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Efimov Physics with a Finite-Range Parameter

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Abstract

Results obtained by the authors in recent works on the exploration of universality in systems living inside the Efimov window are critically analyzed. We discuss how to take into account finite-range corrections by introducing a finite-range parameter necessary to make comparisons to the universal predictions of the Efimov zero-range theory. Firstly we apply our analysis to two different calculations published by other authors. The first one has been used with success to describe ultracold Cs atoms close to a Feshbach resonance and the second one describes a four 4He atom system with a realistic interaction. Finally we use the finite-range parameter to analyze recombination data in experiments with ultracold 7Li atoms. The three selected cases support the introduction of the finite-range parameter as a valuable tool to extend the use of the zero-range theory to describe systems having finite-range interactions.

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References

  1. Braaten E., Hammer H.W.: Universality in few-body systems with large scattering length. Phys. Rep. 428, 259 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  2. Efimov V.: Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B 33, 563 (1970)

    Article  ADS  Google Scholar 

  3. Platter L., Hammer H.W., Meiner U.G.: Four-boson system with short-range interactions. Phys. Rev. A 70, 052101 (2004)

    Article  ADS  Google Scholar 

  4. Hadizadeh M.R., Yamashita M.T., Tomio L., Delfino A., Frederico T.: Scaling properties of universal tetramers. Phys. Rev. Lett. 107, 135304 (2011)

    Article  ADS  Google Scholar 

  5. Hadizadeh M.R., Yamashita M.T., Tomio L., Delfino A., Frederico T.: Binding and structure of tetramers in the scaling limit. Phys. Rev. A 85, 023610 (2012)

    Article  ADS  Google Scholar 

  6. Sornette D.: Discrete-scale invariance and complex dimensions. Phys. Rep. 297, 239 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  7. Efimov, V.: Weak bound states of three resonantly interacting particles. Sov. J. Nucl. Phys. 12, 589 (1971). [Yad. Fiz. 12, 10801090 (1970)]

  8. Gattobigio M., Kievsky A.: Universality and scaling in the N-body sector of Efimov physics. Phys. Rev. A 90, 012502 (2014)

    Article  ADS  Google Scholar 

  9. Wang Y., Julienne P.S.: Universal van der Waals physics for three cold atoms near Feshbach resonances. Nat. Phys. 10, 768 (2014)

    Article  Google Scholar 

  10. Kievsky A., Timofeyuk N.K., Gattobigio M.: N-Boson spectrum from a discrete scale invariance. Phys. Rev. A 90, 032504 (2014)

    Article  ADS  Google Scholar 

  11. Hiyama E., Kamimura M.: Universality in Efimov-associated tetramers in 4 He. Phys. Rev. A 90, 052514 (2014)

    Article  ADS  Google Scholar 

  12. Pollack S.E., Dries D., Hulet R.G.: Universality in three- and four-body bound states of ultracold atoms. Science 326, 1683 (2009)

    Article  ADS  Google Scholar 

  13. Dyke P., Pollack S.E., Hulet R.G.: Finite-range corrections near a Feshbach resonance and their role in the Efimov effect. Phys. Rev. A 88, 023625 (2013)

    Article  ADS  Google Scholar 

  14. Kievsky A., Gattobigio M.: Universal nature and finite-range corrections in elastic atom-dimer scattering below the dimer breakup threshold. Phys. Rev. A 87, 052719 (2013)

    Article  ADS  Google Scholar 

  15. Garrido E., Gattobigio M., Kievsky A.: Recombination rates from potential models close to the unitary limit. Phys. Rev. A 88, 032701 (2013)

    Article  ADS  Google Scholar 

  16. Knoop S., Ferlaino F., Mark M., Berninger M., Schbel H., Ngerl H.C., Grimm R.: Observation of an Efimov-like trimer resonance in ultracold atomdimer scattering. Nat. Phys. 5, 227 (2009)

    Article  Google Scholar 

  17. Gattobigio M., Kievsky A., Viviani M.: Energy spectra of small bosonic clusters having a large two-body scattering length. Phys. Rev. A 86, 042513 (2012)

    Article  ADS  Google Scholar 

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Gattobigio, M., Kievsky, A. Efimov Physics with a Finite-Range Parameter. Few-Body Syst 56, 881–887 (2015). https://doi.org/10.1007/s00601-015-1021-9

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  • DOI: https://doi.org/10.1007/s00601-015-1021-9

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