Quasi-elastic (QEL) scattering measurements have been performed using $^{ 28}$Si projectile off a $^{ 90}$Zr target at energies around the Coulomb barrier. A Bayesian analysis within the framework of coupled channels (CC) calculations is performed in a large parameter space of quadrupole and hexadecapole deformations ($\beta_{ 2}$ and $\beta_{ 4}$) of $^{ 28}$Si. Our results clearly show that $^{ 28}$Si is an oblate shaped nucleus with $\beta_{ 2}$=-$0.38 \pm 0.01$ which is in excellent agreement with electromagnetic probes. A precise value of hexadecapole deformation for $^{ 28}$Si, $\beta_{ 4}$=+$0.03 \pm 0.01$, along with a consistent value of quadrupole deformation has now been determined for the first time using QEL scattering. A remarkable agreement between the experimental $\beta_{ 4}$ value of $^{ 28}$Si and Skyrme-Hartree-Fock based calculations is obtained. The QEL results obtained previously for $^{ 24}$Mg (prolate) and the present result for $^{ 28}$Si (oblate) hereby affirm the strong sensitivity of the quasi-elastic scattering to ground state deformations, thus reinforcing its suitability as a potential probe for rare exotic nuclei.
Categories: nucl-ex nucl-th