Mass dependence of symmetry energy coefficients in Skyrme force

TL;DR

This study investigates how the symmetry energy coefficients in finite nuclei vary with mass using Skyrme forces and semi-classical methods, revealing a consistent value around 22.9 MeV at a specific density.

Contribution

It provides a detailed analysis of the mass dependence of symmetry energy coefficients across multiple Skyrme models using the extended Thomas-Fermi approach.

Findings

Symmetry energy coefficient $a_{sym}$ is approximately 22.9 MeV at $A=260$.

Reference density for this coefficient is about 0.1 fm$^{-3}$.

Standard Skyrme functionals predict negative $I^4$ terms, conflicting with experimental data.

Abstract

Based on the semi-classical extended Thomas-Fermi approach, we study the mass dependence of the symmetry energy coefficients of finite nuclei for 36 different Skyrme forces. The reference densities of both light and heavy nuclei are obtained. Eight models based on nuclear liquid drop concept and the Skyrme force SkM* suggest the symmetry energy coefficient $a_{\rm sym}=22.90 \pm 0.15 $ MeV at $A=260$, and the corresponding reference density is $\rho_A\simeq 0.1$ fm$^{-3}$ at this mass region. The standard Skyrme energy density functionals give negative values for the coefficient of the $I^4$ term in the binding energy formula, whereas the latest Weizs\"acker-Skyrme formula and the experimental data suggest positive values for the coefficient.