Effect of conversion efficiency on gamma-ray burst energy

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 (eta(gamma)), 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 eta(gamma), and found that the gamma-ray energy release is narrowly clustered, whether we use a constant value of eta(gamma) or random values for different gamma-ray bursts.