A Realistic Formalism for 4N Bound State in a Three-Dimensional Yakubovsky Scheme

TL;DR

This paper introduces a three-dimensional formalism for modeling four-nucleon bound states using Yakubovsky equations, simplifying calculations by avoiding partial wave decomposition and effectively incorporating spin-isospin dependencies.

Contribution

It presents a novel 3D formalism for four-nucleon systems that reduces computational complexity compared to traditional partial wave methods.

Findings

Formalism results in a finite set of coupled integral equations.

Coordinate transformations are simplified with continuous angle variables.

The approach is less cumbersome for three-nucleon force calculations.

Abstract

A spin-isospin dependent Three-Dimensional formalism based on the momentum vectors for the four-nucleon bound state is presented. The four-nucleon Yakubovsky equations with two- and three-nucleon interactions are formulated as a function of the vector Jacobi momenta. Our formalism, according to the number of spin-isospin states that one takes into account, leads to only a strictly finite number of the coupled three-dimensional integral equations to be solved. The evaluation of the transition and permutation operators as well as the coordinate transformations due to considering the continuous angle variables instead of the discrete angular momentum quantum numbers are less complicated in comparison with partial wave representation. With respect to partial wave the present formalism with the smaller number of equations leads to higher dimensionality of the integral equations. We have concluded that Three-Dimensional formalism is less cumbersome for considering the three-nucleon forces.