Towards Nuclear Physics of OHe Dark Matter
  The nonbaryonic dark matter of the Universe can consist of new stable charged
particles, bound in heavy "atoms" by ordinary Coulomb interaction. If stable
particles $O^{--}$ with charge -2 are in excess over their antiparticles (with
charge +2), the primordial helium, formed in Big Bang Nucleosynthesis, captures
all $O^{--}$ in neutral "atoms" of O-helium (OHe). Interaction with nuclei
plays crucial role in the cosmological evolution of OHe and in the effects of
these dark atoms as nuclear interacting dark matter. Slowed down in terrestrial
matter OHe atoms cause negligible effects of nuclear recoil in underground
detectors, but can experience radiative capture by nuclei. Local concentration
of OHe in the matter of detectors is rapidly adjusted to the incoming flux of
cosmic OHe and possess annual modulation due to Earth's orbital motion around
the Sun. The potential of OHe-nucleus interaction is determined by polarization
of OHe by the Coulomb and nuclear force of the approaching nucleus. Stark-like
effect by the Coulomb force of nucleus makes this potential attractive at
larger distances, while change of polarization by the effect of nuclear force
gives rise to a potential barrier, preventing merging of nucleus with helium
shell of OHe atom. The existence of the corresponding shallow well beyond the
nucleus can provide the conditions, at which nuclei in the matter of DAMA/NaI
and DAMA/LIBRA detectors have a few keV binding energy with OHe, corresponding
to a level in this well. Annual modulation of the radiative capture rate to
this level can reproduce DAMA results. The OHe hypothesis can qualitatively
explain the controversy in the results of direct dark matter searches by
specifics of OHe nuclear interaction with the matter of underground detectors.
