Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry

Abstract

The geometric factor of a particle detector having either circular or rectangular geometry is derived analytically. Both isotropic and 'cos2 theta ' variations of intensity are considered. An approach based on 'shadow areas' is applied to the case of particles passing through two unequal circular areas, and it is proved that the results are identical with those obtained previously using an approach based on the direct integration of 'infinitesimal areas'. This latter approach is then used for the case of two unequal rectangular areas, which has not been considered previously. The analytical results confirm those obtained previously using numerical techniques.