Van der Waals interaction between microparticle and uniaxial crystal with application to hydrogen atoms and multiwall carbon nanotubes

The Lifshitz theory of the van der Waals force is extended for the case of an atom (molecule) interacting with a plane surface of a uniaxial crystal or with a long solid cylinder or cylindrical shell made of isotropic material or uniaxial crystal. For a microparticle near a semispace or flat plate made of a uniaxial crystal, the exact expressions for the free energy of the van der Waals and Casimir-Polder interaction are presented. An approximate expression for the free energy of microparticle-cylinder interaction is obtained which becomes precise for microparticle-cylinder separations much smaller than the cylinder radius. The obtained expressions are used to investigate the van der Waals interaction between hydrogen atoms (molecules) and graphite plates or multiwall carbon nanotubes. To accomplish this, the behavior of graphite dielectric permittivities along the imaginary frequency axis is found using the optical data for the complex refractive index of graphite for the ordinary and extraordinary rays. It is shown that the position of hydrogen atoms inside multiwall carbon nanotubes is energetically preferable compared with outside.