Rainbows in Proton Channeling in Silicon Crystals

Abstract

In this chapter, some of the high-resolution proton channeling measurements with a very thin (100) Si crystal conducted by the Singapore group [45–48] will be thoroughly analyzed. Those extraordinary measurements have proven to be crucial for verification of the theory of crystal rainbows as the proper theory of ion channeling in crystals. We shall present the results of three experimental and theoretical studies that were induced by those measurements and performed jointly by us and the Singapore group. The first study leads to the very accurate ion-atom interaction potentials [133]. As a continuation, we shall additionally explore the process that is inverse to the transmission process under consideration, and, thus, fully answer the question of its multiplicity, which is directly connected to the essence of the crystal rainbow effect, being the ion focusing along a line reflecting the symmetry of the illuminated crystal. The second study is devoted to the effect of superfocusing of channeled ions, which is the effect of spatial focusing occurring in the middle of each rainbow cycle [134]. The third study contains the proof that the doughnut effect in ion channeling, occurring with tilted crystals, which has been seen and measured many times, is in fact a crystal rainbow effect [130]. Before presenting the results of the second and third studies, we shall describe in detail the superfocusing and doughnut effects, respectively.