A multichannel quantum defect analysis of two-state couplings in diatomic molecules

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Abstract
A multichannel quantum defect analysis (MCQDA) for non-Coulomb potentials is applied to two-channel coupling in diatomic molecules. Given the exact 2×2 scattering matrix S(E) obtained at a single energy above the dissociation threshold E>0, we can extract an analytic, energy-insensitive 2×2 matrix Y(E) which can be extrapolated across thresholds and yield a complete description of predissociating molecules. The predicted widths, shifts, and line shapes obtained from MCQDA are in quantitative agreement with the exact numerical results and confirm the remarkable simplicity that can be achieved in describing diatomic systems near dissociation limits. The analysis is equally applicable to either adiabatic avoided crossings or diabatic curve crossings. The validity of MCQDA is independent of coupling strength and can quantitatively describe strongly overlapped predissociating resonance states. The application of MCQDA to the bound state spectrum, when both channels are closed, is discussed.