We calculate the spectral index of particles accelerated at oblique shocks by a combination of the first-order Fermi mechanism and the shock drift mechanism. By assuming that particles conserve their magnetic moment on crossing the shock, and are scattered in pich angle by turbulence both upstream and downstream of the shock, it is shown that oblique shocks lead to flatter spectra than parallel shocks. Synchrotron spectral indices as low as α ∼ 0 are predicted for highly oblique shocks. Only for extremely non-relativistic shocks is the spectral index independent of the angle between the magnetic field and the shock normal.
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Kirk et al. (1989) studied this question.