Uncertainty quantification in $(p,n)$ reactions

Abstract: Charge-exchange reactions are versatile probes for nuclear structure. In particular, when populating isobaric analog states, these reactions are used to study isovector nuclear densities and neutron skins. The quality of the information extracted from charge-exchange data depends on the accuracy of the reaction models and their inputs; this work addresses these two points. First, we quantify the uncertainties due to effective nucleon-nucleus interactions by propagating the parameter posterior distributions of the recent global optical model KDUQ [1] to $(p,n)$ reaction observables populating the isobaric analogue state, at beam energies in the range of $25-160$ MeV. Our analysis, focusing on $^{48}$Ca, shows that the total parametric uncertainties on the cross sections are around 60-100%. The source of this uncertainty is mainly the transition operator as the uncertainties from the distorted waves alone are less than about 15%. Second, we perform a comparison between two- and three-body models that both describe the dynamics of the reaction within the DWBA. The predictions from these two models are similar and generally agree with the available data, suggesting that 1-step DWBA is sufficient to describe the reaction process. Only at a beam energy of 25 MeV there are possibly signs that a 1-step assumption is not fully correct. This work provides motivation for the quantification of uncertainties associated with the transition operator in three-body model. It also suggests that further constraint of the optical potential parameters is needed for increased model precision.