The ground-state quadrupole moments of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$, ${}_{}{}^{163}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$, and ${}_{}{}^{193}{}_{}{}^{}\mathrm{Ir}$ were determined by measuring the quadrupole hyperfine-splitting energies of muonic $M$ x rays. The results are $Q=0.903\mathrm{}\left(10\right)\mathrm{}e$ b for ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$, $Q=2.412\mathrm{}\left(21\right)\mathrm{} e$ b for ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$, $Q=1.432\mathrm{}\left(8\right)\mathrm{} e$ b for ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$, $Q=2.648\mathrm{}\left(21\right)\mathrm{} e$ b for ${}_{}{}^{163}{}_{}{}^{}\mathrm{Dy}$, $Q=3,565\mathrm{}\left(29\right)\mathrm{} e$ b for ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$, $Q=3.365\mathrm{}\left(29\right)\mathrm{} e$ b for ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, $Q=3.793\mathrm{}\left(33\right)\mathrm{} e$ b for ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$, $Q=0.816\mathrm{}\left(9\right)\mathrm{} e$ b for ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$, and $Q=0.751\mathrm{}\left(9\right)\mathrm{} e$ b for ${}_{}{}^{193}{}_{}{}^{}\mathrm{Ir}$. The present quadrupole moments, compared with values obtained from electronic-atom hyperfine measurements, show that the Sternheimer correction factors used in the rare-earth electronic-atom analysis are unreliable. Systematics of deformation parameters ${\beta }_2$ calculated from the present quadrupole moments for odd-$A$ nuclei, and from $B\left(E2\right)$ values of Coulomb excitation measurements for even-$A$ nuclei, also indicate that the largest deformation change so far known exists between ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$ and ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$. Except at the onset of nuclear deformation, the deformation parameters of the odd-$A$ nuclei are quite consistent with those of the even-$A$ neighbors.

• Received 15 November 1983

DOI:https://doi.org/10.1103/PhysRevC.29.1830