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

The astrophysical capture process $\alpha +d\to {}^6\mathrm{Li}$ 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 ${}^6\mathrm{Li}\left(1^{+}\right)$ 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 of 2.586 estimated from the bound-state wave functions of ${}^6\mathrm{Li}$ and a deuteron.

Figure 1

Contribution of the $E1$-transition operator from the initial isosinglet state to the isotriplet component of the final state for the astrophysical $S$ factor of the capture process $\alpha +d\to {}^6\mathrm{Li}+\gamma$.

Figure 2

Contribution of the $E1$-transition operator from the initial isosinglet state to the isotriplet and isosinglet components of the final state for the astrophysical $S$ factor of the capture process $\alpha +d\to {}^6\mathrm{Li}+\gamma$.

Figure 3

Contribution of the $E2$-transition operator to the astrophysical $S$ factor of the capture process $\alpha +d\to {}^6\mathrm{Li}+\gamma$.

Figure 4

Convergence of the astrophysical $S$ factor for the capture process $\alpha +d\to {}^6\mathrm{Li}+\gamma$ with respect to the number of integration points with the fixed step of $h=0.05\mathrm{fm}$.

Figure 5

Comparison of the contributions of the $E1$- and $E2$-transition operators to the astrophysical $S$ factor of the capture process $\alpha +d\to {}^6\mathrm{Li}+\gamma$.

Figure 6

Comparison of the theoretical estimations obtained in the two- and three-body models for the astrophysical $S$ factor of the capture process $\alpha +d\to {}^6\mathrm{Li}+\gamma$ with available experimental data.