The Neutron Scattering Cross Section and Angular Distribution Measurement Program at LANL
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Kelly, Keegan John↗
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Comparison of Generation of Higher-Order Neutron Scattering Cross Sections
The generation of high-order neutron scattering cross sections consistent with high-fidelity simulations remains an area of active research. Popular options include generating cross sections from continuous energy Monte Carlo calculations or generating cross sections from a deterministic neutron transport calculation with high-fidelity tabulated cross sections. Both options present challenges. Monte Carlo simulations can naturally process continuous energy cross section data and allow for the general description of anisotropic neutron scattering given a scattering law. However, Monte Carlo simulations are inherently related to particle weighting and it has been suggested that this may be unacceptable for generating high-order neutron scattering cross sections. Deterministic neutron transport calculations can easily calculate high-order moments of the flux to appropriately calculate higher-order neutron scattering cross sections but are generally limited by discretization of space, energy, and angle. In this work, the trade-offs between generation of high-order neutron scattering cross sections via Monte Carlo and deterministic neutron transport methods are investigated. The methods implemented in the Monte Carlo computer program Serpent and the deterministic fast reactor neutron cross section generator MC2-3 are compared. Cross sections resulting from these methods are used in Rattlesnake, a deterministic neutron transport code developed by Idaho National Laboratory (INL), and results are compared to a reference continuous energy Monte Carlo calculation. Whereas previous work investigating the effects of anisotropic neutron scattering has focused on light water reactor (LWR) simulations, this work focuses on high-order neutron scattering cross sections as they relate to fast reactor simulations. To investigate the consequences of the Serpent and MC2-3 methodologies, a test problem is developed. The test problem is a one-dimensional geometry with fast reactor materials designed to demonstrate deep penetration and exacerbate the effects of high-order neutron scattering. Based on the results of the deep penetration test problem, it is concluded that P3 neutron scattering cross sections are sufficient to describe anisotropic scattering in fast reactor materials. Any neutron scattering of order higher than P3 offers negligible change in the eigenvalue of the test problem. Additionally, it is determined that the methodology as implemented in Serpent is applicable for generating high-order neutron scattering cross sections through at least P3 in fast reactor materials.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Rovibrationally resolved Rayleigh and Raman scattering cross sections for molecular hydrogen
Accurate Rayleigh and Raman scattering cross sections, tensor components, depolarization ratios, and reversal coefficients for all rovibrational transitions within the X1Σg+ ground electronic state of H2 have been calculated. Raman spectra have been generated using these data. A method for calculating Raman scattering cross sections is formulated that is valid below the ionization threshold and in the region containing resonances, which explicitly accounts for all bound and dissociative vibrational levels of the bound intermediate electronic states and approximately accounts for the ionization continuum. A representative set of cross sections is presented for incident photon energies below 15 eV and compared with existing results in the literature where possible. Convergence of our results with an increasing number of bound intermediate electronic states is demonstrated. The accuracy of the Placzek–Teller approximation is discussed. The effect of accounting for the intermediate ionization continuum is investigated. Local thermal equilibrium cross sections are calculated for Rayleigh and Raman scattering. This work represents the most accurate and complete treatment of Raman scattering for molecular hydrogen to date. A total of 9582 Rayleigh and Raman scattering cross sections have been generated and are openly available on Zenodo under an open-source Creative Commons Attribution license at https://zenodo.org/doi/10.5281/zenodo.13441471.
74 ATOMIC AND MOLECULAR PHYSICS↗
Methodology for Generating Covariance Data of Thermal Neutron Scattering Cross Sections
This paper details and implements a framework for evaluating thermal neutron scattering cross sections that provide S(α,β) data and covariance data for hydrogen in light water. This methodology involves perturbing model parameters of molecular dynamics potentials and fitting the simulation results to experimental data. The framework is general and can be applied to any material or simulation method. The fit is made using the Unified Monte Carlo method to experimentally measure double-differential scattering cross sections of light water at the Spallation Neutron Source at Oak Ridge National Laboratory. Mean values and covariance data were generated for model parameters, phonon density of states, double-differential cross sections, and total scattering cross sections. These posterior parameter values were very similar to their prior values with a maximum relative error of 0.54%. This falls within in the Unified Monte Carlo–calculated uncertainties on the order of 2.7%. Additionally, posterior double-differential cross sections agree favorably with ENDF/B-VIII.0 cross sections. The new thermal scattering law was tested by comparing it against benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook, which showed a slight improvement over the ENDF/B-VIII.0 library. Additionally, the covariance matrix of the phonon density of states was validated to confirm that the spread of k eff from the density of states used to generate the covariance matrix was similar to the spread of k eff from the density of states of the sampled covariance matrix.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Thomson scattering Cross section Calculator
Code to calculate Thomson scattering cross sections.
Swadling, GeorgeF.↗
Finite-Geometry Corrections for Neutron Scattering Cross Section Measurements
In this report, we describe the corrections necessary for neutron scattering cross section measurements in experiments which use finite-geometry scattering samples. A new Geant4 based framework was developed to calculate these corrections which has been benchmarked against a well-measured test case. This framework also calculates the outgoing neutron energy dependence of the correction factors, which is crucial when resolving individual final states in the scatterer is not possible.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Extracting Inelastic Scattering Cross Sections for Finite and Aperiodic Materials from Electronic Dynamics Simulations
Explicit time-dependent electronic structure theory methods are increasingly prevalent in the areas of condensed matter physics and quantum chemistry, with the broad-band optical absorptivity of molecular and small condensed-phase systems nowadays routinely studied with such approaches. Here, in this paper, it is demonstrated that electronic dynamics simulations can similarly be employed to study cross sections for the scattering-induced electronic excitations probed in nonresonant inelastic X-ray scattering and momentum-resolved electron energy loss spectroscopies. A method is put forth for evaluating the electronic dynamic structure factor, which involves the application of a momentum boost-type perturbation and transformation of the resulting reciprocal space density fluctuations into the frequency domain. Good agreement is first demonstrated between the dynamic structure factor extracted from these electronic dynamics simulations and the corresponding transition matrix elements from linear response theory. The method is then applied to some extended (quasi)one-dimensional systems, for which the wave vector becomes a good quantum number in the thermodynamic limit. Finally, the dispersion of many-body excitations in a series of hydrogen-terminated graphene flakes (and twisted bilayers thereof) is investigated to highlight the utility of the presented approach for capturing morphology-dependent effects in the inelastic scattering cross sections of nanostructured and/or noncrystalline materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Measurement of Differential Neutral Current Elastic $ν_μ$-Argon Scattering Cross Sections with MicroBooNE
The MicroBooNE experiment is an 85 ton active mass liquid-argon time projection chamber located in the Fermilab Booster Neutrino Beamline. MicroBooNE’s ability to detect low-energy protons allows us to study single proton events with momenta as low as 300 MeV/c. We present a measurement of the flux-averaged neutral-current elastic differential cross section for neutrinos scattering on argon as functions of four-momentum transfer squared, Q 2 , proton kinetic energy, momentum and angle with respect to the beam direction. Our measured cross section as a function of Q 2 goes as low Q 2 = 0.10 GeV2 . This is our first step towards extracting the strange quark contribution to the axial form factor, which is not only the least-constrained contribution to the neutral-current elastic scattering cross section but is also crucial for understanding the strange quark contribution to the proton spin.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗
Bayesian inference of in-medium baryon-baryon scattering cross sections from HADES proton flow data
Within a Bayesian statistical framework using a Gaussian Process emulator for an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions at intermediate energies, we infer from the HADES proton flow data the posterior probability distribution functions of in-medium baryon-baryon scattering cross section modification factor X with respect to free-space and the corresponding incompressibility K of nuclear matter as well as their correlation function. In conclusion, the mean value of X is found to be $X$ = $1.32_ {+0.28} ^ {-0.40} $ at 68% confidence level assuming the nuclear incompressibility K will not exceed 400 MeV, providing circumstantial evidence for enhanced baryon-braryon scattering cross sections in hot and dense nuclear matter.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Measurement of the total compton scattering cross section between 6.5 and 11 GeV
The total cross section for Compton scattering off atomic electrons, $γ + e → γ' + e'$, was measured using photons with energies between 6.5 and 11.1 GeV incident on a 9 Be target as part of the PrimEx-eta experiment in Hall D at Jefferson Lab. This is the first measurement of this fundamental QED process within this energy range. The total uncertainties of the cross section, combining the statistical and systematic components in quadrature, averaged to 3.4 % across all energy bins. This not only demonstrates the capability of this experimental setup to perform precision cross-section measurements at forward angles but also allows us to compare with state-of-the-art QED calculations.
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↗
(U) Energy-Dependent Perturbations of Scattering Cross Sections Using the PERT Card in MCNP6.2
The PERT card is used for first- and second-order perturbations of material densities, isotope densities, and isotope cross sections in the MCNP6.2 Monte Carlo code. Using the PERT card for firstand second-order sensitivities is straightforward. Reference 2 only looked at density perturbations with no energy dependence. This report looks at the sensitivity of a response to scattering cross sections as a function of energy and finds that there is a bug in the PERT capability. The SENSMG multigroup neutron sensitivity code was recently given the capability of computing sensitivities to user-specified reactions whose cross sections are available in a user-supplied NJOY output file. SENSMG uses the PARTISN multigroup discrete ordinates code for the transport. The NJOY-reaction capability is similar to that of SUSD3D, which also uses PARTISN for the multigroup transport. The PERT bug was identified by comparing MCNP6.2 outputs with SENSMG outputs. The next section of this report describes the test problem. Section III presents the MCNP6.2 PERT bug and proposes a solution. Section IV is a summary and conclusions. The SENSMG and MCNP input files are listed in the appendix.
07 ISOTOPE AND RADIATION SOURCES↗
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 constraints on the dark matter-neutrino and dark matter-photon scattering cross sections from TXS 0506+056
The flux of high energy neutrinos and photons produced in a blazar could get attenuated when they propagate through the dark matter spike around the central black hole and the halo of the host galaxy. Using the observation by IceCube of a few high-energy neutrino events from TXS 0506+056, and their coincident gamma ray events, we obtain new constraints on the dark matter-neutrino and dark matter-photon scattering cross sections. Our constraints are orders of magnitude more stringent than those derived from considering the attenuation through the intergalactic medium and the Milky Way dark matter halo. When the cross-section increases with energy, our constraints are also stronger than those derived from the CMB and large-scale structure.
79 ASTRONOMY AND ASTROPHYSICS↗
Evolution of in-medium baryon-baryon scattering cross sections and stiffness of dense nuclear matter from Bayesian analyses of FOPI proton-flow excitation functions
Within a Bayesian statistical framework using a Gaussian process (GP) emulator for an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions with momentum-independent Skyrme interactions, we infer from the proton directed and elliptical flow in mid-central Au + Au reactions, measured at beam energies from 150 to 1200 MeV/nucleon by the FOPI Collaboration, the posterior probability distribution functions (PDFs) of the in-medium baryon-baryon scattering cross section (BBSCS) modification factor 𝑋 (with respect to their free-space values) and the stiffness parameter 𝐾 of dense nuclear matter. Here, we find that the most probable value of 𝑋 evolves from around 0.7 to 1.0 as the beam energy 𝐸 beam /𝐴 increases. On the other hand, the posterior PDF(𝐾) may have dual peaks having roughly the same height or extended shoulders at high 𝐾 values. More quantitatively, the posterior PDF(𝐾) changes from having a major peak around 220 MeV, characterizing a soft EOS in the reaction at 𝐸 beam /𝐴 = 150 MeV, to one that peaks around 320 MeV, indicating a stiff EOS in the reactions at 𝐸 beam /𝐴 higher than about 600 MeV. The transition from soft to stiff happens in mid-central Au + Au reactions at beam energies around 250 MeV/nucleon in which 𝐾 = 220 MeV and 𝐾 = 320 MeV are approximately equally probable. Altogether, the FOPI proton-flow excitation function data indicate a gradual hardening of hot and dense nuclear matter as its density and temperature increase in reactions with higher beam energies.
nuclear matter↗
DUNE and MINERvA Flux Studies and a Measurement of the Charged-Current Quasielastic Antineutrino Scattering Cross Section with $<E_{\nu}> \sim 6 $ GeV on a CH Target
One of the biggest open questions in physics is the prevalence of matter over anti-matter in the present universe. One of possible answers lies in the violation of charge and parity symmetry in the lepton sector that would favor matter over anti-matter so that the universe becomes dominated by matter over time. Recent results from neutrino experiments like T2K and NOvA have indicated that there is CP violation in the leptonic sector \citep{Abe:2019vii}. However, the precise measurement of CP violation will require an unprecedented level of accuracy in these oscillation experiments. One of the challenges lies with the systematic uncertainties that come with the measurements, which include uncertainties related to the neutrino flux modeling, interaction modeling and detector related systematic uncertainties.\\ The first part of this thesis will go through the challenges related to flux uncertainties. It will discuss the flux uncertainties related to hadron production in the LBN F beamli ne for the DUNE experiment. Hadron production models used in flux simulations vary widely depending on the simulation and choice of physics models used to simulate the hadron production. This thesis will explain the method of using existing hadron production data to constrain these uncertainties, a method which has been used in MINERvA experiment.\\ The second part of the thesis goes through the effect of possible flux mismodeling and MINERvA's approach to address this effect. In doing so, we discovered that the suspected mismodeling could also result from incorrect estimation of the energy scale of the muons. This project not only demonstrated the challenges of flux modeling but also led to a novel approach of using neutrino energy spectra to understand the correlation between detector and neutrino beamline parameters. \\ A high statistics measurement of the anti-neutrino scattering cross section in the charged current quasielastic (CCQE) channel is the final part of the th esis. Th e 2-body interactions in this channel have the advantage of allowing reconstruction of the interaction kinematics from the outgoing muon trajectory which can be measured very well. Double differential cross sections as a function of muon kinematics, one of the deliverables of this analysis, will help future oscillation experiments understand their data. The cross-section as a function of the four-momentum transferred from the leptonic system to the hadronic system ($Q^{2}_{QE}$) can be used to test models used in simulating antineutrino interactions and the nuclear effects that can modify the predicted cross sections. Nuclear effects arise from the complex nuclear environment and both modify the initial scattering and change the fate of the particles produced from in neutrino-nucleus interactions. Study of nuclear effects will help to understand the structure of the atomic nucleus and its impact on neutrino interactions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗