Calculation of Quasiparticle Damping in a Free-Electron Gas

Abstract

A numerical evaluation of the imaginary part of the self-energy function, $\ensuremath{\Sigma}{2}^{}(\mathbf{k},\ensuremath{\omega})$, for the free-electron gas has been performed with the aid of an IBM 7094 computer. The calculation is done within the randomphase approximation using the full Lindhard dielectric-constant function. Results are presented in the form of plots of $\ensuremath{\Sigma}{2}^{}(\mathbf{k},\ensuremath{\omega})$ versus $\ensuremath{\omega}$ for various values of $k$ and electronic density. Comparison is made in the quadratic $\ensuremath{\omega}$-dependent region about the Fermi surface with an analytic calculation using a statically screened Coulomb interaction.