In this paper

the properties of the surface polaron

which is a weak bulk couplingbut a strong surface coupling between the electron and phonon for semi-infinite crystalare sttldied.An effective Hamiltonian of a slow moving surface polaron is derived byusing improved liner combination operator and perturbation method.In the recoil proprocess of an electron

the electron will emit or absorb phonons.Considering the interaction of phonons with different wave vector

the influence of this interaction on the effective Hamiltonian

the induced potential

and the effective mass of surface polaron arediscussed.As an example

the numerical calculation for AgBr crystal has been carried.The results show that the influence of the interaction between phonons of different wavevector in the recoil process on the effective mass and induced potential will be increasedwith increasing coupling constant α1

and the influence on the effective mass will be decreased more with increasing coordinate z

and influence on the induced potential will beincreased more with increasing z.