Fine-structure anomaly of 2p levels in heavy muonic atoms
In plain words
In muonic atoms of heavy elements such as zirconium, tin and lead, the measured gap between two closely spaced muon levels disagreed with theory for decades. Distortion of the nucleus by the muon turned out too small to explain it, and a 2025 calculation blames an incomplete treatment of the recoil of the nucleus instead.
Precise statement
The measured 2p_3/2 - 2p_1/2 fine-structure splittings in muonic Zr-90, Sn-120 and Pb-208 could not be fitted together with the other muonic X-ray lines using one nuclear charge distribution per nucleus; nuclear polarization does not account for the deviation (Valuev et al, arXiv 2201.09638). A treatment including relativistic nuclear recoil (Beyer et al, arXiv 2511.22298) reports consistent fits for Zr-90 and Sn-120, with r_rms(Zr-90) = 4.2732(7) fm, about $3\sigma$ above the accepted value. Determine whether the same treatment removes the anomaly in Pb-208 and whether the shifted charge radii are confirmed by independent data.
What would settle it
A single theory framework that reproduces all measured muonic X-ray energies of Zr-90, Sn-120 and Pb-208 within experimental uncertainty with one nuclear charge distribution per nucleus, checked against new high-resolution muonic X-ray data or electron scattering radii.
Status in the literature
Unverified note
A November 2025 preprint (arXiv 2511.22298) reports that relativistic recoil resolves the Zr-90 anomaly and gives a consistent result for Sn-120; Pb-208 and independent confirmation remain open.