One and two-component hard core plasmas

TL;DR

This paper develops a field theory for particles with Coulomb and hard-core interactions, analyzing one- and two-component plasmas, and derives low-density expansions revealing different behaviors in high-charge limits.

Contribution

It introduces a systematic low-density expansion for hard-core Coulomb plasmas and explores the contrasting high-charge behaviors of one- and two-component models.

Findings

Exact low-density coefficients obtained for both models

OCP coefficients match classical results in high-charge limit

TCP shows diverging coefficients due to ion-pair formation

Abstract

A field theory is presented for particles which interact via Coulomb and hard-core potentials. We apply the method to the one-component plasma (OCP) with hard cores, consisting of identical particles of fixed charge and diameter in a neutralizing background, and the symmetric two-component plasma (TCP) with hard cores, consisting of equal numbers of positively and negatively charged particles of identical size. We obtain exactly the first few coefficients of a systematic low-density expansion of the free energy for both models. The OCP coefficients go over to the classical Abe result in the high-charge (or small hard-core diameter) limit. The TCP, on the other hand, exhibits diverging coefficients in the high-charge limit, which is due to the formation of strongly bound ion-pairs.