Statistical mechanics of dense ionized matter. VI. Electron screening corrections to the thermodynamic properties of the one-component plasma

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Abstract
The thermodynamic properties of one-component ionic plasmas in a responding (polarized) background of fully degenerate electrons are calculated over a wide range of temperatures and densities. The weak and intermediate screening regimes are treated by two complementary methods which take the one-component plasma in a rigid background as a starting point. Thermodynamic perturbation theory is used in the weakly screened ionic plasma typical of white-dwarf matter; this leads to simple, analytic expressions for the thermodynamic properties. Relativistic effects in the very dense electron gas are considered explicitly. A variational method, based on the Gibbs-Bogolyubov inequality, and the physical idea of an effective charge reduction of the ions, yields satisfactory results in the intermediate screening regime typical of the deep interior of Jupiter. Our results are in good agreement with the available Monte Carlo data and represent a significant improvement over previous calculations based on a hard-sphere reference system.