Abstract Beaming effect makes it possible that gamma-ray bursts have a standard energy, but the gamma-ray energy release is sensitive to some parameters. Our attention is focused on the effect of the gamma ray conversion efficiency ( \etaγ), which may range between 0.01 and 0.9, and which probably has a random value for different GRBs under certain conditions. Making use of the afterglow data from the literature, we carried out a complete correction to the conical opening angle formula. Within the framework of the conical jet model, we ran a simple Monte Carlo simulation for random values of \etaγ, and found that the gamma-ray energy release is narrowly clustered, whether we use a constant value of \etaγ or random values for different gamma-ray bursts.
Keywords gamma rays: bursts --- ISM: jets
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