  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.
