In thispaper,some propertiesofasurfaceexciton in polyatomicpolarcrystalsare studied, Effective Hamiltonians in the ground state of the surface exciton for both strongcoupling and weak-couplingpolyatomic polar crystals are obtained by the method of alinear combination operator and simple unitary transformation. The effective mass of a strongcoupling surface exciton is derived using a Lagrange multiplier method. The self-trapping energy and effective potential of the surface exciton could be written as a series in ru;'. the lint term being proportional to rus, the coupling constant. The self-trapping energy and effective potential contain an extra contribution due to crossed t e r m between the different phonon branches. For a surface Wannier exciton the increasing part of the effective mass is proportional to a;

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