Skip to main content
Log in

Few-Body Techniques Using Momentum Space for Bound and Continuum States

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

This article is based on the notes (arxiv:1710.11228) written for a set of three lectures given in a school at the Max Planck Institute for the Physics of Complex Systems in October/2017 before the workshop “Critical Stability of Quantum Few-Body Systems”. The last part of the article includes the specific topic presented in the workshop related to the dimensional effects in three-body systems. These notes are primarily dedicated to the students and are only a tentative to show a technique, among many others, to solve problems in a very rich area of the contemporary physics—the Few-Body Physics.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Q.-D. Wang, The global solution of the N-body problem. Celest. Mech. Dyn. Astron. 50, 73–88 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. M.T. Yamashita.: Momentum space techniques in few-body physics: bound and continuum. arxiv:1710.11228 (2017)

  3. T. Frederico, L. Tomio, A. Delfino, M.R. Hadizadeh, M.T. Yamashita, Scales and universality in few-body system. Few-Body Syst. 51, 87–112 (2011)

    Article  ADS  Google Scholar 

  4. F.E. Low, Boson–Fermion scattering in the Heisenberg representation. Phys. Rev. 97, 1392 (1955)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. A.N. Mitra, The nuclear three-body problem. Adv. Nucl. Phys. 3, 1–70 (1969)

    Google Scholar 

  6. G.V. Skornyakov, K.A. Ter-Martirosyan, Three body problem for short range forces. I. Scattering of low energy neutrons by deuterons. Zh. Eksp. Teor. Fiz. 31, 775 (1957)

    MATH  Google Scholar 

  7. V. Efimov, Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. 33, 563–564 (1970)

    Article  Google Scholar 

  8. T. Kraemer et al., Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 3115 (2006)

    Article  Google Scholar 

  9. E. Nielsen, D.V. Fedorov, A.S. Jensen, E. Garrido, The three-body problem with short-range interactions. Phys. Rep. 347, 373 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. G.S. Danilov, On the three-body problem with short-range forces. Sov. Phys. JETP 13, 349 (1961)

    MathSciNet  MATH  Google Scholar 

  11. M.T. Yamashita et al., Single-particle momentum distributions of Efimov states in mixed-species systems. Phys. Rev. A 87, 062702 (2013)

    Article  ADS  Google Scholar 

  12. E. Braaten, H.-W. Hammer, Universality in few-body systems with large scattering length. Phys. Rep. 428, 259–390 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  13. J.H. Sandoval., et al., Squeezing the Efimov effect. arXiv:1708.00012 (2017)

  14. D.S. Rosa, T. Frederico, G. Krein, M.T. Yamashita, Efimov effect in \(D\) spatial dimensions in \(AAB\) systems. arxiv:1707.06616 (2017)

Download references

Acknowledgements

This work was partly supported by funds provided by the Brazilian agencies Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq Grant No. 142029/2017-3 (D.S.R). Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP Grant No. 2016/01816-2(MTY), Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq grant no. 302075/2016-0(MTY), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—CAPES Grant No. 88881.030363/2013-01(MTY).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. T. Yamashita.

Additional information

This article belongs to the Topical Collection “Critical Stability of Quantum Few-Body Systems”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yamashita, M.T., Rosa, D.S. & Sandoval, J.H. Few-Body Techniques Using Momentum Space for Bound and Continuum States. Few-Body Syst 59, 19 (2018). https://doi.org/10.1007/s00601-018-1347-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-018-1347-1

Navigation