Scavenging of one-dimensional diffusion with random traps

For the process of one-dimensional diffusion in a medium with random traps and homogeneous scavenging, we derive exact expressions for the ultimate trapping and scavenging probabilities and for the lifetimes associated with the two processes. This is done for free diffusion, where results agree with those previously found for discrete random walk, as well as for diffusion in a linear potential. The asymptotic expansions, for small and large ratio of trap concentration to scavenging rate, are given and compared numerically to the exact integrals.