Calculation of NaI(Tl) detector full-energy peak efficiency using the efficiency transfer method for small radioactive cylindrical sources

A direct analytical mathematical method is introduced to calculate the efficiency of gamma ray cylindrical detectors. The efficiency expression is deduced through a straightforward mathematical approach. The presented method is based on the accurate analytical calculation of the average path length covered by the photon within the detector's active volume, effective solid angle, and the efficiency transfer method in an integral form, so as to obtain a simple formula for the detection efficiency. In addition, the self-attenuation coefficient of the source matrix, the attenuation factors of the source container (with a radius smaller than the detector radius) and the detector housing materials are also treated by calculating the average path length within these materials. 152Eu aqueous radioactive sources covering the energy range from 121 keV to 1408 keV were used. Remarkable agreement between the measured and the calculated efficiencies was achieved, with discrepancies less than 6 %. nema