BINDING ENERGIES OF 3H, 3He NUCLEI IN THREE-BODY FADDEEV EQUATIONS WITH DIRECT INTEGRATION

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Abstract

The paper presents a new method for searching for binding energies of three-body systems based on the numerical solution of 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 tried to demonstrate on the simplest systems with three point nucleons the features of the numerical solution of homogeneous Faddeev equations, two-body 𝑡-matrices in which both local and non-local potentials are generated. The characteristic behavior of the binding energies of three bodies has been established depending on the change in the number of nodes of the radial grid of relative momenta. The paper compares the method of Pade approximants and the algebraic method of matrix inversion in the numerical solution of 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 3He, 3H nuclei under consideration at the level of 143 keV.

About the authors

A. Gapchenko

Tomsk State University

Tomsk, Russia

O. Goleva

Tomsk State University

Tomsk, Russia

M. Egorov

Tomsk State University; Joint Institute for Nuclear Research, Bogoliuubov Laboratory of Theoretical Physics

Email: egorovphys@mail.ru
Tomsk, Russia; Dubna, Russia

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