Nonlocal Pseudopotential and the Thermodynamics of Metallic Helium
DOI:
https://doi.org/10.15407/ujpe67.11.790Keywords:
pseudopotential of electron-ion interaction, metallic helium, internal energy, free energy, equation of stateAbstract
Thermodynamic properties of liquid metallic helium have been studied in the framework of perturbation theory of the second-order in the electron-ion interaction pseudopotential. The latter was determined from the first principles and was found to be nonlocal and nonlinear. The pseudopotential nonlocality leads to the appearance of the first-order terms in the series expansions of the internal energy, free energy, and pressure of liquid metallic helium in the pseudopotential. The diagonal matrix element of this term is of the same order of magnitude as that in the zero-order term. As a result, the first-order term makes a substantial contribution to the internal and free energies, so that their dependences on the density and the temperature become stronger. Accordingly, the pressure at which the liquid phase of metallic helium can be realized increases. This pressure is an order of magnitude higher than the corresponding pressure in metallic hydrogen and is currently unattainable experimentally. The analysis of the entropy made it possible to determine the region of existence for the liquid metallic helium phase and the conditions for its crystallization. A comparison between the densities, pressures, and temperatures inside such gas giants as Jupiter and Saturn allowed us to conclude that not only hydrogen but also helium are in the metallic state in the central parts of those planets. However, the pressure in their interiors is insufficient for helium to crystallize.
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