Scattering and absorption of particles emitted by a point source in a cluster of point scatterers

A theory for the scattering and absorption of particles isotropically emitted by a point source in a cluster of point scatterers is described and related to the theory for the scattering of an incident particle beam. The quantum mechanical probability of escape from the cluster in different directions is calculated, as well as the spatial distribution of absorption events within the cluster. A source strength renormalization procedure is required. The average quantum scattering in clusters with randomly shifting scatterer positions is compared to trajectory simulation with the aim of studying the validity of the trajectory method. Differences between the results of the quantum and trajectory methods are found primarily for wavelengths larger than the average distance between nearest neighbour scatterers. The average quantum results include, for example, a local minimum in the number of absorption events at the location of the point source and interference patterns in the angle-dependent escape probability as well as in the distribution of absorption events. The relative error of the trajectory method is in general, though not generally, of similar magnitude as that obtained for beam scattering.