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arXiv:2606.19231

Geometric structure of two-neutron halo nuclei from Efimov physics at the unitary limit

R.M. Francisco, D. S. Rosa, T. Frederico, Marcelo Takeshi Yamashita

Published Jun 17, 2026• 0 citations
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Abstract

We investigate the geometric structure of two-neutron halo nuclei from the perspective of Efimov physics. Using the analytic three-body wave function obtained from the Faddeev equations in the unitary limit, we explore the connection between Efimov universality and the spatial configuration of these weakly bound systems. The internal geometry is quantified through probability densities, root-mean-square interparticle distances and characteristic opening angles, evaluated for different neutron-core mass ratios. Our results reveal a universal trend in the geometry of s-wave dominated halo nuclei, reflecting the universal correlations characteristic of the Efimov-like regime.

DOI
10.48550/arxiv.2606.19231

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We investigate the geometric structure of two-neutron halo nuclei from the perspective of Efimov physics. Using the analytic three-body wave function obtained from the Faddeev equations in the unitary limit, we explore the connection between Efimov universality and the spatial configuration of these weakly bound systems. The internal geometry is quantified through probability densities, root-mean-square interparticle distances and characteristic opening angles, evaluated for different neutron-core mass ratios. Our results reveal a universal trend in the geometry of s-wave dominated halo nuclei, reflecting the universal correlations characteristic of the Efimov-like regime.
Abstract We investigate the geometric structure of two-neutron halo nuclei from the perspective of Efimov physics. Using the analytic three-body wave function obtained from the Faddeev equations in the unitary limit, we explore the connection between Efimov universality and the spatial configuration of these weakly bound systems. The internal geometry is quantified through probability densities, root-mean-square interparticle distances and characteristic opening angles, evaluated for different neutron–core mass ratios. Our results reveal a universal trend in the geometry of s -wave dominated halo nuclei, reflecting the universal correlations characteristic of the Efimov-like regime.
The geometry of Borromean three-body halos, such as two-neutron halo nuclei or triatomic molecules close to dissociation, is investigated using a three-body model. This model enables to analytically derive the universal geometric properties found recently within an effective-field theory for halos made of a core and two resonantly-interacting particles [Phys. Rev. Lett., 128, 212501 (2022)]. It is shown that these properties not only apply to the ground three-body state, but also to all the excited (Efimov) states where the core-particle interaction is resonant. Furthermore, a universal geometry persists away from the resonant regime between the two particles, for any state close to the three-body threshold. This “halo universality”, which applies equally to all states, is different from the Efimov universality, which is only approximate for the ground state. It is explained by the separability of the hyper-radius and hyper-angles close to the three-body dissociation threshold.
The parametric region in the plane defined by the ratios of the energies of the subsystems and the three-body ground state, in which Efimov states can exist, is determined. We use a renormalizable model that guarantees the general validity of our results in the context of short-range interactions. The experimental data for one- and two-neutron separation energies, implies that among the halo nuclei candidates, only 20C{}^{20}\mathrm{C}20C has a possible Efimov state, with an estimated energy less than 14 KeV below the scattering threshold.
Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by continuous scale invariance, which is broken into discrete scale invariance when three or more particles come into play. This symmetry induces a universal behavior for different systems that is independent of the details of the underlying interaction and rooted in the smallness of the ratio ℓ/ a B ≪ 1, where the length a B is associated with the binding energy of the two-body system [Formula: see text], and ℓ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the onset of system-specific nonuniversal effects. In this review, we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which a B → ∞, and we show that nuclear systems belong to this class of universality.
The different kinds of behaviour of three-body systems in the weak-binding limit are classified with specific attention to the transition from a true three-body system to an effective two-body system. For weakly bound Borromean systems approaching the limit of binding we show that the size-binding energy relation is an almost universal function of the three s -wave scattering lengths measured in units of a hyperradial scaling parameter defined as a mass weighted average of two-body equivalent square well radii. We explain why three-body halos follow this curve and why systems appearing above reveal two-body substructures. Three-body quantum halos 2-3 times larger than the limit set by zero hypermoment are possible.
This contribution reports recent investigations on low-energy scaling properties of three-body systems, by considering elastic s –wave collisions of a particle in a bound-state formed by the remaining two-body system. First, some previous results for the case of the halo nucleus 20 C will be revised, for the neutron– 19 C scattering properties near the critical condition for the occurrence of an excited bound state in 20 C, within a neutron–neutron– 18 C configuration. In our approach, we consider the Faddeev formalism with renormalized zero-range two-body interactions. Next, by considering the actual possibilities for verification of low-energy scaling properties in cold-atom laboratories, the approach is extended to atomic strongly-mass-imbalanced three-body systems, with two identical heavy particles and a light one. In this case, we consider that the heavy particle is being scattered by the light-heavy weakly-bound dimer. Our preliminary results for scattering observable are evidencing the universal scaling features.