Formalism for neutron cross section covariances in the resonance region using kernel approximation

Abstract

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 55 Mn(n,γ) and 55 Mn(n,el).

Neutron Cross section Covariances in the Resonance region: 50,53Cr, 54,57Fe and 60Ni

“…[2]. Its key idea is the use of kernel approximation which allowed us to develop analytical formalism of propagating resonance parameter uncertainties from Atlas of Neutron Resonances [4] into cross sections uncertainties.…”

“…If kernel is computed from resonance parameters, then somewhat more involved procedure is needed to propagate resonance parameter uncertainties into kernel uncertainty and thus to average capture cross section [2].…”

“…If several resonances are combined together into one energy bin one computes uncertainty from the binomial expression for quadratic summation of uncertainties, 6) where (∆σ γ ) 2 is the variance for a given energy bin, and i and r stand for individual resonances. This yields…”

“…In accordance with Ref. [2] our default values for these coefficients for each energy bin are uniformly set to corr(A γi , A γr ) = ∆A γi ∆A γr = 0.5. (2.8)…”

“…In both instances we used our new covariance formalism based on kernel approximation described in Ref. [2] with refinements described in Ref. [1].…”