The role of covariance in the analysis of gamma-ray spectra

When a gamma-ray spectrum contains a number of photopeaks originating from the same nuclide, the calculation of nuclide activity depends not only on the values of, and uncertainties in, the photopeak areas, photopeak efficiencies, gamma-ray emission probabilities and peak area correction factors, but also on the correlations that exist between these quantities. When photopeaks corresponding to a group of nuclides overlap or are unresolved, simultaneous estimation of the activities of all the nuclides present in the group is necessary if the information contained in the spectrum is to be used efficiently — a procedure which can prove important when the only prominent photopeak associated with a nuclide of interest overlaps with the photopeak of another nuclide. Two procedures for activity estimation are described: both procedures take correlations into account; one procedure deals with the special case of activity estimation for a single nuclide, where unresolved photopeaks are absent or neglected; the other procedure deals with simultaneous activity estimation using all the photopeaks associated with an interrelated group of nuclides.