  In the fallback disk model for the persistent emission of Anomalous X-ray
pulsars (AXPs) and soft gamma-ray repeaters (SGRs), the hard X-ray emission
arises from bulk- and thermal Comptonization of bremsstrahlung photons, which
are generated in the accretion column. The relatively low X-ray luminosity of
these sources implies a moderate transverse optical depth to electron
scattering, with photons executing a small number of shock crossings before
escaping sideways. We explore the range of spectral shapes that can be obtained
with this model and characterize the most important parameter dependencies. We
use a Monte Carlo code to study the crisscrossing of photons in a radiative
shock in an accretion column and compute the resulting spectrum. As expected,
high-energy power-law X-ray spectra are produced in radiative shocks with
photon-number spectral index larger than or about 0.5. We find that the
required transverse optical depth is between 1 and 7. Such spectra are observed
in low-luminosity X-ray pulsars. We demonstrate here with a simple model that
Compton upscattering in the radiative shock in the accretion column can produce
hard X-ray spectra similar to those seen in the persistent and transient
emission of AXPs and SGRs. In particular, one can obtain a high-energy
power-law spectrum, with photon-number spectral index ~ 1 and a cutoff at 100 -
200 keV, with a transverse Thomson optical depth of ~ 5, which is shown to be
typical in AXPs/SGRs.
