Evaluation Of Neutron Cross Sections Research Articles

Evaluation of Neutron Cross Sections of 48Ti based on the Unified-Monte-Carlo-B Method

Abstract A cross section evaluation of neutron induced reactions on 48Ti is undertaken using the Unified Monte Carlo-B (UMC-B) approach. The evaluation focus on estimating the covarainces and the use of the UMC-B allows avoiding the deficiencies of linear regression brought by the traditional least squares method. Eight main neutron and charged particle emission reactions from n+48Ti in the fast neutron energy region below 20 MeV are studied in this work. The posterior probability density function (PDF) of each neutron cross section is obtained in a UMC-B Bayesian approach by convoluting the model PDFs sampled based on model parameters and the likelihood functions for the experimental data. Nineteen model parameters including level density, pair corrections, optical model and Kalbach matrix element parameter are stochastically sampled with the assumption of normal distributions to estimate the model uncertainty. The Cholesky factorization approach is applied to consider potential parameter correlations. Finally, the posterior covariance matrices are generated using the UMC-B generated weights. The new evaluated results are compared with the CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, TENDL-2021 and JENDL-5 evaluations and differences are discussed.

Covariance evaluation of neutron cross sections in CENDL

The covariance evaluation for neutron cross sections in CENDL is briefly introduced in this work. The methodology for evaluation contains the nuclear reaction theoretical model-dependent approach and the non-model dependent one according to the amount of experimental data. Both approaches are based on the Generalized Least-Squares (GLSQ) method. To obtain more reliable uncertainties from experimental measurement, the analysis of the sources of experimental uncertainties (ASEU) is used rigorously in the evaluation. Moreover, machine learning (ML) methods which can deal with the data mining with a more automatic way are employed to evaluate the cross sections in a large-scale nuclear mass region to compensate the uncertainties on some nuclides and reactions, lack of experimental data for, e.g., unstable nuclei and fission products. The covariance files for 70 fission product nuclei are obtained through the model-dependent method in CENDL-3.2, and the covariances for U and Pu isotopes have also been finished with high fidelity, which will be released as part of the next CENDL.

Testing the Extended SRM against the 238U(3He,4He)237U* surrogate probabilities

Since its introduction in the seventies’, the so-called surrogate-reaction method (SRM) has motivated the development and improvement of theories in connection to direct reactions. A recent work by Bouland and Noguère, Phys. Rev. C 102, 054608 (2020), has shown that the inclusion of experimental probabilities in the neutron cross section evaluation process can be better achieved using tools resulting from the efforts made over the two last decades. In particular, the authors have put forward a new prescription, named after the SRM as extended SRM (ESRM), to convert, with reasonable confidence, probabilities measured in direct reactions to pseudo-experimental neutron-induced reaction cross sections. Applied to the 174Yb(3He,py)176Lu* transfer reaction, the ESRM has demonstrated much more precision than the early use of the SRM. In addition to the ‘direct’ analysis of reaction probabilities measured in direct reactions using the right modeling as developed in Phys. Rev. C 100, 064611 (2019), it is worth to try converting the measured probabilities in pseudo experimental neutron-induced cross sections for neutron reactor data applications. In the present paper, first results, before conversion, are shown by applying the two ESRM equations to a fissile isotope.

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

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

Reconciling surrogate-reaction probabilities and neutron-induced cross sections

Since its inception, the so-called surrogate-reaction method (SRM) has motivated the development and improvement of theories in connection to direct reactions. This paper reassesses some of the developments carried out in previous decades to deal with the representation of direct reaction probability data. It is believed that the experimental probabilities assimilation in the neutron cross section evaluation process can be better estimated using tools resulting from the efforts made over the years. This paper provides a new perspective on this issue both in terms of fission and $\ensuremath{\gamma}$-ray emission probabilities. In addition to the ``natural'' assimilation path that considers analyzing probabilities jointly with cross sections to extract nuclei structural properties, this article puts forward a prescription to convert, with a good level of confidence, measured direct-reaction induced probabilities to pseudoexperimental neutron-induced cross sections. This approach is named after the SRM as extended SRM (ESRM).

Neutron Cross Section Evaluation of Tungsten and Tantalum

The evaluations of neutron cross sections and covariances are presented for tungsten and tantalum which are considered as a prime candidate of plasma facing materials in fusion reactors and/or a structural material of the Korea Helium Cooled Ceramic Reflector (Ko HCCR) Test Blanket Module (TBM). The Fusion Evaluated Nuclear Data Library (FENDL-2.1) has been employed as the nuclear data for the neutronics analysis to obtain the optimal design parameters for Ko HCCR TBM. However, the neutron cross sections and energy and/or angular dependent neutron spectra from FENDL-2.1 showed some discrepancies with the differential and integral measured data available for tungsten and tantalum. In response to these situations, the neutron cross section for 181Ta and 180,182,183,184,186W have been newly evaluated using the up-to-date nuclear reaction code and the measured data available.

Beryllium and Graphite Neutron Total Cross-Section Measurements from 0.4 to 20 MeV

The Gaerttner Laboratory electron linear accelerator at Rensselaer Polytechnic Institute was used in the measurement of the neutron total cross section of natural beryllium and carbon (graphite) in the energy range of 0.4 to 20 MeV. Neutron transmission measurements were made using the time-of-flight method with a 100-m flight path, fast detector response and electronics, and a narrow neutron pulse width to provide good energy resolution. A method was developed to determine the time-dependent background component associated with the transmission measurement using a combination of experimental data and Monte Carlo methods. The signal-to-background ratio combined with low counting statistics error resulted in low uncertainties and highly accurate data. The graphite measurement, showing excellent agreement with the current evaluations, provided a verification of the accuracy in the measurement and analytical methods used. The measurements of beryllium resulted in an accurate measurement of total cross section, showing some deviations with commonly used evaluations and better agreement with ENDF/B-VI.8. These results can be used for the improvement of future neutron cross-section evaluations of beryllium.

Evaluation of Neutron Cross Sections for Hafnium in the Resolved Resonance Range

The international High Priority Request list notes: “In the nuclear industry hafnium is used as neutron absorbing material to regulate the fission process. Interpretation of critical experiments with UOx fuel conducted by CEA in the AZUR zero-power reactors has shown systematic underestimation of the reactivity worth that may be attributed to an overestimated natural hafnium capture cross section in the epi-thermal energy range” To service the request for improved resonance data a PhD project has:a) Improved REFIT R-matrix evaluation code. b) Obtained hafnium oxide samples enriched in Hf176, 177, 178, 179 isotopes. c) Gained support from NUDAME and EUFRAT projects. d) Prepared enriched and natural Hf samples. e) Performed capture and transmission Time of Flight measurements at the GELINA linear accelerator. f) Analysed the capture counts to generate yields using AGS and AGL codes. g) Used REFIT to perform least squares analysis of GELINA measurements. (Included previous ORNL, Harwell and RPI transmissions and capture yields.) h) Submitted results to EXFOR. i) Included resolved resonance parameters in JEFF evaluations taking the resolved range to over 1 keV. j) Tested evaluations with suitable benchmarks. k) Passed resolved resonance data to CEA Cadarache for unresolved analysis. Resultant Hf evaluations will be included in JEFF3.2.

CREOLE experiment study on the reactivity temperature coefficient with sensitivity and uncertainty analysis using the MCNP5 code and different neutron cross section evaluations

In the present work, we analyze the CREOLE experiment on the reactivity temperature coefficient (RTC) by using the three-dimensional continuous energy code (MCNP5) and the last updated nuclear data evaluations. This experiment performed in the EOLE critical facility located at CEA/Cadarache, was mainly dedicated to the RTC studies for both UO 2 and UO 2–PuO 2 PWR type lattices covering the whole temperature range from 20 °C to 300 °C. We have developed an accurate 3D model of the EOLE reactor by using the MCNP5 Monte Carlo code which guarantees a high level of fidelity in the description of different configurations at various temperatures taking into account their consequence on neutron cross section data and all thermal expansion effects. In this case, the remaining error between calculation and experiment will be awarded mainly to uncertainties on nuclear data. Our own cross section library was constructed by using NJOY99.259 code with point-wise nuclear data based on ENDF-BVII, JEFF3.1 and JENDL3.3 evaluation files. The MCNP model was validated through the axial and radial fission rate measurements at room and hot temperatures. Calculation-experiment discrepancies of the RTC were analyzed and the results have shown that the JENDL3.3 and JEFF3.1 evaluations give the most consistent values; the discrepancy is less than 0.23 pcm/°C. Whereas, when using ENDF-BVII evaluation for UOX configuration, this discrepancy reaches a value of 0.63 pcm/°C. In order to specify the source of this relatively large discrepancy in the case of ENDF-BVII nuclear data evaluation, the k eff discrepancy between ENDF-BVII and JENDL3.3 was decomposed by using sensitivity and uncertainty analysis technique. The thermal energy range of 238U( n,γ) absorption cross section was found to contribute to the major part of the observed k eff discrepancy between ENDFB-VII and JENDL3.3 evaluations.

International Evaluation of Neutron Cross Section Standards

Neutron cross section standards are the basis for the determination of most neutron cross sections. They are used for both measurements and evaluations of neutron cross sections. Not many cross sections can be obtained absolutely – most cross sections are measured relative to the cross section standards and converted using evaluations of the standards. The previous complete evaluation of the neutron cross section standards was finished in 1987 and disseminated as the NEANDC/INDC and ENDF/B-VI standards. R-matrix model fits for the light elements and non-model least-squares fits for all the cross sections in the evaluation were the basis of the combined fits for all of the data. Some important reactions and constants are not standards, but they assist greatly in the determination of the standard cross sections and reduce their uncertainties – these data were also included in the combined fits. The largest experimental database used in the evaluation was prepared by Poenitz and included about 400 sets of experimental data with covariance matrices of uncertainties that account for all cross-energy, cross-reaction and cross-material correlations. For the evaluation GMA, a least-squares code developed by Poenitz, was used to fit all types of cross sections (absolute and shape), their ratios, spectrum-averaged cross sections and thermal constants in one full analysis. But, the uncertainties derived in this manner, and especially those obtained in the R-matrix model fits, have been judged to be too low and unrealistic. These uncertainties were substantially increased prior to their release in the recommended data files of 1987. Modified percentage uncertainties were reassigned by the United States Cross Section Evaluation Working Group's Standards Subcommittee for a wide range of energies, and no covariance (or correlation) matrices were supplied at that time. The need to re-evaluate the cross section standards is based on the appearance of a significant amount of precise experimental data and improved developments in the methodology of analysis and evaluation. Initial efforts to produce a new evaluation were made by the United States Cross Section Evaluation Working Group which formed a Task Force. It was realized that international cooperation would be needed to produce the evaluation. The Working Party on International Evaluation Cooperation of the Nuclear Energy Agency Nuclear Science Committee formed a Subgroup, and the International Atomic Energy Agency formed a Coordinated Research Project (CRP). These groups worked cooperatively to improve the evaluation process. The major effort in producing the evaluation was through the CRP. The evaluations of the neutron cross section standards were finalized in October 2005. Previous difficulties experienced with a data evaluation problem known as “Peelle's Pertinent Puzzle” create biases in the fit of correlated data, and they have been addressed to reduce this phenomenon. The new evaluations of the cross section standards also include covariance matrices of the uncertainties that contain fully justifiable values. The product of this international effort has been adopted as the neutron standards for ENDF/B-VII.0.

A Monte Carlo Approach to Nuclear Model Parameter Uncertainties Propagation

The evaluation of neutron cross sections in the low energy range (electron volt, mega-electron-volt) is based on formal nuclear models having different types of parameters. Some of them may be fitted to reproduce experimental datasets giving rise to an adjusted covariance matrix. In this paper, a Monte Carlo method is presented to properly consider the influence of the remaining parameters, having a priori uncertainties, on the fitted parameters covariances. This method is based on an exact mathematical description using conditional probabilities. To explain the key points of the methodology, an academic example of average parameters evaluation in the unresolved resonance range is presented using Hauser-Feshbach model calculations.

Evaluation of Neutron Cross Sections for a Complete Set of Nd Isotopes

Neutron cross sections for a complete set of Nd isotopes, 142,143,144,145,146,147,148,150Nd, were evaluated in the incident energy range from 10−5 eV to 20 MeV. In the low-energy region, including thermal and resolved resonances, our evaluations are based on the latest data published in the Atlas of Neutron Resonances, Fifth Edition: Resonance Parameters and Thermal Cross Sections, Z = 1 – 100. In the unresolved resonance region, we performed additional evaluation by using the averages of the resolved resonances and adjusting them to the experimental data. In the fast neutron region, we used the nuclear reaction model code EMPIRE-2.19 validated against the experimental data. The results are compared to the existing nuclear data libraries, including ENDF/B-VI.8, JENDL-3.3, and JEFF-3.1, and to the available experimental data. The new evaluations are suitable for neutron transport calculations, and they were adopted by the new U.S. evaluated nuclear data ENDF/B-VII.0, released in December 2006.

Critical Mass and Subcritical Experiments Interlaced with Nb-1Zr, Re, Mo, Ta-2.5W Fueled with Highly Enriched Uranium in Support of the Prometheus Project

The National Aeronautics and Space Administration is considering nuclear power sources for space exploration. A series of critical mass experiments was designed to address the development, performance, and design of a space nuclear reactor being considered to support the Prometheus project. These experiments consisted of interlacing the refractory metals rhenium (Re), molybdenum (Mo), tantalum-2.5 wt% tungsten (Ta-2.5W), and niobium-1 wt% zirconium (Nb-1Zr) with moderating materials (graphite or polyethylene) and were fueled by highly enriched uranium plates. These experiments are designed to assess the adequacy of and uncertainty in refractory metal neutron cross-section evaluations for use in Prometheus nuclear reactor design work. The critical experiments were designed in the energy spectrum closely resembling or bracketing that in the proposed space reactor. For each material (Re, Mo, Ta-2.5W and Nb-1Zr), four critical configurations were designed and performed to measure the sensitivity of keff to the material under four different and progressively softer neutron spectra (core center spectrum, harder than core average spectrum, softer than core average spectrum, and accident flooded spectrum). The thicknesses of the graphite or polyethylene moderator and reflector plates were adjusted to achieve the desired neutron spectrum. One critical and 18 subcritical experiments provided for measurements of material neutronic behavior in a simple cylindrical geometry configuration that was modeled in MCNP with ENDF/B-VI.6 cross-section data and compared to the extrapolated or predicted critical mass for all the experiments. These experiments were performed at the Los Alamos National Laboratory using the Planet vertical lift critical assembly at the Los Alamos Critical Experiment Facility.

Evaluation of neutron cross sections for a complete set of Dy isotopes

Neutron cross sections for a complete set of Dy isotopes, 156,158,160,161,162,163,164Dy, were evaluated in the incident energy range from 10 −5 eV to 20 MeV. In the low energy region, including thermal and resolved resonances, our evaluations are based on the latest data published in the Atlas of Neutron Resonances. In the unresolved resonance region we performed additional evaluation by using the averages of the resolved resonances and adjusting them to the experimental data. In the fast neutron region, we used the nuclear reaction model code EMPIRE-2.19 with the model parameters adjusted to the experimental data. The results are compared with the available experimental data and with the existing nuclear data libraries, including ENDF/B-VI.8 and JEFF-3.1. The new evaluations are suitable for neutron transport calculations and they were adopted by the new US evaluated nuclear data library, ENDF/B-VII.0, released in December 2006.

05/02052 Triple-humped fission barrier model for a new 238U neutron cross-section evaluation and first validations

05/02052 Triple-humped fission barrier model for a new 238U neutron cross-section evaluation and first validations

New neutron cross-section measurements at ORELA and their application in nuclear criticality calculations

Many older neutron cross-section evaluations from libraries such as ENDF/B-VI or JENDL-3.2 show deficiencies in energy ranges that are important for criticality safety applications. Consequently, these evaluated data may not be adequate for nuclear criticality calculations where effects such as self-shielding, multiple scattering, or Doppler broadening are important. To support the Nuclear Criticality Safety Program, neutron cross-section measurements have been initiated at the Oak Ridge Electron Linear Accelerator (ORELA). ORELA is ideally suited to measure fission, neutron total, and capture cross-sections in the energy range from 1eV to ∼600keV, which is important for many nuclear criticality safety applications.

Triple-humped fission barrier model for a new 238U neutron cross-section evaluation and first validations

A new neutron-induced cross-section evaluation of 238U from 1 keV up to 200 MeV has been performed using only nuclear reactions models. A new fission penetrability model taking into account a triple humped barrier has been developed. A clear improvement has been observed for K-effective validation tests (up to 30 MeV) with this new evaluation. This improvement is mainly due to a better treatment of the inelastic exit channel.

Calculation of the neutron induced fission cross-section of 233Pa up to 20 MeV

Since very recently, direct measurements of the 233 Pa( n, f) cross-section are available in the energy range from 1.0 to 8.5 MeV. This has stimulated a new, self-consistent, neutron cross-section evaluation for the n+ 233 Pa system, in the incident neutron energy range 0.01–20 MeV. Since higher fission chances are involved also the lighter Pa-isotopes had to be re-evaluated in a consistent manner. The results are quite different compared to earlier evaluation attempts. Since 233Pa is a key isotope in the thorium based fuel cycle the quality of its reaction cross-sections is important for the modeling of future advanced fuel and reactor concepts. The present status of the evaluated libraries is that they differ by a factor of two in the absolute fission cross-section and also in the threshold energy value.

Application of Nuclear Data in Fusion Neutronics

An overview is given of nuclear data applications in fusion neutronics as being addressed in different task areas of the European Fusion Technology Programme. Main applications are in the design and development of breeder blankets for fusion demonstration & power plants and test blanket modules for ITER, the International Thermonuclear Experimental Reactor. Benchmark analyses of integral 14 MeV neutron experiments are conducted to qualify nuclear data evaluations of the European Fusion & Activation Files (EFF/EAF) and to validate neutronic design calculations. Another major application area is in the development of an accelerator based Li-D intense neutron source for high fluence irradiations of fusion reactor materials. The associated development work includes evaluations of neutron cross-sections above 20 MeV and the development of a Li(d, xn) source term model for Monte Carlo calculations. The paper addresses key issues and major achievements in these areas and concludes with guidelines for future developments both with regard to nuclear data improvements and required integral experiments.

Neutron Cross-Section Evaluations of Fission Products in the Fast Energy Region

Neutron cross-sections for 19 high priority fission products were evaluated from the unresolved resonance energy region up to 20 MeV. Evaluation procedures included optical model parameter search, followed by complete nuclear reaction model calculations with parameters carefully validated against experimental data. Calculations were done with the code Empire using the following models: spherical optical and coupled-channels deformed optical, multistep direct and multistep compound, preequilibrium exciton, and Hauser-Feshbach with width fluctuation corrections. Results were converted into the ENDF-6 format and detailed graphical comparisons with both CSISRS experimental data and ENDF files was performed. In most cases a considerable improvement over the current ENDF/B-VI library was achieved.