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Universal properties of the four-body system with large scattering length

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Abstract.

Few-body systems with large scattering length have universal properties that do not depend on the details of their interactions at short distances. We study the universal bound-state properties of the four-boson system with large scattering length in an effective quantum mechanics approach. We compute the four-body binding energies using the Yakubovsky equations for positive and negative scattering length. Moreover, we study the correlation between three- and four-body energies and present a generalized Efimov plot for the four-body system. These results are useful for understanding the cluster structure of nuclei and for the creation of weakly bound tetramers with cold atoms close to a Feshbach resonance.

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References

  1. P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002) [arXiv:nucl-th/0203055].

    Article  ADS  Google Scholar 

  2. E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006) [arXiv:nucl-th/0509032].

    Article  ADS  Google Scholar 

  3. E. Braaten, H.-W. Hammer, Phys. Rep. 428, 259 (2006) [arXiv:cond-mat/0410417].

    Article  ADS  MathSciNet  Google Scholar 

  4. V. Efimov, Yad. Fiz. 12, 1080 (1970) [Sov. J. Nucl. Phys. 12, 589 (1971)].

    Google Scholar 

  5. V. Efimov, Yad. Fiz. 29, 1058 (1979) [Sov. J. Nucl. Phys. 29, 546 (1979)].

    Google Scholar 

  6. P.F. Bedaque, H.-W. Hammer, U. van Kolck, Phys. Rev. Lett. 82, 463 (1999) [arXiv:nucl-th/9809025].

    Article  ADS  Google Scholar 

  7. P.F. Bedaque, H.-W. Hammer, U. van Kolck, Nucl. Phys. A 646, 444 (1999) [arXiv:nucl-th/9811046].

    Article  ADS  Google Scholar 

  8. R.F. Mohr, R.J. Furnstahl, R.J. Perry, K.G. Wilson, H.-W. Hammer, Ann. Phys. 321, 225 (2006) [arXiv:nucl-th/0509076].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. I.R. Afnan, D.R. Phillips, Phys. Rev. C 69, 034010 (2004) [arXiv:nucl-th/0312021].

    Article  ADS  Google Scholar 

  10. L. Platter, D.R. Phillips, Few-Body Syst. 40, 35 (2006) [arXiv:cond-mat/0604255].

    Article  Google Scholar 

  11. L. Platter, Phys. Rev. C 74, 037001 (2006) [arXiv:nucl-th/0606006].

    Article  ADS  Google Scholar 

  12. L. Platter, H.-W. Hammer, Ulf-G. Meißner, Phys. Rev. A 70, 052101 (2004) [arXiv:cond-mat/0404313].

    Article  ADS  Google Scholar 

  13. G.P. Lepage, arXiv:nucl-th/9706029.

  14. R.F.J. Mohr, arXiv:nucl-th/0306086.

  15. L. Platter, H.-W. Hammer, U.-G. Meißner, Phys. Lett. B 607, 254 (2005) [arXiv:nucl-th/0409040].

    Article  ADS  Google Scholar 

  16. B.F. Gibson, D.R. Lehman, Phys. Rev. C 14, 685 (1976).

    Article  ADS  Google Scholar 

  17. A.C. Fonseca, P.E. Shanley, Phys. Rev. C 14, 1343 (1976).

    Article  ADS  Google Scholar 

  18. J.A. Tjon, in Few-body systems and nuclear forces II, edited by H. Ziegel (Springer, Berlin, 1978).

  19. T.K. Lim, Nucl. Phys. A 416, 491 (1984).

    Article  ADS  Google Scholar 

  20. H. Kamada, Phys. Rev. C 64, 044001 (2001).

    Article  ADS  Google Scholar 

  21. D. Blume, C.H. Greene, J. Chem. Phys. 112, 8053 (2000).

    Article  ADS  Google Scholar 

  22. M.T. Yamashita, L. Tomio, A. Delfino, T. Frederico, Europhys. Lett. 75, 555 (2006) [arXiv:cond-mat/0602549].

    Article  ADS  Google Scholar 

  23. A. Nogga, S.K. Bogner, A. Schwenk, Phys. Rev. C 70, 061002 (2004) [arXiv:nucl-th/0405016].

    Article  ADS  Google Scholar 

  24. J.A. Maruhn, M. Kimura, S. Schramm, P.-G. Reinhard, H. Horiuchi, A. Tohsaki, Phys. Rev. C 74, 044311 (2006) [arXiv:nucl-th/0606053].

    Article  ADS  Google Scholar 

  25. C. Chin, T. Kraemer, M. Mark, J. Herbig, P. Waldburger, H.-C. Nägerl, R. Grimm, Phys. Rev. Lett. 94, 123201 (2005).

    Article  ADS  Google Scholar 

  26. D.B. Kaplan, M.J. Savage, M.B. Wise, Phys. Lett. B 424, 390 (1998) [arXiv:nucl-th/9801034].

    Article  ADS  Google Scholar 

  27. U. van Kolck, Nucl. Phys. A 645, 273 (1999) [arXiv:nucl-th/9808007].

    Article  ADS  Google Scholar 

  28. H.-W. Hammer, T. Mehen, Phys. Lett. B 516, 353 (2001) [arXiv:nucl-th/0105072].

    Article  ADS  Google Scholar 

  29. P.F. Bedaque, G. Rupak, H.W. Grießhammer, H.-W. Hammer, Nucl. Phys. A 714, 589 (2003) [arXiv:nucl-th/0207034].

    Article  MATH  ADS  Google Scholar 

  30. H.W. Grießhammer, Nucl. Phys. A 744, 192 (2004) [arXiv:nucl-th/0404073].

    Article  ADS  Google Scholar 

  31. L. Platter, PhD Thesis, Bonn University (2005).

  32. E.W. Schmid, H. Ziegelmann, The Quantum Mechanical Three-Body Problem (Vieweg, 1971).

  33. W. Meier, W. Glöckle, Phys. Rev. C 28, 1807 (1983).

    Article  ADS  Google Scholar 

  34. W. Glöckle, H. Kamada, Nucl. Phys. A 560, 541 (1993).

    Article  ADS  Google Scholar 

  35. J.A. Tjon, Phys. Lett. B 56, 217 (1975).

    Article  ADS  Google Scholar 

  36. G.J. Hanna, D. Blume, Phys. Rev. A 74, 063604 (2006) [arXiv:cond-mat/0607519].

    Article  ADS  Google Scholar 

  37. D.S. Petrov, C. Salomon, G.V. Shlyapnikov, Phys. Rev. Lett. 93, 090404 (2004) [arXiv:cond-mat/0309010].

    Article  ADS  Google Scholar 

  38. G. Rupak, arXiv:nucl-th/0605074.

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Authors and Affiliations

  1. Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Universität Bonn, 53115, Bonn, Germany

    H. -W. Hammer

  2. Department of Physics and Astronomy, Ohio University, 45701, Athens, OH, USA

    L. Platter

Authors
  1. H. -W. Hammer
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  2. L. Platter
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Correspondence to H. -W. Hammer.

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G. Orlandini

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Hammer, H.W., Platter, L. Universal properties of the four-body system with large scattering length. Eur. Phys. J. A 32, 113–120 (2007). https://doi.org/10.1140/epja/i2006-10301-8

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  • DOI: https://doi.org/10.1140/epja/i2006-10301-8

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