Quantum-Mechanical Description of Dark Atom-Nucleus Bound States

We present numerical quantum mechanical description of the formation of low-energy bound states between a dark atom [Formula: see text]He (a neutral atom-like composite of a heavy doubly charged particle [Formula: see text] and a helium nucleus) and ordinary nuclei, with a focus on sodium and iodine. The total effective interaction potential is reconstructed by combining self-consistent nuclear, electromagnetic and centrifugal contributions. For the [Formula: see text]He-Na system, a single shallow bound state is found with binding energy in the 1-6 keV range, which naturally accounts for the annual modulation signal observed by the DAMA/LIBRA experiment if the radiative capture proceeds via an E1 transition. For the [Formula: see text]He-I system, the potential well is much deeper, leading to bound states with energies of order hundreds of keV to MeV and to strongly suppressed capture cross sections, in agreement with the absence of a modulation signal from iodine and with the upper limits on high-energy gamma rays from DAMA. The framework provides a consistent explanation for the target-material dependence in direct dark matter searches and highlights the importance of quantum effects of atomic and nuclear physics in the interpretation of underground detector signals.