The average scavenging probability

This is analogous to the expression given by Rzad et al. [365] and in Chap. 7, Sect. 3.3, but rather more rigorously derived. But it has been noted that / f(f)dt = 1 — fe, so that 

Equation (345) shows that the average scavenging probability of an ion-pair initially separated by a distance r0 is the Laplace transform (into k%c space) of the lifetime distribution function. 

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So far, the discussion has presumed that the ion-pair was formed with a unique initial separation, r0. If the initial distribution extends over a range of distances, tc(r0), in which ut(r0) is normalised to unity, then the average scavenging probability is... 

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