Microscopic coupled-channel calculation of proton and alpha inelastic scattering to the |$4^+_1$| and |$4^+_2$| states of |$^{24}\textrm{Mg}$|.

The triaxial and hexadecapole deformations of the |$K^\pi=0^+$| and |$K^\pi=2^+$| bands of |$^{24}$| Mg have been investigated by the inelastic scatterings of various probes, including electrons, protons, and alpha(⁠|$\alpha$|⁠) particles, for a prolonged time. However, it has been challenging to explain the unique properties of the scatterings observed for the |$4^+_1$| state through reaction calculations. This paper investigates the structure and transition properties of the |$K^\pi=0^+$| and |$K^\pi=2^+$| bands of |$^{24}$| Mg employing the microscopic structure and reaction calculations via inelastic proton and |$\alpha$| scattering. In particular, the |$E4$| transitions to the |$4^+_1$| and |$4^+_2$| states are reexamined. The structure of |$^{24}$| Mg was calculated employing the variation after the parity and total angular momentum projections in the framework of the antisymmetrized molecular dynamics (AMD). The inelastic proton and |$\alpha$| reactions were calculated by the microscopic coupled-channel (MCC) approach by folding the Melbourne |$g$| -matrix |$NN$| interaction with the AMD densities of |$^{24}$| Mg. Reasonable results were obtained on the properties of the structure, including the energy spectra and |$E2$| and |$E4$| transitions of the |$K^\pi=0^+$| and |$K^\pi=2^+$| bands owing to the enhanced collectivity of triaxial deformation. The MCC+AMD calculation successfully reproduced the angular distributions of the |$4^+_1$| and |$4^+_2$| cross sections of proton scattering at incident energies of |$E_p=40$| –100 MeV and |$\alpha$| scattering at |$E_\alpha=100$| –400 MeV. This is the first microscopic calculation to describe the unique properties of the |$0^+_1\to 4^+_1$| transition. In the inelastic scattering to the |$4^+_1$| state, the dominant two-step process of the |$0^+_1\to 2^+_1\to 4^+_1$| transitions and the deconstructive interference in the weak one-step process were essential. [ABSTRACT FROM AUTHOR]