ANALYTIC PROPERTIES OF THE EXACT ENERGY OF THE GROUND-STATE OF A 2-ELECTRON ATOM AS A FUNCTION OF 1/Z

Analytic properties of the ground-state energy of a two-electron atom as a function of lambda=1/Z are studied. In addition to the previously known singular point of this function, lambda(s) approximate to 1.097 660 79, we find a new singular point lambda(infinity) = infinity in the lambda complex plane. We show that the function E(lambda) has a branch-point singularity of the type lambda(gamma) at this point, where the exponent gamma = 2.06+/-0.005. We find that the ansatz previously proposed to reproduce the asymptotic behavior of the large-order coefficients of the perturbation expansion [Baker et al., Phys. Rev. A 41, 1247 (1990)] can, with slight modification, reproduce the behavior of the exact ground-state energy of the two-electron atom around this singular point. We propose a representation of the exact ground-state energy of helium, possessing the required analytic properties.