Fluid hydrogen at high density: Pressure dissociation

Abstract

We develop a model for the Helmholtz free energy of fluid hydrogen at high density and high temperature. This model aims at describing both pressure and temperature dissociation and ionization and bears directly on equations of state of partially ionized plasmas, as encountered in astrophysical situations and high-pressure experiments. This paper focuses on a mixture of hydrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperatures. In the present model, the strong interactions are described with realistic potentials and are computed with a modified Weeks-Chandler-Andersen fluid perturbation theory that reproduces Monte Carlo simulations to better than 3%. Perturbations of the internal partition functions of H and ${\mathrm{H}}_2$ arising in the nonideal fluid are treated self-consistently with a recently developed occupation probability formalism. Theoretical Hugoniot curves derived from our model are in excellent agreement with experimental data. Pressure dissociation occurs over a narrow density range above 0.5 g/${\mathrm{cm}}^3$ and is remarkably temperature insensitive. Molecules remain the dominant species even at high densities.