Correlation Energy of the Electron Gas at Metallic Densities

The electron gas at metallic densities is studied by means of a quadratic boson Hamiltonian which includes the direct and exchange processes among the electrons but neglects the scattering of electron-hole pairs. This Hamiltonian is further separated into two independent parts which describe the singlet and triplet states of the electron-hole pairs. These parts are diagonalized in an approximation in which the exchange interaction is treated on the average. A dielectric function for all momentum transfers is thereby obtained. The correlation energy is the sum of the ground-state energies of the singlet and triplet Hamiltonians. Its value, calculated for the metallic density range (rₛ=1-6), is found to be about two-thirds of that in the random-phase approximation. It is consequently numerically smaller than most other estimates. The triplet contribution is very considerable. The triplet ground state is predicted to be unstable for rₛ>9.4.