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

Hexadecapole ($\beta_{4}$) deformation of the light-mass nucleus $^{24}$Mg has been determined from quasi-elastic measurements at backward angles using $^{16}$O and $^{24}$Mg beams and $^{90}$Zr target. Experimental data were compared with coupled channel calculations using the code CCQEL.Considering $^{16}$O as an inert partner, the strength of vibrational degrees of freedom for $^{90}$Zr ($\lambda$=2 and 3) were determined. CCQEL calculations were carried out for $^{24}$Mg+$^{90}$Zr system with varying quadrupole ($\beta_{2}$) and hexadecapole ($\beta_{4}$) deformation parameters of $^{24}$Mg. The best fit $\beta_{2}$ and $\beta_{4}$ correspond to around 0.4 and -0.1, respectively. These values are consistent with earlier reported values.