CORRELATION IN FERMI LIQUIDS - ANALYTICAL RESULTS FOR THE LOCAL-FIELDCORRECTION IN 2 AND 3 DIMENSIONS

The local-field correction for the two-dimensional and the three-dimen sional electron gas is calculated within a sum-rule version of the sel f-consistent approach of Singwi, Tosi, Land, and Sjolander. Correlatio n effects are studied. Results for 0.001 < r(s) < 100 are given where r(s) is the random-phase-approximation parameter. An analytical expres sion for the static structure factor, representing a generalized Feynm an-Bijl spectrum, is used in the calculation. We derive analytical exp ressions for the density dependence of the local-field correction and we compare the results for the ground-state energy for the interacting electron gas with Monte Carlo computations. The pair-correlation func tion and the compressibility are studied. Exchange and correlation eff ects for quantum wells and heterostructures are calculated: numerical and analytical results are derived. In two dimensions and at low densi ty a roton structure in the plasmon dispersion is found. We discuss an instability in layered structures of two-dimensional electron gases.