"To renormalize or not to renormalize ?'' in the protondeuteron scattering calculations
Abstract
We discuss two approaches which, by applying the screening method, permit one to include the long range protonproton (pp) Coulomb force in protondeuteron (pd) momentumspace scattering calculations. In the first one, based on AltGrassbergerSandhas (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 3dimensional and partialwave projected pp Coulomb tmatrices, identical for both approaches, must appear in transition amplitudes. We investigate importance of these terms for elastic pd scattering below the breakup threshold.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.07163
 arXiv:
 arXiv:2402.07163
 Bibcode:
 2024arXiv240207163W
 Keywords:

 Nuclear Theory
 EPrint:
 17 pages, 6 figures