Paul-Gerhard Reinhard

We report a high-precision determination of the natural-abundance-averaged nuclear charge-radius difference between Yb and Lu using extreme ultraviolet (EUV) spectroscopy of highly charged ions (HCIs). By measuring the $D_1$ transition energies in Na- and Mg-like charge states of Lu and Yb confined in the Tokyo electron-beam ion trap, we extract meV-level energy shifts that are directly sensitive to nuclear-size effects. Transition-energy differences obtained from these spectra are compared with state-of-the-art relativistic many-body perturbation theory, including a new treatment of Mg-like ions. We develop a generalized framework to propagate uncertainties arising from nuclear deformation and surface diffuseness and evaluate corresponding nuclear-sensitivity coefficients. Combining Na- and Mg-like results yields mutually consistent radius differences, demonstrating the robustness of both the experimental calibration and the theoretical predictions. To determine absolute isotopic radii, we perform a generalized least-squares optimization incorporating our HCI constraints together with optical-isotope-shift data and muonic-atom results. This analysis establishes that the $^{175}$Lu charge radius is smaller than that of $^{174}$Yb, restoring the expected odd-even staggering across the $N=94$ isotonic chain. Our recommended value, $R(^{175}\text{Lu}) = 5.291(11)$ fm, reduces the uncertainty of the Lu radius by a factor of three compared with the previous electron-scattering result and resolves a long-standing anomaly in rare-earth nuclear systematics. This work demonstrates that EUV spectroscopy of HCIs provides a powerful and broadly applicable method for precision nuclear-structure studies in heavy, deformed nuclei. The techniques developed here enable future investigations of isotonic and isoelectronic sequences, including radioactive nuclides and higher-$Z$ systems.

Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the Standard Model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden ${}^2S_{1/2} \rightarrow {}^2F_{7/2}$ octupole transition of trapped $^{168,170,172,174,176}$Yb ions. When combined with previous measurements in Yb$^+$ and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to 240$σ$. The trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We also find, with 4.3$σ$ confidence, that there is a second distinct source of nonlinearity, and discuss its possible origin.