Astrophysical S-factors, Thermonuclear Rates, and Electron Screening Potential for the ³He(d,p)⁴He Big Bang Reaction via a Hierarchical Bayesian Model

Abstract

We developed a hierarchical Bayesian framework to estimate S-factors and thermonuclear rates for the 3 He(d,p) 4 He reaction, which impacts the primordial abundances of 3 He and 7 Li. The available data are evaluated and all direct measurements are taken into account in our analysis for which we can estimate separate uncertainties for systematic and statistical effects. For the nuclear reaction model, we adopt a single-level, two-channel approximation of R-matrix theory, suitably modified to take the effects of electron screening at lower energies into account. In addition to the usual resonance parameters (resonance location and reduced widths for the incoming and outgoing reaction channel), we include the channel radii and boundary condition parameters in the fitting process. Our new analysis of the 3 He(d,p) 4 He S-factor data results in improved estimates for the thermonuclear rates. This work represents the first nuclear rate evaluation using R-matrix theory embedded into a hierarchical Bayesian framework, properly accounting for all known sources of uncertainty. Therefore, it provides a test bed for future studies of more complex reactions.

Stress testing the dark energy equation of state imprint on supernova data

“…BBN occurred within the first 20 minutes after the Big Bang and is responsible for the production of the lightest nuclides, providing sensitive constraints on the ΛCDM model (e.g., [11][12][13]). Similarly, the estimated CMB temperature evolution with redshift is corroborated by rotational excitation of molecules and the Sunyaev-Zel'dovich effect [14,15].…”

Indications for a Nonzero Lepton Asymmetry in the Early Universe

“…• PRIMAT driven: Nuclear rates are implemented according to the statistical determination of Refs [63][64][65][66][67][68], i.e. following theoretical ab-initio energy modeling tuned to datasets for which an estimate of systematic errors is available [19,22,47].…”

Revisiting the Gamow Factor Reactions on Light Nuclei

“…To determine the S(E) precisely at these low energies, the R-matrix theory [11,12] has been utilized, providing a more precise evaluation of S(E). Therefore, even with the lack of low energy cross-section data, the nuclear cross-section for nucleosynthesis can be evaluated using the extrapolated S(E) and the Gamow factor, a widely adopted method in nuclear astrophysics [13,14].…”