Energies and Widths of the Ground and Excited States of Hydrogen in a DC Field via Variationally-Based Large-Order Perturbation Theory

Abstract

We have recently computed the energies and widths (complex eigenvalues) of the ground and many (more than 100) excited states of hydrogen in a dc field (the Stark effect) for numerous field strengths by combining a procedure for the analytic continuation of real large-order eigenvalue perturbation series with the perturbational-variational Rayleigh-Ritz (PV-RR) method for generating such series. The analytic continuation is accomplished by shifting the origin of the real eigenvalue series into the complex plane where the relevant divergent series are summed by a twofold application of Pade approximants. Our composite PV-RR method fills a gap in theory and results for the ground and highly excited states of the hydrogenic Stark effect; since the procedure implements large-order perturbation theory with the variational method, it is feasible to extend the technique to larger systems such as light atoms. After introducing the problem, this lecture briefly summarizes previous methods of calculating hydrogenic Stark resonances. Next, the theory of our procedure is outlined, including an explanation and illustration of our novel method of relieving zero-order degeneracy of excited Stark states. Our extensive calculations are then described, and selected results are reported and discussed. Finally, we present our conclusions.