Bayesian Estimation of Thermonuclear Reaction Rates

TL;DR

This paper introduces a Bayesian statistical framework for estimating astrophysical reaction rates and S-factors from nuclear cross section data, addressing systematic effects and uncertainties.

Contribution

It is the first to apply Bayesian methods comprehensively to nuclear reaction rate estimation, improving robustness and uncertainty quantification.

Findings

Bayesian approach yields more reliable reaction rate estimates.

Application to key reactions demonstrates improved uncertainty handling.

Framework can be extended to other nuclear astrophysics problems.

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.