Unification of Airy structure in inelastic $α$ +$^{16}$O scattering and $α$-cluster structure with core excitation in $^{20}$Ne

The Airy structure of the nuclear rainbow and prerainbow in inelastic and elastic $α+^{16}$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 $α$-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 $K=0_3^+$ $α$-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 $α$-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.

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