Variational method for a three-body problem of two-electron atoms

The ground-state wave function of a heliumlike atom is assumed to be Ψ=N(1+μλr₁₂)×exp[-μ(βr>+r<)], where r<,r>=min,0ex0exmax(r₁,r₂), r₁ and r₂ are the distances of the electrons from the nucleus, and r₁₂ is the distance between the electrons. The parameters μ, β, and λ are determined by minimizing the energy of the system and it can be reduced to a two-parameter problem. Numerical results are presented to show the improvement for the groundstate energy from the two- or three-parameter calculations.