Comparison of Relativistic and Non-relativistic Faddeev calculations for Proton-Deuteron Elastic Scattering

Abstract

This investigation compares non-relativistic and relativistic nucleon-nucleon potentials in the context of proton-deuteron scattering. Conventional NN potentials (e.g., CDBonn, AV18, Nijmegen) rely on the nonrelativistic Schroedinger equation, whereas the Kharkiv potential is intrinsically relativistic. We employ the Coester-Pieper-Serduke (CPS) and Kamada-Gloeckle (KG) conversion methods to construct a phenomenological-relativistic potential (PRP) from a realistic NN potential, preserving the deuteron binding energy and phase shifts. Focusing on relativistic effects and not including Coulomb forces to avoid complexity, the solutions are compared by solving relativistic and nonrelativistic Faddeev equations. Calculations of the differential cross section using the relativistic Faddeev equation show that relativistic effects - particularly the deviation at the backward angle - become pronounced at 135 MeV. The differences in the forward angle were attributed to the characteristics of the Kharkiv potential itself. The reverse transformation of the Kharkiv potential into a pseudo-nonrelativistic potential (PNRP) confirms that the backward-angle relativistic effect increases with energy in the range from 100 MeV to 400 MeV. Comparisons of the polarization observables indicate that relativistic effects, as well as the discrepancy between the CPS and KG transformations, become significant above 300 MeV. However, for polarization observations below 300 MeV, the nonrelativistic results from PNRP do not deviate significantly from relativistic calculations.