Determination of the spins and parities for the $0_4^{+}$ and $0_5^{+}$ states in ${}_{100}\mathrm{Zr}$

Two $0^{+}$ states at 1294.5 and 1774.0 keV, together with three $2^{+}$ and one $4^{+}$ levels, were identified or unambiguously spin-parity assigned for the first time in ${}_{100}\mathrm{Zr}$ utilizing $\gamma$-ray spectroscopy and $\gamma -\gamma$ angular correlation techniques with the Gammasphere spectrometer, following the ${\beta }^{-}$ decay of neutron-rich, mass-separated ${}_{100,100m}Y$ isotopes. Comparisons with recent Monte Carlo shell-model calculations indicate that these two states are candidates for the bandhead of a sequence in a shape-coexisting spherical minimum predicted to be located around $\approx 1500$ keV. According to the measured relative $B{\left(E2\right)}_{\mathrm{relative}}$ transition probabilities, the $0_5^{+}$ state exhibits decay properties which more closely align with those predicted for a spherical shape, while the $0_4^{+}$ level is suggested to be associated with a weakly deformed shape similar to one related to the $0_2^{+}$ state.