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

Abstract

Background: The triaxial and hexadecapole deformations of the K=0+ and K=2+ bands of 24Mg have been investigated by the inelastic scatterings of various probes, including electrons, protons, and 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. Purpose: To investigate the structure and transition properties of the K=0+ and K=2+ bands of 24Mg employing the microscopic structure and reaction calculations via inelastic proton and alpha-scattering. Particularly, the E4 transitions to the $4_1^{+}$ and $4_2^{+}$ states were reexamined. Method: The structure of 24Mg 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 24Mg. Results: Reasonable results were obtained on the properties of the structure, including the energy spectra and E2 and E4 transitions of the K=0+ and K=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--100MeV and alpha-scattering at $E_{\alpha }$=100--400MeV. Conclusions: This is the first microscopic calculation that described 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 is the weak one-step process were essential.

Comments: 12 pages, 8 figures