A Spin-Isospin Dependent 3N Scattering Formalism in a 3D Faddeev Scheme

TL;DR

This paper develops a three-dimensional formalism for three-nucleon scattering that incorporates spin and isospin dependencies, using vector Jacobi momenta and quantum numbers to improve the description of scattering processes.

Contribution

It introduces a novel spin-isospin dependent 3D Faddeev approach connecting transition amplitudes to momentum-helicity representations.

Findings

Formulated Faddeev equations in terms of vector Jacobi momenta and spin-isospin quantum numbers.

Derived expressions for nucleon-deuteron elastic scattering amplitudes.

Presented a framework for full breakup process amplitudes.

Abstract

We have introduced a spin-isospin dependent three-dimensional approach for formulation of the three-nucleon scattering. Faddeev equation is expressed in terms of vector Jacobi momenta and spin-isospin quantum numbers of each nucleon. Our formalism is based on connecting the transition amplitude $T$ to momentum-helicity representations of the two-body $t$-matrix and the deuteron wave function. Finally the expressions for nucleon-deuteron elastic scattering and full breakup process amplitudes are presented.