  The DAMA/LIBRA collaboration has detected an annual modulation of the recoil
rate in NaI crystals with the phase expected for WIMP scattering events. This
signal is dramatically inconsistent with upper limits from other experiments
for elastically scattering weak-scale WIMPs. However, the results are
compatible for the case of inelastic dark matter (iDM). The iDM theory, as
implemented by Tucker-Smith and Weiner, constrains the WIMP to a tight contour
in sigma_n-delta space, where delta is the mass difference between the ground
state and excited WIMPs. An urgent priority in direct detection is to test this
scenario. The crucial test of the iDM explanation of DAMA -- an "experimentum
crucis" -- is an experiment with directional sensitivity, which can measure the
daily modulation in direction. Because the contrast can be 100%, it is a
sharper test than the much smaller annual modulation in the rate. We estimate
the significance of such an experiment as a function of the WIMP mass, cross
section, background rate, and other parameters. The proposed experiment
severely constrains the DAMA/iDM scenario even with modest exposure (~1000 kg
day) on gaseous xenon.
