A quantum mechanical study of reactive probabilities for collinear atom-diatom systems



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A new method for treating the reactive scattering of an atom-diatom system is applied to a generalized collinear model reactive system. Coupled rearrangement channel [tau] operator equations are employed to generate coupled integral equations for the amplitude density functions and the coupled integral equations are then reduced to a system of simultaneous linear algebraic equations. Calculations have been performed for several specialized cases of a general piece-wise constant potential and the reactive probabilities as a function of the total energy are presented. Reaction probabilities are given for collinear atom-diatom systems whose piece-wise constant potential surfaces are characterized by simple barriers or wells in the interaction region, with products and reactants having the same asymptotic potential(i.e., [delta]E = 0 for the reaction). Reaction probability curves are also presented for some example endothermic and exothermic reactions, including surfaces having a barrier, well, or zero potential in the "reaction zone". Probability curves for an endoergic reaction with a well in the reaction zone are presented for collisions in which the molecule is initially in its ground vibrational state and when the molecule is initially in its first excited vibrational state. These results are qualitatively consistent with experimental reaction probabilities for the proton transfer reaction He + H[lowered 2, raised +] ---> HeH + H[raised +] and with classical trajectory calculations for this same reaction.