Eur. Phys. J. A (2010) 43: 339-350
https://doi.org/10.1140/epja/i2010-10920-4

Regular Article - Theoretical Physics

3N scattering in a three-dimensional operator formulation

¹ Institut für theoretische Physik II, Ruhr-Universität Bochum, D-44780, Bochum, Germany
² Departemen Fisika Universitas Indonesia, 16424, Depok, Indonesia
³ Institute of Nuclear and Particle Physics, Department of Physics and Astronomy, Ohio University, 45701, Athens, OH, USA
⁴ M. Smoluchowski Institute of Physics, Jagiellonian University, PL-30059, Kraków, Poland

^* e-mail: witala@if.uj.edu.pl

Received: 7 October 2009
Revised: 1 December 2009
Accepted: 12 January 2010
Published online: 16 February 2010

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.