Evidence for a Nonrotational Interpretation of〈0+||M(E4)||4+〉inHf180

Angular distributions for the reaction ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}(\alpha ,{\alpha }^{\prime })$ were measured for laboratory $\alpha$-particle energies of 21 and 24 MeV. Data were obtained for $0^{+}$, $2^{+}$, $4^{+}$, and $6^{+}$ members of the ground-state rotational band. Data for the $4^{+}$ state show unambiguously that $〈0^{+}|\times |M\mathrm{}\left(E4\mathrm{}\right)\mathrm{}\mathrm{}\left|\right|\mathrm{}{4}^{+}〉$ is large and negative. Data for the $6^{+}$ state are not well-fitted by rotational-model coupled-channels calculations. These results may indicate that the interpretation of the $E4\mathrm{}$ matrix element as arising from a static ${\beta }_4$ deformation in the framework of the simple rotational model is incorrect.