Hit probability of a disk shaped detector with particles with a finite range emitted by a point-like source

An analytical analysis of the geometrical efficiency of a circular detector for particles with a finite range, emitted from a point-like source, is given. Several different cases were determined, depending on the particle range, radius of the detector and the position of the source with respect to the detector. These cases were analyzed separately and different expressions for calculating the hit probability were obtained for each of them. Results were compared with Monte Carlo calculations and good agreement was found. The problem considered here might be relevant for alpha-particle detection under specific conditions.