Surface energy of nuclear matter above and below neutron drip with the Skyrme-type effective interactions

Neutron star crust consists of highly neutron excess nuclei, which are inaccessible for laboratory experiments. In the deepest region of the crust (so-called inner crust, located after the neutron drip) atomic nuclei are immersed into the sea of degenerate unbound neutrons. Study of the crust structure and equation of state in such conditions relies on the theoretical nuclear mass models. In particular, it is convenient to use the compressible liquid drop model, which contains the surface tension term. A thermodynamically consistent description must take into account adsorption of neutrons on the nucleus surface (neutron skin) and dependence of surface tension on matter properties in two-phase equilibrium. We calculate the surface tension of nuclear matter by the extended Thomas-Fermi approach. For this aim, we parametrize the number density profile of the two-phase system by Fermi-Dirac type functions, totally containing 5 parameters, and minimize the thermodynamic potential Ω to obtain equilibrium configuration. We use Skyrme-type nuclear interactions SLy4 and BSk24, fulfilling experimental data of atomic nuclei, observational constraints on the maximal neutron star mass and theoretical calculations of high-density nuclear matter. The results are presented as a function of neutron chemical potential, which is useful for compressible liquid drop models in the inner crust of a neutron star.