Knowing What We Don’t Know: Quantifying Uncertainties in Direct Reaction Theory

The discussion of uncertainty quantification is becoming standard within the nuclear theory community, however, methods to do so are just recently being introduced into direct reaction theories. Direct comparisons between models or parameterizations are often used to determine the error that is introduced by the theory, but ultimately, we need a more systematic way to include error bands on our calculations. This talk will discuss our ongoing efforts to systematically quantify the uncertainties due to the parameterization of the optical model potentials. We use Bayesian methods to compute posterior distributions for the optical model parameters constrained by elastic scattering, construct 95% confidence intervals around this data, and propagate the posterior distributions through a three-body reaction model to make predictions for the corresponding (d, p) transfer cross sections. An application to 48Ca (d, p) 49Ca(g.s.) transfer will be shown, and the dependence on the size of the experimental error bars and complexity of the reaction model will be discussed. Finally, we will compare the results from the Bayesian analysis with those obtained with the standard frequentist approach. An outlook on module comparisons to account for more complicated uncertainties will be addressed.