  In the theory of diffusive acceleration at oblique shock fronts the question
of the existence of a discontinuity of energetic particle density is
contentious. The resolution of this problem is interesting from a theoretical
point of view, and potentially for the interpretation of observations of
particle densities at heliospheric shocks and of high-resolution radio
observations of the rims of supernova remnants. It can be shown analytically
that an isotropic particle distribution at a shock front implies continuity of
the particle density -- whether or not the shock is oblique. However, if the
obliquity of the shock induces an anisotropy, a jump is permitted. Both
semi-analytic computations and Monte-Carlo simulations are used to show that,
for interesting parameter ranges, a jump is indeed produced, with accelerated
particles concentrated in a precursor ahead of the shock front.
