Observation of rainbow scattering in ion transmission through graphene

The rainbow effect is a fundamental phenomenon in scattering theory, describing the accumulation of trajectories at characteristic angles associated with Jacobian singularities of the scattering map. In atomically thin materials, rainbow scattering patterns are highly sensitive to projectile-target interactions and lattice symmetry, yet experimental observation has remained elusive. We report the experimental observation of rainbow scattering in ion transmission through single-layer graphene. For 40 keV Xe + ions, a circular outer rainbow at 5.28°, associated with maximum binary collision deflection from individual carbon atoms, and a hexagonal inner rainbow at 0.43°, originating from projectiles interacting with multiple carbon atoms, are observed. Molecular dynamics and binary collision simulations reproduce these regimes but fail to capture the measured intensity distribution at the smallest deflection angles when using radially symmetric interaction potentials. These results establish graphene rainbow scattering as an experimental benchmark for interatomic potentials and reveal limitations of common approximations in many-body scattering dynamics.