Puzzling isotonic odd-even staggering of charge-radii in deformed rare earth nuclei

Abstract Isotonic (constant neutron number) systematics in the deformed rare-earth region have long suggested that nuclei with odd numbers of protons are more compact than their even-proton neighbors—except for Lu, whose recommended nuclear charge radius appeared anomalously large relative to Yb and Hf. We report a high-precision determination of the natural-abundance-averaged Lu-Yb charge-radius difference using extreme-ultraviolet spectroscopy of highly charged Na- and Mg-like ions, supported by high-accuracy relativistic atomic-structure calculations—a recently introduced method with the unique ability to measure inter-element charge-radius differences. Combined with muonic-atom and optical isotope-shift data, our results reestablish a pronounced odd-even staggering along the isotonic chain with neutron number N = 94 . Nuclear density functional theory calculations, including quantified uncertainties, fail to reproduce the large stagger, while successfully reproducing the charge-radii staggering along isotopic chains and in semi-magic nuclei. In this work, we resolve the Lu inversion anomaly and provide new constraints for experimental and theoretical studies of nuclear size.