A semi-empirical method for efficiency calibration of an HPGe detector against different sample densities

In this work, a semi-empirical equation in terms of γ-energy, and sample density is derived, proposed, benchmarked, and applied for the peak efficiency calibration of an HPGe detector with respect to an axial source-to-detector configuration. The samples are in the form of cone-shaped Marinelli beakers of different densities in the range 0.7-1.6 g/cm³. The method employs the experimental measurements with the ANGLE-3 software calculations using the efficiency transfer method. The peak efficiency curve of an HPGe detector is calculated using the experimental measurements of point-like sources (¹³³Ba, ¹³⁷Cs, and ⁶⁰Co). The ANGLE-3 software is then used to calculate the peak efficiency curves for samples with different densities in the γ-energy range 81-1332 keV. The peak efficiency curves are then fitted to get the energy coefficient; in addition, a linear relationship is then constructed between the energy coefficients and sample densities to get the density coefficients, and the derived equation as well. The derived equations are benchmarked using the peak efficiency curves by ANGLE-3 software in comparison with that the equation results. The results are found to be in agreement with an average relative error of about 1.5%. In addition, the derived equations are applied to estimate the activity concentration of radionuclides present in 5 cone-shaped samples with different densities using experimental measurements. The activity results are found to be in agreement with the certified values with an average relative error of about 2%. The limitation of the proposed equations is also discussed with respect to different material densities and different chemical compositions and correction factors for material composition self-attenuation for various materials are also presented.