ΛΛ pairing effects in spherical and deformed multi- Λ hyperisotopes

Abstract

The $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ pairing effects in spherical and deformed multi-$\mathrm{\ensuremath{\Lambda}}$ hyperisotopes are investigated in the framework of the Skyrme-Hartree-Fock approach employing a $\ensuremath{\delta}$ pairing force with the pairing strength of $\mathrm{\ensuremath{\Lambda}}$ hyperons being $4/9$ of that for nucleons. For spherical hyperisotopes, the occurrences of magic numbers $\ensuremath{-}S=2$, 8, 18, 20, 34, 58, 68, and 70, which are attributed to a Woods-Saxon-like $\mathrm{\ensuremath{\Lambda}}$ hyperon potential, are evinced by the sudden drop of $2\mathrm{\ensuremath{\Lambda}}$ separation energies and the vanishing pairing gaps and pairing energies. The results are compared with equivalent ones in recent Hartree-Fock-Bogoliubov and relativistic-Hartree-Bogoliubov calculations. For the deformed hyperisotopes, more possible $\mathrm{\ensuremath{\Lambda}}$ hyperon magic numbers $\ensuremath{-}S=4$, 6, 10, 14, 26, 30, and 32 are found based on the analysis of the single-particle energy levels, and are all sensitive to the quadrupole deformation ${\ensuremath{\beta}}_{2}$. The steps of the $2\mathrm{\ensuremath{\Lambda}}$ separation energies are accordingly smaller than in spherical hyperisotopes, and the possibilities for pairing are consistently reduced.