Hydrogen atom in the instantaneous van der Waals potential: Pitchfork bifurcation and ro-vibrational structure of the energy spectrum

We present a semiclassical study of the energy spectrum of a Rydberg hydrogen atom in the instantaneous van der Waals potential. The results are in good agreement with those obtained by the first-order quantum perturbation theory. Both the semiclassical and the quantum calculations show that vibrational energy levels disappear when the magnetic quantum number |m| increases. This fact is well explained in the framework of classical dynamics of this system for which the pitchfork bifurcation takes place at critical value |m|/n =5/7. © 2001 Elsevier Science B.V