Analytic properties of the ground-state energy of a two-electron atom as a function of λ=1/Z are studied. In addition to the previously known singular point of this function, ${\lambda }_{\mathit{s}}$≊1.097 660 79, we find a new singular point ${\lambda }_{\mathrm{\infty }}$=∞ in the λ complex plane. We show that the function E(λ) has a branch-point singularity of the type ${\lambda }^{\gamma }$ at this point, where the exponent γ=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.

• Received 15 March 1995

DOI:https://doi.org/10.1103/PhysRevA.52.1942