Quantum rainbow channeling of positrons in very short carbon nanotubes

Abstract

This is a theoretical study of transmission of positrons of kinetic energies of 1 and 10 MeV through very short $(11,9)$ single-wall carbon nanotubes of lengths of 200 and 560 nm, respectively. The needed continuum interaction potential of the positron and nanotube is obtained starting from the Moli\`ere's approximation of the Thomas-Fermi interaction potential of a positron and a nanotube atom. We calculate the classical and quantum 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 Schr\"odinger equation is solved. The solutions of these equations are obtained numerically. In the quantum calculations, the initial beam is taken to be an ensemble of noninteracting Gaussian wave packets. The angular distributions are generated using the computer simulation method. Our analysis is concentrated on the rainbow effect, which is clearly seen in the angular distributions. The obtained classical and quantum rainbows are analyzed in detail and compared with each other.