Theory of rainbows in thin crystals: The explanation of ion channeling applied toNe10+ions transmitted through a 〈100〉 Si thin crystal

Abstract

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.

Dynamic polarization effects on the angular distributions of protons channeled through carbon nanotubes in dielectric media

“…Moreover, the rainbow effect has been investigated recently in the context of grazing scattering of atoms from metal surfaces under channeling conditions by Schüller et al [19] who showed that precise measurements of the well-defined maxima in the angular distributions of scattered atoms, attributed to the rainbow effect, can give detailed information on the interaction potential of the atoms with the metal surfaces. On the other hand, the theory of crystal rainbows has been formulated as the proper theory of ion channeling in thin crystals [20], and has been subsequently applied to ion channeling in short carbon nanotubes [21,22,23,24]. It is therefore expected that, in analogy with the surface channeling experiments [19], measurements of the rainbow effect in carbon nanotubes may give precise information on both the atomic configuration and the interaction potentials within such structures, which are not completely known at present.…”

Rainbow Lenses

“…Ne skovi c et al (2011) demonstrated that, notwithstanding the above mentioned conclusion that the interaction potential of the proton and lens did not have the catastrophic character, one could apply the theory of crystal rainbows to address the issue (Petrovi c et al 2000). The lens is assumed to be not very short; the trajectories of the majority of protons cannot be approximated by straight lines.…”

“…The results of the high-resolution proton channeling measurements were explaned later by a detailed morphological analysis based on the theory of crystal rainbows (Motapothula et al 2012c;Petrovi c et al 2000). It was shown that the doughnut effect was the rainbow effect with tilted crystals (Ne skovi c et al 2002;Borka et al 2003).…”

Focusing properties of a square electrostatic rainbow lens

“…As in our previous study [1], we are going to apply to the problem in question the theory of crystal rainbows [4][5][6][7][8]. It is assumed that the proton propagation angle inside the lens and in the drift space after it remains small.…”