Thermodynamic functions (analytic expressions) for partially ionized strongly coupled plasmas. Bound and free states contributions

Abstract
An analytic expression is derived for pressure and free energy. The terms are : (a) classical correlation (which is valid for both Debye-Hueckel, quasi-crystal and intermediate regions), (b) its modification taking into account changing Coulomb potential for the effective pair pseudopotential, (c) quantum second virial coefficients for interaction between various species, (d) atom partition function limited for higher excited states by a principle quantum number depending on either temperature (for ideal plasmas) or density (for strongly coupled plasmas). The validity of the contributions to the analytic expression obtained is tested by comparison with limiting expansions for weakly nonideal plasmas, molecular simulation data for strongly coupled plasmas and experimental shock wave data.