Effect of an external electric field on the diffusion-influenced reversible reaction of a neutral particle and a charged particle in three dimensions

Abstract

The diffusion-influenced reversible reaction of a neutral particle and a charged particle in an external field is analytically solved in three dimensions. A generalized nonisotropic boundary condition is used and a kinetic equation for the probability density function is set up. A tridiagonal matrix equation is derived for the coefficients of the series solution and we obtain the solution within the diagonal approximation in the Laplace domain. We also find that the long time asymptotic behavior of the first term solution shows a kinetic transition from a power law to an exponential behavior as the field strength is increased. The full numerical calculation reveals that the first term solution deviates slightly at short times but gives good result at long times. Thus it contributes dominantly to the kinetic transition behavior at long times. For the irreversible limit, we find a different kinetic transition behavior from a power law to an exponential increase through a constant in the transition region for the initially bound state.