The ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction affects not only the production of ${}^7\mathrm{Li}$ in big bang nucleosynthesis, but also the fluxes of ${}^7\mathrm{Be}$ and ${}^8\mathrm{B}$ neutrinos from the Sun. This double role is exploited here to constrain the former by the latter. A number of recent experiments on ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ provide precise cross section data at $E=0.5–1.0\mathrm{MeV}$ center-of-mass energies. However, there is a scarcity of precise data at big bang energies, 0.1–0.5 MeV, and below. This problem can be alleviated, based on precisely calibrated ${}^7\mathrm{Be}$ and ${}^8\mathrm{B}$ neutrino fluxes from the Sun that are now available, assuming the neutrino flavor oscillation framework to be correct. These fluxes and the standard solar model are used here to determine the ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ astrophysical $S$-factor at the solar Gamow peak, $S_{34}^{\nu }(23_{-5}^{+6}\mathrm{keV})=0.548\pm 0.054\mathrm{keV}\mathrm{b}$. This new data point is then included in a reevaluation of the ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ $S$-factor at big bang energies, following an approach recently developed for this reaction in the context of solar fusion studies. The reevaluated $S$-factor curve is then used to redetermine the ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ thermonuclear reaction rate at big bang energies. The predicted primordial lithium abundance is ${}^7\mathrm{Li}/\mathrm{H}=5.0\times {10}^{-10}$, far higher than the Spite plateau.

• Received 13 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.123526