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

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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 αxy (=αyx) 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 E₂g 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) and (n,0), n-even); 6 ((n,n), n-odd); 8 ((n,0), n-odd).