  We compute the exciton transfer (ET) rate between semiconducting single-wall
carbon nanotubes (SWNTs). We show that the main reasons for the wide range of
measured ET rates reported in the literature are 1) exciton confinement in
local quantum wells stemming from disorder in the environment and 2) exciton
thermalization between dark and bright states due to intratube scattering. The
SWNT excitonic states are calculated by solving the Bethe-Salpeter equation
using tight-binding basis functions. The ET rates due to intertube Coulomb
interaction are computed via Fermi's golden rule. In pristine samples, the ET
rate between parallel (bundled) SWNTs of similar chirality is very high ($\sim
10^{14}\;\text{s}^{-1}$) while the ET rate for dissimilar or nonparallel tubes
is considerably lower ($\sim 10^{12}\;\text{s}^{-1}$). Exciton confinement
reduces the ET rate between same-chirality parallel SWNTs by two orders of
magnitude, but has little effect otherwise. Consequently, the ET rate in most
measurements will be on the order of $ 10^{12}\;\text{s}^{-1}$, regardless of
the tube relative orientation or chirality. Exciton thermalization between
bright and dark states further reduces the ET rate to about
$10^{11}\;\text{s}^{-1}$. The ET rate also increases with increasing
temperature and decreases with increasing dielectric constant of the
surrounding medium.
