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Isospin characters of nuclear excitations in $^{26}$Mg and $^{10}$Be are investigated via proton($p$) and alpha($\alpha$) inelastic scattering. A structure model of antisymmetrized molecular dynamics (AMD) is applied to calculate the ground and excited states of $^{26}$Mg and $^{10}$Be. The calculation describes the isoscalar feature of the ground-band $2^+_1$($K^\pi=0^+_1$) excitation and predicts the neutron dominance of the side-band $2^+_2$($K^\pi=2^+$) excitation in $^{26}$Mg and $^{10}$Be. The $p$ and $\alpha$ inelastic scattering off $^{26}$Mg and $^{10}$Be is calculated by microscopic coupled-channel (MCC) calculations with a $g$-matrix folding approach by using the matter and transition densities of the target nuclei calculated with AMD. The calculation reasonably reproduces the observed $0^+_1$, $2^+_1$, and $2^+_2$ cross sections of $^{26}$Mg+$p$ scattering at incident energies $E_p=$24 and 40 MeV and of $^{26}$Mg+$\alpha$ scattering at $E_\alpha=$104 and 120 MeV. For $^{10}$Be+$p$ and $^{10}$Be+$\alpha$ scattering, inelastic cross sections to the excited states in the $K^\pi=0^+_1$ ground-, $K^\pi=2^+$ side-, $K^\pi=0^+_2$ cluster-, and $K^\pi=1^-$ cluster-bands are investigated. The isospin characters of excitations are investigated via inelastic scattering processes by comparison of the production rates in the $^{10}$Be+$p$, $^{10}$Be+$\alpha$, and $^{10}$C+$p$ reactions. The result predicts that the $2^+_2$ state is selectively produced by the $^{10}$Be+$p$ reaction because of the neutron dominance in the $2^+_2$ excitation as in the case of the $^{26}$Mg+$p$ scattering to the $2^+_2$ state, whereas its production is significantly suppressed in the $^{10}$C+$p$ reaction., Comment: 19 pages, 12 figures

The correspondence between the isoscalar monopole (IS0) transition strengths and $��$ inelastic cross sections, the $B({\rm IS0})$-$(��,��')$ correspondence, is investigated for $^{24}$Mg($��,��'$) 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 ($��,��'$) cross sections. We aim at clarifying how the $B({\rm IS0})$-$(��,��')$ 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 $B({\rm IS0})$-$(��,��')$ correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the $B({\rm IS0})$-$(��,��')$ 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 $��$ cluster state is considered, the $B({\rm IS0})$-$(��,��')$ correspondence becomes less valid. For a quantitative discussion on the $��$ clustering in $0^+$ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary., 7 figures, 4 tables

We investigated cluster correlation and nuclear voricity in low-lying $1^-$ states of $^{24}$Mg within antisymmetrized molecular dynamics framework. We found that the toroidal and compressional dipole modes separately appear as the $K=1$ and $K=0$ states. The $1^-$ ($K=1$) state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the $1^-$ ($K=0$) state is the compressional dipole state having enhanced cluster structure but has the weaker vorticity.

The proton-induced $��$ knockout reaction has been utilized for decades to investigate the $��$ cluster states of nuclei, of the ground state in particular. However, even in recent years, it is reported that the deduced $��$ spectroscopic factors from $��$ knockout experiments and reaction analyses with a phenomenological $��$ cluster wave function diverge depending on the kinematical condition of the reaction. In the present study we examine the theoretical description of the $^{20}$Ne($p$,$p��$)$^{16}$O cross section based on the antisymmetrized molecular dynamics and the distorted wave impulse approximation by comparing with existing experimental data. We also investigate the correspondence between the $��$ cluster wave function and the $��$ knockout cross section. The existing $^{20}$Ne($p$,$p��$)$^{16}$O data at 101.5 MeV is well reproduced by the present framework. Due to the peripherality of the reaction, the surface region of the cluster wave function is selectively reflected to the knockout cross section. A quantitatively reliable $��$ cluster wave function, $p$-$��$ cross section, and distorting potentials between scattering particles, $��$-$^{16}$O in particular, are crucial for the quantitative description of the ($p$,$p��$) cross section. Due to the peripherality of the reaction, the ($p$,$p��$) cross section is a good probe for the surface $��$ amplitude., 6 pages, 7 figures

We derive the equations to calculate the reduced width amplitudes (RWA) of the different size clusters and deformed clusters without any approximation. These equations named Laplace expansion method are applicable to the nuclear models which uses the Gaussian wave packets. The advantage of the method is demonstrated by the numerical calculations of the ${}^{16}{\rm O}+\alpha$ and ${}^{24}{\rm Mg}+\alpha$ RWAs in $^{20}{\rm Ne}$ and $^{28}{\rm Si}$., Comment: 26 pages, 4 figures