ANCs of the Bound States of \(^{16}\)O Deduced from Elastic \(\alpha \)-\(^{12}\)C Scattering Data

Asymptotic normalization coefficients (ANCs) of the \(0_1^+\) $0_1^{+}$ , \(0_2^+\) $0_2^{+}$ , \(1_1^-\) $1_1^{-}$ , \(2_1^+\) $2_1^{+}$ , \(3_1^-\) $3_1^{-}$ ( \(l_{i th}^\pi \) $l_{\mathit{ith}}^{\pi }$ ) bound states of \(^{16}\) ${}^{16}$ O are deduced from the phase shift data of elastic \(\alpha \) $\alpha$ - \(^{12}\) ${}^{12}$ C scattering at low energies. S matrices of elastic \(\alpha \) $\alpha$ - \(^{12}\) ${}^{12}$ C scattering are constructed within cluster effective field theory (EFT), in which both bound and resonant states of \(^{16}\) ${}^{16}$ O are considered. Parameters in the S matrices are fitted to the precise phase shift data below the p- \(^{15}\) ${}^{15}$ N breakup energy for the partial waves of \(l=0,1,2,3,4,5,6\) $l=0,1,2,3,4,5,6$ , and the ANCs are calculated by using the wave function normalization factors of \(^{16}\) ${}^{16}$ O propagators for \(l=0,1,2,3\) $l=0,1,2,3$ . We review the values of ANCs, which are compared with other results in the literature, and discuss uncertainties of the ANCs obtained from the elastic \(\alpha \) $\alpha$ - \(^{12}\) ${}^{12}$ C scattering data in cluster EFT.