Determination of hexadecapole (\(\beta_{4}\)) deformation of the light-mass nucleus \(^{24}\)Mg using quasi-elastic measurement

Quasi-elastic scattering measurements have been performed using \(^{16}\)O and \(^{24}\)Mg projectiles off \(^{90}\)Zr at energies around the Coulomb barrier. Experimental data have been analyzed in the framework of coupled channels (CC) calculations using the code CCFULL. The quasi-elastic scattering excitation function and derived barrier distribution for \(^{16}\)O + \(^{90}\)Zr reaction are well reproduced by the CC calculations using the vibrational coupling strengths for \(^{90}\)Zr reported in the literature. Using these vibrational coupling strengths, a Bayesian analysis is carried out for \(^{24}\)Mg + \(^{90}\)Zr reaction. The \(\beta_{2}\) and \(\beta_{4}\) values for \(^{24}\)Mg are determined to be \(+0.43 \pm 0.02\) and \( - 0.11 \pm 0.02\), respectively. The \(\beta_{2}\) parameter determined in the present work is in good agreement with results obtained using inelastic scattering probes. The hexadecapole deformation of \(^{24}\)Mg has been measured very precisely for the first time. Present results establish that quasi-elastic scattering could provide a useful probe to determine the ground state deformation of atomic nuclei.