Morphological study of the rainbow scattering of protons by graphene

We have studied metamorphoses of the angular rainbow pattern generated by classical rainbow scattering of protons by graphene. To analyze the rainbow pattern, a morphological method was developed. It focuses on the shape of the rainbow pattern rather than on the exact position of rainbow lines or the particle count. It comprises elements of the catastrophe theory, which provides a local model of the rainbow pattern and the reduced potential and an index theory of algebraic topology that allows the evolution of the rainbow pattern to be linked with bifurcations of critical points of the reduced potential. The obtained insight is summarized into five principles that allow an experimentalist to sketch a qualitatively correct rainbow pattern in the impact parameter plane and the distribution of the reduced potential critical points, just by observing the evolution of the angular rainbows. The morphological method should be applicable for the analysis of all structurally stable patterns in nature.