Fermi-like resonances for circular Rydberg states of a hydrogen atom in a magnetic field

A. V. Sergeev

The energy spectrum of Rydberg states of large angular momentum and relatively small value of in an arbitrary magnetic field is calculated by the semiclassical expansion in powers of . The problem is approximated by an anisotropic two-dimensional harmonic oscillator. The anharmonic corrections to the energy are calculated, and the series is summed. Special emphasis is put on excited degenerate states of the harmonic oscillator (similar to Fermi resonances in a molecular vibration theory) when the 1/|m|-expansion fails to converge. Using the fact that the sum and the product of the energies of degenerate states have regular expansions, the quasi-crossings of the levels are obtained. The complex branch points joining the levels are also found.

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