Abstract
We present resently introduced novel approach to include the 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 Coulomb 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 solution of the 3-dimensional Lippmann-Schwinger (LS) equation. Using a simple dynamical model for the nuclear part of the interaction we demonstrate the feasi- bility of that approach. The physical elastic pd scattering amplitude has a well defined screening limit and does not require renormalisation. Well converged elastic pd cross sections are obtained at finite screening radii. Also the proton-deuteron (pd) breakup observables can be determined from the resulting on-shell 3N amplitudes in- creasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after renormalisation of the pp t-matrices.
Highlights
The inclusion of the Coulomb force into the analysis of nuclear reactions with more than 2 nucleons is a long standing problem
We presented recently formulated novel approach to include the pp Coulomb force into the momentum space 3N Faddeev calculations
It is based on a standard formulation for short range forces and relies on a screening of the longrange Coulomb interaction
Summary
The inclusion of the Coulomb force into the analysis of nuclear reactions with more than 2 nucleons is a long standing problem. With increasing energy the theoretical cross sections come close to the data, which indicates that the pp Coulomb force is very probably re-. The partial wave summation up to maximal angular momentum lmax = 3, 5 and 10 are given by dotted, dashed and solid lines, respectively This inability to understand the pp QFS and pd SST cross sections calls for reconsidering the inclusion of the Coulomb force into momentum space Faddeev calculations. In [16,17] we proposed a novel approach to incorporate the pp Coulomb force into the momentum space Faddeev calculations, in which we apply directly the 3-dimensional screened pp Coulomb t-matrix without relying on a partial wave decomposition.
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