The Description of Collective Motions in Terms of Many-Body Perturbation Theory. II. The Correlation Energy of a Free-Electron Gas

The theory developed in a previous paper is applied to calculate the correlation energy of a free-electron gas. The theory involves on cut-off and gives a uniform description of collective motion effects in the long-range limit and of particle motion effects in the short-range limit. It is shown that in the lowest order the theory agrees with Bohm & Pines's plasma oscillation theory in the long-range limit, but is inadequate in the short-range limit. The theory is approximately evaluated to the next order, which is correct in the short-range limit, and is applied to calculate the correlation energy at several gas densities; the results are in good agreement with those of Bohm & Pines.