Three-nucleon bound state in a spin-isospin dependent three dimensional approach

Abstract

A spin-isospin dependent Three-Dimensional approach based on momentum vectors for formulation of the three-nucleon bound state is presented in this paper. The three-nucleon Faddeev equations with two-nucleon interactions are formulated as a function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them with the inclusion of the spin-isospin quantum numbers, without employing a partial wave decomposition. As an application the spin-isospin dependent Faddeev integral equations are solved with Bonn-B potential. Our result for the Triton binding energy with the value of −8.152 MeV is in good agreement with the achievements of the other partial wave based methods.

A new way to perform partial-wave decompositions of few-nucleon forces

“…In Sec. 4 we demonstrate that the same method can be extended to the PWD of a threenucleon force. As a numerical example given in Sec.…”

“…Especially at low energies, i.e. below the pion production threshold, this procedure is still most commonly used, despite the advent of the approaches which use a direct three-dimensional notation [1,2,3,4].…”

Photodisintegration of3Hin a three dimensional faddeev approach

“…For evaluating the Triton wave function we need to make a relation between this wave function in our basic states to the one which has been calculated in the following basis [20]:…”

“…In the first step we ignore three body forces and we just use the single nucleon current. We will use AV18 potential and triton wave function which has been calculated in our previous work [20].…”

General operator form of the non-local three-nucleon force

“…[11,12]. More detailed information about the 3D formalism, with emphasis on few-nucleon bound and scattering states, can be found in works by the Kraków, Bohum, Tehran, Ohio, and University of Iowa groups [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”