FREE-ENERGY MODEL FOR FLUID ATOMIC HELIUM AT HIGH-DENSITY

We develop a free-energy model aimed at describing the thermodynamics of fluid atomic helium at high density and high temperature. This model represents a step towards a consistent description of the pressure ionization of helium, as encountered in astrophysical situations and high-pressure experiments. In the present paper, a perturbation theory is developed to derive the configuration energy of helium at high density, and the modification of internal states in the partition function due to N-body effects is treated self-consistently within an occupation probability formalism. A scaling relationship between the internal levels and the ground state of helium is presented, which reproduces the experimental energy spectrum of helium within 3%. We also develop a density-dependent pair potential for helium, which reduces to the ab initio Ceperley-Partridge potential [D. M. Ceperley and H. Partridge, J. Chem. Phys. 84, 820 (1986)] at low density and includes implicitly the many-body effects at high density. The theoretical Hugoniot curves and the speed of sound derived from our free-energy model are in excellent agreement with the available experimental data, thereby assessing the validity of the present model at high density. These calculations are the extension of a former model for hydrogen [D. Saumon and G. Chabrier, Phys. Rev. A 44, 5122 (1991)] to nonhydrogenic, two-electron systems. The present free-energy model can be used to derive an accurate equation of state for the outermost layers of Jovian planets, brown dwarfs, and white dwarfs. © 1994 The American Physical Society.