Three distinctly different mechanisms are shown to populate the $K^{\pi }=6^{+}$ ($t_{1/2}=77\mathrm{n}\mathrm{s}$), ${16}^{+}$ (31 yr), and $8^{-}$ (4 s) isomer bands of ${}^{\mathrm{178}}\mathrm{H}\mathrm{f}$ by Coulomb excitation. High spin states of the three isomer bands were populated by Coulomb excitation of a hafnium target with a 650 MeV ${}^{\mathrm{136}}\mathrm{X}\mathrm{e}$ beam. Although direct population of high-$K$ bands is highly $K$-forbidden, isomer bands in ${}^{\mathrm{178}}\mathrm{H}\mathrm{f}$ were populated up to spins ${13}_{K=6}^{+}$, ${20}_{K=16}^{+}$, and ${14}_{K=8}^{-}$ with in-band $\gamma$ yields of $\sim {10}^{-4}$ of the ground state band. The data are consistent with a rapid increase in $K$ mixing with increasing spin in the isomer bands.

• Received 31 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.242501