Self-consistent field model for condensed matter

A model for condensed matter is described in which the ions surrounding a particular atom are replaced by a constant density positive charge background outside of a spherical cavity. Electrons provide sufficient negative charge to neutralize the atomic nucleus at the center of the cavity and the positive charge outside. The orbital functions of the electrons, both bound and free, are obtained as solutions of the Dirac equation and are used to self-consistently determine the potential function. A prescription is given for separating the total volume and the total free energy of the system into parts associated with the atom and the surrounding medium. The Wigner-Seitz sphere radius at which the atomic free energy is lowest was found for each of 14 elements including the 5d transition metals. They differ from the sphere radii based on measured densities by from 2 to 8 percent. It is expected that results will improve in the high pressure region for which this model is mainly intended