Effect of splitting of the neutron and proton effective mass on nuclear symmetry energy at finite temperature

TL;DR

This study investigates how the splitting of neutron and proton effective masses influences the temperature dependence of nuclear symmetry energy using Skyrme energy density functionals, revealing a correlation and transition phenomena.

Contribution

It classifies Skyrme interactions based on effective mass splitting and analyzes their impact on symmetry energy at finite temperature, highlighting the role of effective mass splitting.

Findings

Correlation between effective mass splitting and symmetry energy temperature dependence.

Transition from decreasing to increasing symmetry energy with temperature at high densities.

Symmetry energy depends on both symmetry potential and effective mass splitting.

Abstract

We present the temperature and density dependence of symmetry energy for nuclear matter at finite temperature based on the approach of the thermodynamics with Skyrme energy density functional. We first classify the Skyrme interactions into 7 groups according to the range of neutron and proton effective mass in neutron matter limit(99.99 per cent neutron in the matter). We find that there is obvious correlation between the temperature dependence of the symmetry energy and the splitting of the neutron and proton effective mass. For some Skyrme interactions with $m^{*}_{n}>m^{*}_{p}$ and strong splitting of the neutron and proton effective mass in asymmetric nuclear matter, a transition of the temperature dependence of symmetry energy from decreasing with temperature at low densities to increasing with temperature at high densities appears. For other Skyrme interactions, we do not observe such phenomenon. Our study show that the symmetry energy in hot asymmetric matter not only depends on symmetry potential part but also on the splitting of the neutron and proton effective mass to a certain extent.