Theoretical study of the $\alpha+d$ $\rightarrow$ $^6$Li + $\gamma $ astrophysical capture process in a three-body model

TL;DR

This paper models the astrophysical alpha-deuteron capture process to lithium-6 using a three-body approach, providing insights into transition contributions and matching recent experimental data.

Contribution

It introduces a three-body model for the alpha+d to lithium-6 capture process, offering detailed transition estimates and aligning with recent experimental results.

Findings

E1 transition contribution from isosinglet states is negligible.

E2 transition contribution is much smaller than in two-body models.

Model matches new experimental data with a specific spectroscopic factor.

Abstract

The astrophysical capture process $\alpha+d$ $\rightarrow$ $^6$Li + $\gamma$ is studied 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. The contribution of the E1 transition operator from the initial isosinglet states to the isotriplet components of the final state is estimated to be negligible. An estimation of the forbidden E1 transition to the isosinglet components of the final state is comparable with the corresponding results of the two-body model. However, the contribution of the E2 transition operator is found to be much smaller than the corresponding estimations of the two-body model. The three-body model perfectly matches the new experimental data of the LUNA collaboration with the spectroscopic factor 2.586 estimated from the bound-state wave functions of $^6$Li and deuteron.