Analytical approach to calculate the efficiency of 4π NaI(Tl) gamma-ray detectors for extended sources

The 4π NaI(Tl) detectors are usually utilized for low-level radioactivity measurements of environmental samples in gamma-ray spectroscopy due to the near 4π solid angle and high full-energy peak and total efficiencies. An analytical theoretical approach is presented here and used to calibrate a 4π NaI(Tl) (2a×2b×2c) detector, with a central rectangle hole (2l×2m×2c) was left empty for sample access, for isotropic radiating (point, plane and volumetric) sources. The approach depends on the accurate calculation of two important factors; the path length d, the photon traverses within the active volume of a gamma detector, and the geometrical solid angle Ω, subtended by the source to the detector at the point of entrance. The comparisons with the experimental and Monte Carlo method works reported in the literature indicate that the present approach is useful in the efficiency calibration of such complicated gamma-ray spectrometer.