Shape Resonances and Rotationally Predissociating Levels: The Atomic Collision Time-Delay Functions and Quasibound Level Properties of H2(X 1Σg+)

The energy dependence of the collisional time-delay function has been computed for H(1S) atoms interacting via the ab initio H2(X 1Σg+) potential. Peaks in this function determine the scattering resonance energies Er and widths Γ, and the lifetimes for each of the corresponding quasibound vibrational–rotational levels. Small differences are found between these Er and Γ, and the values obtained by a “maximum internal amplitude” approach (intended to characterize the spectroscopically observable predissociating levels). Approximate procedures for rapid, accurate numerical evaluation of Er are appraised; a new outer-boundary-condition criterion for resonances leads to the best agreement with the exact results. Also, a primitive WKB procedure yields Γ's of usable accuracy. For ground-state H2, HD, and D2 the onset of line broadening due to centrifugal barrier penetration is found to occur at energies some hundreds of cm−1 below the locus of barrier maxima. The predissociation method of estimating long-range interatomic forces therefore cannot be expected to yield valid results for hydridic diatomics.