  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
wavefunction 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 rapidliy as the wire radius is shrunk, and the bulk
type optical phonon plays the dominant role for the polaron effects.
