Skip to main content
SpringerLink
Log in

Numerical solution of relativistic problems on bound states of systems of two spinless particles

  • Elementary Particle Physics and Field Theory
  • Published:
Russian Physics Journal Aims and scope

Numerical solutions of the equations of quantum field theory describing bound s-states of systems of two scalar particles have been found for the following three cases: a one-boson exchange potential, a superposition of such potentials, and also the Coulomb potential in the relativistic configuration representation. On the basis of these solutions, the elastic scattering form factors and decay constants for decay of a two-particle system into two photons have been obtained. It is shown that the number of zeros of the elastic form factors coincides with the number of zeros of the wave functions and is equal to the quantum number of the state of the system minus one. The obtained energy spectra and decay constants are compared with the experimentally measured values for positronium.

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. A. A. Logunov and A. N. Tavkhelidze, Nuovo Cimento, 29, No. 2, 380–399 (1963).

    Article  MathSciNet  Google Scholar 

  2. V. G. Kadyshevsky, Nucl. Phys., B6, No. 1, 125–148 (1968).

    Article  ADS  Google Scholar 

  3. V. G. Kadyshevskii, R. M. Mir-Kasimov, and N. B. Skachkov, Fiz. Elem. Chastits Atom. Yadra, 2, No. 3, 635–690 (1972).

    Google Scholar 

  4. N. B. Skachkov and I. L. Solovtsov, Teor. Mat. Fiz., 43, No. 3, 330–342 (1980).

    Article  MathSciNet  Google Scholar 

  5. V. I. Savrin and N. B. Skachkov, CERN Preprint, TH. 2913 (1980).

  6. V. I. Savrin, The Quasi-Potential Method in the Theory of Bound States [in Russian], Publishing House of Samara State University, Samara (2006).

  7. G. A. Kozlov, S. P. Kuleshov, V. I. Savrin, et al., Teor. Mat. Fiz., 60, No. 1, 24–36 (1984).

    Article  Google Scholar 

  8. V. N. Kapshai and T. A. Alferova, Russ. Phys. J., 40, No. 7, 641–648 (1997).

    Article  Google Scholar 

  9. V. N. Kapshai and T. A. Alferova, J. Phys., A32, 5329–5342 (1999).

    MathSciNet  ADS  Google Scholar 

  10. V. N. Kapshai and Yu. A. Grishechkin, Russ. Phys. J., 52, No. 6, 554–563 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  11. N. N. Kalitkin, Numerical Methods [in Russian], BHV-Peterburg, Saint Petersburg (2011).

    Google Scholar 

  12. N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods [in Russian], BINOM, Laboratoriya Znanii, Moscow (2011).

    Google Scholar 

  13. T. A. Alferova and V. N. Kapshai, in: Nonlinear Phenomena in Complex Systems: Proc. Sixth Annual Seminar NPCS’97, Minsk (1998), pp. 78–85.

  14. E. A. Dei, V. N. Kapshai, and N. B. Skachkov, Teor. Mat. Fiz., 82, No. 2, 188–198 (1990).

    Article  MathSciNet  Google Scholar 

  15. T. M. Solov’eva and E. P. Zhidkov, Comp. Phys. Comm., 126, 168–177 (2000).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. A. Messiah, Quantum Mechanics, Vol. 1, North Holland Publishing Company, Amsterdam (1967).

  17. P. J. Mohr, B. N. Taylor, and D. B. Newell, CODATA Recommended Values of the Fundamental Physical Constants: 2010, National Institute of Standards and Technology, Gaithersburg (2012).

  18. M. S. Fee, Phys. Rev. Lett., 70, No. 10, 1397–1400 (1993).

    Article  ADS  Google Scholar 

  19. A. H. Al-Ramadhan and D. W. Gidley, Phys. Rev. Lett., 72, 1632–1635 (1994).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. F. Skorina Gomel’ State University, Gomel’, Belarus

    Yu. A. Grishechkin & V. N. Kapshai

Authors
  1. Yu. A. Grishechkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. N. Kapshai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. N. Kapshai.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 71–8, April, 2013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grishechkin, Y.A., Kapshai, V.N. Numerical solution of relativistic problems on bound states of systems of two spinless particles. Russ Phys J 56, 435–443 (2013). https://doi.org/10.1007/s11182-013-0053-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11182-013-0053-1

Keywords

Search

Navigation