Advances in the Calculation of Virial Expansions for Quantum Plasmas up to Third Order in the Density

Abstract

Since the beginning of the nineties, the renewed interest in the exact calculation of thermodynamic functions for weakly coupled (or, weakly non-ideal), weakly degenerate multicomponent quantum plasmas beyond the Debye–Huckel limiting law has led to a number of profound papers by French, German, and American authors. They derived virial expansions for thermal pressure p and free energy F through the order in the densities from first principles by using the Feynman–Kac formalism and the method of Green’s functions, respectively. These recent works confirmed and supplemented older results by Haga, Friedman, DeWitt, and Ebeling and co-workers from the Rostock School dating back to the fifties and sixties, so that now the virial equation of state for Coulomb fluids is generally accepted as completely known up to order For the present calculations I employ, like Ebeling, Morita’s effective-potential approach which allows, starting with a charging procedure, to easily give an expansion for the Helmholtz free energy in terms of the so-called cluster integrals that correspond to the screened virial coefficients Then, the actual density series follows by expanding with respect to powers of the reciprocal Debye radius where the involved elimination of the Coulomb divergences requires precise knowledge of the asymptotic behavior of the Slater sums for large inter-particle separation. Here I concentrate on all those cluster integrals that contribute to at least the order namely and and present some new contributions of the orders and arising from along with the integral representation of a higher virial function Finally, Haga’s constant that appears in the lowest-order classical term of and was known so far only approximately has been evaluated exactly for the first time.