Rainbow effect in axial ion channeling

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 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.