Skip to main content
SpringerLink
Log in

A New Treatment of 2N and 3N Bound States in Three Dimensions

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

Abstract

The direct treatment of the Faddeev equation for the three-boson system in 3 dimensions is generalized to nucleons. The one Faddeev equation for identical bosons is replaced by a strictly finite set of coupled equations for scalar functions which depend only on 3 variables. The spin-momentum dependence occurring as scalar products in 2N and 3N forces accompanied by scalar functions is supplemented by a corresponding expansion of the Faddeev amplitudes. After removing the spin degrees of freedom by suitable operations only scalar expressions depending on momenta remain. The corresponding steps are performed for the deuteron leading to two coupled equations.

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. Bernard V., Epelbaum E., Krebs H.: Ulf-G.Meißner, Subleading contributions to the chiral three-nucleon force I: long-range terms. Phys. Rev. C 77, 064004 (2008)

    Article  ADS  Google Scholar 

  2. Epelbaum E.: Few-nucleon forces and systems in chiral effective field theory. Prog. Part. Nucl. Phys. B 57, 654 (2006)

    Article  ADS  Google Scholar 

  3. Hüber D., Witała H., Glöckle W.: Momentum space calculations for three-nucleon scattering including a three-nucleon force. Few Body Syst. 14, 171 (1993)

    Article  Google Scholar 

  4. Elster Ch., Schadow W., Nogga A., Glöckle W.: Three body bound state calculations without angular momentum decomposition. Few Body Syst. 27, 83 (1999)

    Article  ADS  Google Scholar 

  5. Liu H., Elster Ch., Glöckle W.: Model study of three-body forces in the three-body bound state. Few Body Syst. 33, 241 (2003)

    Article  ADS  Google Scholar 

  6. Liu H., Elster Ch., Glöckle W.: Three-body scattering at intermediate energies. Phys. Rev. C 72, 054003 (2005)

    Article  ADS  Google Scholar 

  7. Lin T., Elster C., Polyzou W.N., Witała H., Glöckle W.: Poincaré invariant three-body scattering at intermediate energies. Phys. Rev. C 78, 024002 (2008)

    Article  ADS  Google Scholar 

  8. Bayegan S., Hadizadeh M.R., Harzchi M.: Three-nucleon bound state in a spin-isospin dependent three dimensional approach. Phys. Rev. C 77, 064005 (2008)

    Article  ADS  Google Scholar 

  9. Gerjuoy E., Schwinger J.: On tensor forces and the theory of light nuclei. Phys. Rev. 61, 138 (1942)

    Article  ADS  Google Scholar 

  10. Fachruddin I., Glöckle W., Elster Ch., Nogga A.: The operator form of 3H (3He) and its spin structure. Phys. Rev. C 69, 064002 (2004)

    Article  ADS  Google Scholar 

  11. Ericson, T., Weise, W.: Pions and Nuclei. In: The International Series of Monographs in Physics No. 74, p. 49. Clarendon, Oxford (1998)

  12. Fachruddin I., Elster Ch., Glöckle W.: New forms of deuteron equations and wave function representations. Phys. Rev. C 63, 054003 (2001)

    Article  ADS  Google Scholar 

  13. Wolfenstein L.: Possible triple-scattering experiments. Phys. Rev. 96, 1654 (1954)

    Article  MATH  ADS  Google Scholar 

  14. Witała, H., Skibiński, R., Golak, J., Glöckle, W.: A novel treatment of the proton-proton Coulomb force in elastic proton-deuteron Faddeev calculations, nucl-th/0903.1522

  15. Glöckle W.: The Quantum Mechanical Few-Body Problem. Springer, Berlin (1983)

    Google Scholar 

  16. Epelbaum E., Nogga A., Glöckle W., Kamada H., Meissner U.-G., Witała H.: Three-nucleon forces from chiral effective field theory. Phys. Rev. C 66, 064001 (2002)

    Article  ADS  Google Scholar 

  17. Coon S.A., Scadron M.D., McNamee P.C., Barrett B.R., Blatt D.W.E., McKellear B.H.J.: The two pion exchange, three nucleon potential and nuclear matter. Nucl. Phys. A 317, 242 (1979)

    Article  ADS  Google Scholar 

  18. Coon S.A., Glöckle W.: The two pion exchange three nucleon potential: partial wave analysis in momentum space. Phys. Rev. C 23, 1790 (1981)

    Article  ADS  Google Scholar 

  19. Kotlyar, V.: Tensor and operator forms of 3He and 3H wave functions for parity-violating nuclear forces, nucl-th/0712.2680

  20. Stadler A., Glöckle W., Sauer P.U.: Faddeev equations with three-nucleon force in momentum space. Phys. Rev. C 44, 2319 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  21. Hüber D., Kamada, H., Witała, H., Glöckle, W.: How to include a three-nucleon force into Faddeev equations for the 3N continuum: a new form. Acta Phys. Polonica B 28, 1677 (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für theoretische Physik II, Ruhr-Universität Bochum, 44780, Bochum, Germany

    W. Glöckle

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

    Ch. Elster

  3. M. Smoluchowski Institute of Physics, Jagiellonian University, 30059, Kraków, Poland

    J. Golak, R. Skibiński & H. Witała

  4. Department of Physics, Faculty of Engineering, Kyushu Institute of Technology, 1-1 Sensuicho Tobata, Kitakyushu, 804-8550, Japan

    H. Kamada

Authors
  1. W. Glöckle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ch. Elster
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Golak
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. Skibiński
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. Witała
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. H. Kamada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. Glöckle.

Additional information

Dedicated to Prof. W. Plessas on the occasion of his 60th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glöckle, W., Elster, C., Golak, J. et al. A New Treatment of 2N and 3N Bound States in Three Dimensions. Few-Body Syst 47, 25–38 (2010). https://doi.org/10.1007/s00601-009-0064-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-009-0064-1

Keywords

Search

Navigation