Properties of nuclear matter from macroscopic-microscopic mass formulas

TL;DR

This paper derives nuclear matter properties from macroscopic-microscopic mass formulas using Skyrme functionals, providing insights into incompressibility, symmetry energy, and effective masses, with results aligning with other nuclear models.

Contribution

It introduces a method to extract nuclear matter properties from mass formulas using Skyrme energy density functionals, offering new constraints on key nuclear parameters.

Findings

Incompressibility coefficients are around 230-235 MeV.

Slope parameter of symmetry energy is approximately 42-52 MeV.

Effective mass uncertainties increase with density.

Abstract

Based on the standard Skyrme energy density functionals together with the extended Thomas-Fermi approach, the properties of symmetric and asymmetric nuclear matter represented in two macroscopic-microscopic mass formulas: Lublin-Strasbourg nuclear drop energy (LSD) formula and Weizs\"acker-Skyrme (WS*) formula, are extracted through matching the energy per particle of finite nuclei. For LSD and WS*, the obtained incompressibility coefficients of symmetric nuclear matter are $K_\infty=230 \pm 11$ MeV and $235\pm 11$ MeV, respectively. The slope parameter of symmetry energy at saturation density is $L=41.6\pm 7.6$ MeV for LSD and $51.5\pm 9.6$ MeV for WS*, respectively, which is compatible with the liquid-drop analysis of Lattimer and Lim [ApJ. \textbf{771}, 51 (2013)]. The density dependence of the mean-field isoscalar and isovector effective mass, and the neutron-proton effective masses splitting for neutron matter are simultaneously investigated. The results are generally consistent with those from the Skyrme Hartree-Fock-Bogoliubov calculations and nucleon optical potentials, and the standard deviations are large and increase rapidly with density. A better constraint for the effective mass is helpful to reduce uncertainties of the depth of the mean-field potential.