Dielectric versus conductive behaviour in quantum gases: exact results for the hydrogen plasma

TL;DR

This paper provides an exact calculation of the electrical susceptibility of a hydrogen plasma, revealing a transition from conductive to dielectric behavior at short wavelengths, using a novel diagrammatic technique.

Contribution

It introduces a fully coherent, exact method to compute susceptibility in quantum gases, capturing Coulomb effects without approximations.

Findings

Transition from conductive to dielectric behavior at short wavelengths.

Exact susceptibility matches ideal hydrogen atom gas in a specific limit.

Method accounts for screening, binding, and polarization effects coherently.

Abstract

We study the electrical susceptibility of a hydrogen gas at equilibrium, partially ionized by thermal excitations. The gas is described as a quantum plasma of point protons and electrons, interacting via the Coulomb potential. Using the newly developped diagrammatical technique of screened cluster expansions, we calculate exactly the wavenumber-dependent susceptibility in the atomic limit, where most charges are bound into hydrogen atoms. A transition from conductive to dielectric behaviour occurs when the wave length is decreased well below the Debye screening length. The standard formula for the dielectric function of an ideal gas of hydrogen atoms is recovered in an appropriate scaling limit. The derivation treats all effects arising from the Coulomb interaction (screening, binding, polarization) in a fully coherent way, without intermediate approximation nor modelization.