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A class of gamma-ray bursts exists in which the low energy band is delayed in time relative to the high energy band and is also broadened. Scattering in a plasma may be the mechanism causing both the time delay and the broadening. A simulation program has been develped to investiage this. We find that the degree of delay and broadening depends on several parameters such as density and depth of the scattering medium, as well as its temperature, and on the energy and emission period of the photons incident on it. The periodic property of the bursts may disappear after scattering while passing through the medium. In addition, it is found that the auto-correlation function and the cross-correlation function for the scattering can become much more complicated when the source emission is periodic.
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