Abstract
This review is devoted to ion transmission through axial channels of thin crystals. In this process the rainbows occur. The effect is called the crystal rainbow effect. We shall describe its origin and present the experiments in which it has been observed. We shall explain also how the crystal rainbows can be classified using catastrophe theory. This classification has resulted in a universal, simple and accurate approximation to the continuum potential in the channels. Besides, the periodicity of the angular distributions of transmitted ions with the reduced crystal thickness will be considered. It will be introduced via the effect of zero-degree focusing of channeled ions. In addition, we shall mention the doughnut effect in ion channeling, which has proven to be the rainbow effect with tilted crystals. All these considerations will demonstrate clearly the usefulness of the theory of crystal rainbows, which is the proper theory of ion channeling in thin crystals.
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