Parametrization of the surface energy in the ETF approximation

TL;DR

This paper develops a parametrization of surface energy in nuclear matter using extended Thomas-Fermi calculations, focusing on neutron-rich environments relevant to neutron star crusts and supernovae.

Contribution

It introduces a new fitting protocol for surface tension that accounts for in-medium effects and neutron skin, applicable to various energy functionals.

Findings

Accurately reproduces microscopic data with a simple analytical formula.

Shows surface tension depends mainly on cluster's mass and charge.

Demonstrates the method's applicability to different nuclear functionals.

Abstract

We perform extended Thomas-Fermi calculations in the Wigner-Seitz cell below and above neutron drip with realistic functionals. The resulting energy density is decomposed as a sum of bulk terms and a surface term, and a compressible liquid drop analytical formula is used to fit the surface tension. The effect of curvature terms and neutron skin is studied in detail. A very good reproduction of the microscopic data is obtained using an expression that depends only on the mass and charge of the cluster, showing that the in-medium modifications of the nuclear energy in the presence of an external neutron gas can be effectively accounted for in the isospin dependence of the surface tension. In this first application, aimed at establishing the fitting protocol, we concentrate on the Sly4 energy functional, but the study can be easily generalized to different functionals, and the resulting parametrizations can be used for direct applications in pasta calculations in neutron star crusts and supernova matter.