Application of the Monte Carlo - Library Least-Squares (MCLLS) Approach to Nuclear Threat Monitoring
Transactions of the American Nuclear Society, Vol. 101, pp. 329-330 (2009)
The Monte Carlo – Library Least-Squares (MCLLS) approach was developed for two non-linear radioanalyzer techniques; the energy dispersive X-ray fluorescence (EDXRF) and prompt gamma-ray neutron activation (PGNA) analysis [1-4] techniques. These two techniques yield X- or gamma-ray spectra, respectively, that are not only functions of the amounts of the individual elements that are present, but are also functions of the amounts of all other elements present in the sample of interest. The experimental approach that can be used in these cases to analyze for the amount of an element in a sample is to obtain the photon spectrum before and after the addition of a known amount of the element of interest. This approach is called standard addition (or spiking). The disadvantages of this approach is that a “spike” must be added to the original sample separately for every element of interest and it involves the subtraction of one large set of numbers from another. While a number of mathematical inverse approaches have been developed to replace this experimental technique we believe the most accurate is the MCLLS approach. It consists of precalculating by Monte Carlo a number of cases that are close enough to the sample of interest that one can use first-order (linear) extrapolation methods to iterate to the correct answer.