Realistic electrostatic potentials in a neutron star crust

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 is 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 average baryon densities. The electron-to-baryon fraction was fixed at 0.3. Using realistic electron distributions leads to a significant reduction in electrostatic energy and electron chemical potential.