  We analytically study diffusive particle acceleration in relativistic,
collisionless shocks. We find a simple relation between the spectral index s
and the anisotropy of the momentum distribution along the shock front. Based on
this relation, we obtain s = (3beta_u - 2beta_u*beta_d^2 + beta_d^3) / (beta_u
- beta_d) for isotropic diffusion, where beta_u (beta_d) is the upstream
(downstream) fluid velocity normalized to the speed of light. This result is in
agreement with previous numerical determinations of s for all (beta_u,beta_d),
and yields s=38/9 in the ultra-relativistic limit. The spectrum-anisotropy
connection is useful for testing numerical studies and for constraining
non-isotropic diffusion results. It implies that the spectrum is highly
sensitive to the form of the diffusion function for particles travelling along
the shock front.
