Monopole and quadrupole charge distributions of ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ were investigated by muonic atom $K$ and $L$ x-ray measurements. The model-independent Barrett charge radii $R_k$ and the isotope shifts $\Delta R_k$ were measured, and values of $〈r^2〉$ and $\Delta 〈r^2〉$ were deduced. A weak odd-even staggering of the nuclear charge radii was observed for the series ${}_{}{}^{176-178}{}_{}{}^{}\mathrm{Hf}$ and ${}_{}{}^{178-180}{}_{}{}^{}\mathrm{Hf}$. A large negative isomer shift was observed in the $2^{+}$ state of the ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$ nucleus, a fact that existing theories do not explain. The quadrupole moments of the first excited states of the hafnium nuclei were determined to be $Q^{176}\left(2^{+}\right)=-2.10\mathrm{}\left(2\right)\mathrm{} e$ b, $Q^{177}\left({\frac{9}{2}}^{-}\right)=1.30\mathrm{}\left(2\right)\mathrm{} e$ b, $Q^{178}\left(2^{+}\right)=-2.02\mathrm{}\left(2\right)\mathrm{} e$ b, $Q^{179}\left({\frac{11}{2}}^{+}\right)=1.88\mathrm{}\left(3\right)\mathrm{} e$ b, and $Q^{180}\left(2^{+}\right)=-2.00\mathrm{}\left(2\right)\mathrm{} e$ b. These quadrupole moments and the simultaneously determined $B\left(E2\right)$ values for the respective nuclei are in satisfactory agreement with the predictions of the axially symmetric rotor model.

• Received 26 January 1984

DOI:https://doi.org/10.1103/PhysRevC.30.350