Composition analysis of large samples with PGNAA using a fixed point iteration.

Abstract

The composition problem in large sample prompt gamma neutron activation analysis (PGNAA) is a nonlinear inverse problem. The basic form of the nonlinear inverse composition problem is presented. This problem is then formulated in a general way, as a fixed point problem, without addressing any specific application or sample type or linearization approach. This approach of formulating the problem as a fixed point problem suggested a natural fixed point iteration. The algorithm of the fixed point iteration solves the nonlinear composition problem using a combination of measured and computed data. The effectiveness of the fixed point iteration for composition analysis is demonstrated using purely numerical experiments. These numerical experiments showed that the fixed point iteration can be successfully applied to find the bulk composition of large samples, with excellent agreement between the estimated and true composition of the samples, in a few iterations, independent of the initial guess. In order to test the fixed point iteration using real experimental data, a series of large sample PGNAA measurements were performed at ANL-W. These experiments are described and the measured spectra for the samples are presented. Then, the fixed point iteration is applied for these real experiments to find the composition of the samples. In all of the cases, except borated polyethylene, the composition of the large samples are found in a few iterations with errors less than +/-1.3%. The effectiveness of the fixed point iteration is thus demonstrated with many proof-of-principle measurements. While testing the fixed point iteration algorithm, published values of the source spectrum and relative detector efficiencies are used. The sensitivity of the fixed point iteration to source spectrum is investigated and it is shown that the estimated composition results are not very sensitive to the change in the source spectrum. The reason behind the slow convergence for the borated polyethylene sample is also investigated and it is shown that the convergence is slow because of the presence of clean polyethylene in the experiment.