Abstract
In the low-pressure limit, a helium atom embedded in the electron gas appropriate to metallic hydrogen is only weakly perturbed from its free space structure, and its interaction with the electron gas can be represented by an energy-dependent pseudopotential. A calculation is made for the Gibbs energy of mixing for H-He, using an Austin pseudopotential and a fluid state model based on hard-sphere structure factors. A large orthogonalisation hole is predicted, which may crudely represent the gradual transition from a helium atom to a screened alpha -particle as the electron density increases. The helium solubility is predominantly determined by the structure-independent interaction of the electron gas with the repulsive pseudopotential, and is probably least at the lowest pressures. In the hydrogen-helium planets (Jupiter, Saturn) the helium concentration may be at or close to saturation at the molecular-metallic hydrogen transition.