Figure 1

Excitation energies (a), hexadecapole deformations (b), and quadrupole deformations (c) for multi-qp isomeric states in Hf isotopes. Open and filled symbols show the calculated and experimental values [4, 5, 19], respectively. The data for the 2-qp state in ${}^{178}\mathrm{Hf}$ ($N=106$) corresponds to an unperturbed $\pi {}_{8^{-}}^2$ state (see text). Note that no experimental configuration is available for the nuclei with $N⩾112$. The deformations of 4-qp states (not shown for clarity) are similar to those of the corresponding 2-qp states. For all the multi-qp states, $\gamma \approx 0$ and ${\beta }_6\approx 0$. The same configurations are connected by lines to guide the eye. See Table for the neutron configurations $\nu {}^2$ of the 4-qp isomeric states.Reuse & Permissions

Figure 2

Excitation energy relative to a rigid rotor for the lowest-lying 4-qp isomeric states in even-$A$ Hf isotopes. Calculated and experimental values [4, 19] are represented by lines and squares, respectively. The data point for ${}^{186}\mathrm{Hf}$ is not shown, as the $K$ value is unclear. Note that the ${16}^{-}$ state in ${}^{188}\mathrm{Hf}$ has a larger $E_x-E_R$ value than the ${18}^{+}$ state because of the smaller angular momentum.Reuse & Permissions

Figure 3

Calculated potential-energy curves as a function of $\gamma$ deformation. The energy is minimized with respect to ${\beta }_2$ and ${\beta }_4$ deformations. The true minimum of the oblate-deformed ground state in ${}^{190}\mathrm{Hf}$ is at $\gamma =-{60}^{°}$ in the Lund convention.Reuse & Permissions