Avoided crossings of diamagnetic hydrogen as functions of magnetic field strength and angular momentum

The energy levels of diamagnetic hydrogen as a function of two independent parameters, magnetic field strength B, and angular momentum m, are examined . Avoided crossings appear between these energy levels as either parameter is varied while the other is held fixed. These avoided crossings are direct ly related to degeneracies (Fermi resonances) occurring at zeroth order in perturbation theory. The mathematical basis of these degeneracies are the s quare-root branch points that connect the energy levels. It is found that t he locations of avoided crossings in either constant-B or constant-in spect ra can be predicted by visually scanning the locations of these branch poin ts in the complex-delta plane, where delta= 1/(2 + 2 \m\) is the perturbati on parameter used in this research. [S1050-2947(98)07111-X].