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Assuming that AXPs and SGRs accrete matter from a fallback disk, we attemptto explain both the soft and the hard X-ray emission as the result of theaccretion process. We also attempt to explain their radio emission or the lackof it. We test the hypothesis that the power-law, hard X-ray spectra areproduced in the accretion flow mainly by bulk-motion Comptonization of softphotons emitted at the neutron star surface. Fallback disk models invokesurface dipole magnetic fields of $10^{12} - 10^{13}$ G, which is what weassume here. Unlike normal X-ray pulsars, for which the accretion rate ishighly super-Eddington, the accretion rate is approximately Eddington in AXPsand SGRs and thus the bulk-motion Comptonization operates efficiently. As anillustrative example we reproduce both the hard and the soft X-ray spectra ofAXP 4U 0142+61 well using the XSPEC package compTB. Our model seems to explainboth the hard and the soft X-ray spectra of AXPs and SGRs, as well as theirradio emission or the lack of it, in a natural way. It might also explain theshort bursts observed in these sources. On the other hand, it cannot explainthe giant X-ray outbursts observed in SGRs, which may result from theconversion of magnetic energy in local multipole fields.

The Energy Spectrum of Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters