Validation of analytical formula for the efficiency calibration of gamma detectors using coaxial and off-axis extended sources

In this paper, we introduce a direct analytical mathematical method for calculating the geometrical and absolute total efficiencies of gamma NaI scintillation detectors using an arbitrarily positioned point source. Generalizing, the geometrical and absolute total efficiencies are extended to include coaxial and off-axis sources with plane and volumetric shapes. The efficiencies are deduced into straightforward mathematical expressions. The current theoretical and the published efficiency values are in good agreement.