Results in trapping reactions for mobile particles and a single trap

Abstract

We have exploited a stochastic model for the description of diffusion controlled reactions for trapping processes with a single trap in a one-dimensional lattice in order to describe in an exact way the particle distribution as ``seen'' from the trap, being fixed or mobile, as well as for perfect or imperfect reactions. From this we have obtained the exact result for the total number of absorbed particles. Moreover, we have a formal expression for the nearest-neighbor particle distribution that gives the known results in both limits (fixed trap and fixed particles) and also present an approximate expression that works quite well when the particle diffusivity is greater than the trap diffusivity.