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

Abstract

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.

The authors' abstract, as published at the source. Nature Communications, 2026 · DOI ↗