Hierarchical Bayesian Thermonuclear Rate for the ⁷Be(n,p)⁷Li 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 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. This work derives new 7Be(n,p)7Li thermonuclear reaction rates based on all available experimental information. This reaction sensitively impacts the primordial abundances of 7Be and 7Li 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 7Be(n,p)7Li thermonuclear rates. From the resulting posteriors, we extract R-matrix parameters (E r , , ) and derive excitation energies and 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 7Be(n,p)7Li thermonuclear rates have uncertainties between 1.5% and 2.0% at temperatures of ≤1 GK. We compare our rates to previous results and find that the 7Be(n,p)7Li rates most commonly used in big bang simulations have uncertainties that are too optimistic.

Calculation of astrophysical reaction rate and uncertainty for T(d,n)4He using Bayesian statistical approach

“…Bayes’ principle (or Bayesian statistics) is used to fit the existing experimental data in order to further extrapolations. Bayes’ principle in one of its applied forms can be expressed as follows: in which, the numerator expresses the product of the likelihood [ ] (a postulated nuclear model) and the probability density of the priors [π(θ)] (primary form of the studied parameters in term of distribution functions), which gives the posterior (the updated distribution functions of the parameters as the output of the study) (de Souza et al 2020). The denominator of the Equation (1) is a normalisation factor that has no special role in the calculations of this study and is considered as one, because the summation of all the possible probabilities is one.…”

“…Of course, in the end, only the S -factor is reported as the final goal of this study. Same as de Souza et al (2020), in this study, the defined normal probability densities related to the priors of the physical parameters are truncated at zero (to not being negative). The considered priors are specified in Table 1 ( is the Wigner limit with reduced mass of the interacting components, Bohr radius , and Planck constant ).…”

“…Before this study, a number of studies had focused on the calculation of the rates of some reactions of the BBN reaction network (Fig. 1) using Bayesian method, such as d(p,γ) 3 He, 3 He( 3 He,2p) 4 He and 3 He(α,γ) 7 Be (Iliadis et al 2016), d(d,n) 3 He and d(d,p) 3 H (Iñesta, Iliadis, & Coc 2017), 3 He(d,p) 4 He (de Souza et al 2019a), 7 Be(n,p) 7 Li (de Souza et al 2020), 3 H(d,n) 4 He (De Souza, Iliadis, & Coc 2019b), d(p,γ) 3 He (Moscoso et al 2021), and 16 O(p,γ) 17 F (Iliadis, Palanivelrajan, & de Souza 2022), all of which have been reviewed by (Esmaeili et al 2022).

Figure 1. Big Bang Nucleosynthesis reaction network according to Nakamura et al (2017).

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Bayesian Estimation of the D(p,$γ$)$^3$He Thermonuclear Reaction Rate

“…The hierarchical Bayesian model in the present work is similar to the one in Iliadis et al (2016);de Souza et al (2020). This model allows us to take all relevant effects and processes into account impacting the measured data.…”

Constraining the Primordial Lithium Abundance: New Cross Section Measurement of the 7Be + n Reactions Updates the Total 7Be Destruction Rate

“…) channel were too low to observe this channel with their DE-E silicon telescope (Barbagallo et al 2018). de Souza et al (2020) compiled the available 7 Be n p , 7 ( ) Li data by a hierarchical Bayesian model, and an R-matrix fit derived a reaction rate with an evaluated uncertainty (∼2%) that is much smaller than the discrepancy among the different data sets (∼30%) they adopted. However, the contribution of the n p , 1 ( ) channel was not taken into account in their R-matrix analysis since there were no n p , 1 (…”