Diffusion-influenced reversible geminate ABCD reaction in the presence of an external field

We investigate a diffusion-influenced ground-state reversible geminate ABCD reaction in the presence of a constant external field in one dimension. In the Laplace domain, we first obtain the nonreactive Green function from which the reactive Green function is derived. Analytic asymptotic expressions of the survival probability are obtained in the time domain for both short and long time regions. There exist four regimes for the equilibrium survival probability according to the signs of the field intensities a1 and a2 that reactant and product states feel, respectively. Analysis of the long-time asymptotic behavior of the survival probability shows two regimes depending on the sign of a parameter K( identical with a(2)(2)D(2) -a(2)(1)D(1)), where D(1) and D(2) are the relative diffusion constants of corresponding states, respectively. Combining these two results, we predict a total of eight regimes for the long-time asymptotic behavior of the survival probability. We find that the long-time asymptotic behavior of the deviation of the effective survival probability shows the t(-3/2) power law when m( identical with min {a(2)(1)D(1), a(2)(2)D(2)}) not equal 0, whereas it shows t(-1/2) power law when m = 0. When one of the fields is turned off, the long-time asymptotic behavior of the survival probability shows a kinetic transition as the sign of the remaining field changes.