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

Abstract

The energy dependence of the collisional time‐delay function has been computed for $\mathrm{H}\text{(1S)}$ atoms interacting via the ab initio ${\mathrm{H}}_2{\mathrm{(X}}^1{\Sigma }_g^{+})$ potential. Peaks in this function determine the scattering resonance energies $E_r$ and widths $\Gamma$ , and the lifetimes for each of the corresponding quasibound vibrational–rotational levels. Small differences are found between these $E_r$ and $\Gamma$ , 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 $E_r$ 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 $\mathrm{\Gamma \text{'}}\mathrm{s}$ 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.