Rainbow effect in ion channeling

The problem of ion channeling in very thin crystals is considered with use of a method of classical ion-molecule scattering theory complemented with the Monte Carlo method. Special attention is devoted to the rainbow effect. It is shown that this effect is a consequence of the fact that contributions of the atomic strings of the crystal to the probability of ion transmission interfere. In the calculations the projectiles were 7-MeV ${\mathrm{H}}^{+}$ ions, and they were being transmitted through the 〈110〉 channel of a apeq21500-Å-thick Si crystal; the case in which the incident energy is 10 MeV and crystal thickness apeq21000 Å is also analyzed. The effect of thermal vibrations of the atoms of the crystal and the effect of collisions of the ion with the electrons of the crystal are taken into account.