Observation of rotation about the longest principal axis in ${}^{89}\mathrm{Zr}$

High-spin states in ${}^{89}\mathrm{Zr}$ were populated in the ${}^{80}\mathrm{Se}({}^{13}\mathrm{C},4n)$ reaction, and $\gamma$-ray coincidences were measured using the Indian National Gamma Array. The level scheme of ${}^{89}\mathrm{Zr}$ has been extended up to spin $I=49/2$ with the observation of a new dipole band. Directional correlation and polarization asymmetries of the $\gamma$ rays have been measured to determine spin and parity of the levels. Line shapes of several transitions have been analyzed to determine lifetimes of the levels. Possible configurations of the band have been discussed using the cranked Nilsson-Strutinsky model. The calculations suggest a triaxial shape of the nucleus at high spins, and the band may represent rotation of the nucleus about the longest axis.

Figure 1

In panel (a), a coincidence spectrum with a gate on a 215-keV [12] transition is shown, whereas in panel (b), double coincidence spectra with gates on 589- and 675-keV are presented. The transitions energies (in red) marked with asterisks belong to the negative-parity band discussed, whereas other $\gamma$ rays are either belong to the ${}^{89}\mathrm{Zr}$ [12] or from the ${}^{90}\mathrm{Zr}$ level scheme.

Figure 2

Partial level scheme of ${}^{89}\mathrm{Zr}$ showing a regular structure of $M1$ transitions above $I^{\pi }=29/2^{-}$. The thickness of the vertical arrows representing $\gamma$ rays is proportional to the intensity of the corresponding $\gamma$ ray.

Figure 3

Representative spectra (with the gate on the lower transition) along with fitted line shapes for 589- [panels (a) and (c)] and 675-keV [panels (b) and (d)] transitions of ${}^{89}\mathrm{Zr}$. The upper panels (a) and (b) show $\gamma$-ray spectra observed at ${40}^{\circ }$ and panels (c) and (d) for detectors at ${140}^{\circ }$. The calculated Doppler-shifted line shapes are shown in dashed lines, whereas the total line-shape and contamination peaks are shown with solid and dashed-dotted lines, respectively.

Figure 4

Calculated excitation energy relative to a rotating liquid drop energy as a function of spin for negative-parity states in ${}^{89}\mathrm{Zr}$. The closed and the open circles represent the ($\alpha =1/2$) and the ($\alpha =-1/2$) states, respectively. The yrast lines for the two signatures are shown by brown dashed lines. Aligned states are encircled. With increasing spin, configurations become yrast which have more and more particles excited across the $Z=40$ and $N=50$ gaps and, thus, a higher-spin content. For the [33,210] configuration, which is assigned to the observed dipole band, all eight signature combinations are displayed whereas only the configurations which are low in energy are shown for other configurations.

Figure 5

Calculated total energy surface plots for ${}^{89}\mathrm{Zr}$ for the $[3_{+}{3}_{+},{21}_{+}0]$ configuration. The contour line separation is 0.25 MeV.

Figure 6

Calculated total energy surface plot for ${}^{89}\mathrm{Zr}$ for $[3_{+}{3}_{+},{21}_{-}0]$ configuration. The contour line separation is 0.25 MeV.

Figure 7

[Panel (a)] Excitation energies relative to a rotating liquid drop with respect to spin for the observed negative-parity dipole band. [Panel (b)] Calculated energies relative to a rotating liquid drop energy as a function of spin for the configurations $[3_{+}{3}_{+},{21}_{\pm }0]$ where the minimum at negative-$\gamma$ values is followed, cf. Figs. 5 and 6. [Panel (c)] The difference between experiment and calculations.

Figure 8

Sloping Fermi-surface plot illustrating the maximum spin state in [33,210], i.e., the $\pi \left[{\left(fp\right)}^{-3}{g}_{9/2}^3\right]\otimes \nu \left[g_{9/2}^{-2}{\left(dg\right)}^1\right]$ configuration in ${}^{89}\mathrm{Zr}$. The total spin is specified for the proton and neutron configurations where all single-particle states below the sloping Fermi surfaces drawn by red lines are occupied. The fact that the neutron Fermi surface with two $g_{9/2}$ holes goes through the $m=5/2$ and $m=7/2dg$ states indicates that the neutron configurations with one or the other of these orbitals occupied are about equally favored in energy.