On the Numerical Method for Photofission-Based Nuclear Material Isotopic Composition Estimation in Thorium-Uranium Systems

Past studies validated the feasibility of the photofission reaction ratio (PFRR) method using both Gaussian and bremsstrahlung photons to estimate the isotopic composition of nuclear fuel materials without relying on their self-generated neutron information. However, the current PFRR method cannot solve a multinuclide system with more than two nuclides because the instability of the inverse matrix increases with the addition of the number of nuclides. Thus, this research proposes a numerical method for solving the simultaneous equations of a three-nuclide system onto PFRR to estimate the isotopic composition of nuclides. The results show good reproducibility with all cases maintained within a 10% isotopic composition difference except cases 6 and 7 of the first two photon energy combination schemes with maximum composition differences of 15.6% and 13.9% for 10% actual composition, respectively. A 20% actual composition of case 5 for the second photon energy combination scheme has a deviation of 10.6%, which is slightly larger than the 10% composition difference too. Out of three photon energy combination schemes, 6 MeV – 6.5 MeV – 11 MeV has the highest coefficient of determination for all three nuclides and the smallest deviation of below 10% composition difference. Random sampling with normal distribution was performed on the loss to photofission particles from MCNP with 200 sets for each 10 cases on the 6 MeV – 7 MeV – 11 MeV photon energy combination to study the stochastic errors. The isotopic compositions were calculated with the same numerical method, and the difference between the estimated and actual compositions that resulted were fitted with R. The fitting results show good agreement within 91.5% confidence intervals.