Pressure of a partially ionized hydrogen gas: numerical results from exact low temperature expansions

We consider a partially ionized hydrogen gas at low densities, where it reduces almost to an ideal mixture made with hydrogen atoms in their ground-state, ionized protons and ionized electrons. By performing systematic low-temperature expansions within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential, exact formulae for the first.ve leading corrections to the ideal Saha equation of state have been derived[A. Alastuey, V. Ballenegger et al., J. Stat. Phys. 130, 1119 (2008)]. Those corrections account for all effects of interactions and thermal excitations up to order exp(EH /kT) included, where EH ≅ -13.6 eV is the ground state energy of the hydrogen atom. Among the.ve leading corrections, three are easy to evaluate, while the remaining ones involve suitably truncated internal partition functions of H2 molecules and H- and H2+ ions, for which no analytical formulae are available in closed form. We estimate those partitions functions at.nite temperature via a simple phenomenology based on known values of rotational and vibrational energies. This allows us to compute numerically the leading deviations to the Saha pressure along several isotherms and isochores. Our values are compared with those of the OPAL tables (for pure hydrogen) calculated within the ACTEX method (copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)