A New Treatment of 2N and 3N Bound States in Three Dimensions

TL;DR

This paper generalizes the Faddeev equation approach for three-boson systems to nucleons in three dimensions, simplifying the problem to coupled scalar equations that depend only on momenta, facilitating the study of 2N and 3N bound states.

Contribution

It introduces a novel method replacing the Faddeev equation with a finite set of coupled scalar equations for nucleons, simplifying the treatment of 2N and 3N bound states.

Findings

Derived coupled equations for nucleon systems

Simplified treatment of spin-momentum dependence

Applied method to deuteron leading to two equations

Abstract

The direct treatment of the Faddeev equation for the three-boson system in 3 dimensions is generalized to nucleons. The one Faddeev equation for identical bosons is replaced by a strictly finite set of coupled equations for scalar functions which depend only on 3 variables. The spin-momentum dependence occurring as scalar products in 2N and 3N forces accompanied by scalar functions is supplemented by a corresponding expansion of the Faddeev amplitudes. After removing the spin degrees of freedom by suitable operations only scalar expressions depending on momenta remain. The corresponding steps are performed for the deuteron leading to two coupled equations.