Calculation of the decision threshold and detection limit in high-resolution gamma-ray spectrometry

Abstract

We describe a calculator for the decision threshold and detection limit, a tool intended for gamma-ray spectrometry. The tool is an Excel file composed of several sheets, containing procedures for calculating the decision thresholds and detection limits under various assumptions. It is publicly available at https://f2.ijs.si/en/laboratories/lmr/calculator. The input data for the calculations are peak-analysis results, usually listed in peak-analysis reports (peak energies, FWHMs, peak areas and their uncertainties). Besides these quantities, data on the total number of counts in the peak region and the numbers of counts in the peaked background (if present) and their uncertainties are needed for the calculation. The calculation procedures implemented in the Excel sheets make it possible to calculate the decision thresholds and detection limits from peak data obtained using the region-of-interest method and the least-squares method. With the least-squares method it is possible to calculate the decision thresholds and detection limits for both isolated and overlapping peaks. An additional sheet enables the calculation of decision thresholds and detection limits for multi-gamma-ray emitters. We show that, in general, the indications corresponding to the decision threshold depend on the observed value of the indication and that those calculated with the region-of-interest method do not depend on it, except through the width of the peak region.