Ground-State Energy of Metallic Hydrogen. I

The ground-state energy of metallic hydrogen is calculated within the framework of a perturbation expansion by interpreting the perturbation series as that for two simpler systems weakly interacting, one being the electron gas system, the other that of electrons moving in the periodic potential of the lattice neutralized by a uniformly distributed negative charge. The decomposition is conveniently obtained by dividing the Rayleigh-Schrödinger perturbation expansion into three parts, the first two parts representing essentially the energy of the two simpler problems while the third part gives a series expansion for the small interaction terms. The first nonvanishing term in the latter comes from third order in the Rayleigh-Schrödinger series and has the small value $0.001 r_s$ Ry per electron, where $r_s$ is the radius of the unit sphere in atomic units. The interaction between the two systems is therefore assumed to have this order of magnitude.