Unresolved Resonance Region Research Articles

Radiative neutron capture cross section from U236

The $^{236}\mathrm{U}(n,\ensuremath{\gamma})$ reaction cross section has been measured for the incident neutron energy range from 10 eV to 800 keV by using the Detector for Advanced Neutron Capture Experiments (DANCE) $\ensuremath{\gamma}$-ray calorimeter at the Los Alamos Neutron Science Center. The cross section was determined with the ratio method, which is a technique that uses the $^{235}\mathrm{U}(n,f)$ reaction as a reference. The results of the experiment are reported in the resolved and unresolved resonance energy regions. Individual neutron resonance parameters were obtained below 1 keV incident energy by using the $R$-matrix code sammy. The cross section in the unresolved resonance region is determined with improved experimental uncertainty. It agrees with both ENDF/B-VII.1 and JEFF-3.2 nuclear data libraries. The results above 10 keV agree better with the JEFF-3.2 library.

On-the-fly Doppler broadening of unresolved resonance region cross sections

Two methods for computing temperature-dependent unresolved resonance region cross sections on-the-fly within continuous-energy Monte Carlo neutron transport simulations are presented. The first method calculates Doppler broadened cross sections directly from zero-temperature average resonance parameters. In a simulation, at each event that requires cross section values, a realization of unresolved resonance parameters is generated about the desired energy and temperature-dependent single-level Breit-Wigner resonance cross sections are computed directly via the analytical ψ−χ Doppler integrals. The second method relies on the generation of equiprobable cross section magnitude bands on an energy-temperature mesh. Within a simulation, the bands are sampled and interpolated in energy and temperature to obtain cross section values on-the-fly. Both of the methods, as well as their underlying calculation procedures, are verified numerically in extensive code-to-code comparisons. Energy-dependent pointwise cross sections calculated with the newly-implemented procedures are shown to be in excellent agreement with those calculated by a widely-used nuclear data processing code. Relative differences at or below 0.1% are observed. Integral criticality benchmark results computed with the proposed methods are shown to reproduce those computed with a state-of-the-art processed nuclear data library very well. In simulations of fast spectrum systems which are highly-sensitive to the representation of cross section data in the unresolved region, k-eigenvalue and neutron flux spectra differences of <10 pcm and <1.0% are observed, respectively. The direct method is demonstrated to be well-suited to the calculation of reference solutions — against which results obtained with a discretized representation may be assessed — as a result of its treatment of the energy, temperature, and cross section magnitude variables as continuous. Also, because there is no pre-processed data to store (only temperature-independent average resonance parameters) the direct method is very memory-efficient. Typically, only a few kB of memory are needed to store all required unresolved region data for a single nuclide. However, depending on the details of a particular simulation, performing URR cross section calculations on-the-fly can significantly increase simulation times. Alternatively, the method of interpolating equiprobable probability bands is demonstrated to produce results that are as accurate as the direct reference solutions, to within arbitrary precision, with high computational efficiency in terms of memory requirements and simulation time. Analyses of a fast spectrum system show that interpolation on a coarse energy-temperature mesh can be used to reproduce reference k-eigenvalue results obtained with cross sections calculated continuously in energy and directly at an exact temperature to within <10 pcm. Probability band data on a mesh encompassing the range of temperatures relevant to reactor analysis usually require around 100 kB of memory per nuclide. Relative to the case in which probability table data generated at a single, desired temperature are used, minor increases in simulation times are observed when probability band interpolation is employed.

Ta181(n,γ) cross section and average resonance parameter measurements in the unresolved resonance region from 24 to 1180 keV using a filtered-beam technique

A new array of four Deuterated Benzene (${\mathrm{C}}_{6}{\mathrm{D}}_{6}$) detectors has been installed at the Gaerttner Linear Accelerator Center at Rensselaer Polytechnic Institute for the purpose of measuring neutron capture cross sections in the keV region. Measurements were performed on samples of $^{181}\mathrm{Ta}$ in the unresolved resonance region (URR) using a filtered-beam technique, by which a 30 cm iron filter was placed in a white-spectrum neutron beam to remove all time-dependent $\ensuremath{\gamma}$-ray background and all neutrons except those transmitted through resonance-potential interference ``windows'' in the iron. The resulting filtered beam was effectively a quasimonoenergetic neutron source, which was used for performing measurements on isotopes with narrow level spacings in the URR. The capture cross-section results obtained for two thicknesses of tantalum are in agreement with those documented in the JEFF-3.2 library, as are the average resonance parameters obtained via a fit to the data using the sammy-fitacs code.

Simultaneous Measurement of 235U Fission and Capture Cross Sections From 0.01 eV to 3 keV Using a Gamma Multiplicity Detector

The neutron microscopic capture cross section for 235U is a critical parameter for the design and operation of nuclear reactors. The evaluated nuclear data libraries of ENDF/B-VII.1 and JENDL-4.0 have nearly identical values for the neutron capture cross section for neutron energies below 0.5 keV. In the most recent release of the JENDL library the onset of the unresolved resonance region was changed from 2.25 keV to 0.5 keV. In the energy region from 1.5 keV to 2.25 keV the average neutron capture cross section from ENDF/B-VII.1 is about 10% higher than that from JENDL-4.0. In an attempt to address the discrepancies between the libraries, a measurement of the neutron capture cross section of 235U was conducted at the Gaerttner LINAC Center located at Rensselaer Polytechnic Institute. This measurement used a 16-segment -multiplicity NaI(Tl) detector to detect the prompt gammas emitted from neutron interactions with a highly enriched 235U sample. Using the time-of-flight method, detected events were recorded and grouped based on the total gamma energy per interaction and observed multiplicity. A method was developed to separate fission from capture based on total energy deposition and gamma multiplicity. Application of this method in the thermal and resonance region below 0.5 keV for both the fission and capture produced cross sections that are in good agreement with both ENDF/B-VII.1 and JENDL-4.0 evaluations. The measurements support a lower 235U neutron capture cross section in the energy range 0.5 to 2.25 keV, which is closer to JENDL 4.0.

A New Method for Generating Probability Tables in the Unresolved Resonance Region

A new method for constructing probability tables in the unresolved resonance region (URR) has been developed. This new methodology is an extensive modification of the single-level Breit-Wigner (SLBW) pseudo-resonance pair sequence method commonly used to generate probability tables in the URR. The new method uses a Monte Carlo process to generate many pseudo-resonance sequences by first sampling the average resonance parameter data in the URR and then converting the sampled resonance parameters to the more robust R-matrix limited (RML) format. For each sampled set of pseudo-resonance sequences, the temperature-dependent cross sections are reconstructed on a small grid around the energy of reference using the Reich-Moore formalism and the Leal-Hwang Doppler broadening methodology. The effective cross sections calculated at the energies of reference are then used to construct probability tables in the URR. The RML cross-section reconstruction algorithm has been rigorously tested for a variety of isotopes, including 16O, 19F, 35Cl, 56Fe, 63Cu, and 65Cu. The new URR method also produced normalized cross-section factor probability tables for 238U that were found to be in agreement with current standards. The modified 238U probability tables were shown to produce results in excellent agreement with several standard benchmarks, including the IEU-MET-FAST-007 (BIG TEN), IEU-MET-FAST-003, and IEU-COMP-FAST-004 benchmarks.

Neutron capture cross section measurement ofU238at the CERN n_TOF facility in the energy region from 1 eV to 700 keV

The aim of this work is to provide a precise and accurate measurement of the 238U(n,g) reaction cross section in the energy region from 1 eV to 700 keV. This reaction is of fundamental importance for the design calculations of nuclear reactors, governing the behaviour of the reactor core. In particular, fast reactors, which are experiencing a growing interest for their ability to burn radioactive waste, operate in the high energy region of the neutron spectrum. In this energy region most recent evaluations disagree due to inconsistencies in the existing measurements of up to 15%. In addition, the assessment of nuclear data uncertainty performed for innovative reactor systems shows that the uncertainty in the radiative capture cross-section of 238U should be further reduced to 1-3% in the energy region from 20 eV to 25 keV. To this purpose, addressed by the Nuclear Energy Agency as a priority nuclear data need, complementary experiments, one at the GELINA and two at the n_TOF facility, were proposed and carried out within the 7th Framework Project ANDES of the European Commission. The results of one of these 238U(n,g) measurements performed at the n_TOF CERN facility are presented in this work. The gamma-ray cascade following the radiative neutron capture has been detected exploiting a setup of two C6D6 liquid scintillators. Resonance parameters obtained from this work are on average in excellent agreement with the ones reported in evaluated libraries. In the unresolved resonance region, this work yields a cross section in agreement with evaluated libraries up to 80 keV, while for higher energies our results are significantly higher.

An analytic approach to probability tables for the unresolved resonance region

The Unresolved Resonance Region (URR) connects the fast neutron region with the Resolved Resonance Region (RRR). The URR is problematic since resonances are not resolvable experimentally yet the fluctuations in the neutron cross sections play a discernible and technologically important role: the URR in a typical nucleus is in the 100 keV – 2 MeV window where the typical fission spectrum peaks. The URR also represents the transition between R-matrix theory used to described isolated resonances and Hauser-Feshbach theory which accurately describes the average cross sections. In practice, only average or systematic features of the resonances in the URR are known and are tabulated in evaluations in a nuclear data library such as ENDF/B-VII.1. Codes such as AMPX and NJOY can compute the probability distribution of the cross section in the URR under some assumptions using Monte Carlo realizations of sets of resonances. These probability distributions are stored in the so-called PURR tables. In our work, we begin to develop a scheme for computing the covariance of the cross section probability distribution analytically. Our approach offers the possibility of defining the limits of applicability of Hauser-Feshbach theory and suggests a way to calculate PURR tables directly from systematics for nuclei whose RRR is unknown, provided one makes appropriate assumptions about the shape of the cross section probability distribution.

Evaluation of neutron total and capture cross sections on99Tc in the unresolved resonance region

Long-lived fission product Technetium-99 is one of the most important radioisotopes for nuclear transmutation. The reliable nuclear data are indispensable for a wide energy range up to a few MeV, in order to develop environmental load reducing technology. The statistical analyses of resolved resonances were performed by using the truncated Porter-Thomas distribution, coupled-channels optical model, nuclear level density model and Bayes' theorem on conditional probability. The total and capture cross sections were calculated by a nuclear reaction model code CCONE. The resulting cross sections have statistical consistency between the resolved and unresolved resonance regions. The evaluated capture data reproduce those recently measured at ANNRI of J-PARC/MLF above resolved resonance region up to 800 keV.

The 236U neutron capture cross-section measured at the n_TOF CERN facility

The 236U isotope plays an important role in nuclear systems, both for future and currently operating ones. The actual knowledge of the capture reaction of this isotope is satisfactory in the thermal region, but it is considered insufficient for Fast Reactor and ADS applications. For this reason the 236U(n, gamma ) reaction cross section has been measured for the first time in the whole energy region from thermal energy up to 1MeV at the n TOF facility with two different detection systems: an array of C6D6 detectors, employing the total energy deposited method, and a 4p total absorption calorimeter (TAC), made of 40 BaF2 crystals. The two n TOF data sets agree with each other within the statistical uncertainty in the Resolved Resonance Region up to 800 eV, while sizable differences (up to 20%) are found relative to the current evaluated data libraries. Moreover two new resonances have been found in the n TOF data. In the Unresolved Resonance Region up to 200 keV, the n TOF results show a reasonable agreement with previous measurements and evaluated data.

Recovery of the Point Pseudoresonance Structure of Cross Sections in the Region of Unresolved Resonances

A model is proposed for recovering the point cross sections in the region of unresolved resonances. The approach consists in using probability tables P i (σ) to construct the effective cross sections σ ′ (E) on some choice of energy intervals [E i , E i+1]. In constructing the effective cross sections the densities P i (σ′) and P i (σ) are preserved. This makes it possible to preserve on the intervals [E i , E i+1] characteristics of the neutron–matter interactions such as the average cross section, average free path, transmission function, and others. The use of pseudoresonances in the field of unresolved resonances is not distinguished from the use of ordinary point cross sections in the region of resolved resonances. The proposed approach does not require modifications of the library formats and modeling schemes for the neutron trajectories in Monte Carlo programs. The calculations of two problems showed good agreement between the calculations of the change ΔK eff using probability tables and the MCNP code and calculations using the PRIZMA code, in which pseudoresonances were used.

Isotopic Fissile Assay of Spent Fuel in a Lead Slowing-Down Spectrometer System

Abstract A lead slowing-down spectrometer (LSDS) system is under development to analyze isotopic fissile content that is applicable to spent fuel and recycled material. The source neutron mechanism for efficient and effective generation was also determined. The source neutron interacts with a lead medium and produces continuous neutron energy, and this energy generates dominant fission at each fissile, below the unresolved resonance region. From the relationship between the induced fissile fission and the fast fission neutron detection, a mathematical assay model for an isotopic fissile material was set up. The assay model can be expanded for all fissile materials. The correction factor for self-shielding was defined in the fuel assay area. The corrected fission signature provides well-defined fission properties with an increase in the fissile content. The assay procedure was also established. The assay energy range is very important to take into account the prominent fission structure of each fissile material. Fission detection occurred according to the change of the Pu239 weight percent (wt%), but the content of U235 and Pu241 was fixed at 1 wt%. The assay result was obtained with 2∼3% uncertainty for Pu239, depending on the amount of Pu239 in the fuel. The results show that LSDS is a very powerful technique to assay the isotopic fissile content in spent fuel and recycled materials for the reuse of fissile materials. Additionally, a LSDS is applicable during the optimum design of spent fuel storage facilities and their management. The isotopic fissile content assay will increase the transparency and credibility of spent fuel storage.

Neutron Cross Section Processing Methods for Improved Integral Benchmarking of Unresolved Resonance Region Evaluations

In this work we describe the development and application of computational methods for processing neutron cross section data in the unresolved resonance region (URR). These methods are integrated with a continuous-energy Monte Carlo neutron transport code, thereby enabling their use in high-fidelity analyses. Enhanced understanding of the effects of URR evaluation representations on calculated results is then obtained through utilization of the methods in Monte Carlo integral benchmark simulations of fast spectrum critical assemblies. First, we present a so-called on-the-fly (OTF) method for calculating and Doppler broadening URR cross sections. This method proceeds directly from ENDF-6 average unresolved resonance parameters and, thus, eliminates any need for a probability table generation pre-processing step in which tables are constructed at several energies for all desired temperatures. Significant memory reduction may be realized with the OTF method relative to a probability table treatment if many temperatures are needed. Next, we examine the effects of using a multi-level resonance formalism for resonance reconstruction in the URR. A comparison of results obtained by using the same stochastically-generated realization of resonance parameters in both the single-level Breit-Wigner (SLBW) and multi-level Breit-Wigner (MLBW) formalisms allows for the quantification of level-level interference effects on integrated tallies such as k eff and energy group reaction rates. Though, as is well-known, cross section values at any given incident energy may differ significantly between single-level and multi-level formulations, the observed effects on integral results are minimal in this investigation. Finally, we demonstrate the calculation of true expected values, and the statistical spread of those values, through independent Monte Carlo simulations, each using an independent realization of URR cross section structure throughout. It is observed that both probability table and OTF treatments reproduce the true expected values, calculated by averaging the results of many independent simulations, quite well. However, the spread of independent calculation results is shown to be relatively significant. The k eff eigenvalues for fast spectrum systems can differ by more than 250 pcm from one simulation to the next.

Isotopic molybdenum total neutron cross section in the unresolved resonance region

Accurate isotopic molybdenum nuclear data are important because molybdenum can exist in nuclear reactor components including fuel, cladding, or as a high yield fission product. High-resolution time-of-flight neutron transmission measurements on highly enriched isotopic metallic samples of $^{95}\mathrm{Mo}$, $^{96}\mathrm{Mo}$, $^{98}\mathrm{Mo}$, and $^{100}\mathrm{Mo}$ were performed in the resonance energy range from 1 to $620\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$. The measurements were taken with the newly developed modular $^{6}\mathrm{Li}$-glass transmission detector positioned at the 100-m experimental flight station. In the unresolved energy region (URR), new comprehensive methods of analysis were developed and validated in order to obtain accurate neutron total cross-section data from the measurement by correcting for background and transmission enhancement effects. Average parameters and fits to the total cross section for $^{95}\mathrm{Mo}$ were obtained using the Hauser-Feshbach statistical model code fitacs, which is currently incorporated into the sammy code. The fits to the experimental data deviate from the current evaluated nuclear data file/B-VII.1 isotopic Mo evaluations by several percent in the URR.

Experimental neutron capture data of 58Ni from the CERN n_TOF facility

The neutron capture cross section of 58 Ni was measured at the neutron time of flight facility n_TOF at CERN, from 27 meV to 400 keV neutron energy. Special care has been taken to identify all the possible sources of background, with the so-called neutron background obtained for the first time using high-precision GEANT4 simulations. The energy range up to 122 keV was treated as the resolved resonance region, where 51 resonances were identified and analyzed by a multilevel R -matrix code SAMMY. Above 122 keV the code SESH was used in analyzing the unresolved resonance region of the capture yield. Maxwellian averaged cross sections were calculated in the temperature range of kT = 5 – 100 keV, and their astrophysical implications were investigated.

Measurement and analysis of theAm243neutron capture cross section at the n_TOF facility at CERN

Background:The design of new nuclear reactors and transmutation devices requires to reduce the present neutron cross section uncertainties of minor actinides. Purpose: Reduce the $^{243}$Am(n,$\gamma$) cross section uncertainty. Method: The $^{243}$Am(n,$\gamma$) cross section has been measured at the n_TOF facility at CERN with a BaF$_{2}$ Total Absorption Calorimeter, in the energy range between 0.7 eV and 2.5 keV. Results: The $^{243}$Am(n,$\gamma$) cross section has been successfully measured in the mentioned energy range. The resolved resonance region has been extended from 250 eV up to 400 eV. In the unresolved resonance region our results are compatible with one of the two incompatible capture data sets available below 2.5 keV. The data available in EXFOR and in the literature has been used to perform a simple analysis above 2.5 keV. Conclusions: The results of this measurement contribute to reduce the $^{243}$Am(n,$\gamma$) cross section uncertainty and suggest that this cross section is underestimated up to 25% in the neutron energy range between 50 eV and a few keV in the present evaluated data libraries.

Effect of the Target Motion Sampling temperature treatment method on the statistics and performance

Target Motion Sampling (TMS) is a stochastic on-the-fly temperature treatment technique that is being developed as a part of the Monte Carlo reactor physics code Serpent. The method provides for modeling of arbitrary temperatures in continuous-energy Monte Carlo tracking routines with only one set of cross sections stored in the computer memory.Previously, only the performance of the TMS method in terms of CPU time per transported neutron has been discussed. Since the effective cross sections are not calculated at any point of a transport simulation with TMS, reaction rate estimators must be scored using sampled cross sections, which is expected to increase the variances and, consequently, to decrease the figures-of-merit. This paper examines the effects of the TMS on the statistics and performance in practical calculations involving reaction rate estimation with collision estimators.Against all expectations it turned out that the usage of sampled response values has no practical effect on the performance of reaction rate estimators when using TMS with elevated basis cross section temperatures (EBT), i.e. the usual way. With 0 Kelvin cross sections a significant increase in the variances of capture rate estimators was observed right below the energy region of unresolved resonances, but at these energies the figures-of-merit could be increased using a simple resampling technique to decrease the variances of the responses. It was, however, noticed that the usage of the TMS method increases the statistical deviances of all estimators, including the flux estimator, by tens of percents in the vicinity of very strong resonances. This effect is actually not related to the usage of sampled responses, but is instead an inherent property of the TMS tracking method and concerns both EBT and 0K calculations.

Neutron elastic scattering angular distribution in the resolved and unresolved resonance regions

We derive a simple relationship between observed total cross sections and elastic scattering angular distributions for neutron-induced reactions in the fast energy range by combining resonance theory and the optical model (OM). This relationship enables us to estimate the anisotropy in the scattering angular distribution when experimental total cross-section data are available. We apply this method to the angular distributions of 58Ni and 56Fe and compare with the evaluated values which are based on the experimental data. We also explore the method with 90Zr for which the multi-level Breit-Wigner resonance parameters are given.

Working Party on International Nuclear Data Evaluation Cooperation (WPEC)

The OECD Nuclear Energy Agency (NEA) organizes cooperation between the major nuclear data evaluation projects in the world. The NEA Working Party on International Nuclear Data Evaluation Cooperation (WPEC) was established to promote the exchange of information on nuclear data evaluation, measurement, nuclear model calculation, validation, and related topics, and to provide a framework for cooperative activities between the participating projects. The working party assesses nuclear data improvement needs and addresses these needs by initiating joint activities in the framework of dedicated WPEC subgroups. Studies recently completed comprise a number of works related to nuclear data covariance and associated processing issues, as well as more specific studies related to the resonance parameter representation in the unresolved resonance region, the gamma production from fission product capture reactions, the 235U capture cross section, the EXFOR database, and the improvement of nuclear data for advanced reactor systems. Ongoing activities focus on the evaluation of 239Pu in the resonance region, scattering angular distribution in the fast energy range, and reporting/usage of experimental data for evaluation in the resolved resonance region. New activities include two subgroups on improved fission product yield evaluation methodologies and on modern nuclear database structures. Future activities under discussion include a pilot project for a Collaborative International Evaluated Library Organization (CIELO) and methods to provide feedback from nuclear and covariance data adjustment for improvement of nuclear data. In addition to the above mentioned short-term task-oriented subgroups, WPEC also hosts a longer-term subgroup charged with reviewing and compiling the most important nuclear data requirements in a high priority request list (HPRL).

Evaluation of Neutron Resonance Cross Section Data at GELINA

Over the last decade, the EC–JRC–IRMM, in collaboration with other institutes such as INRNE Sofia (BG), INFN Bologna (IT), ORNL (USA), CEA Cadarache (FR) and CEA Saclay (FR), has made an intense effort to improve the quality of neutron-induced cross section data in the resonance region. These improvements relate to both the infrastructure of the facility and the measurement setup, and the data reduction and analysis procedures. As a result total and reaction cross section data in the resonance region with uncertainties better than 0.5 % and 2 %, respectively, can be produced together with evaluated data files for both the resolved and unresolved resonance region. The methodology to produce full ENDF compatible files, including covariances, is illustrated by the production of resolved resonance parameter files for 241Am, Cd and W and an evaluation for 197Au in the unresolved resonance region.

238U Neutron Capture Cross Section Measurements at the GELINA Facility

A set of neutron capture experiments based on the time-of-flight technique were performed in order to determine the 238U capture cross section in the unresolved resonance region. The GELINA facility of the Institute for Reference Materials and Measurements (IRMM) served as the neutron source. A pair of C6D6 liquid scintillators was used to register the prompt gamma rays emerging from the uranium sample. The analysis of the experimental data is based on the total energy principle applied in combination with the pulse height weighting technique. The experimental details along with the analysis process are described. The first results in the resolved resonance region are presented and their validity provide a solid base to extend the analysis and extract the average cross section in the keV region.