The trajectory of the first excited Efimov state is investigated by using a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems. The approach is applied to n–n–18C, where the n–n virtual energy and the three-body ground state are kept fixed. It is shown that such three-body excited state goes from a bound to a virtual state when the n–18C binding energy is increased. Results obtained for the n–19C elastic cross-section at low energies also show dominance of an S-matrix pole corresponding to a bound or virtual Efimov state. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths.
The trajectory of the first excited Efimov state is investigated by using a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems. The approach is applied to n–n–18C, where the n–n virtual energy and the three-body ground state are kept fixed. It is shown that such three-body excited state goes from a bound to a virtual state when the n–18C binding energy is increased. Results obtained for the n–19C elastic cross-section at low energies also show dominance of an S-matrix pole corresponding to a bound or virtual Efimov state. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths.
The universal character of non-relativistic large three-body bosonic systems is addressed, with focus on highly interesting situations that occur in low-energy nuclear and atomic physics. Investigations on the trajectory of the first excited Efimov state, in a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems, are reported. The approach is applied to n-n-18C, where the n - n virtual energy and the three-body ground state are kept fixed. It is shown that the real part of the elastic s-wave phase-shift ([Formula: see text]) presents a zero, or a pole in [Formula: see text], when the system has an Efimov excited or virtual state. A brief discussion is given on the relevance of the approach for ultracold atom physics with tunable scattering lengths.
The emergence of Efimov levels in a three-body system is investigated near the unitarity limit characterized by a resonant two-body interaction. No direct evidence of Efimov levels is seen in the three-nucleon system since the triton is the only physical bound state. We provide a model-independent analysis of nucleon–deuteron scattering at low energy by formulating a consistent effective field theory. We show that virtual states evolve into shallow bound states, which emerge as excited triton levels as we drive the system towards unitarity. Even though we consider this specific system, our results for the emergence of the Efimov levels are universal.
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.
We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s -wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.
The Efimov phenomenon manifests itself as an emergent discrete scaling symmetry in the quantum three-body problem. In the unitarity limit, it leads to an infinite tower of three-body bound states with energies forming a geometric sequence. In this work, we study the evolution of these so-called Efimov states using relativistic scattering theory. We identify them as poles of the three-particle S matrix in the complex energy plane, and we study how they transform from virtual states through bound states to resonances when we change the interaction strength. We dial the scattering parameters toward the unitarity limit and observe the emergence of the universal scaling of energies and couplings---a behavior known from the nonrelativistic case. We additionally find that Efimov resonances follow unusual, cyclic trajectories accumulating at the three-body threshold and then disappear at some values of the two-body scattering length. We propose a partial resolution to this ``missing states'' problem.
In the low-energy limit, non-relativistic particles with short-range interactions exhibit universal behavior that is largely independent of microscopic details. This universality is typically described by effective field theory, in which the two-body interaction is renormalized to a single parameter-the scattering length. For systems of identical bosons, the three-body problem reveals the Efimov effect, a novel phenomenon proposed that necessitates the introduction of an additional three-body parameter. However, the exact relation between this three-body parameter, the coupling constants in the effective field theory, and the binding energies of Efimov states remains unresolved. In this Letter, we address this question through a comprehensive analysis of the Skorniakov-Ter-Martirosian equation with a finite cutoff. We establish an exact renormalization relation for the three-body parameter and determine its connection to the energies of Efimov bound states. These results are validated through high-precision numerical simulations. We expect our findings to be of fundamental interest across various fields, including atomic, nuclear, condensed matter, and particle physics, and to have broad applications in both few-body and many-body physics.