Multichannel quantum-defect theory and an equivalent N-level system

A derivation and geometrical interpretation of multichannel quantum-defect theory (MQDT) is presented. An alternative set of MQDT parameters is suggested which separates into two independent groups, one representing the quantum defect of a Rydberg series in the absence of channel coupling and the other representing the channel coupling itself. An equivalent N-level system is developed so that the MQDT boundary conditions are replaced by a simple energy restriction on the N-level system, resulting in easier solutions of the equations. The equations are solved and spectra are presented for the simple two-channel case and for the three-channel case, where channel interactions lead to interferences in the spectra.