Hidden crossings and the separation constant of a hydrogenlike atom in spheroidal coordinates.

Abstract

Considered as a limiting case of a highly asymmetric two-Coulomb-center problem, the analytic properties of the eigenvalues of the constant of motion allowing separation of variables for a hydrogenlike atom in spheroidal coordinates are studied. Calculations of the positions of the branch points of the eigenvalues in the complex plane of internuclear separations are performed. It is found that they form characteristic series whose limiting points can well be predicted by semiclassical quantization conditions.