Charmed hypernuclei within density-dependent relativistic mean-field theory

The charmed $\Lambda_{c}^{+}$ hypernuclei are investigated within the framework of the density-dependent relativistic mean-field (DDRMF) theory. Starting from the empirical hyperon potential in symmetric nuclear matter, obtained through microscopic first-principle calculations, two sets of $\Lambda_c N$ effective interactions were derived by fitting the potentials with minimal uncertainty (Fermi momentum $k_{F,n} = 1.05~\rm{fm}^{-1}$) and near saturation density ($k_{F,n} = 1.35~\rm{fm}^{-1}$). These DDRMF models were then used to explore the $\Lambda_{c} N$ effective interaction uncertainties on the description of hypernuclear bulk and single-particle properties. A systematic investigation was conducted on the existence of bound $\Lambda_{c}^{+}$ hypernuclei. The dominant factors affecting the existence and stability of hypernuclei were analyzed from the perspective of the $\Lambda_{c}^{+}$ potential. It is found that the hyperon potential is not only influenced by the Coulomb repulsion, but by an extra contribution from the rearrangement terms due to the density dependence of the meson-baryon coupling strengths. Therefore, the rearrangement term significantly impacts the stability description for light hypernuclei, while for heavier hypernuclei, the contribution from Coulomb repulsion becomes increasingly significant and eventually dominant. The discussion then delves into the bulk and single-particle properties of charmed hypernuclei using these models. It is found that even when different models yield similar hyperon potentials for nuclear matter, different treatments of nuclear medium effects could lead to disparities in the theoretical description of hypernuclear structures. This study indicates that constraints on the $\Lambda_{c} N$ interaction at finite densities are crucial for the study of $\Lambda_{c}^{+}$ hypernuclear structures.