Thermodynamics and phase separation of dense fully ionized hydrogen-helium fluid mixtures

The free energy of a hydrogen-helium fluid mixture is evaluated for the temperatures and densities appropriate to the deep interior of a giant planet such as Jupiter. The electrons are assumed to be fully pressure ionized and degenerate. In this regime, an appropriate first approximation to the ionic distribution functions can be found by assuming hard-sphere interactions. Corrections to this approximation are incorporated by means of the perturbation theory of Anderson and Chandler. Approximations for the three-body interactions and the nonlinear response of the electron gas to the ions are included. We predict that a hydrogen-helium mixture, containing 10% by number of helium ions, separates into hydrogen-rich and helium-rich phases below about 8000°K, at the pressures relevant to Jupiter (4-40 Mbar). We also predict that the alloy occupies less volume per ion than the separated phases. The equation of state and other thermodynamic derivatives are tabulated. The implications of these results are mentioned.