Relativistic Faddeev 3D Equations for Three-Body Bound States Without Two-Body $t-$Matrices

Abstract

This paper explores a novel revision of the Faddeev equation for three-body (3B) bound states, as initially proposed in Ref. \cite{golak2013three}. This innovative approach, referred to as \tmatrixfree in this paper, directly incorporates two-body (2B) interactions and completely avoids the 2B transition matrices. We extend this formalism to relativistic 3B bound states using a three-dimensional (3D) approach without using partial wave decomposition. To validate the proposed formulation, we perform a numerical study using spin-independent Malfliet-Tjon and Yamaguchi interactions. Our results demonstrate that the relativistic \tmatrixfree Faddeev equation, which directly implements boosted interactions, accurately reproduces the 3B mass eigenvalues obtained from the conventional form of Faddeev equation, referred to as \tmatrixdependent in this paper, with boosted 2B $t-$matrices. Moreover, the proposed formulation provides a simpler alternative to the standard approach, avoiding the computational complexity of calculating boosted 2B $t-$matrices and leading to significant computational time savings.

References in corpus (25)

• The Four-Boson System with Short-Range Interactions
• Nucleon mass from a covariant three-quark Faddeev equation
• The alpha-particle based on modern nuclear forces
• FaCE: a tool for Three Body Faddeev calculations with core excitation
• Relativistic calculation of the triton binding energy and its implications
• Efimov physics in bosonic atom-trimer scattering
• Universality and scaling limit of weakly-bound tetramers
• Investigation of ${}^{4}H{e}_3$ trimer on the base of Faddeev equations in configuration space
• Three-nucleon force in relativistic three-nucleon Faddeev calculations
• Faddeev-Yakubovsky search for Lambda-Lambda hydrogen-4
• Three Body Bound State Calculations without Angular Momentum Decomposition
• Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space
• Four-Body Bound State Calculations in Three-Dimensional Approach
• Three-Nucleon Bound State in a Spin-Isospin Dependent Three Dimensional Approach
• Realistic two-nucleon potentials for the relativistic two-nucleon Schroedinger equation
• Binding and structure of tetramers in the scaling limit
• Quantitative Relativistic Effects in the Three-Nucleon Problem
• The Relativistic Three-Body Bound State in a 3D Formulation
• A Three-Dimensional Treatment of the Three-Nucleon Bound State
• Trion clustering structure and binding energy in 2D semiconductor materials: Faddeev equations approach
• Calculation of Relativistic Nucleon-Nucleon Potentials in Three-Dimensions
• A three-dimensional momentum-space calculation of three-body bound state in a relativistic Faddeev scheme
• Some applications of the Faddeev-Yakubovsky equations to the cold-atom physics
• Relativistic nucleon-nucleon potentials in a spin-dependent three-dimensional approach
• Four-body bound states in momentum space: the Yakubovsky approach without two-body $t-$matrices