Smoluchowski-like theory for trapping kinetics in a slab

The theory of diffusion-limited reactions is traditionally developed in terms of unconstrained diffusion in an unbounded volume. The Smoluchowski mean-field theory predicts an exponential decay of the survival probability for particles that diffuse among randomly placed static traps. This means that the ensemble of traps may be considered as a uniform absorbing continuum. It is shown that this picture is also correct in the case of constrained diffusion, more specifically for diffusion in a slab constrained by two parallel absorbing planes.