Treatment of Two Nucleons in Three Dimensions

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

^a e-mail: imamf@fisika.ui.ac.id

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.