Precision Muonic-Atom Measurements of Nuclear Quadrupole Moments and the Sternheimer Effect in Rare-Earth Atoms

The ground-state quadrupole moments of ¹⁵¹Eu, ¹⁵³Eu, ¹⁵⁵Gd, ¹⁵⁷Gd, ¹⁵⁹Tb, ¹⁶³Dy, ¹⁶⁷Er, ¹⁷⁷Hf, ¹⁷⁹Hf, ¹⁹¹Ir, and ¹⁹³Ir were determined with an uncertainty of less than one percent by measuring the quadrupole hyperfine-splitting energies of muonic M x rays. The results are used to determine experimentally Sternheimer shielding factors for the $4f$, $5d$, and $6p$ electronic states of the respective atoms. The deduced shielding factors for the $5d$ electronic states were found to vary considerably among these elements, presumably as a result of configuration mixing.