Comparison of the stopping power of plasmons and single-particle excitations for nanotubes

We consider the motion of a charged particle near the surface of a single-walled cylindrical nanotube of radius R. We formulate the problem by considering the case when the charged particle moves parallel to the axis of the nanotube. We calculate the frictional force on the particle due to the electrostatic interaction with the electrons on the surface of the nanotube in terms of its polarization function. We compare the contributions to the energy loss from the plasmons and particle-hole modes as a function of r(0), the impact parameter of the charged particle on the axis of the nanotube. Our calculations show that the plasmon contribution exceeds that from particle-hole modes when the charged particle is not moving close to the surface of the cylinder. However, when R approximate to r(0), the role of these excitations is reversed. We also calculate the image potential of the cylindrical nanotube and show that the effective potential for a charged particle has bound states.