Extreme Ultraviolet Spectroscopy of Highly Charged Lu and Yb Ions for Nuclear Charge Radius Determination

TL;DR

This work addresses the long-standing challenge of precisely determining nuclear charge radii in heavy, deformed nuclei by exploiting extreme ultraviolet spectroscopy of highly charged Lu and Yb ions. By measuring the $D_1$ transitions in Na-like and Mg-like charge states with the Tokyo EBIT and interpreting the results with relativistic many-body perturbation theory plus QED corrections, the authors extract Lu–Yb radius differences and propagate uncertainties due to nuclear deformation and surface diffuseness. A generalized least-squares framework, combining HCI data with optical-isotope shifts and muonic-atom results, yields a robust absolute radius for $^{175}$Lu, $R(^{175} ext{Lu})=5.291(11)$ fm, and restores the expected odd–even staggering along the Lu–Yb isotonic chain. The results demonstrate the precision and versatility of EUV spectroscopy of HCIs for nuclear-structure studies in heavy nuclei and establish a foundation for future isotonic and isoelectronic investigations, including radioactive nuclides.

Abstract

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.

Figures (7)

• Figure 1: Summed spectra from one day of data collection. The targets of this experiment were the Na-like and Mg-like $D_1$ line separations between Lu and Yb. The $D_1$ lines of W previously measured in Gillaspy2009 and the Ne lines listed in the NIST ASD kramida_atomic_2023 were used for calibrating the spectrometer.
• Figure 2: Comparison of the wavelength residuals from a time independent calibration procedure (top) and a time dependent calibration procedure (bottom). The Lu Na-like $D_1$ and Mg-like $D_1$ residuals are shown in dark blue and blue, respectively, with the Yb Na-like and Mg-like residuals shown in red and pink, respectively. Including a linear time dependence over the course of a day removes the majority of the structure in the residuals.
• Figure 3: Top panel: Difference between the calculated $D_1$ transition energies $E(Z)$ and the corresponding Breit-Coulomb Dirac-Fock values $E_{\text{DF}}(Z)$ for $69\leq Z \leq 84$. Bottom panel: estimated theoretical uncertainties in the transition energies. Dots represent calculated values at each nuclear charge $Z$, and curves show polynomial fits to the data. Na-like $D_1$ transitions are shown in red, Mg-like $D_1$ transitions in blue.
• Figure 4: DFT predictions for the $N = 94$ isotonic chain for three EDFs parameterizations as indicated. Top: Pairing energy; Bottom: Quadrupole deformation $\beta$.
• Figure 5: 1-$\sigma$ constraints placed on the joint probability distribution of naturally abundant Yb and Lu. Previous absolute measurements from electron scattering (Sa79: Sasanuma1979) and muonic atom spectroscopy (Ze75: zehnder_charge_1975, Ad75: adler_study_1975) are displayed in red and green bands, respectively. The 1-$\sigma$ confidence region An13 Angeli13 is shown by the gray ellipse, with the 1-$\sigma$ confidence region from Fr04 fricke_nuclear_2004 (which does not list an uncertainty for the Lu radii) shown by the horizontal gray lines. The HCI constraints from this work are shown in blue for Na-like and cyan for Mg-like, with our current recommendation for the Lu and Yb radii represented by a black ellipse.