Quasi-elastic scattering for the nuclear ground state structure: An intriguing case of ${}^{30}$Si

Quasi-elastic (QEL) scattering measurements have been performed using the ${}^{28,30}$Si projectiles off the ${}^{90}$Zr target at energies around the Coulomb barrier. Coupled-channels (CC) calculations were carried out in a large parameter space of quadrupole and hexadecapole deformations for the N=Z, ${}^{28}$Si and N=Z+2, ${}^{30}$Si nuclei. ${}^{28}$Si at the N=Z line is observed to be uniquely oblate shaped in its ground state. In contrast, for ${}^{30}$Si with just two additional neutrons – oblate, prolate, and spherical CC descriptions are equally compatible with the measurements. To further investigate the nuclear structure evolution with varying neutron number, shell-model calculations were performed. These calculations reveal a sudden change in the nuclear structure aspects at ${}^{30}$Si in going from ${}^{28}$Si to ${}^{30}$Si. Combined reaction and structure analyses consistently indicate that ${}^{30}$Si does not possess a well-defined intrinsic shape, and it is a potential candidate for ``shape fluctuations" in its ground state.