Thermodynamic functions of a partially degenerate, fully ionized gas

Abstract

The formalism of GLASSGOLD, HECKROTTE and WATSON for the expansion of the quantum-mechanical grand partition function has been applied to a gas of point charges. The expansion is shown to be closely related to Rayleigh-Schroedinger perturbation theory, and to give the results of MONTROLL and WARD in a simpler form. The theory has been extended to a multicomponent gas of fermions and bosons and the ring diagrams have been summed to give an approximate expression for the equation of state valid for the entire temperature range. The near-classical limit (high temperature and low density so that the gas is only slightly degenerate) is discussed in detail, and useful formulae for numerical computation of pressure and internal energy are derived from the general ring approximation to the equation of state. By expanding the chemical potential in powers of the coupling constant e2, it is possible to eliminate the parametric dependence of pressure and density on the chemical potential and obtain the pressure as a function of density. The classical-limit Debye-Hückel results are obtained when h approaches 0. A general form of the screening length is obtained with the effective screening charge as zieθi, where θi is a measure of the degeneracy of the particle species i.