Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves

Energy spectra of particles accelerated by the first-order Fermi mechanism are investigated at ultrarelativistic shock waves, outside the range of Lorentz factors considered previously. For particle transport near the shock a numerical method involving small amplitude pitch angle scattering is applied for flows with Lorentz factors gamma from 3 to 243. For large gamma shocks a convergence of derived energy spectral indices up to the value sigma(infinity) approximate to 2.2 is observed for all considered turbulence amplitudes and magnetic field configurations. Recently the same index was derived for gamma-ray bursts by Waxman [Astrophys. J. Lett. 485, L5 (1997)].