Estimating the Lorentz factor and rest frame spectral peak energy of gamma-ray bursts with the opening angle of jets

The rest frame spectral peak energy and the Lorentz factor of the bulk motion of gamma-ray bursts for a current sample of jets, suggested by the break time observed in the afterglow light curve, are estimated, assuming that the prompt emission is beamed. We take \\gamma_jet = 1/\\theta_jet,and adopt the law of to estimate the Lorentz factor at the time of the beginning of the afterglow, taft.We collect the earliest time when the afterglow is detected, tearly, and the duration of the prompt emission, tdur, and then allow them to represent taft respectively. When taking taft ? tdur, the results are statistically reasonable. We find in this situation that the Lorentz factor of this sample would peak at 200 and would be distributed mainly within (100, 400), and the peak of the distribution of the rest frame peak energy would be 1keV and its main region would be (0.3keV, 3keV). Logarithmic distributions of the two quantities are well fitted with a Gaussian. By comparing the two well-known mechanisms we find that, during the epoch of the afterglow, the dominated process is likely to be adiabatic rather than radiative.