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

Abstract

The effective surface approximation is extended taking into account derivatives of the symmetry energy density per particle over 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 non-gradient 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 other theoretical approaches.