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 ${}^{100,100m}\mathrm{Y}$ 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.

Figure 1

Partial level scheme of ${}^{100}\mathrm{Zr}$ observed in the $\beta$ decay of ${}^{100}\mathrm{Y}$ and ${}^{100m}\mathrm{Y}$. The newly identified levels, $\gamma$-ray transitions, and assigned spins and parities are provided in red.

Figure 2

Coincidence spectrum for ${}^{100}\mathrm{Zr}$ following the $\beta$ decay of ${}^{100,100m}\mathrm{Y}$ gated on the 212.5-keV ($2_1^{+}\to 0_1^{+}$) transition. The 1082.0-keV ($0_4^{+}\to 2_1^{+}$) and 1561.2-keV ($0_5^{+}\to 2_1^{+}$) transitions are identified.

Figure 3

The $\gamma -\gamma$ angular correlations for the (a) 118.5-212.5 keV, (b) 616.6-212.5 keV, (c) 1082.0-212.5 keV, and (d) 1561.2-212.5 keV pairs of cascade $\gamma$-ray transitions.

Figure 4

(a)–(d) Angular correlations for the 666.1-212.5, 983.3-212.5, 1228.9-212.5, and 1595.2-212.5 keV sequences fitted with the angular correlation function. (e)–(h) Determination of the spins of excited states through comparison with the parameters ($a_2, a_4$) for the possible spin sequences of 1-2-0 (blue dashed line), 2-2-0 (red dashed line), 3-2-0 (green dashed line), and 4-2-0 (black dots). (i)–(l) Calculated ${\chi }^2$ values obtained when varying the mixing ratios $\delta$ for the transition in 2-2-0 cascades, as a function of arctan($\delta$). The horizontal black dashed lines correspond to the ${\chi }_{\min }^2+2$ and ${\chi }_{\min }^2$ values.

Figure 5

Systematic trends of the level energies for the $0^{+}$ states in ${}^{96-102}\mathrm{Zr}$ [15, 26, 27]. The data points shown in red present the newly identified $0_{4,5}^{+}$ states in ${}^{100}\mathrm{Zr}$.