High Temperature Equation of State of Metallic Hydrogen

TL;DR

This paper numerically investigates the high-temperature equation of state of liquid metallic hydrogen, relevant to planetary cores and experimental conditions, using perturbation theory and considering electron and proton interactions.

Contribution

It provides a detailed thermodynamic analysis of metallic hydrogen at high temperatures, including the effects of higher-order perturbation terms, and identifies conditions for its liquid phase existence.

Findings

Thermodynamic potentials increase monotonically with density and temperature.

Pressure values match experimental data for metallic hydrogen production.

Liquid phase exists within specific temperature and density ranges.

Abstract

The equation of state of liquid metallic hydrogen is solved numerically. Investigations are carried out at temperatures, which correspond both to the experimental conditions under which metallic hydrogen is produced on earth and the conditions in the cores of giant planets of the solar system such as Jupiter and Saturn. It is assumed that hydrogen is in an atomic state and all its electrons are collectivized. Perturbation theory in the electron and proton interaction is applied to determine the thermodynamic potentials of metallic hydrogen. The electron subsystem is considered in the randomphase approximation with regard to the exchange interaction and the correlation of electrons in the local field approximation. The interproton interaction is taken into account in the hard spheres approximation. The thermodynamic characteristics of metallic hydrogen are calculated with regard to the zero-, second-, and thirdorder perturbation theory terms. The third-order term proves to be rather essential at moderately high temperatures and densities, although it is much smaller than the second-order term. The thermodynamic potentials of metallic hydrogen are monotonically increasing functions of density and temperature. The values of pressure for the temperatures and pressures that are characteristic of the conditions under which metallic hydrogen is produced on earth coincide with the corresponding values reported by the discoverers of metallic hydrogen to a high degree of accuracy. The temperature and density ranges are found in which there exists a liquid phase of metallic hydrogen.