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

TL;DR

This paper compares relativistic and non-relativistic Faddeev calculations for proton-deuteron elastic scattering, highlighting the importance of relativistic effects at higher energies and evaluating different potential models and transformation methods.

Contribution

It introduces a method to construct pseudo-relativistic potentials from realistic NN potentials and compares their effects on scattering calculations across a range of energies.

Findings

Relativistic effects become significant at 135 MeV, especially at backward angles.

Discrepancies between CPS and KG transformations grow above 300 MeV.

Non-relativistic calculations remain reliable below 300 MeV for polarization observables.

Abstract

This investigation compares non-relativistic and relativistic nucleon-nucleon (NN) potentials in the context of pd scattering. Conventional NN potentials (e.g., CDBonn, AV18) rely on the non-relativistic Schr\"odinger equation, whereas the Kharkiv potential is intrinsically relativistic. We employ the Coester-Pieper-Serduke (CPS) and Kamada-Gl\"ockle (KG) conversion methods to construct a Pseudo-Relativistic Potential (PRP) from a realistic NN potential, preserving the deuteron binding energy and phase shifts. 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-Non-Relativistic 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. Nevertheless, non-relativistic calculations using the PRP remain generally reliable for polarization observables below 300 MeV.