  It is usually assumed that WIMPs interact through spin-independent and
spin-dependent interactions. Interactions which carry additional powers of the
momentum transfer, q^2, are assumed to be too small to be relevant. In theories
with new particles at the ~ GeV scale, however, these q^2-dependent
interactions can be large, and, in some cases dominate over the standard
interactions. This leads to new phenomenology in direct detection experiments.
Recoil spectra peak at non-zero energies, and the relative strengths of
different experiments can be significantly altered. We present a simple
parameterization for models of this type which captures much of the interesting
phenomenology and allows a comparison between experiments. As an application,
we find that dark matter with momentum dependent interactions coupling to the
spin of the proton can reconcile the DAMA annual modulation result with other
experiments.
