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DOE OSTI2021

Making sense of uncertain nuclear data

At its core, and in an imperfect world, the scientific method relies heavily on the concept of uncertain knowledge. Understanding the nature and magnitude of our lack of knowledge on nuclear data has important ramifications on a wide range of nuclear technologies that encompass defense, energy, medicine, astrophysics, among others. Over the span of a long and fruitful carrier, Dr. Massimo Salvatores has made significant contributions to the fields of nuclear reactor physics, nuclear data, and uncertainty quantification and propagation. Advances in machine learning techniques and computational capabilities are enabling a new level of confidence in our ability to predict key nuclear metrics as well as their associated uncertainties across many applications. Here this short article reviews some of those concepts with an eye towards developing a new paradigm to provide nuclear data libraries of benefit to various applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Nuclear Data Sensitivity/Uncertainty Studies of Tantalum-Reflected Systems

Tantalum (Ta) is a refractory metal with high melting point and high corrosion resistance. This makes it useful as a mold material for plutonium casting operations. Unfortunately, there are few criticality benchmarks with high nuclear data sensitivities. Given that, it is desirable to design new experiments to provide additional validation data for nuclear criticality safety, which is the objective of the Thales project. Multiple application models were used to represent process conditions (either normal conditions or credible upset conditions) both at Los Alamos National Laboratory (LANL) and Savannah River Site (SRS). A total of 40 application models were obtained. Given this, it was useful to down-select the number of needed application models. This work documents the down-selection based on several nuclear data sensitivity/uncertainty metrics. In addition to showing the result of the specific down-selection used for the Thales project, this work discusses potential ways to represent a large number of application models with a smaller number of proposed experiment designs.

42 ENGINEERING↗
DOE OSTI2021

Which nuclear data can be validated with LLNL pulsed-sphere experiments? [Slides]

LLNL pulsed sphere are a very valuable experiment series to validate scattering and fission nuclear data. It would be great if they could be evaluated as benchmarks and make it into SINBAD! We see potential issues in ENDF/B-VIII.0 6 Li, 12 C, 16 O, 24- 26 Mg, 27 Al, 48 Ti, 56 Fe, and 208 Pb nuclear data. Good agreement is found with 1,2 H, 7 Li, 9 Be, 14 N, 235,238 U, and 239 Pu nuclear data.

16O and 12C Spheres↗
DOE OSTI2025

Machine Learning to Select Experiments Driven by Fundamental Science and Applications for Targeted Nuclear Data Improvement

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in 239 Pu nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to 239 Pu fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate 63 Cu and 239 Pu total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with Al 2 ⁢O 3 and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Overview of Nuclear Data Measurement and Analysis at RPI [Slides]

This presentation discusses the experimental, simulation, and nuclear data methods that were validated for the RPI γ-Multiplicity Detector. When the neutron capture γ-cascade data is well-known, the γ-emission spectra can be accurately calculated using the modified simulation tools. The RPI γ-Multiplicity Detector system is now ready for analysis and recommendations for isotopes with deficiencies in γ-ray data. The presentation also discusses future work which includes developing a method for analyzing and adjusting nuclear data for 59 Co, 55 Mn and other measured isotopes including 181 Ta. Additionally, future work includes comparing experimental γ-emission spectra with MCNP-6.2/DICEBOX simulations for 238 U and 235 U. In summation, new capture and transmission measurements for 54 Fe will help improve resonance parameter evaluation. Neutron capture gamma cascade spectra and yields were measured in the resolved resonance region and compared to evaluations. In addition, the pulsed neutron die-away method was developed as a tool to provide data for validation of TSLs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Consistent Nuclear Data Evaluations for Criticality Safety

Evaluations of nuclear data are based on statistical analysis of available experimental data and their uncertainties plus model calculations and their uncertainties. As the models are currently rather limited, the evaluations are heavily biassed toward experimental data, with the caveat that a thorough analysis is also required to understand possible discrepancies between data sets. Hence, as new experimental data become available, they are incorporated into the evaluation procedure. Recent measurements of the 233 U capture to fission cross section ratio at the Los Alamos Neutron Science Center have prompted a re-evaluation of the capture cross section in the resonance and fast regions up to 250 keV. We will discuss the challenges of including the new fast neutron experimental data in an evaluation that is consistent with the resonance region. We will also discuss our consistent evaluation procedure based on the Hauser-Feshbach statistical model for nuclear reactions and its application to the evaluations of 239 Pu and 139 La neutron-induced reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Nuclear Data Impact Assessment for the HTR-10 Pebble-Bed Reactor Using SCALE

The HTR-10 was used as a representative pebble-bed high-temperature gas-cooled reactor in this assessment of nuclear data’s impact on important reactor and spent fuel metrics, including safety-related quantities such as the effective multiplication factor (k eff ), temperature reactivity feedback, spent fuel inventory, and decay heat. Using the SCALE code system tools and ENDF/B-VII.1 nuclear data libraries, we quantify the effect of nuclear data uncertainties on these key performance metrics for both fresh fuel and equilibrium core configurations. For reactor core key parameters, important contributors to uncertainty include reactions of 235 U [$\bar{v}$, fission, (n, γ)], 238 U [elastic, (n, γ)], and graphite [elastic, (n, γ)]. Additional important contributors for the equilibrium core include reactions of higher actinides ( 239 Pu, 240 Pu) and fission products ( 135 Xe, 149 Sm). For spent fuel analysis, most nuclide inventory uncertainties remain below 5%. Higher uncertainties up to 11% are being observed for minor actinides like 243 Am and 244 Cm. Additionally, fission product uncertainties in 155 Eu and 155 Gd, of 25% and 23% respectively, are also significant and have implications for burnup credit applications. 110m Ag also shows high uncertainty of up to 11%, mainly due to fission product yield uncertainties. Decay heat relative uncertainties remain below 0.6% up to 10 years’ cooling time after fuel discharge. The highest relative uncertainty of 1.5% occurs at 500 years of cooling; however, because the decay heat value is very low at that time, the absolute uncertainty is not significant. This work demonstrates that extending assessments beyond fresh fuel k eff to include irradiated cores, nuclide inventories, and decay heat is essential in understanding the behavior of uncertainties as a function of fuel burnup and can support improvements of safety margins and spent fuel management.

Nuclear data impact↗
DOE OSTI2020

Relevant Advanced Reactor Benchmarks for Nuclear Data Assessment

Advanced reactor concepts currently being developed throughout the industry are significantly different from light water reactor (LWR) designs with respect to geometry, materials, and operating conditions, and consequently, with respect to their reactor physics behavior. Given the limited operating experience with non-LWRs, the accurate simulation of reactor physics and the quantification of associated uncertainties are critical for ensuring that advanced reactor concepts operate within the appropriate safety margins. Nuclear data are a major source of input uncertainties in reactor physics analysis. As part of an ongoing project at Oak Ridge National Laboratory, the effects of nuclear data uncertainties on key figures of merit associated with advanced reactor safety are being assessed for selected advanced reactor technologies. Key nuclear data relevant for reactor safety analysis for each selected advanced reactor technology were identified in Phase 1, and their impact on important key figures of merit was assessed in Phase 2. This report describes the outcome of Phase 3. Available benchmarks and fuel irradiation data for use in evaluating the impact of uncertainties and gaps in nuclear data that impact reactivity control for advanced reactor designs through the fuel cycle were identified and assessed. Benchmarks were identified by searching (1) the Organisation for Economic Co-operation and Development (OECD)/Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (IRPhEP) handbook, (2) the OCED/NEA International Reactor Physics Experiment Evaluation Project (IRPhEP) handbook, (3) ongoing OECD/NEA benchmark activities, and (4) documentation in public literature. Relevant benchmarks were identified by selecting reactors with geometry, materials, and neutron energy spectra similar to those of selected advanced reactor technologies. This assessment identified six benchmarks, of which three are experimental and three are purely computational. One experimental and one computation benchmark contain depleted fuel; all others are limited to fresh fuel. This report provides short descriptions of the selected benchmarks along with the availability of measured data for comparison.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Nuclear Data Sheets for A=98

Experimental spectroscopic data on nuclear structure and decay are evaluated for known nuclides of mass 98 (Br, Kr, Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In). Detailed evaluation results of individual reactions and decays are presented together with the Adopted values that are recommended for level properties, γ and β radiations, and other spectroscopic information. 98 Mo remains as the most extensively studied nuclide via various reactions and decays. Level schemes of Sr, Y, Zr, Tc, and Pd nuclides in this mass chain are also well established to date; while Kr, Rb, Nb, Ag and Cd are amongst the least-studied ones for excited states, with only limited data available for each. On the neutron-rich side, 98 Br has been identified in the 9 Be(238U,F) reaction, but no spectroscopic data are yet available, while for 98 In on the proton-rich side, only the ground state and an isomer are known with half-lives measured but their spin-parities and the absolute level energy of the isomer yet to be determined. While 98 Ru and 98 Rh have also been extensively studied, large discrepancies exist between the high-spin sections of the proposed level schemes in different measurements, and these need to be clarified and resolved with further experimental investigations to improve the currently-adopted ones, which have been selected from the measurements with higher statistics, considering no other criteria of preference. Furthermore, this work supersedes all the earlier evaluations of A=98 (2003Si07, 1998Si18, 1992Si21, 1983Mu21, 1974Me34).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Advancing the Theory of Nuclear Data Evaluations [Abstract]

We present recent advances in the R-matrix formalism as well as the Bayesian evaluation framework for improved nuclear data evaluations. The advances in the R matrix formalism include: 1) direct processes, 2) doorway, as well as multistep, processes, and 3) various forms of the Reich-Moore approximation for eliminated capture channels. Furthermore, to address unreasonably small posterior uncertainties often encountered in nuclear data evaluations of large data sets using the conventional form of the Bayes’ theorem, we introduce imperfections (of the data or the model) as a formal evaluation tool for taming the evaluated uncertainties in harmony with Bayes’ theorem. These theoretical advances were motivated by the nuclear data evaluations of differential resolved resonance cross section data using the code SAMMY, as well as the integral benchmark experiments using the SCALE code system, being performed at Oak Ridge National Laboratory for the Nuclear Criticality Safety Program. Some pedagogical applications of the new formalism, as well as a snapshot of the SAMMY modernization efforts, will be presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Nuclear data for space exploration

Understanding the harmful effects of galactic cosmic rays (GCRs) on space exploration requires a substantial amount of nuclear data. Specifically, the interaction of energetic GCR charged particles with spacecraft materials generates secondary radiations that, through energy deposition, can harm astronauts and electronic systems. By identifying the gaps in our knowledge of the relevant nuclear data—such as interaction cross sections—and identifying ways to fill those gaps—with measurements, compilations, evaluations, dissemination, reaction modeling, sensitivity studies, and uncertainty quantification—the safety and viability of space exploration can be improved. This work surveys the state of the art in this interdisciplinary field and identifies promising collaborative research topics that have significant potential to advance our understanding of the effects of the space radiation environment on space exploration.

42 ENGINEERING↗
DOE OSTI2022

Nuclear data uncertainty quantification for the nuclide inventory of a Calvert Cliffs spent fuel sample

The impact of nuclear data cross section uncertainties and covariance matrices on the nuclide vector of spent nuclear fuel was investigated; This exercise was carried out for the Calvert Cliffs fuel assembly D047 benchmark available in the SFCOMPO database. Sample P irradiated in rod MKP109 for 4 cycles up to a burnup of approximately 44 GWd/MTU was selected for the analysis. Nuclear data uncertainties were taken from the most recent libraries released by evaluation projects JEFF, ENDF/B and JENDL, and were propagated using the SANDY code via a stochastic sampling approach. This paper provides a quantification of the uncertainty on the concentration of several actinides and fission products relevant for spent fuel management. Uncertainties generally below 5 % were predicted for the concentrations of most of the uranium, neptunium and plutonium isotopes relevant for SNF applications. Curium isotopes carry larger uncertainties that might exceed 10 %. The contribution of cross section uncertainties on the concentrations of fission products was found to be marginal with the exception of a few nuclides. These results can be significantly affected by the lack of evaluated covariance matrices for the capture cross section of several fission products. Burnup tracers such as {sup 148}Nd and {sup 137}Cs have negligible uncertainties because of the power normalisation imposed in every stochastic calculation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Bayesian Monte Carlo Evaluation Framework for Imperfect Nuclear Data

Bayesian evaluation of resolved resonance region (RRR) nuclear data has historically been carried out using the generalized least squares (GLS) formalism, as implemented in, e.g., SAMMY. We have recently developed a prototype of Bayesian Monte Carlo (BMC) evaluation framework, implemented using a Markov Chain Monte Carlo (MCMC) method with a Metropolis-Hastings (MH) acceptance criterion. This was done in order to remove the approximations underlying the conventional GLS evaluations, namely, the linear approximation, and the approximation that all probability density functions (PDFs) are of the normal kind. Recent works by others have used similar stochastic approaches to quantify cross section uncertainties from ENDF evaluated co-variances, and/or, from integral benchmark data, but those have not been conceived as an evaluation framework like the one presented here.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

The Role of Nuclear Data Sensitivities in Prompt α-Eigenvalue Predictions of Delayed Critical Benchmarks

Alpha (α) eigenvalues, which describe the logarithmic time derivative of the neutron population in a multiplying system, are integral to time-dependent behavior and diagnostic applications. However, uncertainties in the evaluated nuclear data can significantly impact the accuracy of transport simulations for such quantities. This work explores the use of machine learning models to predict two key outputs, α-eigenvalues and keff bias, using input features derived from α-eigenvalue sensitivities to nuclear data. The criticality safety benchmark models used in this study come from the International Handbook of Evaluated Criticality Safety Benchmark Experiments. Three models, random forest, XGBoost, and NGBoost, are trained on both energy-resolved and energy-summed α sensitivities. For the α-eigenvalue bias prediction, NGBoost achieved the highest R 2 (0.9476) using energy-resolved features, while XGBoost performed best using summed sensitivities. In contrast, when predicting the keff bias, all the models showed moderate predictive capability (best R 2 ≈ 0.72), as the mapping from the static α-sensitivities to the static keff bias was less direct. SHAP (SHapley Additive exPlanations) analysis was used to interpret the model predictions. Across both prediction tasks, the features associated with neutron capture [H-1 (n, γ)], uranium scattering reactions (such as 235 U elastic/inelastic), and actinide capture/fission reactions (such as 239 Pu and 234 U) were consistently identified as the most impactful. This highlights the key role of specific nuclear reactions and energy ranges in shaping both time-dependent and steady-state criticality behavior. These results demonstrated that α-sensitivities, despite being computed for time-dependent metrics, can provide valuable insights for predicting both α-eigenvalues and the keff bias. Moreover, machine learning models offer a promising pathway for uncovering important nuclear data dependencies and guiding future data evaluation efforts.

Nuclear data↗
DOE OSTI2023

Nuclear Data for Spallation Neutron Radioisotope Production (Final Technical Report)

Over 50 million nuclear medicine procedures are performed annually, leading to a multi-billion dollar market for radioisotope production. The demand for new medical and research isotopes is growing, and radioisotope supply is insufficient. Most radioisotope production today utilizes charged particle or low-energy neutron irradiation of a target. Isotope production with tens to hundred MeV incident energies is a relatively unexplored option. There is a tremendous opportunity associated with a growing number of suitable domestic and international facilities buttressed by hundred million dollar global investments (e.g., the Los Alamos and Brookhaven Isotope Production Facilities, the European Spallation Source in Lund, and the Korean Multi-purpose Accelerator Complex in Gyeongbuk). In part due to a lack of supporting nuclear data that would make modeling radioisotope yields and purities possible, these facilities do not utilize their high-energy neutron fluxes for isotope production. This project attempted to measure neutron reaction excitation functions relevant to the large-scale production of critical radioisotopes, enabling development of cost-efficient isotope production methods, contributing to the improvement of theoretical models, and enhancing the value of national isotope production facilities. Reactions which form 67 Cu, 32 Si, and alpha-emitting isotopes like 225 Ac were chosen for their consistent prioritization by expert panels, representation of diverse reaction mechanisms, and relative lack of supporting nuclear data. Accurate measurement of these data is presently made only using quasi-monoenergetic neutron beams, which are produced by bombarding thin lithium targets with protons at only a few laboratories in the world. Ultimately, the projects efforts were incompletely accomplished due to a combination of multi-year technical issues at the only laboratory in the world which can make the proposed measurements, iThemba Labs in South Africa, and the onset of a global pandemic, which precluded the significant effort and time required to develop an independent measurement capability in the United States.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗