Unresolved Resonance Region Research Articles

Measurement of the neutron capture cross sections of rhenium up to stellar s - and r -process temperatures at the China Spallation Neutron Source Back-n facility

The neutron capture measurement of natural rhenium was performed with the time-of-flight technique at the Back-n facility of the China Spallation Neutron Source in the energy range from 1 to 500 eV of the resolved resonance region (RRR) and from 5 to 400 keV in the unresolved resonance region (URR). Prompt γ-rays originating from neutron-induced capture events were detected by four C6D6 detectors. The pulse height weighting technique and the double-bunch unfolding method based on the Bayesian theory were used in the data analysis. To obtain reliable measurement results, background subtraction, normalization, and corrections were carefully considered. The multilevel R-matrix Bayesian code was used to extract the resonance parameters in the RRR. An absence of resonance near 392 eV is observed in our measurement, which has been observed in previous works. The average cross sections in the URR of natural rhenium relative to Au197 were obtained in logarithmical equidistant energy bins with 20 bins per energy decade. The code was used to describe the average cross sections in the URR; the Maxwellian-averaged cross sections (MACSs) of Re185 and Re187 are given from kT=5 to 100 keV. At a thermal energy of kT=30 keV, the MACS value for Re185 (1469±127 mb) is in good agreement with the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNIS) recommended value (1535±62 mb) within the error bars. By contrast, the value of 1361±118 mb for Re187 shows a discrepancy with the recommended value (1160±57 mb). Published by the American Physical Society 2024

A Compact Model for Unresolved Resonance Region Cross Sections

For decades, the probability table technique has been used to model the behavior of neutron cross sections in the unresolved resonance region with a stochastic approach. Early work from Hwang hinted at the possibility of a universal probability distribution to fit the URR cross section distribution. In this work we present a solution to Hwang’s problem: the normal inverse Gaussian distribution fits the probabilistic behavior of the total cross section almost perfectly for the most important nuclides, both in asymptotic behavior and around the more probable regions.

New Measurements to Resolve Discrepancies in Evaluated Model Parameters of 181Ta

To resolve discrepancies in evaluated cross sections among major nuclear data libraries, energy-differential neutron transmission and radiative capture yield of 181Ta were measured from 0.15 to 100 keV using multiple sample thicknesses. The new measurements provide resolution such that the resolved resonance region (RRR) can be evaluated up to at least 2.5 keV and the unresolved resonance region can be evaluated up to at least 100 keV. The transmission and capture yield measurements were modeled using resonance parameters from three major libraries to assess the predictive capability of each. It was found that JENDL-5.0 performed best in the RRR. Because of the poor performance of the U.S. ENDF/B evaluation, it is recommended that ENDF/B be reevaluated for 181Ta.

Measurement of the ^{181} Ta(n,gamma ) cross sections up to stellar s-process temperatures at the CSNS Back-n

The neutron capture cross section of ^{181} Ta is relevant to s-process of nuclear astrophysics, extraterrestrial samples analysis in planetary geology and new generation nuclear energy system design. The ^{181}Ta(n,gamma ) cross section had been measured between 1 eV and 800 keV at the back-streaming white neutron facility (Back-n) of China spallation neutron source(CSNS) using the time-of-flight (TOF) technique and hbox {C}_{6},hbox {D}_{6} liquid scintillator detectors. The experimental results are compared with the data of several evaluated libraries and previous experiments in the resolved and unresolved resonance region. Resonance parameters are extracted using the R-Matrix code SAMMY in the 1–700 eV region. The astrophysical Maxwell average cross section(MACS) from kT = 5 to 100 keV is calculated over a sufficiently wide range of neutron energies. For the characteristic thermal energy of an astrophysical site, at kT = 30keV the MACS value of ^{181}Ta is 834 ± 75 mb, which shows an obvious discrepancy with the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNiS) recommended value 766 ± 15 mb. The new measurements strongly constrain the MACS of ^{181}Ta(n,gamma ) reaction in the stellar s-process temperatures.

Convergence behavior of statistical uncertainty in probability table for cross section in unresolved resonance region

ABSTRACT The probability table method is a well-known method for addressing self-shielding effects in the unresolved resonance region. A long computational time is required to generate the table. The effective way to reduce the generation time is the reduction of the number of ladders. The purpose of this study is the estimation of the optimal number of ladders using the statistical uncertainty in the probability table. To this end, the statistical uncertainty quantification method of the probability table was developed and the convergence behavior of the statistical uncertainty was investigated. The product of the probability and the average cross section was considered the target of the statistical uncertainty. The convergence behavior was investigated by using Sr-90, U-235, and U-238 from JENDL-4.0. The calculation results revealed that the convergence rate of the statistical uncertainty was different in each nuclide and it was affected by the average level spacing and the average reduced neutron width. The generation time of the probability table was less than half when the input parameter for the iteration condition was changed from the number of ladders to the tolerance value. The developed method leads to the efficient generation of probability tables and the reduction of processing time.

A new 103Rh Unresolved Resonance Region evaluation

A new evaluation in the Unresolved Resonance Region has been performed for 103Rh, an important fission product. The evaluation was done in coordination with and is consistent with a new Resolved Resonance Region evaluation. It was determined using measured total cross section data that there is significant structure in the underlying dilute-average cross section within the unresolved resonance energy range of the evaluation (8–40.146 keV). Energy-dependent strength functions are provided to more accurately represent this structure. A covariance matrix for the average parameters that represent the entire Unresolved Resonance Region is provided to comply with the current ENDF-6 format. This new evaluation more closely matches the experimental data available when compared to the current evaluations.

First measurement of the 94Nb(n,γ) cross section at the CERN n_TOF facility

One of the crucial ingredients for the improvement of stellar models is the accurate knowledge of neutron capture cross-sections for the different isotopes involved in the s-,r- and i- processes. These measurements can shed light on existing discrepancies between observed and predicted isotopic abundances and help to constrain the physical conditions where these reactions take place along different stages of stellar evolution. In the particular case of the radioactive 94Nb, the 94Nb(n,γ) cross-section could play a role in the determination of the s-process production of 94Mo in AGB stars, which presently cannot be reproduced by state-of-the-art stellar models. There are no previous 94Nb(n,γ) experimental data for the resolved and unresolved resonance regions mainly due to the difficulties in producing highquality samples and also due to limitations in conventional detection systems commonly used in time-of-flight experiments. Motivated by this situation, a first measurement of the 94Nb(n,γ) reaction was carried out at CERN n_TOF, thereby exploiting the high luminosity of the EAR2 area in combination with a new detection system of small-volume C6D6-detectors and a high quality 94Nb-sample. The latter was based on hyper-pure 93Nb material activated at the high-flux reactor of ILL-Grenoble. An innovative ring-configuration detection system in close geometry around the capture sample allowed us to significantly enhance the signal-to-background ratio. This set-up was supplemented with two conventional C6D6-detectors and a highresolution LaCl3(Ce)-detector, which will be employed for addressing reliably systematic effects and uncertainties. At the current status of the data analysis, 18 resonance in 94Nb+n have been observed for the first time in the neutron energy range from thermal up to 10 keV.

233U(n,γ) measurements at LANSCE

Uranium-233 plays an important role in the Th-U fuel cycle, which has been proposed as an alternative to the U-Pu fuel cycle due to its reduced amount of transuranium elements. The available experimental 233U(n,γ) cross section data in the literature are scarce, [1–3]. In 2008, the 233U(n,γ) cross section was investigated at LANL using the DANCE detector combined with a PPAC, however the statistics in the keV regime were inadequate for a reliable extraction of the cross section at 100 keV. An accurate measurement of the 233U(n,γ) cross section is required by the NCSP to complete the neutron-induced cross section data; a new evaluation reported the need of 233U capture data. The challenge in this measurement lies in the difficulty of measuring capture cross section data due to the competing capture and fission channels. Fission reactions are around one order of magnitude more likely than capture for 233U. The accuracy in the capture cross section measurement relies on the discrimination between the γ-rays produced in capture and fission reactions, for which an experimental setup combining capture and fission detectors is needed. Following this requirement, a new measurement has been performed at LANSCE combining the γ-ray array DANCE with the neutron detector NEUANCE to identify fission and neutron-capture events. This measurement will provide results of the 233U capture-to-fission ratio in the Resolved and Unresolved Resonance regions.

Statistical Uncertainty Quantification of Probability Tables for Unresolved Resonance Cross Sections

The probability table method is an important method to treat the self-shielding effect in the unresolved resonance region. A probability table is generated by using many “ladders” that represent pseudo resonance structures. This study developed a quantification method of the statistical uncertainty of a probability table. The product of the probability table and average cross section in each probability bin was considered as the target of the statistical uncertainty of the probability table. The central limit theorem (CLT), bootstrap method, and jackknife method were adopted to calculate the statistical uncertainty. The statistical uncertainties calculated using these methods were compared with the reference results. The calculation results showed that the statistical uncertainties obtained by CLT were similar to those of the other methods. Because the CLT calculation time was faster than that of the other methods, CLT was deemed as the best method for calculating the statistical uncertainty of the probability table. The statistical uncertainty quantification of the probability table developed in this study was implemented in nuclear data processing code FRENDY version 2. FRENDY version 2 can generate a probability table using the tolerance of the statistical uncertainty of the probability table.

Improved Mo95 neutron resonance parameters and astrophysical reaction rates

Background: Improved $^{95}\mathrm{Mo}$ neutron resonance parameters and reaction rates are important for nuclear astrophysics, testing nuclear models, and nuclear criticality safety. However, despite many previous neutron-capture and total cross-section measurements on this nuclide, there still is much room for improvement as well as several discrepancies. For example, there are very few firm resonance spin and parity assignments; average resonance parameters are available only for each parity, the currently recommended astrophysical reaction rate results in disagreements between stellar models and meteoric isotopic anomalies, and there are substantial disagreements in the neutron-capture cross section at low energies important for nuclear criticality safety.Purpose: To obtain an improved set of neutron resonance parameters and astrophysical reaction rates for $^{95}\mathrm{Mo}$.Method: High-resolution neutron-capture and transmission data were measured at the Oak Ridge Electron Linear Accelerator (ORELA) using highly isotopically enriched $^{95}\mathrm{Mo}$ samples. The neutron-capture apparatus, data reduction, and analysis were improved so that information contained in the $\ensuremath{\gamma}$-ray cascade following neutron capture were used to assign resonance ${J}^{\ensuremath{\pi}}$ values. Following this, simultaneous analysis of the new neutron-capture and transmission data was used to obtain resonance energies, gamma widths, and neutron widths and their uncertainties to a maximum energy of 10 keV. Accurate neutron-capture cross sections also were obtained for the unresolved resonance region to a maximum energy of 500 keV and, together with the new resonance parameters, used to calculate the astrophysical reaction rates in the temperature range from 5 to 30 keV.Results: A vastly improved set of $^{95}\mathrm{Mo}$ neutron resonance parameters and an astrophysical reaction rate accurate to about 3% were obtained. Firm ${J}^{\ensuremath{\pi}}$ assignments were determined for 261 of the 314 observed resonances. This is a very large improvement over the previously published 32 firm ${J}^{\ensuremath{\pi}}$ assignments for 108 resonances. Also, the number of resonances having both firm ${J}^{\ensuremath{\pi}}$ assignments and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$ values was increased by almost a factor of 24---from 11 to 261. Neutron- and total-radiation-width distributions and average resonance spacings, average total radiation widths, and neutron strength functions were obtained for the six different $s$- and $p$-wave possibilities. Parameters for the lowest $s$-wave resonance, which is most important for criticality benchmarks, were obtained with high accuracy.Conclusions: Simple modification of the neutron-capture apparatus and expansion and improvement of data analysis techniques led to a large increase in firm ${J}^{\ensuremath{\pi}}$ assignments for $^{95}\mathrm{Mo}$ neutron resonances. The resulting astrophysical reaction rate is 20%--30% larger than the currently recommended rate at $s$-process temperatures, which should lead to better agreement between stellar models and meteoric isotopic anomalies. The neutron-capture cross section at low energies is substantially larger than recommended in the latest evaluation, which is problematical for criticality benchmarks. The average resonance spacing as a function of spin and parity is significantly different from current models. The total-radiation-width distributions are significantly broader than predicted by theory and show significant departures from the expected Gaussian shapes.

Measurement of 232Th (n, γ) cross section at the CSNS Back-n facility in the unresolved resonance region from 4 keV to 100 keV

The neutron capture cross section of 232Th was measured at the neutron time-of-flight facility Back-n of China Spallation Neutron Source (CSNS) for the first time. The measurement was performed with 4 hydrogen-free deuterated benzene C6D6 liquid scintillation detectors, in the ES#2 experiment station on the beam line, at a distance of about 76 m from the neutron-production assembly. The total energy detection principle in combination with the pulse height weighting technique (PHWT) was applied to analyze the measured data. Results of the 232Th (n, γ) reaction cross section in the unresolved resonance region from 4 keV to 100 keV were obtained, which shows a good agreement with the existing experimental data from EXFOR, as well as with the evaluated data from the ENDF/B-VIII.0 and CENDL-3.1. In addition, the excitation function of 232Th (n, γ)233Th reaction in the unresolved resonance region was theoretically calculated by using the code TALYS-1.95. By fitting the experimental cross section and theoretical data, the average parameters in the unresolved resonance region were extracted. The datasets are openly available at http://dx.doi.org/10.11922/sciencedb.j00113.00015.

DIAGNOSIS OF THE UNRESOLVED DOMAIN TREATMENT IN MONTE CARLO TRANSPORT CALCULATIONS THROUGH THE IDENTIFICATION AND MODELLING OF CRITICALITY SAFETY EXPERIMENTS

Monte Carlo neutron transport codes can be used for high-fidelity predictions of the performance of nuclear systems. However, validation against experiments is required in order to establish the credibility in the results and identify the inaccuracies due to the used calculation scheme and associated databases. The International Handbook of Evaluated Criticality Safety Benchmark Experiments (ICSBEP) contains criticality safety benchmarks derived from experiments that have been performed at various nuclear critical facilities around the world and are very valuable for validation purposes. The main objective of this work is the identification and modelling of experimental benchmarks included at ICSBEP in support of the validation of Monte Carlo neutron transport calculations when applied to fast systems, and in particular, KENO-VI and associated AMPX-formatted continuous-energy libraries from SCALE package. In such systems, the predicted k-eff values can be very sensitive to the treatment of nuclear data in the Unresolved Resonance Region (URR). Consequently, benchmarks with intermediate and fast spectra are identified and modelled with KENO-VI. Then, calculated results with and without probability tables in the URR are compared with each other in order to identify the most sensitive configurations to the URR. As a result of the proposed study, recommendations are given about the benchmarks that should be modelled and analysed to qualify the processed continuous-energy libraries before their use in Monte Carlo transport codes for practical fast reactor applications.

INVESTIGATION OF APPROPRIATE LADDER NUMBER ON PROBABILITY TABLE GENERATION

The probability table method is widely used for continuous energy Monte Carlo calculation codes to treat the self-shielding effect in the unresolved resonance region. The ladder method is used to calculate the probability table. This method generates pseudo resonance structures using random numbers based on the averaged resonance parameters. The probability table affects the ladder number, i.e., the number of pseudo resonance structures. Since the higher the ladder number the longer it takes to create a cross-section library, reducing the value of the ladder number is an effective way to reduce the time spent in the creation of a cross-section library. However, the exact value of the most appropriate ladder number to use has not been found. Currently, users have to use a nuclear data processing system to manually set the ladder number to a large enough value in order to obtain a sufficiently converged probability table. In this study, the probability tables for all nuclides prepared in JENDL-4.0 are used to find the optimal ladder number. The results show that the probability table differences are small enough when the ladder number is 100. The impact of these differences on neutronics calculations is found to be small.

On-the-fly temperature-dependent cross section treatment under extremes in RMC code

Neutron transport relevant to inertial confinement fusion always involves extremes, in which the physical quantities are extremely high, widely distributed and changes rapidly with space and time. In order to solve the memory and efficiency problems in nuclear data storage and processing, the on-the-fly temperature-dependent cross section treatment technique was investigated and developed under extremes in RMC code. Different strategies were adopted for different energy regions, i.e., the free gas model in the thermal region, the TMS method with 0K basis cross section temperature in the resolved resonance region, and the infinite dilution cross section in the unresolved resonance region, whereas the high energy region above the unresolved resonance region was not treated currently. The test results of Godiva sphere and plutonium sphere show that the on-the-fly technique has high accuracy, but the efficiency of the proposed technique still needs to be improved for some cases, and the optimization work with the elevated basis cross section temperatures is ongoing.

Implementation of Probability Table Generation Using Ladder Method in Ruler

Probability table is one of the most important and natural methods used to simulate the neutron transport in unresolved resonance range in reactor physics. A new module for generating probability tables in the unresolved-resonance region has been developed for the nuclear data processing code Ruler, using ladder method. In order to validate and verify the accuracy of this module, Probability tables have been calculated and compared with NJOY2016. Agreement is observed in the comparisons of the probability tables and corresponding cross-section values that are calculated by Ruler and NJOY2016. Ruler has improved computational efficiency greatly comparing with NJOY2016 as multi-thread parallel algorithm is applied.

Measurement of the 242Pu(n, γ) cross section from thermal to 500 keV at the Budapest research reactor and CERN n_TOF-EAR1 facilities

The design and operation of innovative nuclear systems requires a better knowledge of the capture and fission cross sections of the Pu isotopes. For the case of capture on 242Pu, a reduction of the uncertainty in the fast region down to 8-12% is required. Moreover, aiming at improving the evaluation of the fast energy range in terms of average parameters, the OECD NEA High Priority Request List (HPRL) requests high-resolution capture measurements with improved accuracy below 2 keV. The current uncertainties also affect the thermal point, where previous experiments deviate from each other by 20%. A fruitful collaboration betwen JGU Mainz and HZ Dresden-Rossendorf within the EC CHANDA project resulted in a 242Pu sample consisting of a stack of seven fission-like targets making a total of 95(4) mg of 242Pu electrodeposited on thin (11.5 μm) aluminum backings. This contribution presents the results of a set of measurements of the 242Pu(n, γ) cross section from thermal to 500 keV combining different neutron beams and techniques. The thermal point was determined at the Budapest Research Reactor by means of Neutron Activation Analysis and Prompt Gamma Analysis, and the resolved (1 eV - 4 keV) and unresolved (1 - 500 keV) resonance regions were measured using a set of four Total Energy detectors at the CERN n_TOF-EAR1.

Validation of Unresolved Neutron Resonance Parameters Using a Thick-Sample Transmission Measurement

Often discrepancies can be found in the corresponding cross sections of different evaluated nuclear data libraries. Traditional integral benchmarks that are used to validate such libraries are sensitive to cross-section values across many different energies. This means an erroneously low cross section at one energy may compensate for an erroneously high cross section at another energy, and the integral benchmark value may still be met. While the evaluated cross section may agree with that single benchmark, it could affect other systems differently. To reduce the potential for this error, an energy differential validation method is proposed herein for continuous energy Monte Carlo neutron transport models in the resolved resonance region and the unresolved resonance region (URR). The proposed method exposes the underlying physics of the URR and validates both the average cross section and resonance self-shielding effect driven by the fluctuations in that cross section. This is done by measuring the neutron transmission of a thick sample that, by its nature, exaggerates the resonance self-shielding effect. This validation method is shown to be very sensitive to the cross-section model used (resolved versus unresolved) and the fluctuation correction employed, allowing it to probe the validity of the previously mentioned cross-section evaluations. Tantalum-181 is used as an example to demonstrate the impact of different resonance evaluations. It was found that the JEFF-3.3 and JENDL-4.0u evaluations made reasonable choices for cross-section models of 181Ta; none of the current evaluations, however, can be used to properly model the validation transmission over all energies. It was also found that updating resonance parameters in the URR provided better agreement with the validation transmission.

Improvement of few-group cross-section generation in fast reactor analysis system SARAX

For better accuracy, the few-group cross-section generation module, named TULIP, in the SARAX code system was further improved. In the new TULIP, the pure deterministic method was used for the spectrum calculation and self-shielding treatment. The improvements contained two parts. One was the method for resonance treatments in the unresolved resonance region. The probability table method was adopted and the self-shielding factors for different reaction types were distinguished. The background cross-section interpolation points of major actinides were refined for the Bondarenko interpolation. These techniques significantly improved the accuracy of self-shielded cross-sections and contributed to better Doppler constant calculation. The other improvement was the method of Energy-collapsing SuPer-Homogenization technique for the group condensation. It preserved the reaction rates conservation in the multigroup-fewgroup equivalence and improved the accuracy in the strong heterogeneous problems. Several numerical and experimental benchmarks have been done to test the improvements. The results showed that the accuracy of homogenized cross-sections, k-infinity and Doppler constant in subassembly calculation was significantly improved, also for the k-effective, power distribution and reaction rate distribution in the core calculation.

Impact of alternative transmission coefficient parametrizations on Hauser-Feshbach theory

We investigate different formulations of the transmission coefficient $T_c$, including the form implied by Moldauer's ``sum rule for resonance reactions'' [P.A. Moldauer, Phys. Rev. Lett. 19, 1047 (1967)], the SPRT method [G. Noguere, et al. EPJ Web Conf. 146, 02036 (2017)] and the Moldauer-Simonius form [M. Simonius, Phys. Lett. 52B, 279 (1974); P.A. Moldauer, Phys. Rev. 157, 907 (1967)]. Within these different formulations, we compute the neutron transmission coefficients in the resolved and unresolved resonance regions, allowing a direct comparison with the transmission coefficients computed using an optical model potential. For nuclei for which there are no measured resonances, these approaches allow one to predict the average neutron resonance parameters directly from the optical model and level densities. Some of the approaches are valid in both the strong and weak coupling limits (i.e., any value of the average width and mean level spacing). Finally, both the Moldauer-Simonius and Moldauer's Sum Rule forms approaches suggest that superradiance, that is, the quantum chaotic enhancement of certain channels, may be a common phenomena in nuclear collisions. Our results suggest why superradiance has been previously overlooked. We apply our approach to neutron reactions on the closed shell $^{90}$Zr nucleus and the mid-shell $^{197}$Au nucleus.

Measurement and analysis of theAm241neutron capture cross section at the n_TOF facility at CERN

The Am241(n,γ) cross section has been measured at the n_TOF facility at CERN with the n_TOF BaF2 Total Absorption Calorimeter in the energy range between 0.2 eV and 10 keV. Our results are analyzed as resolved resonances up to 700 eV, allowing a more detailed description of the cross section than in the current evaluations, which contain resolved resonances only up to 150–160 eV. The cross section in the unresolved resonance region is perfectly consistent with the predictions based on the average resonance parameters deduced from the resolved resonances, thus obtaining a consistent description of the cross section in the full neutron energy range under study. Below 20 eV, our results are in reasonable agreement with JEFF-3.2 as well as with the most recent direct measurements of the resonance integral, and differ up to 20–30% with other experimental data. Between 20 eV and 1 keV, the disagreement with other experimental data and evaluations gradually decreases, in general, with the neutron energy. Above 1 keV, we find compatible results with previously existing values.8 MoreReceived 31 January 2018DOI:https://doi.org/10.1103/PhysRevC.97.054616Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNeutron physicsNuclear reactorsRadiative capturePropertiesA ≥ 220Nuclear Physics