  Properties of the matter in the inner crust of a neutron star are
investigated in a Hartree-Fock plus BCS approximation employing schematic
effective forces of the type of the Skyrme forces. Special attention is paid to
differences between a homogenous and inhomogeneous description of the matter
distribution. For that purpose self-consistent Hartree Fock calculations are
performed in a spherical Wigner-Seitz cell. The results are compared to
predictions of corresponding Thomas Fermi calculations. The influence of the
shell structure on the formation of pairing correlations in inhomogeneous
matter are discussed.
