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 less than a thousand seconds old. It determines the abundances of the lightest nuclides, which give rise to the subsequent history of the visible matter in the Universe. This 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. We critically evaluate all available data and disregard experimental results that are questionable. 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. In the fitting of the data, we consistently model all known sources of uncertainty, including discrepant absolute normalizations of different data sets, 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 ($E_r$, ${\gamma }_n^2$, ${\gamma }_p^2$) and derive excitation energies, partial and total widths. Our fit is sensitive to the contributions of the first three levels above the neutron threshold. Reaction rates were computed by integrating 10,000 samples of the reduced cross section. Our ${}^7$Be(n,p)${}^7$Li thermonuclear rates have uncertainties between 1.5% and 2.0% at temperatures of $\le$1 GK. We compare our rates to previous results and find that the ${}^7$Be(n,p)${}^7$Li rates most commonly used in big bang simulations have too optimistic uncertainties.

arXiv comment24 pages, 8 figures, ApJ in press

References in corpus (22)

• Programming with models: writing statistical algorithms for general model structures with NIMBLE
• Big Bang Nucleosynthesis: 2015
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Towards a More Complete and Accurate Experimental Nuclear Reaction Data Library (EXFOR): International Collaboration Between Nuclear Reaction Data Centres (NRDC)
• One percent determination of the primordial deuterium abundance
• The R-matrix theory
• The effects of He I 10830 on helium abundance determinations
• Precision big bang nucleosynthesis with improved Helium-4 predictions
• High-precision measurement of the atomic mass of the electron
• Compilation and R-matrix analysis of Big Bang nuclear reaction rates
• The metal-poor end of the Spite plateau. 1: Stellar parameters, metallicities and lithium abundances
• Charged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions
• High-precision measurement of the proton's atomic mass
• Radiative neutron capture on a proton at BBN energies
• The ${}^7$Be($\mathbf{n},\mathbf{p}$)${}^7$Li reaction and the Cosmological Lithium Problem: measurement of the cross section in a wide energy range at n_TOF (CERN)
• Bayesian Estimation of Thermonuclear Reaction Rates
• Bayesian estimation of thermonuclear reaction rates for deuterium+deuterium reactions
• Thermonuclear fusion rates for tritium + deuterium using Bayesian methods
• Astrophysical S-factors, thermonuclear rates, and electron screening potential for the ${}^3$He(d,p)${}^4$He Big Bang reaction via a hierarchical Bayesian model
• n + p -> d + gamma in Effective Field Theory
• New broad 8Be nuclear resonances
• Calculation of resonance energies from Q-values

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