Poincar\'e Invariant Three-Body Scattering at Intermediate Energies

TL;DR

This paper develops a relativistic three-nucleon scattering model using the Poincaré invariant Faddeev equation, solving it directly in momentum space, and compares the results to nonrelativistic models at intermediate energies up to 2 GeV.

Contribution

It introduces a Poincaré invariant formulation of three-body scattering without partial wave decomposition and demonstrates its numerical feasibility and stability.

Findings

Relativistic effects become significant at energies above 1 GeV.

The direct momentum space solution is stable and converges well.

Relativistic calculations differ notably from nonrelativistic ones at intermediate energies.

Abstract

The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. The equation is solved through Pad\'e summation, and the numerical feasibility and stability of the solution is demonstrated. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincar\'e group on the three-nucleon Hilbert space. Based on a Malfliet-Tjon type interaction, observables for elastic and break-up scattering are calculated for projectile energies in the intermediate energy range up to 2 GeV, and compared to their nonrelativistic counterparts. The convergence of the multiple scattering series is investigated as a function of the projectile energy in different scattering observables and configurations. Approximations to the two-body interaction embedded in the three-particle space are compared to the exact treatment.