On collisional energy transfer in recombination and dissociation reactions: A Wiener-Hopf problem and the effect of a near elastic peak

The effect of the large impact parameter near-elastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions is studied. To this end, the conventional single exponential model, a biexponential model that fits the literature classical trajectory data better, a model with a singularity at zero energy transfer, and the most realistic model, a model with a near-singularity, are fitted to the trajectory data in the literature. The typical effect of the energy transfer on the recombination rate constant is maximal at low pressures and this region is the one studied here. The distribution function for the limiting dissociation rate constant k0 at low pressures is shown to obey a Wiener-Hopf integral equation and is solved analytically for the first two models and perturbatively for the other two. For the single exponential model, this method yields the trial solution of Troe. The results are applied to the dissociation of O3 in the presence of argon, for which classical mechanical trajectory data are available. The k0's for various models are calculated and compared, the value for the near-singularity model being about ten times larger than that for the first two models. This trend reflects the contribution to the cross section from collisions with larger impact parameter. In the present study of the near-singularity model, it is found that k0 is not sensitive to reasonable values for the lower bound. Energy transfer values <ΔE>'s are also calculated and compared and can be similarly understood. However, unlike the k0 values, they are sensitive to the lower bound, and so any comparison of a classical trajectory analysis for <ΔE>'s with the kinetic experimental data needs particular care.