Abstract
Elastic and inelastic scattering of $\ensuremath{\alpha}$ particles on the deformed nucleus $^{12}\mathrm{C}$ are investigated in the range of incident $\ensuremath{\alpha}$-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 $\ensuremath{\alpha}$ particle and the deformed nucleus $^{12}\mathrm{C}$ is employed for the relative motion between the $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$ 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.
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