Schematic Model for the Differences between Neutron and Proton Quadrupole Deformation Parameters in Open-Shell Nuclei

The schematic model is extended to open-shell nuclei. The quasiparticle random-phase approximation plus core polarization are used to calculate multipole matrix elements ${M}_{n}$ and ${M}_{p}$. Calculated trends in the ratio of deformation parameters $\frac{{\ensuremath{\beta}}_{n}}{{\ensuremath{\beta}}_{p}}$ are compared with experimental ratios for several sets of isotopes and isotones. The systematics indicate a rather abrupt change toward equality of ${\ensuremath{\beta}}_{n}$ and ${\ensuremath{\beta}}_{p}$ when $N$ or $Z$ is changed from a closed-shell value.