Cluster virial expansion of the equation of state for hydrogen plasma withe-H2contributions

Abstract

The equation of state of partially ionized hydrogen plasma is considered with special focus on the contribution of the e-H(2) interaction. Traditional semiempirical concepts such as the excluded volume are improved using microscopic approaches to treat the e-H(2) problem. Within a cluster virial expansion, the Beth-Uhlenbeck formula is applied to infer the contribution of bound and scattering states to the temperature-dependent second virial coefficient. The scattering states are calculated using the phase expansion method for the polarization interaction that incorporates experimental data for the e-H(2) scattering cross section. We present results for the scattering phase shifts, differential scattering cross sections, and the second virial coefficient due to the e-H(2) interaction. The influence of this interaction on the composition of the partially ionized hydrogen plasma is confined to the parameter range where both the H(2) and the free-electron components are abundant.

Skye: A Differentiable Equation of State

“…For very low densities this results in an ideal gas with a different mean molecular weight. Several EOSs have been developed for this regime, including those based on free energy minimization (Saumon et al 1995;Irwin 2004), cluster activity expansions (Rogers 1974(Rogers , 1981Rogers & Nayfonov 2002), cluster viral expansions (Omarbakiyeva et al 2015;Ballenegger et al 2018), density-functional theory molecular dynamics (Militzer & Hubbard 2013;Becker et al 2014), path integral Monte Carlo (Militzer & Ceperley 2001), quantum Monte Carlo (Mazzola et al 2018), Feynman-Kac path integral representations (Alastuey et al 2020), and asymptotic expansions (Alastuey & Ballenegger 2012). Using these EOSs in stellar evolution calculations typically requires pretabulating results for fixed compositions due to the computational cost of solving for ionization equilibrium.…”