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Model-independent determination of nuclear charge radii from Li-like ions

V. A. Yerokhin, B. Ohayon

TL;DR

This work shows that the absolute nuclear charge radius $r_C$ can be determined from electronic Li-like ion spectra in a model-independent way by constraining the nuclear charge distribution through electron-scattering data. It develops a robust fns correction framework and demonstrates that fixing the first three moments $\langle r^2\rangle$, $\langle r^4\rangle$, and $\langle r^6\rangle$ eliminates model dependence to negligible levels for high-$Z$ ions. The authors extract $r_C$ for $^{208}$Pb and $^{209}$Bi from Li-like $2p_j-2s$ transitions, obtaining results consistent with muonic-atom measurements while highlighting the dominant role of experimental energy uncertainties and remaining theoretical two-loop QED effects. The approach offers a path to high-precision radii with reduced nuclear-model uncertainty and motivates future experimental and theoretical advancements in high-$Z$ bound-state QED. It also suggests using ab initio nuclear inputs for isotopes lacking scattering data and compiling comprehensive nuclear moment databases for broader applicability.

Abstract

We demonstrate that recent advances in QED theory of Li-like ions [V. A. Yerokhin et al., Phys. Rev. A 112, 042801 (2025)] enable determinations of absolute nuclear charge radii for heavy elements. By incorporating constraints derived from electron-scattering data, we obtain radii that are independent of the assumed model of the nuclear charge distribution. Our approach is validated for $^{208}$Pb, a well-studied spherical nucleus, and is then applied to $^{209}$Bi, where low-lying nuclear excitations complicate the interpretation of muonic-atom data.

Model-independent determination of nuclear charge radii from Li-like ions

TL;DR

This work shows that the absolute nuclear charge radius can be determined from electronic Li-like ion spectra in a model-independent way by constraining the nuclear charge distribution through electron-scattering data. It develops a robust fns correction framework and demonstrates that fixing the first three moments , , and eliminates model dependence to negligible levels for high- ions. The authors extract for Pb and Bi from Li-like transitions, obtaining results consistent with muonic-atom measurements while highlighting the dominant role of experimental energy uncertainties and remaining theoretical two-loop QED effects. The approach offers a path to high-precision radii with reduced nuclear-model uncertainty and motivates future experimental and theoretical advancements in high- bound-state QED. It also suggests using ab initio nuclear inputs for isotopes lacking scattering data and compiling comprehensive nuclear moment databases for broader applicability.

Abstract

We demonstrate that recent advances in QED theory of Li-like ions [V. A. Yerokhin et al., Phys. Rev. A 112, 042801 (2025)] enable determinations of absolute nuclear charge radii for heavy elements. By incorporating constraints derived from electron-scattering data, we obtain radii that are independent of the assumed model of the nuclear charge distribution. Our approach is validated for Pb, a well-studied spherical nucleus, and is then applied to Bi, where low-lying nuclear excitations complicate the interpretation of muonic-atom data.

Paper Structure

This paper contains 9 sections, 27 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Finite nuclear size correction
  3. Model dependence of nuclear-size correction
  4. Determination of V24 and V26 from electron-scattering data
  5. Nuclear radii determination from Li-like transition energies
  6. Charge radius of
  7. Charge radius of
  8. Conclusion and outlook
  9. Nuclear models

Figures (1)

  • Figure 1: Nuclear charge distributions for $^{208}$Pb with $r_C = 5.5030$ fm in various models: 1-parameter models (left graph), 2-parameter models (middle graph), 3-parameter models (right graph). Model parameters are specified in Table \ref{['tab:FNS']}.