Nodal Expansion For Strongly Coupled Classical Plasmas

Abstract

Perturbative expansions provide the basis of many of the most powerful results as well as the ground of many qualitative powerful pictures. In the equilibrium theory of fluids, the paridigm of perturbation methods is the nodal expansion of the statistical (correlation functions, structure factors, etc.) and the thermodynamic quantities with respect to a small parameters, which implies the exact knowledge of the unperturbed state, and also the existence of a well-defined extrapolating procedure (through resummations for instance) to arbitrarily large values of the expansion parameter. In the case of fully ionized classical Coulomb gases, it is a well-known fact that the “smallness” parameter is uniquely defined [Montroll and Ward, 1958] by the plasma parameter

$$\Lambda = \frac{{\left| {{\text{binary Coulomb energy at screening length }}{\lambda _D}} \right|}}{{{k_B}T}}$$

while the reference state is the perfect gas. The nodal expansion is then nothing but that the required adaptation [Salpeter, 1958] of the Mayer density expansion to the case of long-ranged interactions endowed with a well defined Fourier transform in k space.