The Atomic Rainbow

When light enters a raindrop, different colors refract at different angles, producing a rainbow. The mechanism requires three things: a spectrum of wavelengths in the incoming light, a medium whose refractive index depends on wavelength, and a geometry (the spherical drop) that maps the angular spectrum into a visible arc. The rainbow is a caustic — a boundary where the density of refracted rays diverges.

When 40 keV xenon ions pass through single-layer graphene, the same optics happens at the atomic scale. The “spectrum” is the set of impact parameters — how far off-center each ion passes relative to the carbon atoms. The “refractive index” is the potential energy surface of the graphene lattice, which deflects ions by different amounts depending on their trajectory through the hexagonal lattice. The “geometry” is the arrangement of carbon atoms.

The result is an atomic rainbow: a hexagonal inner ring and a circular outer ring in the angular distribution of scattered ions. The inner hexagon arises from ions that interact with multiple carbon atoms simultaneously — their trajectories trace the hexagonal symmetry of the lattice. The outer circle arises from ions that undergo close binary collisions with individual atoms — one-on-one encounters that scatter isotropically.

The two rings probe different physics. The hexagonal ring reads the collective potential of the crystal — it is sensitive to lattice constant, symmetry, and the smoothness of the electron density between atoms. The circular ring reads the single-atom potential — it is sensitive to the nuclear charge and screening electrons of individual carbon atoms. One ion beam, one target, two distinct structural measurements encoded in two different rainbow features.

The through-claim: scattering patterns are maps of the potential energy landscape. A rainbow is not just a pretty pattern — it is the caustic where the mapping from impact parameter to scattering angle has a singularity. At the rainbow angle, the scattering cross-section diverges (in the classical limit), making the structure maximally visible. The lattice is most legible at exactly the angles where the scattering is most extreme.