Skip to main content
SpringerLink
Log in

On the modification of the Efimov spectrum in a finite cubic box

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Three particles with large scattering length display a universal spectrum of three-body bound states called “Efimov trimers”. We calculate the modification of the Efimov trimers of three identical bosons in a finite cubic box and compute the dependence of their energies on the box size using effective field theory. Previous calculations for positive scattering length that were perturbative in the finite-volume energy shift are extended to arbitrarily large shifts and negative scattering lengths. The renormalization of the effective field theory in the finite volume is explicitly verified. We investigate the effects of partial-wave mixing and study the behavior of shallow trimers near the dimer energy. Moreover, we provide numerical evidence for universal scaling of the finite-volume corrections.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  ADS  Google Scholar 

  2. L. Platter, Few Body Syst. 46, 139 (2009) (arXiv: 0904.2227 [nucl-th])

    Article  Google Scholar 

  3. V. Efimov, Phys. Lett. B 33, 563 (1970)

    Article  ADS  Google Scholar 

  4. V. Efimov, Sov. J. Nucl. Phys. 29, 546 (1979)

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. T. Kraemer, M. Mark, P. Waldburger, J.G. Danzl, C. Chin, B. Engeser, A.D. Lange, K. Pilch, A. Jaakkola, H.-C. Nägerl, R. Grimm, Nature 440, 315 (2006)

    Article  ADS  Google Scholar 

  8. S. Knoop, F. Ferlaino, M. Mark, M. Berninger, H. Schoebel, H.-C. Naegerl, R. Grimm, Nat. Phys. 5, 227 (2009) (arXiv:0807.3306 [cond-mat])

    Article  Google Scholar 

  9. T.B. Ottenstein, T. Lompe, M. Kohnen, A.N. Wenz, S. Jochim, Phys. Rev. Lett. 101, 203202 (2008) (arXiv:0806.0587 [cond-mat])

    Article  ADS  Google Scholar 

  10. J.H. Huckans, J.R. Williams, E.L. Hazlett, R.W. Stites, K.M. O’Hara, Phys. Rev. Lett. 102, 165302 (2009) (arXiv:0810.3288 [physics.atom-ph])

    Article  ADS  Google Scholar 

  11. G. Barontini, C. Weber, F. Rabatti, J. Catani, G. Thalhammer, M. Inguscio, F. Minardi, Phys. Rev. Lett. 103, 043201 (2009) (arXiv:0901.4584v1 [cond-mat.other])

    Article  ADS  Google Scholar 

  12. N. Gross, Z. Shotan, S. Kokkelmans, L. Khaykovich, Phys. Rev. Lett. 103, 163202 (2009) (arXiv:0906.4731v1 [cond-mat.other])

    Article  Google Scholar 

  13. M. Zaccanti, B. Deissler, C. D’Errico, M. Fattori, M. Jona-Lasinio, S. Müller, G. Roati, M. Inguscio, G. Modugno, Nat. Phys. 5, 586 (2009) (arXiv:0904.4453v1 [cond-mat.quant-gas])

    Article  Google Scholar 

  14. D.L. Canham, H.-W. Hammer, Eur. Phys. J. A 37, 367 (2008) (arXiv:0807.3258 [nucl-th]) and references therein

    Article  ADS  Google Scholar 

  15. K.G. Wilson, Nucl. Phys. Proc. Suppl. 140, 3 (2005) (arXiv:hep-lat/0412043)

    Article  ADS  Google Scholar 

  16. S.R. Beane, P.F. Bedaque, M.J. Savage, U. van Kolck, Nucl. Phys. A 700, 377 (2002) (arXiv:nucl-th/0104030)

    Article  MATH  ADS  Google Scholar 

  17. S.R. Beane, M.J. Savage, Nucl. Phys. A 717, 91 (2003) (arXiv:nucl-th/0208021)

    Article  ADS  Google Scholar 

  18. S.R. Beane, M.J. Savage, Nucl. Phys. A 713, 148 (2003) (arXiv:nucl-th/0206113)

    Article  ADS  Google Scholar 

  19. E. Epelbaum, U.-G. Meißner, W. Glöckle, Nucl. Phys. A 714, 535 (2003) (arXiv:nucl-th/0207089)

    Article  MATH  ADS  Google Scholar 

  20. E. Braaten, H.-W. Hammer, Phys. Rev. Lett. 91, 102002 (2003) (arXiv:nucl-th/0303038)

    Article  ADS  Google Scholar 

  21. E. Epelbaum, H.-W. Hammer, U.-G. Meißner, A. Nogga, Eur. Phys. J. C 48, 169 (2006) (arXiv:hep-ph/0602225)

    Article  ADS  Google Scholar 

  22. H.-W. Hammer, D.R. Phillips, L. Platter, Eur. Phys. J. A 32, 335 (2007) (arXiv:0704.3726 [nucl-th])

    Article  ADS  Google Scholar 

  23. S.R. Beane, P.F. Bedaque, K. Orginos, M.J. Savage, Phys. Rev. Lett. 97, 012001 (2006) (arXiv:hep-lat/0602010)

    Article  ADS  Google Scholar 

  24. S.R. Beane et al., Phys. Rev. D 80, 074501 (2009) (arXiv:0905.0466 [hep-lat])

    Article  Google Scholar 

  25. S.R. Beane, K. Orginos, M.J. Savage, Int. J. Mod. Phys. E 17, 1157 (2008) (arXiv:0805.4629 [hep-lat])

    Article  ADS  Google Scholar 

  26. S.R. Beane, P.F. Bedaque, A. Parreno, M.J. Savage, Phys. Lett. B 585, 106 (2004) (arXiv:hep-lat/0312004)

    Article  ADS  Google Scholar 

  27. S. Tan, Phys. Rev. A 78, 013636 (2008) (arXiv:0709.2530 [cond-mat])

    Article  ADS  Google Scholar 

  28. S.R. Beane, W. Detmold, M.J. Savage, Phys. Rev. D 76, 074507 (2007) (arXiv:0707.1670 [hep-lat])

    Article  ADS  Google Scholar 

  29. W. Detmold, M.J. Savage, Phys. Rev. D 77, 057502 (2008) (arXiv:0801.0763 [hep-lat])

    Article  ADS  Google Scholar 

  30. S.R. Beane, W. Detmold, T.C. Luu, K. Orginos, M.J. Savage, A. Torok, Phys. Rev. Lett. 100, 082004 (2008) (arXiv:0710.1827 [hep-lat])

    Article  ADS  Google Scholar 

  31. W. Detmold, M.J. Savage, A. Torok, S.R. Beane, T.C. Luu, K. Orginos, A. Parreno, Phys. Rev. D 78, 014507 (2008) (arXiv:0803.2728 [hep-lat])

    Article  ADS  Google Scholar 

  32. W. Detmold, K. Orginos, M.J. Savage, A. Walker-Loud, Phys. Rev. D 78, 054514 (2008) (arXiv:0807.1856 [hep-lat])

    Article  ADS  Google Scholar 

  33. L. Pricoupenko, Y. Castin, J. Phys. A 40, 12863 (2007) (arXiv:0705.1502 [cond-mat])

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. M. Lüscher, Nucl. Phys. B 354, 531 (1991)

    Article  ADS  Google Scholar 

  35. M. Lüscher, Nucl. Phys. B 364, 237 (1991)

    Article  ADS  Google Scholar 

  36. V. Bernard, U.-G. Meißner, A. Rusetsky, Nucl. Phys. B 788, 1 (2008) (arXiv:hep-lat/0702012)

    Article  MATH  ADS  Google Scholar 

  37. V. Bernard, M. Lage, U.-G. Meißner, A. Rusetsky, JHEP 08, 024 (2008) (arXiv:0806.4495 [hep-lat])

    Article  ADS  Google Scholar 

  38. S. Kreuzer, H.-W. Hammer, Phys. Lett. B 673, 260 (2009) (arXiv:0811.0159 [nucl-th])

    Article  ADS  Google Scholar 

  39. F.C. von der Lage, H.A. Bethe, Phys. Rev. 71, 612 (1947)

    Article  MATH  ADS  Google Scholar 

  40. S.L. Altmann, A.P. Cracknell, Rev. Mod. Phys. 37, 19 (1965)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. E. Braaten, H.W. Hammer, M. Kusunoki, Phys. Rev. A 67, 022505 (2003) (arXiv:cond-mat/0201281)

    Article  ADS  Google Scholar 

  42. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, third edition (Cambridge University Press, 2007)

Download references

Author information

Authors and Affiliations

  1. Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany

    S. Kreuzer & H. -W. Hammer

Authors
  1. S. Kreuzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. -W. Hammer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Kreuzer.

Additional information

Communicated by M.C. Birse

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kreuzer, S., Hammer, H.W. On the modification of the Efimov spectrum in a finite cubic box. Eur. Phys. J. A 43, 229–240 (2010). https://doi.org/10.1140/epja/i2010-10910-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epja/i2010-10910-6

Keywords

Search

Navigation