Charmed hypernuclei within density-dependent relativistic mean-field theory

The charmed ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ hypernuclei were 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 ${\mathrm{\ensuremath{\Lambda}}}_{c}N$ effective interactions were derived by fitting the potentials at a certain density either with minimal model uncertainty (Fermi momentum ${k}_{F,n}=1.05\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$) or nearby the saturation point (${k}_{F,n}=1.35\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$). These DDRMF models were then used to explore the ${\mathrm{\ensuremath{\Lambda}}}_{c}N$ effective interaction uncertainties on the description of hypernuclear bulk and single-particle properties. A systematic investigation was conducted on the existence of bound ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ hypernuclei. The dominant factors affecting the existence and stability of hypernuclei were analyzed from the perspective of the ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ potential. It was found that the hyperon potential is influenced not only 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 focuses on the bulk and single-particle properties of charmed hypernuclei using these models. It is shown that different treatments of nuclear medium effects could lead to discrepancies in the theoretical description of hypernuclear structures, even when different models yield similar hyperon potentials within nuclear matter, indicating that constraints on the ${\mathrm{\ensuremath{\Lambda}}}_{c}N$ interaction at finite densities are crucial for the study of ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ hypernuclear structures.