Effect of an external field on the reversible reaction of a neutral particle and a charged particle in three dimensions. II. Excited-state reaction.

The excited-state reversible reaction of a neutral particle and a charged particle in an external electric field is studied in three dimensions. This work extends the previous investigation for the ground-state reaction [S. Y. Reigh et al., J. Chem. Phys. 129, 234501 (2008)] to the excited-state reaction with two different lifetimes and quenching. The analytic series solutions for all the fundamental probability density functions are obtained with the help of the diagonal approximation. They are found to be in excellent agreement with the exact numerical solutions of anisotropic diffusion-reaction equations. The analytical solutions for reaction rates and survival probabilities are also obtained. We find that the long-time kinetic transition from a power-law decrease to an exponential increase can be controlled by the external field strength or excited-state decay rates or both.