Three-body scattering in Poincar\'e invariant quantum mechanics

TL;DR

This paper develops a relativistic quantum mechanical framework for three-nucleon scattering using Poincaré invariance, enabling direct numerical solutions at high energies without partial wave decomposition.

Contribution

It introduces a Poincaré invariant formulation of the three-nucleon problem that preserves symmetry and cluster properties, solving Faddeev equations directly at high energies.

Findings

Successfully solved relativistic Faddeev equations without partial waves.

Achieved accurate modeling of elastic and breakup reactions up to 2 GeV.

Maintained Poincaré invariance and cluster properties in the solutions.

Abstract

The relativistic three-nucleon problem is formulated by constructing a dynamical unitary representation of the Poincar\'e group on the three-nucleon Hilbert space. Two-body interactions are included that preserve the Poincar\'e symmetry, lead to the same invariant two-body S-matrix as the corresponding non-relativistic problem, and result in a three-body S-matrix satisfying cluster properties. The resulting Faddeev equations are solved by direct integration, without partial waves for both elastic and breakup reactions at laboratory energies up to 2 Gev.