Isovector deformation and its link to the neutron shell closure

DWBA analysis of the inelastic $^{30-40}$S$(p,p')$ and $^{18-22}$O$(p,p')$ scattering data measured in the inverse kinematics has been performed to determine the isoscalar ($\delta_0$) and isovector ($\delta_1$) deformation lengths of the 2$^+_1$ excitations in the Sulfur and Oxygen isotopes using a compact folding approach. A systematic $N$-dependence of $\delta_0$ and $\delta_1$ has been established which shows a link between $\delta_1$ and the neutron-shell closure. Strong isovector deformations were found in several cases, e.g., the 2$^+_1$ state in $^{20}$O where $\delta_1$ is nearly three times larger than $\delta_0$. These results confirm the relation $\delta_1>\delta_0$ anticipated from the core polarization by the valence neutrons in the open-shell (neutron rich) nuclei. The effect of neutron shell closure at N=14 or 16 has been discussed based on the folding model analysis of the inelastic $^{22}$O+$p$ scattering data at 46.6 MeV/u measured recently at GANIL.