A recent composite-dark-matter scenario assumes that the dominant fraction of dark matter consists of O-helium (OHe) dark atoms, in which a lepton-like doubly charged particle O is bound with a primordial helium nucleus. It liberates the physics of dark matter from unknown features of new physics, but it demands a deep understanding of the details of known nuclear and atomic physics, which are still unclear. Here, we consider in detail the physics of the binding of OHe to various nuclei of interest for direct dark matter searches. We show that standard quantum mechanics leads to bound states in the keV region, but does not seem to provide a simple mechanism that stabilizes them. The crucial role of a barrier in the OHe-nucleus potential is confirmed for such a stabilization.
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