Binding, bonding and charge symmetry breaking in $\Lambda$-hypernuclei

Recent experiments have presented more accurate data on the $\Lambda\Lambda$-binding energies of a few $\Lambda\Lambda$- hypernuclei. This is important as the $\Lambda\Lambda$- bond energies ($\Delta B_{\Lambda\Lambda}$) of double-$\Lambda$ hypernuclei provide a measure of the in-medium strength of the $\Lambda\Lambda$ interaction. A mass formula, optimized with the newly available $\Lambda\Lambda$ binding energy data, is used to estimate the binding energy and bond energy over a wide range of hypernuclei. The $\Delta B_{\Lambda\Lambda}$ values calculated with this mass formula are in good agreement with the experimental data, predictions of the quark mean-field (QMF) model and the relativistic mean-field (RMF) model as well. The $\Lambda\Lambda$-bond energy is found to diminish with neutron numbers, approaching zero near the neutron-drip line. In this formalism, the calculated binding energy difference in mirror nuclei arises from the Coulomb contributions and can be utilized to extract the Coulomb-corrected charge symmetry breaking effect.