Calculation of the Dielectric Function for a Degenerate Electron Gas with Interaction. II. Frequency Dependence

Starting from an expression for the dielectric function earlier derived, we calculate explicitly the $\omega$ dependence of the $G(k,\omega )$ function which describes correlation and exchange effects. The full frequency dependence of this function is found to be rather significant; in particular it improves the accuracy with which the $f$ sum rule is satisfied, which confirms the goodness of the approximations involved in the calculation of the dielectric function.