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Background: The triaxial and hexadecapole deformations of the K=0+ and K=2+bands of 24Mg have been investigated by the inelastic scatterings of variousprobes, including electrons, protons, and alpha particles, for a prolongedtime. However, it has been challenging to explain the unique properties of thescatterings observed for the $4^+_1$ state through reaction calculations.Purpose: To investigate the structure and transition properties of the K=0+ andK=2+ bands of 24Mg employing the microscopic structure and reactioncalculations via inelastic proton and alpha-scattering. Particularly, the E4transitions to the $4^+_1$ and $4^+_2$ states were reexamined. Method: Thestructure of 24Mg was calculated employing the variation after the parity andtotal-angular momentum projections in the framework of the antisymmetrizedmolecular dynamics(AMD). The inelastic proton and alpha reactions werecalculated by the microscopic coupled-channel (MCC) approach by folding theMelbourne g-matrix NN interaction with the AMD densities of 24Mg. Results:Reasonable results were obtained on the properties of the structure, includingthe energy spectra and E2 and E4 transitions of the K=0+ and K=2+ bands owingto the enhanced collectivity of triaxial deformation. The MCC+AMD calculationsuccessfully reproduced the angular distributions of the $4^+_1$ and $4^+_2$cross sections of proton scattering at incident energies of $E_p$=40--100MeVand alpha-scattering at $E_\alpha$=100--400MeV. Conclusions: This is the firstmicroscopic calculation that described the unique properties of the $0^+_1\to4^+_1$ transition. In the inelastic scattering to the $4^+_1$ state, thedominant two-step process of the $0^+_1\to 2^+_1\to 4^+_1$ transitions and thedeconstructive interference is the weak one-step process were essential.

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