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We calculate neutron-neutron relative-energy distributions of $s$-wavetwo-neutron ($2n$) halo nuclei using Halo Effective Field Theory (Halo EFT) atleading order. At this order these systems are described by the $2n$ separationenergy, the neutron-core ($nc$) virtual-state energy and the neutron-neutron($nn$) scattering length. We focus on knockout reactions where the removal ofthe core is sudden, such that the final-state interactions are dominated by the$nn$ interaction. We consider the neutron relative-energy distribution for thenuclei $^{11}$Li, $^{14}$Be, $^{17}$B, $^{19}$B, and $^{22}$C. We show that theground-state neutron momentum distributions of all these nuclei stem from asingle curve, which can be obtained by taking both the neutron-core andneutron-neutron interaction to the unitary limit. This universal descriptioncan be extended to the final distribution measured in experiment by including$nn$ final-state interactions via the approximate technique of enhancementfactors. For all the nuclei considered we find good agreement between the fullleading-order Halo EFT calculation and the universal prediction obtained inthis way. The universality of the ground-state momentum distribution intwo-neutron Borromean halos can thus be tested by dividing the experimentalresults from sudden core knockout by the enhancement factor and comparing tothe unitary-limit prediction.

Universality of $nn$ distributions of $s$-wave $2n$ halos and the unitary limit