Evolution of the Spatial Distribution of Hydrogen Atoms Channeling along Non-Chiral Carbon Nanotubes

Abstract

The exact potentials of the interaction of channeled hydrogen atoms with non-chiral carbon nanotubes of \(\left( {n,0} \right)\) and \(\left( {n,n} \right)\) types are calculated using the Lennard-Jones potential. After expansion in a two-dimensional Fourier series of one-dimensional reciprocal lattice vectors and azimuthal harmonics, these potentials are used to analyze the motion of atoms in the channel. Numerical solution of the Schrödinger equation with the averaged electrostatic interaction potential for a \(\left( {10,10} \right)\) nanotube ensures discrete transverse energy levels and corresponding wave functions. The evolution of the spatial distribution of channeled hydrogen atoms moving in the longitudinal direction under the influence of the periodic perturbing interaction potential as a function of the longitudinal velocity is studied by means of fundamental solution of the kinetic equation. The ability to induce the focusing effect at the center of a nanotube for moving hydrogen atoms is shown as well.