Simple Physical Picture of the Overhauser Screened Electron-Electron Interaction

TL;DR

This paper introduces a simple physical model for the screened electron-electron interaction in many-electron systems, emphasizing the 'dressed-dressed' picture and confirming its qualitative accuracy for high-density electron gases.

Contribution

It proposes a straightforward 'dressed-dressed' interaction model that improves understanding of electron-electron interactions, especially regarding spin polarization effects.

Findings

The 'dressed-dressed' interaction is qualitatively correct for high-density gases.

The 'bare-dressed' interaction is overly repulsive and lacks symmetry.

The original Overhauser model does not account for spin polarization dependence.

Abstract

As shown by Overhauser and others, the pair-distribution function $g(r)$ of a many-electron system may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion $V(r)$. We propose a simple physical picture in which this screened repulsion is the ``dressed-dressed'' interaction between two neutral objects, each an electron surrounded by its full-coupling exchange-correlation hole. For the effective interaction between two electrons of antiparallel spin in a high-density uniform electron gas of arbitrary spin polarization, we confirm that this picture is qualitatively correct. In contrast, the ``bare-dressed'' interaction is too repulsive, and does not have the expected symmetry $V_{\ud}(r) = V_{\du}(r)$. The simple original Overhauser model interaction, independent of the relative spin polarization $\zeta$, does not capture the $\zeta$-dependence of the correlation contribution to $g(r=0)$.