Impurity effects of hyperons in hypernuclei with relativistic mean field theory in complex-momentum representation

Utilizing the recently formulated relativistic mean field theory in complex momentum representation, we delve into the impurity effects of hyperons in hypernuclei. Our findings reveal that hyperons exert considerable effects on single-neutron levels, particularly in the deeply bound states such as $1s$ and $1p$. In the case of $^{60}\mathrm{Ca}+\mathrm{\ensuremath{\Lambda}}$, $^{60}\mathrm{Ca}+{\mathrm{\ensuremath{\Sigma}}}^{0}$, $^{60}60+{\mathrm{\ensuremath{\Xi}}}^{0}$, and $^{60}\mathrm{Ca}+{\mathrm{\ensuremath{\Sigma}}}^{+}$, the neutron levels are noticeably lower compared to the baseline $^{60}\mathrm{Ca}$, indicating an increased neutron capacity and a shift in the neutron drip line. Notably, the introduction of ${\mathrm{\ensuremath{\Xi}}}^{0}$ and ${\mathrm{\ensuremath{\Sigma}}}^{+}$, especially ${\mathrm{\ensuremath{\Sigma}}}^{+}$, hyperons results in a more pronounced reduction in neutron levels, partially attributed to the positive charge of the latter. Conversely, for $^{60}\mathrm{Ca}+{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ and $^{60}\mathrm{Ca}+{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$, the neutron levels are elevated, partly due to Coulomb attraction. The impurity effects of hyperons are further evidenced in their density distributions. Neutral $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Sigma}}}^{0}$ hyperons exhibit similar patterns, but Coulomb effects notably alter the density distributions of ${\mathrm{\ensuremath{\Sigma}}}^{+}$ and ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$. While $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ possess comparable central densities, the diffuse distribution of ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hints at the formation of a hyperon halo. This study offers valuable insights into the intricate interactions between hyperons and nucleons within hypernuclei.