Excited-state reversible geminate reaction. III. Exact solution for noninteracting partners

An analytic solution is derived for the Green function and survival probability of excited-state reversible recombination reactions of noninteracting geminate particles in solution, which have different lifetimes in their bound and unbound states and participate in a competing quenching reaction. The behavior of the three roots of the cubic polynomial, on which this solution depends, is investigated in the complex plane. Two kinds of "complex plane maps'' are identified on which three types of transitions may occur. One root may vanish, or two roots coincide, or the three real parts coincide. The first transition leads to a corresponding transition in the long-time asymptotic behavior, which is derived in the sequel. The quenching and lifetime effects result in nonmonotonic dependence of the binding probability on the initial separation distance. (C) 1999 American Institute of Physics. [S0021-9606(99)50519-9].