A variational approach to correlation in an electron gas

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Abstract
A method is proposed for calculating correlation energies and pair functions associated with an electron gas at any density. Upper bounds to the exact energy, lying however at least as low as the corresponding plane wave results are guaranteed and exact solutions are obtained in the high and low-density limits. The technique used is that of allowing a periodic electron density and a proof emerges of the recent conjecture of Overhauser that there exist one-particle states energetically more favourable than the usual plane wave orbitals. It is concluded that in the ground state a single-particle approximation implies static spin density waves of wavelength proportional to the usual separation electron parameter r 2, at least for r 8 sufficiently large.