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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Braaten E., Hammer H.W.: Universality in few-body systems with large scattering length. Phys. Rep. 428, 259 (2006)
Efimov V.: Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B 33, 563 (1970)
Platter L., Hammer H.W., Meiner U.G.: Four-boson system with short-range interactions. Phys. Rev. A 70, 052101 (2004)
Hadizadeh M.R., Yamashita M.T., Tomio L., Delfino A., Frederico T.: Scaling properties of universal tetramers. Phys. Rev. Lett. 107, 135304 (2011)
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)
Sornette D.: Discrete-scale invariance and complex dimensions. Phys. Rep. 297, 239 (1998)
Efimov, V.: Weak bound states of three resonantly interacting particles. Sov. J. Nucl. Phys. 12, 589 (1971). [Yad. Fiz. 12, 10801090 (1970)]
Gattobigio M., Kievsky A.: Universality and scaling in the N-body sector of Efimov physics. Phys. Rev. A 90, 012502 (2014)
Wang Y., Julienne P.S.: Universal van der Waals physics for three cold atoms near Feshbach resonances. Nat. Phys. 10, 768 (2014)
Kievsky A., Timofeyuk N.K., Gattobigio M.: N-Boson spectrum from a discrete scale invariance. Phys. Rev. A 90, 032504 (2014)
Hiyama E., Kamimura M.: Universality in Efimov-associated tetramers in 4 He. Phys. Rev. A 90, 052514 (2014)
Pollack S.E., Dries D., Hulet R.G.: Universality in three- and four-body bound states of ultracold atoms. Science 326, 1683 (2009)
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)
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)
Garrido E., Gattobigio M., Kievsky A.: Recombination rates from potential models close to the unitary limit. Phys. Rev. A 88, 032701 (2013)
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)
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)
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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