Helion-$\alpha$ charge radius difference from electronic versus muonic helium
In plain words
The difference in size between helium-3 and helium-4 nuclei can be measured with ordinary helium atoms or with muonic helium ions. The two methods disagree by about four standard errors.
Precise statement
The squared charge-radius difference $r_{h}^{2} - r_{\alpha}^{2}$ extracted from the $2^{1}\mathrm{S}-2^{3}\mathrm{S}$ isotope shift in electronic helium differs by $3.6\, \sigma$ from the muonic He-3 and He-4 Lamb-shift values (2023). Determine whether the discrepancy is due to missing atomic theory (hyperfine mixing, QED recoil), nuclear-structure (polarizability) corrections, or experiment.
What would settle it
An independent measurement of the electronic helium isotope shift on a different transition, together with complete theory, giving $r_{h}^{2} - r_{\alpha}^{2}$ in agreement with the muonic value.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
A 2024 chiral-EFT analysis of nuclear-structure corrections (arXiv 2401.13424) raised the tension to about $4\,\sigma$, while a late-2024 complete second-order hyperfine calculation (arXiv 2411.05621) reports that it largely resolves the disagreement; the two claims have not been reconciled.
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