**Abstract**

The energy spectrum of circular 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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Designed by A. Sergeev.