POWER-SERIES WITH RATIONAL COEFFICIENTS FOR 2-ELECTRON ATOM ENERGIES

The method of o(4, 2) operator replacements is generalized. As a resul t, the series whose limiting values when the variable goes to + infini ty should correspond to the two-electron atom energies now have ration al coefficients. This generalization allows one also to compute the se ries for the case of singlet S symmetry, a case which could not be con sidered in the previous original formulation of the method. Series wit h rational coefficients for the helium singlet and triplet S ground-st ate energy are calculated up to order 41 and 45, respectively. Moreove r, symbolic computations also allow one to give the first few coeffici ents of these series for arbitrary values of the nuclear charge Z. Fin ally, a new method for analytic continuation to the limit + infinity i s presented for the energies of the helium singlet and triplet ground states. (C) 1997 John Wiley & Sons, Inc.