Determination of hexadecapole (${\hat{I}}_4^2$) deformation of the light-mass nucleus ${}^{24}$Mg using quasi-elastic measurement

Abstract

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 ${\hat{I}}_2^2$ and ${\hat{I}}_4^2$ values for ${}^{24}$Mg are determined to be $+0.43\pm 0.02$ and $-0.11\pm 0.02$, respectively. The ${\hat{I}}_2^2$ 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.

This is a slightly modified version, accepted for publication in Phys. Lett. B