General formula to calculate the efficiency of n-sides NaI(Tl) scintillation detector

Variations in detector geometry and shape can significantly influence the detection efficiency of inorganic NaI(Tl) scintillation gamma-ray detectors. The structural design and optimization conditions of these detectors are crucial in applications where detailed knowledge of interaction probabilities and related detection efficiency is essential. The present study introduces a general formula for determining the detection efficiency of n-sided gamma-ray detectors. The impact of novel scintillation geometries “featuring different numbers of sides” will be investigated using an analytical-numerical technique, aiming to identify the most efficient detector configurations. To accomplish this, the geometrical solid angle, effective solid angle, geometrical efficiency, and total efficiency will be evaluated, along with the average path length within the active medium of the detector. All evaluations will be carried out assuming that the radioactive point source is positioned axially to the detector main axis. The results of the analytical-numerical approach can serve as a guideline for optimizing NaI(Tl) scintillation detector designs. Furthermore, the method can be extended to accommodate a wide range of geometries and modified to suit specific configurations by applying appropriate setup conditions. The obtained results show strong agreement with those from Monte Carlo Simulations and (Angle 4) software, supporting the validity and reliability of the current proposed approach.