{Once more about astrophysical $S$ factor for the $\alpha +d\to {}^6\mathrm{Li}+\gamma$ reaction

Abstract

Recently to study the radiative capture $\alpha +d\to {}^6\mathrm{Li}+\gamma$ process a new measurement of the ${}^6\mathrm{Li}(\mathrm{A}150\mathrm{MeV})$ dissociation in the field of ${}^{208}\mathrm{Pb}$ has been reported in [F. Hammache {\it et al.} Phys. Rev $C82$, 065803 (2010)]. However, the dominance of the nuclear breakup over the Coulomb one prevented from obtaining the information about the $\alpha +d\to {}^6\mathrm{Li}+\gamma$ 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 ${}^6\mathrm{Li}\to \alpha +d$, which controls the overall normalization of the peripheral $\alpha +d\to {}^6\mathrm{Li}+\gamma$ 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 $C82$, 065803 (2010)]. We recalculate also the reaction rates, which are also lower than those obtained in [F. Hammache {\it et al.} Phys. Rev $C82$, 065803 (2010)].

arXiv comment6 pages and 2 figures

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