Slope-dependent nuclear-symmetry energy within the effective surface approximation

TL;DR

This paper extends the effective-surface approximation to include derivatives of the symmetry-energy density, improving calculations of surface symmetry energy, neutron skins, and isovector resonance energies in nuclei.

Contribution

It introduces an extended effective-surface approximation that accounts for gradient terms of the symmetry energy, enhancing the modeling of nuclear surface properties.

Findings

Calculated surface symmetry-energy constants for Skyrme forces.

Predicted neutron skin thicknesses and isovector stiffnesses.

Achieved reasonable agreement with experimental data on giant-dipole resonances.

Abstract

The effective-surface approximation is extended taking into account derivatives of the symmetry-energy density per particle with respect to the mean particle density. The isoscalar and isovector particle densities in this extended effective-surface approximation are derived. The improved expressions of the surface symmetry energy, in particular, its surface tension coefficients in the sharp-edged proton-neutron asymmetric nuclei take into account important gradient terms of the energy density functional. For most Skyrme forces the surface symmetry-energy constants and the corresponding neutron skins and isovector stiffnesses are calculated as functions of the Swiatecki derivative of the nongradient term of the symmetry-energy density per particle with respect to the isoscalar density. Using the analytical isovector surface-energy constants in the framework of the Fermi-liquid droplet model we find energies and sum rules of the isovector giant-dipole resonance structure in a reasonable agreement with the experimental data, and they are compared with other theoretical approaches.