We systematically measured the differential cross sections of inelastic $\alpha$ scattering off self-conjugate $A=4n$ nuclei at two incident energies $E_{\alpha }=130\mathrm{MeV}$ and $386\mathrm{MeV}$ at Research Center for Nuclear Physics, Osaka University. The measured cross sections were analyzed by the distorted-wave Born-approximation (DWBA) calculation using the single-folding potentials, which are obtained by folding macroscopic transition densities with the phenomenological $\alpha N$ interaction. The DWBA calculation with the density-dependent $\alpha N$ interaction systematically overestimates the cross sections for the $\mathrm{\Delta }L=0$ transitions. However, the DWBA calculation using the density-independent $\alpha N$ interaction reasonably well describes all the transitions with $\mathrm{\Delta }L=0$–4. We examined uncertainties in the present DWBA calculation stemming from the macroscopic transition densities, distorting potentials, phenomenological $\alpha N$ interaction, and coupled channel effects in ${}^{12}\mathrm{C}$. It was found that the DWBA calculation is not sensitive to details of the transition densities nor the distorting potentials, and the phenomenological density-independent $\alpha N$ interaction gives reasonable results. The coupled-channel effects are negligibly small for the $2_1^{+}$ and $3_1^{-}$ states in ${}^{12}\mathrm{C}$, but not for the $0_2^{+}$ state. However, the DWBA calculation using the density-independent interaction at $E_{\alpha }=386\mathrm{MeV}$ is still reasonable even for the $0_2^{+}$ state. We concluded that the macroscopic DWBA calculations using the density-independent interaction are reliably applicable to the analysis of inelastic $\alpha$ scattering at $E_{\alpha }\sim 100\mathrm{MeV}/\mathrm{u}$.

• Received 16 October 2017

DOI:https://doi.org/10.1103/PhysRevC.97.014601