Influence of Nucleon-Nucleon Collisions on Multi-Fragmentation and Nuclear Flow

Abstract

The present work deals with the theoretical study of multi-fragmentation and its related phenomena like rapidity distribution, collective ow and nuclear stopping for asymmetric colliding nuclei at intermediate energy heavy-ion collisions. The theoretical investigations are carried out using microscopic isospin-dependent quantum molecular (IQMD) model. We aim to discuss the role of Coulomb interactions, nuclear equations of state (NEOS) and various rapidity bins by taking mass asymmetry into account. An attempt will also be made to understand the disappearance of directed transverse ow and elliptical ow and hence balance energy and transition energy, respectively. We shall also present the comparison of theoretical simulations with data produced by various experimental collaborations. The present thesis is divided into following seven chapters. Chapter 1 outlines the general introduction and background of the present work. The di erent phenomena, observables at intermediate energies i.e. NEOS, isospin physics, multifragmentation, collective Flow, as well as nuclear stopping are introduced. It also presents the status of the available experimental and theoretical attempts made to understand the above mentioned phenomena. Chapter 2 gives the detail of primary and secondary models. The primary models include various theoretical models used in literature to study the phase space of nucleons in heavy-ion reactions and secondary models include the di erent clusterization algorithms. In the rst part, the di erent theoretical models like Boltzman Uehling-Uhlenbeck (BUU) model, Classical Molecular Dynamics (CMD) model, Quantum Molecular Dynamics (QMD) model, Relativistic QMD (RQMD) model and Isospin-dependent QMD (IQMD) model are discussed to study heavy-ion reactions. The second part presents the di erent secondary models used to analyze the phase space of nucleons generated by the primary models. These secondary models include Minimum Spanning Tree (MST) method, MST with momentum cut (MSTP), MST with binding energy cut (MSTB), and Simulated Annealing Clusteriza- 1 tion Algorithm (SACA). Since our theoretical basis is the QMD and IQMD model, we shall discuss these two models in detail, while the detail of MST method is given where ever it is used. In Chapter 3, we present a complete systematic theoretical study of multi-fragmentation for free nucleons and various fragments by simulating di erent asymmetric reactions at incident beam energies between 50 and 600 MeV/nucl. at semi-central impact parameter using soft and hard NEOS. While the total mass of the system stays constant, mass asymmetry varies between 0.2 and 0.7. We nd that in the case of nearly symmetric reaction, spectator parts will come from both projectile and target, whereas in the case of highly asymmetric reaction, no spectator part will come from projectile i.e. only target will contribute to the spectators. Although nearly symmetric nuclei depict a well-known trend of rising and falling for intermediate mass fragment (IMF's) production with peak around E= 100 MeV/nucl., this trend, however, is completely missing for large asymmetric colliding nuclei. The measured distributions are also given as a function of the total charge of all projectile fragments, Zbound. The highly asymmetric system produces largest Zbound, while, maximum number of intermediate mass fragments (IMF's) are produced at Zbound = 20. This observation may throw light on the formation mechanisms behind multi-fragmentation. Moreover, the brief study of the directed transverse ow shows that balance energy is a ected by the Coulomb interactions as well as di erent NEOS. This balance energy is further parametrized in terms of mass power law. In Chapter 4, within the semi-classical transport simulations of energetic semi-central collisions of the 79Au197+79Au197 reaction, we present a new investigation of the interplay between the participant and spectator regions in terms of rapidity distributions. The maxima and minima in the incident energy dependence of elliptical ow are produced by di erent contributions of the passing time of the spectator and the expansion time of the participant. The shadowing of the spectator matter plays an important role up to later times due to the comparable magnitude of the passing and expansion times up to energies of 400 MeV/nucl. However, at high energies the shadowing e ect is dominant only at earlier times due to the 2 fact that the passing time is shorter than the expansion time. The transition from in-plane to out-of-plane emission is observed only when the mid-rapidity region is included into the rapidity bin. Otherwise, no transition is observed. The transition energy is found to be strongly dependent on the size of the rapidity bin, while only depends weakly on the type of the rapidity distributions. The transition energy is parameterized by a straight-line interpolation. A comparison with experimental bins reveals that a competition is observed between the rapidity bins of jY redj 0:1 and jY redj 0:3. In Chapter 5, we present the systematic theoretical results on elliptical ow by analyzing nearly symmetric and asymmetric reactions at di erent incident energies. In the case of nearly symmetric reactions, general features of the elliptical ow are investigated with the help of theoretical simulations, particularly, the transverse momentum, impact parameter, system size and incident energy dependence. Special emphasis is put on the energy dependence of the elliptical ow. We also compare our theoretical calculations with 4 Array data. This comparison, performed for the reaction of 18Ar40 +21 Sc45 shows that the hard NEOS explains the data nicely. In general, a reasonable agreement is obtained between the data and calculations. We also predict that elliptical ow for di erent kind of fragments follows power law dependence C(Atot) . Moreover, in the case of asymmetric reactions, elliptical ow is analyzed by varying the mass asymmetry of colliding nuclei while total mass is kept xed. The mass asymmetry dependence of elliptical ow (in terms of transverse momentum dependence) for free nucleons and LMF's shows a weaker squeeze-out ow as compared to larger asymmetric reactions. Moreover, the elliptical ow is found to show a transition from in-plane to out-of-plane in the mid rapidity region with incident energy, while no such transition is observed when integrated over the entire rapidity region. The transition energy, at which elliptical ow < V2 > changes sign from positive to negative values, is di erent for di erent mass asymmetries, and is found to increase with the mass asymmetry for lighter fragments. The comparison with experimental data of INDRA@(GSI+GANIL) and MSU collaborations supports our ndings. 3 In Chapter 6, we study the nuclear stopping in asymmetric colliding channels by keeping total mass xed. The calculations are carried out by varying the mass asymmetry of the colliding pairs with di erent neutron-proton ratios at incident beam energy 250 MeV/nucl. The contribution of the neutrons and protons is checked in terms of anisotropy ratio < R > and quadrupole moment < Qzz >. The maximum stopping is obtained for nearly symmetric systems. Also a reasonable agreement is observed between theoretical results of anisotropy ratio < R > and energy dependent anisotropy ratio < RE > with the experimental data of INDRA collaboration. Finally, we will summarize our results in Chapter 7.