  Gravitational collapse of dark matter, merger of dark matter haloes and tidal
disruption of satellites are among processes which lead to the formation of
fine and dense dark matter shells, also known as dark matter caustics. The
putative weakly interacting species which may form the dark matter are expected
to strongly annihilate in these dense regions of the Milky Way halo and
generate in particular antiprotons and positrons. We derive the flux of these
rare antimatter particles at the Earth and show that it depends significantly
on the cut-off radius of the dark matter distribution at the galactic centre.
Boost factors of ~30 are found with respect to a smooth NFW profile for
high-energy antiprotons and low-energy positrons if this cut-off radius is
taken to be 300 pc -- a somewhat extreme value though. This yields a detectable
antiproton signal around hundreds of Gev in models where the annihilation cross
section today is enhanced by non--perturbative effects as in the generic case
of a heavy Wino. However, dark matter caustics cannot provide a better
explanation for the HEAT excess reported above ~10 GeV than a smooth NFW or
isothermal cored distribution.
