Relativistic mean-field approach for Λ,Ξ , and Σ hypernuclei

Abstract

We systematically study the properties of single-$\mathrm{\ensuremath{\Lambda}},\mathrm{\ensuremath{\Xi}}$, and $\mathrm{\ensuremath{\Sigma}}$ hypernuclei within the framework of relativistic mean-field model. The $YN$ coupling constants are constrained according to the experimental data and previous theoretical efforts. By adding a hyperon to $^{40}\mathrm{Ca}$, we investigate its mean-field potentials, single-hyperon levels, density distributions, and binding energies, where the consequences of introducing different types of hyperons ($\mathrm{\ensuremath{\Lambda}},{\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Sigma}}}^{+,0,\ensuremath{-}}$) are examined. In general, the $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Sigma}}}^{0}$ hyperons show similar behaviors in bulk properties since both of them are electroneutral and have similar coupling constants; ${\mathrm{\ensuremath{\Xi}}}^{0}$ hyperon owns the shallowest mean-field potential well with the most extended density distribution; and Coulomb interactions play vital roles in the charged ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}},\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Sigma}}}^{+}$ hyperons. As a result, those hyperons have different impurity effects on the nuclear core $^{40}\mathrm{Ca}$. The $\ensuremath{\omega}YY$ tensor couplings are included and show remarkable effects on the spin-orbit splitting which even change the level ordering of $\mathrm{\ensuremath{\Xi}}$ hyperon. Finally, the single-hyperon binding energy of hypernuclei generally increases with the mass number. However, there is a turning point for ${\mathrm{\ensuremath{\Sigma}}}^{+}$ hypernuclei at $_{{\mathrm{\ensuremath{\Sigma}}}^{+}}^{91}\mathrm{Nb}$ where the binding energy begins to decrease. This is mainly due to the increasing Coulomb repulsive potential at large proton numbers.