Five-body cluster structure of double-$\Lambda$ hypernucleus $^{11}_{\Lambda \Lambda}$Be

Understand

Energy levels of the double $\Lambda$ hypernucleus, $^{11}_{\Lambda \Lambda}$Be are calculated within the framework of an $\alpha \alpha n \Lambda \Lambda$ five-body model.

• Interactions between constituent particles are determined so as to reproduce reasonably the observed low-energy properties of the $\alpha \alpha$, $\alpha \alpha n$ nuclei and the existing data for $\Lambda$-binding energies of the $\alpha \Lambda$, $\alpha \alpha \Lambda$, $\alpha n \Lambda$ and $\alpha \alpha n \Lambda$ systems.
• An effective $\Lambda \Lambda$ interaction is constructed so as to reproduce, within the $\alpha \Lambda \Lambda$ three-body model, the $B_{\Lambda \Lambda}$ of $^6_{\Lambda \Lambda}$He, which was extracted from the emulsion experiment, the NAGARA event.
• With no adjustable parameters for the $\alpha \alpha n \Lambda \Lambda$ system, $B_{\Lambda \Lambda}$ of the ground and bound excited states of $^{11}_{\Lambda \Lambda}$Be are calculated with the Gaussian Expansion Method.