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

Borasoy, B.; Meissner, U.G.; Krebs, H.; Epelbaum, E.; Lee, D.

doi:10.1140/epja/i2007-10500-9

Journal Article

PreJuSER-61122

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

Borasoy, B.FZJ* ; Epelbaum, E.FZJ* ; Krebs, H.FZJ* ; Lee, D.FZJ* ; Meissner, U. G.FZJ*

2007
Springer Berlin

The European physical journal / A 34, 185 - 196 (2007) [10.1140/epja/i2007-10500-9]

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Please use a persistent id in citations: http://hdl.handle.net/2128/10505 doi:10.1140/epja/i2007-10500-9

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.

Keyword(s): lattice field theory ; partial wave ; mixing angle ; symmetry: SO(3,Z) ; coupled channel ; nucleon nucleon: interaction ; potential ; group theory: representation ; transfer matrix ; numerical calculations