Application of realistic effective interactions to the structure of the Zr isotopes

We calculate the low-lying spectra of the zirconium isotopes $(Z=40)$ with neutron numbers from $N=52$ to $N=60$ using the ${1p}_{1/2}{0g}_{9/2}$ proton and ${2s1d0g}_{7/2}{0h}_{11/2}$ neutron subshells to define the model space. Effective proton-proton, neutron-neutron, and proton-neutron interactions have been derived using ${}^{88}\mathrm{Sr}$ as closed core and employing perturbative many-body techniques. The starting point is the nucleon-nucleon potential derived from modern meson exchange models. The comprehensive shell-model calculation performed in this work provides a qualitative reproduction of essential properties such as the subshell closures in ${}^{96}\mathrm{Zr}$ and ${}^{98}\mathrm{Zr}.$