Influence of the dynamical image potential on the rainbows in ion channeling through short carbon nanotubes

We investigate the influence of the dynamic polarization of the carbon valence electrons on the angular distributions of protons channeled through short (11,9) single-wall carbon nanotubes at speeds of 3 and 5 a.u. (corresponding to the proton energies of 0.223 and 0.621 MeV), with the nanotube length varied from 0.1 to 0.3 mu m. The dynamic image force on protons is calculated by means of a two-dimensional hydrodynamic model for the nanotube's dielectric response, whereas the repulsive interaction with the nanotube's cylindrical wall is modeled by a continuum potential based on the Doyle-Turner interatomic potential. The angular distributions of channeled protons are generated by a computer simulation method using the numerical solution of the proton equations of motion in the transverse plane. Our analysis shows that the inclusion of the image interaction causes qualitative changes in the proton deflection function, giving rise to a number of rainbow maxima in the corresponding angular distribution. We propose that observations of those rainbow maxima could be used to deduce detailed information on the relevant interaction potentials, and consequently to probe the electron distribution inside carbon nanotubes.