Surface energy coefficient of a N2LO Skyrme energy functional : a semiclassical Extended Thomas-Fermi approach

TL;DR

This paper extends the semiclassical Extended Thomas-Fermi method to N2LO Skyrme functionals, providing a practical formula for surface energy that aids in constraining new parametrizations in nuclear physics.

Contribution

It generalizes the semi-classical approach to N2LO Skyrme functionals, deriving an easy-to-use surface energy formula including higher-order contributions.

Findings

The derived formula simplifies surface energy calculations for N2LO Skyrme functionals.

The N2LO parametrization shows a shift similar to traditional Skyrme models when compared to Hartree-Fock results.

The approach facilitates constraining surface properties of advanced Skyrme parametrizations.

Abstract

We generalize to N2LO Skyrme functionals the semi-classical approach of Grammaticos and Voros in order to calculate the Extended Thomas Fermi expressions of the new densities and currents appearing at the N2LO level. Within a one dimensional symmetric semi infinite nuclear matter model and using a simple Fermi-like density profile, we obtain an easy-to-use formula for the surface energy including the contributions of the central, density-dependent and spin-orbit terms up to $\hbar^2$. Such a formula can be easily used as a first attempt to constrain the surface properties of new N2LO Skyrme parametrizations. The N2LO parametrization tested in this paper is shown to exhibit a shift (compared to a full Hartree-Fock calculation) which is quantitatively similar to the one obtained with the traditional Skyrme parametrizations.