Nonuniqueness of the Phase Shift in Central Scattering due to Monodromy

Scattering at a central potential is completely characterized by the phase shifts which are the differences in phase between outgoing scattered and unscattered partial waves. In this Letter, it is shown that, for 2D scattering at a repulsive central potential, the phase shift cannot be uniquely defined due to a topological obstruction which is similar to monodromy in bound systems.