The local-field correction for the interacting electron gas: Many-body effects for unpolarized and polarized electrons

The local-field correction for the three-dimensional and two-dimensional electron gas is calculated within a three-sum-rule version of the self-consistent approach of Singwi, Tosi, Land and Sjolander. Results for 0.01 < r(s) < 100 are given and r(s) is the RPA-parameter. Correlation effects are studied for the paramagnetic (unpolarized) state and the ferromagnetic (polarized) state and compared with Monte-Carlo calculations and good agreement is found. We conclude that the pair-correlation function and the correlation energy, if calculated within the three-sum-rule approach, shows a better behavior at large r(s) than if calculated within the two-sum-rule approach. Using the compressibility sum-rule we propose a new analytical form of the local-field correction and we compare the dielectric function with recent Monte-Carlo results. We also discuss some new aspects of the one-dimensional electron gas with short-range interaction.