We present a study of polaron self-energies in a cylindrical quantum wire considering both volume and surface phonon modes in the dielectric continuum approximation. Full advantage is taken of the problem symmetries, and a generalization of the Lee-Low-Pines unitary transformation has been used. For the interaction with the volume phonon modes, we show that two opposite behaviors can be found for the self-energy as a function of the wire size, depending on whether or not the phonon modes are confined. These results are consistent with those concerning the mass renormalization and the first wire excited-state self-energy. Finally, we have also calculated the polaron self-energy for the electron- surface-phonon interaction showing that in this case the self-energy depends on the difference between the wire and embedding medium dielectric constants; it increases on reducing the wire size and can cross the volume confined polaron self-energy.

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