Calculation of the Dielectric Function for a Degenerate Electron Gas with Interactions. I. Static Limit

A new procedure for calculating the frequency- and wave-vector-dependent dielectric response function is described. It is based on decoupling and solving the equations of motion for the Green's functions of the charge-density operators by a moment-conserving method which is discussed. By use of this method an expression for the dielectric function in the static limit ($\omega \to 0$) is obtained; it depends on a function $G\left(k\right)\mathrm{}$, for which numerical values are calculated and tabulated. Evidence that the procedure described here leads to reliable values of $G\left(k\right)\mathrm{}$ for small, intermediate, and large values of $k$ is presented.