Neutron transition strengths of $2^+_1$ states in the neutron rich Oxygen isotopes determined from inelastic proton scattering
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A coupled-channel analysis of the $^{18,20,22}$O$(p,p')$ data has been performed to determine the neutron transition strengths of 2$^+_1$ states in Oxygen targets, using the microscopic optical potential and inelastic form factor calculated in the folding model. A complex density- and \emph{isospin} dependent version of the CDM3Y6 interaction was constructed, based on the Brueckner-Hatree-Fock calculation of nuclear matter, for the folding model input. Given an accurate isovector density dependence of the CDM3Y6 interaction, the isoscalar ($δ_0$) and isovector ($δ_1$) deformation lengths of 2$^+_1$ states in $^{18,20,22}$O have been extracted from the folding model analysis of the $(p,p')$ data. A specific $N$-dependence of $δ_0$ and $δ_1$ has been established which can be linked to the neutron shell closure occurring at $N$ approaching 16. The strongest isovector deformation was found for 2$^+_1$ state in $^{20}$O, with $δ_1$ about 2.5 times larger than $δ_0$, which indicates a strong core polarization by the valence neutrons in $^{20}$O. The ratios of the neutron/proton transition matrix elements ($M_n/M_p$) determined for 2$^+_1$ states in $^{18,20}$O have been compared to those deduced from the mirror symmetry, using the measured $B(E2)$ values of 2$^+_1$ states in the proton rich $^{18}$Ne and $^{20}$Mg nuclei, to discuss the isospin impurity in the $2^+_1$ excitation of the $A=18,T=1$ and $A=20,T=2$ isobars.
Version accepted for publication in Physical Review C
Version accepted for publication in Physical Review C