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

TL;DR

This paper presents a three-body model calculation of the astrophysical S-factor, reaction rates, and primordial abundance of $^6$Li from the $ ext{alpha}+ ext{d}$ capture process, aligning well with recent experimental data.

Contribution

It introduces a detailed three-body model for the $ ext{alpha}+ ext{d}$ capture process, accurately reproducing experimental S-factors and primordial $^6$Li abundance.

Findings

The model reproduces recent LUNA data within experimental error.

Estimated $^6$Li/H abundance ratio matches recent measurements.

Corrections to asymptotics improve the accuracy of the S-factor calculations.

Abstract

The astrophysical S-factor and reaction rate of the direct capture process $\alpha+d$ $\rightarrow$ $^6$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.