Carbon nanotubes are the sheets of carbon atoms rolled up into cylinders with the atoms lying at the hexagonal crystal lattice sites. It has been predicted that they can be used to channel positively charged particles. This means that nanotubes could be used for guiding such beams. It has been also shown that the rainbow effect plays an important role in proton and positron channeling in nanotubes. This plenary speech is devoted to channeling of positrons of kinetic energy of 1 MeV in (11, 9) chiral single-wall carbon nanotubes of lengths between 50 and 200 nm. We present the classical and quantum spatial and angular distributions of transmitted positrons. In the classical calculations, the approach is via the equations of motion, and in the quantum calculations, the time-dependent Schrödinger equations is solved. The solutions of these quations are obtained numerically. In the quantum calculations, the initial beam is taken to be an ensemble on noninteracting Gaussian wave packets. The spatial and angular distributions are generated using the computer simulation method. The analysis is concentrated on the rainbow effects, which is clearly seen in the spatial and angular distributions. The obtained classical and quantum rainbows are analyzed in detail and compared with each other. We give a full quantum mechanical explanation of the quantum rainbows.IV Serbian Ceramic Society Conference - Advanced Ceramics and Application : new frontiers in multifunctional material science and processing : program and the book of abstracts; September 21-23, 2015; Belgrad
