Weak interference between the 1${}^{-}$ states in the vicinity of $\alpha$-particle threshold of ${}^{16}$O

Abstract

The subthreshold 1${}_1^{-}$ state at an excitation energy $E_x=7.12$ MeV in ${}^{16}$O has been believed to enhance the $S$-factor of ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O. The enhancement seems to originate from strong interference between 1${}_1^{-}$ and 1${}_2^{-}$ ($E_x\approx 9.6$ MeV) in the vicinity of the $\alpha$-particle threshold. However, weak interference between them and a resulting small $E$1 $S$-factor are exemplified with $R$-matrix theory. Including a higher-order correction of the resonance parameters, the present example appears to reproduce the experimental data consistently. It would therefore be possible that the $E$1 $S$-factor is reduced at low energies.

Comments: 3 pages, 1 figure; to appear in "Springer Proceedings in Physics", Proc. of Nuclei in the Cosmos XV, LNGS Assergi, Italy, 24-29 June 2018