Decoupling of Background and Resonance Scatterings in Multichannel Quantum Defect Theory and Extraction of Dynamic Parameters from Lu-Fano Plot

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.