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 $\frac{{\beta }_n}{{\beta }_p}$ are compared with experimental ratios for several sets of isotopes and isotones. The systematics indicate a rather abrupt change toward equality of ${\beta }_n$ and ${\beta }_p$ when $N$ or $Z$ is changed from a closed-shell value.