Bayesian Estimation of Thermonuclear Reaction Rates

Abstract

The problem of estimating non-resonant astrophysical S-factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied in the past to this problem, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extra-solar planets, gravitational waves, and type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We present astrophysical S-factors and reaction rates based on Bayesian statistics. We develop a framework that incorporates robust parameter estimation, systematic effects, and non-Gaussian uncertainties in a consistent manner. The method is applied to the d(p,$\gamma$)$^3$He, $^3$He($^3$He,2p)$^4$He, and $^3$He($\alpha$,$\gamma$)$^7$Be reactions, important for deuterium burning, solar neutrinos, and big bang nucleosynthesis.