Abstract
The centre of mass and relative motion of the two electrons in the non-relativistic fixed-nucleus atom are considered independent particles moving in central field orbitals specified by quantum numbers n1l1 and n2l2 respectively. For atomic number Z=0 the orbital of the relative motion must be hydrogen-like. This is taken into account by the variation-perturbation scheme assuming both orbitals nili are hydrogen-like with effective charges Z1 and Z2 adjusted from the first-order variational principle. For strongly correlated electrons, the first-order energy calculated according to this scheme gives a good approximation to the usual Z-expansion of energy. The states 1s2 1S and 2p2 3P are investigated more thoroughly for Z=1 and Z=0. For Z=1, the expectation values ( psi 0 mod Omega mod psi 0) of some operators Omega are improved if the approximate coefficients of Zn (n=1, 2, ...) resulting from the first-order calculation are substituted by their exact counterparts.
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