Muonic x-ray measurement of the monopole and quadrupole charge parameters ofGd154−158,160

Abstract

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 $\ensuremath{\Delta}{R}_{k}$ were measured, and values of $〈{r}^{2}〉$ and $\ensuremath{\Delta}〈{r}^{2}〉$ were deduced. A pronounced even-odd staggering effect of the nuclear charge radii was observed for the series $^{156\ensuremath{-}158}\mathrm{Gd}$. The quadrupole moments of the first excited states of the even-$A$ Gd nuclei were determined to be ${Q}^{154}({2}^{+})=\ensuremath{-}1.82(4) e$ b, ${Q}^{156}({2}^{+})=\ensuremath{-}1.93(4) e$ b, ${Q}^{158}({2}^{+})=\ensuremath{-}2.01(4) e$ b, and ${Q}^{160}({2}^{+})=\ensuremath{-}2.08(4) e$ b, and the quadrupole moments of the ${\frac{3}{2}}^{\ensuremath{-}}$ ground states of the odd-$A$ $^{155,157}\mathrm{Gd}$ nuclei were determined to be ${Q}^{155}({\frac{3}{2}}^{\ensuremath{-}})=1.27(3) e$ b and ${Q}^{157}({\frac{3}{2}}^{\ensuremath{-}})=1.35(3) e$ 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 $B(E2)$ 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 $\frac{Q({2}^{+})}{B(E2:{0}^{+}\ensuremath{\rightarrow}{2}^{+})}$.NUCLEAR STRUCTURE $^{154\ensuremath{-}158,160}\mathrm{Gd}$; measured muonic x-ray spectra; deduced monopole and quadrupole charge parameters; isotope and isomer shifts.