Theoretical study of the direct $\alpha +d$ $\to$ ${}^6$Li + $\gamma$ astrophysical capture process in a three-body model II. Reaction rates and primordial abundance

Abstract

The astrophysical S-factor and reaction rate of the direct capture process $\alpha +d$ $\to$ ${}^6$Li + $\gamma$, as well as the abundance of the ${}^6$Li element are estimated in a three-body model. The initial state is factorized into the deuteron bound state and the $\alpha +d$ scattering state. The final nucleus ${}^6$Li(1+) is described as a three-body bound state $\alpha +n+p$ in the hyperspherical Lagrange-mesh method. Corrections to the asymptotics of the overlap integral in the S- and D-waves have been done for the E2 S-factor. The isospin forbidden E1 S-factor is calculated from the initial isosinglet states to the small isotriplet components of the final ${}^6$Li(1+) bound state. It is shown that the three-body model is able to reproduce the newest experimental data of the LUNA collaboration for the astrophysical S-factor and the reaction rates within the experimental error bars. The estimated ${}^6$Li/H abundance ratio of $(0.67\pm 0.01)\times 10^{-14}$ is in a very good agreement with the recent measurement $(0.80\pm 0.18)\times 10^{-14}$ of the LUNA collaboration.

Comments: 8 pages, 2 tables and 6 figures