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 directly related to degeneracies (Fermi resonances) occurring at zeroth order in perturbation theory. The mathematical basis of these degeneracies are the square-root branch points that connect the energy levels. It is found that the locations of avoided crossings in either constant-B or constant-m spectra can be predicted by visually scanning the locations of these branch points in the complex-{δ} plane, where δ=1/(2+2|m|) is the perturbation parameter used in this research.