Theoretical reaction rates of the ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O reaction from the potential model

Abstract

The radiative capture cross sections of ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O and derived reaction rates are calculated from the direct capture potential model. The resulting $S$-factor at low energies is found to be dominated by $E$2 transition to the ${}^{16}$O ground state. The $E$1 and $E$2 $S$-factors at $E_{c.m.}=0.3$ MeV are $S_{E1}\approx 3$ keV~b and $S_{E2}=150_{-17}^{+41}$ keV~b, respectively. The sum of the cascade transition through the excited state of ${}^{16}$O is $S_{\mathrm{casc}}=18\pm 4.5$ keV~b. The derived reaction rates at low temperatures seem to be concordant with those from the previous evaluation. For astrophysical applications, our reaction rates below $T_9=3$ are provided in an analytic expression.

Comments: 6 pages, 4 figures, Proceedings of Nuclei in the Cosmos (NIC XIII). 7-11 July 2014. Debrecen, Hungary