Coulomb screening in the momentum-space description of proton-deuteron elastic scattering: Examination of the need for renormalization

Proton-deuteron elastic scattering is considered in the framework of momentum-space Faddeev equations with the screening method for the Coulomb interaction. It is shown how the interplay of the proton-proton Coulomb potential and the deuteron pole in the neutron-proton transition operator leads to coinciding singularities in the Faddeev equation. The coincidence of those singularities was not taken into account in a previous work [Wita\l{}a et al., Eur. Phys. J. A 41, 369 (2009)], leading to a conjecture that no renormalization is needed. However, the coinciding singularities closely resemble those of the point deuteron-proton system, naturally suggesting that the renormalization of the scattering amplitude is needed in the unscreened Coulomb limit and can be performed conveniently in terms of the point deuteron-proton system.