Monopole and quadrupole charge distributions of ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{155}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{157}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{158}{}_{}{}^{}\mathrm{Gd}$, and ${}_{}{}^{160}{}_{}{}^{}\mathrm{Gd}$ 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 pronounced even-odd staggering effect of the nuclear charge radii was observed for the series ${}_{}{}^{156-158}{}_{}{}^{}\mathrm{Gd}$. The quadrupole moments of the first excited states of the even-$A$ Gd nuclei were determined to be $Q^{154}\left(2^{+}\right)=-1.82\mathrm{}\left(4\right)\mathrm{} e$ b, $Q^{156}\left(2^{+}\right)=-1.93\mathrm{}\left(4\right)\mathrm{} e$ b, $Q^{158}\left(2^{+}\right)=-2.01\mathrm{}\left(4\right)\mathrm{} e$ b, and $Q^{160}\left(2^{+}\right)=-2.08\mathrm{}\left(4\right)\mathrm{} e$ b, and the quadrupole moments of the ${\frac{3}{2}}^{-}$ ground states of the odd-$A$ ${}_{}{}^{155,157}{}_{}{}^{}\mathrm{Gd}$ nuclei were determined to be $Q^{155}\left({\frac{3}{2}}^{-}\right)=1.27\mathrm{}\left(3\right)\mathrm{} e$ b and $Q^{157}\left({\frac{3}{2}}^{-}\right)=1.35\mathrm{}\left(3\right)\mathrm{} e$ b. Comparison with a separate measurement of the odd-$A$ ground-state quadrupole moments based on the static hyperfine splitting of the muonic $M$ x rays showed that the model error in the extracted quadrupole moments of these nuclei is less than 2 percent. The quadrupole moments and the $B\left(E2\mathrm{}\right)\mathrm{}$ values obtained in the present experiment for the low-lying Gd states are in satisfactory agreement with the axially symmetric rotational model. However, the ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$ nucleus exhibits a considerable softness as indicated by the isomer shift of the $2^{+}$ excited state and by the experimental value of the ratio $\frac{Q\left(2^{+}\right)}{B(E2:0^{+}\to 2^{+})}$.

NUCLEAR STRUCTURE ${}_{}{}^{154-158,160}{}_{}{}^{}\mathrm{Gd}$; measured muonic x-ray spectra; deduced monopole and quadrupole charge parameters; isotope and isomer shifts.

• Received 22 November 1982

DOI:https://doi.org/10.1103/PhysRevC.27.1772