### 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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