Three-body problem of two-electron atoms

The ground-state wave function of a heliumlike atom is assumed to be ψ=φ(r3)exp(-αr>-βr<), where r<, r>=min, max(r1, r2), r1 and r2 being the distances of the electrons from the nucleus. An equation which determines the electron-electron correlation function φ(r3) is derived and numerically solved. The parameters α and β are determined by minimizing the energy of the system. This is an extension of the Feshbach-Rubinow-type approximation which has recently …