We investigated the phonon symmetries in the Raman spectra of single and mu
ltiwall nanotubes. By using linearly and circularly polarized light we meas
ured the Raman tensor invariants on unoriented carbon nanotubes, The ratio
between the antisymmetric and the isotropic invariant shows that Raman scat
tering in semiconducting single wall tubes is mainly due to fully symmetric
A(1(g)) phonons with a strongly uniaxial Raman tensor. With the help of re
cent experiments on aligned nanotubes we calculate the relative intensities
for the high-energy modes of different symmetry. Compared to single wall t
ubes the intensity of the E-1(g) and E-2(g) symmetry phonons in multiwall t
ubes is 1.5 times stronger. The antisymmetric component of the resonant Ram
an process was found to be zero in all measurements.