Note of the usefulness of perturbation theory in calculating energy levels and transitions of hydrogen Rydberg atoms in strong magnetic fields

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Abstract
The author investigates in quantitative terms, how far a standard perturbation calculation can produce reliable results at the principal quantum numbers and magnetic field strengths for which quite recent experiments with magnetised hydrogen atoms in highly excited states have successfully been performed (n approximately 25, B<or approximately=6 T). Energy levels and oscillator strengths of the states originating from the n=22-26 manifolds are determined for B=4.7 T using perturbation theory and are compared with corresponding results obtained previously by Clark and Taylor (1980-2) in the framework of a far more sophisticated numerical method. An unexpected finding is that their Sturmian approach is not able to reproduce the oscillator strength patterns of Balmer transitions to m=0 even-parity states predicted by perturbation theory. The author traces this back to a phase error which seems to occur, in their calculation, in the coherent superposition of the dipole contributions from the s and d partial waves of the Rydberg states. Furthermore, he checks the quality of approximate analytical formulae for the diamagnetic energies in perturbation theory which have recently become available through the exact separation of the diamagnetic interaction in momentum space.