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Puzzling Isotonic Odd-Even Staggering of Charge Radii in Deformed Rare Earth Nuclei

Endre Takacs, Hunter Staiger, Steven A. Blundell, Naoki Kimura, Hiroyuki A. Sakaue, Ronald F. Garcia Ruiz, Witold Nazarewicz, Paul-Gerhard Reinhard, Chowdhury A. Faiyaz, Chihiro Suzuki, Dipti, István Angeli, Yuri Ralchenko, Izumi Murakami, Daiji Kato, Yuki Nagai, Ryuji Takaoka, Yoshiki Miya, Nobuyuki Nakamura

TL;DR

This work tackles the puzzling isotonic charge-radius behavior in deformed rare-earth nuclei, specifically the Lu inversion anomaly. By employing high-precision charge-radius differences obtained from extreme-ultraviolet spectroscopy of Na-like and Mg-like Lu and Yb ions and anchoring to muonic-atom data, the study resolves the Lu anomaly and reveals an unexpectedly large odd–even staggering along the $N=94$ isotonic chain. The experimental results are confronted with nuclear DFT predictions (Skyrme SV-min and Fayans functionals), highlighting a significant discrepancy in the OESR that current models fail to reproduce. The findings demonstrate the power of highly charged ion spectroscopy for cross-element radius measurements and provide stringent benchmarks to guide future theoretical developments in nuclear-size systematics.

Abstract

The nuclear charge radius is a fundamental observable that encodes key aspects of nuclear structure, deformation, and pairing. Isotonic (constant neutron number) systematics in the deformed rare-earth region have long suggested that odd-$Z$ nuclei are more compact than their even-$Z$ neighbors - except for Lu, whose recommended 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-like 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 result resolves the longstanding Lu inversion anomaly and reestablishes a pronounced odd-even staggering along the $N=94$ isotonic chain. The magnitude of this staggering is unexpectedly large, far exceeding that observed in semi-magic nuclei and in deformed isotopic sequences. State-of-the-art nuclear density functional theory calculations, including quantified uncertainties, fail to reproduce this enhancement, possibly indicating missing structural effects in current models. Our work demonstrates the power of highly charged ions for precise, element-crossing charge-radius measurements and provides stringent new constraints for future theoretical and experimental studies of nuclear-size systematics.

Puzzling Isotonic Odd-Even Staggering of Charge Radii in Deformed Rare Earth Nuclei

TL;DR

This work tackles the puzzling isotonic charge-radius behavior in deformed rare-earth nuclei, specifically the Lu inversion anomaly. By employing high-precision charge-radius differences obtained from extreme-ultraviolet spectroscopy of Na-like and Mg-like Lu and Yb ions and anchoring to muonic-atom data, the study resolves the Lu anomaly and reveals an unexpectedly large odd–even staggering along the isotonic chain. The experimental results are confronted with nuclear DFT predictions (Skyrme SV-min and Fayans functionals), highlighting a significant discrepancy in the OESR that current models fail to reproduce. The findings demonstrate the power of highly charged ion spectroscopy for cross-element radius measurements and provide stringent benchmarks to guide future theoretical developments in nuclear-size systematics.

Abstract

The nuclear charge radius is a fundamental observable that encodes key aspects of nuclear structure, deformation, and pairing. Isotonic (constant neutron number) systematics in the deformed rare-earth region have long suggested that odd- nuclei are more compact than their even- neighbors - except for Lu, whose recommended 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-like 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 result resolves the longstanding Lu inversion anomaly and reestablishes a pronounced odd-even staggering along the isotonic chain. The magnitude of this staggering is unexpectedly large, far exceeding that observed in semi-magic nuclei and in deformed isotopic sequences. State-of-the-art nuclear density functional theory calculations, including quantified uncertainties, fail to reproduce this enhancement, possibly indicating missing structural effects in current models. Our work demonstrates the power of highly charged ions for precise, element-crossing charge-radius measurements and provides stringent new constraints for future theoretical and experimental studies of nuclear-size systematics.

Paper Structure

This paper contains 9 sections, 5 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Atomic Structure Theory
  3. Nuclear Structure Theory
  4. Scaled Radius Difference
  5. Experimental Details
  6. Data Analysis
  7. Results
  8. Discussion and Conclusions
  9. Acknowledgments

Figures (3)

  • Figure 1: 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) are displayed in red and green bands, respectively. The 1-$\sigma$ confidence region from Angeli13 is shown by the dashed ellipse. The highly charged ions constraints from this work are shown in blue (blue for Na-like, cyan for Mg-like) with the combined result of our result and Ze75 shown by a black ellipse.
  • Figure 2: (a) Charge radii along the $N = 94$ isotonic chain. The recommended values are anchored mostly by muonic atom spectroscopy Angeli13Angeli1999, with the exception of $R_{^{160}\mathrm{Dy}}$, which was taken from fricke_nuclear_2004 due to an apparent overestimation of uncertainty in Angeli13; they include the measurement from this work (solid red circles) alongside electron-scattering data Sasanuma1979 for $Z = 70$–71 (green hexagons). Nuclear DFT predictions using Skyrme (SV-min) and Fayans (Fy(IVP), Fy($\Delta r$,HFB) functionals are also shown. (b) The corresponding OESR (\ref{['OESR']}). The calculated values of OESR and their uncertainties are multiplied by five for the sake of visibility.
  • Figure 3: DFT predictions and experimental recommended values Angeli13 for $\Delta_R^{(3)}$ in isotonic (left) and isotopic (right) chains of selected spherical (top) and deformed (bottom) nuclei. Note the dramatic change of the experimental OESR magnitude for the deformed $N=94$ chain when compared to other cases.