Identify the source of disagreement between calculated Ag isotope-shift factors

Identify the source of the poor agreement between the specific mass-shift and total mass-shift factors calculated in the present relativistic coupled-cluster study and those calculated by Ohayon et al. for neutral Ag, despite the use of relativistic coupled-cluster methods and higher-order corrections in both studies.

Background

The paper calculates field-shift and mass-shift factors for several Ag optical transitions using relativistic coupled-cluster theory, including higher-order correlation, Breit, and QED corrections. The field-shift factors agree with the previous ab initio calculations within approximately two standard deviations, but the mass-shift factors—particularly the specific mass-shift factors—show substantial disagreement.

Because both calculations use relativistic coupled-cluster approaches with higher-order corrections, the discrepancy cannot be explained straightforwardly by the broad methodological distinction alone. The unresolved source limits the ability to reconcile the two independent theoretical determinations and motivates further methodological investigation.

References

For the $F$ factor, the present values are in 2$\sigma$ agreement with those by Ohayon et al. On the other hand, the agreement for $K$ factor is poor, especially for $K_{\rm SMS}$. Considering that in both the present work and the work of Ohayon et al. the factors were calculated with relativistic coupled cluster theory (but different versions of RCC and different codes) and including higher-order corrections, it is unclear what the source of the limited agreement is.

— Nuclear moments, charge radii, and magnetization distribution parameters of Ag isotopes from laser spectroscopy and \textit{ab initio} electronic-structure calculations  (2609.40130 - Skripnikov et al., 30 Sep 2026) in Section 3, subsection “Computational results”

Since the same experimental isotope shifts underlie the charge radius differences in both this work and Ref., this discrepancy primarily reflects differences in the calculated atomic isotope-shift factors. The agreement of the present results with the independent muonic-data determination therefore provides additional support for the isotope-shift factors calculated in this work, although the origin of the discrepancy with Ref. remains to be understood.

— Nuclear moments, charge radii, and magnetization distribution parameters of Ag isotopes from laser spectroscopy and \textit{ab initio} electronic-structure calculations  (2609.40130 - Skripnikov et al., 30 Sep 2026) in Section 3, subsection “Nuclear charge radii of Ag isotopes”