The $\Xi^- +d\to n+\Lambda+\Lambda$ reaction as a probe of the $\Lambda\Lambda$ interaction

Within the framework of the Faddeev equations we demonstrate that a $\Lambda\Lambda-\Xi N$ interaction that gives a $\Lambda\Lambda$ scattering length comparable to the $nn$ scattering length, and the binding energy of $^{\ 6}_{\Lambda\Lambda}$He as an $\alpha\Lambda\Lambda-\alpha\Xi N$ system, produces a final state interaction peak in the neutron spectrum for the reaction $\Xi^- d \to n\Lambda\Lambda$. This suggests that this reaction could be used to constrain the $\Lambda\Lambda$ scattering length.