  We revisit the WIMP-type dark matter scattering on electrons that results in
atomic ionization, and can manifest itself in a variety of existing
direct-detection experiments. Unlike the WIMP-nucleon scattering, where current
experiments probe typical interaction strengths much smaller than the Fermi
constant, the scattering on electrons requires a much stronger interaction to
be detectable, which in turn requires new light force carriers. We account for
such new forces explicitly, by introducing a mediator particle with scalar or
vector couplings to dark matter and to electrons. We then perform state of the
art numerical calculations of atomic ionization relevant to the existing
experiments. Our goals are to consistently take into account the atomic physics
aspect of the problem (e.g., the relativistic effects, which can be quite
significant), and to scan the parameter space: the dark matter mass, the
mediator mass, and the effective coupling strength, to see if there is any part
of the parameter space that could potentially explain the DAMA modulation
signal. While we find that the modulation fraction of all events with energy
deposition above 2 keV in NaI can be quite significant, reaching ~50%, the
relevant parts of the parameter space are excluded by the XENON10 and XENON100
experiments.
