We calculate the spectra of inverse Compton (IC) emissions in gamma-ray burst (GRB) shocks produced when relativistic ejecta encounters the external interstellar medium, assuming a broken power-law approximation to the synchrotron seed spectrum. Four IC processes, including the synchrotron self-Compton (SSC) processes in GRB forward and reverse shocks, and two combined-IC processes (i.e., scattering of reverse shock photons on the electrons in forward shocks and forward shock photons on the electrons in reverse shocks), are considered. We find that the SSC emission from reverse shocks dominates over other emission processes in energy bands from tens of MeV to tens of GeV, for a wide range of shock parameters. This mechanism may be responsible for the prompt high-energy gamma rays detected by EGRET. At TeV energy bands, however, the combined-IC emissions and/or the SSC emission from the forward shocks become increasingly dominant for a moderately steep distribution of shocked electrons.
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