We develop a theory to calculate exciton binding energies of both two- and three-dimensional spin polarized exciton gases within a mean field approach. Our method allows the analysis of recent experiments showing the importance of the polarization and intensity of the excitation light on the exciton luminescence of GaAs quantum wells. We study the breaking of the spin degeneracy observed at high exciton density (5×${10}^{10}$ ${\mathrm{cm}}^2$). Energy level splitting between spin +1 and spin -1 is shown to be due to many-body interexcitonic exchange while the spin relaxation time is controlled by intraexciton exchange. © 1996 The American Physical Society.

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