ANNALS OF PHYSICS 86, 197-232 (1974) A New Nodal Expansion for Classical Plasmas* THOMAS J. BUCKHOLTZ L-O, Lawrence Licermore Laboratory, Livermore, California 94550 Received March 16, 1973 In calculating the equation of state for plasmas we find that diagrammatic expansions for the free energy become unwieldy at high density. At best, many terms must be retained in order to obtain meaningful results. We present a new expansion technique which can be applied to plasmas in the interiors of Jupiter and white dwarf stars. In such cases the older techniques are unsatisfactory because of the size of the ion coupling parameter. Our work yields expansions for which this parameter is supplanted by ion correlation functions, which can be supplied by external computations. In this paper we assume a two-species plasma of classical particles, thereby focusing on combinatorial techniques. The final result is a new nodal expansion in terms of ion correlation func- tions and an electron coupling parameter. 1. INTRODUCTION Diagrammatic expansions are used to calculate thermodynamic properties of gases and liquids [l]. Such an expansion consists of a power series in a coupling parameter, such as the particle density, with coefficients involving cluster integrals of functions of the interparticle potential [2]. This technique is particularly success- ful at low density because reasonable accuracy can be achieved with the first few terms [3]. At higher densities more terms must be computed, and the series become unwieldy or divergent. Results have been obtained by two methods: Monte Carlo simulation and selective summation of diagrams. In the former, a system of particles is simulated on a computer; for example, Brush, Sahlin, and Teller (cited as BST) [4] and Hubbard and Slattery [5] determine pressures, free energies, and pair correlation functions for nuclei in dense stellar matter. One class of summation schemes gives nodal expansions [6-81, which are useful for a Coulomb gas at moderate density [9]. Other summations yield a change of coupling constant * Work performed under the auspices of the U.S. Atomic Energy Commission and supported in part by the National Science Foundation. 197 Copyright 0 1974 by Academic Press, Inc. All rights of reproduction in any form reserved.