Theory of electron liquids. II. Static and dynamic form factors, correlation energy, and plasmon dispersion

We use the Ceperley and Alder Green's-function Monte Carlo data for the static form factor, $S\left(q\right)\mathrm{}$, of an electron liquid to calculate the static local-field correction, $G\left(q\right)\mathrm{}$, to the dielectric function which takes into account short-range electron correlations. The resulting local-field correction in the long-wavelength limit is obtained by smoothly fitting to the results of Iwamoto and Pines, which are exact in this limit. We use the $G\left(q\right)\mathrm{}$ thus obtained to calculate the static and dynamic form factors, the contribution to the correlation energy from different momentum transfers, plasmon dispersion, and the plasmon-dispersion coefficient. We compare these theoretical quantities with the available experimental data, and use the ${\omega }^3$-sum rule (which we also calculate from the Monte Carlo data) to discuss the limitations arising from the use of the static local-field correction.