Modeling and determination of radionuclide concentrations by using matrix algebra

A mathematical procedure is presented which will set up a model to determine concentrations and Working Levels of radon and thoron daughters. By using simple operational matrices the model can be easily developed. Each matrix represents an instrument dependent or independent function. In this way, parameters such as conversion factors, efficiencies, plate-out, spectrum overlaps, etc., can be simply incorporated. The resulting model is in the form which can be implemented on a small computer. The model is then solved utilizing a matrix version of the least squares method for solving a system of equations. At this point standard numerical analysis on the solution can be done to optimize parameters such as sensitivity to individual radionuclide concentrations. One example is given; an alpha spectroscopy determination of radon thoron daughter concentrations. The method can be expanded to include beta counting methods and other radionuclide analysis