The $Ξ^- +d\to n+Λ+Λ$ reaction as a probe of the $ΛΛ$ interaction

Abstract

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