Kinetic Theory for Electron Dynamics Near a Positive Ion

Details Kinetic Theory for Electron Dynamics Near a Positive Ion Kinetic Theory for Electron Dynamics Near a Positive Ion

2008-09-12

arxiv.org/abs/0809.2234v1

Physics

Condensed Matter

Statistical Mechanics

30 pages, 5 figures, submitted to Journal of Statistical Mechanics: Theory and Experiment

Scientific paper

10.1088/1742-5468/2008/10/P10021

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.

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