Neutron Cross Section Covariances In The Resonance Region

We present a detailed analysis of the impact of resonance parameter uncertainties on covariances for neutron capture and fission cross sections in the resolved resonance region. Our analysis uses the uncertainties available in the recently published Atlas of Neutron Resonances employing the Multi-Level Breit-Wigner formalism. We consider uncertainties on resonance energies along with those on neutron-, radiative-, and fission-widths and examine their impact on cross section uncertainties and correlations. We also study the effect of the resonance parameter correlations deduced from capture and fission kernels and illustrate our approach on several practical examples. We show that uncertainties of neutron-, radiative- and fission-widths are important, while the uncertainties of resonance energies can be effectively neglected. We conclude that the correlations between neutron and radiative (fission) widths should be taken into account. The multi-group cross section uncertainties can be properly generated from both the resonance parameter covariance format MF32 and the cross section covariance format MF33, though the use of MF32 is more straightforward and hence preferable.

We evaluated covariances for neutron capture and elastic scattering cross sections on major structural materials, 52Cr, 56Fe and 58Ni, in the resonance region which extends beyond 800 keV for each of them. Use was made of the recently developed covariance formalism based on kernel approximation along with data in the Atlas of Neutron Resonances. The data of most interest for AFCI applications, elastic scattering cross section uncertainties at energies above about few hundred keV, are on the level of about 12% for 52Cr, 7-8% for 56Fe and 5-6% for 58Ni.

We evaluated covariances in the neutron resonance region for capture and elastic scattering cross sections on minor structural materials, {sup 50,53}Cr, {sup 54,57}Fe and 6°Ni. Use was made of the recently developed covariance formalism based on kernel approximation along with data in the Atlas of Neutron Resonances. Our results of most interest for advanced fuel cycle applications, elastic scattering cross section uncertainties at energies around 100 keV, are on the level of about 7-10%.

We describe analytical formalism for estimating neutron radiative capture and elastic scattering cross section covariances in the resolved resonance region. We use capture and scattering kernels as the starting point and show how to get average cross sections in broader energy bins, derive analytical expressions for cross section sensitivities, and deduce cross section covariances from the resonance parameter uncertainties in the recently published Atlas of Neutron Resonances. The formalism elucidates the role of resonance parameter correlations which become important if several strong resonances are located in one energy group. Importance of potential scattering uncertainty as well as correlation between potential scattering and resonance scattering is also examined. Practical application of the formalism is illustrated on 55Mn(n, [gamma]) and 55Mn(n, el).

Recent evaluations of neutron cross section covariances in the resolved resonance region reveal the need for further research in this area. Major issues include declining uncertainties in multigroup representations and proper treatment of scattering radius uncertainty. To address these issues, the present work introduces a practical method based on kernel approximation using resonance parameter uncertainties from the Atlas of Neutron Resonances. Analytical expressions derived for average cross sections in broader energy bins along with their sensitivities provide transparent tool for determining cross section uncertainties. The role of resonance-resonance and bin-bin correlations is specifically studied. As an example we apply this approach to estimate (n,?) and (n, el) covariances for the structural material 55Mn.

Atlas of Neutron Resonances: Resonance Properties and Thermal Cross Sections Z=61-102, Sixth Edition, contains an extensive list of detailed individual neutron resonance parameters for Z=61-102, thermal cross sections, capture and fission resonance integrals, average resonance parameters, and a short survey of the physics of thermal and resonance neutrons. The long introduction contains: nuclear physics formulas aimed at neutron physicists; topics of special interest such as valence neutron capture, nuclear level density parameters, and s-, p-, and d-wave neutron strength functions; and various comparisons of measured quantities with the predictions of nuclear models, such as the optical model neutron-induced fission. As in the last edition, additional features have been added to appeal to a wider spectrum of users. These include: spin-dependent scattering lengths that are of interest to solid-state physicists, nuclear physicists and neutron evaluators; calculated and measured Maxwellian average 5-keV and 30-keV capture cross sections of importance to astrophysicists involved in nucleosynthesis modeling; s-, p-, and d- wave average radiative widths; nuclear level density parameters; and average fission widths derived from average fission cross sections. Provides a comparison of average resonance parameters with optical model calculations and with the generalized Landau-Fermi model Presents scattering radii for various partial waves from the analysis of total neutron cross sections in the keV to MeV energy region Includes a brief review of sub-threshold fission Features consistent treatment of average neutron parameters with values from the resolved resonance region

Oak Ridge National Laboratory (ORNL) has recently completed the resonance parameter evaluation of four tungsten isotopes, i.e., 182,183,184,186W, in the neutron energy range of thermal up to several keV. This nuclear data work was performed with support from the US Nuclear Criticality Safety Program (NCSP) in an effort to provide improved tungsten cross section and covariance data for criticality safety analyses. The evaluation methodology uses the Reich-Moore approximation of the R-matrix formalism of the code SAMMY to fit high-resolution measurements performed in 2010 and 2012 at the Geel linear accelerator facility (GELINA), as well as other experimental data sets on natural tungsten available in the EXFOR library. In the analyzed energy range, this work nearly doubles the resolved resonance region (RRR) present in the latest US nuclear data library ENDF/B-VII. 1. In view of the interest in tungsten for distinct types of nuclear applications and the relatively homogeneous distribution of the isotopic tungsten--namely, 182W(26.5%), 183W(14.31%), 184W(30.64%), and 186W(28.43%) - the completion of these four evaluations represents a significant contribution to the improvement of the ENDF library. This paper presents an overview of the evaluated resonance parameters and related covariances for total and capture cross sections on the four tungsten isotopes.

We describe new method for energy-energy covariance calculation from the thermal energy up to 20 MeV. It is based on three powerful basic components: (i) Atlas of Neutron Resonances in the resonance region; (ii) the nuclear reaction model code EMPIRE in the unresolved resonance and fast neutron regions, and (iii) the Bayesian code KALMAN for correlations and error propagation. Examples for cross section uncertainties and correlations on 9°Zr and 193Ir illustrate this approach in the resonance and fast neutron regions.

Atlas of Neutron Resonances: Resonance Properties and Thermal Cross Sections Z= 1-60, Sixth Edition, contains an extensive list of detailed individual neutron resonance parameters for Z=1-60, as well as thermal cross sections, capture resonance integrals, average resonance parameters and a short survey of the physics of thermal and resonance neutrons. The long introduction contains: nuclear physics formulas aimed at neutron physicists; topics of special interest such as valence neutron capture, nuclear level density parameters, and s-, p-, and d-wave neutron strength functions; and various comparisons of measured quantities with the predictions of nuclear models, such as the optical model. As in the last edition, additional features have been added to appeal to a wider spectrum of users. These include: spin-dependent scattering lengths that are of interest to solid-state physicists, nuclear physicists and neutron evaluators; calculated and measured Maxwellian average 5-keV and 30-keV capture cross sections of importance to astrophysicists involved in nucleosynthesis modeling; s-, p-, and d-wave average radiative widths; and, nuclear level density parameters. Provides a comparison of average resonance parameters with optical model calculations and with the generalized Landau-Fermi model Presents scattering radii for various partial waves from the analysis of total neutron cross sections in the keV to MeV energy region Includes a brief review of sub-threshold fission Examines consistent treatment of average neutron parameters with values from the resolved resonance region