LOCAL-FIELD CORRECTION FOR THE ELECTRON-GAS - EFFECTS OF THE VALLEY DEGENERACY

The valley-degeneracy dependence of the local-field correction for the two-dimensional anti the three-dimensional electron gas is calculated. We use a sum-rule version of the self-consistent approach of Singwi et al. to calculate the local-field correction. Results for 0.01 < r(s) < 40 are given and r(s) is the random-phase-approximation parameter. We derive expressions for the electron density dependence of the local-field correction for different valley degeneracy. We find that with increasing valley degeneracy the kinetic energy and the exchange energy decrease while the correlation energy increases. For very large valley degeneracy, the local-field correction of the electron gas approaches the local-field correction of the Bose condensate. We find that in semiconductors with large valley degeneracy the correlation effects are enhanced and that many-body effects are very important, even at high electron density.