Influence of the dynamic polarization effect on the angular distributions of protons channeled in double-wall carbon nanotubes

We investigate the influence of the effect of dynamic polarization of the carbon atom valence electrons on the angular distributions of protons channeled in (6, 4)@(11, 9) double-wall carbon nanotubes. The proton velocities are 3 and 5 a.u., corresponding to energies of 0.223 and 0.621 MeV, while the nanotube lengths are 0.1-0.2 μm. The interaction between a proton and the nanotube atoms is described by the Doyle-Turner potential whereas the image force acting on the proton is calculated by a two-dimensional hydrodynamic model of the dynamic response of the nanotube valence electrons. 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 image force induces additional extrema in the proton deflection functions, giving rise to the rainbow maxima in the angular distributions that do not exist when the proton is subject to the atomic force only. These maxima could be used to probe the total interaction potential in proton channeling in nanotubes.