Unresolved Resonance Research Articles

Benchmarking of probability tables with TRIPOLI-5®

In this work we present the verification of the unresolved resonance range treatment implementation in the Monte Carlo code TRIPOLI-5®, which relies on probability tables. For this purpose, we perform extensive code-to-code comparisons with respect to TRIPOLI-4® and OpenMC using two probability tables models (PURR and CALENDF), on a set of benchmark configurations. These tests allow on one hand verifying TRIPOLI-5® and on the other hand analyzing a number of discrepancies related both to the use of different probability tables models and more generally to the handling of nuclear data in the Monte Carlo codes.

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.

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.

Current status of the verification and processing system GALILÉE-1 for Evaluated Data

This paper describes the current status of GALILÉE-1 [1], the new verification and processing system for evaluated data, developed at CEA. It consists of various components respectively dedicated to read/write the evaluated data independently of the format, to diagnose inconsistencies in the evaluated data and to provide continuous-energy and multigroup data as well as probability tables for particle transport and depletion codes. All these components are written in C++ language and share the same objects. In this paper, we detail themain advances made in GALILÉE-1 : Unresolved Resonance Range (URR) treatment, Thermal Scattering Law (TSL) processing and anisotropy calculations from resonance parameters.

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.

Development and verification of a new nuclear data processing code AXSP

The advanced reactor design needs an accurate cross-section generation code. In this study, a new nuclear data processing code AXSP is developed, and the method and performance of which are described. Compared with the NJOY program, the precision of the unresolved resonance processing module UnresXS has been significantly improved due to the adoption of a more accurate solution method and the consideration of in-sequence overlap integrals. The time consumption of PUnresXS has been decreased significantly due to an optimized sorting algorithm. At the same time, other modules of AXSP are relatively comprehensive. The function of resolved resonance cross-section reconstruction and linearization is the ReconXS module. The Doppler broadening module is BroadXS by using Gauss–Hermite quadrature and Gauss–Legendre quadrature from 0 K temperature pointwise cross section to any temperature which is defined by the user. The shielding factor in the unresolved resonance energy region is calculated by the UnresXS or the PUnresXS module, which are developed based on the Bondarenko method and the probability table method, respectively. The ACE formatted cross sections for the Monte Carlo code is processed by the ACEXS module, and the multigroup cross sections are generated by the GroupXS module. The cross sections processed by different modules were verified by the NJOY2016 code, and the multigroup cross sections were also verified by using the critical benchmarks. The multiplication factor difference between AXSP and NJOY2016 is less than 20 pcm. In addition to this, the ZPR6/7 fast reactor is used for ACE format library verification. The results show that the criticality calculated by AXSP has a good agreement with that of NJOY2016.

EPR study of intrinsic defects within NaYGeO4 olivine

An intense electron paramagnetic resonance (EPR) spectrum has been unexpectedly observed at room temperature in polycrystalline samples of NaYGeO4 with olivine crystal structure. Signals were registered in a wide range of fields up to 6000 ​G. Along with strongly broadened unresolved resonance lines, the relatively narrow spectral components were found. It is shown that the spectrum profile depends on synthesis conditions and mechanical treatment of samples, all suggesting a partial orientational order of microcrystallites in the powders. The spectra are interpreted under the assumption of strong superhyperfine interaction between the oxygen-deficient centers like [GeO3]3- and the nuclei of Na+ cations. In addition, a sharp anisotropic resonance at g-values exceeding free-electron value is attributed to oxygenic-hole centers. The density functional theory (DFT) calculations are employed for the estimation of the thermodynamic stability of various intrinsic defects.

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.

On the Self-Shielding in the Unresolved Resonance Range

Abstract Resonance behavior is a feature of nuclear reaction cross sections. Resonance density increases with increasing incident particle energy and they begin to overlap, until they can no longer be resolved experimentally, but they still contribute to self-shielding and must be accounted for. This is usually done by representing them with statistical average parameters according to methods and approximations described in standard text-books. Self-shielding factors are commonly used in deterministic transport codes, while statistical Monte Carlo codes use probability tables or multiband parameters. An exercise was conducted at the International Atomic Energy Agency (IAEA) to validate codes and methods for generating data that account for self-shielding in deterministic and Monte Carlo codes. A simple numerical model problem was defined, considering a sphere of 1 m radius with a 20 MeV isotropic neutron source at the center. The chosen material for testing was 139La from the ENDF/B-VIII.0 library, which clearly showed anomalous behavior.

The Effect of Serpent 2 Calculation Parameters on Evaluated Spent Nuclear Fuel Source Term

Abstract The estimation of spent nuclear fuel source term (decay heat, reactivity, nuclide inventory, etc.) has several sources of uncertainty such as uncertainties in nuclear data, uncertainties in the operation history, and choice of calculation parameters. In this work the effect of calculation parameters is studied by estimating the source term with the built-in burnup capability of serpent. The effect of the following parameters is considered: depletion zone division, burnup steps, unresolved resonance probability table sampling, Doppler-Broadening Rejection Correction (DBRC) and energy-dependent branching ratios. As a test case, a 2D Boiling Water Reactor (BWR) fuel assembly was modeled by first running a burnup calculation followed by a decay calculation. The following source term components were considered when investigating the effect of the studied parameters: total decay heat, photon emission rate and spontaneous fission rate. In general, the differences resulting from the use of different parameter variations were small for all three studied source term components. For the decay heat largest absolute relative difference was approximately 0.6% and for the photon emission rate approximately 1.1%. For the spontaneous fission rate maximum absolute relative difference of nearly 8% was observed. For all three components the variation of the depletion zone division resulted in the largest relative differences. Clear differences were also observed for burnup step length and DBRC variations. The use of unresolved resonance probability table sampling and energy-dependent branching ratios had an insignificant effect on the studied source term components.

Bis-(Fluorene)-Embedded Hexaphyrins.

The polyaromatic hydrocarbon containing expanded porphyrins, bis-(fluorene)-embedded hexaphyrins, were synthesized by condensing fluorene-based tripyrrane with pentafluorobenzaldehyde in CH2Cl2 in the presence of 1 equiv of BF3·OEt2 under an inert atmosphere followed by oxidation with DDQ in open air at room temperature. The reaction worked only when 1 equiv of BF3·OEt2 was added to the reaction mixture under concentrated reaction conditions. The bis-(fluorene)-embedded macrocycles were characterized and studied by high-resolution mass spectrometry (HRMS), nuclear magnetic resonance (NMR), absorption, electrochemical, and density functional theory (DFT)/time-dependent (TD)-DFT techniques. In 1H NMR, the hexaphyrins showed a few broad unresolved resonances at room temperature, but the NMR spectra were well-resolved at lower temperatures, indicating that the hexaphyrins were very flexible. The DFT-optimized structures indicated that the two fluorene units at the crossing point of the figure-eight loop makes an angle of ∼79.73° with each other, the fluorene moieties maintained their own planarity, and one of the fluorene moieties was not involved in conjugation with the rest of the macrocycle. The absorption spectra of hexaphyrins showed one intense sharp band in the higher energy region and a broad band in the lower energy region. The electrochemical studies indicated that expanded hexaphyrins are relatively electron-rich and showed three easier oxidations and one reduction. The DFT/TD-DFT studies are in agreement with the experimental observations.

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.

Orientational Jahn–Teller Isomerism in the Dark‐Stable State of Nature's Water Oxidase

AbstractThe tetramanganese–calcium cluster of the oxygen‐evolving complex of photosystem II adopts electronically and magnetically distinct but interconvertible valence isomeric forms in its first light‐driven oxidized catalytic state, S2. This bistability is implicated in gating the final catalytic states preceding O−O bond formation, but it is unknown how the biological system enables its emergence and controls its effect. Here we show that the Mn4CaO5 cluster in the resting (dark‐stable) S1 state adopts orientational Jahn–Teller isomeric forms arising from a directional change in electronic configuration of the “dangler” MnIII ion. The isomers are consistent with available structural data and explain previously unresolved electron paramagnetic resonance spectroscopic observations on the S1 state. This unique isomerism in the resting state is shown to be the electronic origin of valence isomerism in the S2 state, establishing a functional role of orientational Jahn–Teller isomerism unprecedented in biological or artificial catalysis.

Orientational Jahn-Teller Isomerism in the Dark-Stable State of Nature's Water Oxidase.

The tetramanganese–calcium cluster of the oxygen‐evolving complex of photosystem II adopts electronically and magnetically distinct but interconvertible valence isomeric forms in its first light‐driven oxidized catalytic state, S2. This bistability is implicated in gating the final catalytic states preceding O−O bond formation, but it is unknown how the biological system enables its emergence and controls its effect. Here we show that the Mn4CaO5 cluster in the resting (dark‐stable) S1 state adopts orientational Jahn–Teller isomeric forms arising from a directional change in electronic configuration of the “dangler” MnIII ion. The isomers are consistent with available structural data and explain previously unresolved electron paramagnetic resonance spectroscopic observations on the S1 state. This unique isomerism in the resting state is shown to be the electronic origin of valence isomerism in the S2 state, establishing a functional role of orientational Jahn–Teller isomerism unprecedented in biological or artificial catalysis.

An approach for performing resolved and unresolved resonance evaluation based on few or none experimental data available: Application to unstable and short-lived isotopes

Fluctuations in the neutron cross sections resulting from resonance structures have to be accounted for in the calculation of a nuclear system. Regardless of the approach used, deterministic or stochastic, the depression in the neutron flux due to the resonance effects in the cross section must be well understood for the purpose of providing a good understanding of the self-shielding effects and an accurate calculation of any nuclear system. The R-Matrix theory is the mechanism most appropriate to represent the resonance region providing a detailed description of the cross sections thru resonance parameters.The objective of this work is to present an alternative to generate resonance region evaluation on the basis of the R-matrix theory in the resolved and unresolved energy regions. The proposed methodology can be applied to situations where few or none experimental data are available such as the energy dependent neutron cross section. It leverages over the knowledge of information such as thermal cross section values, Westcott factor, resonance integral, coherent and incoherent scattering lengths, scattering radius, and more important, knowledge of average resonance parameters. The approach is demonstrated and validated with applications for an isotope with a well-known resonance evaluation, that is the 103Rh, and afterwards to an isotope with minimum experimental data available. The latter is the 156Eu isotope.