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The Fourier transform v(p) of the exciton–exciton interaction energy is derived. The excitons are situated in a semiinfinite polar crystal near the surface. The character of the interaction depends essentially on the symmetry of the spin functions under the permutation of identical particles. On the base of v(p) the shift of the surface excitons level with increasing exciton density nex is obtained. The numerical value is listed for GaAs. The effective Hamiltonian of surface excitons interacting through exchange by virtual surface longitudinal optical phonons is derived.
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Bobrysheva et al. (1980) studied this question.
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