The screened cluster equation of state for hydrogen-helium mixtures: Atomic, molecular, and ionic contributions from first principles

We present a method that provides reliable equations of state for partially ionized gases at moderate densities. The gas is described within the physical picture in terms of a quantum plasma made with nuclei and electrons interacting via the Coulomb potential. The method relies on the screened cluster representation derived elsewhere and is obtained by resummations of Mayer-like diagrammatics for the equivalent classical gas of loops. The contributions to the thermodynamics of atoms, molecules, or ions are described by cluster functions built with simple diagrams involving a few elementary particles and screened interactions. All quantum and collective mechanisms at work are embedded in these cluster functions, which can be computed numerically by sampling the corresponding path integrals. The usefulness and accuracy of this formalism is illustrated by considering a hydrogen-helium mixture under solar interior conditions. As a by-product of our calculations, we also exhibit the density dependence of the two-body cluster function analogous to the second virial coefficient in a hydrogen gas.