Equation of state for a partially ionized gas. II

The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. A spherical cellular model is deduced for the hot curve limit (or ideal Fermi gas). Next the Coulomb interactions are added to the spherical cellular model for general ionic charge Z. Then an independent electron model within a Z electron cell plus several many-body effects are employed. Numerical examples of the theory for several elements (H, Li, N, Na, K, Ni, Rb, Pd, Cs, and Er) are reported. These results reduce in various limits of temperature and density to the expected behavior. They display electron, localization-delocalization phase transitions of liquid-gas character. In the higher Z elements, a second possible critical point has been found. The critical pressure, electron density and temperature for the lower-density critical points seem to obey power laws as a function of Z.