Measurement of spin and parity of high spin rotational bands and the de-orientation effect in $^{178}$Hf

Coulomb-excited rotational bands including the high K-isomer K=16+ ($\tau_{\frac{1}{2}}$=31yr), have been populated in $^{178}$Hf. The excitation mechanism, which requires 14 times K-forbidden transitions from the ground state band, is not understood. A 0.5 mg/cm$^{2}$ $^{208}$Pb target was bombarded by a $^{178}$Hf beam at 985 MeV to investigate how the 16+ isomer is Coulomb-excited. Particles in coincidence with $\gamma$-rays were detected by CHICO and Gammasphere. Several new bands, including an a-band and t-band, were seen to high spins. These could contribute to the population of the K=16+ band. The spins, parities, as well as the mixing ratios of decaying transitions (E2/M1 or E1/E3), were deduced for the a-band and t-band based on the particle-$\gamma$ angular correlation. The Coulomb excitation code GOSIA was used to fit to the experiment data. In this experiment, the ground-state band angular distribution of E2 decays was accurately reproduced by GOSIA. Best $\chi^{2}$ fits of $\gamma$-$\gamma$ angular correlation led to the assignment of positive parity for both the a-band and t-band. The spin assignments of both bands were confirmed with reasonable measurements on the mixing ratio of their decaying transitions to the ground state band.