Pressure ionization in the spherical ion-cell model of dense plasmas and a pressure formula in the relativistic Pauli approximation

We study the continuity of pressure of dense plasmas in the case of pressure ionization. Pressure is calculated using a quantum-mechanical stress-tensor pressure formula in the self-consistent-field spherical ion-cell model. It appears that in order to preserve the continuity of calculated pressure one must take narrow shape resonances into account during the calculations of the self-consistent atomic potential, electron number density, and pressure. We also derive a relativistic pressure formula in the Pauli approximation. The obtained formula is only slightly different from a nonrelativistic one. When there are no very loosely bound levels, relativistic corrections only affect bound electrons, while when very loosely bound levels exist, relativistic corrections to free electron states become important. Hence, if relativistic corrections are applied only to bound electron states, it may lead to a discontinuity in the pressure-versus-density curve even in the case of small-Z elements. This observation stresses the need for a coherent description of bound and free electrons in the spherical ion-cell models.