Perturbed Rydberg series: Relationship between quantum-defect and configuration-interaction theory

In this paper the theory of a single Rydberg series perturbed by an interloping state is examined. General analytic expressions are presented which apply both to the bound-state regions and to the autoionizing regions above the Rydberg ionization limit. The parameters are expressed in terms of configuration-interaction matrix elements, which can be calculated a priori. There is no restriction to weak-perturbation theory, and the wave function and all its associated properties, such as transition moments, can be extracted. Explicit calculations are presented for the Cd(5s nd)¹D₂ series perturbed by the Cd(5p²)¹D₂ valence state, and excellent results are obtained.