Uncertainties In Cross Sections Research Articles

Measurement of the neutron total cross section of 9Be at the Back-n white neutron source of CSNS

Abstract The neutron total cross section data of 9Be play an important role in nuclear structure model research of light nuclei and nuclear power installations. A measurement of the neutron total cross section of 9Be in the 0.3 eV-120 MeV energy region has been carried out by using time-of-flight method and transmission method with the Neutron Total Cross Sectional Spectrometer (NTOX) based on the multi-cell fast fission chamber at the China Spallation Neutron Source (CSNS)- Back-n white neutron source (Back-n). The fission count-neutron energy distributions of 235U and 238U without sample and with Be samples in three thicknesses were measured in the double-bunch operation mode during beam power of 100 kW. The Bayesian method is used to eliminate the influence of the double-bunch problem on neutron measurement in the energy region above 10 keV. The neutron total cross section of 9Be results is well consistent with ENDF/B-VIII.0 evaluation library data in 0.3 eV-20 MeV energy region. In the energy range of 0.3 eV to 10 keV, the deviation between our results and the evaluation results of ENDF/B-VIII.0 is within 2.5%, which is within 15% from 0.01-20 MeV. In the resonance energy region, the measured resonance energies in our experiment are 0.63 MeV, 0.82 MeV and 2.8 MeV respectively. The results show that the total cross section uncertainties of three thicknesses Be samples are within 2.2% in the energy region below 1 MeV. The total cross section uncertainty of 30 mm Be from 235U is the smallest and less than 5% in the energy region 0.3 eV-120 MeV. The results of this experiment can provide technical support for further data analysis and related nuclear data evaluation.

Production pair of higher excited massive quarkonium at super Z factory

Abstract Sizable amounts of massive quarkonium events should be produced through $Z^0$ boson decays at a future super $Z$ factory. Such channels will provide a suitable platform to study the precisely properties of massive quarkonium. We show that sizable amounts of events for pair of the higher excited states quarkonia can also be produced at the super Z factory. Therefore, we make a further study on calculate the exclusive production of pair of the higher excited charmonium, pair of the higher excited bottomonium, and pair of the higher excited $B_c$ mesons via $e^+e^-\to Z^0 \to |(Q\bar{Q^\prime})[n]\rangle + |(Q^\prime \bar{Q})[n']\rangle$ ($Q,~Q^\prime=c$- or $b$-quarks) at the future $Z$ factory under the NRQCD, where the $[n]$/$[n^\prime]$ represents the color-singlet states $[n^1S_0], [n^3S_1],~[n^1P_1]$, and $[^3P_J]$ ($[n]=1,2,3;J=0,1,2$).
The differential angle distribution of cross sections $d\sigma/dcos\theta$ is given. For a sound estimate,
we discus the uncertainties of total cross sections caused by varying quark masses and the renormalization scale $\mu$. The numerical results show that the future super $Z$ factory should be also a good platform to study the exclusive production of pair of the higher excited massive quarkonium.

Comparison and evaluation of resolved resonance region covariance representations

ABSTRACT The covariance matrices for the evaluated resolved resonance region parameters are typically processed into a grouped covariance representation for use in uncertainty propagation studies. An alternative method for performing uncertainty propagation would be to use the resonance parameters covariance matrix to sample many realizations of resonance parameters, and then perform a simulation with each sample, employing the total Monte Carlo method. In this paper, we demonstrate that these two techniques can yield drastically different estimations of the uncertainty on k eff . Furthermore, we provide reasoning as to why the grouped covariance approximation is a nonphysical approximation for the resolved resonance region, and how sampling resonance parameters is able to capture variations in the structure of the point-wise cross sections. Our recommendation is that the community move away from the grouped covariance approximation and towards a continuous energy representation, which could be generated by sampling resonance parameters, and ensure that the resonance parameter covariance matrices in evaluated libraries yield realistic grouped cross section uncertainties, regardless of group structure.

Experimental 7Be production cross section from the [formula omitted] reaction at Ep = 3.5 − 13 MeV

The Li7(p,n)7Be reaction is widely used as neutron source for neutron induced reaction cross section measurements, and for 7Be radioactive source production. There are two prominent structures in the excitation function, a narrow resonance between Ep=2.2−2.3 MeV, and a broad peak, around Ep=5 MeV. There are tension between the experimental data sets both in the position and the width of this latter structure, as well as in the absolute scale of the data. In the present work the Li7(p,n)7Be reaction is investigated using the activation technique, with the aim of providing comprehensive cross section data covering the second structure and connecting prior literature data sets. The irradiations were performed with the Atomki cyclotron accelerator with pairs of thin foil targets, thus with precisely controlled reaction energy in the range of Ep=3.5−13 MeV. After the irradiations the activity of the samples was measured using a high-purity germanium detector. The energy uncertainty of the new data points is much smaller than in any of the previous works, while the cross section uncertainty is comparable with the most precise literature data. A consistent data set was obtained connecting the most recent and most precise literature data sets. With the new data the absolute magnitude of the Li7(p,n)7Be reaction cross section is constrained and became more precise.

Applying approximate Bayesian computation to reduce uncertainty in multigroup 235-U cross-sections using ICSBEP experimental data

The multiplication factor (keff) and its uncertainty are critical design parameters in nuclear reactors. The keff uncertainty must be considered for operation, safety, and economic reasons. Consequently, reducing uncertainty in keff has been of interest to the nuclear industry for as long as nuclear reactors were designed. Two methods of reducing this uncertainty are in use – Generalized Linear Least Squares (GLLS) and A General Monte Carlo-Bayes Procedure for Improved Predictions of Integral Functions of Nuclear Data (MOCABA). Both methods have the ability to reduce the keff uncertainty by reducing uncertainty in cross-sections through the assimilation of measured critical systems’ or nuclear reactors’ operational data. The algorithms require means of simulating the experimental data and that the calibrated parameters are described by specific statistical distributions. GLLS is limited to linear models and multivariate normal prior and posterior, while MOCABA can use any (non-linear) model but is also limited to multivariate normal prior and posterior. This work implements a universal and rigorous algorithm called Sequential Monte Carlo – Approximate Bayesian Computation (SMC-ABC) for the same application. It is found that SMC-ABC, GLLS, and likely MOCABA give essentially the same results for the same problems. The paper also presents a reliable method for validating the results based on so-called “synthetic experiments”. Synthetic experiments are computationally generated data used in place of experiments. The method allows for verifying whether there is a risk of overfitting the calibrated parameters (cross-sections in case of this work) during the data assimilation. This novel method shows the potential of using SMC-ABC and other Bayesian calibration methods to generate improved general-purpose neutron cross-section libraries.

Measurement of Photoneutrons from Depleted Uranium and Comparison Study Using MCNPX-PoliMi

High-energy photon interrogation is a nondestructive technique that is used to detect special nuclear materials and characterize nuclear waste. The development of such systems is complex and requires Monte Carlo simulations to optimize system performance. Monte Carlo simulations rely on various scattering, absorption, and photonuclear cross-section data. While the scattering and absorption cross-section data have been extensively studied and validated with experiments, the results obtained from photonuclear simulations are often found to underpredict measured results, indicating uncertainties in the photonuclear cross sections themselves. Thus, there is a need for new measured results that can be used to quantify underpredictions in simulations using photonuclear cross-section data. In the present work, we interrogated depleted uranium with a 9-MV electron linac and detected photoneutrons with trans-stilbene organic scintillators. The measurement of photoneutrons with organic scintillators is challenging due to the presence of the intense photon flux, which causes issues such as pulse pile-up, detector saturation, and poor signal-to-background ratio. To mitigate these challenges, we used iron and polyethylene shielding of varying thicknesses around the depleted uranium target and a neural network–based digital pulse processing algorithm to recover neutron and photon information from piled-up events. Our goal was to compare the measured photoneutron count rate with the simulated rate obtained using the MCNPX-PoliMi transport code. For a light output window of 0.28 to 2.67 MeVee (1.66- to 6.85-MeV proton recoil energy), we found that the simulated count rate obtained using the ENDF/B-VII photonuclear cross-section library underpredicts the measured rate by 32.8% ± 3.2%. Additionally, we compared the simulated and measured photoneutron light output distributions. For the least thicknesses of shielding, the simulation was found to underpredict measurements in the 0.70- to 2.67-MeVee light output window. For the greatest thicknesses of shielding, the simulation was found to underpredict the measurement across the entire light output window of 0.28 to 2.67 MeVee.

Cross-sectional uncertainty and stock market volatility: New evidence

This study investigates the potential of cross-sectional uncertainty (CSU) to predict stock market volatility. Empirical findings reveal that the newly developed variance-based index conditioned on economic policy uncertainty exhibits greater predictive power than the widely used economic policy uncertainty index. Sparse methods consider multiple predictors and perform well. Further research has demonstrated that the CSU index contains more valuable information and delivers better predictive performance and economic value, especially under financial crises. Our study extends the application of the CSU index and provides novel evidence for volatility prediction.

The effects of electron energy distribution and ionization cross section uncertainty on charge breeder ion source diagnostics with pulsed 1+ injection

The consecutive transients (CT) method is a plasma diagnostic technique of charge breeder electron cyclotron resonance ion source plasmas. It is based on the short-pulse injection of singly charged ions and the measurement of the resulting transients of the extracted multi-charged ion beams. Here, we study the origin of the large uncertainty bounds yielded by the method to reveal avenues to improve its accuracy. We investigate effects of the assumed electron energy distribution (EED) and the uncertainty inherited from the ionization cross section data of K4+–K12+ ions on the resulting plasma electron density ne, average energy ⟨Ee⟩, and the characteristic times of ion confinement τq, electron impact ionization τinzq, and charge exchange τcxq provided by the CT method. The role of the EED was probed with Kappa and double-Maxwellian distributions, the latter resulting in a shift of the ne and ⟨Ee⟩ distributions. The uncertainty of the ionization cross section σq→q+1inz was artificially curtailed to investigate its impact on values and uncertainties of the plasma parameters. It is demonstrated that the hypothetical perfect knowledge of σq→q+1inz significantly reduces the uncertainties of τq, τinzq, and τcxq, which motivates the need for improved cross section data.

Measurement of the (n, 2n) reaction cross-sections of iodine and cesium induced by D-T neutrons with covariance analysis* *Supported by the Key Laboratory of Nuclear Data Foundation (JCKY2022201C151), and the National Natural Science Foundation of China (11975113).

The cross-sections of the 127I (n, 2n) 126I and 133Cs (n, 2n) 132Cs reactions at neutron energies of 13.83 ± 0.05, 14.33 ± 0.10, and 14.79 ± 0.10 MeV were measured relative to the 93Nb (n, 2n) 92mNb reaction using the activation technique in combination with off-line γ-ray spectrometry. A neutron beam was generated from the T (d, n) 4He reaction using the K-400 neutron generator at the China Academy of Engineering Physics. Considering the correlations between different attributes, detailed uncertainty propagation was performed using covariance analysis, and the cross-sections were reported with their uncertainties and correlation matrix. The uncertainty of the measurement cross-sections ranged from 4.84 to 5.90%, which is lower than previous experimental data. Furthermore, the theoretical excitation functions of the 127I (n, 2n) 126I and 133Cs (n, 2n) 132Cs reactions were calculated using the TALYS-1.95 and EMPIRE-3.2.3 codes. Then, the experimentally determined cross-sections were analyzed by comparing them with literature data available in the EXFOR database and evaluated nuclear data in the ENDF/B-VIII.0, JEFF-3.3, JENDL-5, BROND-3.1, CENDL-3.2, and TENDL-2021 databases. Compared with the values previously reported in the 13.8-14.8 MeV energy region, the precision of the results obtained in this study was greatly improved. The current experimental results with thorough uncertainties and covariance information are critical for verifying the reliability of the theoretical model and improving the quality of the nuclear database.

Cross sections of partial photoneutron reactions: the problems with reliability and new data

The (𝛾, 1𝑛), (𝛾, 2𝑛) and (𝛾, 3𝑛) reactions cross sections the majority of which were obtained using beams of quasimonoenergetic annihilation photons were discussed. The significant systematic uncertainties of the experimental results far exceeding the achieved statistical accuracy were considered. The results of experiments for about 50 nuclei from 51V to 209Bi were analyzed using objective physical criteria of data reliability. It was shown that in many cases the systematic uncertainties of experimental cross sections were significant and data do not satisfy physical criteria. The experimental theoretical method for evaluation of cross sections satisfying those criteria was described. The systematic uncertainties of several types due to shortcomings of the method of photoneutron multiplicity sorting used in experiments and specific features of neutron detectors used. The new evaluated reliable cross sections of the partial reactions and total photoneutron reaction (𝛾, 1𝑛)+(𝛾, 2𝑛)+(𝛾, 3𝑛) were presented.

Cross-sectional uncertainty and expected stock returns

Cross-sectional uncertainty and expected stock returns

Key nuclear data for non-LWR reactivity analysis

An assessment of nuclear data performance for non-light-water reactor (non-LWR) reactivity calculations was performed at Oak Ridge National Laboratory that involved a thorough literature review to collect related observations made across different research institutions, an interrogation of the latest ENDF/B evaluated nuclear data libraries, and propagation of nuclear data uncertainties to key figures of merit associated with reactor safety for six non-LWR benchmarks. The outcome of this comprehensive study was published in a technical report issued by the US Nuclear Regulatory Commission. This paper provides a summary of the study’s key observations and conclusions and demonstrates with two examples how the various methods available in the SCALE code system were used to identify key cross section uncertainties for non-LWR reactivity analyses.

Cross-Sectional Uncertainty and the Business Cycle: Evidence from 40 Years of Options Data

This paper presents a novel and unique measure of cross-sectional uncertainty constructed from stock options on individual firms. Cross-sectional uncertainty varied little between 1980 and 1995 and subsequently had three distinct peaks—during the tech boom, the financial crisis, and the coronavirus epidemic. Cross-sectional uncertainty has had a mixed relationship with overall economic activity, and aggregate uncertainty is much more powerful for forecasting aggregate growth. The data and moments can be used to calibrate and test structural models of the effects of uncertainty shocks. In international data, we find similar dynamics and a strong common factor in cross-sectional uncertainty. (JEL D21, D81, E23, E24, E32, G13, O34)

Can the production cross-section uncertainties explain the cosmic fluorine anomaly?

The stable secondary-to-primary flux ratios of cosmic rays (CRs), represented by the boron-to-carbon ratio (B/C), are the main probes of the galactic CR propagation. However, the fluorine-to-silicon ratio (F/Si) predicted by the CR diffusion coefficient inferred from B/C is significantly higher than the latest measurement of AMS-02. This anomaly is commonly attributed to the uncertainties of the F production cross sections. In this work, we give a careful test to this interpretation. We consider four different cross-section parametric models. Each model is constrained by the latest cross-section data. We perform combined fits to the B/C, F/Si, and cross-section data with the same propagation framework. Two of the cross-section models have good overall goodness of fit with ${\ensuremath{\chi}}^{2}/{n}_{\mathrm{d}.\mathrm{o}.\mathrm{f}.}\ensuremath{\sim}1$. However, the goodness of fit of the cross-section part is poor with ${\ensuremath{\chi}}_{\mathrm{cs}}^{2}/{n}_{\mathrm{cs}}\ensuremath{\gtrsim}2$ for these models. The best-fitted B production cross sections are systematically larger than the measurements, while the fitted cross sections for F production are systematically lower than the measurements. This indicates that the F anomaly can hardly be interpreted by neither the random errors of the cross-section measurements nor the differences between the existing cross-section models. We find that by developing a hypothetical parametrization this anomaly could be explained, while future measurements will test this possibility. We then propose that the spatially dependent diffusion model could help to explain B/C and F/Si consistently. In this model, the average diffusion coefficient of the Ne-Si group is expected to be larger than that of the C-O group.

Leasing as a Mitigation of Financial Accelerator Effects

Abstract We document that leased capital accounts for about 20% of total physical productive assets used by US public firms, and its proportion is more than 40% among small and financially constrained firms. The leased capital ratio exhibits a strong countercyclical pattern over business cycles and a positive correlation with cross-sectional idiosyncratic uncertainty. We argue that existing macro models with financial frictions assume that firms cannot rent capital and overlook the effects of leasing activities on business cycle dynamics. We explicitly introduce a buy-versus-lease decision into the Bernanke–Gertler–Gilchrist financial accelerator model setting to demonstrate a novel and quantitatively important economic mechanism: that the increased use of leased capital when financial constraints become tighter in bad states significantly mitigates the financial accelerator mechanism and thus also mitigates the response of macroeconomic variables to negative total factor productivity shocks and risk shocks. We provide strong empirical evidence to support our mechanism.

Establishment of DeCART/MIG stochastic sampling code system and Application to UAM and BEAVRS benchmarks

In this study, a DeCART/MIG uncertainty quantification (UQ) analysis code system with a multi-correlated cross section stochastic sampling (S.S.) module was established and verified through the UAM (Uncertainty Analysis in Modeling) and the BEAVRS (Benchmark for Evaluation And Validation of Reactor Simulations) benchmark calculations. For the S.S. calculations, a sample of 500 DeCART multi-group cross section sets for two major actinides, i.e., 235U and 238U, were generated by the MIG code and covariance data from the ENDF/B-VII.1 evaluated nuclear data library. In the three pin problems (i.e. TMI-1, PB2, and Koz-6) from the UAM benchmark, the uncertainties in kinf by the DeCART/MIG S.S. calculations agreed very well with the sensitivity and uncertainty (S/U) perturbation results by DeCART/MUSAD and the S/U direct subtraction (S/U-DS) results by the DeCART/MIG. From these results, it was concluded that the multi-group cross section sampling module of the MIG code works correctly and accurately. In the BEAVRS whole benchmark problems, the uncertainties in the control rod bank worth, isothermal temperature coefficient, power distribution, and critical boron concentration due to cross section uncertainties were calculated by the DeCART/MIG code system. Overall, the uncertainties in these design parameters were less than the general design review criteria of a typical pressurized water reactor start-up case. This newly-developed DeCART/MIG UQ analysis code system by the S.S. method can be widely utilized as uncertainty analysis and margin estimation tools for developing and designing new advanced nuclear reactors.

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering: Part III. Uncertainty Propagation and Multigroup Covariance Matrices

An analytic benchmark for nuclear data uncertainty propagation in k-eigenvalue calculations is demonstrated. Flat-flux-weighted cross-section covariance matrices are available in the ENDF/B library for many isotopes. For application-specific purposes, flux-weighted multigroup cross sections with carefully constructed energy group boundaries are desired. In this paper, we use the covariance information from ENDF/B-VII.1 for the defined continuous-energy cross section and an artificially inflated variance version of the same covariance matrix for first-order and Monte Carlo propagation of uncertainty calculations. A flat-flux weighting function is used for the continuous-energy cross-section uncertainty collapse resulting in a higher propagated uncertainty on the k-eigenvalue as the group structure becomes coarser. The results of this analytic benchmark suggest that the reporting of flat-flux-weighted multigroup cross-section covariance matrices at the ENDF level may lead to inaccurate predictions of the uncertainty on the k-eigenvalue for certain applications. This work implies that not only should the resonance parameter uncertainties that go into the calculation of the continuous-energy cross sections be published, but the parameter uncertainties should also be processed into continuous-energy cross-section uncertainties that can be collapsed to application-specific multigroup cross-section covariance matrices.

Initial Neutronics Investigation of a Chlorine Salt–Based Breeder Blanket

Tritium breeding blankets within D-T-fueled fusion reactors contain lithium compounds and typically require neutron multiplier materials to achieve a tritium breeding ratio (TBR) consistent with self-sustaining operation. Liquid breeder blankets have some advantages over solid blankets, and previous blanket studies have investigated liquid metal as well as liquid salt–based blankets. Liquid salts have reduced magnetohydrodynamic effects as compared to liquid metals, but typically have a lower TBR. Recently, advanced fission reactor concepts have considered chloride-based salts in their design, and there is a significant amount of research work occurring to study these salts. Chloride salts have previously been considered for fusion reactors, but studies have typically found lower breeding ratios than for fluoride salts, such as 2(LiF)-BeF2 (flibe) so they have not been further developed. In this work, we use a one-dimensional cylindrical radiation transport model of a conceptual tokamak fusion reactor to investigate the neutronics feasibility of using a chloride salt–based blanket that uses chlorine enriched in 37Cl, which has both a low capture cross section and a substantial (n,2n) cross section. It is found that chloride salts (LiCl mixed with BeCl2 and/or PbCl2) can potentially achieve a ~3% to 5% higher TBR than fluoride molten salts, notably flibe, in the absence of a solid multiplier. Including a solid multiplier, however, does narrow this advantage, with TBRs estimated within ~1% of flibe with a 2-cm Be multiplier. Chloride salts can also reach lower melting points than flibe, potentially improving the scope for the use of reduced activation ferritic-martensitic steel as a structural material. There is substantial uncertainty in the calculations driven by limited thermochemical data for the Cl salts, plus cross-section uncertainties. The production of 36Cl through 35Cl(n,g) and 37Cl(n,2n) has the potential to challenge the waste disposal rating of the blanket. Calculations indicate that, while this is not an immediate showstopper, this case depends upon the exact waste disposal rating criteria used for 36Cl. Further work could reduce these uncertainties with improved thermochemical data, higher-fidelity modeling for downselected salts, and more refined waste disposal calculations and regulatory guidance. Finally, it must be recognized that, as for all molten salts, corrosion and chemistry can present appreciable technical challenges that require further assessment in developing a practical blanket concept, and also that the enrichment of chlorine presents an additional technical and supply chain challenge.

Analysis of the preliminary campaign for the PETALE program

The PETALE program aims to provide new experimental data to constrain the stainless steel nuclear data. In this frame, a preliminary measurement campaign has been performed to characterize the neutron flux in key positions of the CROCUS reactor and to develop analysis tools. During this preliminary campaign detailed in the present paper, an efficiency ratio technique has been developed and tested to speed up HPGe measurements by a factor of 30. A second objective of the campaign concerns the propagation of nuclear data uncertainty from the core neutron cross-sections to the reaction rates in the dosimeters. Uncertainties in the core cross sections, such as the uranium cross section, are nuisance parameters that add uncertainty to the dosimeter reaction rate calculation. This component must be fully characterized with covariances to constrain the metal reflector component for Bayesian assimilation. The experimental results are compared to the calculations with different nuclear databases for the nuclear data uncertainty propagation. A good agreement is obtained with the ENDF/B-VII.1 database and a systematic underestimation of around 5–10% in the fast range is observed with the ENDF/B-VIII.0 and JEFF-3.3 databases.

Templates of expected measurement uncertainties for (n, xn) cross sections

A template is provided for evaluating experimental uncertainties for neutron elastic and inelastic scattering cross sections andγ-ray production cross sections from (n, xn) measurements at laboratories with monoenergetic or white neutron sources. A typical range of uncertainties is presented for experiments detecting the scattered neutrons or the resulting de-excitationγrays based on a survey of available data and input from many experimentalists and theorists with extensive knowledge in the field. Models commonly used to evaluate the resulting cross-sections are also discussed. Suggestions are made regarding what experimental and uncertainty information is needed for data evaluations and should be included when reporting experimental (n, xn) cross sections. Uncertainty values and correlations are recommended if these values cannot be estimated for past data from the literature.