Bayesian estimation of the S factor and thermonuclear reaction rate for 16O(p,)17F

The 16O(p,gamma)17F reaction is the slowest hydrogen-burning process in the CNO mass region. Its thermonuclear rate sensitively impacts predictions of oxygen isotopic ratios in a number of astrophysical sites, including AGB stars. The reaction has been measured several times at low bombarding energies using a variety of techniques. The most recent evaluated experimental rates have a reported uncertainty of about 7.5% below 1 GK. However, the previous rate estimate represents a best guess only and was not based on rigorous statistical methods. We apply a Bayesian model to fit all reliable 16O(p,gamma)17F cross section data, and take into account independent contributions of statistical and systematic uncertainties. The nuclear reaction model employed is a single-particle potential model involving a Woods-Saxon potential for generating the radial bound state wave function. The model has three physical parameters, the radius and diffuseness of the Woods-Saxon potential, and the asymptotic normalization coefficients (ANCs) of the final bound state in 17F. We find that performing the Bayesian S-factor fit using ANCs as scaling parameters has a distinct advantage over adopting spectroscopic factors instead. Based on these results, we present the first statistically rigorous estimation of experimental 16O(p,gamma)17F reaction rates, with uncertainties (+/- 4.2%) of about half the previously reported values.