3N Scattering in a Three-Dimensional Operator Formulation

TL;DR

This paper extends a 3D operator formulation for two- and three-nucleon bound states to three-nucleon scattering, enabling efficient calculations at higher energies and with chiral forces without partial wave expansion.

Contribution

It introduces a three-dimensional operator approach for three-nucleon scattering that simplifies spin-momentum dependence and facilitates high-energy and chiral force applications.

Findings

Formulation allows analytical treatment of spin degrees of freedom.

Enables direct 3D integrations over scalar functions.

Suitable for high-energy and chiral force calculations.

Abstract

A recently developed formulation for a direct treatment of the equations for two- and three-nucleon bound states as set of coupled equations of scalar functions depending only on vector momenta is extended to three-nucleon scattering. Starting from the spin-momentum dependence occurring as scalar products in two- and three-nucleon forces together with other scalar functions, we present the Faddeev multiple scattering series in which order by order the spin-degrees can be treated analytically leading to 3D integrations over scalar functions depending on momentum vectors only. Such formulation is especially important in view of awaiting extension of 3N Faddeev calculations to projectile energies above the pion production threshold and applications of chiral perturbation theory 3N forces, which are to be most efficiently treated directly in such three-dimensional formulation without having to expand these forces into a partial wave basis.