How many Raman - active vibrations do exist in carbon nanotubes ?

In this paper we present the results on Raman-active modes calculation in achiral (n, n) and (n, 0) carbon nanotubes (CNTs). vibrational spectra are derived as the eigenvalues of corresponding dynamical matrix at the Γ-point of Brillouin zone. Diagonal components and α xy (= α yx) are the only non-zero components of polarization tensor. Selection rules for Raman-active modes are determined by direct estimations of matrix elements responsible for the intensities of corresponding vibrational transitions. Few E 2g modes can be non-Raman-active because of their " fine " vibrational structure. We claim that numbers of Raman-active modes for achiral CNTs are: 5 ((n, n)