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

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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)

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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)

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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

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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

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

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

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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

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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.

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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

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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

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

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

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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)

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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

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Obrigado pela sua attenção!

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

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