  We have investigated atom-nanotube van der Waals (vdW) coupling in atomically
doped carbon nanotubes (CNs). Our approach is based on the perturbation theory
for degenerated atomic levels, thus accounting for both weak and strong
atom-vacuum-field coupling. The vdW energy is described by an integral equation
represented in terms of the local photonic density of states (DOS). By solving
it numerically, we demonstrate the inapplicability of standard
weak-coupling-based vdW interaction models in a close vicinity of the CN
surface where the local photonic DOS effectively increases, giving rise to an
atom-field coupling enhancement. An inside encapsulation of atoms into the CN
has been shown to be energetically more favorable than their outside adsorption
by the CN surface. If the atom is fixed outside the CN, the modulus of the vdW
energy increases with the CN radius provided that the weak atom-field coupling
regime is realized (i.e., far enough from the CN). For inside atomic position,
the modulus of the vdW energy decreases with the CN radius, representing a
general effect of the effective interaction area reduction with lowering the CN
curvature.
