A new nodal expansion for classical plasmas

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 functions and an electron coupling parameter.