Analysis of the Rate Kernel

The dynamic process that enter into the rate kemal expression [(9.46) or (8.9)] are, of course, those that have been included in the kinetic equation, as discussed briefly in Section VII. We discuss now the specific processes, which are relevant for the rate kernel, in more detail. The kinetic theory expression contains all the collision events that one might anticipate would be important for liquid state reactions. The analysis of the rate kernel in the limit where velocity relaxation effects are neglected bears a strong similarity to the derivation of Stokes law from kinetic theory, and we also explore this relationship. 

The rate kernel can be analyzed in a variety of ways depending on how the propagator [z —is represented. In the present discussion, we consider the simple reactive collision model of Section VI and drop the soft-force terms. We write L (12 z) of (9.1) in the form 

This propagator differs from introduced in (7.29) in that z) is 

The terms in this expansion correspond to a fairly sophisticated representation of the dynamics Each vertex describes the collision events schematically depicted in Fig. 7.4, while the propagation between these collisions contains effects of the correlated motion of the two solute molecules in the solvent. To see this more clearly, consider AA j (z), 

We discussed the structure of the repeated ring operator in Section VII.D and pointed out that it contains a variety of dynamic events such as a series of correlated collisions identical to those that appear in the singlet theory via the operators and R. These operators represent the correlated collisions of a single solute molecule with the solvent and serve to renormalize the single-particle motion. Other events in R represent the coupling of the motion of the two solute molecules. In view of this, it is convenient to introduce the propagator for independent motion of the pair 

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