Density Functional approach for multistrange hypernuclei: Competition between Λ and Ξ0,− hyperons

The question of the competition between $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$ in the ground state of multistrange hypernuclei is addressed within a nonrelativistic density functional approach, partially constrained by ab initio calculations and experimental data. The exploration of the nuclear chart for $10lZl120$ as a function of the strangeness number is performed by adding hyperons to a nuclear core, imposing either conserved total charge $Q$ or conserved proton number $Z$. We find that almost all $\mathrm{\ensuremath{\Lambda}}$ hypernuclei present an instability with respect to the strong interaction decay of $\mathrm{\ensuremath{\Lambda}}$ towards ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$ and that most of the instabilities generates ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ (${\mathrm{\ensuremath{\Xi}}}^{0}$) in the case of conserved total charge $Q$ (proton number $Z$). The strangeness number at which the first ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$ appear is generally lower for configurations explored in the case of conserved $Q$ compared to the case of conserved $Z$, and corresponds to the crossing between the $\mathrm{\ensuremath{\Lambda}}$ and the neutron or proton chemical potentials. About two to three hundred thousand pure $\mathrm{\ensuremath{\Lambda}}$ hypernuclei may exist before the onset of ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$. The largest uncertainty comes from the unknown $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ interaction, since the $N\mathrm{\ensuremath{\Lambda}}$ and the $N\mathrm{\ensuremath{\Xi}}$ ones can be constrained by a few experimental data. The uncertainty on the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ interaction can still modify the previous estimation by 30--40%, while the impact of the unknown $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ interaction is very weak.