Perturbed hydrogenic manifolds studied by the recursive residue generation method

Abstract

A method for calculating the perturbation of hydrogenic manifolds, the emerging bound states and resonances, for arbitrary combinations of external fields, is presented. It requires the combined use of complex dilation, an orthonormal Laguerre basis e- lambda rL2l+2k( lambda r) rather than the non-orthogonal Sturmians e- lambda rL2l+1k( lambda r), and the recursive residue generation method (RRGM) version of the Lanczos algorithm. Generalized eigenvalue problems are avoided. Furthermore, direct computation of the residues of resolvents, transition amplitudes and sum rules is achieved. Comparison with other methods and with previous calculations, suitable for one perturbation at a time, indicates that high accuracy is achieved separately both for the 1s Stark resonance and for the 1s Zeeman effect. Accurate results for the 1s Stark-Zeeman resonance, for various combinations of fields, are given.