Treatment of Two Nucleons in Three Dimensions

TL;DR

This paper presents a novel three-dimensional approach to two-nucleon scattering that avoids partial wave decomposition by using momentum vectors and handles spin operators analytically, simplifying calculations of NN interactions.

Contribution

It extends a new method for bound states to scattering problems, providing a more direct and potentially efficient way to analyze NN interactions without partial wave expansion.

Findings

Developed a set of six coupled equations for scalar functions in NN T-matrix

Successfully applied the method to two-nucleon scattering calculations

Avoided partial wave decomposition, simplifying the computational process

Abstract

We extend a new treatment proposed for two-nucleon (2N) and three-nucleon (3N) bound states to 2N scattering. This technique takes momentum vectors as variables, thus, avoiding partial wave decomposition, and handles spin operators analytically. We apply the general operator structure of a nucleon-nucleon (NN) potential to the NN T-matrix, which becomes a sum of six terms, each term being scalar products of spin operators and momentum vectors multiplied with scalar functions of vector momenta. Inserting this expansions of the NN force and T-matrix into the Lippmann-Schwinger equation allows to remove the spin dependence by taking traces and yields a set of six coupled equations for the scalar functions found in the expansion of the T-matrix.