Gaussian characterization of two-neutron halo nuclei
The halo nucleon-core system is, by definition, a shallow state nucleus. The nucleon, in most cases a neutron, is loosely bound to the other nucleons forming the core. Accordingly, the system is located inside the universal window; the halo nucleon most likely resides far from the rest of the nucleons, showing a remarkable insensitivity to details of the interaction with the core. The system can be described using a simple nucleon-core interaction, and this description can be extended to the nucleon-nucleon-core system. Specifically, treating the neutron-core and the neutron-neutron-core systems with a Gaussian interaction as a reference, we show trajectories inside the universal window governed by interaction parameters determined from low-energy observables, such as the neutron-core binding energy, scattering length, and effective range. In this way, we can relate properties of different halo nuclei that might seem uncorrelated. In particular, we determine the three-body parameter, the binding momentum at the unitary limit, and show that the two-neutron halo nuclei emerge from that limit following a linear trajectory depending on the neutron-core range.