The solid (dashed) lines correspond to single (weighted) source momentum conservation calculation. The single source used 2H nucleons. viii 68 69 79 8O 81 82 83 8A 87 IV*21 IV~22 IV-23 IV-ZU IV-25 IV—26 IV-27 IV-28 IV-29 IV-3O IV-31 IV‘32 IV‘33 IV-3u IV-35 IV-36 Proton energy spectra for the HP (opp. side) and the BP (same side) in coin~ cidence with a carbon in the BCS for 30 MeV/A C+C. The solid (dashed) lines correspond to single (weighted) source momentum conservation calculation. The single source used 2“ nucleons. ..... Proton energy spectra for the HP (opp. side) and the BP (same side) in coin- cidence with a lithium in the BCS for 30 MeV/A C+Au. The solid lines correspond to single (38 nucleons) source momentum conservation calculation. Proton energy spectra for the HP (opp. side) and the BP (same side) in coin- cidence with a carbon in the BCS for 30 MeV/A C+Au. The solid lines correspond to single (38 nucleons) source momentum conservation calculation. Ratio of opposite (HP) to same (BP) side temperatures from the moving source fits for 15 MeV/A C+Au for protons. . ......... Same as FIGURE IV-ZA for 15 C+C. ........ Same as FIGURE IV-ZA for 30 C+Au. ....... Same as FIGURE IV-2N for 30 C+C. .. ..... . Ratio of opposite (HP) to same (BP) side velocities from the moving source fits for 30 MeV/A C+Au for protons. .......... Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+Au for protons. ..... ..... Same as FIGURE IV-29 for deuterons. ..... Same as FIGURE IV-29 for tritons. ....... u Same as FIGURE IV-29 for He. Same as FIGURE IV-29 for 30 MeV/A C+C. Same as FIGURE IV-33 for deuterons. ..... Same as FIGURE IV-33 for tritons. ....... 3 Same as FIGURE IV-33 for He. ........... ix 88 90 91 92 93 9A 95 97 98 99 100 101 102 103 10" 105 IV‘37 IV-38 IV‘39 IV-UO IV-U1 IV-U2 Same Same Same Same Same Same as as as as as as FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE IV‘33 IV-29 IV-38 IV-38 IV-29 IV-A1 for for for for for for u 15 MeV/A C+Au. 15 MeV/A C+C. He. tritons. 0.0.00 deuterons. deuterons. 106 107 108 109 CHAPTER I INTRODUCTION Research scientists have for years used heavy ion beams to probe the structure and dynamical properties of the nucleus. Heavy ions with bombarding energies below 10 MeV/nucleorxamud at relativistic energies above 200 MeV/nucleon have been studied extensively [Sc 81]. Nuclear science has over the last few decades, used nuclear spectroscopy as a means to study the nucleus at the low excitation energies by studying giant dipole resonance, giant quadrapole resonance, and transfer reactions. Higher energies allow one to investigate the prOperties of hot and dense nuclear matter. The collective and dynamical effects of a strongly interacting many body system is observed at these higher excitation energies and compared to such models as hydrodyamics [St 80] and cascade [Kr 85]. Particle emission is the primary mode of de-excitation. For lxnv energy nuclear reactions, a compound nucleus can be formed and decays after full statistical equilibrium is reached. The decay of the compound nucleus can be Lmderstood in terms of the Hauser~Feshbach theory [Ha 52] and fermi gas formulation. With increasing energy, 11mm; particle emission prior to the attainment of full statistical equilibrium becomes important, termed pre- equilibrium particles, possibly showing some forms of 1 2 collective and dynamic effects. As the energy is raised, the concept of an expanding gas of nuclear matter in thermodynamic equilibrium becomes applicable. These ideas have been successfully applied to light particle emission from a variety of systems [Go 78, Ka 77]. The understanding of the reaction mechanisms in these two energy regimes has developed two very different theoretical models. Collisions in the low energy regime are dominated by the nuclear mean field, with such dynamical models as the time-dependent Hartree-Fock (TDHF) approach [W0 82]. At very high energies a pure mean-field approach becomes inadequate and instead, dynamical models such as hydrodynamics cm" two-body scattering become important [St 80, So 81]. In the intermediate energy region between 10 and 200 MeV/ruuflleon a transition is expected to occur from the mean field description of low energy interactions to the nucleon— nucleon scattering behavior characteristic of high energy collisions [Sc 81]. This transition 143 expected tx>1~esult when the velocity of the colliding nucleons surpasses both the Fermi velocity and the velocity of nuclear sound. It is however, unlikely that the transition is a sharp one [da 8A]. This critical transition region is where the possible coexistence of the gas and liquid phases may be present with possible signatures of a liquid-gas_phase transition [R0 82]. The experimental observation of a phase transition and the determination its critical temperattnwaivould be of interest in studying an equation of state for nuclear 3 matter. The current generation of nuclear accelerators, including the super conducting cyclotron facility here at Michigan State University, are well suited to study this region of transition between 10 and 200 MeV/nucleon, along with GANIL, ORNL, LBL, and SARA. V The observation of energetic light particles (p, d, t, 3He, and a) is a useful method for studying heavy ion reactions. These particles are assumed to originate frmn the overlap of the projectile and target. The first generation of experiments was to measure the inclusive spectra of light particles produced in these collisions. The data has IMHHT analyzed with the participant-spectator model in which the light particles, ennitted from a thermalized participant region of target and projectile nucleons, are fitted to the energy spectra assuming a single moving source. The parameters extracted from these fits have been very useful in quantifying a large amount of data. The fitting processes will be described in more detail in chapter IV. The parameters describing the data have been shown to vary smoothly with bombarding energy [We 82], indicating that the transition to mechanisms typical of relativistic energy reactions is a smooth one. At these energies, 15 and 30 MeV/nucleon, it has been suggested that the participants and spectators are not well separated. There is instead a local thermalized zone, or hot spot, which is formed [Go 79, St 81, Fr 83, Fi 8A]. This hot spot begins to break away from the target as the txnnbarding energy increases and becomes an independent participant zone. This heated region of the nuclear surface would attain much higher temperatures than the compound nucleus and after its formation would possibly decay by thermal diffusion into the adjacent nuclear matter or by the emission of energetic light particles. Taking a more dynamical aunncoach, intermediate or lighter mass particles might be emitted from the target due to the transfer of momentum showing some form of a collective, dynamical effect. The emission of particles from heavy ion reactions can be broken up into two major modes. The first of which descritxns the particles as being emitted from a thermalized source in a statistical frameworkm. 'The particles are usually fitted to a Maxwell-Boltzmann distribution and assumptions about thermal and chemical. equilibriwun are usually made. Models that have incorporatmdtfius form of emission include the Fireball [We 76] and Quantum Statistical [G03 78, Su 81, St 83] models. The second mode assumes the particles are emitted frwnn a dynamical framework. These models incorporate a two~body or fluid dynamical approach to a calculation and examples include the single scattering knock-out [Ko 77, Ha 79], cascade [Be 76, Ya 81, Cu 82, To 83, Kr 85], and hydrodynamic [Bu 81, St 80, Bu 83] models. Figure I-1 shows a comparison of these two approachs with an incoming projectile on a stationary target nucleus in the lab frame [We 83], Figure I-1a shows the FIGURE I-1. Schematic illustration of two possible heavy-ion processes, a) fireball model b) hydrodynamic model. 6 geometry of the Fireball model [We 76] and Figure I-1b is an example of tflue hydrodynamical approach [St 80]. These two modes on the other hand are not mutually exclusive. For these intermediate energy reactions,21nuwe realistic approach would be a combination of these two methods of particle emission. All of these models do a godd job of predicting the inclusive data. To distinguish amoung them one must use coincidence measurements to separate different classed of events. Evidence for thermal emission is abundant as will be seen later, but observations of dynamical effects are not as easy. Dynamical effects require complex coincidence experiments (i.e. the plastic ball) wereas evidence for thermal emission can be found in inclusive singles data. It has been shown that for the lower irnuunnediate energy regime, 10 11 , 15 8 ‘1' 6 1,! ' 7 9 f I} ; A CHANNEL FIGURE II-6 Charge spectrum from the BCS for 35 58 the reaction Cl+ Ni at 230 MeV. 22 calibration for a 30 MeV/nucleon 12C + 12C experiment, as obtained from the punch through line, is shown in Fig. II-7. The second method of reading out the BCS is by storing the entire current signal from the anode onto magnetic tape. This signal is digitized by a flash encoder that integrates the charge in 75 nsec time bins. A typical Bragg curve, measured with the flash ADC for the reaction Au(‘“N,X) at 35 MeV/nucleon is shown in Fig. 11-8. The advantage of this method is the ability to playback the entire anode signal at some later time and analysis it "off-line" with different methods. All of the analysis of the BSC in this thesias has incorporated the first method. The second subsystem of the Bragg Curve Detectcn' is an array of six CaF2 - plastic scintillator "phoswich" telescopes as seen in Fig. II-1, which sit:¢i,t,3He, sand ‘Wie are: clear] ly separated. The hexagonal shape of the Bragg Curve Detectcn‘ system was developed to be a prototype subarray for a An detector [We 85]. The shape of the An detector is based on a thirty- two face truncated icosahedron containing 20 regular 26 4——* RNODE SIGNRL PLRSTIC SCINTILLRIOR I: “in- ‘jf‘_"- 11"” t=0 80 240 FIGURE II‘9 E DOC GRTE Con [__— AE ROC GRTE I I I I I I T nsec 22“ “SOC Timing diagram for the scintillator array telescopes. The anode is a sum of the fast plastic scintillator component and the slow CaF2 component. 27 MSU-84-617 O L 1 L 1 O IOO E (CHANNELS) FIGURE II—10 Contour plot of the AE (vertical) Vs. E (horizontal) for a Can/ plastic scintillator telescope in the BCS. 28 hexagonal faces and 12 regular pentagonal faces (a "soccer ball" geometry). In addition, each subarray will include a low pressure Multi-Wire Proportional Counter (MWPC) for fission fragments, which will be in front of the Bragg Curve Spectrometer. Both the Can and the plastic scintillator were machined at MSU. Because of its low meltiru; point and tendency to craze near regions of high temperatures, the plastic scintillator was machined with great carer. No more than 10 mils of material per out were taken off and it was cooled with a continuous flow of water soluble oil. The scintillator was then sanded with a fine grade waterproof polishing paper immersed in water and finally polished with optical. polishing alumina. The CaF2 elements were machined from 12.5 cm diameter by 3 mm thick disks of CaF2(Eu). Because of the great stress in these large but fairly thin” cnsks, a number of techniques were used to cut them into triangulin~ shapes. The only technique that was able to cut the crystals without fracturing them, was with a vertical table sander cooled with a continuous stream of water and set on a very slow speed. This technique alleviated the stress slowly from the end so that the crystal would not crack. A clear lucite lightpipe was also machined to match the plastic scintillator to the photomultiplier tube. In order to minimize the space between each telescope and not allow light to cross from one scintillator to the next ("cross talk"), it was necessary to assembled 29 reflective TiO2 with epoxy. All six plastic scintillators were combined in this manner. The Can, lightpipes, and photomultiplier tubes for each telescope were attached with optical epoxy. The entire array of six telescopes was then epoxyec1<3nto the rear of the Bragg Curve Spectrometer. The lightpipes were painted with a TiO2 water based reflective paint [Bi 67]. B. HIT DETECTOR This detection system is also composed of two subsystems; an array of seven light-particle "Phoswich" telescopes capable of determining the energy and identity of light isotopes (Fig. II-11), and a multiwire proportional counter, which gives more precise position information on these same light particles, positioned in front of the telescope array. The plastic scintillator is 17 cm thick and the Can is 2 mm thick. The telescopes were designed to close pack in a spherical geometry as six tapered hexagonal shaped detectors surrounding a seventh tapered hexagonal shaped detector. Figure II-12 shows a AE-E plot for an HP telescope. An important consideration for both detechm‘systems was the low energy cutoff imposed by the relatively thick Can fawn“; element. (Salculated cutoffs are given in Table II—1 for the hydrogen and helium isotopes for Can thicknesses of 2 and 3 mm. The cutoffs imposed by these 30 usux-ez-3ss Photomultiplier Tube NE I02 Plastic E . Detector Co F2 as detector FIGURE II-11 Seven telescope scintillator array used in the Hit detector, i.e. the Hit plastics (HP). 31 .LOuomumu pa: 0:» :H caoomcamu Loumaaachom oHpana \mmmo m com AHmScONHLonV m .n> flamedugo>v m< on» no Scan Lacucoo NpuHH mmaon mo._.<._1__._.z_om oCmnja “ m mm¢1n013m2 3303:3117 32 TABLE II-I CALCIUM FLUORIDE PUNCH THROUGH ENERGIES (MeV/n) THICKNESS 2 mm 3 mm Proton 21.5 27.0 Deuteron , 1A.S 18.2 Triton 11.5 1A.5 ’Helium 25.2 31.5 “Helium 21.5 27.0 33 detector thicknesses were considered to be sufficiently low for the beam energies to be used. CHAPTER III EXPERIMENTAL The experiment was done at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University in the 60 inch scattering chamber. Beams of 15 and 30 MeV/nucleon 12C were used on both a goldeuuia carbon target. The targets used were all self-supporting and consisted of 2.A5 mg/cm2 Au and 201 pg/cm2 C. A. EXPERIMENTAL SETUP The experimental setup, as seen in Fig. III-1, consisted of two plastic scintillator arrays, ILit plastics (HP)'auui Bragg plastics (BP), for light particle detection (see Chapter II). In front of the Bragg plastics there was a Bragg Curve Spectrometer (BCS) for slow moving Target-Like Fragments. The plastic scintillator arrays were positioned in the chamber with the bottom two telescopes for both arrays at the beam height and each were moved during the experiment. A high energy fragment detector was placed at a fixed angle of 15 degrees from the beam axis as a projectile-like fragment detector (PLF) consisting of a two element silicon stack. A U00 um Si detector was used for the AE and a 5 mm for the E detector. The positions and solid angles for the detectors are given in Table III-1. The negative angles of the Hit detector indicates that it 311 35 HIV ocncm a ‘7 V m: 00' surname munch ‘ FIGURE III -1 Chamber setup during the expiment. 36 TABLE III-1 DETECTOR ANGLES .---------_-----—---------—_---------‘----‘-------‘--fl—-- DETECTOR THETA (DEG) SOLID ANGLE (MSR) PLF 15.0 7.8 Hp(a)v ~A5.0,-90.0(b) 1A.9/element (a) (b) BCS 45.0.90.0 55.A/e1ement (a) Angles are for the central element of the array. (b) The arrays for the C target were at 95° only. 37 was on the oppisite side of the beam from the Bragg Curve System and PLF detector. Both coincidence and scaled down singles events were taken. Coincidence requirments consisted of any two or more plastics from either array or any one or more plastic scintillators in coincidence with a trigger detector. Both the BCS and the PLF detector served as a trigger detector. The electronics diagram is shown in Fig. III-2. The data acquisition system at NSCH. is based on a multiprocessor, multitasking system. A DEC VAX 750 minicomputer with an LSI-11/23 as a front end data capture device was used [Au 83]. The software in both of these computers isrmflddtasking,tflm LSI-11 not only takes event data, but has programs which are responsible for the run control, accumulation,zuuitflm live display of a number of sealers. fNMB'VAX software includes programs which display the accumulated histograms as well as programs which are responsible for binning the raw event data. A Kinetic Systems CAMAC serial highway connects the VAX to the data acquistion hardware. This system consists of an LSI-11/23 which is resident in a CAMAC crate, and an assorment of scalers, analog to digital converters (ADC), time to digital converters (TDC), and charge integration to digital converters (QDC). The spectra accumluated on line are displayed on an Advanced Electronics Design (AED) model 512 color graphics terminal. This terminal is capable of displaying monochrome one dimensional Iristograms euui color 38 .ucosfiewqxo on» non oaumeocom moficocuooam NIHHH mmaon c9. .llaaa .88. 818 “nu a .58 s .35 no If ..So a ,2! Eu 3.2 >35 .3 ....» 8» 38 a: 8 at... ..zi 3: Fa , .A ...! .88 2...... ... 18a . , 0.. o 8 no.3 .3888. ...:......8 5» 5.855» co :2... .8. 53...» 2... a. .... .... S... s A: E a... a 83 8» “a u :8 a 1...... ... ...-8 a. «a» 5.. :- 3 09. $3 3 3.00. 3.08 :2... 8» ud 5.534 1. Q .290 03 . 9.0 3.2:: =- .308 3.8 838m in... ..o 3 «a» 03 2 ...}. u .34 ... 3 - 004 o. in N i! .0. . autism d 3 3mm! 39 density plots of two dimensional spectra with 512x512 pixel resolution. The VAX is used for the actual on line analysis and event taping of data buffers sent to it by the LSI-11. The 15 and 30 MeV/nucleor1 ‘H: beam currents were monitored in a shielded faraday cup placed approximately two meters beyond the exit port of the scattering chamber. The current inns integrated in a BIC Current Integrator and was recorded in the computer using a CAMAC scaltn'tnodule. The beam intensity varied from 1.5 particle namps (9x109 particles per second) to 10 particle namps (6x10’° particles per second). B. DATA REDUCTION AND ANALYSIS The data taken in the expriment was recorded on magnetic tape in event mode. All runs with the same detector setting were summed together. Since this was a coincidence experiment, it was necessary to optimize the statistics for each type of coincidence event, therefore all of the Hit plastics were summed together as if‘ it were single detector. The same was done for the Bragg plastics. In addition, the singles events were scaled down so that better statistics could be obtained for the coincidence events. The absolute normalization was based on the integrated beam current in the faraday cup. The event data was later played backed onto the computer and sorted by particle type using software gates which had been created with the aid of a two dimensional no color display from the AED terminal. The sorted data were then calibrated, binned into histograms, and then normalized to obtain the final absolute normalized spectra. The data was corrected for several experimental effects including reaction loss, scatter out and computer dead time. Energy calibrations for the scintillator array telescopes were based on both direct beam calibration and fits to previously calibrated data. A beam of 25 MeV/nucleon alpha particles was used to calibrate the detectors. However, since the minimum energy for an alpha particle which penetrates the Can in the Hit and Bragg plastics are 22 and 27 MeV/nucleon respectively, and since the calibration for protons and alphas are not the same, this calibration was found to be inadequate. By using a least squares fitting routine to previously calibrated 30 MeV/nuclmniC+Au data [Ha 8A], a calibration was obtained for each telescope. Values of the reduced X2 for the fits were typically less then 5 and a comparison to the beam calibration indicated that a satisfactory calibration was obtained. The energy calibration for the silicon PLF detectors was done by injecting a known amount of charge by means of a chopper inrlser in the irunit stage of the detector preamplifiers and using the measured values of the ionization energy of silicon, c=3.67 MeV/ion pair [Pe 68]. C. Reaction Loss Correction A1 The plastic scintillator telescope spectra were corrected for reaction losses of the light particles stopping in the detectors. Nuclear interactions, as compared to atomic electron interactions, tend to broaden the full energy peak on the low energy side. Inelastic collisions in the detector typically have neutrons, gammas, and alphas as 13u31~eaction products. The light output in the detector is less for these reaction products than it would have been for the original particles because of the nonlinearity of the response of scintillation materials to more highly ionizing particles and production of uncharged particles. These effects result in the loss of the particle from the full energy peck. The particles then no longer fall into particle identification lines and appear as a smooth background in the Fig. II-10. The fraction of reaction loss for protons as a function of proton energy was taken from Measday and Richard-Serre [Me 69]. In order to make the corrections, the detector was divided up into slices, and the particle energy of each slice calculated from the entrance energy using energy—range tables generated by the code DONNA. The reaction cross section was then calculated by parameterization obtairuui by fitting a form of the standard reaction cross section oR=nR=<1—vC/E)<1—(K/E>*) (111—1) A2 to measured cross sections tabulated by Measday and Richard— Serre [Me 69]. Where the nuclear interaction radius R is given by R=ro(A11/3+A21/3-1) (fm), (III-2) where ro=1.2 fm, the coulomb potential at the interaction radius V0 is, vc=1.uu(z,z,/R) (MeV), (III-3) and K and Aznwethe adjustable parameters. An adjustable overall normalization factor was also included in the fit. The reaction cross section for each snaice was then calculated and the reaction probability of a particle was given by the integration over the slices r=1—exp(—Znioi), (III-A) i . where n1 is the number of atoms/01112 in the ith cell and Oi is the calcnfilated cross section in each cell. The parameterized fit was for protons in scintillator. The values for K and A were K=20 MeV and A=1.2, with the normalization constants being 1.A5 for plastic scintillator and 2.7 fWM° CaF2. 'The reaction probability was calculated A3 for each energy bin in the spectrum of each particle, and the cross section corrected by the factor 1/(1-f). D. Scattering Out Correction The need for large area detectors in multi-particle coincidence experiments lead to the construction of high density plastic scintillator arrays in which the individual telescopes were not collimated. A scattering out correction was necessary because particles incident near the edge of a plastic scintillator detector were likely to scatter out and not be identified as valid events. Particles scattering into the detectors from neighboring telescopes would not 1x3 identified as valid events since there would be no CaF2 (AB) signal for such events. A Monte Carlo calxnxlation was developed to simulate the scattering out effects of transverse straggling of the particles. First the code calulated the total range of a given energy particle in the plastic scintillator and then calculated the transverse straggling based on a gaussian distribution with a root mean sqaure projected angle given by the formula [Pa 8A] Z IELEIEn) 1/2 l _-i --- epr0j= A t(t+2mo) ) [1+ LOSIOIL/LRIIII + ] [L/L.R 9 where t=Incident kinetic energy per nucleon, AA mo=931.5, L=Thickness of material traversed (g/cmz), LR=Radiation length, A,A8=Mass number of particle, medium, Z=Atomic number of particle. The radiation length for different materials are tabulated in the literature [Pa 8A]. For those materials that do not have measured radiation lengths, they were calculated based on a formulation given by Tsani [Ts 7A]. The entrance point for each particle and each energy were fcnuui using a Monte Carlo technicnua in which the geometry of the front face of the telescope was treated with equal probability. The transverse scattering in the Can was calculated first and the particles new trajectory was tnuni used for time calculation in the plastic scintillator. The final calculated trajectory of the particflxe1was checked against the actual geometry of the detector to ascertain if the pmrticle would have scattered out. The fraction scattered out, R, was calculated as the number of simulated events for which the particle scattered out divided by the total number of events. The scatter out correction factor for each bin of the energy spectra was divided by (1—R). CHAPTER IV RESULTS In this chapter, light particle (Z=1,2) spectra are presented as inclusive and coincidence cross sections. The coincidence spectra are in coincidence with intermediate mass fragments (3:256) in the Bragg Curve Spectrometer (BCS) at A5° and the Projectile-Like Fragment (PLF) detector at 15°. The requirement that the spectra have sufficient statistics dictated the need to sum all of the plastic scintillators 1J1 each of the arrays, as if each of the arrays were one detector. The inclusive spectra for the trigger (PLF and BCS) detectors are also shown. The error bars shown in each of the spectra are statistical. Positive angles for an array indicates that it is on the same side of the reaction plane as the trigger particle, negatiina angles imply the opposite side. A. 15 and 30 MeV/nucleon 12C+Au,C Inclusive Spectra 1. Light Particle Inclusive Spectra Figures IV-1 and IV-2 show the double differential cross sections of the hydrogen and helium isotopes f01a H5 MeV/nucleon C+Au and C targets, respectively, and figures IV-3 and IV-A show the double differential cross sectioms for the 30 MeV/nucleon C+Au and C targets, respectively. The 30 MeV/nucleon C+Au spectra consist of angle A5 A6 15 MeV/nucleon C+Au IIIIIIIIIII 1Hh111 3 He J. IIIIIIIIIII OI 111l111111 FIGURE IV-I 400 Energy (MeV/nucleon) Light particle inclusive for 15 MeV/A C+Au. /—\ L1 0 (p 1() :1u1un1nnlnulninegIniuulunlnn HIHHIH a ’ - 1 o d 1 t .93 11 1' " 0 as a :3 .1 1 I: . . \\\ 3: Y ” > a; a 0’ 1: : S. . 1 L-J \ ~ v-Q EE i g 1: 1 c: 1 1’ ”U 3? I m —5' 4| " I I 13 1() IHHIHHIHHIIIlHIHllHIHHIIHlHHIlHIHIIH ‘\i 0 4O 80 1200 40 80 0 40 O b "U 40 energy spectra 117 0 15 MeV/nucleon C+C 10 :7. IIUIWUIIIIIIIIIIIHFEI IIIIIIIIIUIITIII IIIIIIIUII I IIIIIIIII I l l ffiT‘V t a V 1 1 LIJLLLI T ‘ V'VVV' llLLLl . ...", 1 5' " L 1C) LHIHIHIHIIUIH 11h111nln1h1d1u1n111fl11 HIIIHIHII 0 40 80 1201) 40 80 0 40 0 40 Energy (MeV/nucleon) ‘ A A AJALAI V d2 (T/dE d0 (mb/[MeV/nucleon]-sr) FIGURE IV-2 Light particle in clusive ene for 15 MeV/A C+C. PSY Spectra d2 U/dE d0 (mb/[MeV/nucleon]~sr) A8 30 MeV/nucleon C+Au FIGURE IV‘3 1 illirrrlllrillillllilii‘ 11[111]111]111[111§111[111[111 111[111|111 111[1111111 o " p 3 He E 1 " _1” E —2* '. _3: . 45: ‘ ‘ g. 90 § I e 1 + 1’ —41 I a I ‘1 _ IHIHIHHIUIUIUIUFlHIthHIIlhllthlMllllHth ,lUIHI u 0 40 80 1200 40 80 O 40 O 40 0 40 Energy (MeV/nucleon) for 30 MeV/A C+Au. Light particle inclusive energy spectra ’49 30 MeV/nucleon C+C 10 :IIIIIIIIIIIIIIIIIIIIlllllllfilIIIIIIIIIIIIIIIIIIEJIIIIWIIII IIIIIIIIIII IIIIIIIIIII q I b ’ He 1- II D D b i 10 4 lllILllIlliIlllIlllIlllIlIll 1111111111111 11111 mlml 11 1111111111 11111111 11 o 40 so ’1200 40 500 400 400 40 Energy (MeV/nucleon) d2 o/dE d0 (mb/[MeV/nucleon]-sr) FIGURE IV—A Light particle inclusive energy spectra for 30 MeV/A C+C. 50 measurements of HS and 90° in the laboratory. The solid curves in the figures correspond to moving source fits. All of the inclusive spectra are smooth and similar in shape and were fit well with the moving source parameterization. The C+C data were fit assuming the velocity of the source was the center of mass velocity. 2. Moving Source Parameterization The ,light particles emitted can be parameterized by assuming the they come from a single source with a Maxwellian energy distribution observed in a moving frame. This source emits particles isotropically in its rest frame which is moving at approximately half the beam velocity. The light particle energy spectra frwmm the plastic scintillator arrays are fit by a single moving source parameterization. Heavy ion reactions have tKHHl described‘ as having three distdrunsrregions from which particles are emitted. 1wus idea is known as the participant~spectator picture of nuclear collisions [We 76, Go 78, Aw 81]. Tme participant region is described as the overlap region between the projectile and target consisting of a highly excited system of nucleons and light nuclei, whereas the spectator region is described as the cold remnants of tme target and projectile that did not.overlap. The single moving source parameterization refers to a fit of the energy spectra taking into account only the participant region emission of light particles. 51 In order to isolate the participant region or intermediate velocity source in the energy spectra,iJ;is necessary to exclude those parts of the spectra that correspond to the spectator region, that is the projectile and target velocity sources. The projectile source is usually associated with fragments at the beam velocity centered around 0°. Because the center of the most forward angle light particle detector array is at ”5°, we are not sensitive to the PLF's. A target velocity source due to target fragmentaticn1:is usually associated with low energy particles distributed almost isotropically in the laboratory frame. A low energy out off of about 25 MeV/nucleon eliminates most of the target velocity source, although there are certainly'stdll.contributions from the spectator region in the energy spectra. A parameterization using three moving sources have been attempted for relativistic heavy ion reactions [Ja 83]. It should be noted that the participant regicnian~ the present energies is not always thought of as a separate non-interacting entity from the target and projectile, but instead emits particles while still very close to the spectator regions [80 8“]. However, we still apply the moving source parameterization as convenient method of extracting informaticn1:from the light particle spectra. The moving source parameterization is a useful tool for comparing large volumes of data in which the data can be condensed into just three parameters (described below) which 52 were fit to all the data. The idea of a thermalized region emitting particles, has had great success in describing data over a wide range of bombarding energies and systems [Ba 75, Am 75, So 75, We 76, Da 81, We 82]. Therefore a parameterization based on such a formulation:h3Lweful in comparing various sets of data and seeking evidence for thermalization. The energy spectra is fitted to a relativistic Maxwell- Boltzmann energy distribution which is isotropic in the rest frame of the source. The distribution is given by dzo o __________ §§2£:§£:2 .......... -_“--- Pzdpdn = H}53 2(I/m)2 K1(m/T)+(T/m)K°(m/I) (IV-1) where p and E: are the momentum and total energy, respectively, of a particle in the source rest frame. Ko and K1 are MacDonald functions, also known as modified' Bessel functions of the second kind. The particle mass is given by m, o is the energy-integrated cross section, and 1 is the source temperature. The distribution is assumed to be isotropic in a frame moving with the velocity, 8, in the laboratory frame. The double differential __2 I , _1 a. g 10 .L 5 ‘fi #it 7'. : 1 10 _ i :‘ c \ * BEE C I'D ‘1 m- - 10 \Ei ‘3‘ E E hfiflfiduflwNH‘; .-2 fl --1 % 10 r r r + :EB: 10 F; e e E e = 13-1 I ; “Mfg N ”U 10"1 -. 1o—2 ‘11 b E s E E1 5 m S . _2' _3 '1 1310 “2111.10 .1911- O 200 400 O 200 400 FIGURE IV‘9 Energy (MeV) Projectile-like fragment inclusive energy spectra for the PLF detector at 15° for 30 MeV/A C+C. 62 are plotted as double differential cross sections as a function of the total fragment energy. Projectile-Like Fragment spectra can be broken up into two distinct reaction mechanisms, projectile fragmentation - few nucleon transfer reaction otherwise known as quasi- elastim: (QE) and an intermediate rapidity or deep-inelastic (DI) part. Projectile fragmentation can be described as an interaction occurring at large impact parametmwsixlwhich the incoming projectile nucleus becomes excited upon contact with the target nucleus. The velocity of this projectile fragment is not appreciably redwned by the collision. The excitnui projectile either breaks up near the target nucleus before equilibration of the excitation energy or decays ir1 flight after thermal equilibrium is established. The fragment velocity distributions for the projectile fragmentation process can be characterized by observed peaks which are gaussian in shape with their centrwfixfl between 85 and 90 percent of the projectile velocity. The beryllium and boron fragment-velocity distribution seem to be dominated by this reaction mechanism. The QE part of tme PLF spectra could also be associated with a few nucleon transfer reaction mechanism. This phenomenum involves the exchange between target and projectile nuclei of one or more nucleons., 'The fragment velocity distributions for the transfer process are characterized by narrow peaks centered near the beam velocity. The carbon and nitrogen fragment velocity distribution seem to be dominated by this reaction 63 mechanism. Hasselquist et al. [Ha 85] have shown that it is difficult to distinguish these different processes for these energies and systems. Because the energies for there processes are not well separated, it is assumed that a combination of these processes are involved. The DI part of the PLF energy spectra can be associated with smallmn~ impact parameters. This mechanism is usually associated with particles which are nunflu lower 1J1 velocity then the beam velocity and are emitted from a more thermalized source. This reaction mechanism can be thought of as the transfer of nucleons between the projectile and target while they rotate usually less than one turn, then the projectile fragment is ejected. By using that part of the PLF energy Spectra which is below the quasi-elastic: peak, one can be assured of getting only the DI reaction part of the spectra. B. 15 and 30 MeV/nucleon 12C+Au,C Coincidence Spectra 1. Momentum Conservation Model In order two interpret coincidence spectra as a collective and dynamic effect, the effects due simply to momeniuun conservaticnirnust be considered. This precaution would prevent you from assigning any special significance to effects VHHJNIEM"€ simply due to conservation laws. It is therefore necessary to use a simple momentum conservation model anud construct a theoretical coincidence spectra. By 6A comparing these theoretical calculations with the actual data, one can now eliminate any simple momentum conservation effects. However, it is impossible to reconstruct realistically any nuclear reaction with any simple model that must have limitations due to assumptions which are made in order to simplify the calculations. It is still useful to be able to compare measured data with even the simplest level of calculation. The momentum conservation calculation is based on a treatment by Lynch, et al. [Ly 82] and formulated by Hasselquist [Ha 8A]. The calculation assumes that particles are emitted isotropically in the rest frame of a moving thermal source with a fixed number of nucleons. The energy distribution is given by the relativistic Maxwell-Boltzmann distribution (IV-1). The coincidence spectra are calculated based on the moving source fits to the inclusive spectra. Tfim calculation is performed assuming that two coincident particles are emitted sequentially from a single moving source. In reality, more than two particles are usually emitted ownn these type of reactions, however, the requirement of the emission of two particles is essential to the calcnfilation. By knowing the momentum of the first particle, it is possible to calculate the reduction ir1 excitation energy of the source and its recoil momentum. The second particle is then emitted from this new cooled down and recoiling source. It is impossib1e1HJCMtermine which particle was emitted first, therefore both 65 cunnbinations of sequential emission must be considered and then combined to give the final coincidence spectra. The initial source parameters used in the calculations were those extracted from the inclusive light particle spectra for the particle of interest. The initial calculations were done with the size of the emitting source corresponding to a fireball formed at the most probable impact parameter [We 76]. In order to obtain a more realistic3p,,,,+XBC L4 -1 £10 .. ,. ,- ,. 1 1, [firms C3 : I o _ . . Q) -2 . .—1 10 g X=Ll B i L) : : :1 : : {104. E > '45 a) : : E10”? x q, \ E 5 "E E E _2' .. v 10 E: X=Be X=C g N E f c: _3_ - it) 1() g 9 g m E 1 1' .j -o _4: . ' _ \bxlo 111111 1111 IIJllLIIiL.11111111IILL11-11 co 0 25 50 75 O 2 50 '75 100 Energy (MeV/nucleon) FIGURE IV-13 Energy spectra for protons at ”5° in the Hit plastics in coincidence with the BCS for 30 MeV/A C+C. Solid lines correspond to a moving source fit. 70 energy cuts as the inclusive data. The extracted moving source fit parameters for the BCS triggered proton coincidence spectra are tabulated in TablasIN-3-10. The temperatures from the fits for 30 MeV/nucleon C+Au,C are plotted in Figures IV-1A and IV-15, respectively, as ratios to the inclusive values. The square symbols are the light paricles on the same side of the trigger detector and the triangle symbols are for the light particles on the opposite side. There seems to be no significant dependence of the temperature and velocity parameters on trmernass of the trigger Ixncticle. ‘The deviations from 1 appear to have no significance. The 15 MeV/nucleon temperature ratios showed the same trend. The protons were the only light particle fit to a moving source because the other light particles did not have enough statistics to do so. Another form of light particle or mass dependence in which all the light particles can be compared, is found by simply integrating the coincidence energy spectra and comparing correlations. These correlation functions will be presented later in this chapter. 3. Light Particle - Projectile Like Fragment Coincidence The proton spectra that are in coincidence with the quasirwelasticz (QE) and deep inelastic (DI) part of the projectile-like fragments in the PLF detector are shown in Figures IV-16-19, respectively for the 30 MeV/nucleon C+Au,C. The extracted moving source fit parameters for the 71 TABLE IV-3 MOVING SOURCE PARAMETERS 30 MeV/A C+Au+p (COINCIDENCE HP) Fragment Temperature Cross section Velocity Mass T a 8 (MeV) (mb) (0) QE 7 12.311.1 35.215.2 0.30210.006 9 10.611.A 30.518. 0.1u510.008 11 7.511.0 75.130. 0.10610.006 12 1A.111.5 39.515.7 0.08A10.005 DI 7 12.611.5 31.16. 0.11210.006 9 18.15. 9.12. 0.11810.002 11 22.15. 11.12. 0.13610.002 12 15.13. 12.13. 0.1”710.002 BC 7 11.11. 2.310.“ 0.1110.05. 9 8.610.5 4.310.6 0.1u10.ou 11 8.610.6 2.910.u 0.1610.05 12 9.710.9 1.610.3 0.1610.09 72 TABLE IV-N MOVING SOURCE PARAMETERS 3O MeV/A C+Au+p (COINCIDENCE BP) Fragment Temperature Cross section Velocity Mass T a 8 (MeV) (mb) (0) QB fl. 9.910.3 226.112. 0.1310.02 7 9.010.8 u8.18. 0.171o.ou 9 12.13. 11.12. 0.1610.09 11 9.11 26.17. 0.1010.05 12 10 810 8 “1.16. 0.1210.03 DI fl 9 910 2 378.115. 0.1310.01 7 11.11 21.13. 0.1410.05 9 13.113. 6.11. 0.1610.01 11 10.12. 13.1”. 0.11810.009 12 10.11. 19.13. O.1MN10.0Q6 ac 7 12.12 0.761.111 0.13210.006 9 9 A10.” 3.210.2 0.20610.003 11 7.910.5 2.u:o.3 0.18110.00u 12 10 610 6 1.710.2 0.19610.00H 1A 0.6810.9 0.1910.01 73 TABLE IV-5 MOVING SOURCE PARAMETERS 30 MeV/A C+C+p (COINCIDENCE BP) Particle Temperature Cross section I 0 (MeV) (mb) OS A 7.8910.0A 357.17. 7 7.u710.09 79.13. 9 7.010.5 3H.12. 11 7.210.8 20.12. 12 11.13. 1.110.5 DI A 8.8u10.06 862.19. 7 8.810.2 97.13. 9 8.210.H 57.13. 11 8.210.2 116.13. 12 7.H10.1 83.13. BC 7 9.110.3 1.5“10.05 9 9.3810.05 5.810.1 11 9.610.1 5.210.1 12 9 810 2 2.510.7 13.13. 0.2510.007 1U 7“ TABLE IV-6 MOVING SOURCE PARAMETERS 3O MeV/A C+C¢p (COINCIDENCE HP) Particle Temperature Cross section I 0 (MeV) (mb) QE M 8.110.2 289.18. 7 8.510.u 68.1A. 9 7.710.2 38.13. 11 8.010.u 22.12. 12 7.13. 8.12. DI u 8.910.1 916.113. 7 8.710.3 116.15. 9 9.110.5 61.13. 11 9.310.2 1uo.15. 12 8.910.u 105.1u. 14 19.15. 10.11. BC 7 8.u10.2 7.810.2 9 8.7110.06 8.u10.2 11 8.910.1 9.510.2 12 9.110.2 5.310.1 1" 37.115. 0.0710.02 75 TABLE IV‘7 MOVING SOURCE PARAMETERS 15 MeV/A C+C+p (COINCIDENCE HP) Particle Temperature Cross section 1’ 0 (MeV) (mb) QE H 6.810.9 130.116. 7 1u.1u. 9.13. DI u 5 510.5 131.1uo. 9 10.17. 5.12.7 11 6.010 5 56.113. 12 8.12. 22.17. BC 7 6.110.“ 22.11.11 9 5.710.3 50.12. 11 5 710.2 70.13. 12 5.710 2 su.13. 1H 7.13. 1.10.3 76 TABLE IV-B MOVING SOURCE PARAMETERS 15 MeV/A C+C+p (COINCIDENCE BP) 1H 8.12. Particle Temperature Cross section I 0 (MeV) (mb) OH H 5 910.2 270.111. 7 7 12.5 13.13. 11 7 910 7 5.810.2 12 10.13. 5.12. DI u 6 210.2 396.116. 7 u “10.9 6u.111. 9 7.710.9 7.11.8 11 5.310.5 51.17.5 12 6.810.3 M2.15. BC 7 6.N10.2 7.510.“ 9 5.910.1 6u.11. 11 5.9710.09 78.11. 12 5.910.1 11.11. o.uu10.08 77 TABLE IV‘9 MOVING SOURCE PARAMETERS 15 MeV/A C+Au+p (COINCIDENCE HP) Particle Temperature Cross section I 0 (MeV) (mb) QE u 9.1“. o.u1o.3 7' 7.610.8- 8.110.1 9 6.110.7 17.12. 11 5.510.2 66.15. 12 6.0u10.02 H688.132. 1n 6.810.7 22.12 DI u 6.210.3 85.1u 7 15.15. 0.710.2 9 17.16. 1 210.3 11 6.210.6 8.11.3 12 5.71o.u 50.11. In 6.610.8 2 010.6 BC 7 6 110.3 1.910.1 9 6.310.3 2.210.1 11 6 210 1 2.110.1 12 5 910.“ 1.710.1 9.12 1H 0.0310.01 78 TABLE IV-1O MOVING SOURCE PARAMETERS 15 MeV/A C+Au+p (COINCIDENCE BP) Particle Temperature Cross section T 0 (MeV) (mb) QE 7 6 010.“ 15.11. 9 5 510 2 28.11.5 11 5 610 2 66.12.2 12 5.9810.01 “972.117. 111 6.11101 31.11.2 DI M 5 510.1 1H0.1u. 7 7.13. 2.110.3 9 6.11. 5.210.7 11 S.H10.3 17.11.2 12 5.9610.06 u7.11.7 1n 6 910.5 1 610.3 BC 7 6 310 2 0.3210.02 9 6 010 1 2.u10.06 11 6.110.1 2.310.05 12 6 010 2 1.910.05 7 610.5 0.0510.006 1N 79 30 MeV/nucleon C+Auep+X 1‘2“: QE 1 1 3 1.0} ----------------------- * ................ i ............ .3 0.8:- 1 : 0.6 ffi 5 f 5 L 1 t e 1 L .— ..1.4E 0 I .2 {1.2;- DI J : 2 1.();:’ """""""""""""""""""" 1 """"""" ': *‘ 0.8:- .3 0.6_ = . 1 . .1 . - 1 1‘ 1.4—- : 1.23- BC 1 + 1 1.0—- ................................................ -1! 0.81 1 1 j 0.6~L~#-1.L-L11-.. O 2 4 6 8 10 12 14 16 Fragment Mass FIGURE IV-1u Ratio of coincident to inclusive temperatures from the moving source fits of protons for the quasi-elastic (QB), deep-inelastic (DI) and the bragg curve (BC) as a function of fragment mass from.30 MeV/A C+Au. 80 30 MeV/nucleon C+C->p+X E QE 3 1-0: ---------------------- +------------t ---------------- -; _. ‘ _ O 8 b P I L 1— % 1 1 I 1 Ir 1 A " - D1 .1 .1 F _ _— >11. ..... 1- 1-41 _ k: : o : 0.8 _ 1 1L 1 r 1* = '1 r r i + 1r r _ : BC * . 1 * : 1.0 :" """"""""""" T ------ .- ------ 1 ---------------- : 0.8 " 0 2 4 6 810121416 Fragment Mass FIGURE IV-15 Ratio of coincident to inclusive temperatures from the moving source fits of protons for the quasi-elastic (QB), deep-inelastic (DI) and the bragg curve (BC) as a function of fragment mass from 30 MeV/A C+C. 81 Z: 30 MeV/nucleon C+Au-9P1“: +XQE 0 £10 1 11.1...1111... .,.r....,.....1....5 :: , i 8 __1 X=L1 X=B ~ .—. 10 w E 8 1+ + + C1 __ I \102 1 + 1 .,_. % -45° 2 190° 3 2 ‘3 ..A I: d “‘4 1C) ‘ ‘ i \ E 5 .0 : 1 E3 _1' )<=I3€3 )(=(: 1 \_/ 1() E i 1: 5 '9 10 1; r1] E “U _3: E10 ...11111111 11.71.17.1111H111111111 1.._ :20 O 25 50 75 O 25 5O 75 100 FIGURE IV-16 Energy (MeV/nucleon) Energy spectra for protons at u5° in the Hit plastics in coincidence with the QB for 30 MeV/A C+Au. Solid lines correspond to a moving source fit. 82 15 30 MeV/nucleon C+Au-1pm, +Xm r-1 -1 5110‘ . WW ..1. 3 E 1 X=L1 3E 11 1 =13 é; : qb : c: _2 1- . g 10 _ 45. E a) ; " \E 1\ 2 - 590‘ q- I l—J " .1... -3 ‘ E10 : 1-1%: 1'11\::1L:1:: A. E 5 Be 3; 2 10'2; "u . \:t \E; ’ -P \\\\\\ . ?U10—3+4111111111NKL1111 llJLllllllll 1111;; O 25 5O '75 O 25 50 75 100 Energy (MeV/nucleon) FIGURE IV~17 Energy spectra for protons at ”5° in the Hit plastics in coincidence with the DI for 30 MeV/A C+Au. Solid lines correspond to a moving source fit. 10 t—* 0 d3 o/dE d02 (mb/[MeV/nucleonlsrz) 3 FIGURE IV-18 O —3 0255 33 30 MeV/nucleon C+C-9pH,,+X0E I 1111"" I 1'“ 111111111 irrrrflll r I I I I T—liririI—I I X=B I T I r 1 1111111] 1 1111111 1 1 1111111 1 IIIII 1 1111111] 1 I Illllll 1111 L 111 L l 1L111 1L1. 1 1111111] 1 1111111 1 1 11111] O '7 025 50 75 Energy (MeV/nucleon) 100 Energy spectra for protons at uso in the Hit plastics in coincidence with Solid lines correspond to a moving source fit. the QB for 30 MeV/A C+C. 8N 2) 30 MeV/nucleon 1...; CD .4 .4 ..1 -1 -1 -1 I T I IIIII l l 1 L111; I I I I TTI 11111 H H 1 1 111111[ 1 1 111111] I I IIIIII] J 1 1411111 .41- 1 111111 I TIIIII l I 111111 T I IITITI l L 1 1_L1111 I r ITTITT I r1111”; 1 I 1 1111111] lo—Z‘L‘LI‘L1‘1“1 111. LL111411L1LIL111L11 0 25 50 75 o 25 50 75100 d3 o/dE dQ2 (mb/[MeV/nucleon]-sr Energy (MeV/nucleon) FIGURE IV-19 Energy spectra for protons at N5° in the Hit plastics in coincidence with the DI for 30 MeV/A C+C. Solid lines correspond to a moving source fit. 85 PLF triggered proton coincidence spectra are tabulated in Tables IV-3-10. The temperatures from the fins are plotted in Figures Ill-111 and IV-15 as ratios to the inclusive values. There again seems to be no significant dependence of the temperature parameter on the mass of the trigger particle. It would at first be expected that the different coincident particles would come from different sources which in turn would have different temperatures. u. Same Side - Opposite Side Comparison In order to observe any collective and dynamic effects one cmu11neasure light particles in coincidence with a heavier fragment on the same and opposite sides of the reaction plane. All nuclear reaction events can be described in terms of a reaction plane described by an azimuthal angle of ¢=O and 180°. For the light particle -' PLF reactions, an azimuthal angle of ¢=0° corresponds to the side of the reaction plane on which the PLF particle was detected. These particles would be detected in the bragg curve leastic scintillator (BP) detectors. Light particles on the opposite side of the PLF would be associated with ¢=180° and hue detected iri'the hit plastic (HP) scintillators. For the case of the light particle - BCS coincidence data, the reaction plane is not as easy to define. If we assign the slow moving particles detected in the bragg cuu~ve spectrometer as being emitted from the 86 target then we might associate this side as ¢=180° and where the projectile is incident on the target as the ¢=O° side. First consider the light particle - BCS spectra, Figures IV-20 and IV-21 show the 30 MeV/nucleon C+C proton spectra in coincidence with lithium and carbon in the BCS at “5°, respectively. The curved lines correspond to momentum conservation calculations. In figure IV-ZO the solid line refers to a single source size which best fits the data which corresponds to 18 nucleons, the dashed line refers to the weighted source size calculation. One can fit the data to a single size source but when a more realistic calculation is done, it over-predicts the data. The solid line in figure IV-21 is a single scunwna size momentum conservation calculation using the maximum number of nucleons possible, that being 2“ nucleons. The calculation over predicts the difference between the opposite and same side as compared to the data even though it uses the largest possible source size. The largest possible source size should produce the-smallest possible difference from momenthlcmanservation laws. The calculation using the weightedsunmce sizes produces an even larger difference. The implication of these two figures is thatiflmemomentwn conservation calculation does not explain these differences. This in turn might imply that they do not come from the same source instead, these particles may come from different sources such as the target fragment. These are often called target-like fragments (TLF). If one now considers the 30 87 _1Protons in Coincidence with Lithium '_W I I‘ll I T IIHTI IIFII II'I I [l’l III: 0 Opp. Side - Same Side lllll J 7 ...; O I I IIIII lillJllU d’a/dE .dfl d0.“ (mb/MeV sr’) _. 10” a :1 ‘1 1- " __ 30 MeV/n C+C 10 E at 45/45° a .. \ \: 10’5f111LL141111111114 11L 111 O 25 50 75 100 125 Energy (MeV) FIGURE IV-ZO Proton energy spectra for the HP (opp. side) and the 8? (same side) in coin- cidence with a lithium in the BCS for 30 MeV/A C+C. The solid (dashed) lines correspond to single (weighted) source momentum conservation calculation. The single source used 2“ nucleons. 88 -1 Proton in Coincidence with Carbon I I III I ....s -CD ('0 I WIIIIIIITI H C) A. lIITlll] d’a/dE d0 d0,“ (mb/MeV sr’) I # H C) ErIIl—FIII ITTWIIIW IIIIIIrTa I . Opp. Side 3 . Same Side 1 . - i 1 1 4»- + 111mm] 30 MeV/n C+C at 45/45° + \ 111l1111l1111L11111111 l I CD FIGURE IV-21 25 50 75 100 125 Energy (MeV) Proton energy spectra for the HP (opp. side) and the 8? (same side) in coin- cidence with a carbon in the BCS for 30 MeV/A C+C. The solid (dashed) lines correspond to single (weighted) source momentum conservation calculation. The single source used 2“ nucleons. 89 MeV/nucleon C+Au system, figures IV~22 and IV-23 show the proton spectra in coincidence with lithium and carbon in the bragg cnn~ve detector at ”5°, respectively. The solid lines refer to momentum conservation calculations with a single source size of 38 nucleons which corresponds to a source formed from the most probable impact parameter in a fireball geometryu (Zalculaticnus with weighted source sizes produce much larger differences. The data seem to show an almost isotropic emission of protons in coincidence with fragments detected in the BCS. Whereas the momentum conservation calculation seems to predict a large difference between the opposite and same side, which will be more evident in the integrated cross section ratios. Differences between the light particle spectra on the same side and opposite side of a trigger detector can be examined by comparing the temperature parameters from the moving source fits. Figures IV-2u-25 show the ratios of the temperatures for the protons on the same side to those on the opposite side 15 MeV/nucleon C+Au,C respectively. Figures IV-26-27 are shown for the 30 MeV/nucleon C+Au,C respectively. The figures are broken up into three different sections, the top two correspond to protons in coincidence with the quasi-elastic (OE) and deep-inelastic (DI) part of the PLF spectrum at 15°. The bottom section refers tn) protons 111 coincidence with the BCS at uso. The proton spectra for both the same side and the opposite side were taken at 45°. The only system that varied the velocity 90 _1Protons in Coincidence with Lithium 1 ETTT—r—n—T—T—rTv—finj—r—rTrr—I "1"1‘E z-x : ’ _ "1.. _. 0 Opp. Side 1 m ' ‘ '4 > h- I Same Side - 0 t- _ a «4 .010 E 4 z 3 E + : § _ I c — —1 "U cm”): + : 'U I .1 13:1 3 - E _ 30 MeV/n C+Au " 9c: at 45/45° ‘ 10$111l111111111111 1111 O 25 50 75 100 125 Energy (MeV) FIGURE IV-22 Proton energy spectra for the HP (opp. side) and the 3? (same side) in coin- cidence with a lithium in the BCS for 30 MeV/A C+Au. The solid lines correspond to single (38 nucleons) source momentum conservation calculation. 91 -1 Proton in Coincidence with Carbon 1 r11r111111T111r1T1111r11j A E . : "3., e - Opp. Side .. m C I Same Side : a; _' A 2 _'2 E10 L; j E E i g C? _ -1 '1: 1-3l C10 c.- ____ “U : : m C 3 Q .. 30 MeV/n C+Au . 1 .5 — AT 45/45° —. 10" 11LL111LLJ1111L1\L1LLL1 0 25 50 75 100 125 - Energy (MeV) FIGURE IV—23 Proton energy spectra for the HP (opp. side) and the BP (same side) in coin- cidence with a carbon in the BCS for 30 MeV/A C+Au. The solid lines correspond to single (38 nucleons) source momentum conservation calculation. 92 1 5 MeV/nucleon C+Au-1p +X 3 r . -1 :- : 2: QE 5 15. ................. _ i i i = 3 E 3 m _ _ 1.1- O_ r r r . as 1r L . : 1 %‘ x _ _ 3. : 3 l~ 2: DI a \ E .1 E 1:- ---------------------------- '1 ------------ “J n — ‘ : g 0: s #1 as + 1 s ~ if r s e: 1~ : E 2: BC ‘3 1;. ...................... ... ...... . ...... ...... 1--.-5. .. I O —, 1 . L #1 . . . L - , .3 O 2 4 6 8 10 12 14 16 . Fragment Mass FIGURE 1v-2u Ratio of opposite (HP) to same (BP) side temperatures from the moving source fits for 15 MeV/A C+Au for protons. 93 15 MeV/nucleon C+C+p+X 3: e- . 1: 2E- QE 1 i C — 1:- ...................................................... _: 3’ E E m - L L A . . 1 k L L L L _ IIJ O_ f l ' I r ' fi 2 — —1 3‘. C: : l~ 2: D1 : \ : 1* 2 g 1:— --------------------- -1» ------ J-"i ............ _: a E E g 0: r ‘ glr * % Lfifi gs i t 1r :: F E 3 2: BC __. 1 E— --------------------- T """" I """ 1""3 ------ f—-.—;-: F 3 0 2, 4 6 8 10 12 14 16- Fragment Mass FIGURE IV-25 Ratio of Opposite (HP) to same (BP) side temperatures from the moving source fits for 15 MeV/A C+C for protons. 9H 30 MeV/nucleon C+Au-+p+X 3: -_ 23 QE —3 E 1 1 E m 1: i 1 : E O: 1‘4 1 ::.l.: E 3 I : 11‘ 2;— D1 I g \g 1: 1 l. 4 Z a 03 J - +~ e E 1~ E : 2: BC .3 1 E f i J i f i O 2 4 6 810121416 Fragment Mass FIGURE IV-26 Ratio of opposite (HP) to same (BP) side temperatures from the moving source fits for 30 MeV/A C+Au for protons. 9S 30 MeV/nucleon C+C->p+X 3 ~ _. 2 E- QE E 1 E. ....................... s ....... 1 ...... .1 .............. _ 3 g : 1 E :1 O _ t w r ‘r + ‘r ‘ _ 2 ' : g : _ 1. 2 : DI | 2 \ E . : g 1 1— ---------------------- -.- ------ !-------' ---------------- -: a ' I j a: O E s .L e 1 L 4 : L r L + L . ' - g i‘ : : 2 : BC ': 1 E- --------------------- 'r ‘‘‘‘‘ :--—----.---r ----------- “E O L 4 L l n L L l n L k l L l L 0 2 4 6 8 10 12 14 16 Fragment Mass FIGURE IV-27 Ratio of opposite (HP) to same (BP) side temperatures from the moving source fits for 30 MeV/A C+C for protons. 96 in the moving source fit was 30 MeV/nucleon C+Au, therefore the ratios of the velocities are shown in figure IV-28. There seems to be no general trend or deviation from 1 iri the ratios (M? the temperatures and velocities. This would indicate that the light particles come from similar sources. A more sensitive indicator of variations is the integrated cross section. By comparing the integrated cross sections for the opposite and same sides one can now compare not only protons but almost all the light particles measured in the plastic scfinuxtllator telescopes. Figures IV-29-u2 show the ratios of the integrated coincidence cross sections for the 15 and 30 MeV/nucleon C+Au,C for most of the 11y“: particles as a function of the fragment mass detected in the trigger detector. Each figure is broken up into three sections as described previously. Because of the lower cross section and the low energy out off of the plastic scintillator, the 15 MeV/nucleon data had fewer statistics for the He isotopes and therefore not enough for coincidence cross section comparison. The lines represent the momentum conservation calculation integrated over the weighted source sizes. For time 30 MeV/Wnusleon C+Au one finds very little variation from a ratio of 1, except for the protons, whereas the momentum calculation shows a marked increase in the ratio as a function of fragment mass. This trend shows the effects (M? momenth1 conservation since an increase in mass of the trigger particle woulcicanly irun~ease the rnunber of 97 30 MeV/nucleon C+Au—>p+X 3 j : 2 9: QE :3- t .1 : 1 E- """"""""""""""""" + """ T"i """""" *: “J " 1 9 e __ m — J 1 f 4% 4r 11.1 0 h- f r r : 2 ‘- ... :1. : _1 Q). 2 :- DI : \ E 1 1 ____________ E 5 1 3‘ """"""""""""""""" 1 """"" f """""" 2 g 0 ...... r r F L L F; P 1r L A L T : m. E 2 2 : BC 3 1 5’ """""""""""" 1 """" ; “““ 1 "‘1 """" 1' ""3 O" . . L 1 i 1 L in . r .1 L . L O 2 4 6 8 10 12 14 16 Fragment Mass FIGURE IV‘28 Ratio of Opposite (HP) to same (BP) side velocities from the moving source fits for 30 MeV/A C+Au for protons. 98 30 MeV/nucleon C+Au—+p+X. QE / 1111111r1111111111 111111m11111111 11111111111111111111111l1111l1111l1111 I1 I 11 1 II I II 1 C712 OPP smm://(712 SAME $05 CD IV) $> (33 CD +—> DO ()3 CD P—> PO (A) 4> 4 6 8 10 12 14 16 Fragment Mass CD m _ FIGURE IV-29 Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+Au for protons. 99 30 MeV/nucleon C+Au—>d+X L— — — _ E — — '.—' F- P h— _ * _u- --------------------- — ---------------------------- _ ,— L l 1 l l L V r r I r r * 012 OPP. SIDE /Ui2 SAME SIDE |.__\ CD CD mewor—emwe IIIITW1|Hl HIIIIIIIIHIHIIH BC H111111111111HIH1H1n1h1u H1H1u1h1uln11 _______________ t---_-- ------ --- ------ ---- "f """ 1 ' ‘ Y ll‘T i L A 4 4 2 4 6 810121416 Fragment Mass CDC: FIGURE IV-3O Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+Au for deuterons. 30 MeV/nucleon C +A'11->t+X EQE /: l lll‘lllllmIIIlII 012 OPP. SIDE /012 SAME SIDE 1._s (31 CD CD F“IN) CO CD IN) 4: CD IIIITIIIITH 11111111111111 1u1ln11h11H11u CD CD 1 W 1 I I 1 I I 1 I I I I I 1 I I {..— i I I I Q I I I I i I I ‘ 1 I I 1 l 1 I I 2 4 6 810121416 Fragment Mass FIGURE IV-31 Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+Au for tritons. 101 30 MeV/nucleon C+Au->4 He +X QE 20 —- ~— 15 - /\ 1 g 1()" ////1’ ‘— 5 —- - g o ------ 4- ————————— 1 ....... 6 10 3 D1 /\/\ E \ 5 E E E E 2* "‘ — j 35 O "":“‘1"':':";'":"1' """ 1"1‘“1"‘1"':"“L";— 6 10 BC 5 1| 1|1111 [1111 11111111111111 "'7'"]"‘I"'C-'7'-'T'-'b"I"_1'°'f_'1'-'1"'T"1_"'1' 4 6 8 10 12 14 16 Fragment Mass CZJCD 00 FIGURE IV-32 Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+Au for “He. 102 30 MeV/nucleon C+C—>p+X 15_ 1 rrr w 1 1_ E QE : 10;— _ j :- 3 .5 53 1 j m _ a w , : _____________ - ........... - ....... '. -.---..- ................ .2 og+ : e .1 ‘3‘- : DI I b __ _ \\\ 53:: + ': UJ g — _ (f1 — ' — 93' Oner L if #‘rfi N _ _ E3(j _ b 10— —~ I . .- + 1 () --------------- ;--: ---------------------------------------- O 2 4 6 810121416 Fragment Mass FIGURE Iv-33 Ratio of opposite (HP) to same (BP) side 1 integrated cross sections for for 30 MeV/A C+C for protons. 103 15 30 MeV/nucleon C+C->d+X _ I L- — I 2 1‘5 5 :- ‘ — 1.. —1 1n 1: _1 M v .. 2 O """"""""""""""""""""""""""" "‘ < m N " _ \ -— _ \ w 1()__ ._ Q . 171 __ _ 3': O --.: ----- ;'-T-'L—-- O N "' _- . O ...................................... 4---; ....... L ...... O 2 4 6 810121416 Fragment Mass FIGURE IV-3u Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+C for deuterons. 10” 30 MeV/nucleon C+C->t+X QE / fi }_~. 0 ”1111111111111” 012 OPP. SIDE /012 SAME SIDE (\D O ”1111111111111” 1111111111111111111 111111111111111111111111111111111 ‘1 . O --‘E--1---z--j'--L ------- - --1---L—--1----L'--1---I--J- ------ O 2 4 6 8 10 12 14 16 ' Fragment Mass FIGURE IV-35 Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+C for tritons. 105 20 30 MeV/nucleon C+C4’He+X ...—x CD IIIIIITIHITIIT 11111111111111 1n11nn1hu1fl111 IlrrlrrTlllll U12 OPP. SIDE /012 SAME SIDE 111h11u11u11n () ‘ -- --- __ .-- .-- ----.- -.- -.- _. --. --- --. -- --- 0246810121416 Fragment Mass FIGURE IV-36 Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+C for 3He. 106 40 30 MeV/nucleon C+C-9" He+X 30- QE / .1 g C‘ ': 6 \ E 6 O 2 4 6 810121416 Fragment Mass FIGURE IV-37 Ratio of opposite (HP) to same (BP) side integrated cross sections for for 30 MeV/A C+C for “He. 107 1 1 15 MeV/nucleon C+Aii->p+X r ' I - r v r r t . fi/ (QIC + { III‘IIIIIIITTIIHI mlmulmlnrr 012 OPP. SIDE /Ui2 SAME SIDE H . 01 O OHNCDOt—ANOORB 111111111111 \‘ h u.- p 4 .- 11111111111111111111111111111111 111111111111111111 O 1: 11 PE +1 CD N 11> CUP CD ...L 01- ...; N1- 1—8. pp. hi 1 CD Fragment Mass FIGURE IV-38 Ratio of opposite (HP) to same (BP) side integrated cross sections for for 15 MeV/A C+Au for protons. 108 15 MeV/nucleon C+Au-9d+X Q1. / ”11111111111111 012 OPP. SIDE /012 SAME SIDE 11111111111111111111111111111111111 ------------------------------- .--_--.‘---=—----- -—-— L 1 4 L 11u1u1u1n1h1n u1d1n1h1n1u111n1h1u1u1fl1u1 I—‘ I—* - CD CIIIZD CD CD PA»ZY)ILJ C) F‘ ($1133 4* 4 6 8 10 12 14 16 Fragment Mass CD FIGURE IV-39 Ratio of opposite (HP) to same (BP) Side integrated cross sections for for 15 MeV/A C+Au for deuterons. 109 15 MeV/nucleon C+Au+t+X f r r __ QE f L 1 1 1 1 1 i 1 1 1 1 . g g 1 O.12 OPP. SIDE /012 SAME SIDE IHIH1H1HTH1 1u1u1d1n1h1u ha ha CD Cfl (21131 CD IV) 1&8 CD IV) $8 C21 1 r r 1 "C"i""".‘""€"'1“"i"-‘.""1"-!“fi"‘1"'l""":""1"“2" 2 4 6 8 10121416 Fragment Mass CD Ratio of opposite (HP) to same (BP) side integrated cross sections for for 15 MeV/A C+Au for tritons. FIGURE IV-HO 15 MeV/nucleon C+C—>p+X 4:1 1 1 1: 3E- QE 1. E 2% * 1 -= g E = fi 1,:- """"""""""""""""""""""""""""" “E 1n 2 d 30 ~ 11 N _ '1 .— 6 6_ D1 _ \ 4:- 1 j 2— ° 1 1 + —+ 1— ------------------------------------------------------- _- g OL-‘fi: : % r rr+it eke? f: N t; ESE: IBC: _ 4: . — 2__ I a 1 _1 O 11 1 2 4 6 8 10121416 Fragment Mass 0 FIGURE IV-HI Ratio of opposite (HP) to same (BP) side' integrated cross sections for for 15 MeV/A C+C for protons. 15 MeV/nucleon C+C—>d+X 4----r V #— l—I — 3' QB : 2?. = - t: In : 1 "‘ 9 .. 11 3 n 1 :f """"""" 1 ------------------------ “fi """"""" "_ u I I 2 O- L L L4 L L L 14‘ ( _ ffir I r r r '— lfl : j “ 37- D1 = t5 "’ ‘ \ 2:- E : '1 _- 3 L'- 1 : .7, 1:— ------------ ; -------- - v ----- - ---------------------- -.: .1 : no. 0 :1 :4 1 E % . #:1‘ : ~ 4E 1 ~ I 2— 1 .1 1 1.. .............................. . ...... I ........... ------ 4 6 8 10 12 14 16 Fragment Mass 0 N 1 FIGURE Iv—uz Ratio of opposite (HP) to same (BP) side integrated cross sections for for 15 MeV/A C+C for deuterons. 112 light particles emitted on the opposite side in order to tnlance momentum. This difference is most noticeable with the light particles in coincidence with the BCS. Differences between the opposite and same side cross :sections in the calculations can be as much as 10 to 15 times, whereas the data does not reflect this sort of difference. IDifferences between the data and momentum conservation calculations seem to increase witnizincreasing light particle mass for not only the BCS but also for the OE and DI part of the PLF trigger. One certainly would not expect to find any real variations for the light particles in coincidence with the deep-inelastic part of the PLF spectra because of the thermal origin of these fragments. It is although, surprising to not find any variations in the light particles in coincidence with the quasi-elastic part of the PLF spectra. One would expect to find some momentum conservation effects which would enhance sumne differences. The data differ from what Caskey et al. [Ca 85] found with 35 MeV/nucleon N+Ho for which neutrons were measured from 10 to 135 degrees in coincidence with the quasi-elastic part of the PLF spectra at 10 degrees. They found an enhancement of the neutrons on the same side as compared to the opposite side for neutrons measured at 10°, whereas for neutrons rneasured at IM)°, the opposite side of the PLF detector had an enhancement of neutrons. In another experiment it was 113 observed that this enhancement was not as prominent when the PLF detector was at 15 degrees [Re85]. The 30 MeV/nucleon C+C data definitely show a somewhat higher value than 1 for the opposite to same side ratio, especially for the protons. Yet the momentum conservation calculation can at times be as much as 10 times larger than the data. The light particle — deep inelastic ratios show a marked increase with fragment mass. This increase, although not as large as the momentum conservation calculation, shows the effects of a single emitting source for time two particles. ‘The protons in coincidence with the quasi— elastic part of the PLF do not show this same effect.. 'This can be interpreted in terms of the amount of interaction between the projectile and target. The QE mechanism is associated witflu large impact parameters with a limited interaction with the target. The DI part of the PLF spectra is associated with smaller impact parameters. Collective and dynamic effects associated with strong target interactions is observed in the proton - DI coincidence integrated cross section ratios by its enhancement of the opposite side and the similar trend as the calculation. The momentum calculation in fact, predicts that there is not enough energy to emitt both particles in some cases. This is because of the smaller source sizes associated with C+C reactions. These cases include protons in coincidence with the QE particles above a mass of 9, deuterons in coincidence all QE particles and tritons in coincidence with all the 11H trigger particles. The calculation predicts the helium isotopes to be in coincidence with all the trigger particles because of a coulomb repulsion term in the calculation. The nunnentum conservation calculation consistently predicts a much higher ratio. A single source size with even the maximum number of nucleons for the C+C reaction (24) does not even come close to the data, as was shown previouslyn. This disagreement would indicate that the two coincident particles do not come from a single thermalized source. 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