Exploring experimental conditions to reduce uncertainties in the optical potential

Abstract

Background: Uncertainty quantification for nuclear theories has gained a more prominent role in the field, with more and more groups attempting to understand the uncertainties on their calculations. However, recent studies have shown that the uncertainties on the optical potentials are too large for the theory to be useful. Purpose: The purpose of this work is to explore possible experimental conditions that may reduced the uncertainties on elastic scattering and single-nucleon transfer cross sections that come from the fitting of the optical model parameters to experimental data. Method: Using Bayesian methods, we explore the effect of the uncertainties of optical model parameters on the angular grid of the differential cross section, including cross section data at nearby energies, and changes in the experimental error bars. We also study the effect on the resulting uncertainty when other observables are included in the fitting procedure, particularly the total (reaction) cross sections. Results: We study proton and neutron elastic scattering on 48Ca and 208Pb. We explore the parameter space with Markov- Chain Monte Carlo, produce posterior distributions for the optical model parameters, and construct the corresponding 95% confidence intervals on the elastic-scattering cross sections. We also propagate the uncertainties on the optical potentials to the 48Ca(d,p)49Ca(g.s.) and 208Pb(d,p)209Pb(g.s.) cross sections. Conclusions: We find little sensitivity to the angular grid and an improvement of up to a factor of 2 on the uncertainties by including data at a nearby energy. Although reducing the error bars on the data does reduce the uncertainty, the gain is often considerably smaller than one would naively expect.