Surface energy coefficient of an N2LO Skyrme energy functional: A semiclassical extended Thomas-Fermi approach

We generalize to N2LO Skyrme functionals the semiclassical 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 model of semi-infinite symmetric nuclear matter and using a simple Fermi-like density profile, we obtain an easy-to-use formula for the surface-energy coefficient including the contributions of the central, density-dependent, and spin-orbit terms up to h over bar 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 with a full Hartree-Fock calculation) which is quantitatively similar to the one obtained with the traditional Skyrme parametrizations.

Automated summary

We generalize the semiclassical approach of Grammaticos and Voros to N2LO Skyrme functionals to calculate the extended Thomas-Fermi expressions of the new densities and currents at N2LO level. Using a simple Fermi-like density profile in a one-dimensional model, we obtain an easy-to-use formula for the surface-energy coefficient, incorporating contributions from central, density-dependent, and spin-orbit terms up to h bar 2. This formula serves as a first attempt to constrain the surface properties of new N2LO Skyrme parametrizations. The tested N2LO parametrization in this paper exhibits a quantitatively similar shift compared to traditional Skyrme parametrizations.