Study of Isospin Effects in Heavy-Ion Collision at Intermediate Energies - Rajni (My University, 2012)
In this work, theoretical investigations are carried out using the microscopic isospindependent quantum molecular dynamics (IQMD) model. We have tried to study the influ- ence of isospin dependent cross-section on the balance energy. For this study, we analyze the effect of isospin dependent cross-section on fragmentation and collective flow (directed and elliptic) in heavy-ion collisions. An attempt is also made to study the effect of Gaus- sian width on the disappearance of flow and multifragmentation. We also aim to present a systematic study for the cut in momentum and phase space needed for fragmentation and their correlation with impact parameter, energy and mass of colliding nuclei. The results obtained from these studies are then compared with the experimental data of ALADIN, NSCL, FOPI, INDRA, and PLASTIC BALL Collaborations. The present thesis is divided into following eight chapters. Chapter 1 presents the general outline of the present work. The various phenomena measured/predicted at intermediate energies are explained in this chapter. It outlines the status of the available experimental attempts for multifragmentation and collective flow by different collaborations. The attempts of different theoretical models for these phenomenon are also presented. Chapter 2 gives the overview of various theoretical models (Primary and Secondary) used in the literature. Primary model generates the phase space of nucleons and can group them into Statistical and Dynamical models. In this chapter, different dynamical models are explained. These dynamical models at intermediate energies can be subdivided into two classes. One which follows the time evolution of one-body phase space distribution (BUU, IBUU, SMF) and others based on the N-body molecular dynamics (QMD and IQMD) are studied in detail. This chapter presents the idea about how one model overcome the limitation of the other one. In this chapter, IQMD model is explained in detail. Some secondary algorithms used for the study of clusterization of nucleons is also described in brief. These include Minimum Spanning Tree (MST), MST with momentum cut (MSTP), and Simulated Annealing Clusterization Algorithm (SACA). In this thesis, the MST and MSTP methods have been used for the clusterization of nucleons. 1 In chapter 3, we present a systematic optimization for isospin-dependent cross-section (σ= 0.7 to 1.3 σNN), on directed flow for a variety of systems 12C6 + 12C6, 20Ne10 + 27Al11, 40Ar18 + 45Sc21, 40Ar18 + 51V23, 86Kr36 + 93Nb41, 64Zn30 + 58Ni28, 93Nb41 + 93Nb41 129Xe54 + 118Sn50, 139La57 + 139La57, and 197Au79 + 197Au79 (for which experimental balance energies are available) using an IQMD model. We show that balance energies are sensitive towards isospin-dependent cross-sections for light systems, while nearly no effect exists for the heavier nuclei. A reduced cross-section σ = 0.9σNN with stiff equation of state is able to explain experimental balance energies for most of the systems. The interactions among the nucleons remain either attractive or repulsive throughout the time evolution which depends on the incident energy, isospin-dependent cross-section, as well as the composite mass of the system. We notice a change in the sign of the slope of transverse momentum when plotted as a function of the rapidity distribution. The directed flow goes from a negative to positive value with an increase in the incident energy. This is the general trend and is explained many times in the literature by taking the concept of mean field and NN cross-sections. Lighter systems remain in the environment of mean field compared to NN collisions at any given incident energy. It is also observed that a higher incident energy is needed in lighter nuclei to balance the attractive and repulsive forces compared to heavier systems. This is due to the dominance of Coulomb repulsion with an increase in the composite mass of the system. A power law behavior is also given for the mass dependence of balance energy, which also follows the N/Z dependence. In chapter 4, we analyze the fragmentation of colliding nuclei 197Au79 +197 Au79, 139La57 +139 La57, 93Nb41 +93 Nb41, 86Kr36 +93 Nb41, 64Zn30 +58 Ni28, 40Ar18 +45 Sc21 using IQMD model. The corresponding energy of vanishing flow (EVF) for these system were reported to be 48, 58, 62, 56, 64, 80 MeV/nucleon respectively in chapter 3. The calcula- tions are performed with the isospin-dependent reduced cross sections (σ = 0.9σNN) and are also done below and above the EVF. In the present calculations, mass dependent Gaus- sian width has been employed to achieve maximum stability of colliding nuclei. The free nucleons, light mass fragments (LMFs) are emitted from the participant source that scales with the size of the emitting source while medium mass fragments (MMFs) and intermediate mass fragments (IMFs) come from the spectator part showing well known universality in the multiplicity. Since for lighter system energy of vanishing flow is very high. The transition from the spectator to participant matter is swift and sudden. The reverse is true for heavy systems. Final results are compared with NSCL experimental data. It is found that no 2 particular fragment structure found at the EVF. In chapter 5, we study the correlation between the balance energy and transition energy of fragments in heavy-ion collisions for different systems 40Ar18 + 45Sc21, 93Nb41 + 93Nb41, 139La57 + 139La57, and 197Au79 + 197Au79 at incident energies between 40 and 1200MeV/nucl. using the IQMD model. With increase in incident energy, elliptic flow shows a transition from positive (in-plane) to negative (out-of-plane) values. This is due to the fact that mean field at low energy, which contributes to the formation of a rotating compound system, becomes less important and the collective expansion process based on the nucleon-nucleon scattering starts to be predominant. This transition energy is found to depend on the size of the fragments, composite mass of the reacting system, and the impact parameter of the reaction. The free and LMFs feel the mean field directly, while heavy fragments have weaker sensitivity. The free particles and LMFs, which originate from the participant zone, show a systematic behavior with the beam energy and with the composite mass of the system. The heavier the system is, the greater the Coulomb repulsion is and the more negative the elliptical flow is. A close agreement with experimental data of INDRA, FOPI, and PLASTIC Ball collabo- ration is obtained in the presence of the hard equation of state and with σ = 0.9σNN for Z=2 particles. There is a correlation between transition energy and balance energy as their difference decreases with an increase in the total mass of colliding nuclei. In chapter 6, we present the analysis for different system size effects, excitation energies and colliding geometries. We study the multifragmentation using a soft equation of state along with enhanced and reduced clusterization range (Rclus) and momentum constraints (Pclus) with an isospin-dependent reduced cross-section. For a given set of input parameters, we find that effect of a different range of momentum and spatial constraints depends on the mass, energy and colliding geometry of the system. We note that all model ingredients have sizable effect on the fragmentation pattern. Fragments are formed with minimum spanning tree method. For Rclus = 4 fm there is a systematic trend for different value of Pclus compared to other clusterization parameters. In this clusterization range, there is no change in the production of the hMIMF i above Pclus = 240 MeV/c. Our analysis indicates that the effect on fragment production is stronger if a cut in the relative momentum of two nucleons is 240 MeV/c at a spatial separation of 4 fm. Our results for 197Au +197 Au collisions are in good agreement with the experimental data of ALADIN and for 129Xe +139 La, 86Kr +93 Nb, 40Ar +45 Sc with the NSCL data. 3 In chapter 7, we simulate for different system size effect, excitation energy, colliding geometry and study the role of interaction range on multifragmentation using σ = 0.9σNN and soft equation of state. We change the value of scaled Gaussian width (SGW) by reduc- ing and enhancing SGW from normal SGW. In the case of broader Gaussian, the particles in a cluster are bound to a large number of other nucleons inside a cluster. A reduced width leads to fluctuations which results in a large number of light and intermediate mass frag- ments. Broader Gaussian produces more excited fragments compared to narrow Gaussian. We find that the effect of the width of Gaussian wave packet associated with a nucleon depends on the mass of colliding system. We noted the range of SGW from time evolution of largest fragment and see its effect on balance energy. This range is then compared with the experimental data of ALADIN and NSCL. It is noted that either the highest or lowest range is in agreement with the experimental data. The lowest SGW gives more positive value of flow and also gives large multiplicity of IMF hMIMF i as compared to highest SGW. The reason is that as we decrease the Gaussian width, the probability of reaction taking place increases, which further results in an increase in NN collisions and hence more positive value of directed flow. For a given set of input parameters, we find that width has a sizable effect. At the same time, we know that different set of parameter can influence the reaction dynamics drastically. Hence, in our opinion it may not be possible to pin down the width to a very narrow level. Our studies shows that SGW influence the reaction dynamics. Finally, we will summarize our results and outlook of the present work in chapter 8. 4
Doctor of Philosophy
Keywords: Isospin; multifragmentation; collective flow; heavy ion