Screened interaction and self-energy in an infinitesimally polarized electron gas via the Kukkonen-Overhauser method

The screened electron-electron interaction W-sigma,W-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,W-sigma' are identified in terms of the relevant response functions of the electron gas. The self-energy is obtained from W-sigma,W-sigma' by making use of the GW method which in this case represents a consistent approximation. Contact with previous calculations is made.