Determination of hexadecapole ( ) Deformation of the Light-mass Nucleus Mg using quasi-elastic scattering measurements

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 $+0.43±0.02$ and $-0.11±0.02$, 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.