  The old and still not solved problem of dark atom solution for the puzzles of
direct dark matter searches is related with rigorous prove of the existence of
a low energy bound state in the dark atom interaction with nuclei. Such prove
must involve a self-consistent account of the nuclear attraction and Coulomb
repulsion in such interaction. In the lack of usual small parameters of atomic
physics like smallness of electromagnetic coupling of the electronic shell or
smallness of the size of nucleus as compared with the radius of the Bohr orbit
the rigorous study of this problem inevitably implies numerical simulation of
dark atom interaction with nuclei. Our approach to such simulations of
$OHe-$nucleus interaction involves multi-step approximation to the realistic
picture by continuous addition to the initially classical picture of three
point-like body problem essential quantum mechanical features.
