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Analysis of SCALE Criticality and Sensitivity Calculations for Reflected HEU Cylinders

The SCALE code package offers multiple nuclear data libraries and sensitivity and uncertainty (S/U) methods supporting and derived from Monte Carlo (MC) transport. The CSAS and TSUNAMI-3D sequences use KENO MC, utilizing either continuous-energy (CE) cross sections or multigroup (MG) cross section libraries. TSUNAMI-3D has two CE calculational methods: the iterated fission probability (IFP) method, and the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method. Previous work has shown poor agreement between CLUTCH and confirmatory direct perturbation calculations in specific applications (e.g., fissionable and polyethylene reflectors). The HEU-MET-FAST-084 (HMF-084) International Criticality Safety Benchmark Evaluation Project evaluation consists of 27 cylindrical highly enriched uranium metal cores with 14 unique reflector materials of 0.5 and 1 in. thicknesses. Included in this list of reflector materials are natural uranium and polyethylene. This work utilized SCALE 6.2.4 models of the HMF-084 evaluation, with additional non-physical configurations to test both the MG bias and CLUTCH functionality across a variety of reflector material thicknesses. The evaluation’s use of concentric cylinders allowed for examination of several MG self-shielding methods: infinite homogenous, cylindrical, and spherical. The results indicate that the use of polyethylene reflectors with CLUTCH is not fundamentally impossible but sensitive to geometry. The poor performance of CLUTCH with fissionable reflectors was reaffirmed. The 2 in. and greater polyethylene-reflected calculations demonstrate the necessity of using the 302-group library for fast systems. The nickel MG bias was substantial, as discussed in a companion paper, as were cobalt and iron.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Extension of the Hauser-Feshbach fission fragment decay model to multichance fission

The Hauser-Feshbach fission fragment decay model, HF 3 D, which calculates the statistical decay of fission fragments, has been expanded to include multichance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input prescission quantities—fission probabilities and the average energy causing fission—and postscission quantities—yields in mass, charge, total kinetic energy, spin, and parity. From these fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions, allowing for the calculation of prompt neutron and γ properties, such as multiplicity and energy distributions, both independent and cumulative fission yields, and delayed neutron observables. Here, we describe the implementation of multichance fission in the HF 3 D model, and show an example of prompt and delayed quantities beyond first-chance fission, using the example of neutron-induced fission on 235 U. This expansion represents significant progress in consistently modeling the emission of prompt and delayed particles from fissile systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Total Radioisotope Yield Calculator

An initial number of fissions on a fissile/fissionable material, defined by ENDF library availability, is used to produce an initial inventory of fission products (FPs). The FPs are decayed using full, analytical solutions to the Bateman equations to calculate the FP inventory at a user-specified time. Output can contain information about activity, mass, dose rate, and gamma-ray intensities based on user-defined parameters, given as .txt or .xlsx file formats. Full execution and display of results takes 5-10 seconds, depending on the complexity of the input parameters.

Holschuh, ThomasV [Idaho National Laboratory (INL)↗

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2

Large-scale models of nuclear structure are currently the only way to provide consistent datasets for the many properties of thousands of exotic nuclei that are required by nucleosynthesis simulations. In [W. Ryssens et al., Eur. Phys. J. A 58, 246 (2022)], we recently presented the new BSkG2 model based on an energy density functional of the Skyrme type. Relying on a flexible three-dimensional coordinate representation of the nucleus, the model takes into account both triaxial deformation and time-reversal symmetry breaking. BSkG2 achieves a state-of-the-art global description of nuclear ground state (g.s.) properties and reproduces in particular the known masses with a root-mean-square (rms) deviation of 678 keV. Moving beyond g.s. properties, the model also reproduces all empirical values for the primary and secondary barriers as well as isomer excitation energies of actinide nuclei with rms deviations below 500 keV, i.e. with unprecedented accuracy. Here we discuss in detail the extension of our framework to the calculation of the fission barriers of 45 actinide nuclei, including odd-mass and odd-odd systems. We focus in particular on the impact of symmetry breaking which is key to the accuracy of the model: we allow systematically for axial, reflection and time-reversal symmetry breaking. The effect of the latter on the fission properties of odd-mass and odd-odd nuclei is small, but we find that allowing for shapes with triaxial or octupole deformation, as well as shapes with both, is crucial to achieving this accuracy. Here, the numerical accuracy of our coordinate space approach, the variety of nuclear configurations explored and the simultaneous successful description of fission properties and known masses makes BSkG2 the tool of choice for the large-scale study of nuclear structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC

Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.

Equilibrium core↗

Sister Rod Destructive Examinations (FY2021) Appendix C: Rod Internal Pressure, Void Volume, and Gas Transmission Tests

As a part of the DOE NE High Burnup Spent Fuel Data Project, Oak Ridge National Laboratory (ORNL) is performing destructive examinations (DEs) of high burnup (HBU) (>45 GWD/MTU) spent nuclear fuel (SNF) rods from the North Anna Nuclear Power Station operated by Dominion Energy. The SNF rods, called the sister rods or sibling rods, are all HBU and include four different kinds of fuel rod cladding: standard Zircaloy-4 (Zirc-4), low-tin (LT) Zirc-4, ZIRLO, and M5. This Appendix C documents the status of the ORNL Phase 1 DE activities [C-2, C-3] related to rod internal pressure and void volume measurement techniques, fission gas stack flow measurements applied to selected sister rods, and fission gas release calculations in Phase 1 of the sister rod test program.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Sister Rod Destructive Examinations (FY22) Appendix C: Rod Internal Pressure, Void Volume, and Gas Transmission Tests

As a part of the DOE NE High Burnup Spent Fuel Data Project, Oak Ridge National Laboratory (ORNL) is performing destructive examinations (DEs) of high burnup (HBU) (>45 GWD/MTU) spent nuclear fuel (SNF) rods from the North Anna Nuclear Power Station operated by Dominion Energy [C-1]. The SNF rods, called the sister rods or sibling rods, are all HBU and include four different kinds of fuel rod cladding: standard Zircaloy-4 (Zirc-4), low-tin (LT) Zirc-4, ZIRLO, and M5. The DEs are being conducted to obtain a baseline of the HBU rod’s condition before dry storage and are focused on understanding overall SNF rod strength and durability. Both fuel rods and empty cladding will be tested to derive material properties. Although the data generated can be used for multiple purposes, one primary goal for obtaining the postirradiation examination data and the associated measured mechanical properties is to support SNF dry storage licensing and relicensing activities by (1) addressing identified knowledge gaps and (2) enhancing the technical basis for post-storage transportation, handling, and consolidation activities. This appendix documents the status of the ORNL Phase 1 DE activities [C-2, C-3] related to rod internal pressure and void volume measurement techniques, fission gas stack flow measurements applied to selected sister rods, and fission gas release calculations in Phase 1 of the sister rod test program.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

238 U PFNS Evaluation Update [Slides]

Experimental 238 U PFNS were reviewed in detail including Chi-Nu PFNS. 7/10 data sets have been accepted. We have performed a detailed UQ using LANL code ARIADNE and templates of expected PFNS measurement uncertainties. we have included Chi-Nu PFNS in experimental data base. The extended Los Alamos model in CoH was used for prior calculation. Multiple chance fission and pre-equilibrium (with exciton model) contributions were modeled.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Sister Rod Destructive Examinations (FY23) Appendix C: Rod Internal Pressure, Void Volume, and Gas Transmission Tests

As a part of the DOE NE High Burnup Spent Fuel Data Project, Oak Ridge National Laboratory (ORNL) is performing destructive examinations (DEs) of high burnup (HBU) (>45 GWD/MTU) spent nuclear fuel (SNF) rods from the North Anna Nuclear Power Station operated by Dominion Energy. The SNF rods, called the sister rods or sibling rods, are all HBU and include four different kinds of fuel rod cladding: standard Zircaloy-4 (Zirc-4), low-tin (LT) Zirc-4, ZIRLO, and M5. The DEs are being conducted to obtain a baseline of the HBU rod’s condition before dry storage and are focused on understanding overall SNF rod strength and durability. Both fuel rods and empty cladding will be tested to derive material properties. Although the data generated can be used for multiple purposes, one primary goal for obtaining the postirradiation examination data and the associated measured mechanical properties is to support SNF dry storage licensing and relicensing activities by (1) addressing identified knowledge gaps and (2) enhancing the technical basis for post-storage transportation, handling, and consolidation activities. This appendix documents the status of the ORNL Phase 1 DE activities related to rod internal pressure and void volume measurement techniques, fission gas stack flow measurements applied to selected sister rods, and fission gas release calculations in Phase 1 of the sister rod test program.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Analysis of SCALE Criticality and Sensitivity Calculations for Reflected HEU Cylinders [Abstract]

The SCALE code package offers several nuclear data libraries to support Monte Carlo (MC) transport, as well as MC-based derivation of $\kappa$ eff sensitivity and uncertainty (S/U) data. The CSAS sequence using the KENO MC code can utilize continuous-energy (CE) cross sections, or pre-generated multigroup (MG) cross section libraries. The use of MG libraries introduces bias into calculations in exchange for faster transport solutions. The TSUNAMI-3D sequence also utilizes KENO MC calculations. TSUNAMI-3D has two CE calculational methods: the Iterated Fission Probability (IFP) method, and the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method. Previous work has shown poor agreement between CLUTCH and confirmatory direct perturbation calculations in specific applications, e.g., fissionable and polyethylene reflectors

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Shedding light on the 239Pu fission source term with new high-precision experiments and advanced fission modeling

In the last decade, there has been a renaissance of fission research resulting in new high-precision experiments and advanced fission modeling. For instance, the Chi-Nu and CEA teams supplied, for the first time, the 239 Pu prompt fission neutron spectrum (PFNS) for broad ranges of incident and outgoing neutron energies. The CEA team also measured 239 Pu average prompt neutron multiplicities, ν ̄ p , with lower statistical uncertainties and a technique significantly different than the one used in the past. The NIFFTE collaboration provided 239 Pu( n ,f)/ 235 U( n ,f) cross section shape ratios with uncertainties below 1% utilizing a novel detector type. Advanced fission event generators were developed, among them CGMF, FIFRELIN, FREYA, and GEF, which calculate post-scission fission observables in a correlated manner. These new experimental data and more consistent fission models change the evaluated PFNS, ν ̄ p , and ( n ,f) cross sections, some only modestly, compared to ENDF/B-VIII.0. In turn, the individual new nuclear data distinctly change simulated effective neutron multiplication factors of fast critical assemblies, but their combined impact is small, while affecting the prediction of LLNL pulsed sphere neutron leakage spectra and reaction rates only within experimental uncertainties. Also, the parameters obtained from fitting to ν ̄ p reproduce various post-scission fission observables within the uncertainties of experimental data. This indicates that new differential experiments and consistent fission modeling reduce compensating errors present in ENDF/B-VIII.0.

fission cross section↗

Destructive PIE and Safety Testing of Six AGR-2 UO 2 Capsule 3 Compacts

The Advanced Gas Reactor (AGR) Fuel Development and Qualification Program’s second irradiation experiment (AGR-2) was irradiated in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL) from June 2010 to October 2013 (Collin 2014). The fuel compacts in this experiment held either tristructural isotropic (TRISO)-coated spherical kernels of uranium oxide (UO2) or TRISO-coated kernels containing both uranium carbide and uranium oxide phases (UCO). There were six separately monitored and controlled capsules in the AGR-2 test train. Capsule 3 held twelve compacts containing UO2-TRISO particles fabricated by BWX Technologies Nuclear Operations Group. The AGR-2 TRISO particles were fabricated in a pilot-scale fluidized-bed chemical vapor deposition (FB-CVD) furnace with a coating chamber inner diameter of 150 mm (Phillips, Barnes, and Hunn 2010), which was a change from the first irradiation experiment (AGR-1) particles that had been coated in a lab-scale FB-CVD coating system with a chamber inner diameter of 50 mm (Lowden 2006). The TRISO particles were overcoated with resinated graphite flake at Oak Ridge National Laboratory (ORNL), and the overcoated particles were pressed into one-inch-long, half-inch-diameter cylinders (Hunn, Montgomery, and Pappano 2010). Each cylindrical compact held an average of 1,543 TRISO particles with 9.6% enriched UO2 kernels that had a nominal diameter of 500 μm (Hunn, Savage, and Silva 2012). Capsule 3 compacts were irradiated to average calculated burnups of 9.01–10.69% fissions per initial metal atom (FIMA), and the average calculated fluences of fast neutrons with energies E n > 0.18 MeV were 3.05–3.53×10 25 n/m 2 (Sterbentz 2014). The calculated time-average, volume-average Capsule 3 compact temperatures were 996–1,062°C. However, Capsule 3 compact temperatures varied several hundred degrees across each compact, and the timeaverage minimum (TA min ) and time-average maximum (TA max ) temperatures were between 889–999°C and 1,072–1,105°C, respectively (Hawkes 2014). After irradiation, the AGR-2 test train was transferred from ATR to the INL Materials and Fuels Complex for inspection and disassembly (Ploger, Demkowicz, and Harp 2015). The initial inspection included dimensional metrology of the compacts and graphite fuel holders. Like all the AGR-2 compacts, the compacts in Capsule 3 shrank slightly during irradiation, as expected, with an average length reduction of 1.07–1.24% and an average diameter reduction of 0.13–0.41%. Post-irradiation examination (PIE) of the capsule components was completed to measure select fission products ( 90 Sr, 110m Ag, 134 Cs, 137 Cs, 144 Ce, and 154 Eu) outside the compacts (Stempien and Demkowicz 2020). This involved gamma counting of the graphite and graphoil spacers at the top and bottom of each capsule, acid leaching for radiochemical analysis of fission products on the metallic capsule components, and burn-leach analysis of the graphite holders. The total amount of 110mAg measured on the Capsule 3 components was 13% of the calculated capsule inventory. This was significantly lower than the amount of 110m Ag measured on the three UCO capsule components, which ranged from 32–70%. The lower 110m Ag release in Capsule 3 was likely due to lower peak temperatures compared with the UCO fuel capsules (Hawkes 2014). Measured inventories of the other select fission products were also lower in Capsule 3.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Primary fission fragment mass yields across the chart of nuclides

In this work, we have calculated a complete set of primary fission fragment mass yields, Y(A), for heavy nuclei across the chart of nuclides, including those of particular relevance to the rapid neutron capture process (r process) of nucleosynthesis. We assume that the nuclear shape dynamics are strongly damped, which allows for a description of the fission process via Brownian shape motion across nuclear potential-energy surfaces. The macroscopic energy of the potential was obtained with the Finite-Range Liquid-Drop Model (FRLDM), while the microscopic terms were extracted from the single-particle level spectra in the fissioning system by the Strutinsky procedure for the shell energies and the BCS treatment for the pairing energies. For each nucleus considered, the fission fragment mass yield, Y(A), is obtained from 50 000 to 500 000 random walks on the appropriate potential-energy surface. The full mass and charge yield, Y(Z,A), is then calculated by invoking the Wahl systematics. With this method, we have calculated a comprehensive set of fission-fragment yields from over 3800 nuclides bounded by 80 ≤ Z ≤ 130 and A ≤ 330; these yields are provided as an ASCII formatted database in the Supplemental Material. We compare our yields to known data and discuss general trends that emerge in low-energy fission yields across the chart of nuclides.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

β — -delayed fission in the coupled quasiparticle random-phase approximation plus Hauser-Feshbach approach

Beta-delayed neutron emission and β-delayed fission (βdf) probabilities were calculated for heavy, neutronrich nuclei using the Los Alamos coupled quasiparticle random-phase approximation plus Hauser-Feshbach (QRPA + HF) approach. In this model, the compound nucleus is initially populated by β decay and is followed through subsequent statistical decays taking into account competition among neutrons, γ rays, and fission. The primary output of these calculations includes branching ratios along with neutron and γ -ray spectra. Here, we find a relatively large region of heavy nuclides where the probability of βdf is near 100%. For a subset of nuclei near the neutron drip line, delayed neutron emission and the probability of fission are both large, which leads to the possibility of multichance βdf (mc-βdf). We comment on prospective neutron-rich nuclei that could be probed by future experimental campaigns and provide a full table of branching ratios in ASCII format in the Supplemental Material for use in various applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Covariant density functional theory input for r-process simulations in actinides and superheavy nuclei: The ground state and fission properties

A systematic investigation of the ground-state and fission properties of even-even actinides and superheavy nuclei with Z = 90–120 from the two-proton up to two-neutron drip lines with proper assessment of systematic theoretical uncertainties has been performed for the first time in the framework of covariant density functional theory (CDFT). Furthermore, these results provide a necessary theoretical input for the r-process modeling in heavy nuclei and, in particular, for the study of fission cycling. Four state-of-the-art globally tested covariant energy density functionals (CEDFs), namely, DD-PC1, DD-ME2, NL3*, and PC-PK1, representing the major classes of the CDFT models are employed in the present paper. Ground-state deformations, binding energies, two-neutron separation energies, α-decay Q α values and half-lives, and the heights of fission barriers have been calculated for all these nuclei. Theoretical uncertainties in these physical observables and their evolution as a function of proton and neutron numbers have been quantified and their major sources have been identified. Spherical shell closures at Z = 120, N = 184, and N = 258 and the structure of the single-particle (especially, high-j) states in their vicinities as well as nuclear matter properties of employed CEDFs are two major factors contributing to theoretical uncertainties. However, different physical observables are affected in a different way by these two factors. For example, theoretical uncertainties in calculated ground-state deformations are affected mostly by the former factor, while theoretical uncertainties in fission barriers depend on both of these factors.

190 ≤ A ≤ 219↗

Modeling fission dynamics at the barrier in a discrete-basis formalism

A configuration-interaction model is presented for the barrier region of induced fission. The configuration space is composed of seniority-zero configurations constructed from self-consistent mean-field wave functions. The Hamiltonian matrix elements between configurations include diabatic and pairing interactions between particles. Other aspects of the Hamiltonian are treated statistically, guided by phenomenological input of compound-nucleus transmission coefficients. In this exploratory study the configuration space is restricted to neutron excitations only. A key observable calculated in the model is the fission-to-capture branching ratio. We find that both pairing and diabatic interactions are important for achieving large branching to the fission channels. In accordance with the transition-state theory of fission, the calculated branching ratio is found to be quite insensitive to the fission decay widths of the pre-scission configurations. Furthermore, the barrier-top dynamics appear to be quite different from transition-state theory in that the transport is distributed over many excited configurations at the barrier top.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Update of the Cesium-136 Cumulative Fission Yields at Multiple Neutron Energies

Nuclear data is foundational to several fields, including nuclear forensics. Nuclear forensics investigations of fission events, relies heavily on the cumulative fission yields, however several highly useful fission products suffer from very poor nuclear data including cumulative fission yields or associated uncertainties in that value. Cesium-136 is a highly relevant example of this issue, where the cumulative fission yield may be accurate but its uncertainty high enough to preclude its usefulness. In this work we evaluate and calculate an updated cumulative fission yield for 136 Cs for 235 U, 238 U, and 239 Pu at multiple neutron energies or sources using data obtained from irradiation campaigns. In all cases these newly determined cumulative fission yields provided small changes to the actual fission yields but had dramatic improvements to the uncertainty in those yields. These improvements in uncertainty will enable nuclear forensics end users to use 136 Cs data with more confidence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

CONFLUX: A standardized framework to calculate reactor antineutrino flux

Nuclear fission reactors are abundant sources of antineutrinos for neutrino physics experiments. The flux and spectrum of antineutrinos emitted by a reactor can indicate its activity and composition, suggesting potential applications of neutrino measurements beyond fundamental scientific studies that may be valuable to society. The utility of reactor antineutrinos for applications and fundamental science is dependent on the availability of precise predictions of these emissions. For example, in the last decade, disagreements between reactor antineutrino measurements and models have inspired revision of reactor antineutrino calculations and standard nuclear databases as well as searches for new fundamental particles not predicted by the Standard Model of particle physics. Past predictions and descriptions of the methods used to generate them are documented to varying degrees in the literature, with different modeling teams incorporating a range of methods, input data, and assumptions. The resulting difficulty in accessing or reproducing past models and reconciling results from differing approaches complicates the future study and application of reactor antineutrinos. The CONFLUX (Calculation Of Neutrino FLUX) software framework is a neutrino prediction tool built with the goal of simplifying, standardizing, and democratizing the process of reactor antineutrino flux calculations. CONFLUX includes three primary methods for calculating the antineutrino emissions of nuclear reactors or individual beta decays that incorporate common nuclear data and beta decay theory. The software is prepackaged with the current nuclear databases, including ENDF.B/VIII, JEFF-3.3, and ENSDF, and it includes the capability to predict time-dependent reactor emissions, adjust nuclear database or beta decay inputs/assumptions, and propagate related sources of uncertainty. Here, this paper describes the CONFLUX software structure, details the methods used for flux and spectrum calculations, and provides examples of potential use cases.

Zhang, Xianyi [Lawrence Livermore National Laborat↗