Variational perturbation approach to the Coulomb electron gas

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.