The exciton ground state and excited state energies are obtained within the single band approximation for a model system of an infinitely long cylindrical wire. The effective Coulomb potential between the electron and the hole is studied as function of the wire radius and difference in dielectric permittivity inside and outside of the wire. Within the adiabatic approximation, we obtain “exact” numerical results for the effective exciton potential and the lowest exciton energy levels. The effective exciton potential is fitted to a tractable analytical expression that will facilitate further calculations.

• Received 18 July 2006

DOI:https://doi.org/10.1103/PhysRevB.74.235321