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.
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