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arXiv:nucl-th/9708023 · Physical Review C

Universal aspects of Efimov states and light halo nuclei

Antonio Eduardo Assis Amorim, T. Frederico, Lauro Tomio

Published Nov 1, 1997• 97 citations
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Abstract

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 ${}^{20}\mathrm{C}$ has a possible Efimov state, with an estimated energy less than 14 KeV below the scattering threshold.

DOI
10.1103/physrevc.56.r2378

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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.
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.
Quantum halos are defined as systems with dominating few-body structure and radii large compared to the sizes of the classically allowed regions. Dimensionless, universal scaling plots of radii vs. binding energies of two- and three-body systems are constructed to characterize and classify halo states. Short-range as well as long-range interactions are considered and molecular, atomic and nuclear states appear on the same plot. Specific two- and three-body systems are discussed, including Efimov states.
Effective Field Theory (EFT) provides a powerful framework to exploit a separation of scales in order to perform systematically improvable, model-independent calculations. We apply this method to strongly interacting quantum systems with short-range interactions and large scattering length. Such systems display remarkable universal properties which include a geometric spectrum of shallow three-body states called "Efimov states" and log-periodic dependence of scattering observables on the scattering length. We review the EFT for large scattering length and some of its applications in the physics of cold atoms and nuclear physics. In particular, we discuss the possibility of an infrared limit cycle in QCD and the extension of the EFT to halo nuclei.
Effective Field Theory (EFT) provides a powerful framework to exploit a separation of scales in order to perform systematically improvable, model-independent calculations. We apply this method to strongly interacting quantum systems with short-range interactions and large scattering length. Such systems display remarkable universal properties which include a geometric spectrum of shallow three-body called Efimov states and log-periodic dependence of scattering observables on the scattering length. We review the EFT for large scattering length and some of its applications in the physics of cold atoms and nuclear physics. In particular, we discuss the possibility of an infrared limit cycle in QCD and the extension of the EFT to halo nuclei.