Аннотация:Modern gas dynamic codes use equations of state (EOS) of substances. These EOS must have good accuracy in a wide range of temperatures and densities and must be thermodynamically self-consistent. In the present paper, we describe new improvements of the ionization equilibrium model for plasma. They account for finite volumes of ion cores and partial electron degeneration. This permits to expand this model to the super high densities and low temperatures. Thus, the enhanced Saha model becomes a wide range EOS itself.