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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 athree-body bound state $\alpha+n+p$ in the hyperspherical Lagrange-mesh method.  The contribution of the E1 transition operator from the initial isosingletstates to the isotriplet components of the final state is estimated to benegligible. An estimation of the forbidden E1 transition to the isosingletcomponents of the final state is comparable with the corresponding results ofthe two-body model.  However, the contribution of the E2 transition operator is found to be muchsmaller than the corresponding estimations of the two-body model.  The three-body model perfectly matches the new experimental data of the LUNAcollaboration with the spectroscopic factor 2.586 estimated from thebound-state wave functions of $^6$Li and deuteron.

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