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

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.

arXiv comment8 pages, 1 figure

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Cited by in corpus (13)

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• Solutions of the bound state Faddeev-Yakubovsky equations in three dimensions by using NN and 3N potential models
• 3N Scattering in a Three-Dimensional Operator Formulation
• Bound states in the B-matrix formalism for the three-body scattering
• Tri-meson bound state $BB{B}^{\ast }$ via delocalized $\pi$~Bond
• Deuteron-alpha scattering: separable vs nonseparable Faddeev approach
• The n-n-alpha System in a Continuum Faddeev Formulation
• A Spin-Isospin Dependent 3N Scattering Formalism in a 3D Faddeev Scheme
• Weighted-residual methods for the solution of two-particle Lippmann-Schwinger equation without partial-wave decomposition
• Triton photodisintegration in three-dimensional approach
• Direct numerical solution of the two-particle Lippmann-Schwinger equation in coordinate space using the multi-variable Nystrom method