• Bulletin of the Korean Chemical Society
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• v.23 no.11
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• pp.1560-1567
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• 2002

The transformation devised by Lecomte and Ueda for the study of resonance structures in the multichannel quantum defect theory (MQDT) is used to analyze partial photofragmentation cross section formulas in MQDT analogous to Fano's resonance formula obtained in the previous work for the system involving two open and one closed channels. Detailed comparison of the MQDT results with the configuration mixing (CM) ones is made. Resonance structures and their geometrical relations in the MQDT formulation are revealed and classified by combining Lecomte and Ueda's theory with the geometrical method devised to study the coupling between background and resonance scatterings.

• Bulletin of the Korean Chemical Society
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• v.30 no.8
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• pp.1783-1792
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• 2009

Although overlapping resonances have been studied extensively in conventional resonance theories, there have not been many studies on them in multichannel quantum defect theories (MQDT). In MQDT, overlapping resonances occur between the channels instead of states, which pose far greater difficulty. Their systematic treatment was obtained for cases involving degenerate closed channels by applying our previous theory, which decouples background scattering from the resonance scattering in the MQDT formulation. The use of mathematical theory on con-diagonalization and con-similarity was essential for handling the non-Hermitian symmetric complex matrix. Overlapping resonances in rare gas spectra of Ar, Kr and Xe were analyzed using this theory and the results were compared with the ones of the previous alternative parameterizations of MQDT which make the open-open part $K^{oo}$ and closed-closed part $K^{cc}$ of reactance submatrices zero. The comparison revealed that separation of background and resonance scatterings achieved in our formulation in a systematic way was not achieved in the representation of $K^{oo}\;=\;0\;and\;K^{cc}$ = 0 when overlapping resonances are present.

• Bulletin of the Korean Chemical Society
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• v.23 no.7
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• pp.971-984
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• 2002

The multichannel quantum defect theory (MQDT) is reformulated into the form of the configuration mixing (CM) method using the geometrical construction of the S matrix developed for the system involving two open and one closed channels. The reformulation is done by the phase renormalization method of Giusti-Suzor and Fano. The rather unconventional short-range reactance matrix K whose diagonal elements are not zero is obtained though the Lu-Fano plot becomes symmetrical. The reformulation of MQDT yields the partial cross section formulas analogous to Fano's resonance formula, which has not easily been available in other's work.

• Bulletin of the Korean Chemical Society
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• v.30 no.4
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• pp.891-896
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• 2009

Giusti-Suzor and Fano introduced translations of the scales of Lu-Fano plots by phase renormalization in order to decouple the intra- and inter-channel couplings in multichannel quantum defect theory (MQDT). Their theory was further developed by others to deal with systems involving a larger number of channels. In different directions, MQDT was reformulated into forms with a one-to-one correspondence to those in Fano's configuration mixing theory of resonance for photofragmentation processes involving one closed and many open channels. In this study, the theory was further developed to fully reveal the coupling nature, decoupling of the background and resonance scattering in physical scattering matrices as well as to further extract the dynamic parameters undiscovered by Fano and his colleagues. This theory was applied to the photoabsorption spectrum of $H_2$ observed by Herzberg's group.

• Bulletin of the Korean Chemical Society
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• v.16 no.10
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• pp.957-968
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• 1995

Generalized Multichannel Quantum Defect theory (MQDT) was implemented to the vibrational predissociation of triatomic van der Waals molecules in the previous paper [Bull. Korean Chem. Soc, 12, 228 (1991)]. Implementation was limited to the calculation of the scattering matrix. It is now extended to the calculation of the predissociation spectra and the final rotational distribution of the photofragment. The comparison of the results with those obtained by other methods, such as Golden-rule type calculation, infinite order sudden approximation (IOS), and close-coupling method, shows that the implementation is successful despite the fact that transition dipole moments show more energy dependence than other quantum defect parameters. Examination of the short-range channel basis functions shows that they resemble angle-like functions and provide the validity of the IOS approximation. Besides the validity of the latter, only a few angles are found to play the major role in photodissociation. In addition to the implementation of MQDT, more progress in MQDT itself is made and reported here.

• Bulletin of the Korean Chemical Society
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• v.32 no.5
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• pp.1519-1526
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• 2011

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$^{\circ}$ 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.

• Bulletin of the Korean Chemical Society
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• v.31 no.11
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• pp.3201-3211
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• 2010

Previous work on the phase-shifted version of the multichannel quantum-defect theory (MQDT) for a system involving 2 closed and many open channels (Lee, C.-W. Bull. Korean Chem. Soc. 2010, 31, 1669) was extended to obtain the formulae of the spectral shape parameters with the structure of a pole extracted explicitly for general cases only limited by 2 non-degenerate closed channels. The theory was applied to the narrow $6p_{1/2,3/2}np$ J = 1 autoionizing Rydberg series in barium perturbed by the $6p_{3/2}nf$ states obtained by de Graaff et al.

• Bulletin of the Korean Chemical Society
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• v.31 no.6
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• pp.1669-1680
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• 2010

The phase-shifted version of the multichannel quantum-defect theory (MQDT) was reformulated by disentangling the interloper spectrum from the perturbed dense Rydberg series for a systems involving 2 closed and more than 1 open channel. The theory was applied successfully to Martins and Zimmermann's photoionization spectra of the Rydberg series Cu I $3d^9\;4s(^1D_2)\;nd^2G_{9/2}$ perturbed by the interloper, $3d^9\;4p^2\;^4F_{9/2}$, for which Cohen's 4 channel QDT had failed. The zero surface graphic of the perturbed Fano's asymmetry parameter q of the autoionization spectrum of dense Rydberg series by the interloper was determined by only two parameters for this system. It was used as a map to trace the transformation route of the 3 channel autoionization spectra to the 4 channel spectra when the channel coupling of the closed channels with a newly added open channel was turned on progressively.

• Bulletin of the Korean Chemical Society
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• v.17 no.11
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• pp.1065-1073
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• 1996

The dissociative recombination of O2+(v+)＋e-→O(1S)＋O(1D) has been theoretically investigated using the multichannel quantum defect theory (MQDT). Cross sections and rate coefficients at various electron energies are calculated. The resonant structures in cross section profile, which are hardly measurable in experiments, are also determined and the existence of Rydberg states is found to affect the rates. The theoretical rate coefficients are computed to be smaller than experimental ones. The reasons for this difference are explained. The two-step MQDT procedure is found to be very useful and promising in calculating the state-to-state rates of the dissociative recombination reaction which is a very important and frequently found phenomenon in Earth's ionosphere.

• Bulletin of the Korean Chemical Society
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• v.31 no.2
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• pp.315-326
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• 2010

This study examined the overlapping resonances in the systems involving 1 open and 2 closed channels using the phase-shifted version of multichannel quantum-defect theory (MQDT). The results showed that 21 patterns for the q reversals in the autoionization spectra are possible depending on the relative arrangements of the two simple poles and roots of the quadratic equations. Complete cases could be generated easily using the q zero planes determined using only 3 asymmetric spectral line profile indices. The transition of the spectra of the coarse interloper Rydberg series from the lines into a structured continuum by being dispersed onto the entire Rydberg series was found. The overall behavior of the time delays was found to be governed by the dense Rydberg series, which is quite different from the one of the autoionization cross sections that is governed by an interloper, indicating that different dynamics prevail for them. This is in contrast to the two channel system where both quantities behave similarly. The dynamics obtained in the presence of overlapping resonances is as follows. The absorption process is instant and dominated by a transition to the interloper line. This process is followed by rapid leakage into the dense Rydberg series, which has a longer residence time before ionization than that of the interloper state. This is because the orbiting period is proportional to $\upsilon^3$ so that an excited electron has a shorter lifetime in the interloper state belonging to a lower member of the Rydberg series.