  We propose an analytical method for solving the problem of barrierless
reactions in solution, modeled by a particle undergoing diffusive motion under
the influence of both reactant and product potentials. The coupling between
these two potentials is taken to be a Dirac Delta function. The diffusive
motion in this paper is described by the Smoluchowskii equation. Our solution
requires only the knowledge of the Laplace transform of the Green's function
for the motion in both the uncoupled potentials. Our model is more general than
all the earlier models, because we are the first one to consider the potential
energy surfaces of both the reactant and product explicitly.
