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Templates of expected measurement uncertainties for total neutron cross-section observables

This paper provides a template of expected uncertainties and correlations for measurements of total neutron cross-section observables by transmission. Measurements with time-of-flight and mono-energetic neutron sources are covered. The information required for evaluations in the resonance region and high energy region is detailed, along with the template of uncertainties and correlations that can be used in the absence of other information.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Measurement of the 73 As ⁢(𝑛,𝛾) cross section at thermal neutron energies

A measurement of the thermal neutron capture cross section of 73 As (t 1/2 = 80.3 d) was performed utilizing the University of Missouri Research Reactor. Two sealed quartz tubes containing 73 As were prepared and characterized before being irradiated for ≈1 week. The resulting production of 74 As was quantified with γ-ray spectroscopy. Monitor foils of Fe, Zr, and Mo were irradiated alongside the 73 As samples to assess the thermal and resonance region neutron fluxes. In conclusion, the thermal 73 As ⁢(𝑛,𝛾) cross section was determined to be 56.1 ± 8.9 b based on the average of the two 73 As samples and represents the first neutron-induced reaction cross section measured on 73 As.

and nuclear chemistry↗

Bayesian Monte Carlo Evaluation of Imperfect (n, 233 U) Data and Model

Conventional nuclear data evaluation methods using generalized linear least squares make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate to minimize the cost function (even for nonlinear models); the model (e.g., of neutron cross section) and experimental data (including covariance data) are without defect and prior PDFs of parameters and measured data are known perfectly. Neglect of covariance between model parameters and measured data in conventional evaluations contributes to imperfections. These assumptions are inherent to the generalized linear least squares minimization method commonly used for resolved resonance region neutron cross section evaluations but are often not justified due to the presence of non-normal PDFs, nonlinear models (e.g., R-matrix formalism), and inherent imperfections in data and models (e.g., imperfect covariance data). Here, these assumptions are removed in a mathematical framework of Bayes’ theorem, which is implemented using the Metropolis-Hastings Monte Carlo method. Most importantly, new parameters are introduced to parameterize discrepancies between the theoretical model and measured data to quantify judgement about discrepancies or imperfections in a reproducible manner. An evaluation of 233U in the eV region using the ENDF-B/VIII.0 library and transmission data (Guber et al.) is presented, and posterior parameters are compared to those obtained by conventional evaluation methods. This example illustrates the effects of removing the most harmful assumption: that of model-data perfection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Investigating Gadolinium-Lined Sodium-Iodide Neutron Detectors for Mobile Applications

For enhancing the effectiveness of nonproliferation efforts in neutron detection, most portable instruments rely on 6 Li scintillators, 10 B-based detectors, or gas-filled 3 He proportional counters. Additionally, gamma-ray detectors based on scintillators and semiconductors are often employed for search applications to find radioactive material in the field. These systems typically include dedicated detectors along with separate high voltage supplies and processing electronics for the gamma-ray and neutron detectors. Ideally, a portable radiation detection system should be lightweight, compact, and cost-effective. In the field, scintillators can serve a dual purpose: (1) detecting gamma-rays and (2) detecting neutrons. Gamma-ray detection with scintillators is based on the interaction of gamma-rays within the scintillating material, whereas neutron detection depends indirectly on neutron capture events. These capture events generate conversion electrons and gamma-rays, which can interact with the scintillator. For enhancing neutron capture, the scintillator can be surrounded by neutron absorber materials with a high neutron cross section. The resulting secondary electrons and gamma-rays from neutron interactions, depending on the absorber material used, can then be analyzed to detect the presence of neutron sources. Similarly, semiconductor-based detectors can be employed along with neutron absorbers as liners for neutron detection. 158 Gd has a significantly larger neutron cross section than 3 He, commonly used in gas-filled proportional counters, as shown in Figure 1. For thermal (0.025 eV) neutrons, the absorption cross section of 158 Gd is 10,000 times greater than that of 3 He (refer to Figure 1). This feature makes naturally occurring gadolinium, which consists of 24.8% 158 Gd, a promising neutron absorber material for use in combination with gamma-ray detectors–yielding a hybrid detector–for neutron detection.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Extraction of neutron-capture cross sections on 92 Zr using the charge-exchange Oslo method

The 93 Nb (𝑡, 3 He ) reaction at 115 MeV/nucleon was studied to demonstrate that nuclear level densities and 𝛾-ray strength functions can be extracted from charge-exchange reactions at intermediate energies using the Oslo technique. The matrix of excitation energy in 93 Zr, reconstructed from the (𝑡, 3 He ) reaction, versus the energy of 𝛾 rays emitted by the excited 93 Zr nuclei, was obtained in an experiment with the S800 Spectrograph operated in coincidence with the GRETINA 𝛾 -ray detector. The extracted level density and 𝛾 -ray strength function obtained by applying the Oslo method to this matrix were used to estimate the 92 Zr⁢(𝑛,𝛾) ⁢93 Zr cross section by combining the new results with other experimental data and theoretical calculations for 𝐸⁢1 and 𝑀⁢1 strength functions at higher energies. Good agreement with direct measurements of the 92 Zr⁢(𝑛,𝛾)⁢ 93 Zr cross section was found. The contribution from the upbend in the extracted 𝛾-ray strength function was important to achieve the consistency, as the neutron-capture cross section without this contribution is significantly below the direct measurements otherwise. Since charge-exchange reactions at intermediate energies have long been used for extracting Gamow-Teller strengths, the successful demonstration of the charge-exchange Oslo method enables experiments in which (𝑛,𝛾) cross sections and Gamow-Teller strengths can be measured simultaneously, which is of benefit for astrophysical studies.

90 ≤ A ≤ 149↗

Evaluation of Thermal Neutron Scattering Cross Section of Uranium Silicide with Ab Initio Lattice Dynamics

Uranium silicide (U 3 Si 2 ) is a candidate material for the high-density nuclear fuel in commercial light water reactors [1], [2]. Its higher uranium density, 11.3 g-U/cm3, compared to that of uranium dioxide (UO 2 ), 9.7 g-U/cm3, can improve the performance of a nuclear reactor while using low enriched uranium (LEU) and diversify the choice of cladding materials [1]–[3]. It also has a higher thermal conductivity than UO 2 , which can reduce the thermal stress on the material caused by a temperature gradient across the fuel pellet and provide a larger margin for some postulated accidents [1], [2], [4]. Furthermore, compared to U3Si, another high-density fuel candidate, it has better resistance to in-pile swelling due to less irradiation-induced rapid amorphization [1], [3]. Corresponding to its importance in nuclear engineering, many previous studies have reported the properties of U3Si2. Experiments showed that U 3 Si 2 is a paramagnetic (PM) metal, where a slight linear increase in magnetic susceptibility was measured with increasing temperature [5], [6]. In addition, thermodynamic quantities such as thermal expansion coefficient, heat capacity, and thermal conductivity were experimentally determined over a wide temperature range [1], [7], [8]. In several computational studies, ab initio atomistic simulations based on density functional theory (DFT) were performed to calculate various properties including elastic constants, electronic density of states (DOS), and phonon dispersion curves [9]–[12]. Nevertheless, thermal neutron scattering cross sections, which are critical to the prediction of the parameters in reactor physics that are ultimately related to reactor criticality, have not yet been evaluated for U3Si2. The scattering cross section can be calculated from the phonon DOS, or the energy spectrum of lattice vibrations, of the crystalline system [13], [14]. However, there is also no experimental data available for the phonon DOS of U 3 Si 2 . While some computational studies reported the phonon DOS and/or dispersion curves from ab initio simulations [9]–[12], the accuracy cannot be guaranteed because it is unclear whether the spin-polarization behavior of PM U 3 Si 2 was properly described. In the present study, the thermal neutron scattering cross section for U 3 Si 2 is evaluated for the first time by calculating the phonon DOS for U3Si2 from ab initio lattice dynamics (AILD) simulations based on DFT. First, U 3 Si 2 is modeled based on the experimental structure, and AILD simulations are performed on the modeled U3Si2 to optimize the structure. Next, AILD simulations are performed for supercells with atomic displacement to calculate Hellmann-Feynman forces. Based on the calculated forces, partial phonon DOSs for U and Si are obtained, and the thermal neutron scattering law (TSL) for U 3 Si 2 is finally evaluated. To verify the accuracy of the calculations in the present study, the calculation results are compared with experimental data on the structure and heat capacity of U3Si2 [1], [7], [8], [15].

Geometry Optimization↗

Influence of neutron cross-section resonances on organ/tissue equivalent and effective dose coefficients for the ICRP voxel phantoms

The materials which compose the ICRP Voxel phantoms used in the computation of conversion coefficients involve neutron interaction cross-sections that have resonances at specific energies. Depending on the energy bin structure used in the computations, these cross-section resonances may occur at energies that fall between energies at which dose coefficients are computed, thus their effects may not be completely accounted for in the reported coefficients. Here In this study, a highly refined energy grid that closely follows the resonance structure in the phantom material cross-sections was identified and used to calculate dose coefficients. Both the equivalent organ/tissue doses for male and female voxel phantoms were computed as well as their summation to obtain the effective dose coefficients. The used refined energy grid tracks very closely the cross-sections in the vicinity of the resonances. The resulting refined energy grid coefficients are compared to coefficients for the coarser energy grid used in ICRP Publication 116. Additionally, reference spectra have been folded with both the fine and coarse sets of conversion coefficients. The resulting total effective doses for these reference spectra are used to assess the adequacy of the dose coefficients calculated on the original ICRP 116 energy grid. The dose coefficients were similarly computed for the local skin dose on the trunk of the body using the ICRU Report 95 phantom. The overall impact of the resonances on the organ/tissue equivalent dose, the effective dose, and the local skin dose are presented and discussed. In general, it was found that resonances can impact neutron dose coefficients, but in most cases the wide range of neutron energies encountered minimized this effect. The impact of resonances was further limited when computing effective dose due to organ/tissue summing and sex-averaging. For the neutron fields studied here, the impact was below 5%.

36 MATERIALS SCIENCE↗

s-process studies in the light of new experimental cross sections - Distribution of neutron fluences and r-process residuals

A best set of neutron-capture cross sections has been evaluated for the most important s-process isotopes. With this data base, s-process studies have been carried out using the traditional model which assumes a steady neutron flux and an exponential distribution of neutron irradiations. The calculated sigma-N curve is in excellent agreement with the empirical sigma-N-values of pure s-process nuclei. Simultaneously, good agreement is found between the difference of solar and s-process abundances and the abundances of pure r-process nuclei. The abundance pattern of the iron group elements where s-process results complement the abundances obtained from explosive nuclear burning is discussed. The results obtained from the traditional s-process model such as seed abundances, mean neutron irradiations, or neutron densities are compared to recent stellar model calculations which assume the He-burning shells of red giant stars as the site for the s-process.

Kaeppeler, F.↗

Cross section of neutrons from the H 2 ( n , 2 n ) reaction at E n = 15 MeV

In this work, the double-differential cross section of the deuteron breakup reaction 2 H(n, 2n) has been studied experimentally with a neutron beam energy of 15 MeV. Special attention has been devoted to estimation of background condition and multiple scattering effect in the scattering sample. Experimental data have been compared with models based on phase-space approximation used in the ENDF/B-VIII.0 data library and in the MCNP neutron transport code, as well as with rigorous model based on Faddeev equations used for cross section evaluations in JENDL data library. It was found that experimental data are better reproduced by Faddeev model, however, the model overestimates data in the low-energy region of the neutron spectrum (<4 MeV)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measuring the Multi-Neutron Antineutrino Cross Section at Low Charged Hadron Energy in MINERvA

Current and future accelerator neutrino oscillation experiments need neutrino interaction models with smaller systematic uncertainties to resolve much of delta CP phase space. Final state interactions (FSI) and scattering off of correlated nuclei (2p2h) are poorly understood processes that currently contribute large uncertainties to leading models. These processes have proven difficult to study because they often produce relatively low energy nucleons. Protons up to about 100 MeV are below the detection threshold of some accelerator neutrino detectors, and neutrons are usually discounted as undetectable. This poster presents a measurement of the multi-neutron antineutrino cross section at low available energy using the MINERvA detector at Fermilab. This interaction channel is particularly sensitive to FSI and 2p2h interactions. A sideband-driven background constraint that greatly reduces uncertainties on the result will be presented. The measured cross section is compared to GENIE v3 models with different FSI treatments and the SuSA model's 2p2h predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Non-Neutron Transmutation of Used Nuclear Fuel (Final Report)

The primary goal of this study is to develop a national facility concept for transmuting long-lived fission products (LLFP) to substantially reduce the disposal impact by minimizing the need for a geologic-timescale repository. As a charter for this study, the national transmutation facility was required to reduce the radiotoxicity and decay heat of LLFP isotopes by at least 90% relative to their values at discharge from a commercial LWR, while consuming less than 10% of the reactor's energy. The identified LLFP isotopes are Se-79, Zr-93, Tc-99, I-129, Sn-126, and Cs-135, whose radiotoxicity is about 99% of the total radiotoxicity of all fission products at 1,000 years. Approximately ~72 kg of LLFPs is discharged every year from a 1,000 MWe commercial or advanced nuclear reactor. First, LLFP transmutation options with non-neutron beams (photons and protons) were explored. The study concluded that LLFP transmutation is feasible with high-energy, high-intensity photons or protons, but impractical on an engineering scale due to low transmutation rates and the high energy requirements to produce the desired photon or proton beams. As alternatives, LLFP transmutation options with neutrons from fission, fusion, and spallation reactions were additionally explored. The transmutation options using advanced critical reactors are attractive only for selective LLFP isotopes because the production rates of several LLFP isotopes (Zr-93, Sn-126, and Cs-135) from fission reactions are larger than the transmutation rates. The transmutation options with only spallation neutrons are favorable to transmute all LLFP isotopes, but as a tradeoff, the net transmutation rates are reduced. The national transmutation facility concept was developed following an exploration of transmutation options using various incident particles. The proposed national LLFP transmutation comprises a dedicated molten-salt reactor (MSR), a proton accelerator, and a spallation neutron-based transmuter. The MSR power was set at 300 MWt and 120 MWe, with the thermal power approximately 10% of that of a commercial 1,000 MWe PWR. The electricity generated by the MSR powers the accelerator and transmuter. The accelerator produces 1 GeV, 30 mA protons, which are introduced into the spallation neutron-based transmuter. The spallation neutron-based transmuter consists of a central spallation target and LLFP target pins merged in a heavy water tank. The six LLFP isotopes are separated into two groups. Tc-99, I-129, and Se-79, having larger neutron cross sections, belong to group A, while Zr-93, Sn126, and Cs-135, having smaller neutron cross sections, belong to group B. Then, for effective transmutation, LLFPs in groups A and B are transmuted in the dedicated MSR and in a spallation neutron-based transmuter, respectively. The estimated capital cost of the national transmutation facility is approximately $\$$3.1B, and its annual O&M cost is expected to be ~$\$$182M. Radiotoxicity and decay heat of LLFPs were calculated and compared with those of the original LLFPs. It was assumed that the targets were made with elementwise LLFP rather than isotopic LLFP, owing to the potentially high cost of isotopic separation from used nuclear fuels. The decay heat of LLFPs can be reduced by more than 90% using a single national transmutation facility. However, radiotoxicity decreases by 79–84%, which does not meet the transmutation performance requirement, primarily because Cs-135 is produced rather than depleted. Thus, to meet the design requirement, Cs-135 should be separated from other Cs isotopes and irradiated in a spallation neutron-based transmuter. Then, radiotoxicity decreases by ~92%.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluation of Thermal Neutron Scattering Cross Sections for CaH 2

Solid metal hydrides have long been considered viable moderators for nuclear reactor designs due to their moderating ratios, hydrogen densities, high dissociation temperatures, and mechanical properties. CaH 2 is an orthorhombic saline-hydride that has recently been investigated and shows promise for use as a moderator in microreactors. At present, there is no Thermal Scatting Law (TSL) evaluation for CaH 2 in the ENDF/B-VIII.0 database. An evaluation does exist in the JEFF-3.3 database, performed by Serot, however it was limited by the implemented methods and thus both drastically over-predicts the incoherent elastic contribution and completely ignores the coherent elastic contribution to scattering from the metal ions. The thermal neutron scattering cross sections of CaH 2 are evaluated in this work to establish accurate data for use in reactor design. The present evaluation corrects the inaccuracies of the JEFF-3.3 data, and yields three distinct libraries: Ca in CaH 2 , H 1 in CaH 2 , and H 2 in CaH 2 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Thermal neutron scattering cross sections for amorphous carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm{sup 3}. From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical optical peak at 0.25 eV for the ideal graphite disappears for amorphous carbon, in good agreement with the expected structure. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Deployment of neural-network-based neutron microscopic cross sections in the Griffin reactor physics application

The capability to utilize neural networks to predict macroscopic and microscopic cross section parametric spaces has been developed for the Griffin reactor physics application. The LibTorch interface enables Griffin's MOOSE-based materials to interact with LibTorch-trained models, allowing for the evaluation of complex macroscopic or microscopic cross section spaces, which are then used to evaluate the neutronic properties of the Griffin finite element model. This study benchmarks traditional ISOXML-formatted tabulation libraries against neural network-based models for 279 nuclides on 20,160 grid points for zero-dimensional and two-dimensional reactor models. Benchmark metrics include the fundamental mode eigenvalue, fission and absorption rates, and various temperature coefficients of reactivity (isothermal, fuel, and moderator). From the perspective of storage space, the complete set of LibTorch models uses 11 MB on disk, compared to the 10 GB for the ISOXML multigroup library that covers the same grid space. For the two-dimensional performance case considered in Griffin, the Torch model uses 97% less RAM than the reference ISOXML dataset while runtime increases by a factor of 3 when using the LibTorch model compared to the ISOXML dataset with multi-linear interpolation. The LibTorch model consistently yields errors within 0.01% for most analyzed quantities except for the temperature coefficients of reactivity where the maximum discrepancies are up to 0.3 $\frac{pcm}{K}$. Due to the neural network attempting to best predict quantities with no regard for a positive or negative bias for any given quantity, predictions may experience random fluctuations, resulting in both positive and negative errors. Future work will entail both depletion and coupled transient analysis to determine the predictive capabilities of Griffin with neural network-based cross sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Enhancement of sub-thermal neutron flux through cold polyethylene

Total thermal neutron cross section measurements serve as the primary means of validation for thermal neutron scattering kernels, an important quantity for neutron transport calculations. In an effort to improve the quality of thermal neutron scattering kernels, researchers at Rensselaer Polytechnic Institute (RPI) designed and constructed a polyethylene based cold moderation system to enhance neutron flux below 10 meV when coupled with the Enhanced Thermal Target (ETT) at the RPI Gaerttner LINAC. The final design yielded an increase in sub-thermal neutron flux (below 10 meV) by a factor of 4.5 for a moderator temperature of 37.5 K relative to the ETT alone. A further increase to a factor of 6 is expected after a minor geometry modification and decrease in polyethylene temperature to 25 K. This novel capability will be used to conduct total thermal neutron cross section measurements from 0.0005–10 eV for different materials including moderator materials.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Thermal Neutron Scattering Cross Sections for Graphitic Amorphous Carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm 3 . From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical features and the optical graphitic peak at 0.25 eV for the ideal graphite DOS disappear for graphite-like amorphous carbon, which shows good agreement with the expected structure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

New Parameterization of Neutron Absorption Cross Sections

Recent parameterization of absorption cross sections for any system of charged ion collisions, including proton-nucleus collisions, is extended for neutron-nucleus collisions valid from approx. 1 MeV to a few GeV, thus providing a comprehensive picture of absorption cross sections for any system of collision pairs (charged or uncharged). The parameters are associated with the physics of the problem. At lower energies, optical potential at the surface is important, and the Pauli operator plays an increasingly important role at intermediate energies. The agreement between the calculated and experimental data is better than earlier published results.

Tripathi, Ram K.↗