Equation of state of hydrogen, helium, and solar plasmas

The equation of state (EOS) for plasmas of the two lightest elements H and He, and mixtures as typical for the plasmas in the sun are calculated. The contributions of deep bound states are included by using inverted fugacity expansions. The inversion of fugacities to densities is reduced to solvable algebraic problems and expressed by rational polynomials. The calculation of relative pressures is carried out separately for low and high densities. Near the crossing point, in between, the separate solutions are connected to each other by smooth concatenation. Applications to hydrogen-helium plasmas in the sun including estimates for the isentropic EOS are discussed.