Differential encounter theories

This is a clear demonstration that a differential encounter theory is not a reasonable alternative to an integral one, when the energy transfer is reversible and occurs between the unstable reactants. Since the lifetimes are not equal, the rate constant of the energy transfer from the short-lived to the long-lived particle does not exist (diverges) at long times. In contrast, in integral formalism we do not encounter any difficulties. This is illustrated by the simplest example of contact transfer considered below. 

In this respect the SA equations are rather unnatural and their distribution functions pA and p/ describe pairs surrounded by other particles rather than isolated pairs as n and m in encounter theory. On the other hand, the macroscopic SA equations include the pumping term 7(f) that allows for then-stationary solution, which is incorrect in differential encounter theory. The accuracy of this solution inspected in Ref. 133 was found to be satisfactory for the irreversible quenching. Unfortunately, for the reversible transfer, this is not the case. 

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