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The bound state of dark atom with the nucleus of substance

T. E. Bikbaev, M. Yu. Khlopov, A. G. Mayorov

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.

The bound state of dark atom with the nucleus of substance

Abstract

The hypothesis of composite 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 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 -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 -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.

Paper Structure

This paper contains 4 sections, 25 equations, 3 figures.

Table of Contents

  1. Dark atoms of $X$-helium
  2. Low energy binding of dark atoms to nuclei
  3. Calculation of the cross-section of radiative capture in the OHe-nucleus system
  4. Conclusions

Figures (3)

  • Figure 1: Hypothetical qualitative image of the shape of the effective interaction potential of $X$He dark atom with the nucleus of atom of matter Khlopov:2010ik.
  • Figure 2: Interaction potentials within the OHe--Na system, presented as functions of the distance between the OHe dark atom and nucleus of Na, ${R}_{OA}$: the Stark potential (red dotted curve), the centrifugal potential (green dotted curve), nuclear potential (black dotted curve), the electric interaction potential $U_{\rm XHe}^{\rm e}$ of unpolarized dark atom with the nucleus (yellow dotted curve) and the total effective interaction potential (blue dotted curve). This particular configuration corresponds to a total angular momentum quantum number for the OHe-sodium nucleus interaction of $\Vec{J}_{\rm OHe-Na} = \overrightarrow{5/2}$. The calculations were performed utilizing the results of the Bikbaev_2025 paper.
  • Figure 3: The figure illustrates the dependence of the total effective interaction potential between the $O$He dark atom and the sodium nucleus (solid blue curve) and the probability density given by the squared modulus of the wave function (solid red curve) from the radius vector of sodium nucleus. Squared modulus of the wave function correspond to the ground state energy level of $E_{1_{Na}}\approx-2.4\space\text{keV}$ for sodium within the $O$He--$Na$ system's effective potential.