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 = SBSR 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.
Highlights
The autoionization spectra of atoms frequently show complex overlapping resonances caused by interlopers and are analyzed routinely by experimentalists with only a few parameters using multichannel quantum defect theory (MQDT) [1]
Complex autoionization spectra involving two closed and one open channels were studied by Giusti-Suzor and Lefebvre-Brion, Cook and Cromer, Wintgen and Friedrich and Ueda using the phase-shifted MQDT
One approach is to use a phase-shifted MQDT formula based on the neglect of resonances might be expected to be isolated
Summary
The autoionization spectra of atoms frequently show complex overlapping resonances caused by interlopers and are analyzed routinely by experimentalists with only a few parameters using multichannel quantum defect theory (MQDT) [1]. In the context of the phase-shifted MQDT, this model system was studied extensively by Giusti-Suzor and Lefebvre-Brion [12], Wintgen and Friedrich [10] and Ueda [8] They examined the phenomena in complex resonances, such as intensity borrowing, q reversals and truly bound states in continuum. Fano and Cooper long ago showed that a discrete state can interact with only one type of continuum [14] Mies developed their theory further and proposed the use of an overlapping matrix to represent the extent of overlap when a complete superimposition of overlapping resonances is no longer obtained when more than one open channel is involved in the CM theory [15]. The scope of this review will be restricted to the development in mathematical formulations of parameterizing the resonance structures and its use in analyzing the effect of inter-series interactions on the autoionizing Rydberg spectra
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