Numerical Modeling of the Interaction of Dark Atoms with Nuclei to Solve the Problem of Direct Dark Matter Search

Abstract

The puzzle of the direct dark matter search can be resolved by examining the concept of «dark atoms», which consist of hypothetical stable lepton-like particles with a charge of −2n, where n is any natural number, bound to n nuclei of primordial helium. These «dark atoms», known as «XHe» (X-helium) atoms, remain undiscovered in experiments due to their neutral atom-like states. In this model, the positive results of the DAMA/NaI and DAMA/LIBRA experiments could be explained by the annual modulation of radiative capture of XHe atoms engaging in low-energy bound states with sodium nuclei. This specific phenomenon does not occur under the conditions of other underground experiments. The proposed solution to this puzzle involves establishing the existence of a low-energy bound state of «dark atoms» and nuclei while also considering the self-consistent influence of nuclear attraction and Coulomb repulsion. Resolving this complex issue, which has remained unsolved for the past 17 years, necessitates a systematic approach. To tackle this problem, numerical modeling is employed to uncover the fundamental processes behind the interaction of «dark atoms» with nuclei. To comprehend the essence of XHe’s interaction with baryonic matter nuclei, a classical model is employed wherein quantum physics and nuclear size effects are progressively incorporated. A numerical model describing the interaction between XHe «dark atoms» and nuclei is developed through the continuous inclusion of realistic features of quantum mechanics in the initial classical three-body problem involving the X-particle, the helium nucleus, and the target nucleus. This approach yields a comprehensive numerical model that encompasses nuclear attraction and electromagnetic interaction between the «dark atom» and nuclei. Finally, this model aids in supporting the interpretation of the results obtained from direct underground dark matter experiments through the lens of the «dark atom» hypothesis.