ABSTRACT
In this work, an absolute method to calibrate an α-spectrometer is proposed taking into account the Source-to-Detector, and lateral distances due to eccentric source distribution. An analytical formula to calibrate an α-spectrometer is derived and the Simpson's integration method was utilized to solve these equations in its integral form numerically using a written C computer code. The general Monte Carlo N-particle code, MCNP as well as experimental measurements for some standard α-emitters are used to benchmark the proposed method. An agreement was found between the efficiency results calculated by MC and the proposed method with a maximum relative difference of about 0.5%. While, experimental measurement of α-emitters activity employing the proposed method differs by about 1.65% from the certified values. Accounting for the man made error allows to accurately quantify the assayed sample. Therefore, the inaccuracy in the efficiency results due to non-accurate inputs pertained to the source, and detector radii, Source-Detector distances, and eccentric source distribution are investigated in the Source-to-Detector distance range of (4 to 44 mm). The results show that a difference of ±1% in the detector radius, and Source-to-Detector distance than the normal values yields a relative difference of about ±2%, while a difference of ±50% in the source radius or source lateral distance from detector symmetry axis could only yields inaccuracy of less than ±3% in the efficiency results.
ABSTRACT
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.
ABSTRACT
A previously proposed hybrid analytical-numerical method for efficiency calibration of a NaI detector for a point γ-source is extended and applied for other shapes of sources. The shapes include line, disk, and cylindrical sources of various dimensions and locations with respect to the right circular cylindrical NaI detector. The results obtained by this method have been evaluated through comparison with Monte Carlo (MC) calculations. A relative maximum difference of 3.5% is found between the two methods.
