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

Abstract

Abstract 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.