A novel treatment of the proton-proton Coulomb force in proton-deuteron Faddeev calculations

¹ M. Smoluchowski Institute of Physics, Jagiellonian University, PL-30059 Kraków, Poland
² Institut für theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany

^a e-mail: witala@if.uj.edu.pl

Abstract

We present resently introduced novel approach to include th e proton-proton (pp) Coulomb force into the momentum space three-nucleon (3N) Faddeev calculations. It is based on a standard formulation for short range forces and relies on a screening of the long-range Coul omb interaction. In order to avoid all uncertainties connected with an application of the partial wave expansion, unsuitable when working with long-range forces, we apply directly the 3-dimensional pp screened Coulomb t-matrix. That main new ingredient, the 3-dimensional screened pp Coulomb t-matrix, is obtained by a numerical sol ution of the 3-dimensional Lippmann-Schwinger (LS) equation. Using a simple dynamical model for the nuclear part of the interaction we demonstrate the feasibility of that approach. The physical elastic pd scattering amplitude has a well defined screening limit and does not require renormalisation. Well converged elastic pd cro ss sections are obtained at finite screening radii. Also the proton-deuteron (pd) breakup observables can be determ ined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd e lastic scattering, the screening limit exists only after renormalisation of the pp t-matrices.