Bound states of ${}_{c\bar{c}}^9$Be within $c\bar{c}+\alpha +\alpha$ cluster models based on state-of-the-art HAL QCD charmonium-nucleon interactions

Abstract

The possible bound state of the ${}_{c\bar{c}}^9$Be, a charmonium-nucleus system, is investigated. The analysis is carried out within a three-cluster model, where its binary subsystems are represented as $c\bar{c}\text{+}\alpha$ and $\alpha +\alpha$. The hyperspherical harmonics method is employed to facilitate a convenient description of this three-cluster configuration. The calculations are done by employing the effective $c\bar{c}\text{-}\alpha$ potentials. These potentials were derived recently based on state-of-the-art lattice QCD calculations, which provided interactions for the spin 3/2 $J/\psi N$, spin 1/2 $J/\psi N$, spin 1/2 ${\eta }_{c}N$ and spin-averaged $J/\psi N$ interactions, all obtained with nearly physical pion masses. The Coulomb interaction was also incorporated into the current calculations. It is determined that, despite neither the ${}_{c\bar{c}}^5$He nor the ${}^8$Be binary subsystems being bound, a bound state of the $c\bar{c}\text{-}\alpha \alpha$ nuclear system could potentially exist. The maximum central binding energy is found to be approximately 1.71 MeV, based on the spin 1/2 $J/\psi N$ interaction, while a minimum value of about 0.56 MeV is obtained from calculations involving the spin 1/2 ${\eta }_{c}N$ interaction.

Comments: 14 pages, 1 figure , 1 table