New Types of Hydrogenlike matter Composed of Electron(s) and Meson(s)

TL;DR

This paper predicts new hydrogenlike matter composed of electrons and mesons, calculates their binding energies and bond lengths, and discusses potential implications for exotic hadronic states.

Contribution

It introduces and theoretically analyzes new hydrogenlike atoms, ions, and molecules involving mesons, providing binding energies, bond lengths, and considering strong interactions.

Findings

Hydrogenlike atoms have binding energy $E_n=-\frac{1}{2n^2}$.

Binding energies for molecular ions and molecules are approximately -0.587 and -1.139 atomic units.

Strong interaction effects are negligible on these hydrogenlike systems.

Abstract

In the present work, we predict the existence of new types of hydrogenlike matter, including hydrogenlike atoms ($\pi^+e^-$, $K^+e^-$, $D^+e^-$), hydrogenlike molecular ions ($\pi^+\pi^+e^-$, $K^+K^+e^-$, $D^+D^+e^-$) and hydrogenlike molecules ($\pi^+\pi^+e^-e^-$, $K^+K^+e^-e^-$, $D^+D^+e^-e^-$). By solving the Schr\"{o}dinger equation, the binding energy of hydrogenlike atoms is obtained as $E_n=-\frac{1}{2n^2}$. For hydrogenlike molecular ions and molecules, the variational method is employed to calculate the binding energies, i.e., $E_+=-0.587$ and $E_0=-1.139$ for hydrogenlike molecular ions and molecules, respectively. And the bond lengths for hydrogenlike molecular ions and molecules are also calculated, whose values are $2.003$ and $1.414$, respectively. Here all the quantities are in atomic units for convenience. In addition, the strong interaction between the two constituent mesons is considered in our calculations, where we find that its influence on the hydrogenlike molecular ions and molecules can be neglected. Comparisons of hydrogenlike molecular ion and molecule with the systems governed by the strong interaction are made, which suggests the possible existence of doubly heavy triquark, hidden heavy-flavor tetraquarks and doubly heavy tetraquarks. Hopefully, these types of matter would be observed in the future with the improvement of accuracy in the high energy physical experiments.