{Once more about astrophysical $S$ factor for the $α+ d \to {}^{6}{\rm Li} + γ$ reaction

Abstract: Recently to study the radiative capture $\alpha + d \to {}^{6}{\rm Li} + \gamma$ process a new measurement of the ${}^{6}{\rm Li}({\rm A\,150\,MeV})$ dissociation in the field of ${}^{208}{\rm Pb}$ has been reported in [F. Hammache {\it et al.} Phys. Rev ${\bf C 82}$, 065803 (2010)]. However, the dominance of the nuclear breakup over the Coulomb one prevented from obtaining the information about the $\alpha + d \to {}^{6}{\rm Li} + \gamma$ process from the breakup data. The astrophysical $S_{24}(E)$ factor has been calculated within the $\alpha-d$ two-body potential model with potentials determined from the fits to the $\alpha-d$ elastic scattering phase shifts. However, the scattering phase shift itself doesn't provide a unique $\alpha-d$ bound state potential, which is the most crucial input when calculating the $S_{24}(E)$ astrophysical factor at astrophysical energies. In this work we emphasize an important role of the asymptotic normalization coefficient (ANC) for ${}^{6}{\rm Li} \to \alpha + d$, which controls the overall normalization of the peripheral $\alpha + d \to {}^{6}{\rm Li} + \gamma$ process and is determined by the adopted $\alpha-d$ bound state potential. We demonstrate that the ANC previously determined from the $\alpha-d$ elastic scattering $s$-wave phase shift in [Blokhintsev {\it et. al} Phys. Rev. {\bf C 48}, 2390 (1993)] gives $S_{24}(E)$, which is at low energies about 38% lower than the one reported in [F. Hammache {\it et al.} Phys. Rev ${\bf C 82}$, 065803 (2010)]. We recalculate also the reaction rates, which are also lower than those obtained in [F. Hammache {\it et al.} Phys. Rev ${\bf C 82}$, 065803 (2010)].