Since Haken had firstly studied the exciton in polar crystals

a lot of scholars discussed the exciton but many of them mainly concentrated their attention on the weak and intermediate coupling cases. In the early 1970's

Huybrechts proposed a linear combination operator method

by which a strong-coupling polaron was studied.S.W.Gu et al discussed the internal motion of strong-coupling exciton in polar "crystal by using the method advanced by Huybrechts. The properties of the exciton in the surface layer of crystals influenca the optical properties of the crystals very remarkably.Most polar crystals are diatomic.In these crystals there is only one mode of longitudinal optical (LO) phonon. The properties of crystals have been studied by a great variety of techniques

in which discussions are limited only for the case of one LO phonon branch. However

a large number of polar crystals

with several atoms per unit cell

have more than one LO phonon branch. For example

in cuprite such as CuO

2

there are two LO phonon modes and TiO

2

GaAs

1-x

P

x

and

in a large number of perovskites (SrTiO

3

LiNbO

3

....) and quaternary compound semiconductor crystal (AlGaAsSb....) there are more than two modes. In recent years

a lot of scholars investigated the polaron problem of multiple LO phonon branches. However

the exciton in polyatomic polar crystal has not yet been investigated. The ground state energy of the polaron in polyatomic polar crystal is now calculated by using Haga method and the effective Hamiltonian of the exciton in polyatomic polar crystal by means of perturbation method.In this paper

studies on some properties of a strong-coupling surface exciton in polyatomic polar crystals are reported. An effective Hamiltonian of the surfaca exciton is derived by using a linear-combination-operator and Lagrange multiplier method

The renormalized mass of a strong-coupling surface exciton is obtained.In the case of multiple LO phonon branches

the total Hamiltonian of a polyatomic crystal can be written by

<

img style="vertical-align: middle" alt="" order="0" src="http://www.rhhz.net/qikantupian/fgxb-19920106-26-1.gif" /

>

We introduce the creation and annihilation operator b+ and b

<

img style="vertical-align: middle" alt="" order="0" src="http://www.rhhz.net/qikantupian/fgxb-19920106-26-2.gif" /

>

and carrying out the unitary transformation

<

img style="vertical-align: middle" alt="" order="0" src="http://www.rhhz.net/qikantupian/fgxb-19920106-26-3.gif" /

>

The ground state wave function of the system is Φ=φ(p)|0

>

We calculated the effective Hamiltonian and the renormalized mass of surface exciton by variational approach

<

img style="vertical-align: middle" alt="" order="0" src="http://www.rhhz.net/qikantupian/fgxb-19920106-26-4.gif" /

>

.The result indicates that the self-trapping energy and the effective potential of a Wannier exciton can be written as a series in orJ

the first term being proportional to a

the coupling constant. The self-trapping energy and the effective potential not only includes the coupling contribution between the electron-hole and the different LO phonon branches

but also an extra contribution due to crossed terms between the different branches and the different wave vector virtual phonons

which is emitted via the excitonic recoil. The renormalized mass is obtained by Lagrange multiplier method. For Wannier exciton increasing part of the renormalized mass is proportional to a.