Dark Atoms of the Universe: towards OHe nuclear physics
  The nonbaryonic dark matter of the Universe is assumed to consist of new
stable particles. A specific case is possible, when new stable particles bear
ordinary electric charge and bind in heavy "atoms" by ordinary Coulomb
interaction. Such possibility is severely restricted by the constraints on
anomalous isotopes of light elements that form positively charged heavy species
with ordinary electrons. The trouble is avoided, if stable particles $X^{--}$
with charge -2 are in excess over their antiparticles (with charge +2) and
there are no stable particles with charges +1 and -1. Then primordial helium,
formed in Big Bang Nucleosynthesis, captures all $X^{--}$ in neutral "atoms" of
O-helium (OHe). Schrodinger equation for system of nucleus and OHe is
considered and reduced to an equation of relative motion in 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 small distances between nuclear
surfaces of He and nucleus. The values of coupling strength and mass of
$\sigma$-meson, mediating scalar isoscalar nuclear potential, are rather
uncertain. Within these uncertainties and in the approximation of rectangular
potential wells and wall we find a range of these parameters, at which the
sodium nuclei have a few keV binding energy with OHe. The result also strongly
depend on the precise value of parameter $d_o$ that determines the size of
nuclei. At nuclear parameters, reproducing DAMA results, OHe-nucleus bound
states can exist only for intermediate nuclei, thus excluding direct comparison
with these results in detectors, containing very light (e.g. $^3He$) and heavy
nuclei (like Xe).
