Universality of nn distributions of s -wave 2n halo nuclei and the unitary limit

We calculate neutron-neutron relative-energy distributions of s-wave two-neutron ($2n$) halo nuclei using halo effective field theory (halo EFT) at leading order. At this order these systems are described by the $2n$ separation energy, the neutron-core ($nc$) virtual-state energy, and the neutron-neutron ($nn$) scattering length. We focus on knockout reactions where the removal of the core is sudden, such that the final-state interactions are dominated by the $nn$ interaction. We consider the neutron relative-energy distribution for the nuclei ¹¹Li, ¹⁴Be, ¹⁷B, ¹⁹B, and ²²C. We show that the ground-state neutron momentum distributions of all these nuclei stem from a single curve, which can be obtained by taking both the neutron-core and neutron-neutron interaction to the unitary limit. This universal description can be extended to the final distribution measured in experiment by including $nn$ final-state interactions via the approximate technique of enhancement factors. For all the nuclei considered we find good agreement between the full leading-order halo EFT calculation and the universal prediction obtained in this way. The universality of the ground-state momentum distribution in two-neutron Borromean halos can thus be tested by dividing the experimental results from sudden core knockout by the enhancement factor and comparing them to the unitary-limit prediction.