The theory of crystal rainbows is presented. It enables the generation and full explanation of the angular distribution of ions transmitted through thin crystals. The angular distribution of the transmitted ions is generated by the computer simulation method. Then, the rainbow lines in the scattering angle plane are determined. These lines ensure the full explanation of the angular distribution. The theory is applied to the transmission of Ne 10ϩ ions through a ͗100͘ Si thin crystal. The ion energy is 60 MeV and the crystal thickness is varied from 105 to 632 atomic layers, i.e., from the beginning of the first rainbow cycle to the beginning of the second rainbow cycle.

We analyze here the energy dependence of the effect of zero-degree focusing of Nelo+ ions transmitted through the (100) channels of a Si crystal. The thickness of the crystal is 1 km and the ion energy is varied from 1.0 to 37 MeV per nucleon. The angular distributions of the transmitted ions were obtained by the computer simulation method using the numerical solution of the equations of motion of the ion, and two continuum interaction potentials of the ion and the crystal ~ Lindhard's potential, and the corresponding catastrophic potential. We demonstrate that the effect of zero-degree focusing is periodic with the respect to variable E-''*, where E is the ion energy, and that it decays with this variable. This periodicity is explained by the harmonic part of the continuum interaction potential, and the decay is attributed to the anharmonic part of the potential.

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