Gyromagnetic ratios and octupole collectivity in the structure of theZr90–96isotopes

Abstract

Shell model calculations have been performed for low-excitation states in the Zr isotopes between $^{90}\mathrm{Zr}$ and $^{96}\mathrm{Zr}$ with an emphasis on the $g$ factors and electromagnetic decay rates for the lowest ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states. Overall the ${2}^{+}$ states are reasonably well described. In contrast, the ${3}^{\ensuremath{-}}$ states present a puzzle because the measured $g$ factors imply a single-particle configuration whereas the experimental $E3$ transition rates imply collective structures that cannot be explained by shell model calculations. A consistent description of the ${3}^{\ensuremath{-}}$ states in $^{90}\mathrm{Zr}$ and $^{96}\mathrm{Zr}$ is sought in terms of coupling between the single-particle structure and a collective octupole vibration.