Quantum-mechanical numerical model of interaction between dark atom and nucleus of substance

Abstract

The hypothesis of composite $XHe$ dark atoms may provide solution to the long-standing problem of direct searches for dark matter particles. The main problem of the $XHe$ dark atom is its ability to strongly interact with the nucleus of substance, arising from the unshielded nuclear attraction between the helium nucleus and the nucleus of matter. It is assumed that in order to prevent the destruction of the bound structure of dark atom, the effective potential of interaction between $XHe$ and the nucleus of substance must have dipole Coulomb barrier that prevents the fusion of dark matter atom particles with the nucleus of substance. The problem in describing the interaction between dark atom and substance nucleus is the three-body problem, for which an exact analytical solution is not available. Consequently, to assess the physical meaning of the proposed scenario, it is essential to develop a numerical approach. Our approach involves consistently developing an accurate quantum mechanical description of this three-body system, comprising bound dark atom and the external nucleus of substance. We incorporate the necessary effects and interactions to enhance the precision of the results, which helps to elucidate the most significant aspects of the proposed dark atom scenario.