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

TL;DR

This paper presents a lattice method to determine two-particle scattering phase shifts and mixing angles, applicable to nonrelativistic effective theories, using a spherical wall boundary condition to analyze standing wave energies.

Contribution

The authors introduce a lattice approach for extracting phase shifts and mixing angles in two-particle scattering, including channels with partial-wave mixing, applicable to nonrelativistic theories.

Findings

Successfully computed phase shifts and mixing angles for spin-1/2 particles.

Demonstrated the method with an attractive Gaussian potential including tensor forces.

Validated the approach through lattice simulations with spherical boundary conditions.

Abstract

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any nonrelativistic 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.