Study of Focusing Effects during the Channeling of Hydrogen Atoms in Non-Chiral Single-Layer Carbon Nanotubes

The potentials of interaction between hydrogen atoms and nonchiral single-layer nanotubes of (n, 0) and (n, n) types are calculated using the one-particle Lennard-Jones potential. The transverse energy levels and the corresponding wave functions for channeled hydrogen atoms (for example, in nanotubes of the (17, 0) and (10, 10) types with close geometrical parameters) are numerically calculated using the solution of the Sturm-Liouville problem. The probabilities of transitions between these quantum states are studied within the framework of nonstationary perturbation theory, as a result of which diffusion coefficients are calculated. The populations of levels as functions of the longitudinal coordinate and the velocity of a channeled atom are found using the diffusion equation. As a result of construction of the radial probability density functions for the location of hydrogen atoms in the channels of the nanotubes under study, it is shown that atoms are focused in the central region of the nanotubes. In this case, it is shown that the focusing effect increases with decreasing atom velocities and also is manifested more strongly for nonchiral nanotubes of the (n, 0) type.