The correspondence between the isoscalar monopole (IS0) transition strengths and $\alpha$ inelastic cross sections, the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence, is investigated for $^{24}$Mg($\alpha,\alpha'$) 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 ($\alpha,\alpha'$) cross sections. We aim at clarifying how the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon–nucleon effective interaction in the scattering process, and the coupled-channel effect. It is found that these effects are significant and the explanation of the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the $B({\rm IS0})$–$(\alpha,\alpha')$ 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 compromised 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 $B({\rm IS0})$–$(\alpha,\alpha')$ 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.

中文翻译：

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等标量单极子强度与 24Mg 上的 $\alpha$ 非弹性截面的对应关系

对于24}$Mg($\alpha,\alpha'$) 在 130 和 386 MeV。我们采用微观耦合通道反应框架将结构输入、对角线和跃迁密度联系起来，对于通过反对称分子动力学获得的 $^{24}$Mg 到 ($\alpha,\alpha'$) 横截面。我们旨在阐明 $B({\rm IS0})$–$(\alpha,\alpha')$ 对应如何受到核畸变的影响，在散射中对核子-核子有效相互作用的介质修改过程和耦合通道效应。发现这些影响是显着的，$B({\rm IS0})$–$(\alpha,\alpha' )$ 平面波极限与通常使用的长波长近似的对应是没有意义的。然而，$B({\rm IS0})$–$(\alpha,\alpha')$ 对应往往保持不变，因为对基态和 $0^+$ 激发态之间的跃迁密度有很强的限制。发现该对应关系在 386 MeV 处保持，误差约为 20%–30%，而在 130 MeV 处严重受损，主要是由于强核畸变。还发现，当考虑与简单 $\alpha$ 簇状态具有不同结构的 $0^+$ 状态时，$B({\rm IS0})$–$(\alpha,\alpha') $ 对应变得不那么有效。对于 $0^+$ 原子核激发态中的 $\alpha$ 聚类的定量讨论，