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

Abstract

The first-order, in terms of electron-interaction in the perturbation theory, of the proper linear response function $\Pi (\mathbf{k},\omega )$ gives rise to the exchange-contribution to the dielectric function $\epsilon (\mathbf{k},\omega )$ in the electron liquid. Its imaginary part, $Im{\Pi }_1(\mathbf{k},\omega )$, is calculated exactly. An analytical expression for $Im{\Pi }_1(\mathbf{k},\omega )$ is derived which after refinement has a quite simple form.

15 pages