of two quantities: One is the total energy measured from the breakup threshold of $\alpha +x+ \Lambda + \Lambda$ which is denoted as $E_{\Lambda \Lambda}$. The other is $B_{\Lambda \Lambda}$ which is the binding energy of two $\Lambda$ particles with respect to the ground-state nuclear core $\alpha+x$.

The calculated values of $B_{\Lambda \Lambda}$ can be compared with some experimental data, though they are quite limited at present. The most recent and clear data of the NAGARA event is used as a basic input of our model so that our $\Lambda \Lambda$ interaction is adjusted to reproduce the experimental value $B_{\Lambda \Lambda}^{\rm exp}(^{\ 6}_{\Lambda\Lambda}$He)$
=7.25 \pm 0.19\pm ^{0.18}_{0.11}$ MeV [@Nagara]. It is of particular interest to compare the present result with another data which is not used in the fitting procedure. There is an event found in the E373 experiment, named as [*Demachi-Yanagi*]{} event [@Ichi99; @Ichi01]; the most probable interpretation of this event is a production of a bound state of $_\Lambda^{ }$$_\Lambda^{\!\!\!10}$Be having $B^{\rm exp}_{\Lambda \Lambda}
=12.33 \pm^{0.35}_{0.21}$ MeV which is obtained by assuming $B^{\rm exp}_{\Xi}=0.15 \pm ^{0.3}_{0.1}$ MeV. In the emulsion analysis there is no direct evidence for the production of $^{10}_{\Lambda \Lambda}$Be in an excited state. However, if 