Correspondence between isoscalar monopole strengths and $α$ inelastic cross sections on $^{24}$Mg
The correspondence between the isoscalar monopole (IS0) transition strengths and $α$ inelastic cross sections, the $B({\rm IS0})$-$(α,α')$ correspondence, is investigated for $^{24}$Mg($α,α'$) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for $^{24}$Mg obtained with antisymmetrized molecular dynamics to the ($α,α'$) cross sections. We aim at clarifying how the $B({\rm IS0})$-$(α,α')$ correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon-nucleon effective interaction in the scattering process, and the coupled-channels effect. It is found that these effects are significant and the explanation of the $B({\rm IS0})$-$(α,α')$ correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the $B({\rm IS0})$-$(α,α')$ correspondence tends to remain because of a strong constraint on the transition densities between the ground state and the $0^+$ excited states. The correspondence is found to hold at 386 MeV with an error of about 20%-30%, while it is seriously stained at 130 MeV mainly by the strong nuclear distortion. It is also found that when a $0^+$ state that has a different structure from a simple $α$ cluster state is considered, the $B({\rm IS0})$-$(α,α')$ correspondence becomes less valid. For a quantitative discussion on the $α$ clustering in $0^+$ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.