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Pascal Naidon Microscopic origin and universality classes of the three-body parameter Shimpei Endo Masahito Ueda The University of Tokyo.

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Presentation on theme: "Pascal Naidon Microscopic origin and universality classes of the three-body parameter Shimpei Endo Masahito Ueda The University of Tokyo."— Presentation transcript:

1 Pascal Naidon Microscopic origin and universality classes of the three-body parameter Shimpei Endo Masahito Ueda The University of Tokyo

2 3 particles (bosons or distinguishable) with resonant two-body interactions single-channel two-body interaction no three-body interaction

3 R x Hyperradius The Efimov effect (1970) y z The Efimov 3-body parameter Three-body parameter Parameters describing particles at low energy Scattering length a dimer trimer 3-body parameter (2-body parameter)

4 R x Hyperradius The Efimov effect (1970) y z The Efimov 3-body parameter Three-body parameter Parameters describing particles at low energy Scattering length a dimer trimer 3-body parameter (2-body parameter)

5 Microscopic determination? Universality for atoms r short- range details van der Waals Two-body potential Effective three-body potential Hyperradius R short- range details Efimov 4 He 7 Li 6 Li 39 K 23 Na 87 Rb 85 Rb 133 Cs no universality of the scattering length universality of the 3-body parameter

6 Three-body with van der Waals interactions Phys. Rev. Lett (2012) J. Wang, J. D’Incao, B. Esry, C. Greene Lennard-Jones potentials supporting n = 1, 2, 3,...10 s-wave bound states Hyperradius R

7 Interpretation: two-body correlation Asymptotic behaviour Interatomic separation r Strong depletion

8 Interpretation: two-body correlation squeezed equilateral elongated Excluded configurations induced deformation Kinetic energy cost due to deformation deformation Excluded configurations

9 Confirmation 1: pair correlation model  Model =  Efimov x  (r 12 )  (r 23 )  (r 31 ) (product of pair correlations) (hyperangular wave function) 3-body potential Pair model (for Lennard-Jones two-body interactions) Exact Efimov attraction

10 Reproduces the low- energy 2-body physics Scattering length Effective range Last bound state …. Confirmation 2: separable model Parameterised to reproduce exactly the two-body correlation at zero energy.

11 Hyperradius R Integrated probability Hyperradius R Energy Confirmation 2: separable model Parameterised to reproduce exactly the two-body correlation at zero energy. n Exact Pair model Separable model

12 Confirmation 2: separable model Parameterised to reproduce exactly the two-body correlation at zero energy. S. Moszkowski, S. Fleck, A. Krikeb, L. Theuÿl, J.-M.Richard, and K. Varga, Phys. Rev. A 62, (2000). Other potentials Potential Yukawa Exponential Gaussian Separable model Exact calculations at most 10% deviation

13 Summary two-body correlation three-body deformation three-body repulsion three-body parameter universal

14 Two-body correlation universality classes Power-law tails Faster than Power-law tails Probability density Van der Waals Step function correlation limit Universal correlation

15 Separable model Number of two-body bound states Binding wave number at unitarity 3-body parameter in units of the two-body effective range Atomic physics Nuclear physics ? ? (= size of two-body correlation)

16 P. Naidon, S. Endo, M. Ueda, PRL 112, (2014) P. Naidon, S. Endo, M. Ueda, PRA 90, (2014) Summary The 3-body parameter is (mostly) determined by the low-energy 2-body correlation. Reason: 2-body correlation induces a deformation of the 3-body system. Consequences: the 3-body parameter is on the order of the effective range. has different universal values for distinct classes of interaction

17 Obrigado pela sua attenção!

18 Separable model Parameterised to reproduce exactly the two-body correlation at zero energy. …


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