Scattering of $\alpha$-particles and $^{3}$He by $^{24}$Mg nuclei at energies about 50–60 MeV

Abstract

Differential cross sections of elastic and inelastic scattering with excitation of states of the rotational band of the ground state of $^{24}$Mg were measured at an $\alpha$-particle energy of 50.5 MeV and $^{3}$He 60 MeV. The angular distributions were analyzed using an optical model and a coupled channel method. A number of potentials with significantly different geometries are obtained, which describe well the elastic scattering at the measured angular range. The collective model was used in the calculations via the coupled channel method. In addition to the ground state, three low-lying states of $^{24}$Mg, 2$^{+}$ (1.368 MeV), 4$^{+}$ (4.122 MeV), and 4.238 MeV (2$^{+}$), were included in the coupling scheme. The values of quadrupole ($\beta _{2}$) and hexadecapole ($\beta _{4}$) deformation parameters were extracted. According to the analysis of scattering of $\alpha$-particles, they are 0.52 and 0.05. For $^{3}$He, they are 0.75 and 0.07, respectively. The extracted parameters correspond to the previously obtained values from the scattering of protons, deuterons and $\alpha$-particles.