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 π = 0 + and K π = 2 + bands of 24 Mg have been investigated by the inelastic scatterings of various probes, including electrons, protons, and alpha(α) 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 π = 0 + and K π = 2 + bands of 24 Mg employing the microscopic structure and reaction calculations via inelastic proton and α-scattering. Particularly, the E4 transitions to the 4 + 1 and 4 + 2 states were reexamined. Method 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 α reactions were calculated by the microscopic coupled-channel (MCC) approach by folding the Melbourne g-matrix N N interaction with the AMD densities of 24 Mg.Results Reasonable results were obtained on the properties of the structure, including the energy spectra and E2 and E4 transitions of the K π = 0 + and K π = 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 α-scattering at Eα = 100-400 MeV.Conclusions This is the first microscopic calculation that described the unique properties of the 0 + 1 → 4 + 1 transition. In the inelastic scattering to the 4 + 1 state, the dominant two-step process of the 0 + 1 → 2 + 1 → 4 + 1 transitions and the deconstructive interference is the weak one-step process were essential.

Probing negative-parity states of Mg24 probed with proton and α inelastic scattering

“…We can solve this problem with another version of the AMD calculation that yields superior results for the excitation energies and transition properties of the K π = 0 + and K π = 2 + bands. In the next paper [63], we will present a detailed investigation of proton and α inelastic scattering to the 4 + 1 state using the MCC+AMD approach with improved AMD densities for 24 Mg.…”

“…Higher-order effects beyond the present structure model may be a reason for such overestimation. In the next paper [63], we will present an improved result of the AMD calculation for the K π = 2 + band.…”