We present a new method for computing the spectrum of one4ectron Rydberg states of non-hydrogenic atoms in a magnetic field, at conslant scaled energy. It is based on a variant of the R-matrix melhod allowing the computation of mmy energy levels in a single diagonalization. The results are compared with recenlly obtained high-resolution cxptrimentd spectra of the helium atom. The relation h e e n peaks observed in the Fourier transform of suled spectra and classical closed orbits is discussed. We show the existence of 'ghost' peaks not corresponding to any closed orbir and also of peaks existing only in non-hydrogenic specua, due the scattering of the electron by the ionic WE.

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We consider n = 20 Rydberg states of the hydrogen atom interacting with a nearby metal surface over an atom-surface distance range of 105 nm-530 nm. We show that the traditional quadratic approximation to the potential is insufficient to follow the true potential and one needs to include higher order terms to obtain accurate energies for these Rydberg states. We include terms up to eighth order in the electron-proton distance in the potential and demonstrate by means of basis set calculations that the resulting spectra differ significantly from those obtained in the quadratic approximation. We observe an energy spread of the n = 20 manifold which is roughly twice that given by the quadratic approximation. Observed level repulsions are attributed to z-parity symmetry breaking. We compare our results with those from degenerate perturbation theory.

The spectrum of hydrogen in a magnetic field is a paradigm of quantum chaos and may be analyzed accurately by periodic-orbit-type theories. In nonhydrogenic atoms, the core induces pure quantum effects, especially additional spectral modulations, which cannot be analyzed reliably in terms of classical orbits and their stability parameters. Provided core-scattered waves are included consistently, core-scattered modulations as well as corrected amplitudes for primitive orbits are in excellent agreement with quantum results. We consider whether these systems correspond to quantum chaos.

The R-matrix and complex coordinate techniques are combined for the first time and applied to the problem of the positive energy spectrum of a non-hydrogenic atom in a laboratory strength magnetic field. Quantum defect theory is extended to calculate the appropriate irregular Coulomb function at complex energy and complex radial distance. Calculations are carried out for lithium to compare with previous experimental measurements and with a corresponding calculation for hydrogen.