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.

High Temperature Equation of State of Metallic Hydrogen

A theoretical description for optical conduction experiments in dense fluid hydrogen is presented. Different quantum statistical approaches are used to describe the mechanism of electronic transport in hydrogen's high-temperature dense phase. We show that at the onset of the metallic transition, optical conduction could be described by a strong rise in atomic polarizability, due to increased ionization, whereas in the highly degenerate limit, the Ziman weak scattering model better accounts for the observed saturation of reflectance. The inclusion of effects of partial ionization in the highly degenerate region provides great agreement with experimental results. Hydrogen's fluid metallic state is revealed to be a partially ionized free-electron plasma. Our results provide some of the first theoretical transport models that are experimentally benchmarked, as well as an important guide for future studies.

https://link.aps.org/accepted/10.1103/PhysRevE.97.043205

Dynamic conductivity and partial ionization in dense fluid hydrogen

The electrical resistivity of liquid metallic hydrogen at a temperature of 3000 K and a density of 0.35 mol/cm3 is calculated. Hydrogen is considered as a three-component system consisting of electrons, protons, and neutral hydrogen atoms. The second order of perturbation theory in electron-proton and electron-atom interactions is used to determine the inverse relaxation time for electric conductivity. The Coulomb electron-electron interaction is taken into account in the random phase approximation and the exchange interaction and correlation of conductivity electrons are included in the local-field approximation. The model of hard spheres is used for the proton and atomic subsystems. The concentration of the electrically neutral atomic component proved to be significantly lower than the value assumed by the discoverers of metallic hydrogen.

Metallization degree of hydrogen at a pressure of 1.4 Mbar and a temperature a 3000 K

The effective ion-ion interaction, free energy, pressure, and electric resistance of metallic liquid helium have been calculated in wide density and temperature ranges using perturbation theory in the electron-ion interaction potential. In the case of conduction electrons, the exchange interaction has been taken into account in the random-phase approximation and correlations have been taken into account in the local-field approximation. The solid-sphere model has been used for the nuclear subsystem. The diameter of these spheres is the only parameter of this theory. The diameter and density of the system at which the transition of helium from the singly ionized to doubly ionized state occurs have been estimated by analyzing the pair effective interaction between helium atoms. The case of doubly ionized helium atoms has been considered. Terms up to the third order of perturbation theory have been taken into account in the numerical calculations. The contribution of the third-order term is significant in all cases. The electric resistance and its temperature dependence for metallic helium are characteristic of simple divalent metals in the liquid state. The thermodynamic parameters—temperature and pressure densities-are within the ranges characteristic of the central regions of giant planets. This makes it possible to assume the existence of helium in the metallic state within the solar system.

Equation of state of metallic helium

The electrical resistivity of liquid metallic hydrogen at a temperature of 3000 K and a density of 035 mol/cm is calculated Hydrogen is considered as a three-component system consisting of electrons, protons, and neutral hydrogen atoms The second order of perturbation theory in electron–proton and electron–atom interactions is used to determine the inverse relaxation time for electric conductivity The Coulomb electron–electron interaction is taken into account in the random phase approximation and the exchange interaction and correlation of conductivity electrons are included in the local-field approximation The model of hard spheres is used for the proton and atomic subsystems The concentration of the electrically neutral atomic component proved to be significantly lower than the value assumed by the discoverers of metallic hydrogen

/pdf/metal-dielectric-transition-in-hydrogen-rf68uivfzp.pdf

Metal{Dielectric Transition in Hydrogen

We calculate the electroresistivity of metallic hydrogen within the framework of perturbation theory in electronproton interaction. To this end we employ the Kubo linear response theory while using the two-time retarded Green functions method to calculate the relaxation time. The expressions for the second and third order contributions are given. To describe the electron subsystem, the random phase approximation is used, allowing for the exchange interactions and correlations in a local field approximation. Thermodynamics of the proton subsystem is assumed to be given by the Percus-Yevick equation. At a given density and temperature the only parameter of the theory is the hard sphere diameter, which is calculated from effective pair ionic interaction. For a completely degenerated electron gas, the latter is determined by the density of the system. The dependence of the second and the third order contributions on the parameters of the theory is investigated. For all densities and temperatures examined here the third order contribution constitutes more than half of the second order term. The corresponding magnitude of resistivity is about 100 � 250µ cm.

/pdf/ionic-interaction-and-conductivity-of-metallic-hydrogen-46fky918af.pdf

S. V. Savenko

Papers

Ionic interaction and conductivity of metallic hydrogen