B Behera

Momentum dependence of the mean field and equation of state of nuclear matter

Abstract The momentum and density dependence of the mean field and other properties of nuclear matter are studied with finite-range effective interactions having different functional forms by evaluating the single-particle momentum distribution function self-consistently. In these calculations relativistic effects and supraluminous behaviour of nuclear matter are also taken into account. The equation of states obtained from these effective interactions are used to study liquid–gas phase transition in nuclear matter.

Momentum and density dependence of the mean field in nuclear matter

The momentum and density dependence of the mean field in nuclear matter has been studied with phenomenological effective interactions with particular emphasis on the influence of the functional form of the interaction in determining the high density and high momentum behaviour of the mean field. Emphasis is also given to choosing the effective interaction in a form simple enough to permit analytical calculations of various properties of nuclear matter with a minimum number of adjustable parameters. These simple effective interactions are found to have a zero-range density-dependent part similar to Skyrme interactions and a long-range density-independent part of conventional form, such as Yukawa, Gaussian and exponential. It is observed that the high density and the high momentum behaviour of the mean field in nuclear matter is essentially governed by the nature of the density dependence and the precise functional form of the long-range part of the exchange component of the effective interaction. The parameters of these interactions can be constrained to obtain a mean field in nuclear matter which is independent of the functional form of the exchange interaction in the range of momentum k = 0- and up to a density four times the standard nuclear matter density. However, beyond this range the functional form of the exchange interaction becomes important in determining the momentum and density dependence of the mean field in nuclear matter.

Neutron?proton effective mass splitting and thermal evolution in neutron-rich matter

The thermal evolution of properties of neutron rich asymmetric nuclear matter such as entropy density, internal energy density, free energy density and pressure are studied in the non-relativistic mean field theory using finite range effective interactions. In this framework the thermal evolution of nuclear matter properties is directly connected to the neutron and proton effective mass properties. Depending on the magnitude of neutron-proton effective mass splittings, two distinct behaviours in the thermal evolution of nuclear matter properties are noticed.The thermal evolution of properties of neutron-rich asymmetric nuclear matter such as entropy density, internal energy density, free energy density and pressure is studied in the non-relativistic mean field theory using finite range effective interactions. In this framework, the thermal evolution of nuclear matter properties is directly connected to the neutron and proton effective mass properties. Depending on the magnitude of neutron–proton effective mass splittings, two distinct behaviours in the thermal evolution of nuclear matter properties are noticed.

Proton radioactivity with a Yukawa effective interaction

The half-lives of proton radioactivity of proton emitters are investigated theoretically. Proton-nucleus interaction potentials are obtained by folding the densities of the daughter nuclei with a finite-range effective nucleon-nucleon interaction having Yukawa form. The Wood-Saxon density distributions for the nuclei used in calculating the nuclear as well as the Coulomb interaction potentials are predictions of the interaction. The quantum mechanical tunneling probability is calculated within the WKB framework. These calculations provide reasonable estimates for the observed proton radioactivity lifetimes. The effects of neutron-proton effective mass splitting in neutron-rich asymmetric matter as well as the nuclear matter incompressibility on the decay probability are investigated.

Temperature dependence of the nuclear symmetry energy and equation of state of charge neutral n + p + e + μ matter in beta equilibrium

The temperature and density dependence of the nuclear symmetry energy is studied in the nonrelativistic mean field theory by using a density-dependent finite range effective interaction. The temperature evolution of the interaction part of symmetry energy is decided by the nature of the finite range exchange interactions acting between a pair of like and unlike nucleons, an area which is less understood. In view of this, two cases corresponding to different strengths of exchange interaction between two like nucleons are considered to examine their influence on the temperature dependence of the nuclear symmetry energy. The symmetry energy obtained as a function of temperature and density is used to study the temperature dependence of leptonic fractions, proton fraction and equation of state of charge neutral n + p + e + μ matter under β-equilibrium for the two different cases.

Simple effective interaction: infinite nuclear matter and finite nuclei

The mean field properties and equation of state for asymmetric nuclear matter are studied using a simple effective interaction, which has a single finite-range Gaussian term. The study of finite nuclei with this effective interaction is done by constructing a quasilocal energy density functional for which the single-particle equations take the form of Skryme–Hartree–Fock equations. The predictions of binding energies and charge radii of spherical nuclei are found to be compatible with the results of successful mean field models, as well as with the experimental data.

Proton radioactivity half-lives with Skyrme interactions

The potential barrier impeding the spontaneous emission of protons in the proton radioactive nuclei is calculated as the sum of nuclear, Coulomb and centrifugal contributions. The nuclear part of the proton-nucleus interaction potential is obtained in the energy density formalism using the Skyrme effective interaction that results into a simple algebraic expression. The half-lives of the proton emitters are calculated for the different Skyrme sets within the improved WKB framework. The results are found to be in reasonable agreement with the earlier results obtained for more complicated calculations involving finite-range interactions.

Causal violation of the speed of sound and the equation of state of nuclear matter

The causal violation of the adiabatic speed of sound in nuclear matter at high density and/or high temperature is studied with phenomenological density-dependent effective interactions within the framework of the density matrix expansion and the non-relativistic Fermi-gas model. This study shows that the causal violation is essentially governed by the range of the exchange component and the nature of the density dependence of the effective interaction used to derive the equation of state (EOS) of nuclear matter as a function of density and temperature. With a model effective interaction consisting of a short-range density-dependent part of -function form and a long-range density-independent part of Gaussian form, it is observed that the causal violation can be completely avoided if the long-range part of the exchange component of the interaction has a range and if the density dependence of the interaction is chosen in the form ( with ) instead of the Skyrme approximation . The implications of these restrictions on the effective interaction imposed by causality are also discussed.

The single-particle potential, symmetry coefficient and effective mass in nuclear matter

The single-particle potential, its isotopic spin dependence, symmetry coefficient and effective mass in nuclear matter have been calculated using a simple effective interaction consisting of a density-dependent delta-function repulsion and a gaussian attraction. The density dependence in the interaction has been considered in three different forms: rho 2/3, rho 1/3 and rho 1/6. The three parameters of the interaction are determined so as to reproduce the correct binding energy and density in nuclear matter and the ground-state energy of 16O. With the above interaction, simple relations for the single-particle potential, symmetry coefficient, effective mass and other related quantities in nuclear matter are derived. It is found that the Hugenholtz-Van Hove theorem is satisfied exactly and the results for these quantities are in good agreement with those referred to in the literature.

Energy per particle, effective mass and magnetic susceptibility in neutron matter

Relations for energy per particle, effective mass and magnetic susceptibility in neutron matter are derived using a simple three-parameter density-dependent effective interaction constructed in an earlier work (see ibid., vol.5, no.1, p.85 (1979). The effective mass M*/M, which has a value 0.985 at kn=0.5 fm-1, decreases steadily with increase in density. The ratio chi F/ chi of the magnetic susceptibility of a Fermi gas of non-interacting neutrons to that of neutron matter increases with density up to kn=1.4 fm-1 and then decreases. The results of Haensel (1975) calculated with the Mongan nonlocal separable potential show a similar trend where chi F/ chi decreases beyond knp2.4 fm-1. As chi F/ chi is quite sensitive to the odd-state interaction energy, which is usually negligible up to a density corresponding to kn=2 fm-1, the results of magnetic susceptibility obtained with the simple effective interaction mentioned above acting in even states only are expected to be reliable only below this region of density.