A proposed numerical method for absolute efficiency calibration of α-spectrometers and its application for activity calculation

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 $\pm 1\text{\%}$ in the detector radius, and Source-to-Detector distance than the normal values yields a relative difference of about $\pm 2\text{\%}$, while a difference of $\pm 50\text{\%}$ in the source radius or source lateral distance from detector symmetry axis could only yields inaccuracy of less than $\pm 3\text{\%}$ in the efficiency results.