Nonlinear variational study of perturbation theory for atoms and ions

Using the 1/Z(=λ) perturbation format, analytical properties of eigenstates in the complex λ plane have been studied for two- and three-electron atoms, using simple nonlinear variational calculations. The ground states for both systems are included, as well as four excited states for two electrons. The results suggest a general partitioning of bound states into two categories: (i) If the singly charged anion is bound, analytical continuation in λ along the positive real axis causes the energy to penetrate the continuum, and subsequently to terminate at a branch point. (ii) If the singly charged anion is unbound, the energy is tangent to the continuum edge, and analytic continuation in λ to larger positive values creates a non-normalizable wave function.