Screened Interaction and Self-Energy in an Infinitesimally Polarized Electron Gas via the Kukkonen-Overhauser Method

TL;DR

This paper extends the Kukkonen-Overhauser approach to derive the screened electron-electron interaction and self-energy in an infinitesimally polarized electron gas, connecting response functions with many-body approximations.

Contribution

It introduces a consistent extension of the Kukkonen-Overhauser method to polarized electron gases, linking response functions with self-energy calculations.

Findings

Derived expressions for the screened interaction $W_{\sigma, \sigma'}$

Obtained the electron self-energy using a GW approximation

Connected the results with previous theoretical calculations

Abstract

The screened electron-electron interaction $W_{\sigma, \sigma'}$ and the electron self-energy in an infinitesimally polarized electron gas are derived by extending the approach of Kukkonen and Overhauser. Various quantities in the expression for $W_{\sigma, \sigma'}$ are identified in terms of the relevant response functions of the electron gas. The self-energy is obtained from $W_{\sigma, \sigma'}$ by making use of the GW method which in this case represents a consistent approximation. Contact with previous calculations is made.