  We discuss two approaches which, by applying the screening method, permit one
to include the long range proton-proton (pp) Coulomb force in proton-deuteron
(pd) momentum-space scattering calculations. In the first one, based on
Alt-Grassberger-Sandhas (AGS) equation, presented in Phys. Rev. C{\bf{71}},
054005 (2005) and {\bf{73}}, 057001 (2006), one needs to renormalize elastic
scattering amplitude before calculating observables. In the second treatment,
proposed by us in Eur. Phys. Journal A {\bf{41}}, 369 (2009), {\bf{41}}, 385
(2009), and arXiv:2310.03433 [nucl.th], this renormalization is avoided. For
the proton induced deuteron breakup reaction both approaches require
renormalization of the corresponding transition amplitudes. We derive the basic
equations underlying both methods under the assumption that all contributing
partial wave states are included and explain why in our approach
renormalization of the elastic scattering amplitude is superfluous. We show
that in order to take into account in the screening limit all partial waves it
is required that four additional terms, based on the 3-dimensional and
partial-wave projected pp Coulomb t-matrices, identical for both approaches,
must appear in transition amplitudes. We investigate importance of these terms
for elastic pd scattering below the breakup threshold.
