Structure of BeΛ9 and BeΛΛ10 using the beyond-mean-field Skyrme-Hartree-Fock approach

Based on the beyond-mean-field Skyrme-Hartree-Fock model, the up-to-date Skyrme-type $N\mathrm{\ensuremath{\Lambda}}$ interaction, SLL4, is used to investigate the properties of $_{\mathrm{\ensuremath{\Lambda}}}^{9}\mathrm{Be}$ comprehensively. Energies of different configurations, such as $^{8}\mathrm{Be}\ensuremath{\bigotimes}\mathrm{\ensuremath{\Lambda}}[000]1/{2}^{+}, ^{8}\mathrm{Be}\ensuremath{\bigotimes}\mathrm{\ensuremath{\Lambda}}[110]1/{2}^{\ensuremath{-}}, ^{8}\mathrm{Be}\ensuremath{\bigotimes}\mathrm{\ensuremath{\Lambda}}[101]3/{2}^{\ensuremath{-}}$, and $^{8}\mathrm{Be}\ensuremath{\bigotimes}\mathrm{\ensuremath{\Lambda}}[101]1/{2}^{\ensuremath{-}}$ are given and used to study the effects of $\mathrm{\ensuremath{\Lambda}}$ occupying different orbitals. The calculated energy spectra, including both positive- and negative-parity levels, are given and compared to the experimental data. The observed positive-parity spin doublets ($3/{2}^{+},5/{2}^{+}$) are successfully reproduced, but the energy difference needs further investigation. The two well-known band structures corresponding to the genuine hypernuclear states and the $^{9}\mathrm{Be}$-analog states are also obtained and compared with the observed ones. The shrinkage effect of $\mathrm{\ensuremath{\Lambda}}$ occupying $\mathrm{\ensuremath{\Lambda}}[000]1/{2}^{+}$ is investigated through the density distributions of nuclear core. And finally, the $E2$ transition rates are given and compared with the observed data and with the results of the hypernuclear particle-rotor model. Properties of $_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{10}\mathrm{Be}$ are also studied to show the completeness of this current model.