Eur. Phys. J. A (2007) 34: 185-196
https://doi.org/10.1140/epja/i2007-10500-9

Regular Article - Theoretical Physics

Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles

¹ Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Universität Bonn, Nußallee 14-16, D-53115, Bonn, Germany
² Institut für Kernphysik (Theorie), Forschungszentrum Jülich, D-52425, Jülich, Germany
³ Department of Physics, North Carolina State University, 27695, Raleigh, NC, USA

^* e-mail: djlee3@ncsu.edu

Received: 22 August 2007
Accepted: 7 November 2007
Published online: 27 November 2007

Abstract

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any non-relativistic effective theory of point particles on the lattice. In the center-of-mass frame of the two-particle system we impose a hard spherical wall at some fixed large radius. For channels without partial-wave mixing the partial-wave phase shifts are determined from the energies of the nearly spherical standing waves. For channels with partial-wave mixing further information is extracted by decomposing the standing wave at the wall boundary into spherical harmonics, and we solve coupled-channels equations to extract the phase shifts and mixing angles. The method is illustrated and tested by computing phase shifts and mixing angles on the lattice for spin-1/2 particles with an attractive Gaussian potential containing both central and tensor force parts.