Surface energy coefficient of a N2LO Skyrme energy functional : a semiclassical Extended Thomas-Fermi approach

Abstract

We generalize to N2LO Skyrme functionals the semi-classical 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 symmetric semi infinite nuclear matter model and using a simple Fermi-like density profile, we obtain an easy-to-use formula for the surface energy including the contributions of the central, density-dependent and spin-orbit terms up to ${\hslash }^2$. 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 to a full Hartree-Fock calculation) which is quantitatively similar to the one obtained with the traditional Skyrme parametrizations.

arXiv comment19 pages, 3 figures, to be published

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Cited by in corpus (1)

• Impact of choices for center-of-mass correction energy on the surface energy of Skyrme energy density functionals