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Few-Body Systems

, 59:19 | Cite as

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

  • M. T. Yamashita
  • D. S. Rosa
  • J. H. Sandoval
Article
  • 51 Downloads
Part of the following topical collections:
  1. Critical Stability 2017

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.

Notes

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).

References

  1. 1.
    Q.-D. Wang, The global solution of the N-body problem. Celest. Mech. Dyn. Astron. 50, 73–88 (1991)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    M.T. Yamashita.: Momentum space techniques in few-body physics: bound and continuum. arxiv:1710.11228 (2017)
  3. 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)ADSCrossRefGoogle Scholar
  4. 4.
    F.E. Low, Boson–Fermion scattering in the Heisenberg representation. Phys. Rev. 97, 1392 (1955)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    A.N. Mitra, The nuclear three-body problem. Adv. Nucl. Phys. 3, 1–70 (1969)Google Scholar
  6. 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)zbMATHGoogle Scholar
  7. 7.
    V. Efimov, Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. 33, 563–564 (1970)CrossRefGoogle Scholar
  8. 8.
    T. Kraemer et al., Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 3115 (2006)CrossRefGoogle Scholar
  9. 9.
    E. Nielsen, D.V. Fedorov, A.S. Jensen, E. Garrido, The three-body problem with short-range interactions. Phys. Rep. 347, 373 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    G.S. Danilov, On the three-body problem with short-range forces. Sov. Phys. JETP 13, 349 (1961)MathSciNetzbMATHGoogle Scholar
  11. 11.
    M.T. Yamashita et al., Single-particle momentum distributions of Efimov states in mixed-species systems. Phys. Rev. A 87, 062702 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    E. Braaten, H.-W. Hammer, Universality in few-body systems with large scattering length. Phys. Rep. 428, 259–390 (2006)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    J.H. Sandoval., et al., Squeezing the Efimov effect. arXiv:1708.00012 (2017)
  14. 14.
    D.S. Rosa, T. Frederico, G. Krein, M.T. Yamashita, Efimov effect in \(D\) spatial dimensions in \(AAB\) systems. arxiv:1707.06616 (2017)

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • M. T. Yamashita
    • 1
  • D. S. Rosa
    • 1
  • J. H. Sandoval
    • 1
  1. 1.Instituto de Física TeóricaUniversidade Estadual PaulistaSão PauloBrazil

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