Elastic $α$-$^{12}$C scattering at low energies with the resonant $2_2^+$ and $2_3^+$ states of $^{16}$O

Shung-Ichi Ando

Published 2021-08-05Version 1

The elastic $\alpha$-$^{12}$C scattering for $l=2$ at low energies is studied in effective Lagrangian approach. We explicitly include two resonant $2_2^+$ and $2_3^+$ states of $^{16}$O in the scattering amplitude and fit the parameters to the phase shift data. We also study three contributions from higher order, the resonant $2_1^+$ state of $^{12}$C, the resonant $2_4^+$ state of $^{16}$O, and a vertex correction of the initial and final state interactions of the amplitude for the $2_3^+$ state of $^{16}$O, by imposing three conditions at the very low energies where the phase shift data are not available, and calculate the asymptotic normalization coefficient (ANC) for the sub-threshold $2_1^+$ state of $^{16}$O. We find that the previously reported small and large values of the ANC can be reproduced depending on the imposed conditions, but we obtain a large error bar to the large ANC value reported from the $\alpha$ transfer reactions.