Pole approximation for unimolecular decay dynamics

Time-dependent transition probabilities and final product distributions for unimolecular decay are approximated from the corresponding integral expressions in terms of poles and residues reflecting contributions from bound and resonance states. Poles in the integrands at complex resonance energies are located by an efficient iterative search for the poles of low-dimensional resolvent matrices. These matrices and the residues needed for the calculation are computed using Wigner's R -matrix method. Calculations are performed for two collinear triatomic systems previously treated by an accurate technique. By comparing the approximate and accurate results, the magnitude of branch cut contributions to time-dependent transition probabilities is determined. The pole approximation is found to yield time-dependent probabilities that are qualitatively (and, sometimes, quantitatively) accurate once direct dissociation has ceased. This approximation, however, is found to be less satisfactory for calculation of final product distributions unless direct molecular dissociation is negligible.