Other analyses of geminate radical recombination

There have been many other theoretical analyses of geminate radical recombination probabilities, some of which are considered further below. They can be divided into three types (a) diffusion equation treatments, (b) first passage time methods, and (c) kinetic theory applications. 

Monchick [36, 273] has used the diffusion equation and radiation boundary conditions [eqns. (122) and (127)] to discuss photodissociative recombination probabilities. His results are similar to those of Collins and Kimball [4] and Noyes [269]. However, Monchick extended the analysis to probe the effect of a time delay in the dissociation of the encounter pair. It was hoped that such an effect would mimic the caging of an encounter pair. Since the cage oscillations have periods 1 ps, and the diffusion equation is hardly adequate over such times (see Chap. 11, Sect. 2), this is a doubtful improvement. Nor does using the telegraphers equation (Chap. 11, Sect. 3.3) help significantly as it is only valid for times longer than a few picoseconds. 

The dissociation of a molecule in solution and the approach to an equilibrium distribution of molecules and radicals has been treated by Berg [278]. His detailed and careful analysis uses the diffusion equation exclusively to describe microscopic motion. During molecular dissociation on a microscopic scale (i.e. involving only a few molecules), molecules dissociate, recombine, dissociate etc. many times. The global rate of dissociation is much less than that of an individual molecule, indeed smaller by a factor of (1 + kACijAiiRD), that is an average number of times the molecule dissociates and recombines. For reactions which do not go to completion 

As each encounter has a probability of reaction, a, the probability of recombination at a time t is 

The Laplace transform of a convolution integral is simply the product of the Laplace transformed functions within the integral. Consequently, the Laplace transform of the equation aoove is 

Evans and Fixman [274] suggested that the initial distribution of iodine atoms formed in the laser-induced photodissociation of iodine molecules by Chuang et al. [266] might not be unique. Instead, they have considered various combinations of iodine atom separations of 0.27 or 

---