Diffraction and channeling in nanotubes

A theory of the interaction of fast charged particles and gamma rays with nanotubes with different helicity is developed. Analytical expressions are obtained for the potential and the electron density of a nanotube taking account of the anisotropic thermal vibrations of the atoms. A system of equations determining the quantum states of the transverse motion of relativistic electrons, positrons, and x-ray photons in a superlattice consisting of nanotubes is formulated, and methods for solving this system are developed. Calculations of the soft x-ray Bragg reflection coefficients of a superlattice are performed in the two-wave approximation of the dynamical theory of diffraction.