A New Approach to the 3D Faddeev Equation for Three-Body Scattering

TL;DR

This paper introduces a new momentum-space method for solving the three-body Faddeev equation at arbitrary energies, effectively handling complex singularities without partial wave decomposition.

Contribution

It presents a novel approach that simplifies the singularity structure of the Faddeev equation, enabling direct solution in momentum space for three-body scattering.

Findings

Simplifies singularity handling in three-body scattering equations.

Enables direct momentum-space solutions without partial wave expansion.

Provides a more straightforward numerical integration method.

Abstract

A novel approach to solve the Faddeev equation for three-body scattering at arbitrary energies is proposed. This approach disentangles the complicated singularity structure of the free three-nucleon propagator leading to the moving and logarithmic singularities in standard treatments. The Faddeev equation is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation for identical bosons, which we are using, is an integral equation in five variables, magnitudes of relative momenta and angles. The singularities of the free propagator and the deuteron propagator are now both simple poles in two different momentum variables, and thus can both be integrated with standard techniques.