  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.
