Systematic analysis of inelastic α scattering off self-conjugate A=4n nuclei

We systematically measured the differential cross sections of inelastic $\ensuremath{\alpha}$ scattering off self-conjugate $A=4n$ nuclei at two incident energies ${E}_{\ensuremath{\alpha}}=130\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $386\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ 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 $\ensuremath{\alpha}N$ interaction. The DWBA calculation with the density-dependent $\ensuremath{\alpha}N$ interaction systematically overestimates the cross sections for the $\mathrm{\ensuremath{\Delta}}L=0$ transitions. However, the DWBA calculation using the density-independent $\ensuremath{\alpha}N$ interaction reasonably well describes all the transitions with $\mathrm{\ensuremath{\Delta}}L=0$--4. We examined uncertainties in the present DWBA calculation stemming from the macroscopic transition densities, distorting potentials, phenomenological $\ensuremath{\alpha}N$ 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 $\ensuremath{\alpha}N$ interaction gives reasonable results. The coupled-channel effects are negligibly small for the ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in $^{12}\mathrm{C}$, but not for the ${0}_{2}^{+}$ state. However, the DWBA calculation using the density-independent interaction at ${E}_{\ensuremath{\alpha}}=386\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ 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 $\ensuremath{\alpha}$ scattering at ${E}_{\ensuremath{\alpha}}\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}/\mathrm{u}$.