The gamma-ray data analysis methodology originally developed for the MGA code to determine the relative detection efficiency curve may also be used to determine the relative amounts of the isotopes being measured. This analysis approach is based on the fact that the intensity of any given gamma ray from a sample is determined by the amount of the emitting isotope present in the sample, the emission probability for the gamma ray being measured, the sample self attenuation, the attenuation due to absorbers between the sample and detector, and the detector efficiency. An equation can be written that describes a measured gamma-ray peak intensity in terms of these parameters. By selecting appropriate gamma-ray peaks from the isotopes of interest, we can solve a set of equations for the values of the parameters in any particular measurement including the relative amounts of the selected isotopes. The equations representing the peak intensities are very nonlinear and require an iterative least squares method to solve. We have developed software to ensure that during the iterative process the parameters stay within their appropriate ranges and converge properly in solving the set of equations under various measurement conditions. We have utilized and reported on this approach for determining the plutonium isotopic abundances in samples enriched in Pu-238 and to determine the U-235 enrichment of uranium samples in thick-walled containers. Recently, we have used this approach to determine the plutonium isotopic abundances of plutonium samples in thick-walled containers. We will report on this most recent application, and how this general approach can be adapted quickly to any isotopic analysis problem.
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