Propagation of uncertainties in sample properties to the uncertainty of the counting efficiency in gamma-ray spectrometry

Explicit expressions are derived describing the variance of the counting efficiency for a homogeneous cylindrical sample, placed coaxially on the detectorʹs symmetry axis, in terms of the variances of the sample properties thickness, density and composition. In the derivation, the emission of gamma-rays parallel to the sample axis and the efficiency for an area source proportional to the solid angle subtended by the source from the effective point of interaction of the gamma-rays within the detector crystal are assumed. For the uncertainties of the mass attenuation coefficients, as well as for the uncertainties of concentrations of admixtures to the sample matrix, constant relative uncertainties are assumed.