Screened cluster expansions for partially ionized gases

TL;DR

This paper develops a cluster expansion method for partially ionized quantum gases, integrating path integral and Mayer diagrammatics to accurately model phenomena like recombination and screening.

Contribution

It introduces a novel cluster expansion framework combining path integrals and Mayer diagrams for quantum plasmas in the Saha regime.

Findings

Provides a diagrammatic formalism with clear physical interpretation

Accurately accounts for recombination, screening, and diffraction effects

Lays groundwork for future applications to thermodynamics and dielectric properties

Abstract

We consider a partially ionized gas at thermal equilibrium, in the Saha regime. The system is described in terms of a quantum plasma of nuclei and electrons. In this framework, the Coulomb interaction is the source of a large variety of phenomena occuring at different scales: recombination, screening, diffraction, etc. In this paper, we derive a cluster expansion adequate for a coherent treatment of those phenomena. The expansion is obtained by combining the path integral representation of the quantum gas with familiar Mayer diagrammatics. In this formalism, graphs have a clear physical interpretation: vertices are associated with recombined chemical species, while bonds describe their mutual interactions. The diagrammatical rules account exactly for all effects in the medium. Applications to thermodynamics, van der Waals forces and dielectric versus conductive behaviour will be presented in forthcoming papers.