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Correlated energy uncertainties in reaction rate calculations

Monte Carlo methods can be used to evaluate the uncertainty of a reaction rate that arises from many uncertain nuclear inputs. However, until now no attempt has been made to find the effect of correlated energy uncertainties in input resonance parameters. Our goal is to investigate the impact of correlated resonance energy uncertainties on reaction rates. Using a combination of numerical and Monte Carlo variation of resonance energies, the effect of correlations are investigated. Five reactions are considered: two fictional, illustrative cases and three reactions whose rates are of current interest. The effect of correlations in resonance energies depends on the specific reaction cross section and temperatures considered. When several resonances contribute equally to a reaction rate, and when they are located on either side of the Gamow peak, correlations between their energies dilute their effect on reaction rate uncertainties. If they are both located above or below the maximum of the Gamow peak, however, correlations between their resonance energies can increase the reaction rate uncertainties. This effect can be hard to predict for complex reactions with wide and narrow resonances contributing to the reaction rate.

79 ASTRONOMY AND ASTROPHYSICS↗

Power deposition in He from the volumetric He-3/n,p/H-3 reaction

Calculations are presented in this paper which show the amount of power that can be expected to be deposited in He-3 for typical direct nuclear-pumped lasers presently in use. The calculations were performed taking into consideration the cylindrical geometry of the system, the depletion of the thermal flux across the tube cross section, and the energy loss of the protons to the cell walls. If a laser efficiency of 1% is assumed, the results indicate a steady-state laser output of 12.5 kW from a volume of 152.6 cu cm or 82 W/cu cm can be achieved.

De Young, R. J.↗

Evaluation of experimental constraints on the 44 Ti(α,p) 47 V reaction cross section relevant for supernovae

Due to its importance as an astronomical observable in core-collapse supernovae (CCSNe), the reactions producing and destroying 44 Ti must be well constrained. Generally, statistical model calculations such as Hauser-Feshbach are employed when experimental cross sections are not available, but the variation in such adopted rates can be large. Here, data from the literature is compared with statistical model calculations of the 44 Ti(α,p) 47 V reaction cross section and used to constrain the possible reaction rate variation over the temperatures relevant to CCSNe. Suggestions for targeted future measurements are given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Primer on Nuclear "Recoil" Data

For many years the ENDF-6 format has existed to contain evaluated nuclear data. One primary driver for the format and the data is neutron transport calculations. Evaluated data can be processed by a code like NJOY into either continuous energy form (ACE format) for Monte Carlo codes like MCNP or into multi-group form (NDI tables) for deterministic codes like Partisn. The reaction cross sections are found in the MF 3 section of the ENDF-6 format. If the reaction produces one or more neutrons as outputs, then secondary neutron data must also be given in MF 4,5 or 6 sections of the format. Energy and angular distributions for the output neutrons must be given in one of several available formats. The most general formats are found in MF 6. MF 4 is for angular distributions, MF 5 is for Energy distributions, and MF 6 contains both. In recent years, more interest has developed in the other output particles (i.e., the “recoil” particles) from neutron induced reactions. This has been driven by interest in charged particle transport and in more specialized partial kermas. ( A separate total neutron kerma has been available for a long time.) Partial kermas are a breakdown of the Kinetic Energy Released into the MAterial by output particle or by neutron reaction. The sum of the partial kermas should be equal to the total kerma on a group-wise basis. The ENDF-6 format is general enough for these new data requirements. Ideally, evaluated data would exist for every output particle (including the secondary neutrons) from every neutron-induced reaction. In the MF 6 format section, data for multi-particle outputs may be entered using the LAW =1 option. This option explicitly allows energy and angular output distributions for each particle produced in the reaction. Such information should preserve the balance between partial kermas and the total kerma at the groupwise level as well as the individual particle averaged energies. For simpler 2-body reactions, LAW = 2 is available. This allows the evaluation to specify only enough data to specify the 2-body reaction fully. Such a simplification does not exist for 3 (or more) body breakups. A simplified form of LAW 2, i.e., LAW 3, also exists to generate approximate recoil output distributions in the absence of full data. However, evaluated data does not generally exist at this fine granularity for reactions involving more than 2 output particles ( e.g., the 3-body break-up reaction). When the multi-body detailed output distribution data is not available, LAW=6 may be employed in NJOY. LAW 6 produces approximate output distributions for all the particles produced in the reaction. Just like in the 2-body case, the smaller particles will generally carry off more energy. At any particular energy, the balance between the sum of the partial kermas and the total kerma will not necessarily be preserved. However, the average energy of each output particle from a reaction is preserved.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

More solar models and neutrino fluxes.

Derivation of neutrino fluxes from a sequence of solar models that differ from one another in regard to opacity, equation of state, and nuclear cross-section factors. Using current estimates of the relevant input parameters, capture rates are obtained that range between three and ten times the most recent result of the Davis Cl 37 neutrino-capture experiment. The contribution to a theoretical capture rate due to neutrinos from all reactions other than B 8 decay ranges from 0.5 to 1.5 times the latest observational result. Comparison with results of other solar model calculations indicates reasonable agreement when results are normalized to the same input parameters.

Abraham, Z.↗

Measurement of the Ne 18 ( α , p ) Na 21 reaction with the ANASEN active-target detector system at E c . m . = 2.5 – 4 MeV

The 18 Ne(α,p) 21 Na reaction plays a significant role in Type-I X-ray bursts. It is a major path in the breakout from the hot-CNO cycles to the synthesis of heavier elements in the αp- and rp-processes. An experiment to determine the cross section of this reaction was performed with the ANASEN active-target detector system, determining the cross section at energies between 2.5 and 4 MeV in the center-of-mass frame. The measured cross sections for reactions populating the ground state in 21 Na are consistent with results obtained from the time-inverse reaction, but significantly lower than the previously published experimental data of direct measurements. The total cross sections are also compared with those derived from indirect methods and statistical-model calculations. Furthermore, this experiment establishes a new experimental data set on the excitation function of the 18 Ne(α,p) 21 Na reaction, revealing the significance of the excited states' contributions to the total reaction cross section and allowing us to separate the contribution of the (α,2p) reaction. The impact of the measured cross section on thermal reaction rates is discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Calculations of the $np→dγ$ reaction in chiral effective field theory

Here, we present a calculation of the radiative capture cross section of the $np→dγ$ reaction in the low-energy range, where the M⁢1 reaction channel dominates. Employing the LENPIC nucleon-nucleon interaction up to the fifth order (N4LO) that is regularized by the semilocal coordinate space regulators, we obtain the initial and final state wave functions, and evaluate the phase shifts of the scattering state and deuteron properties. We derive the transition operator from the chiral effective field theory up to the next-to-next-to leading order (N2LO), where we also regularize the transition operator using regulators consistent with those of the interactions. We compute the capture cross sections, and the results show a converging pattern with the chiral-order expansion of the nucleon-nucleon interaction, where the regulator dependence of the results is weak when higher-order nucleon-nucleon interactions are employed. We quantify the uncertainties of the cross-section results due to the chiral-order truncation. The chirally complete and consistent cross-section results are calculated up to N2LO and they compare well with the experiments and other theoretical predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Review of Neutron Yield from (α, n) Reactions: Data, Methods, and Prospects

Understanding the radiogenic neutron production rate through the (α, n) reaction is crucial in many areas of physics, including dark matter searches, neutrino studies, and nuclear astrophysics. In addition to its relevance for fundamental research, the (α, n) reaction also plays a significant role in nuclear energy technologies, for example by contributing to neutron production in subcritical systems using UO2, as well as in applications such as medical physics. This review examines the current state of (α, n) yield calculations and neutron spectra, describes the computational tools used for their estimation, and discusses the available cross-section data. We discuss the uncertainties affecting (α, n) yield estimations and propose a strategy to enhance their accuracy. Furthermore, this paper discusses and emphasizes the need for new measurements of (α, n) cross-sections for a variety of relevant materials. Such measurements are essential for improving neutron flux predictions, which are crucial for reducing uncertainties in sensitivity estimates for next-generation physics experiments operating in the keV—MeV range.

(α, n)reactions↗

Multinucleon transfer mechanism in Cf 250 + Th 232 collisions using the quantal transport description based on the stochastic mean-field approach

Production cross sections of heavy neutron-rich isotopes are calculated by employing quantal transport description in 250 Cf + 232 Th collisions. This quantal transport description is based on the stochastic mean-field approach, and it provides a microscopic approach beyond time-dependent Hartree-Fock theory to include mean-field fluctuations. Deexcitation of primary fragments is determined by employing the statistical GEMINI++ code. Here, calculations provide predictions for production cross sections of neutron rich transfermium isotopes without any adjustable parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Recognizing Unrecognized Sources of Uncertainty (USU) in Nuclear Data

Historically, time-of-flight (TOF) nuclear cross section measurements on different nuclides are assumed to be uncorrelated if they were recorded in different facilities with identical methods, identical facilities with different methods, and even identical facilities with identical methods. Ideally, measurements of different nuclides would truly be uncorrelated thus providing independent assessments of some cross section. In reality, correlations exist between measurements but are simply assumed to be unimportant. To eliminate these qualitative assumptions, in this paper we make a counter-intuitive suggestion to perform an intentionally correlated measurement of energy-differential fission and capture reactions for nuclides in a single criticality safety benchmark during a single experimental campaign. While this would introduce undesirable correlations, it would fully quantify correlations between datasets, rather than assume that the correlations do not exist.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

12 C(p,p') 12 C Reaction ( E p =19.5–30 MeV) for Active Interrogation of Special Nuclear Material

Passive detection of special nuclear material (SNM) is challenging due to its inherently low rate of spontaneous emission of penetrating radiation, the relative ease of shielding, and the fluctuating and frequently overwhelming background. Active interrogation, the use of external radiation to increase the emission rate of characteristic radiation from SNM, has long been considered to be a promising method to overcome those challenges. Current active-interrogation systems that incorporate radiography tend to use bremsstrahlung beams, which can deliver high radiation doses. Low-energy ion-driven nuclear reactions that produce multiple monoenergetic photons may be used as an alternative. The 12 C ( p , p ' ) 12 C reaction is one such reaction that could produce large yields of highly penetrating 4.4- and 15.1-MeV gamma rays. This reaction does not directly produce neutrons below the approximately 19.7 MeV threshold, and the 15.1-MeV gamma-ray line is well matched to the photofission cross section of 235 U and 238 U . In this article, we report the measurements of thick-target gamma-ray yields at 4.4 and 15.1 MeV from the 12 C ( p , p ' ) 12 C reaction at proton energies of 19.5, 25, and 30 MeV. Measurements are made with two 3 -in. EJ-309 cylindrical liquid scintillation detectors and thermoluminescent dosimeters placed at 0 ° and 90 ° , with an additional 1.5 -in. Na I ( Tl ) cylindrical scintillation detector at 0 ° . We estimate the highest yields of the 4.4- and 15.1-MeV gamma rays of 1.65 × 10 10 and 4.47 × 10 8 sr - 1 μ C - 1 at a proton energy of 30 MeV, respectively. The yields in all experimental configurations are greater than in a comparable deuteron-driven reaction that produces the same gamma-ray energies— 11 B ( d , n γ ) 12 C . However, a significant increase of the neutron radiation dose accompanies the proton energy increase from 19.5 to 30 MeV.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Quantifying uncertainties due to optical potentials in one-neutron knockout reactions

One-neutron knockout reactions have been widely used to extract information about the single-particle structure of nuclei from the valley of stability to the drip lines. The interpretation of knockout data relies on reaction models, where the uncertainties are typically not accounted for. In this work, we quantify uncertainties of optical potentials used in these reaction models and propagate them, for the first time, to knockout observables using a Bayesian analysis. We study two reactions in the present paper, the first of which involves a loosely bound halo projectile, 11 Be, and the second a tightly bound projectile, 12 C. We first quantify the parametric uncertainties associated with phenomenological optical potentials. Complementing this approach, we also quantify the model uncertainties associated with the chiral forces that can be used to construct microscopic optical potentials. For the phenomenological study, we investigate the impact of the imaginary terms of the optical potential on the breakup and stripping components of the knockout cross sections as well as the impact of the angular range. For the 11 Be case, the theoretical uncertainty from the phenomenological method is on the order of the experimental uncertainty of the knockout observables; however, for the 12 C case, the theoretical uncertainty is significantly larger. Additionally, the widths of the uncertainty bands for the knockout observables obtained for the microscopic study and the phenomenological approach are of similar orders of magnitude. Based on this work we conclude that structure information inferred from the ratio of the knockout cross sections will carry a theoretical uncertainty of at least 20% for halo nuclei and at least 40% for tightly bound nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of γ -ray production via the neutron- O 16 reaction using a 77 MeV quasimonoenergetic neutron beam

Understanding of γ-ray production via neutron interactions on oxygen is essential for the study of neutrino neutral-current quasielastic interactions in water Cherenkov detectors. A measurement of γ-ray production from such reactions was performed using a 77 MeV quasi-monoenergetic neutron beam. Several γ-ray peaks, which are expected to come from neutron- 16 O reactions, are observed and production cross sections are measured for nine γ-ray components of energies between 2 and 8~MeV. Finally, these are the first measurements at this neutron energy using a nearly monoenergetic beam.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dynamical model of J/ψ photoproduction on the nucleon

Here, a dynamical model based on a phenomenological charm quark-nucleon (c – N) potential v cN and the Pomeronexchange mechanism is constructed to investigate the J/ψ photoproduction on the nucleon from threshold to invariant mass W = 300 GeV. The J/ψ – N potential, V J/ψN (r), is constructed by folding v cN into the wave function φ J/ψ ($c\bar{c}$) of J/ψ within a constituent quark model (CQM) of Segovia et al. [Int. J. Mod. Phys. E 22, 1330026 (2013)]. A photoproduction amplitude is also generated by v cN by a $c\bar{c}$–loop integration over the γ → $c\bar{c}$ vertex function and φ J/ψ ($c\bar{c}$). No commonly used vector meson dominance assumption is used to define this photoproduction amplitude which is needed to describe the data near the threshold. The c – N potential v cN (r) is parameterized in a form such that the predicted V J/ψN (r) at large distances has the same Yukawa potential form extracted from a lattice QCD (LQCD) calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)]. The parameters of vcN are determined by fitting the total cross-section data of Jefferson Laboratory (JLab) by performing calculations that include J/ψ – N final-state interactions (FSI). The resulting differential cross sections dσ /dt are found in good agreements with the data. It is shown that the FSI effects dominate the cross section in the very near-threshold region, allowing for sensitive testing of the predicted J/ψ – N scattering amplitudes. By imposing the constraints of J/ψ – N potential extracted from the LQCD calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)], we have obtained three J/ψ – N potentials which fit the JLab data equally well. The resulting J/ψ – N scattering lengths are in the range of a = [-0.05, -0.25] fm. With the determined v cN (r) and the wave functions generated from the same CQM, the constructed model is used to predict the cross sections of photoproduction of η c (1S) and ψ(2S) mesons for future experimental tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Impact of Thermal Scattering Law on Similarity Assessment in Light-Water or Polyethylene-Moderated Systems

A collaborative effort between Pacific Northwest National Laboratory (PNNL) and Oak Ridge National Laboratory (ORNL) is underway to provide a technical basis and methodology for the criticality safety community to use the sum of fractions (SoF) method for generating limits for mixtures of “selected actinide nuclides” included in the ANSI/ANS 8.15 standard. The PNNL scope in this project is to define a range of mixtures of 233 U, 235 U, and 239 Pu moderated with either light water or polyethylene and to examine the critical masses for these mixtures. The ORNL scope is primarily to provide validation support for these studies. More complete discussion of the project and its validation aspects will be presented at the upcoming International Conference on Nuclear Criticality Safety (ICNC) this Fall in Sendai, Japan. Clear differences in benchmark similarity to application systems as assessed by the integral parameter ck are noted in the validation studies performed as part of this project as a function of moderator. The c k value is a correlation coefficient that represents that amount of shared uncertainty in k eff due to cross sections between two systems. Individual nuclide-reaction contributions between the two systems can be simply summed to arrive at the total c k value. Specifically, the c k values for light-water–moderated solution experiments are higher for a water-moderated application than for a polyethylene-moderated application. This result is neither totally unexpected nor surprising, but the magnitude of the difference was difficult to anticipate. The TSUNAMI sequence, in the SCALE 6.2.4 code package developed by ORNL, was used to generate eigenvalues and reactivity effects with perturbation-theory based approach through sensitivity coefficients for all nuclides in the system with all reactions and energy groups. The TSUNAMI-Indices and Parameters (IP) sequence then uses the sensitivity data generated through TSUNAMI to generate relational parameters (i.e., c k ) to determine the degree of similarity between systems. One detail of the SCALE material and data implementation must be discussed at this point. Several thermal scattering laws (TSLs) are available for 1 H. SCALE uses a different nuclide ID number for each TSL; essentially, each version of 1 H is treated as a unique nuclide. For example, 1 H bound in water ( 1 H-H2O) is assigned the nuclide ID 1001, whereas 1 H bound in polyethylene (h-poly) is assigned the nuclide ID 9001001. The same cross section data are used for all reactions in 1 H, regardless of TSL, except for scattering below the TSL cutoff energy. TSUNAMI-IP treats different nuclide IDs as different nuclides; thus, no uncertainty is shared between 1 H-H2O and h-poly, despite much of the same data, including covariance data, being used for both nuclides. This presents a question: how much of the difference in assessed similarity between water- and polyethylene-moderated systems is due to the moderators, and how much is caused by the treatment of 1 H-H2O and h poly with cross section and covariance data. The extended edits generated by TSUANMI-IP allow for an investigation of this issue specifically, as well as a demonstration of the general techniques available within TSUNAMI to understand the results of the similarity assessment. This paper presents and analyzes the similarity assessment of both water- and polyethylene-moderated systems for a single benchmark: PST-002-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

16 O ⁡(𝑒,𝑒′⁢𝛼)⁢ 12 C measurements and the 12 C ⁡(𝛼,𝛾)⁢ 16 O astrophysical reaction rate

The 12 C ⁡(𝛼,𝛾)⁢ 16 O reaction, an important component of stellar helium burning, has a key role in nuclear astrophysics. It has significant impact on the evolution and final state of heavy to low mass stars, maximum mass of stellar formed black holes and also shapes the elemental abundances resulting from nucleosynthesis in such stars. Providing a reliable estimate for the energy dependence of this reaction at stellar helium burning temperatures has been a longstanding and important goal. In this work, we study the role of potential new 𝐸⁢1 and 𝐸⁢2 measurements of the 16 O ⁡(𝑒,𝑒′⁢𝛼)⁢ 12 C reaction in reducing the overall uncertainty in the astrophysical 𝑆 factor for the 12 C ⁡(𝛼,𝛾)⁢ 16 O 𝐸⁢1 and 𝐸⁢2 ground state capture extrapolated to a stellar energy of 300 keV. A multilevel 𝑅-matrix analysis is used to make extrapolations of the 𝑆 𝐸⁢1 (300 keV) and 𝑆 𝐸⁢2 (300 keV) factors for the 12 C ⁡(𝛼,𝛾)⁢ 16 O reaction from existing ground state capture data. Bayesian analysis is used to quantify the uncertainties in the extrapolations for both the existing data alone and also when possible new experimental data are included. In particular, we consider a new experiment that would make use of a high-intensity low-energy electron beam that impinges on a windowless oxygen gas target as a means to determine the total 𝐸⁢1 and 𝐸⁢2 ground state cross sections for this reaction. Here we find that the new data could significantly reduce the 𝑆⁡(300) uncertainties. Splitting the new data into high and low energy regions shows that both low and high energy data are effective in reducing the uncertainty.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Report to NCSP on 2008 DANCE measurements of 233 U($\eta$,$\gamma$)

Uranium-233 plays an important role in the Th-U fuel cycle, with substantial production in the cycle. This cycle has been proposed as an alternative to the U-Pu fuel cycle due to its reduced production of transuranic elements. An accurate measurement of the 233 U($\eta$,$\gamma$) cross section is required by the National Criticality Safety Program (NCSP) to complete the neutron-induced cross section data, where experimental capture cross section data are scarce and were measured decades ago. The most recent capture cross section data available in the literature were measured in 2007 at the n_TOF facility (CERN); in the 60s measurements were performed at Rensselaer Polytechnic Institute (RPI) and at LANL. Finally, as reported by ORNL, a new evaluation with a revised (renormalized) fission cross section is needed on 233 U. The challenge for this measurement lies in the difficulty of measuring the capture cross section data in the competing fission background, as the fission cross section is around one order of magnitude larger than the capture cross section for 233 U. The accuracy of a capture cross section measurement depends on discrimination between $\gamma$’s produced in capture and fission reactions, for which an experimental setup combining capture and fission detectors is needed. For the ($\eta$,$\gamma$) cross section measurement at LANSCE, this discrimination is achieved by combining the Detector for Advanced Neutron Capture Experiments (DANCE), to measure $\gamma$’s from capture reactions, with a Parallel Plate Avalanche Counter (PPAC) to tag the $\gamma$’s produced by fission. This method was successfully used to measure 235 U and 239 Pu capture cross sections. In these measurements, the neutron capture cross section was determined in a large fission background well above 100 keV. As part of the NCSP nuclear data effort, we have looked at past DANCE measurements on 233 U($\eta$,$\gamma$) and evaluated whether existing data is adequate to apply this technique.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Consistent Nuclear Data Evaluations for Criticality Safety

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

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗