Cluster virial expansion for the equation of state of partially ionized hydrogen plasma

TL;DR

This paper introduces a novel application of the Beth-Uhlenbeck approach to accurately calculate the electron-atom contribution to the equation of state in partially ionized hydrogen plasma, incorporating phase-shifts, binding energies, and plasma effects.

Contribution

It is the first to use the Beth-Uhlenbeck method with experimental and pseudopotential data to compute the second virial coefficient for electron-atom interactions in plasma.

Findings

Provides a benchmark for semi-empirical models

Calculates pressure, composition, and chemical potential across densities and temperatures

Generalizes the virial expansion to near solid density plasmas

Abstract

We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-virial expansion. For the first time, we use the Beth-Uhlenbeck approach to calculate the second virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase-shifts and binding energies. Experimental scattering cross-sections as well as phase-shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase-shift calculation, we generalize the cluster-virial expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the virial expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semi-empirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom interaction represents a benchmark for other, semi-empirical approaches.