Classification of diagrams for a plasma equation-of-state

Abstract

Utilizing the Montroll-Ward approach to quantum statistics, generalized to many components, we seek an equation of state for a high-temperature low-density plasma. We propose a classification of diagrams analogous to that used by Meeron and by Friedman in classical statistical mechanics. In the resulting expansion, the leading term is the ideal gas contribution plus the lowest-order exchange contribution plus the ring contribution, the latter representing the effect upon the pressure of collective motions of a completely ionized plasma. The next term appears to represent a contribution due to modifications of free particle motion due to the interaction of the single particles with the rest of the plasma. The third term represents the contribution of two-particle states, both of positive energy between all particle pairs, and negative energy (bound states) between pairs of opposite charge sign. The third term also contains parts representing modifications of the motion of the pair of particles due to interaction of the individual particles with the rest of the plasma. Higher terms represent, successively, contributions of three-, four-, etc., particle states, again including modifications of the single-particle motions. The classification automatically eliminates the ultraviolet catastrophe which ordinarily arises in the treatment of Coulomb force bound states in statistical mechanics, since, in effect, it uses a screened Coulomb potential instead of the ordinary potential. In addition, the short range divergence, which occurs in classical theory because of the `fall' of the electron to the nucleus, does not arise, being prevented by the uncertainty principle.