$K^{\pi }{=8\mathrm{}}^{-}$ rotational band and its fragmented decay through the $K^{\pi }{=6\mathrm{}}^{+}$ intrinsic state in ${}^{170}\mathrm{Hf}$

A $K^{\pi }{=8\mathrm{}}^{-}$ strongly coupled rotational band, which is built upon a 23 ns isomeric state, has been established in ${}^{170}\mathrm{Hf}.$ The single-particle configuration of the band has been determined from the in-band to out-of-band branching ratios and associated $|{(g}_K-g_R)|{/Q}_0$ values. The $\gamma$-ray decay of the $K^{\pi }{=8\mathrm{}}^{-}$ isomeric state proceeds through a $K^{\pi }{=6\mathrm{}}^{+}$ intrinsic state, in accordance with the K-selection rule. A complex array of delayed $\gamma$-ray transitions have been observed to link this $K^{\pi }{=6\mathrm{}}^{+},$ intrinsic bandhead state into the yrast states. In particular, a new $\Delta K=8,$ 1141 keV, $E1\mathrm{}$ transition links the $K^{\pi }{=8\mathrm{}}^{-}$ isomeric state directly to the ground-state band. The $\gamma$-ray reduced hindrance factor for this $E1\mathrm{}$ decay in ${}^{170}\mathrm{Hf}$ is the smallest $\Delta K=8\mathrm{}$ transition observed in the Hf nuclei. However, its value is consistent with that expected on the basis of the increased Coriolis mixing which occurs in the lighter Hf isotopes.