Dielectric function with exact exchange contribution in the electron liquid. II. Analytical expression

TL;DR

This paper derives an exact analytical expression for the imaginary part of the exchange contribution to the dielectric function in an electron liquid, enhancing theoretical understanding of electron interactions.

Contribution

It provides the first exact analytical formula for the imaginary part of the exchange contribution to the dielectric function in the electron liquid.

Findings

Exact analytical expression for Im Π₁(k, ω) derived.

Refined formula has a simple, usable form.

Advances theoretical modeling of electron interactions.

Abstract

The first-order, in terms of electron-interaction in the perturbation theory, of the proper linear response function $\Pi ({\bf k}, \omega )$ gives rise to the exchange-contribution to the dielectric function $\epsilon ({\bf k} , \omega)$ in the electron liquid. Its imaginary part, $Im \Pi_1 ({\bf k}, \omega)$, is calculated exactly. An analytical expression for $Im \Pi_1 ({\bf k}, \omega)$ is derived which after refinement has a quite simple form.