Correspondence between isoscalar monopole strengths and $\alpha$ inelastic cross sections on ${}^{24}$Mg

Abstract

The correspondence between the isoscalar monopole (IS0) transition strengths and $\alpha$ inelastic cross sections, the $B(IS0)$-$(\alpha ,{\alpha }^{\prime })$ correspondence, is investigated for ${}^{24}$Mg($\alpha ,{\alpha }^{\prime }$) 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 ($\alpha ,{\alpha }^{\prime }$) cross sections. We aim at clarifying how the $B(IS0)$-$(\alpha ,{\alpha }^{\prime })$ 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 $B(IS0)$-$(\alpha ,{\alpha }^{\prime })$ correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the $B(IS0)$-$(\alpha ,{\alpha }^{\prime })$ 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 $\alpha$ cluster state is considered, the $B(IS0)$-$(\alpha ,{\alpha }^{\prime })$ correspondence becomes less valid. For a quantitative discussion on the $\alpha$ clustering in $0^{+}$ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.

Comments: 7 figures, 4 tables