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

P. Proust (1) , Y. Lallouet , D. Davesne (1) , J. Meyer (1)

1 IP2I Lyon - Institut de Physique des 2 Infinis de Lyon

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 $\hbar^2$. 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.

Domaines: Physique Nucléaire Théorique [nucl-th]

P. Proust, Y. Lallouet, D. Davesne, J. Meyer. Surface energy coefficient of a N2LO Skyrme energy functional : a semiclassical Extended Thomas-Fermi approach. Phys.Rev.C, 2022, 106 (5), pp.054321. ⟨10.1103/PhysRevC.106.054321⟩. ⟨hal-03690489⟩