Rainbow effect in axial ion channeling

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Abstract
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 Å). Measured angular distributions obtained in the 〈100〉 and 〈110〉 directions using a two-dimensional (2D) position-sensitive detector (resolution ≲0.015°) 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.