We study the electrostatic properties of inhomogeneous nuclear matter
which can be formed in the crusts of neutron stars or in supernova
explosions. Such matter can be represented by Wigner–Seitz cells of
different geometries (spherical, cylindrical, cartesian), which contain
nuclei, free neutrons and electrons under the conditions of electrical
neutrality. Using the Thomas–Fermi approximation, we have solved the Poisson equation for the electrostatic potential and calculated the
corresponding electron density distributions in individual cells. The
calculations are done for different shapes and sizes of the cells and
different baryon densities. We have performed calculations for a
simplified model of nuclei chosen as a Woods-Saxon distribution as well
as for realistic nuclear structure calculations within the RMF model.