Bound State Calculations of the Three-Dimensional Yakubovsky Equations with the inclusion of Three-Body Forces

Abstract

The four-body Yakubovsky equations in a Three-Dimensional approach with the inclusion of the three-body forces is proposed. The four-body bound state with two- and three-body interactions is formulated in Three-Dimensional approach for identical particles as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angles between them. The modified three dimensional Yakubovsky integral equations is successfully solved with the scalar two-meson exchange three-body force where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the energy eigenvalue and the four-body wave function, as well as accuracy of our numerical calculations are presented.The four-body Yakubovsky equations in a Three-Dimensional approach with the inclusion of the three-body forces is proposed. The four-body bound state with two- and three-body interactions is formulated in Three-Dimensional approach for identical particles as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angles between them. The modified three dimensional Yakubovsky integral equations is successfully solved with the scalar two-meson exchange three-body force where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the energy eigenvalue and the four-body wave function, as well as accuracy of our numerical calculations are presented.

arXiv comment23 pages, 2 eps figures, 5 tables. Major changes; version to appear in European Physical Journal A

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• Three-Nucleon Bound State in a Spin-Isospin Dependent Three Dimensional Approach
• Calculations of three-nucleon reactions with N3LO chiral forces: achievements and challenges
• Solutions of the bound state Faddeev-Yakubovsky equations in three dimensions by using NN and 3N potential models
• The three dimensional calculations of NN bound and scattering states with chiral potential up to N3LO
• Calculation of Relativistic Nucleon-Nucleon Potentials in Three-Dimensions
• Low-momentum effective interaction in the three-dimensional approach
• A Spin-Isospin Dependent 3N Scattering Formalism in a 3D Faddeev Scheme
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• Numerical study of the two-boson bound-state problem with and without partial-wave decomposition