The effects of exciton-optical phonon interaction on the
binding energy and the total and reduced effective masses of an
exciton in a cylindrical quantum wire have been investigated. We
adopt a perturbative-PLL
[T.D. Lee, F. Low, and D. Pines, Phys. Rev. B90
(1953) 297] technique to construct an effective
Hamiltonian and then use a variational solution to deal with
the exciton-phonon system. The interactions of exciton with the
longitudinal-optical phonon and the surface-optical phonon
have been taken into consideration. The numerical
calculations for GaAs show that the influences of phonon modes on
the exciton in a quasi-one-dimensional quantum wire are
considerable and should not be neglected. Moreover the numerical
results for heavy- and light-hole exciton are obtained, which
show that the polaronic effects on two types of excitons are very
different but both depend heavily on the sizes of the wire.