Possible Existence of Charmonium-Nucleus Bound States

TL;DR

This paper investigates the potential for bound states between charmonium particles and nuclei, using Gaussian potentials to relate scattering lengths to binding energies, suggesting certain conditions for such states to exist.

Contribution

It introduces a model connecting scattering lengths with binding energies for charmonium-nucleus systems, providing criteria for their possible existence.

Findings

Bound states require scattering lengths $a \,\le\, -0.95$ fm for $ ext{eta}_c$ and $J/\psi$ with nucleons.

A $J/\psi$-helium-4 bound state may exist if $a \le -0.24$ fm.

The study offers theoretical conditions for charmonium-nucleus bound states based on scattering parameters.

Abstract

Possible existence of $(c\bar{c})-$nucleus bound states are examined. We adopt Gaussian potentials for the $\eta_{c}-N$ and $J/\psi-N$ interactions. The relations between the scattering lengths $a$ of $(c\bar{c})-N$ interactions and the binding energies of $\eta_{c}-NN$, $J/\psi-NN$ and $J/\psi-^{4}$He are given. The results show that scattering lengths $a \le -0.95$ fm are needed to make $\eta_{c}-NN$ and $J/\psi-NN$ bound states, while for $a \le -0.24$ fm there may exist a $J/\psi-^{4}$He bound state.