Evidence for Coexisting Shapes through Lifetime Measurements in ${}^{98}\mathrm{Zr}$

The lifetimes of the first excited $2^{+}$, $4^{+}$, and $6^{+}$ states in ${}^{98}\mathrm{Zr}$ were measured with the recoil-distance Doppler shift method in an experiment performed at GANIL. Excited states in ${}^{98}\mathrm{Zr}$ were populated using the fission reaction between a $6.2\mathrm{MeV}/\mathrm{u}$ ${}^{238}\mathrm{U}$ beam and a ${}^9\mathrm{Be}$ target. The $\gamma$ rays were detected with the EXOGAM array in correlation with the fission fragments identified by mass and atomic number in the VAMOS++ spectrometer. Our result shows a very small $B(E2;2_1^{+}\to 0_1^{+})$ value in ${}^{98}\mathrm{Zr}$, thereby confirming the very sudden onset of collectivity at $N=60$. The experimental results are compared to large-scale Monte Carlo shell model and beyond-mean-field calculations. The present results indicate the coexistence of two additional deformed shapes in this nucleus along with the spherical ground state.

Figure 1

Gamma-ray spectra showing the $2^{+}\to 0^{+}$, $4^{+}\to 2^{+}$, $6^{+}\to 4^{+}$, and $3^{-}\to 2^{+}$ transitions in ${}^{98}\mathrm{Zr}$, observed in the detectors at 135° for seven target-degrader distances. The spectra are Doppler-corrected using the velocity measured in VAMOS++ after the degrader. The dotted and dashed lines indicate the positions of the shifted and unshifted components, respectively. Also displayed are the Gaussian fits to the spectra (green), and the individual fits to the shifted (red) and unshifted (blue) components.

Figure 2

Comparison of calculated $B(E2;2_1^{+}\to 0_1^{+})$ values with experimental data for the Zr isotopes. Experimental data points are from Refs. [24, 29, 40, 41, 42]. Theoretical values are taken from Refs. [8, 12, 18, 21, 39].

Figure 3

Comparison between the experimental and theoretical level schemes for ${}^{98}\mathrm{Zr}$. The excitation energy and spin are mentioned against each state. Labels and widths of the arrows represent calculated [8, 21] and measured $B(E2)$ values in W.u.

Figure 4

Occupation numbers of (a) protons and (b) neutrons for the states in ${}^{98}\mathrm{Zr}$.