Quantify the three-body effect of using point-charge versus folded Coulomb interactions

Quantify the systematic three-body uncertainty in the Coulomb displacement calculations caused by representing the alpha-proton interaction with a point-charge Coulomb force rather than a short-distance-softened folded Coulomb force.

Background

The paper calculates the Coulomb displacement of three-cluster nuclei using a point-charge Coulomb interaction in the alpha-proton channel. Other cluster-model calculations use a folded Coulomb force, which is softer at short distances. A two-body test cited by the authors indicates that folding can shift the dressed alpha-proton forbidden state, but the corresponding uncertainty has not been determined within the three-body calculations presented here.

Resolving this issue would establish how much of the difference between the reported three-body Coulomb displacements and those from folded-Coulomb cluster models is attributable specifically to the short-range treatment of the Coulomb interaction.

References

One systematic uncertainty of this comparison is not quantified at the three-body level: the $\alpha p$ Coulomb force is the point-charge one, whereas the folded force of those models is softer at short distances, and Ref. finds in a one-channel test that the folding raises the dressed $\alpha p$ $0s$ state by about $0.5$~MeV.

— The Fock representation of the Coulomb interaction. II. Three-body bound states  (2610.08520 - Nishonov, 6 Oct 2026) in Section 4.2, 'The three-cluster nuclei' (subsection label sec:a3a6)