  When an excess charge carrier is added to a one-dimensional (1D)
semiconductor immersed in a polar solvent, the carrier can undergo
self-localization into a large-radius adiabatic polaron. We explore the local
optical absorption from the ground state of 1D polarons using a simplified
theoretical model for small-diameter tubular structures. It is found that about
90% of the absorption strength is contained in the transition to the second
lowest-energy localized electronic level formed in the polarization potential
well, with the equilibrium transition energy larger than the binding energy of
the polaron. Thermal fluctuations, however, cause a very substantial -- an
order of magnitude larger than the thermal energy -- broadening of the
transition. The resulting broad absorption feature may serve as a signature for
the optical detection of solvated charge carriers.
