The high-density electron gas: How its momentum distribution n(k) and its static structure factor S(q) are mutually related through the off-shell self-energy Sigma(k,omega)

TL;DR

This paper details how the self-energy of the high-density electron gas determines key properties like momentum distribution and structure factor, using many-body approximation methods and connecting various theoretical results.

Contribution

It provides a comprehensive analysis of the mutual relations between n(k), S(q), and the self-energy Sigma(k,omega) in the high-density electron gas, integrating multiple prior results.

Findings

Derived explicit relations between Sigma(k,omega), n(k), and S(q).

Unified several existing theoretical results in a coherent framework.

Highlighted identities linking different many-body quantities.

Abstract

It is shown {\it in detail how} the ground-state self-energy $\Sigma(k,\omega)$ of the spin-unpolarized uniform electron gas (with the density parameter $r_s$) in its high-density limit $r_s\to 0 $ determines: the momentum distribution $n(k)$ through the Migdal formula, the kinetic energy $t$ from $n(k)$, the potential energy $v$ through the Galitskii-Migdal formula, the static structure factor $S(q)$ from $e=t+v$ by means of a Hellmann-Feynman functional derivative. The ring-diagram partial summation or random-phase approximation is extensively used and the results of Macke, Gell-Mann/Brueckner, Daniel/Vosko, Kulik, and Kimball are summarized in a coherent manner. There several identities were brought to the light.