We calculate the synchrotron self-Compton emission from internal shocks occurring in relativistic winds as a source of gamma-ray bursts, with allowance for self-absorption. For plausible model parameters most pulses within a Gamma-Ray Burst (GRB) are optically thick to synchrotron self-absorption at the frequency at which most electrons radiate. Up-scattering of photon number spectra harder than ν⁰ (such as the self-absorbed emission) yields inverse Compton photon number spectra that are flat, therefore our model has the potential of explaining the low-energy indices harder than ν-2/3 (the optically thin synchrotron limit) that have been observed in some bursts. The optical counterparts of the model bursts are sufficiently bright to be detected by such experiments as LOTIS, unless the magnetic field is well below equipartition.
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