Effect of Open Channels on the Isolation of Overlapping Resonances in the Uniformly Perturbed Rydberg Systems Studied by Multichannel Quantum Defect Theory

Abstract

A previous study (Lee, C. W. J. Phys. B 2010, 43, 175002) that isolated the overlapping resonances in the photoionization spectra using multichannel quantum defect theory (MQDT) in systems involving a single open channel was extended to manage many open channels when the closed channels are degenerate. The theory was applied to the dipole allowed J = 1 o spectra from the ground state with excitation energies lying between the lowest ionization thresholds for rare gas atoms, Ar, Kr, and Xe, and also for group IV elements, Ge, Sn and Pb.

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

“…In [27], a diagonalization of Instead of usual use of the biorthogonal base sets for the diagonalization of such a non-normal matrix [44,45], another diagonalization called condiagonalization was adopted in [45]. Then, one obtains:…”

“…where n c denotes the number of closed channels (Equation (23) corrects error in Equation (27) of [27]). Equation (23) tells us that the transition amplitude to the autoionizing state is given as a sum of Beutler-Fano amplitudes contributed from each resonance eigenchannel.…”

“…where c n denotes the number of closed channels (Equation (23) corrects error in Equation (27) of [27]). …”

“…In [27], a diagonalization of det(tan β + κ cc ) is used to isolate overlapping resonances. This diagonalization requires that two conditions be met.…”

“…If there is more than one nondegenerate closed channel, it is meaningless to move the resonance center of each eigen-series to its own origin because of the local, non-uniform and thus aperiodic nature of inter-series channel coupling (see Figure 1) [27]. Instead, its utility is in the simplification of the parameters for resonance structure.…”