The properties of exciton in the surface layer of crystals influence the optical properties of the crystals very remarkably. In recent years

many scholars

[1-2]

discussed the properties of the surface exciton. Most polar crystals are diatomic. In these crystals there is one mode of the longitudinal optical (LO) phonon. However

a large number of polar crystals

with several atoms per unit cell

have more than one LO phonon branch. In recent years the polar on problem with many LO phonon branches has been studied

[3-4]

. However

the exciton in polyatomic polar crystals has not been investigated so far. The ground state energy of a weak

intermediate and strong coupling exciton in polyatomic polar crystals has been obtained by means of perturbation and linear -combination-operator method by one of authors

[5-6]

. Recently the effective Hamiltonian of the surface exciton in polyatomic polar crystals was derived by using perturbation method by author

[7]

. When we consider the interaction between phonons of different wave vector in the recoil process

the influence on effective potential between the electron and the hole

the self-trapping energy and the self-trapping condition are discussed.The Hamiltonian of a polyatomic surface exciton-phonon system is

<

img style="vertical-align: middle" alt="" order="0" src="http://www.rhhz.net/qikantupian/fgxb-19920408-331.gif" /

>

. We introduce two unitary transformations U

1

and U

2

.