Prediction for ( p,n ) charge-exchange reactions with uncertainty quantification

Abstract

Background: Charge-exchange reactions are a powerful tool for exploring nuclear structure and nuclear astrophysics; however, a robust charge-exchange reaction theory with quantified uncertainties is essential for extracting reliable physics.Purpose: The goal of this work is to determine the uncertainties due to optical potentials used in the theory for charge-exchange reactions to isobaric analog states.Method: We implement a two-body reaction model to study $(p,n)$ charge-exchange transitions and perform a Bayesian analysis. The $(p,n)$ reaction to the isobaric analog states of $^{14}\mathrm{C}$, $^{48}\mathrm{Ca}$, and $^{90}\mathrm{Zr}$ targets are studied over a range of beam energies. We compare predictions using standard phenomenological optical potentials with those obtained microscopically.Results: Charge-exchange cross sections are reasonably reproduced by modern optical potentials. However, when uncertainties in the optical potentials are accounted for, the resulting predictions of charge-exchange cross sections have very large uncertainties.Conclusions: The charge-exchange reaction cross section is strongly sensitive to the input interactions, making it a good candidate to further constrain nuclear forces and aspects of bulk nuclear matter. However, further constraints on the optical potentials are necessary for a robust connection between this tool and the underlying isovector properties of nuclei.