Localized atomic vibrations caused by point impurity in long chains of noble gas atoms adsorbed in outer grooves of carbon nanobundle

The characteristics of discrete vibrational levels caused by a point three-parameter substitutional impurity in long linear chain of inert gas atoms adsorbed in groove on the surface of carbon nanobundle are studied. The impurity atom differs from the atoms of the chain in the following parameters: the mass, the parameter of interaction with neighboring atoms and the parameter of interaction with the substrate. Analytical expressions for the frequencies of the localized vibrations and the intensities of these vibrations are obtained. The conditions for the existence of localized vibrations both below and above the band of the quasi-continuous spectrum of the adsorbed chain are also obtained.