Kinetic Theory for Electron Dynamics Near a Positive Ion

TL;DR

This paper develops a semi-classical kinetic theory to describe electron dynamics near a positive ion, capturing correlations and bound states, and provides practical trajectory approximations for strong coupling regimes.

Contribution

It introduces a linear kinetic theory incorporating initial correlations via renormalized potentials and proposes a simple, accurate trajectory approximation for strong electron-ion coupling.

Findings

The theory accurately predicts electron autocorrelation functions near ions.

Bound states significantly influence electron dynamics and correlations.

A simple trajectory model works well across a wide range of coupling strengths.

Abstract

A theoretical description of time correlation functions for electron properties in the presence of a positive ion of charge number Z is given. The simplest case of an electron gas distorted by a single ion is considered. A semi-classical representation with a regularized electron - ion potential is used to obtain a linear kinetic theory that is asymptotically exact at short times. This Markovian approximation includes all initial (equilibrium) electron - electron and electron - ion correlations through renormalized pair potentials. The kinetic theory is solved in terms of single particle trajectories of the electron - ion potential and a dielectric function for the inhomogeneous electron gas. The results are illustrated by a calculation of the autocorrelation function for the electron field at the ion. The dependence on charge number Z is shown to be dominated by the bound states of the effective electron - ion potential. On this basis, a very simple practical representation of the trajectories is proposed and shown to be accurate over a wide range including strong electron - ion coupling. This simple representation is then used for a brief analysis of the dielectric function for the inhomogeneous electron gas.