T. R. Routray

Cluster radioactivity in very heavy nuclei: a new perspective

Abstract Exotic cluster decay of very heavy nuclei is studied using the microscopic nuclear potentials obtained by folding density dependent M3Y effective interaction with the densities of the cluster and the daughter nuclei. The microscopic nuclear potential, Coulomb interaction and the centrifugal barrier arising out of spin-parity conservation are used to obtain the potential between the cluster and the daughter nuclei. Half life values are calculated in the WKB framework and the preformation factors are extracted. The latter values are seen to have only a very weak dependence on the mass of the emitted cluster.

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.

Anisotropic cosmological model with variable G and Λ

Anisotropic Bianchi-III cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Without assuming any specific forms for Λ and the metric potentials, we have tried to extract the time variation of G and Λ from the anisotropic model. The extracted G and Λ are in conformity with the present day observations. Basing upon the observational limits, the behavior and range of the effective equation of state parameter are discussed.