Quantum Mechanical Numerical Model for Interaction of Dark Atom with Atomic Nucleus of Matter

Within the framework of the XHe hypothesis, the positive results of the DAMA/NaI and DAMA/LIBRA experiments on the direct search for dark matter particles can be explained by the annual modulation of the radiative capture of dark atoms into low-energy bound states with sodium nuclei. Since this effect is not observed in other underground WIMP (weakly interacting massive particle) search experiments, it is necessary to explain these results by investigating the possibility of the existence of low-energy bound states between dark atoms and the nuclei of matter. Numerical modeling is used to solve this problem, since the study of the XHe–nucleus system is a three-body problem and leaves no possibility of an analytical solution. To understand the key properties and patterns underlying the interaction of dark atoms with the nuclei of baryonic matter, we develop the quantum mechanical description of such an interaction. In the numerical quantum mechanical model presented, takes into account the effects of quantum physics, self-consistent electromagnetic interaction, and nuclear attraction. This approach allows us to obtain a numerical model of the interaction between the dark atom and the nucleus of matter and interpret the results of direct experiments on the underground search for dark matter, within the framework of the dark atom hypothesis. Thus, in this paper, for the first time, steps are taken towards a consistent quantum mechanical description of the interaction of dark atoms, with unshielded nuclear attraction, with the nuclei of atoms of matter. The total effective interaction potential of the OHe–Na system has therefore been restored, the shape of which allows for the preservation of the integrity and stability of the dark atom, which is an essential requirement for confirming the validity of the OHe hypothesis.