Quantum Theory of (H,H2) Scattering: Approximate Treatments of Reactive Scattering

Abstract

A quantum-mechanical study is made of reactive scattering in the (H, ${\mathrm{H}}_{2}$) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g., the reaction configuration) are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom, and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and the semiempirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, ${\mathrm{H}}_{2}$) reaction, a much simpler approximation method, the "linear model," is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision, and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational-state dependence, and other properties of the total and differential reaction cross sections are determined. These results of the quantum-mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shift toward the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.