Elastic α -12C scattering at low energies with the resonant 22+ and 23+ states of 16O

The elastic α -¹²C scattering for l =2 at low energies is studied in an effective Lagrangian approach. I explicitly include two resonant 2₂⁺ and 2₃⁺ states of ¹⁶O in the scattering amplitudes and construct an S matrix assuming that three amplitudes, nonresonant part of the amplitude which has the subthreshold 2₁⁺ state of ¹⁶O and those of the two resonant states, are represented by the summation of corresponding parts of the phase shift. Then, I fit the parameters in the S matrix to the phase shift data by imposing three conditions at the very low energies where the phase shift data are not available. By using the fitted parameters, the asymptotic normalization coefficients (ANC) of the 2₁⁺ state of ¹⁶O are calculated, and I find that the previously reported small and large values of the ANC can be reproduced depending on the imposed conditions. While large error bars for the large ANC values which are reported from the α transfer reactions are also obtained.