Exciton states in cylindrical nanowires

The exciton ground state and excited state energies are calculated 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. Within the adiabatic approximation, we obtain `exact' numerical results for the effective exciton potential and the lowest exciton energy levels which are fitted to simple analytical expressions. Furthermore, we investigated the influence of a magnetic field parallel to the nanowire on the effective potential and the exciton energy.