Direct mathematical solutions for the gamma-ray detectors geometrical and total efficiencies integrable formulae

A new mathematical solution for the geometrical and total efficiencies integrable equations of cylindrical and spherical gamma-ray detectors is proposed. the efficiencies integrable equations are based on the accurate analytical computation of the photon path length traverses within the detector active medium,and the geometrical solid angle,ω,subtended by the source to the detector at the point of entrance. the comparison between the efficiencies calculated values by the use of both,the integrable and direct solution formulae,showing very good agreement. © school of engineering,taylor’s university.