Collective States inHf178via Coulomb Excitation

Coulomb-excitation experiments have been performed to measure transition probabilities of collective quadrupole states in ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$. A search for $\beta$-vibrational levels yielded negative results. Upper limits are placed on the excitation of the known $2^{+}$ levels at 1276 and 1496 keV. The $B{\mathrm{}\left(E2\mathrm{}\right)\mathrm{}}_{\mathrm{exc}}$ values are $<~2\times {10}^{-51\mathrm{}}{e}^2$ ${\mathrm{cm}}^4$ and $<~{10}^{-50\mathrm{}}{e}^2$ ${\mathrm{cm}}^4$ for the 1276- and 1496-keV levels, respectively. Neither of these levels has sufficient excitation strength to be designated as the $2^{+}$ level of the collective $\beta$ band. The $J=2\mathrm{}$ level of the $K^{\pi }=2^{+}$ collective $\gamma$ band is established at 1175 keV, with $B{\mathrm{}\left(E2\mathrm{}\right)\mathrm{}}_{\mathrm{exc}}=(10.0\mathrm{}\pm 0.8)\times {10}^{-50\mathrm{}}{e}^2$ ${\mathrm{cm}}^4$. The angular distribution of the deexcitation $\gamma$ rays from this level yields $\delta =-32\mathrm{}$ with limits $\delta >32\mathrm{} or <-11\mathrm{}$, and $>99\% E2\mathrm{}$ multipolarity for the 1081.5-keV $2_{\gamma }^{+}\to 2_g^{{}^{+}}$ transition. The reduced $\gamma$-ray branching ratio of the ($2_{\gamma }\to 2_g$)-to-($2_{\gamma }\to 0_g$) transition yields a band-mixing parameter $z_2=(23\mathrm{}\pm 10)\times {10}^{-3\mathrm{}}$.