Exploration of Nuclear Matter Properties and Related Thermodynamical Aspects

Abstract

The present thesis aims to understand the properties of nuclear matter over a wide range of temperatures, density, isospin-asymmetry, pressure and magnetic field. The precise knowledge of the effect of these variables on the nuclear matter is of prime importance due to their relevance in various nuclear physics and astrophysical phenomena such as heavy-ion reactions, nuclear multifragmentation, the neutron star, supernovae etc. The effective relativistic mean field model (E-RMF) is used for the nuclear interaction to achieve these objectives. The nuclear matter is investigated in three forms: infinite nuclear matter, finite nuclei and the neutron star. In the first part, the infinite nuclear matter is investigated to estimate the critical properties in the context of liquid-gas phase transition, finite temperature effects and modifications in the equation of state (EoS) due to temperature. Extending the infinite matter, the second part of the thesis studies various properties of hot nuclei and their dependence on the EoS. Possible correlations among the critical properties with respect to a hot nucleus and infinite nuclear matter are discussed in this part. The third part of the thesis aims to study the neutron star interior with a main focus on the neutron star crust. The neutron star crust is investigated for the unmagnetised and magnetised matter, in context to pulsars and magnetars. The thesis is divided into eight chapters which are briefly described below. Chapter 1 discusses the essential concepts and definitions used in the thesis with an appropriate literature review. It begins with the description of the nuclear matter phase diagram advocating the importance of precise knowledge of nuclear interaction to describe various associated phenomena. The liquid-gas phase transition in the nuclear matter in the lowdensity regime is discussed for both infinite and finite nuclear matter. Next, the neutron star, a prominent aspect of the phase diagram, is discussed in detail with emphasis on its interior structure. The importance of EoS in nuclear physics is discussed with available constraints on various nuclear matter observables. Finally, the E-RMF framework is discussed, citing its suitability and success in describing various nuclear matter properties. In Chapter 2, the methodology is discussed. It starts with a brief description of E-RMF theory which is then extended to the finite temperature regime. The finite temperature effects, such as phase transition in symmetric/asymmetric nuclear matter and the effects of temperature on EoS, are discussed. The Gibbs and Maxwell phase rules are discussed for the description of liquid-gas phase transition in nuclear matter. Extending the infinite iii iv nuclear matter to a finite nucleus, a simplistic liquid drop model is considered with the aprropriate density dependence in various coefficients. The free energy of the nucleus in terms of the liquid drop model is formulated to study a hot finite nucleus and associated phenomena. The relevance of various properties such as excitation energy, level density, limiting temperature is discussed in context of nuclear dimensions. Finally, the outer crust using the Baym-Pethick-Sutherland (BPS) model and inner crust using compressible liquid drop model (CLDM) are discussed to understand the internal structure of a neutron star. Global properties of a neutron star, such as mass, radius, the moment of inertia, crust mass etc., are also described. In Chapter 3, various finite temperature properties of isospin symmetric and asymmetric nuclear matter over a wide range of density and pressure are investigated. The E-RMF formalism employing the FSUGarnet, IOPB-I and G3 forces, along with one of the most used NL3 parameter sets, are used in the finite temperature limit realising their narrow range of bulk matter properties at zero temperature. The liquid-gas phase transition in context to symmetric and asymmetric matter is discussed. The binodal and spinodal diagrams in reference to the symmetric and asymmetric matter are estimated due to their relevance in neutron star and supernovae physics. The effects of the temperature of the EoS and various nuclear matter observables, such as symmetry energy, are worked out. The thermal properties of state variables in context to their importance in supernovae matter is also discussed. In Chapter 4, thermal properties of hot nuclei are investigated within E-RMF formalism. The free energy of a nucleus is estimated by using temperature and density-dependent parameters of the liquid-drop model. The surface free energy is parametrised using two approaches based on the sharp interface of the liquid-gaseous phase and the semi-classical Seyler-Blanchard interaction. Various properties, such as limiting temperature, Excitation energy, level density, fissility etc., are evaluated for a wide atomic mass range. Since the calculations are inevitably model dependent, a detailed correlation matrix analysis is worked out to account for large deviations in the magnitude of critical parameters among various E-RMF sets. In Chapter 5, using the E-RMF model, the crustal properties of the neutron star are investigated. The unified equations of state (EoS) are constructed using recently developed E-RMF parameter sets, such as FSUGarnet, IOPB-I, and G3. The outer crust composition is determined using the atomic mass evaluation 2020 data along with the available Hartree-Fock-Bogoliubov mass models for neutron-rich nuclei. The structure of the inner crust is estimated by performing the compressible liquid drop model calculations using the same E-RMF functional as that for the uniform nuclear matter in the liquid core. Various neutron star properties such as mass-radius (M −R) relation, the moment of inertia (MI), the fractional crustal moment of inertia (Icrust/I), mass (Mcrust) and thickness (lcrust) of the crust are calculated with three unified EoSs. The crustal properties are found to be sensitive to the density-dependent symmetry energy and slope parameter advocating the importance of the unified treatment of neutron star EoS. The three unified EoSs, IOPB-I-U, FSUGarnet-U, and G3-U, reproduced the observational data obtained with different pulsars, NICER, and glitch activity and are found suitable for further description of the structure of the neutron star. Extending above analysis, Chapter 6 investigates the properties of pasta structures and v their influence on the neutron star observables employing the E-RMF model. The compressible liquid drop model is used to incorporate the finite size effects, considering the possibility of nonspherical structures in the inner crust. The unified equation of states are constructed for several E-RMF parameters to study various properties such as pasta mass and thickness in the neutron star’s crust. The majority of the pasta properties are sensitive to the symmetry energy in the subsaturation density region. Using the results from Monte Carlo simulations, the shear modulus of the crust in the context of quasiperiodic oscillations from soft gamma-ray repeaters and the frequency of fundamental torsional oscillation mode in the inner crust is estimated. Global properties of the neutron star such as mass-radius profile, the moment of inertia, crustal mass, crustal thickness, and fractional crustal moment of inertia etc. are worked out. The results are consistent with various observational and theoretical constraints. In Chapter 7, the crustal properties of a neutron star are investigated within E-RMF framework in the presence of magnetic field strength ∼ 1017G. The equilibrium composition of the outer crust is calculated by minimizing the Gibbs free energy using the most recent atomic mass evaluations. The magnetic field significantly affects the equation of state (EoS) and the properties of the outer crust, such as neutron drip density, pressure, melting temperature etc. For the inner crust, the compressible liquid drop model is used for the first time to study the crustal properties in a magnetic environment. The inner crust properties, such as mass and charge number distribution, isospin asymmetry, cluster density, etc., show typical quantum oscillations (De Haas–van Alphen effect) sensitive to the magnetic field’s strength. The density-dependent symmetry energy influences the magnetic inner crust like the field-free case. The primary aim here is to study the probable modifications in the pasta structures and it is observed that their mass and thickness changes by ∼ 10−15% depending upon the magnetic field strength. The fundamental torsional oscillation mode frequency is investigated for the magnetized crust in the context of quasiperiodic oscillations (QPO) in soft gamma repeaters. The magnetic field strength considered in this work influences only the EoS of outer and shallow regions of the inner crust, which results in no significant change in global neutron star properties. However, the outer crust mass and its moment of inertia increase considerably with increase in magnetic field strength. Finally, Chapter 8 summarises important results of the thesis and the possible future scopes are outlined here.