Statistical properties of the nearest-neighbour distance at a single imperfect trap

We consider a one-dimensional system consisting of a single partially absorbing trap in the presence of diffusing particles. The probability density function of the closest distance between the trap and the untrapped particle is calculated exactly. In particular we show the equivalence between our result and that of earlier treatments with the radiation boundary condition, only when the initial distribution of particles is uniform throughout the infinite space. Our result differs from the earlier treatments when the initial particle distribution is non-uniform.