Direct and indirect $\alpha$ transfer in the elastic $^{16}$O+$^{12}$C scattering

The extensive elastic $^{16}$O+$^{12}$C scattering data measured at low energies show consistently an oscillating enhancement of the elastic cross section at backward angles that is difficult to describe within the conventional optical model. Given the significant $\alpha$ spectroscopic factors predicted for the dissociation $^{16}$O$\to\alpha+^{12}$C by the shell model (SM) and $\alpha$-cluster model calculations, the contribution of the $\alpha$ transfer channels to the elastic $^{16}$O+$^{12}$C scattering should not be negligible, and is expected to account for the enhanced oscillation of the elastic cross section at backward angles. To reveal the impact of the $\alpha$ transfer, a systematic coupled reaction channels (CRC) analysis of the elastic $^{16}$O+$^{12}$C scattering has been performed where the multistep couplings between the elastic and inelastic scattering channels, the direct and indirect $\alpha$ transfer channels were treated explicitly, using the real optical potentials and inelastic scattering form factors determined by the double-folding model. We show that a consistent CRC description of the elastic $^{16}$O+$^{12}$C data at different energies can be obtained over the whole angular region, using the $\alpha$ spectroscopic factors determined recently in the large scale SM calculation. The present CRC results are, therefore, of interest not only for the nuclear scattering studies but also provide an important spectroscopic information on the cluster dissociation of $^{16}$O.