Since Haken first investigated the problem of exciton-phonon interaction in polar semiconductor

this field has been greatly studied by other theoretical and experimental methods.Current carrier is restricted at three directions therefore the superposition of hole-electron louds is greatly enhanced

and that lead to the strengthen of coulomb binding energy and oscillator strength

so the effect of exciton play a very important role in semiconductor quantum dot.For the complexing of the exciton's structure

a variety of theoretical model have been adopted to research exciton in semiconductor quantum dot.Such as

under the effectivemass appro-(ximation)

the energy of the ground state and the binding energy of exciton have been calculated by literature in spheroidal

circular and cube quantum dots without considering the effect of the surface polaron.Lin and Zunger using PM method studied the band gap of spheroidal circular and gamma matrix in SI quantum dot.Xie

et al

.studied the properties of exciton in semiconductor quantum dot by using the method of few-body physics.Yosuke Kayanuma and Lavanya

et al

.discussed the quantum sizes effect of exciton in a spherical quantum dot by using variational calculational method.The effective Hamiltonian of weak and middle-coupling surface excitons of the pure 2D polar crystal are obtained by using Huybrecht's linear-combination operator method by Gu

et al

.Under parabolic energy band structure

EMA method been mostly used for its intuition property.In this paper

within the effective mass approximation

the energy of the ground state in GaAs quantum dot is calculated by using linear-combination operator method and only considering the influence of the(electron)-phonon-weak coupling.The properties of exciton in parabolic semiconductor quantum dot are studied by using the methods of a linear-combination operator and unitary transformation.Within the effective-mass approximation

numerical calculations are performed for GaAs semiconductor.The result illustrates that for weak-coupling

the energies of the ground state of the light-hole and the heave-hole excitons will increase with the decreasing of the radius of quantum dot and increase with the increasing ω

0

of the confinement strength.