Determine which screened-Coulomb amplitudes require renormalization

Determine which scattering amplitudes in momentum-space few-body calculations with screened Coulomb interactions require renormalization in the zero-screening-radius limit.

Background

Momentum-space few-body calculations commonly treat the long-range Coulomb interaction by screening it at a finite radius, solving the resulting equations, and then removing the screening through an asymptotic renormalization procedure. The paper notes that the necessity of this renormalization may depend on the particular amplitude being calculated.

The issue remains unresolved in the cited literature: Deltuva argues that renormalization is necessary for the elastic scattering amplitude, whereas Witała and collaborators have presented screened calculations that omit it and continue to defend that treatment. The paper identifies the determination of which amplitudes require renormalization as an outstanding methodological question, but does not resolve it.

References

Which amplitudes require the renormalization is still debated: Deltuva finds it necessary for the elastic scattering amplitude, where the screened treatment of Wita\l a et al. had omitted it, and those authors maintain their view in response.

— The Fock representation of the Coulomb interaction. I. Two-body problem  (2609.16585 - Nishonov, 15 Sep 2026) in Section 1, Introduction