Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory

Details Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983apj...272..301m&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 272, Sept. 1, 1983, p. 301-310.

Physics

Condensed Matter

Statistical Mechanics

6

Fermi-Dirac Statistics, Gas Giant Planets, Helium Hydrogen Atmospheres, Perturbation Theory, Planetary Cores, Statistical Mechanics, Equations Of State, Gibbs Free Energy, Phase Separation (Materials)

Scientific paper

A numerical technique for solving the Thomas-Fermi-Dirac (TED) equation in three dimensions, for an array of ions obeying periodic boundary conditions, is presented. The technique is then used to calculate deviations from ideal mixing for an alloy of hydrogen and helium at zero temperature and high presures. Results are compared with alternative models which apply perturbation theory to calculation of the electron distribution, based upon the assumption of weak response of the electron gas to the ions. The TFD theory, which permits strong electron response, always predicts smaller deviations from ideal mixing than would be predicted by perturbation theory. The results indicate that predicted phase separation curves for hydrogen-helium alloys under conditions prevailing in the metallic zones of Jupiter and Saturn are very model dependent.

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