Resolved Resonance Region Research Articles

R-Matrix Evaluation of 16O Neutron Cross Sections up to 6.3 MeV

We have evaluated 16O neutron cross sections in the resolved resonance region with the multilevel Reich-Moore code SAMMY. Resonance parameters were determined by a consistent analysis, including both Doppler and resolution broadening effects. To properly treat the α particle exit channel, an algorithm to calculate charged particle penetrabilities and shifts was incorporated into SAMMY.

Fission of 239Pu with resonance neutrons

A measurement of fission fragment energy and mass distributions in the 239Pu(n, f) resolved resonance region has been performed applying the twin Frisch-gridded ionization chamber technique. An improved pile-up rejection system has been developed to cope with the strong α background.The results for the mass and mean total kinetic energy (TKE) distributions for resolved resonances do not show any strong ‘pattern’ of fluctuations, unlike it was the case for 235U(n, f) in the same neutron energy region. This can be explained in the frame of existing theoretical models, according to which the only possible low-energy spin states available (Jπ=0+, 1+) belong to two well separated (~1.25 MeV) transition state bands with given fission fragment properties. An anti-correlation between TKE and ⊽p was found to be not significant. The obtained small spin dependence of TKE of about 70 keV is in agreement with literature values. A slight correlation was found between TKE versus 1/Γf. But also this was considered not to be significant.

Reinvestigation of 85Kr Branching in the Light of New 82, 84, 86Kr Neutron Capture Cross Section Measurements

High resolution neutron capture cross section measurements of 3 stable krypton isotopes, 82Kr, 84Kr and 86Kr, have been performed at the Geel Linear Accelerator (GELINA) on both resolved and unresolved resonance region. In addition, a total cross section measurement on 84Kr has also been performed in the energy range from 1 eV up to 120 kev. Accurate values of the Maxwellian–averaged capture cross section have been derived for all isotopes for stellar temperatures ranging from kT=5 up to 100 keV. A re–investigation of the s–process in the mass region around the prominent branching at 85Kr has been undertaken in the light of our new results.

Uncertainty Analyses in the Resolved Resonance Region of 235U, 238U, and 239Pu with the Reich-Moore R-Matrix Theory for JENDL-3.2

A simple method to estimate covariances for resolved resonance parameters was developed. Although a large number of resolved resonances are observed for major actinides, uncertainties in averaged cross sections are more important than those in resonance parameters in reactor calculations. The method developed here derives a covariance matrix for the resolved resonance parameters which gives an appropriate uncertainty of the averaged cross sections. The method was adopted to evaluate the covariance data for 235U, 238U, and 239Pu resonance parameters in JENDL-3.2, with the Reich-Moore R-matrix formula.

The n + 239Pu System - New Data Evaluation and Validation Methods

A new evaluation of n + 239Pu cross sections has been performed at incident energies from the resolved resonance region to 30 MeV. Above 30 keV, this evaluation heavily relies upon solid reaction models and predictions. These are based on the coupled channel formalism extended to include dispersion relations corrected for nonlocality, level densities built using microscopic model predictions as guides, and explicit coupling between class I and class II states for fission channels in an evaporation/preequilibrium reaction model. Below 30 keV, these predictions are complemented with data from existing libraries. The final evaluation has been compiled in the ENDF-6 format, processed and checked for internal consistency, tested in various benchmark studies, and finally validated through comparisons with integral experiments.

Uncertainty Analyses in the Resolved Resonance Region of 235U, and 238U, and 239Pu with the Reich-Moore R-Matrix Theory for JENDL-3.2.

A simple method to estimate covariances for resolved resonance parameters was developed. Although a large number of resolved resonances are observed for major actinides, uncertainties in averaged cross sections are more important than those in resonance parameters in reactor calculations. The method developed here derives a covariance matrix for the resolved resonance parameters which gives an appropriate uncertainty of the averaged cross sections. The method was adopted to evaluate the covariance data for 235U, 238U, and 239Pu resonance parameters in JENDL-3.2, with the Reich-Moore R-matrix formula.

Validation of the Characteristic Function Model for the Unresolved Resonance Region

There is a significant extension of the region of resolved resonances (RRR) for some nuclei to higher energies, and this has repercussions on the last updated versions of the evaluated nuclear data libraries. This energy extension covers intervals of the resonant cross-section structure, previously treated as an unresolved resonance region (URR). The reality of this situation provides an opportunity to verify a new statistical model of the resonant cross-section structure in the URR based on the characteristic function F of the R-matrix element distribution. For this purpose, the average cross sections and self-shielding factors obtained by the characteristic function model are compared with the corresponding quantities calculated by the Reich-Moore formalism of the R-matrix theory of nuclear reactions with the evaluated resonance parameters in the RRR. The ENDF/B-VI and JENDL 3.2 resolved resonance parameters of 56Fe and 238U are used for the cross-section calculations.

Treatment of External Levels in Neutron Resonance Fitting: Application to the Nonfissile Nuclide 52Cr

Measured neutron resonance cross sections are usually analyzed and parametrized by fitting theoretical curves to high-resolution point data. Theoretically, the cross sections depend mainly on the “internal” levels inside the fitted energy range but also on the “external” levels outside. Although the external levels are mostly unknown, they must be accounted for. If they are simply omitted, the experimental data cannot be fitted satisfactorily. Especially with elastic scattering and total cross-section data, one gets troublesome edge effects and difficulties with the potential cross section between resonances. Various ad hoc approaches to these problems are still being used, involving replacement of the unknown levels by equidistant (“picket fence”) or Monte Carlo-sampled resonance sequences, or replication of the internal level sequence; however, more convenient, better working, and theoretically sound techniques have been available for decades. These analytical techniques are reviewed. They describe the contribution of external levels to the R matrix concisely in terms of average resonance parameters (strength function, effective radius, etc.). A more recent, especially convenient approximation accounts for the edge effects by just one fictitious pair of very broad external resonances. Fitting the thermal region, including accurately known thermal cross sections, is often done by adjusting a number of bound levels by trial and error, although again a simple analytical recipe involving just one bound level has been available for a long time. For illustration, these analytical techniques are applied to the resolved resonance region of 52Cr. The distinction between channel radii and effective radii, crucial in the present context, is emphasized.

Self-shielding and energy dependence of dilution cross-section in the resolved resonance region

In the calculation of flux weighted multigroup neutron cross-sections of a nuclide present in a homogeneous mixture of several nuclides, by the well known Bondarenko approach, the contributions from the other nuclides to the flux weighting function, are contained in a parameter called ‘dilution’. Under the narrow resonance approximation and with assumed non-overlap of resonances, the energy fluctuations of the dilution are usually ignored within an energy group. The ‘self-shielding factor’ (SSF), which is the ratio of the group cross section for a given dilution to that at infinite dilution, is a smooth function of dilution. A conventional multigroup cross section set, apart from the infinite dilution cross-sections, gives SSF over a dilution grid, from which the effective SSF for any dilution could be obtained by interpolation. The effective SSF multiplied by the infinite dilution cross-section then gives the effective cross-section to be used in the neutronic analyis. Though this conventional procedure works well, the accuracy of this procedure depends on the interpolation scheme used and on the fineness of the dilution grid. The effect of fineness of the dilution grid and the effect of energy dependence of the dilution on the effective SSF are observed, for a specific case, and the results presented in this paper. The JENDL-2 basic nuclear data was used and the benchmark fast critical assembly ZPR-6-7 analysed for a temperature of 300K. The study was restricted to the resolved resonance regions of the nuclides involved. The results appear significant with respect to the target accuracies demanded for the SSF.

Partial-Wave Analysis with the Optical Model for the Resolved and Unresolved Resonance Regions of 56Fe

An accurate database is used to study optical model fits to total neutron cross sections of 56Fe in the resolved and unresolved resonance regions. Averages over resolved resonances are calculated from resonance parameters in a Reich-Moore (reduced R matrix) approximation with Lorentzian weighting. Optical potential parameters are obtained for the s, p, and d waves that reproduce the smoothed cross sections in the resolved resonance region. The p-wave optical potential is found to differ from the s-wave potential. When the appropriate higher angular momentum contributions are added, the average total cross sections can be fitted quite well, from the resolved resonance region all the way up to 20 MeV.

Determination of 147Sm and 148Sm resonance parameters

Cross sections of S-neutron capture and scattering by 147,148Sm were measured by the gamma-multiplicity method in the resolved resonance region. The pulsed booster IBR-30 and multisectional scintillation detector system were used. The values of Γ γ for 26 resonances of 147Sm and values of Γ γ and Γ n for some resonances of 148Sm were obtained. The 147Sm resonances were identified by spin using gamma multiplicity.

Neutron cross sections of 122Te, 123Te, and 124Te between 1 and 60 keV.

The currently favored s process scenario of helium shell burning in low mass stars involves a range of thermal energies from kT=12 to 25 keV with most of the neutron exposure taking place at low temperatures. Therefore, differential cross sections are required down to the region of resolved resonances for the reliable determination of the Maxwellian-averaged cross sections typical of the stellar plasma. This work deals with the neutron capture cross sections of the important s only isotopes $^{122}\mathrm{Te}$, $^{123}\mathrm{Te}$, and $^{124}\mathrm{Te}$, which were measured between 1 and 60 keV neutron energy with a setup of Moxon-Rae detectors. The systematic uncertainties achieved in this experiment are \ensuremath{\sim}5%, but statistical uncertainties are smaller than 2%. In addition to the Moxon-Rae detectors, the setup includes a $^{6}\mathrm{Li}$ glass detector which could be used to determine the total neutron cross sections simultaneously. These results represent the first set of experimental data in this energy range.

R-matrix analysis of the239Pu neutron cross sections

Abstract 239Pu neutron cross-section data in the resolved resonance region were analyzed with the R-Matrix Bayesian Program SAMMY. Below 30 eV the cross sections computed with the multilevel parameters are consistent with recent fission and transmission measurements as well as with older capture and alpha measurements. Above 30 eV no suitable transmission data were available and only fission cross-section measurements were analyzed. However, since the analysis conserves the complete covariance matrix, the analysis can be updated by the Bayes method as transmission measurements become available. To date, the analysis of the fission measurements has been completed up to 300 eV.

Multilevel analysis of Pu-239 neutron cross sections in the resolved resonance region

Abstract The new approach to the multilevel analysis of Pu-239 based on the S-matrix unitarity property is developed.

Neutron absorption cross section of239Pu in the region of resolved resonances

Neutron absorption cross section of239Pu in the region of resolved resonances

Evaluation of neutron-induced and γ-ray-production cross sections for elemental sulfur

A new evaluation for natural S is described, this was a completely new evaluation done for ENDF/B-V. The secondary neutron cross sections and angular distributions as well as the secondary neutron energy distribution for the continuum inelastically scattered neutrons have been included. In addition, the isotopic cross sections for the various (n, particle) reactions were evaluated with the help of experimental data and model-calculated results to construct the corresponding natural S files. Precompound effects were included. The least abundant isotope 36S was not considered in the evaluation. The resolved resonance region for natural S extends from 1.0 × 10 −5 eV to 1091.0 keV, and the resonance parameters for the three S isotopes 32S, 33S and 34S have been evaluated from experimentally determined resonance parameters. The Karlsruhe total S cross-section data extending up to 20 MeV were used to construct a smooth cross-section file. Measurements due to other investigators were also used in the evaluation.

Interface effects in multiregion reactors

The spatial dependence of effective cross sections in large multiregion reactors was investigated in the resolved resonance region of 238U. The effective capture cross section was found to be quite sensitive to the interface effect. In general, in fast systems it was not possible to obtain a fundamental-mode (FM) spectrum in regions less than 30 cm thick. Indeed, in the blanket region of the ZPR-6/5 reactor the cross section was never equal to its FM value. The deviation from the FM can be as large as 12%. In TRX-3, the small mean-free-path of neutrons in water limited the interface effects to very short distances (∼1 cm).

Spin determination of resonance structure in (U235+n) below 25 keV

Measurements made with a polarized neutron beam and a polarized target of /sup 235/U have been analyzed to obtain spin-separated fission cross sections of (/sup 235/U + n) below 25 keV neutron energy. Analysis of the cross section data in the resolved resonance region has been carried out to obtain a better estimate of average parameters than has been previously available. The average parameters have been used as the starting point for an extraction of energy-dependent average parameters in the unresolved resonance region. The results of this analysis show evidence for intermediate structure in the spin-4 component.

Multi-Level Correction to Breit-Wigner Single-Level Formula

A formula for neutron cross sections of heavy nuclei is derived on the basis of the Wigner-Eisenbud theory. The derived formula is the same as the single-level one introduced by Breit and Wigner except for the inclusion of additional interference parameters (u, v) which represent the contribution of the interference effect between resonances. The present formula is therefore applicable to reactor calculations without much modifications of the existing resonance integral codes. The present formula has been applied to the analyses of the 235U and 233U fission cross sections and the 238U total cross sections in the resolved resonance region. By the use of least squares fits of the experimental data, the interference parameters (u, v) are obtained for resonance levels of these nuclei in their typical resonance regions. It is shown that the present formula well represents the experimental data. In the unresolved resonance region, both the single-level resonance parameters and the present interference parameter...

Thermal-Reactor Lattice Analysis Using ENDF/B-IV Data with Monte Carlo Resonance Reaction Rates

Uranium fueled thermal-reactor lattice benchmarks, as well as some other experimental assemblies, were analyzed with ENDF/B-IV data and calculational techniques based on integral transport and SN methods together with Monte Carlo calculations in the resolved resonance region. Only a relatively small overprediction of the $sup 238$U resonance events--3 to 4 percent--remains when the present version of the ENDF/B data is used. It accounts for a considerable part of the 1 percent underprediction of criticality. Uranium-235 resonance absorption was found to be influenced noticeably by shielding due to the $sup 238$U resonances. For both $sup 235$U epithermal and $sup 238$U fast fissions, the agreement between calculation and experiment, although relatively good, showed greater fluctuations than in the case of the $sup 238$U capture. Calculated temperature variations of material buckling with temperature were greater than in the measurements, especially near room temperature, but the discrepancies were smaller in the critical than in the exponential assemblies.