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Banner Highlight for Structure-Dependent Doppler Broadening Using a Generalized Thermal Scattering Law [DOI 10.3390/jne2020013].
Thermal neutron scattering laws are important nuclear data for many nuclear science and engineering applications. Validation helps to ensure that a thermal neutron scattering law has a high quality and often employs critical benchmarks as integral experiments. Recently, pulsed-neutron die-away benchmarks have been used as an experiment to validate thermal neutron scattering laws. Herein, we evidence how this alternative integral experiment has a high sensitivity to these nuclear data by performing an uncertainty quantification analysis. The analysis randomly sampled the nuclear model parameters associated with hydrogen bound in light water thermal neutron scattering law and sampled other nuclear data that influenced the experiment’s integral parameter (e.g., elastic scattering, absorption in hydrogen and oxygen) from their respective covariance matrices. The thermal neutron scattering law caused an uncertainty in the integral parameter that reached 2.67%, which exceeds by an order of magnitude the uncertainties induced in commonly used thermal solution critical benchmarks. The validation performed here, although limited due to a poor description of the historical experiment, indicated that the ENDF/B-VIII.0 thermal neutron scattering law well predicted the integral parameter. These results motivate further benchmark and validation efforts using pulsed-neutron die-away experiments.
Five plutonium baseline experiments completed in September of 2018 from the Thermal Epithermal eXperiments (TEX) program have been accepted by the International Criticality Safety Benchmark Evaluation Project as PU-MET-MIXED-002 and will be included in the 2020 version of the handbook. The experiments were made up of stacked layers of plutonium Zero Power Physics Reactor (ZPPR) plates moderated by polyethylene (PE, chemical formula C2H4) to varying degrees to create configurations with five different neutron spectra, including one fast configuration, one thermal configuration, and three mixed configurations. Calculations of the benchmark show overprediction of k eff when using the most recent release of the Evaluated Nuclear Data File Version B (ENDF/B) library release (VIII.0) cross sections, particularly when compared to the previous ENDF/B-VII.1 results. One potential source of overprediction was hypothesized to be the new Molecular Dynamics (MD) generated PE Thermal Scattering Law (TSL). The overprediction was shown via calculation to not be caused by the new ENDF/B-VIII.0 thermal scattering law, and in fact the overprediction was mitigated by the new PE TSL.
Inelastic thermal neutron scattering in materials that act as neutron moderators, reflectors, and filters results in shaping the neutron spectrum at low energies. This phenomenon is described using differential scattering cross sections calculated from three components including the bound atom (i.e., nuclear) scattering cross section of the neutron, the ratio of the outgoing and incoming neutron energy, and the thermal scattering law (TSL), i.e., S(α,β), where α and β represent dimensionless momentum and energy exchange variables, respectively. To date, no TSL libraries are generated using measured data. However, valuable information may be derived from measurements and “targeted” experiments that can validate TSL data and the related inelastic scattering cross sections. As a demonstration, a suite of coordinated measurements and experiments is described that was designed and used to support the evaluation of the TSL for “nuclear” graphite. This experimental suite includes neutron powder diffraction (for structure analysis), positron annihilation (for nano porosity assessment), inelastic neutron scattering measurements using a chopper spectrometer, transmission experiments using neutrons with energy below the Bragg cutoff thereby accessing the total (inelastic) cross section, and a slowing-downtime experiment to observe the developing neutron spectrum in the material. We find that this experimental suite was key to understanding the difference in TSL between “nuclear” and “ideal” graphite and for the inclusion of “nuclear” graphite in the ENDF/B-VIII.0 nuclear data library release.
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Neutron transport computations employ thermal scattering laws (TSLs) to account for the influence of material structure and collective excitations at low energy (≲ 10 eV). Recent work has been undertaken to improve TSL accuracy and expand the number of available materials in the Evaluated Nuclear Data File (ENDF). However, comparison of TSL to measured data is often sparse. In this work, we present a method to evaluate TSL accuracy in the Monte Carlo N-Particle (MCNP) code by simulating inelastic neutron scattering (INS) measurement and comparing to data. The method is briefly described with example application to the recently released ENDF-VIII TSL library for polyethylene as well as a cryogenic PE TSL we are separately developing.
The Full Law Analysis Scattering System Hub ( FLASSH ) is an advanced code which evaluates the thermal scattering law (i.e. TSL, S(α,β)) for thermal scattering cross sections and resonance Doppler broadening. The ability to accurately capture these two key cross section features is dependent on accurate, high fidelity TSL evaluations. FLASSH 1.0 provides advanced physics capabilities resulting in an improved, generalized TSL to most accurately represent the lattice dynamics within any material. This improved TSL will allow for consistent analysis in both the thermal and epithermal energy ranges. The features for TSL analysis are packaged within the FLASSH GUI for easy user interface along with data output in many file formats including ENDF File 7 and ACE files.
The thermal scattering law for uranium silicide, a candidate material for high-density nuclear fuel, was evaluated from the temperature-dependent phonon density of states obtained using the quasi-harmonic approximation. For uranium silicide model systems of various volumes near the equilibrium volume, Hellmann-Feynman forces were calculated by performing ab initio lattice dynamics simulations based on density functional theory. Subsequently, the quasi-harmonic approximation was applied by interpolating the results of the harmonic approximation for each volume system. As a sensitivity test, the phonon density of states was calculated for the structures with temperature-dependent volumes at 298 K and 1000 K, obtained by the quasi-harmonic approximation, and the corresponding thermal neutron scattering cross section was evaluated. The temperature-dependent volume and heat capacity of uranium silicide obtained by the quasi-harmonic approximation showed reasonable agreement with experimental data while lattice thermal expansion showed deviation from experimental observations. Thermal scattering cross sections evaluated from 0 K and temperature-dependent phonon density of states exhibited differences of up to 4.1% at 1000 K. This study examines the impact of temperature on the thermal scattering law, employing ab initio lattice dynamics simulations through the quasi-harmonic approximation.
Accurate thermal scattering laws (TSLs) are essential for reliable neutron transport simulations, particularly for systems with low-energy neutrons. Pulsed-neutron die-away (PNDA) experiments provide a highly sensitive platform for TSL validation but face challenges from fast neutron leakage and material constraints in nonhydrogenous targets such as beryllium. This work investigates the use of high-density polyethylene (HDPE) as a premoderator to reduce leakage, improve thermalization, and shorten experimental run times while preserving sensitivity to the Be TSL. Here, three premoderated configurations, encapsulation, slab, and interstitial, were evaluated using MCNP6.3® simulations with ENDF/B-VIII.0 nuclear data. The effects of the Be TSL was quantified by comparing decay constants from simulations with and without 𝑆(𝛼,𝛽) treatments for both beryllium and HDPE. The results show that premoderation enables the use of as little as 5.20% of the beryllium volume required for an unreflected geometry, achieving uncertainties below 0.5% and reducing run time by up to 72.2% in the studied configurations. The interstitial configuration achieved the best balance between low statistical uncertainty and high TSL sensitivity, outperforming the slab and encapsulation designs. These findings demonstrate that carefully optimized premoderation can significantly enhance the efficiency, feasibility, and precision of PNDA experiments for Be TSL validation.
The presentation discusses the eight new Thermal Scattering Law (TSL) evaluations that have been submitted to the National Nuclear Data Center (NNDC). It explains that evaluations are performed using the NCSU FLASSH code and that NJOY/LEAPR input files are provided to allow for independent testing. The presentation concludes by stating that more evaluations are expected to be submitted before the end of 2020.
Lawrence Livermore National Laboratory is conducting new Pulsed-Neutron Die-Away (PNDA) benchmark experiments to validate neutron thermal scattering laws (TSLs). TSLs are important data for modeling thermal fission reactors, criticality safety scenarios, and radiation protection and detection, i.e. any application with thermal neutrons. These simulations require high-quality nuclear data, with confidence in their quality established through validation.
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Light water is the most important neutron moderator in many reactor applications. Thermal neutron scattering kernels for H bound in H 2 O are represented by ENDF-format thermal scattering laws (TSLs) evaluated at discrete temperatures T . Nuclear data evaluations are conventionally validated utilizing a combination of critical benchmarks and experimental cross section data. Existing public critical benchmarks may be inadequate for testing water TSLs over the full range of T of interest in reactor applications, and experimental thermal scattering cross section data for water is sparse at elevated T . In this work, MC21 is used to simulate the decay of the equilibrium thermal neutron flux in light-water spheres of several radii. The fundamental-mode time eigenvalue $\mathcal{a}$ is calculated at 22 °C and 227 °C (at saturation pressure) for each sphere using three different H-H 2 O TSLs. Fitting $\mathcal{a}$ to a polynomial function of geometric buckling allows calculation of the thermal neutron diffusion length L . Extrapolation lengths are treated as a function of the transport mean free path and geometry. Experimental L data from 25 publications at 49 temperatures (from 10 °C to 295 °C), computed by several different time-dependent and space-dependent decay methods, is used to develop an empirical fit of L vs. T . The MC21-calculated L for the TSLs tested are within ±1% of the predicted values at 22 °C and 227 °C. This validation approach, which may be repeated at arbitrary T , constitutes an integral benchmark specific to and characterizing the detailed physics of the thermal scattering kernel applied.
Scattering of thermal neutrons and Doppler broadening of epithermal neutron resonances in uranium and its compounds may be sensitive to crystal binding. The thermal scattering law (TSL) for uranium dioxide, which captures crystal binding effects, has been reevaluated for ENDF/B-VIII.0. Phonon spectra were generated using ab initio lattice dynamics for the paramagnetic phase and validated against experiment. Improved agreement with the Debye-Waller coefficient as a function of temperature is found relative to the spectrum used for the ENDF/B-VII.1 evaluation. The TSL was generated using the phonon expansion method within the NJOY nuclear data processing package and was found to be in reasonable agreement with inelastic neutron scattering measurements. The present evaluation predicts a reduction in the inelastic scattering cross section relative to ENDF/B-VII.1 and a total scattering cross section consistent with neutron transmission experiments
Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)
Paraffin wax is frequently used as a neutron moderator and shielding material. The main component of paraffin wax is straight-chain alkanes (n-alkanes). The deposition of paraffin wax is primarily attributed to the crystallization of n-alkanes. It is important to gain a deeper understanding of the mechanisms underlying the behavior of paraffin wax, which would impact the thermal scattering Law (TSL) and cross sections and affect the analysis of neutronic and critical systems. In this work, a classical molecular dynamics (CMD) simulation model was used in LAMMPS to create the TSL and cross sections at room temperature and pressure. To generate the required velocity autocorrelation functions (VACF), previously published data were used to validate the approach and models by comparing them with key model parameters. The phonon density of state (DOS) was calculated using Fourier transformation of the normalized VACF. This DOS was used as the primary input to estimate the TSL (S($a$, $β$)) and cross sections of hydrogen in paraffin wax. The TSL and cross sections of hydrogen were estimated using the Full Law Analysis Scattering System Hub (FLASSH) code. The cross section of hydrogen in paraffin wax is consistent with other hydrocarbon materials such as polyethylene with deviations due to structure in the lowest energy region.
Precise estimation of neutron thermalization in moderators relies on high-fidelity thermal scattering cross-section data governed by the thermal scattering law (TSL). The Institut de Radioprotection et de Sûreté Nucléaire (IRSN) has been working on the development of improved TSL for light water ice. Many polymorphic phases of light water ice exist depending on the thermodynamic conditions. The most common type of ice at standard pressure and temperature below water freezing point (273.15 K) is ice-Ih. It is essential to have high-resolution experimental double differential data for developing and/or validating TSL for moderator materials.Existing experimental double-differential scattering data for ice-Ih are extremely sparse and of limited quality. New high-quality double-differential measurements for ice-Ih over multiple temperatures and incident neutron energies would directly support the validation and improvement of ice-Ih TSL models for criticality safety applications.Series of time-of-flight (TOF) inelastic neutron scattering experiments on ice-Ih at temperatures starting at 271 K and down to 6 K, have been carried out at the SEQUOIA spectrometer at the Spallation Neutron Source (SNS) at the Oak Ridge National Laboratory (ORNL), United States. The experiments have been performed for incident neutron energies, Ei= 11, 55, 160, 250, and 600 meV, to explore different excitation energies in the vibrational phonon spectrum. This paper presents the thermodynamic conditions and the details of the TOF measurements on ice-Ih and the derived phonon spectrum from the experimentally measured double differential data. A study of the variation of the phonon spectrum of ice-Ih as a function of temperature is highlighted, and a preliminary TSL evaluation is developed based on the experimental phonon spectrum.
The Full Law Analysis Scattering System Hub (FLASSH) is a modern, advanced code which evaluates the thermal scattering law (TSL) along with accompanying cross sections. FLASSH features generalized methods which accommodate any material structure. Historical approximations including the incoherent and cubic approximations have been removed. Instead, the latest release of FLASSH features advanced physics options including distinct corrections (1-phonon contributions) and non-cubic formulations. The non-cubic elastic and inelastic contributions are necessary to accurately evaluate 1-phonon contributions. Both non-cubic and 1-phonon calculations require high-density sampling of the various scattering directions. Optimization and parallelization of these routines were therefore necessary to produce results in a reasonable timeframe. With these notable improvements to the generalized TSL, FLASSH 1.0 meets benchmark requirements, demonstrating noticeable agreement with experiment for both TSLs and the resulting integrated cross sections. Additional features including a graphical user interface (GUI), plotting diagnostics, and formatted output options including ACE files allow users to complete a TSL evaluation with minimal input and maximum flexibility. The user GUI creates input files for FLASSH, reducing user error and also providing built-in error checks. Autofill options and suggested input values help make TSL evaluation accessible to novice users. The FLASSH code is compiled to run on both Windows and Linux platforms with automatic parallelization. (authors)