Free-energy model for fluid helium at high density

We present a semianalytical free-energy model aimed at characterizing the thermodynamic properties of dense fluid helium, from the low-density atomic phase to the high-density fully ionized regime. The model is based on a free-energy minimization method and includes various different contributions representative of the correlations between atomic and ionic species and electrons. This model allows the computation of the thermodynamic properties of dense helium over an extended range of density and temperature and leads to the computation of the phase diagram of dense fluid helium, with its various temperature and pressure ionization contours. One of the predictions of the model is that pressure ionization occurs abruptly at rho greater than or similar to 10 g cm(-3), i.e., P greater than or similar to 20 Mbar, from atomic helium He to fully ionized helium He2+, or at least to a strongly ionized state, without a He+ stage, except at high enough temperature for temperature ionization to become dominant. These predictions and this phase diagram provide a guide for future dynamical experiments or numerical first-principle calculations aimed at studying the properties of helium at very high density, in particular its metallization. Indeed, the characterization of the helium phase diagram bears important consequences for the thermodynamic, magnetic, and transport properties of cool and dense astrophysical objects, among which are the solar and the numerous recently discovered extrasolar giant planets.