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

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.

Figure 1

The elastic and inelastic angular distributions (solid lines) of $\alpha$ scattering from ${}^{16}$O calculated using the coupled channel method are compared with the experimental data (red points) at $E_L=40.5$ MeV [26], 50 MeV, 80.7 MeV [27], and 146 MeV [28]. In (b) the elastic scattering angular distribution calculated at 48.7 MeV is displayed to be compared with the data (orange triangles) measured up to very large angles at 48.7 MeV [8]. The calculated cross sections for elastic scattering (solid lines) are shown decomposed into the farside component (dashed lines) and the nearside component (dotted lines).

Figure 2

The energy evolution of the Airy minimum in the calculated (solid lines) and experimental (red points and orange triangles) angular distributions of prerainbow and rainbow $\alpha +{}^{16}$O scattering, is displayed for (a) elastic scattering, (b) inelastic scattering to the $0_2^{+}$ state, and (c) inelastic scattering to the $3^{-}$ state. The farside cross sections are shown with dashed lines. The experimental data (red points) at 50 MeV are also included for the 48.7 MeV case in (a).

Figure 3

The double folding diagonal (a) and coupling (b) potentials for the $\alpha +{}^{16}$O system calculated at $E_L=50$ MeV.

Figure 4

The energy evolution of the farside component of the angular distributions calculated in 4 MeV steps for (a) elastic scattering and (b) inelastic scattering to the $0_2^{+}$ state (solid lines) and the experimental data (points) [8, 27].

Figure 5

The energy evolution of the angular distributions in elastic $\alpha$ $+$ ${}^{16}$O scattering calculated using the coupled channel method (solid lines) is displayed in comparison with the experimental data (points), 20.7 MeV [29], 23.7 MeV [30], 24.28 MeV [29], 25.2 MeV [31], 30.3 MeV [31], 48.7 MeV, 54.1 MeV [8], 69.5 MeV [7], 50 MeV, 80.7 MeV [27], and 146 MeV [28].

Figure 6

The experimental $K=0_1^{+}$, $K=0_1^{-}$, and $K=0_4^{+}$ bands with the $\alpha +{}^{16}$O(g.s.) structure (a), and the $K=0_3^{+}$ band with the $\alpha +{}^{16}$O${}^{*}$($0_2^{+}$) structure (c) are compared with the calculated energy levels with the folding potentials for the $\alpha +{}^{16}$O (b) and $\alpha +{}^{16}$O${}^{*}$($0_2^{+}$) (d) channels, respectively.