The effect of electron-optical phonon interaction on the hydrogenic impurity binding energy in a cylindrical quantum wire is studied. By using Landau and Pekar variational method, the Hamiltonian is separated into two parts which contain phonon variable and electron variable, respectively. A perturbative-variational technique is then employed to construct the trial wave function for the electron part. The effect of confined electron-optical phonon interaction on the binding energies of the ground state and an excited state are calculated as a function of wire radius. Both the electron-bulk optical phonon and electron-surface optical phonon coupling are considered. It is found that the energy corrections of the polaron effects on the impurity binding energies increase rapidly as the wire radius is shrunk, and the bulk-type optical phonon plays the dominant role for the polaron effects.
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