Precise determination of quadrupole and hexadecapole deformation parameters of the $sd$-shell nucleus, ${}^{28}$Si

Abstract

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 (${\hat{I}}_2^2$ and ${\hat{I}}_4^2$) of ${}^{28}$Si. Our results clearly show that ${}^{28}$Si is an oblate shaped nucleus with ${\hat{I}}_2^2$=-$0.38\pm 0.01$ which is in excellent agreement with electromagnetic probes. A precise value of hexadecapole deformation for ${}^{28}$Si, ${\hat{I}}_4^2$=+$0.03\pm 0.01$, 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 ${\hat{I}}_4^2$ 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.