Practical Method For Estimating Neutron Cross Section Covariances In The Resonance Region

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.

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).

We present the NNDC-BNL methodology for estimating neutron cross section covariances in thermal, resolved resonance, unresolved resonance and fast neutron regions. The three key elements of the methodology are Atlas of Neutron Resonances, nuclear reaction code EMPIRE, and the Bayesian code implementing Kalman filter concept. The covariance data processing, visualization and distribution capabilities are integral components of the NNDC methodology. We illustrate its application on examples including relatively detailed evaluation of covariances for two individual nuclei and massive production of simple covariance estimates for 307 materials. Certain peculiarities regarding evaluation of covariances for resolved resonances and the consistency between resonance parameter uncertainties and thermal cross section uncertainties are also discussed.

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 review neutron cross section covariances in both the resonance and fast neutron regions with the goal to identify existing issues in evaluation methods and their impact on covariances. We also outline ideas for suitable covariance quality assurance procedures. We show that the topic of covariance data remains controversial, the evaluation methodologies are not fully established and covariances produced by different approaches have unacceptable spread. The main controversy is in very low uncertainties generated by rigorous evaluation methods and much larger uncertainties based on simple estimates from experimental data. Since the evaluators tend to trust the former, while the users tend to trust the latter, this controversy has considerable practical implications. Dedicated effort is needed to arrive at covariance evaluation methods that would resolve this issue and produce results accepted internationally both by evaluators and users.

We suggest a procedure for estimating uncertainties in neutron cross sections calculated with a nuclear model descriptive of a specific mass region. It applies standard error propagation techniques, using a model-parameter covariance matrix. Generally, available codes do not generate covariance information in conjunction with their fitting algorithms. Therefore, we resort to estimating a relative covariance matrix a posteriori from a statistical examination of the scatter of elemental parameter values about the regional representation. We numerically demonstrate our method by considering an optical-statistical model analysis of a body of total and elastic scattering data for the light fission-fragment mass region. In this example, strong uncertainty correlations emerge and they conspire to reduce estimated errors to some 50% of those obtained from a naive uncorrelated summation in quadrature. 37 references.

We completed estimates of neutron cross section covariances for 55Mn and 9°Zr, from keV range to 25 MeV, considering the most important reaction channels, total, elastic, inelastic, capture, and (n,2n). The nuclear reaction model code EMPIRE was used to calculate sensitivity to model parameters by perturbation of parameters that define the optical model potential, nuclear level densities and strength of the pre-equilibrium emission. The sensitivity analysis was performed with the set of parameters which reproduces the ENDF/B-VII.0 cross sections. The experimental data were analyzed and both statistical and systematic uncertainties were extracted from almost 30 selected experiments. Then, the Bayesian code KALMAN was used to combine the sensitivity analysis and the experiments to obtain the evaluated covariance matrices.

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%.