Hierarchical Bayesian Thermonuclear Rate for the \(^7\)Be(n,p)\(^7\)Li Big Bang Nucleosynthesis Reaction

Abstract

Big bang nucleosynthesis provides the earliest probe of standard model physics, at a time when the universe was between 100 seconds and 1000 seconds old. It determines the abundances of the lightest nuclides, which give rise to the subsequent history of the visible matter in the Universe. The present work derives new \(^7\)Be(n,p)\(^7\)Li thermonuclear reaction rates based on all available experimental information. This reaction sensitively impacts the primordial abundances of \(^{7}\)Be and \(^7\)Li during big bang nucleosynthesis. For the nuclear model, we adopt an incoherent sum of single-level, two-channel R-matrix approximation expressions, which are implemented into a hierarchical Bayesian model, to analyze the remaining six data sets we deem most reliable. The nuclear structure of \(^8\)Be near the neutron threshold has also been evaluated to estimate appropriate prior densities for our analysis. In the fitting of the data, we consistently model all known sources of uncertainty and also take the variation of the neutron and proton channel radii into account, hence providing less biased estimates of the \(^7\)Be(n,p)\(^7\)Li thermonuclear rates. From the resulting posteriors, we extract R-matrix parameters and derive excitation energies, partial and total widths. Our fit is sensitive to the contributions of the first three levels above the neutron threshold. Values of excitation energies and total widths for these states are in overall agreement with previous results, although our results have significantly smaller uncertainties. Our \(^7\)Be(n,p)\(^7\)Li thermonuclear rates have uncertainties between 1.5% and 2.0% at temperatures of \(\leq\)1 GK. We compare our rates to previously published results and find that the \(^7\)Be(n,p)\(^7\)Li rates most commonly used in big bang simulations have too optimistic uncertainties.