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.

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.

Full details are presented of the new method of Halley et al. (1992) for the calculation of near-threshold resonance-dominated spectra. This method combines the R-matrix and complex coordinate techniques and has necessitated an extension of quantum defect theory to calculate an appropriate irregular Coulomb function for complex energy and complex radial distance. The method is discussed in particular in its application to the near-threshold photoabsorption spectra of a non-hydrogenic atom in a laboratory strength magnetic field and applied here to the examples of strontium and barium. Excellent agreement is obtained with experimental measurements.