Elastic and inelastic scattering of $\alpha$ particles on the deformed nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are investigated in the range of incident $\alpha$-particle energies of 9 to 11 MeV by using the coupled-channel method with an orthogonality condition. A doubly folded potential generated by the shell model wave functions of the $\alpha$ particle and the deformed nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is employed for the relative motion between the $\alpha$ particle and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Good agreement between theory and experiment is obtained for the elastic and inelastic angular distributions and the resonance structures. It is found, from the Born series expansion of the $T$ matrix, that the orthogonality constraint stresses the effects of the channel coupling between the elastic and inelastic processes, and it indicates that the distorted-wave Born approximation does not work well in this system.

NUCLEAR REACTIONS Elastic and inelastic scattering of $\alpha$ particles on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; coupled-channel orthogonality condition model, folded potential; calculated angular distributions and phase shifts, resonances of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; Born series of $T$ matrices.

• Received 26 November 1980

DOI:https://doi.org/10.1103/PhysRevC.23.2414