Abstract
The paper presents a new method for searching for binding energies of three-body systems based on the numerical solution to a system of homogeneous Faddeev equations with respect to the matrix \(T\) with direct numerical integration without the traditional partial wave decomposition. In this paper, we use the simplest systems with three point nucleons to demonstrate the features of the numerical solution to homogeneous Faddeev equations in which two-body t-matrices are generated by both local and nonlocal potentials. The characteristic behavior of the binding energies of three bodies is established depending on the change in the number of radial grid nodes for relative momenta. The paper compares the method of Padé approximants and the algebraic method of matrix inversion in the numerical solution to the Lippmann–Schwinger equations. It is shown that both methods can be used in problems of searching for binding energies of systems of three bodies. In the chosen numerical scheme, the influence of Coulomb repulsion and the three-body \(NNN\) force on the binding energies of the systems under consideration is estimated. It is shown that the missing \(NNN\) interaction must be charge-dependent in order to explain the skew in the missing contributions to the binding energies of the \({}^{3}\) He and \({}^{3}\) H nuclei under consideration at a level of 143 keV.
