Skip to main content
Log in

Exact solutions to the three-body problem for S-wave interactions of the centrifugal type

  • Nuclei
  • Theory
  • Published:
Physics of Atomic Nuclei Aims and scope Submit manuscript

Abstract

The simplest exact solutions to the Schrödinger and Faddeev equations for S-wave pair interactions of the centrifugal type are constructed and investigated for the case of zero total orbital angular momentum of three particles.

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. R. Machleidt, K. Holinde, and Ch. Elster, Phys. Rep. 149, 1 (1987).

    Article  Google Scholar 

  2. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1974; Pergamon, Oxford, 1977).

    Google Scholar 

  3. F. M. Pen'kov, Zh. Éksp. Teor. Fiz. 106, 1046 (1994) [JETP 79, 568 (1994)].

    Google Scholar 

  4. B. N. Efimov, Yad. Fiz. 12, 1080 (1970) [Sov. J. Nucl. Phys. 12, 589 (1971)]; V. Efimov, Nucl. Phys. A 210, 157 (1973).

    Google Scholar 

  5. A. K. Motovilov, S. A. Sofianos, and E. A. Kolganova, Chem. Phys. Lett. 275, 168 (1997); Phys. Rev. A 56, 1686 (1997); J. Phys. B 31, 1279 (1998); A. K. Motovilov et al., Eur. Phys. J. D 13, 33 (2001).

    Article  Google Scholar 

  6. V. A. Roudnev and S. L. Yakovlev, Comput. Phys Commun. 126, 162 (2000); Chem. Phys. Lett. 328, 97 (2000).

    ADS  Google Scholar 

  7. R. A. Aziz et al., J. Chem. Phys. 70, 4330 (1979).

    ADS  Google Scholar 

  8. L. D. Faddeev and S. P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer, Dordrecht, 1993).

    Google Scholar 

  9. S. P. Merkuriev, G. Gignoux, and A. Laverne, Ann. Phys. (N.Y.) 99, 30 (1976).

    Article  MathSciNet  Google Scholar 

  10. N. W. Schellingerhout, L. P. Kok, and G. D. Bosveld, Phys. Rev. A 40, 5568 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  11. V. V. Pupyshev, Yad. Fiz. 43, 1318 (1986) [Sov. J. Nucl. Phys. 43, 846 (1986)].

    MathSciNet  Google Scholar 

  12. C.-Y. Hu, A. A. Kvitsinsky, and S. P. Merkuriev, Phys. Rev. A 45, 2723 (1992).

    Article  ADS  Google Scholar 

  13. V. V. Kostrykin, A. A. Kvitsinsky, and S. P. Merkuriev, Few-Body Syst. 6, 97 (1989).

    Article  MathSciNet  Google Scholar 

  14. Y. Avishai, J. Math. Phys. 16, 1491 (1975).

    Article  ADS  Google Scholar 

  15. V. V. Pupyshev, Phys. Lett. A 140, 151 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  16. V. V. Pupyshev, Preprint R5-2000-296, OIYaI (Joint Insitute for Nuclear Research, Dubna, 2000).

  17. R. I. Jibuti and N. B. Krupennikova, Method of Hyperspherical Functions in Few-Body Quantum Mechanics (Metsniereba, Tbilisi, 1984).

    Google Scholar 

  18. V. V. Pupyshev, Fiz. Élem. Chastits At. Yadra 30, 1562 (1999) [Phys. Part. Nucl. 30, 689 (1999)].

    Google Scholar 

  19. M. Moshinsky, The Harmonic Oscillator in Modern Physics: From Atoms to Quarks (Gordon and Breach, New York, 1969; Mir, Moscow, 1972).

    Google Scholar 

  20. V. V. Pupyshev, Teor. Mat. Fiz. 125, 253 (2000).

    MATH  MathSciNet  Google Scholar 

  21. Ya. A. Smorodinskii and V. D. Éfros, Yad. Fiz. 17, 210 (1973) [Sov. J. Nucl. Phys. 17, 107 (1973)].

    Google Scholar 

  22. B. B. Voevodin, Computational Principles of Linear Algebra (Nauka, Moscow, 1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Yadernaya Fizika, Vol. 66, No. 1, 2003, pp. 64–76.

Original Russian Text Copyright © 2003 by Pupyshev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pupyshev, V.V. Exact solutions to the three-body problem for S-wave interactions of the centrifugal type. Phys. Atom. Nuclei 66, 61–74 (2003). https://doi.org/10.1134/1.1540658

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1540658

Keywords

Navigation