Power series with rational coefficients for two-electron atom energies

Abstract

The method of o(4,2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to + {infinity} should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit + {infinity} is presented for the energies of the helium singlet and triplet ground states.