VIRIAL EXPANSIONS FOR QUANTUM PLASMAS - FERMI-BOSE STATISTICS

This paper is devoted to the calculation of the density expansions (at fixed non-zero temperature) of the thermodynamic functions for quantu m plasmas. The Maxwell-Boltzmann forms of these expansions have been s tudied in two previous papers. Here we include the exchange contributi ons due to Fermi or Bose statistics, via a perturbative scheme where t he reference ingredients are computed in the framework of Maxwell-Bolt zmann statistics. The whole scheme is based on the Feynman-Kac path in tegral representation which amounts to introducing classical auxiliary systems made of extended objects, the filaments. The quantities of in terest are then evaluated by applying familiar diagrammatical methods of classical statistical mechanics. The exact density expansions of th e free energy and of the pressure are explicitly calculated up to orde r rho(5/2) in the density rho. The corresponding expressions include, in a systematic and coherent way, the contributions of various physica l effects such as screening, diffraction, recombination, scattering, a nd exchange. At order rho(2), we recover the expansions obtained via t he effective-potential method. Our terms of order rho(5/2) correctly r eproduce results which are known in some particular limits. Moreover, the high-temperature expansions which can be easily inferred from our virial expansions do coincide with those obtained from the Feynman gra phs in the usual many-body theory.