Formal and computational studies of molecular collision dynamics

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1977

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Abstract

The dynamics of rotational energy transfer in atom-molecule collisions is studied formally, and computationally within the framework of the coupled states and infinite order sudden approximations. Both approximations are rederived here from a new point of view and demonstrated to lead to approximate wavefuctions and amplitude densities which are non-diagonal in the R-helicity projection of the rotor angular momentum. The formal theory of relaxation phenomena is derived within the framework of these approximations and tested computationally. The results presented here represent the first rigorous formal and computational study of relaxation phenomena using fully quantum mechanical approximations. Some interesting consequences of the approximations studied here are investigated. We demonstrate that the sudden approximation allows a simple parametrization of data which leads to an accurate description of the full cross section matrix. The obtained separation of kinematical and dynamical factors is of particular interest in the inversion problem. The rearrangement collision problem is studied using one of the connected kernel equations methods, the channel coupling array method. The bound state variational principle for the channel coupling array method is formulated. The method is applied computationally to the collinear rearrangement problem. Algebraic equations resulting from this method where the potential is separable are also derived.

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