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.
Categories: cond-mat.str-el