Skyrme-Hartree-Fock calculations of nuclear properties in the drip-point region of neutron star crust

In the present paper we explore the neutron-drip region of cold non-rotating isolated neutron stars. We have performed extended nuclear-structure calculations for nuclei embedded in the electron gas. For modeling the outer crust we use a set of Wigner-Seitz cells, where every cell contains one nucleus surrounded by a cloud of relativistic electrons. Above the drip point a non-relativistic neutron gas occurs in the cell. These calculations are carried out within the Hartree-Fock approach in combination with Skyrme effective interactions. For every baryon density we have determined the configuration with a minimal total energy. The drip elements and corresponding drip densities have been determined for about 240 different parametrizations of Skyrme forces used in the literature. We demonstrate that the calculated drip-point densities depend essentially on the Skyrme parametrization used. Even the drip elements and the occupied shells in the drip region differ for different parametrizations. We have found that the number of neutrons building the neutron gas at the drip point also depends essentially on the Skyrme force chosen. Nevertheless, the number density of the neutron gas in the drip-region is more or less the same ($\sim 10^{-5} \frac{neutrons}{{fm}^{3}}$). The drip densities obtained within our approach are generally lower than predicted earlier.