Ground-State Energy of Two-Electron Atoms

Abstract

We examine the ground‐state energy ε(λ) for two electrons bound to an infinite‐mass point nucleus regarded as a function of the complex coupling constant λ for the interelectron interaction. In the units used, the ground states of the homologous series H⁻, He, Li⁺, Be⁺⁺, ···, correspond, respectively, to λ=1, ½, ⅓, ¼, ···, so the λ power‐series expansion of ε(λ) is equivalent to the familiar expansion in inverse nuclear charge Z⁻¹. It is argued that the power series has a finite radius of convergence imposed by the existence of a branch point on the positive real axis at λ=λ^*≅1.1184 with exponent approximately 6/5. Furthermore, ε(λ^*) apparently lies above the continuum limit, but still corresponds to a localized wavefunction.