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

TL;DR

This paper demonstrates that the neutron-neutron relative-energy distributions in s-wave two-neutron halo nuclei exhibit a universal behavior that can be described by the unitary limit, regardless of specific nuclear details, at leading order in Halo EFT.

Contribution

The study introduces a universal description of neutron-neutron distributions in two-neutron halo nuclei using Halo EFT at leading order, connecting it to the unitary limit and validating with experimental data.

Findings

Ground-state momentum distributions follow a universal curve.

The universal behavior is consistent with the unitary limit predictions.

Good agreement between EFT calculations and experimental enhancement factors.

Abstract

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 $^{11}$Li, $^{14}$Be, $^{17}$B, $^{19}$B, and $^{22}$C. 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 to the unitary-limit prediction.