The $s{p}^3$ tight-binding model is used to calculate electronic structures of single-walled carbon nanotubes. The static dielectric function is evaluated from the random-phase approximation. $ϵ$ strongly depends on the momentum $\left(q\right)$ and angular momentum $\left(L\right)$ transfer in the $e\text{‐}e$ interactions. $ϵ$ of $L=1$ at long wavelength limit represents the screening ability in the presence of a uniform transverse electric field. $ϵ(q=0,L=1)$ mainly comes from the $p\pi$ electrons, but not the $s{p}^2\sigma$ electrons. The external field is greatly reduced. The dependence of $ϵ(q=0,L=1)$ on the chiral angle, the nanotube radius, the magnetic flux, and the temperature is not strong. The transverse dielectric screening is largely enhanced by the increasing free carriers in conduction bands.

• Received 27 June 2005

DOI:https://doi.org/10.1103/PhysRevB.72.193412