Abstract
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 20C will be revised, for the neutron–19C scattering properties near the critical condition for the occurrence of an excited bound state in 20C, within a neutron–neutron–18C 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.
Highlights
First shown by Efimov [1] for the case that we have three-identical particles in the unitary limit, a discrete geometrical scaling emerges in the corresponding bound-state energy spectrum, which has an infinite number of three-body levels
Considered as a quantum mechanics pathology in the beginning [2], the Efimov effect was demonstrated in [3] to arise from essentially the same singularity structure of the kernel of the scattering equation, which is responsible for the Thomas collapse [4] of the three-body ground state when the twobody range r0 is reduced to zero
The experimental observation of this effect in different ultracold laboratories [14,15,16,17,18], which was possible in view of the quantum-mechanical control of the two-body interactions provided by Feshbach resonance mechanisms [19], attracted a lot of new theoretical and experimental investigations on low-energy quantum few-body systems
Summary
First shown by Efimov [1] for the case that we have three-identical particles in the unitary limit (when the absolute value of the two-body scattering length |a| becomes infinity), a discrete geometrical scaling emerges in the corresponding bound-state energy spectrum, which has an infinite number of three-body levels. 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.
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