"Nuclear reactions are important for studying the properties of nuclei across the nuclear chart and in answering the biggest questions in nuclear science, ranging from the formation of the elements in the universe to societal applications. The exact description of nuclei in terms of a few degrees of freedom is not known, so models are developed to mimic the resulting phenomena. Because these prescriptions are, by definition, approximations, it is crucial to quantify the uncertainties that result from these approximations. These uncertainties arise not only from the simplifications that are made to the solutions of the scattering problem and degrees of freedom removed from the model space, but also from the parameterization of the effective potentials. Although it is important to rigorously quantify each uncertainty, we take the first step by systematically studying the effect of parametric uncertainties arising from fitting optical model parameters to elastic-scattering data. To do this, we use simple reaction models, the distorted-wave Born approximation (DWBA) and the adiabatic wave approximation (ADWA), for computationally inexpensive calculations. Two methods of parametric uncertainty quantification were explored in this work, a frequentist approach and a Bayesian approach. In the frequentist study, chi 2 minimization was used to constrain optical model parameters in the incoming scattering channel, using neutron and deuteron elastic-scattering data. Then 95% confidence bands were constructed around the best-fit calculation for elastic scattering and were propagated in order to compute 95% confidence bands for predicted (d,p) and (n,n0 ) cross sections using DWBA. A correlated chi 2 fitting function was introduced to take into account the angular correlations within the elastic-scattering model. Using this correlated chi 2 function led to broader confidence bands and more physical descriptions of the angular distributions. For the Bayesian study, a wide Gaussian prior was used in conjunction with neutron, proton, and deuteron elastic-scattering data to construct posterior distributions through a Markov Chain Monte Carlo. From the posterior distributions, 95% confidence intervals were constructed for the elastic-scattering cross sections and then propagated to predict 95% confidence intervals for (d,p) and (d,n) reactions using either ADWA or DWBA. In this way, the parametric uncertainties from ADWA and DWBA could be directly compared, and ADWA was found to have smaller uncertainties. The effect of artificially reducing the experimental errors on elastic-scattering data was studied, and it was found that the uncertainties in the transfer cross section decreased but not by the same percent that the experimental errors were reduced. Overall, the uncertainties on the predicted cross sections due to fitting optical model parameters to elastic-scattering data ranged from 20 - 120%, significantly larger than the 10-30% uncertainties that are assumed to be introduced by these fits. Uncertainties beyond those introduced by fitting to data must also be included, such as those introduced by the few-body approximations. In addition, the propagation of uncertainties has to be reliable. A full description of theoretical uncertainties is vital for predictions, especially as we move toward the edge of the nuclear landscape."--Pages ii-iii.
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