Worry, Gary and Marcus, R. A. (1977) On the theory of translational energy distributions of product molecules of molecular beam reactions involving transient complexes. II. Journal of Chemical Physics, 67 (4). pp. 16361646. ISSN 00219606. http://resolver.caltech.edu/CaltechAUTHORS:WORjcp77

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Abstract
A statistically adiabatic model for chemical reactions involving a tight or loose transition state in the exit channel was used in Part I to obtain an integral equation for the individual reaction probabilities, i.e., for the magnitude of the S matrix elements. In the present paper this integral equation is explicitly solved for the general case of product orbital (l) and rotational (j) angular momenta constrained only by energy and angular momentum conservation. The reaction probabilities are shown to be related to a contour integral of a product of canonical partition functions. The theory includes an effect of the evolution of the bending vibrations of the transition state into free rotations of the product molecules. The distribution of final translational energy for the general (l,j) case is then obtained by averaging the reaction probabilities over various quantum states of the product molecules. The results are compared with the special cases in the literature for which (i) the transition state in the exit channel is loose (''phase space theory''), (ii) this case but with l>>j, and (iii) tight transition state theory with l>>j (Part I). The results are also compared with experimental data obtained from the molecular beam reaction F+(CH3)2C=CH2 >F(CH3)2CCH2*>CH3+FCH3C=CH2. The data and the theoretical results are now in better agreement. In the treatment described here and in Part I a loose transition state in the entrance channel was assumed. Expressions for the energy distribution are also given for the case when the entrance channel transition state is tight. Finally, a statistically adiabatic S matrix, which is useful for reactions proceeding through longlived collision complexes having tight transition states, is described, and its possible application to angular distributions and angular momentum polarization experiments is discussed.
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Additional Information:  Copyright © 1977 American Institute of Physics. Received 8 March 1977. We are pleased to acknowledge a helpful discussion with Professor Donald Secrest of this department on numerical methods for solving integral equations, and to acknowledge support of the present research by a grant from the National Science Foundation.  
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