Electron Correlations and Moment Sum Rules

A theory of electron correlations based on a generalized random-phase approximation is presented. An expression for the local-field correction is obtained using the third frequency moment of the spectral function of the electron-density response function. The local field is a functional of the structure factor $S\left(\overrightarrow{\mathrm{q}}\right)$ which in turn is related to the imaginary part of the dielectric function via the fluctuation-dissipation theorem. The equations are self-consistently solved to determined $S\left(\overrightarrow{\mathrm{q}}\right)$ as originally suggested by Singwi et al. The pair-correlation function, compressibility, plasma dispersion, and correlation energy of electron liquid at metallic densities have been calculated.