The Airy structure of the nuclear rainbow and prerainbow in inelastic and elastic $\alpha+^{ 16}$O scattering is studied with the coupled channel method using a folding potential derived from the microscopic wave functions of $^{ 16}$O. The theoretical calculations reproduce the characteristic energy evolution of the Airy minimum of the experimental angular distributions. The energy levels with $\alpha$-cluster structure in $^{ 20}$Ne are reproduced well using the potentials determined from the analysis of scattering. It is shown that the emergence of the $K=0_3^+$ $\alpha$-cluster band with core excitation at 7.19 MeV in $^{ 20}$Ne is intimately related to the emergence of the prerainbow and rainbow in inelastic scattering to the $^{ 16}$O($0^+_2$). It is found that the $\alpha$-cluster states with core excitation, the prerainbow and the rainbow in inelastic scattering are understood in a unified way as well as in the case of elastic scattering.
Categories: nucl-th nucl-ex