  Positive results of dark matter searches in DAMA/NaI and DAMA/LIBRA
experiments, being put together with negative results of other groups, can
imply nontrivial particle physics solutions for cosmological dark matter.
Stable particles with charge -2 bind with primordial helium in O-helium "atoms"
(OHe), representing a specific Warmer than Cold nuclear-interacting form of
dark matter. Slowed down in the terrestrial matter, OHe is elusive for direct
methods of underground Dark matter detection like those used in CDMS
experiment, but its reactions with nuclei can lead to annual variations of
energy release in the interval of energy 2-6 keV in DAMA/NaI and DAMA/LIBRA
experiments. Schrodinger equation for system of nucleus and OHe is solved for
spherically symmetrical potential well, formed by the Yukawa tail of nuclear
scalar isoscalar attraction potential, acting on He beyond the nucleus, and
dipole Coulomb repulsion between the nucleus and OHe at distances from the
nuclear surface, smaller than the size of OHe. The window of parameters of this
potential is found, at which the sodium and/or iodine nuclei have a few keV
binding energy with OHe. At nuclear parameters, reproducing DAMA results, the
energy release predicted for detectors with chemical content other than NaI
differ in the most cases from the one in DAMA detector. In particular, it is
shown that in the case of CDMS the energy of OHe-germanium bound state is
beyond the range of 2-6 keV and its formation should not lead to ionization in
the energy interval of DAMA signal. (abridged)
