Rainbow effect in axial ion channeling

We have studied the angular scattering distributions produced in axial channeling when incident protons (7 MeV) are well aligned to the axial direction of a thin silicon crystal (1400 A\r{}). Measured angular distributions obtained in the 〈100〉 and 〈110〉 directions using a two-dimensional (2D) position-sensitive detector (resolution \ensuremath{\lesssim}0.015\ifmmode^\circ\else\textdegree\fi{}) have been interpreted by comparison with Monte Carlo trajectory calculations for these channels in the momentum approximation. The measured angular distributions show structures at certain off-axis angles which are in good agreement with the calculations. The general shape and structure in the angular contour map for a given channel have been shown to be a consequence of extrema in the 2D classical deflection functions for the two Cartesian scattering angles in the detection plane. The occurrence of the extrema in a very thin crystal (i.e., a rainbow effect in axial channeling) is a consequence of the channeling geometry when atomic strings surrounding the axial channel interact with the projectile simultaneously.