Asymmetry energy of nuclear matter: Temperature and density dependence, and validity of semi-empirical formula

TL;DR

This paper performs a microscopic calculation of the asymmetry energy in nuclear matter, examining how it varies with temperature and density, and assesses the validity of the semi-empirical formula.

Contribution

It introduces a detailed variational approach using the AV18 potential to analyze asymmetry energy's dependence on temperature and density, evaluating the semi-empirical approximation.

Findings

Asymmetry energy depends on both density and temperature.

The parabolic approximation is generally valid but other terms can improve accuracy.

Calculated energies align well with semi-empirical mass formula.

Abstract

In this work, we have done a completely microscopic calculation using a many-body variational method based on the cluster expansion of energy to compute the asymmetry energy of nuclear matter. In our calculations, we have employed the $AV_{18}$ nuclear potential. We have also investigated the temperature and density dependence of asymmetry energy. Our results show that the asymmetry energy of nuclear matter depends on both density and temperature. We have also studied the effects of different terms in the asymmetry energy of nuclear matter. These investigations indicate that at different densities and temperatures, the contribution of parabolic term is very substantial with respect to the other terms. Therefore, we can conclude that the parabolic approximation is a relatively good estimation, and our calculated binding energy of asymmetric nuclear matter is in a relatively good agreement with that of semi-empirical mass formula. However, for the accurate calculations, it is better to consider the effects of other terms.