Influence of Isospin Dependent Nuclear Charge Radius in Heavy Ion Collisions at Intermediate Energies

Abstract

The study of isospin degree of freedom in the heavy-ion collisions (HICs) at intermediate energies signifies the abstraction of nuclear equation of state of isospin-asymmetric nuclear matter under the high pressure and density. This has been done in the literature via Coulomb interactions, symmetry energy, isospin momentum dependent interactions as well as isospin dependent nucleon-nucleon cross-section. The objective of present work is to emphasize the isospin effects through isospin dependent nuclear charge radius. A detailed theoretical investigation has been performed by using the dynamic microscopic theory- Isospin dependent Quantum Molecular Dynamics (IQMD) model on the multifragmentation, nuclear stopping, thermalization, directed flow and elliptical flow. The results thus obtained are compared with the experimental data. In chapter 1 the comprehensive description of nuclear reactions and development of various heavy-ion accelerators from beam energy of KeV/nucleon to GeV/nucleon has been presented. The heavy-ion collisions at intermediate energies and its importance with the help of phase diagram of the nuclear matter has been described. The isospin dependence of nuclear equation of state has been discussed through isospin dependent hydrodynamical model ingredients: Coulomb interactions, symmetry energy and nucleon-nucleon cross section. In addition to that the isospin degree of freedom through an essential model ingredient i.e. isospin dependent nuclear charge radii parameterizations and its possibility to affect the reaction dynamics at intermediate energies has been discussed. The chapter also outlines a brief experimental as well as theoretical literature review of the various phenomena occurring at intermediate energies. Various theoretical tools to define the evolution of nuclear reaction dynamics at intermediate energies has been discussed in chapter 2. A detailed description about the IQMD model has been presented. The secondary algorithms viz. Minimum Spanning Tree (MST) method, its updated versions MSTM (with momentum constraint) method has also been discussed which are further used to identify fragments from the final stage phase-space of the reaction generated by IQMD.In chapter 3, study on the initialization effects via nuclear charge radii on fragmentation for the whole mass range of periodic table by taking isospin-asymmetric nuclear reactions using IQMD model is presented. Calculations are performed for three different isospin dependent nuclear charge radii parameterizations as well as for liquid drop model (LDM) radius. Our study reveals that there is a significant role of nuclear charge radii on fragmentation at incident energy E = 50 MeV/nucleon. In addition to that the study done on the isospin degree of freedom through nuclear charge radii on the the initial N/Z dependence of various fragments: free nucleons (FNs) [A= 1], light mass fragments (LMFs) [2 A 4], medium mass fragments (MMF’s) [5 A 9] and intermediate mass fragments (IMFs) [5 A Atot/6] has been described. Moreover, the isospin dependent radius is more suitable to reproduce experimental findings of INDRA Collaboration for the multiplicity of IMF’s as a function of Zbound. Chapter 4 describes the structural and isospin effects through isospin dependent and independent nuclear charge radii parameterizations on the nuclear flow: (i) reduced flow and (ii) elliptical flow within the framework of IQMD model. The calculations have been carried out by using two different approaches: (i) for the reaction series having fixed N/Z ratio and (ii) for the isobaric reaction series with different N/Z ratio. Our results indicate that there is a considerable effect of radii parameterizations on the excitation function of reduced flow ( @v1 @Y red ) and elliptical flow (v2). Both balance energy (Ebal) and transition energy (Etrans) are enhanced with increase in the radii of reacting nuclei and found to follow a power law. The exponent τ values show that the elliptical flow is more sensitive towards different nuclear charge radii as compared to reduced flow. Moreover, our theoretical calculation of impact parameter dependence of Ebal and Etrans are in the agreement with the experimental data provided by FOPI, INDRA and ALADIN collaborations. The study of influence of nuclear charge radius has been extended to obtain the balancing and transition geometries from the scaled impact parameter dependence of reduced flow and elliptical flow. The role of clusterization technique by keeping the momentum constraint as per the isospin dependent nuclear charge radii parametrization has been optimized on the azimuthal angle dependence of dN/d(Cos2ϕ).Chapter 5 represents the significance of initialization effects on the nuclear stopping for entire regime of intermediate energy. The initialization effects on the global nuclear stopping parameters via different nuclear charge radii parameterizations using IQMD model at E = 50 MeV/nucleon is presented. From the study, it has been concluded that, as the production of fragments increases, the values of global stopping parameters, anisotropy ratio and quadrupole moment decreases with increase in the nuclear charge radii. The influence of nuclear charge radii on nuclear stopping is almost same for central and semi-central collisions. In addition, the role of isospin dependent nuclear charge radii parameterizations on the N/Z dependence of global stopping parameters is also studied. The excitation function of nuclear stopping has been depicted at incident energies between 30 to 1500 MeV/nucleon by including and also by excluding the momentum dependent interactions (MDI). Our study reveals that role of change in the radius parametrization on the nuclear stopping is more emphasized around 400 MeV/nucleon. MDI affects the nuclear stopping at relatively low energy and its role diminishes with increase in the incident energy. Moreover, the isospin dependent radius parametrization along with MDI is able to reduce the gap between theoretical calculations and experimental findings of INDRA and ALADIN collaborations. In chapter 6, the structural effects through nuclear charge radius on the multifragmentation as well as thermal equilibrium achieved in the HICs have been studied for mass-symmetric and mass-asymmetric collisions using IQMD model. The role of nuclear charge radii parameterizations on the thermal equilibrium by studying the correlation of maximal value of average temperature achieved in the highly interacting nuclear matter and multiplicity of FNs and LMFs with momentum-based anisotropy ratio over the entire collision geometry has been emphasized. The influence of radius on the contribution of projectile and target nuclei in the nuclear stopping has been studied in detail. Our study reveals that the increase in the available phase space at initial stage through different nuclear charge radii parameterizations, enhance the temperature of nuclear system and reduces the nuclear stopping for both types of reactions. The influence of nuclear charge radii on the thermalization is more pronounced for mass-symmetric reactions compared to mass-asymmetric reactions. Moreover, the lighter colliding pair are good probe to study the role of nuclear radius in the thermalization. Finally, in chapter 7, the results obtained in this study are summarized. Based on this study conclusion drawn is presented. Also, the extension of this work has been presented as future work.