Equation of state of dense, partially degenerate, reacting plasmas

A method is presented for treating ionization equilibrium in the presence of plasma coupling, which allows for the fact that heavy ions may be strongly coupled (liquidlike) while electrons are only moderately coupled (gaslike). The theory utilizes a many-body perturbation expansion of the grand canonical partition function. Three distinct renormalizations are required to handle the general problem. They account for (1) formation of electron-nucleus composites, (2) coupling of the composite particles to the plasma, and (3) strong coupling of multiply charged heavy ions. Five dimensionless parameters, which are the ratios of two lengths, are required to define the limits of applicability of the theory. Equation-of-state calculations for Ar have been carried out. Corrections to the Saha equation are found to be significantly smaller than predicted by the Debye-H\"uckel theory. At moderate density this is due to decreased net Coulomb attraction. At high density core repulsion tends to offset (or exceed) the Coulomb attraction term.