Measurement and model-independent analysis of the x rays of muonicSm150andSm152

Precision measurements, using a highly linear Ge(Li) spectrometer system, have been made of the muonic x-ray spectra of the ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ transitional nuclei. Equivalent Barrett nuclear charge radii for both of the isotopes have been determined. Generalized quadrupole moments of the charge distribution as probed by muonic atoms have been determined in a nearly model-independent way, and equivalent quadrupole radii for static and transitional quadrupole charge distributions of the 2+ states have been determined by comparison with Coulomb excitation data. The isomer shift of the 2+ state of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ was measured directly from the $K$ x rays, while that of ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ was determined from the observed nuclear $\gamma$ ray. A phenomenological rotation-vibration-interaction model provides a satisfactory explanation for the observed quadrupole moment and isomer shift of the 2+ state in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$.