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We revisit the high-energy spectral cutoff originating from theelectron-positron pair creation in the prompt phase of gamma-ray bursts (GRBs)with numerical and analytical calculations. We show that the conventionalexponential and/or broken power law cutoff should be drastically modified to ashallower broken power-law in practical observations that integrate emissionsfrom different internal shocks. Since the steepening is tiny for observations,this "smearing" effect can generally reduce the previous estimates of theLorentz factor of the GRB outflows. We apply our formulation to GRB 080916C,recently detected by the Large Area Telescope detector on the Fermi satellite,and find that the minimum Lorentz factor can be ~600 (or even smaller values),which is below but consistent with the previous result of ~900. Observing thesteepening energy (so-called "pair-break energy") is crucial to diagnose theLorentz factor and/or the emission site in the future observations, especiallycurrent and future Cherenkov telescopes such as MAGIC, VERITAS, and CTA.

Can we probe the Lorentz factor of gamma-ray bursts from GeV-TeV spectra integrated over internal shocks?