3D solution of the full Faddeev equations for the Nd break-up reaction without 3NF effect

TL;DR

This paper extends a 3D formalism for nucleon-deuteron breakup by solving the full Faddeev equations without three-nucleon-force effects, improving the treatment of singularities at higher energies.

Contribution

It introduces a novel 3D approach to solve the full Faddeev equations without 3NF, efficiently handling moving singularities in few-body scattering.

Findings

Developed a new method for treating moving singularities directly in the energy domain.

Enabled systematic investigation of complex singularities in three-nucleon scattering.

Applicable to projectile energies above pion-production threshold.

Abstract

A recently developed three-dimensional formalism for the nucleon-deuteron breakup channel initially considered only the leading-order term of the Faddeev equations, using the nucleon-nucleon T-matrix to compute the breakup amplitude. In the present study, we extend that formalism by solving the full three-nucleon Faddeev equation without three-nucleon-force contributions in a three-dimensional approach in which momentum vectors are used directly as variables. This formalism is well suited for projectile energies in scattering processes above the pion-production threshold, where partial-wave expansions become inefficient. To treat the moving singularities of the free three-nucleon propagator, we introduce a new method that treats these singularities in a manner analogous to the simple poles appearing in the Lippmann-Schwinger equation. This approach evaluates the moving singularities directly through the center-of-mass energy of the 23-subsystem and eliminates the need to partition the q-domain into intervals. The resulting formulation opens a pathway toward a systematic investigation of the complex singularities in few-body scattering processes within the Faddeev framework.