Z-1 perturbation theory applied to the correlation energy problem of atoms

Rayleigh--Schroedinger Perturbation Theory is applied to obtain directly exact and explicit analytic formulas for the electron correlation energies of N electron systems in terms of their pairwise interactions through second order in Z-1, where Z is the nucleus of the atom. It is demonstrated that the second order correlation energy may be expressed as exactly the sum of pairwise correlation energies. In the case of no zeroth order degeneracy, the zeroth and first order terms vanish. The expression for the pairwise energies is an infinite sum, all terms of which are of the same sign. There is no numerical differencing. In the case of zeroth order degeneracy it is shown that the above statement concerning the second order energy still holds, but the expressions are a bit more complicated. It is shown that they ''almost'' reduce to a much simpler form. Also, the computation of the first order correlation energy is considered