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Spectral and energetic characteristics of the cooperative recombination of high density electrons and holes in bulk GaAs are experimentally studied at room temperature. It is shown that the properties and parameters of femtosecond superradiant pulses are conditioned by the collective properties of electrons and holes. Electron-hole pairing and the formation of a short-living coherent e-h BCS state distinguish strongly the regime of cooperative emission from all radiative e-h recombination regimes, which have been observed earlier. The dependences of the energy gap (the order parameter), the Fermi energy, and the band gap of the coherent e-h BCS state on the concentration of electron-hole pairs are obtained.