A numerical evaluation of the imaginary part of the self-energy function, $\Sigma 2^{}(\mathbf{k},\omega )$, 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 $\Sigma 2^{}(\mathbf{k},\omega )$ versus $\omega$ for various values of $k$ and electronic density. Comparison is made in the quadratic $\omega$-dependent region about the Fermi surface with an analytic calculation using a statically screened Coulomb interaction.

• Received 29 August 1966

DOI:https://doi.org/10.1103/PhysRev.155.379