Three-body resonances of $\alpha\alpha M$ clusters ($M=\phi$, $J/\psi$, $\eta_c$) in $^{8}_{M}{\mathrm{Be}}$ nuclei

Abstract

Motivated by the recently obtained HAL QCD potentials for the $N$-$\phi$, $N$-$J/\psi$, and $N$-$\eta_c$ interactions, we investigate the structure of the exotic nuclei $^{8}_{\phi}{\text{Be}}$, $^{8}_{J/\psi}{\text{Be}}$, and $^{8}_{\eta_c}{\text{Be}}$ as $\alpha+\alpha+M$ three-body systems ($M$ denotes the meson). The bound and resonant states are calculated consistently using the Gaussian expansion method, with resonances identified via the complex scaling method. For the $\alpha\phi$ and $\alpha$-charmonium interactions, a folding potential is constructed based on the HAL QCD potentials and fitted to a Woods-Saxon form. We find that the $\phi$ meson exhibits a strong ``glue-like" effect, binding the $0^+_1$, $2^+_1$, and $4^+_1$ resonant states of $^8$Be into stable states and significantly reducing the $\alpha$-$\alpha$ distance. In contrast, the interactions of $J/\psi$ and $\eta_c$ with the nucleus are weaker, forming only shallow bound states with the $0^+_1$ state of $^8$Be and even increasing the $\alpha$-$\alpha$ separation. Notably, our analysis predicts weakly bound $\alpha$-$J/\psi$ states in the $^4S_{3/2}$ and $^2S_{1/2}$ channels, a result not reported in prior studies, which suggests that $^{8}_{J/\psi}{\text{Be}}$ may not be a Borromean nucleus. The sensitivity of the $^{8}_{M}{\mathrm{Be}}(4^+_1)$ state-transitioning from bound to resonant depending on the $\alpha$-particle radius-highlights the subtle dynamics at play. These results provide a systematic theoretical comparison of how different vector mesons modify nuclear clustering, offering critical predictions for future experimental searches of such exotic hadron-nucleus systems.