Sensitivity analysis of neutron total and absorption cross sections within the optical model

Abstract

Distinct maxima and minima in neutron total and absorption cross-section uncertainties when optical-model parameters are varied have been observed in large-scale covariance calculations. These features were seen over a wide mass range (20--210) and for energies up to 20 MeV. Here we investigate the physical origin of the observed patterns over an extended energy range (1 keV to 200 MeV). We have calculated the sensitivity of the cross sections for a specific nucleus ($^{56}\mathrm{Fe}$) to variations of the 15 parameters of a standard global optical potential parametrization, and have also carried out calculations for alternative global optical potentials over the original wide mass and energy ranges. We find that simple physical descriptions can be found in two energy ranges. Below approximately 100 keV, the patterns arise from the interplay of the $s$- and $p$-wave single-particle resonances. Above approximately 4 MeV, a single-phase-shift approximation (the Ramsauer model) describes the observed behavior. We discuss the potential importance of such sensitivity studies for further development of optical potentials.