The bound state of dark atom with the nucleus of substance

TL;DR

This paper develops a quantum mechanical model to analyze the formation of bound states between hypothetical dark atoms and atomic nuclei, addressing stability issues and implications for dark matter detection experiments.

Contribution

It introduces a novel numerical approach to model electromagnetic-nuclear couplings in dark atom-nucleus systems, overcoming analytical intractability and validating dark atom hypotheses.

Findings

Demonstrates formation of dark atom-nucleus bound states

Reveals how potential features influence low-energy capture

Supports interpretation of experimental dark matter signals

Abstract

The hypothesis of composite $XHe$ dark atoms offers a compelling framework to address the challenges in direct dark matter particles detection, as their neutral, atom-like configuration evades conventional experimental signatures. A critical issue may arise in interaction between $XHe$ and atomic nuclei due to the unshielded nuclear attraction, which could destabilize the dark atom's bound state. To resolve this, we propose a novel numerical quantum mechanical approach that accounts for self-consistent electromagnetic-nuclear couplings. This method addresses to eliminate the inherent complexity of the $XHe$-nucleus three-body system, where analytical solutions are intractable. By reconstructing the effective interaction potential - including dipole Coulomb barrier and shallow potential well - we demonstrate how these features lead to the formation of $XHe$-nucleus bound states and modulate low-energy capture processes. Our model enables validation of the dark atom hypothesis, particularly in interpreting experimental anomalies like annual modulation signals observed in DAMA/LIBRA. These findings advance the theoretical foundation for dark matter interactions and provide a robust framework for future experimental design.