Bayesian Estimation of the $S$ Factor and Thermonuclear Reaction Rate for $^{16}$O(p,$\gamma$)$^{17}$F

TL;DR

This paper applies Bayesian statistical methods to accurately estimate the thermonuclear reaction rate of $^{16}$O(p,$3$)$^{17}$F, reducing uncertainties and improving previous estimates for astrophysical models.

Contribution

It introduces a Bayesian framework for fitting nuclear reaction data, explicitly accounting for uncertainties, and provides the first statistically rigorous reaction rate estimate for $^{16}$O(p,$3$)$^{17}$F.

Findings

Reaction rate uncertainty reduced to a0a0 4.2%

Bayesian fit using ANCs is more effective than spectroscopic factors

First rigorous statistical estimate of the reaction rate

Abstract

The $^{16}$O(p,$\gamma$)$^{17}$F 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 $^{16}$O(p,$\gamma$)$^{17}$F 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 $^{17}$F. 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 $^{16}$O(p,$\gamma$)$^{17}$F reaction rates, with uncertainties ($\pm 4.2$\%) of about half the previously reported values.