Maximum Likelihood Spectrum Decomposition for Isotope Identification and Quantification

A spectral decomposition method has been adapted to identify and quantify isotopic source terms in high resolution gamma-ray spectroscopy in scenarios with static geometry and shielding. Monte-Carlo simulations were used to build the response matrix of a shielded high purity germanium detector monitoring an effluent stream with a Marinelli configuration. The decomposition technique was applied to a series of calibration spectra taken with the detector using a multi-nuclide standard. These results are compared to decay corrected values from the calibration certificate. For most nuclei in the standard ($^{241}$Am, $^{109}$Cd, $^{137}$Cs, and $^{60}$Co) the deviations from the certificate values were generally no more than $6$\% with a few outliers as high as $12$\%. For $^{57}$Co the deviations from the standard reached as high as $25$\%, driven by the very low statistics of the source's presence in the calibration spectra. Additionally, a full treatment of error propagation for the technique is presented.