Dark atom solution for the puzzles of direct dark matter search

: The puzzle of direct dark matter searches can b solved in the model of an O He dark atom, which consists of a stable O −− lepton core and a nuclear interacting (alpha particle) shell of a primordial helium nuclei. In this model, positive results of the DAMA group can be explained by annual modulation of radiative capture of O He atoms to low-energy bound states with sodium nuclei, which does not take place under the conditions of other underground experiments. The existence of such a low-energy bound state is the key problem of the O He model of composite dark matter. The complexity of this problem, which has not found a correct solution during the last 15 years, requires a consistent approach to its solution. Within the framework of the proposed approach to such modeling, in order to reveal the essence of the processes of interaction of O He with the nuclei of baryonic matter, a classical model is used, to which the effects of quantum physics and final size of nuclei are successively added. The numerical model of the interaction of the “dark” O He atom with the nuclei is developed by successive addition of realistic features of a quantum-mechanical description to the initial classical problem of three point-like bodies ( O −− particle, the He nucleus and the target nucleus). The developed approach leads to a numerical model describing the O He-nucleus system with self-consistent accounting for nuclear attraction and electromagnetic interaction of dark atom with nuclei. The model can prove the interpretation of the results of the direct underground experimental dark matter search in the terms of the dark atom hypothesis.