Low energy binding of composite dark matter with nuclei as a solution
  for the puzzles of dark matter searches
  Positive results of dark matter searches in experiments DAMA/NaI and
DAMA/LIBRA taken 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 low energy binding 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 a spherically symmetrical potential, 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 values of coupling strength
and mass of meson, mediating scalar isoscalar, are rather uncertain. Within the
uncertainties of parameters of nuclear potential we find a range of these
parameters, 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 germanium state has binding energy with OHe beyond the
range of 2-6 keV and its formation should not lead to ionization in the energy
range of DAMA signal. (abridged)
