Three-quasiparticle isomer in ${}^{173}\mathbf{Ta}$ and the excitation energy dependence of $K$-forbidden transition rates

Using the ${}^{168}\mathrm{Er}({}^{10}\mathrm{B},5n)$ reaction at a beam energy of 68 MeV, new data have been obtained for the population and decay of a $T_{1/2}=148$ ns, $K^{\pi }=21/2^{-}$ three-quasiparticle isomer at 1717 keV in ${}^{173}\mathrm{Ta}$. Revised decay energies and intensities have been determined, together with newly observed members of a rotational band associated with the isomer. By comparison with other isomers in the $A\approx 180$ deformed region, the ${}^{173}\mathrm{Ta}$ isomer properties help to specify the key degrees of freedom that determine $K$-forbidden transition rates. In particular, when all three quasiparticles are of the same nucleon type, there is a strong dependence of the $E2$ reduced hindrance factor on the isomer excitation energy.

Figure 1

Partial level scheme for ${}^{173}\mathrm{Ta}$ above the $9/2^{-}$ bandhead at 173 keV, showing transitions related to the $K^{\pi }=21/2^{-}$ three-quasiparticle isomer.

Figure 2

Examples of coincidence $\gamma$-ray spectra decaying from and feeding into the ${}^{173}\mathrm{Ta}$ isomer at 1717 keV. The top panel shows the sum of coincidence gates on selected out-of-beam transitions (i.e., between the beam bursts). The bottom panel looks very similar, though with lower statistics. It is from a single gate on the 321 keV transition above the isomer, with a time-difference requirement, so that only “delayed” transitions below the isomer are seen. The middle panel is from two gates below the isomer, with a time-difference condition that selects “early” transitions that feed the isomer.

Figure 3

Time-difference decay curves for two isomers in ${}^{173}\mathrm{Ta}$. The upper panel is for the $K^{\pi }=9/2^{-}$ isomer, while the lower panel is for the $K^{\pi }=21/2^{-}$ isomer. The specific gating energies either side of each isomer are indicated, together with the measured half-lives.

Figure 4

Reduced hindrance, $f_{\nu }$, shown as a function of excitation energy relative to a rigid rotor of $A$ atomic mass units, for $E2$ decays with $\nu \ge 4$, from three-quasiparticle isomers in the deformed $A\approx 180$ region. Numerical values are given in Table 2. The triangles and square are for isomer configurations with three nucleons of the same type ($3\pi$ or $3\nu$) and the circles correspond to isomers in ${}^{181}\mathrm{W}$ and ${}^{185}\mathrm{Ta}$, where there is no consensus regarding the configuration [6, 27, 28]. The new data point for ${}^{173}\mathrm{Ta}$ is represented by the filled square, with $f_{\nu }=12.5$ and $E_K-E_R=970$ keV. The rigid-rotor moment-of-inertia reference is chosen as 85 ${\hslash }^2{\text{MeV}}^{-1}$ for $A=178$, scaling as $A^{5/3}$. The uncertainties in the $f_{\nu }$ values are typically smaller than the data points.