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Discrete peaks are seen in the photoluminescence excitation spectra of GaAs-(AlGa)As multiple-quantum-well samples which we identify as the excited $2s$ state of the $n=1$ heavy- and light-hole excitons. The 1s-2s splitting of the excitons is accurately determined and combined with calculations of the $2s$ heavy-hole exciton binding energy to give an accurate determination of the binding energy of the ground state.
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Dawson et al. (1986) studied this question.
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