Explain the Hf and Cm charge-radius anomaly

Determine the origin of the unexplained charge-radius anomaly predicted for the light hafnium isotopes and curium isotopes by the DG and D2 Gogny interactions.

Background

The DG interaction was designed to control binding-energy drifts and to leave room for correlation effects in charge radii. Its calculated charge-radius deviations are generally compatible with the expected role of beyond-mean-field correlations, but anomalous behavior remains for the light hafnium isotopes and for curium isotopes. The review explicitly states that this anomaly has not been explained and mentions experimental uncertainties as a possible consideration, leaving its theoretical origin unresolved.

References

The light Hf isotopes and Cm anomaly is not explained but one indicates the existence of large experimental error bars in comparison with the other isotopic chains.

— Gogny interaction from beginnings to current challenges  (2609.11425 - Pillet et al., 10 Sep 2026) in Section 1, subsection “Fully finite-range Gogny force including a tensor term: the DG Gogny interaction family”