Determination of independent and cumulative fission product yields with gamma spectrometry
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Fission product yields are vital to nuclear forensics and safeguards missions, especially active interrogation technologies and post-event forensic response. However, there have been limited experimental measurements performed to date, and the majority of the existing data is based on nuclear models. Updates to the nuclear data such as branching ratios have been made over time, the need for new measurements has come to light as datasets are no longer self-consistent and there are significant discrepancies between datasets. A method has been developed to determine independent and cumulative fission product yields using Bayesian inference. The methodology combines gamma-ray spectrometry, nuclide transmutation and burnup modeling, numerical optimization, and Monte Carlo sampling. The developed convex optimization was solved using three solvers: the Nelder-Mead Simplex direct search, the Levenberg-Marquardt algorithm, and Newton’s Method. Sources of uncertainty were treated using sensitivity coefficient estimation with perturbation analysis as well as Monte Carlo sampling to determine uncertainty in the estimated values for fission product yields and produce uncertainty budgets. Each part of the analysis method was verified using controlled data analysis experiments with known results and then validated with two experiments. The Levenberg-Marquardt algorithm is the fastest and most reliable approach to optimization of three algorithms tested, and Monte Carlo sampling better treated uncertainty by explicitly treating correlations between input parameters, accounting for higher-order effects neglected by first-order sensitivity coefficients, and providing entire probability distributions for results. Thermal irradiations were performed at The University of Texas to produce fission products by bombarding naturally enriched U₃O₈ in a thermal neutron field provided by the 1.1 MW TRIGA reactor's thermal pneumatic transfer irradiation facility. Eleven long-lived fission products were identified and quantified using a series of gamma-ray spectra collected of the sample after the end of irradiation. Molybdenum-99 was used as an internal standard to estimate the time-averaged neutron flux incident on the sample, resulting in a value of (2.26 ± 0.24) × 10¹⁰ cm⁻²s⁻¹, which agrees with prior operator experience. Fission product yields for the other ten identified radionuclides were estimated. The results agreed reasonably with literature values. Biases relative to literature values are positive and negative with an average bias of 6.3%, and the absolute relative error is 9.7%, suggesting that no systematic biases or major sources of untreated error were present in the analysis. Scientists at Pacific Northwest National Laboratory irradiated a 220 mg ²³⁵U foil with greater than 99% enrichment in a 14.1 MeV neutron field using a neutron generator and collected list-mode gamma-ray counting data. These data were parsed at The University of Texas to create sets of twenty-minute and twelve-hour gamma-ray spectra that were used to identify and quantify short- and long-lived fission products, respectively. In total, nineteen fission products with half-lives ranging from 3.2 minutes to 64.0 days were studied. The neutron flux of (2.36 ± 0.11) × 10⁸ cm⁻²s⁻¹ was estimated using ⁹⁹Mo as an internal standard, and the determined value was used to calculate fission product yields of the remaining fission products. Determined values differ greatly from literature values; however, literature values for 14.1 MeV neutrons are less studied, especially for short-lived nuclides, and gamma-ray measurements of long-lived fission products are unreliable due to the small number of fissions that occurred during irradiation. Despite the limitations of the data, the results of the analyses are positive and confirm the viability of the developed methodology for further fission product yield analysis, as well as other nuclear data measurements, and application to nuclear forensics and safeguards inverse problems.