Systematic and non-systematic effects of the uncertainty of the sample position in gamma-ray spectrometry

When cylindrical samples placed coaxially with the detector are measured on a gamma-ray spectrometer, the position of the sample very often deviates from an ideal one with the axes of the sample and the detector less than perfectly aligned. If a calibrated source is used prior to the measurement and is presumed to have been positioned correctly, one might conclude that the misalignment of the measured sample should result in an uncertainty of the reported nuclide activity, since the efficiencies of the sample and the calibrated source are effectively different due to the difference in placement. The efficiency of a displaced cylindrical sample, however, is always lower than the one of a sample that is perfectly aligned. The net effect of misalignment can therefore be not only an increase in the uncertainty of the activity, but also a systematic error in its evaluation. Since the Guide to the Expression of Uncertainty in Measurement requires that all such systematic effects be corrected for, we have developed a method to assess the change in the efficiency resulting from misalignment and to introduce the required correction. The calculation of this correction only requires knowledge of basic sample and detector data. The uncertainty of the reported activity can then also be assessed and is influenced by the uncertainty of the efficiency evaluated around its new, corrected value. An appropriate expression for this uncertainty has been derived.