Physical origin of oscillations in the three-dimensional collision amplitudes of heavy–light–heavy systems. Semiclassical quantization of chaotic scattering

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Abstract
The dynamics of three‐dimensional heavy–light–heavy chemical reactions is studied using a new model which emphasizes the central importance of rotational motion in the reactive collisions. The single fastest vibrational motion is adiabatically eliminated. The reaction probability is then computed from a coherent sum of scattering amplitudes for two‐atom–rigid‐rotor scattering problems. The results for the reaction I+HI are shown to be accurate by comparison with available converged quantum results. Most of the analysis is devoted to a study of oscillations which appear in the reaction probability vs collision energy. The oscillations are found to result from extreme inelastic effects in the rotational scattering which are wholly unrelated to the light‐atom exchange process and to the occurrence of rotational thresholds. In fact, similar oscillations are shown to exist in the nonreactive collision process, Ar+HBr. The primitive classical S‐matrix semiclassical theory of Miller and Marcus is employed to relate the oscillations to interference between families of classical root orbits. These root orbits (which can number 50 or more per energy) generally exhibit extreme rotational–translational energy conversion, often including multiple scattering where the diatom rotates completely in the collision complex. The classical S matrix is shown to be useful even when the scattering dynamics is chaotic. The extreme sensitivity of the root orbits to initial conditions is suppressed since the boundary conditions are enforced at the beginning and end of the scattering process. This leads to a phenomenon of ‘‘phase coherence’’ where the semiclassical amplitudes add without the random phase cancellation one might expect in chaotic scattering.