Detection efficiency of a disk shaped detector with a critical detection angle for particles with a finite range emitted by a point-like source

Detection efficiency of a circular detector for particles with a finite range, emitted from a point-like source was investigated, taking a critical detection angle into account. Particles emitted from the source lose some of their energy in the surrounding medium, before entering the detector material. Incident-energy dependence of the critical detection angle was taken into account. The part of the detector exposed to the particles impacting at angles greater than the critical angle (with respect to the detector surface), was determined. Several different cases were investigated, depending on the radius of the detector and the position of the detector with respect to the source. Detection probability expressions were derived for each of the cases. Results obtained using these expressions were compared with Monte Carlo calculations.

► Sensitivity of a circular detector for particles with a finite range was investigated.
► Point like source and existence of critical detection angle was considered.
► Dependence of the critical detection angle on incident energy was taken into account.
► Analytical solutions are given for each several different geometrical cases.
► Analytical results were compared with Monte Carlo calculation.