A comparison of approximations for the elastic electron–electron scattering amplitude in jellium

An approximation for the electron–electron scattering amplitude, Γ, in jellium, motivated by comparing formal many-body theory and density-functional theory expressions for the jellium response function, is suggested. The approximation is compared with previously suggested approximations for Γ, using an exact result for the forward scattering limit to assess the reliability of each approximation. It is pointed out that the magnetic interaction contribution to Γ becomes dominant at low density in jellium and that this contribution is absent in most commonly adopted approximations. Mean free paths for low energy electrons in jellium-like metals have been calculated for various approximations to Γ and the magnetic-interaction effect is identified as being responsible for a previously noted discrepancy between Thomas–Fermi-like and more sophisticated approximations to Γ. A systematic method, using the parquet expansion technique, has been proposed for antisymmetrizing the density-functional based approximation to Γ when necessary.