Inter-Series Interactions on the Atomic Photoionization Spectra Studied by the Phase-Shifted Multichannel-Quantum Defect Theory

Abstract

Development in mathematical formulations of parameterizing the resonance structures using the phase-shifted multichannel quantum defect theory (MQDT) and their use in analyzing the effect of inter-series interactions on the autoionizing Rydberg spectra is reviewed. Reformulation of the short-range scattering matrix into the form analogous to S = S B S R in scattering theory are the crucial step in this development. Formulation adopts different directions and goals depending on whether autoionizing series converge to the same limit (degenerate) or to different limits (nondegenerate) because of the different nature of the perturbation. For the nondegenerate case, finding the simplest form of profile index functions of the autoionizing spectra with the minimal number of parameters is the main goal and some results are reviewed. For the degenerate case where perturbation acts uniformly throughout the entire series, isolation of the overlapped autoionizing series into the unperturbed autoionizing series is the key objective in research and some results in that direction are reviewed.

Analytical Property of Scattering Matrix:Spectroscopy Phenomena and Sharp Overlapping Autoionization Resonances

“…With the energy levels and autoionization profiles calculated, it should also be helpful to resonance ionization spectroscopy (RIS) experimental designs in choosing the appropriate intermediate state and laser wavelength 39 . We note that there are some theoretical studies on complex overlapping resonances using analytical formulations based on the phase-shifted MQDT parameters 40 , 41 and configuration interactions (CI) method 42 . Compared with these methods, the MQDT physical parameters are directly calculated in the R-R-eigen method and no fitting parameters are needed.…”