Rainbow effect in channeling of high energy protons through single-wall carbon nanotubes

We studied theoretically the angular distributions and the rainbows in the case of 1 GeV protons channeled in the ropes of (10, 10) single-wall carbon nanotubes. It was assumed that the transverse cross section of a rope could be described via a (two-dimensional) hexagonal superlattice with one nanotube per lattice point. The rope length was varied between 2.4 and 7.2 μm, corresponding to the reduced rope lengths associated with the transverse proton motion close to the centers of the regions in between three neighboring nanotubes, Λb, between 0.17 and 0.50, respectively. The angular distributions of channeled protons were generated by the computer simulation method using the numerical solution of the proton equations of motion in the transverse plane. We used the Molière's expression for the interaction potential of the proton and a carbon atom. The rainbow lines were determined numerically too. We showed that they ensured the full explanation of the angular distributions. The effect of zero-degree focusing of channeled ions for the reduced rope length Λb = 0.50 was also observed, indicating the existence of the rainbow cycles in the evolution of the angular distribution. We noted a strong influence of the rainbow effect on the effect of zero-degree focusing.