Conditional lifetimes in geminate recombination

In addition to overall mean lifetimes, with which one is well acquainted in the theory of reactive diffusion processes, mean conditional lifetimes for absorption in a given sink also have physical significance. In the theory of geminate recombination of nonisolated pairs, when one imposes an additional outer absorbing sphere, the conditional lifetime for absorption in the inner sphere is the risetime for the recombination products. In the theory of geminate recombination in an homogeneous scavenger concentration, both overall and conditional lifetimes are physically significant. The first describes reactants' decay, the second products' formation. We derive, in the backward equation formalism, equations governing the initial variable dependence of these lifetimes. We give the explicit solution for geminate recombination of neutrals (free diffusion). Experimental measurements of recombination lifetimes would supply new data, independent of the yields typically measured in such experiments.