Microscopic coupled-channel calculation of proton and alpha inelastic scattering to the 4+ 1 and 4+ 2 states of 24Mg

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 Ep=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.