This book discusses the effects modeling latest results and nanotechnology applications of
rainbows that appear during channeling of charged particles in crystals and nanotubes. The
authors begin with a brief review of the optical and particle rainbow effects followed by a
detailed description of crystal rainbows which appear in ion channeling in crystals and their
modeling using catastrophe theory. The effects of spatial and angular focusing of channeled
ions are described with special attention given to the applications of the former effect to
subatomic microscopy. The results of a thorough study of the recent high-resolution channeling
experiments performed with protons of energies between 2.0 and 0.7 MeV and a 55 nm thick
silicon crystal are also provided. This study opens up the potential for accurate analysis of
very thin crystals. Also presented are recent results related to rainbows occurring in proton
transmission through carbon nanotubes and a detailed quantum consideration of the transmission
of positrons of an energy of 1 MeV through very short carbon nanotubes. This process is
determined by the rainbow effect. The initial positron beam is represented as an ensemble of
non-interacting Gaussian wave packets and the principal and supernumerary primary rainbows
appearing in the spatial and angular distributions of transmitted positrons are clearly
identified. They are explained by the effects of wrinkling concentration and coordination of
the wave packets.
