Correlation Energy of an Electron Gas at High Density: Plasma Oscillations

Abstract

The contribution from zero-point plasma oscillations to the correlation energy of an electron gas at high density is considered, using the exact high-density theory of Gell-Mann and Brueckner and of Sawada. The plasmon energy is determined as a function of $q$ by an eigenvalue equation identical with the dispersion relation of Bohm and Pines. The plasma solutions are stable only below the energy-momentum values at which they merge with the continuum spectrum arising from particle excitation, thus introducing a natural cutoff into the theory. At high density, however, it is shown that this cutoff can be allowed to become infinite without affecting the correlation energy.The contribution from the plasma energy is exactly re-expressed in terms of the contribution from the scattering states by making use of the analytic properties of the scattering amplitudes. This transformation also establishes the connection between the Gell-Mann-Brueckner and Sawada results.Some remarks are finally made on the relation between these results and those of Bohm and Pines.