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 it's 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 shows 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.