Lu-Fano plots for potentials with non-Coulomb tails: application to vibrational spectra of long-range diatomic molecules

The multichannel quantum defect theory was originally developed for potenti als with Coulomb asymptotic behavior Generalization to non-Coulombic potent ials was focused on the representation of the scattering observables in ter ms of a pair of functions solution of the radial equation in the long-range region. We show how one of the basic tools of quantum defect theory, namel y the method to construct the famous Lu-Fano plots (Lu K T and Fano U 1970 Phys. Rev. A 2 81), can be extended to the potentials with general non-Coul omb asymptotes by considering only the law linking the energies and asympto tic phases to the quantum numbers. This provides an efficient method for th e analysis of molecular spectra close to dissociation limit, generalizing t he Le Roy-Bernstein approach to two coupled channels.