EXCHANGE CORRECTIONS AND THE CONVERGENCE OF THE PERTURBATION EXPANSION FOR THE MOMENTUM DISTRIBUTION FUNCTION FOR AN INTERACTING ELECTRON GAS AT METALLIC DENSITIES

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Abstract
The ground-state momentum distribution of an interacting electron gas at metallic densities is investigated by means of many-particle perturbation theory. Approximation methods and computational techniques are developed for the evaluation of the leading exchange corrections to the Random Phase Approximation. It is concluded that the straightforward perturbation expansion, which includes only single direct and exchange self-energy insertions, does not converge at the lower metallic densities and that it is necessary to include "higher-order" effects by renormalizing the electron propagator. When this is done, a large gap at the Fermi surface remains in the momentum distribution even for rs ~ 6.