Asymmetry sum rule for molecular predissociation

In the case of weak diatomic molecular predissociation by noninteracting, optically inactive continuum states, it is demonstrated that the predissociation line shape is more accurately represented by a Beutler-Fano profile than by a Lorentzian. The weak asymmetry that is found to occur is due principally to interactions with neighboring vibrational resonances. For this type of predissociation in the case of multiple continua, a sum rule for the corresponding line-shape asymmetry is derived. This sum rule is verified numerically using single-channel and multichannel coupled Schrödinger-equation calculations for the Schumann-Runge band system of O₂. Similar results are presented for the case of optically active continua.