Neutron transition strengths of21+states in the neutron-rich oxygen isotopes determined from inelastic proton scattering

Abstract

A coupled-channel analysis of the $^{18,20,22}\mathrm{O}(p,{p}^{'})$ data has been performed to determine the neutron transition strengths of the ${2}_{1}^{+}$ states in oxygen targets, using the microscopic optical potential and inelastic form factor calculated in the folding model. A complex density- and isospin-dependent version of the CDM3Y6 interaction was constructed, based on the Brueckner-Hartree-Fock calculation of nuclear matter, for the folding model input. Given an accurate isovector density dependence of the CDM3Y6 interaction, the isoscalar (${\ensuremath{\delta}}_{0}$) and isovector (${\ensuremath{\delta}}_{1}$) deformation lengths of the ${2}_{1}^{+}$ states in $^{18,20,22}\mathrm{O}$ have been extracted from the folding model analysis of the $(p,{p}^{'})$ data. A specific $N$ dependence of ${\ensuremath{\delta}}_{0}$ and ${\ensuremath{\delta}}_{1}$ has been established which can be linked to the neutron shell closure occurring at $N$ approaching 16. The strongest isovector deformation was found for the ${2}_{1}^{+}$ state in $^{20}\mathrm{O}$, with ${\ensuremath{\delta}}_{1}$ about 2.5 times larger than ${\ensuremath{\delta}}_{0}$, which indicates a strong core polarization by the valence neutrons in $^{20}\mathrm{O}$. The ratios of the neutron/proton transition matrix elements (${M}_{n}/{M}_{p}$) determined for the ${2}_{1}^{+}$ states in $^{18,20}\mathrm{O}$ have been compared with those deduced from the mirror symmetry, using the measured $B(E2)$ values of the ${2}_{1}^{+}$ states in the proton-rich $^{18}\mathrm{Ne}$ and $^{20}\mathrm{Mg}$ nuclei, to discuss the isospin impurity in the ${2}_{1}^{+}$ excitation of the $A=18$, $T=1$ and $A=20$, $T=2$ isobars.