Anomalous Isotopes In Dark Atoms models

TL;DR

The paper investigates dark atoms formed by a heavy charged particle $X^{--}$ binding with $^4$He to yield neutral bound states $OHe$, and analyzes their potential to generate anomalous isotopes such as $OBe$ during Big Bang Nucleosynthesis. It solves the Schrödinger equation for bound states with a finite-size nucleus, employing a piecewise potential that models the nuclear charge distribution and finds binding energies well below the Coulomb estimate, along with wavefunctions indicating increased core localization. It then estimates reaction rates for dark recombination and subsequent captures using a rescaled Kramers-like formula and an isospin-violating $E1$ capture cross-section, predicting cross-sections around $10^{-36}$ cm$^2$ at $T\sim100$ keV. Using the LINX BBN code, it finds substantial production of anomalous isotopes, notably $OBe$ and $OBe^{++}$, highlighting a significant viability challenge for the dark atom scenario and the need for a more complete network of nuclear processes and possible destruction channels.

Abstract

In this work, we study some aspects of the dark atom model. We consider a finite-size nucleus to find the wave functions of the bound state of a stable particle with a charge of $-2n$ and helium-4 $^4He^{++}$. Then we address the problem of calculating the abundance of anomalous isotopes arising from the capture of helium nuclei by dark atoms during Big Bang nucleosynthesis. We use an analogy with the proton-neutron capture process to calculate the reaction cross section and thus determine the concentration of OBe nuclei.

Figures (2)

• Figure 1: The physical radial functions $R(\rho)=P(\rho)/\rho$ for $X^{-2n}-^4$He (left panel) and electrically neutral $X-N$ bound states.
• Figure 2: Concentrations of bound states during nucleosynthesis