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

An analytic solution is derived for the Green function and survival probabi lity of excited-state reversible recombination reactions of noninteracting geminate particles in solution, which have different lifetimes in their bou nd and unbound states and participate in a competing quenching reaction. Th e behavior of the three roots of the cubic polynomial, on which this soluti on depends, is investigated in the complex plane. Two kinds of "complex pla ne 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 a symptotic behavior, which is derived in the sequel. The quenching and lifet ime 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].