How Bayesian methods can improve $R$-matrix analyses of data: the example of the $dt$ Reaction
Abstract
The reaction is of significant interest in nuclear astrophysics and nuclear applications. It is an important, early step in big-bang nucleosynthesis and a key process in nuclear fusion reactors. We use one- and two-level -matrix approximations to analyze data on the cross section for this reaction at center-of-mass energies below 215 keV. We critically examine the data sets using a Bayesian statistical model that allows for both common-mode and additional point-to-point uncertainties. We use Markov Chain Monte Carlo sampling to evaluate this -matrix-plus-statistical model and find two-level -matrix results that are stable with respect to variations in the channel radii. The factor at 40 keV evaluates to MeV b (68% credibility interval). We discuss our Bayesian analysis in detail and provide guidance for future applications of Bayesian methods to -matrix analyses. We also discuss possible paths to further reduction of the -factor uncertainty.
Keywords
Cite
@article{arxiv.2105.06541,
title = {How Bayesian methods can improve $R$-matrix analyses of data: the example of the $dt$ Reaction},
author = {Daniel Odell and Carl Brune and Daniel Phillips},
journal= {arXiv preprint arXiv:2105.06541},
year = {2022}
}