Detection limit calculations for peak evaluation methods in HPGe gamma-ray spectrometry according to ISO 11929

Abstract

Two peak area estimation methods in gamma-ray spectrometry, the total peak area (TPA) and the background step function (BSF) methods are re-considered first. For least-squares (LS) peak fitting then, a new net peak area uncertainty model is established. It results in a new function fB replacing a TPA method internal design factor. This allows applying the TPA-related decision threshold (DT) and detection limit (DL) formulae, based on ISO 11929(2010), also for peak fitting. Linear LS adapted to Poisson counting data is suggested to derive fB values for a single peak and different combinations of background shape components including a fitted BSF. fB is then adapted to penalized non-linear fitting including Poisson maximum likelihood estimation by MC simulations. Within the DL iteration the fB method is much faster than with non-linear re-fitting. The fitted peak area uncertainty can be safely modeled for peak areas up to 10 DT which is sufficient for DL calculations. The extension for peak multiplets is indicated.