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

TL;DR

This study investigates how well the relationship between isoscalar monopole transition strengths and alpha inelastic scattering cross sections holds for $^{24}$Mg, considering various nuclear effects and energy dependencies, revealing it is valid at higher energies with some limitations.

Contribution

It provides a microscopic analysis of the $B({ m IS0})$-$( ext{α,α'})$ correspondence, highlighting the effects of nuclear distortion and energy on its validity.

Findings

The correspondence is accurate within 20-30% at 386 MeV.

Nuclear distortion significantly affects the correspondence at 130 MeV.

The validity of the correspondence depends on the structure of the excited states.

Abstract

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-channels 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 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 $B({\rm IS0})$-$(\alpha,\alpha')$ 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.