  Based on the tight binding method with hopping integral between the
nearest-neighbor atoms, an oscillator strength $\int_0^{\infty} \d \omega {\rm
Re} \sigma (\omega)$ is discussed for armchair and metallic zigzag carbon
nanotubes. The formulae of the oscillator strength are derived for both types
of nanotubes and are compared with the result obtained by a linear chain model.
In addition, the doping dependence is investigated in the absence of Coulomb
interaction. It is shown that the oscillator strength of each carbon nanotube
shows qualitatively the same doping dependence, but the fine structure is
different due to it's own peculiar band structure. Some relations independent
of the radius of the tube are derived, and a useful formula for determining the
amount of doping is proposed.
