Reduced $E$1 $S$-factor of ${}^{12}$C($\alpha$,${\gamma }_0$)${}^{16}$O

Abstract

The astrophysical $S$-factor of $E$1 transition for ${}^{12}$C($\alpha$,${\gamma }_0$)${}^{16}$O is discussed in the $R$-matrix theory. The reduced $\alpha$-particle widths of the 1${}_1^{-}$ ($E_x=7.12$ MeV) and 1${}_2^{-}$ ($E_x=9.59$ MeV) states are extracted from the result of the potential model. The formal parameters are obtained without the linear approximation to the shift function. The resultant $E$1 $S$-factor is not strongly enhanced by the subthreshold 1${}_1^{-}$ state if the channel radius is 4.75 fm. The calculated $\beta$-delayed $\alpha$-particle spectrum of ${}^{16}$N and the $p$-wave phase shift of $\alpha$+${}^{12}$C elastic scattering are also found to be consistent with the previous studies. The small channel radius leads to the low penetrability to the Coulomb barrier, and it makes the reduced $E$1 $S$-factor below the barrier. Owing to the large reduced width from the molecular structure, the $R$-matrix pole of the 1${}_2^{-}$ state is shifted in the vicinity of 1${}_1^{-}$. The proximity of the two poles suppresses the interference between the states. The transparency of the $\alpha$+${}^{12}$C system appears to be expressed as the shrinking strong interaction region.

Comments: 12 pages, 9 figures, 2 tables. Submitted to PRC