Skip to main content
SpringerLink
Log in

The generalized Coulomb interactions for relativistic scalar bosons

  • Physics of Elementary Particles and Atomic Nuclei. Theory
  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

Abstract

Approximate analytical solutions of Duffin–Kemmer–Petiau (DKP) equation are obtained for the truncated Coulomb, generalized Cornell, Richardson and Song–Lin potentials via the quasi-exact analytical ansatz approach.

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.

Similar content being viewed by others

References

  1. N. Kemmer, “Quantum theory of Einstein-Bose particles and nuclear interaction,” Proc. R. Soc. A 166, 127 (1938).

    Article  ADS  MATH  Google Scholar 

  2. R. J. Duffin, “On the characteristic matrices of covariant systems,” Phys. Rev. 54, 1114 (1938).

    Article  ADS  MATH  Google Scholar 

  3. N. Kemmer, “The particle aspect of meson theory,” Proc. R. Soc. A 173, 91 (1939).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. G. Petiau, “Knots and Feynman diagrams,” Acad. R. Belg., A. Sci. Mem. Collect. 16, 2 (1936).

    Google Scholar 

  5. T. R. Cardoso and L. B. Castro, and A. S. de Castro, “Effects due to a scalar coupling on the particle-antiparticle production in the Duffin-Kemmer-Petiau theory,” Int. J. Theor. Phys. 49, 10–17 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Chetouani, M. Merad, T. Boudjedaa, and A. Lecheheb, “Solution of Duffin-Kemmer-Petiau equation for the step potential,” Int. J. Theor. Phys. 43, 1147 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. S. de Castro, “Bound states of the Duffin–Kemmer–Petiau equation with a mixed minimal–nonminimal vector cusp potential,” J. Phys. A: Math. Theor. 44, 035201 (2011).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. M. Nowakowski, “The electromagnetic coupling in Kemmer–Duffin–Petiau theory,” Phys. Lett. A 244, 329 (1998).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. J. T. Lunardi, B. M. Pimentel, R. G. Teixeira, and J. S. Valverde, “Remarks on Duffin–Kemmer–Petiau theory and gauge invariance,” Phys. Lett. A 268, 165 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. E. Fischbach, M. M. Nieto, and C. K. Scott, “Duffin–Kemmer-–Petiau subalgebras: representations and applications,” J. Math. Phys. 14, 1760 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  11. B. M. Pimentel and V. Y. Fainberg, “Equivalence of many-gluon green’s functions in the Duffin–Kemmer–Petieu and Klein–Gordon–Fock statistical quantum field theories,” Math. Phys. 143, 792 (2005).

    MathSciNet  MATH  Google Scholar 

  12. V. Y. Fainberg and B. M. Pimentel, “Duffin–Kemmer–Petiau and Klein–Gordon–Fock equations for electromagnetic, Yang–Mills and external gravitational field interactions: proof of equivalence,” Phys. Lett. A 271, 16 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. V. Y. Fainberg and B. M. Pimentel, “On equivalence of Duffin–Kemmer–Petiau and Klein–Gordon equations,” Braz. J. Phys. 30, 275 (2000).

    Article  ADS  MATH  Google Scholar 

  14. V. Y. Fainberg and B. M. Pimentel, “On equivalence of Duffin–Kemme–Petiau and Klein–Gordon equations,” Theor. Math. Phys. 124, 1234 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  15. B. C. Clark, S. Hama, G. R. Kälbermann, R. L. Mercer, and L. Ray, “Relativistic impulse approximation for meson-nucleus scattering in the Kemmer–Duffin-Petiau formalism,” Phys. Rev. Lett. 55, 592 (1985).

    Article  ADS  Google Scholar 

  16. G. Kalbermann, “Kemmer–Duffin–Petiau equation for pionic atoms and anomalous strong interaction effects,” Phys. Rev. C 34, 2244 (1986).

    Article  ADS  Google Scholar 

  17. R. E. Kozack, “Spin-one Kemmer–Duffin–Petiau equations and intermediate-energy deuteron-nucleus scattering,” Phys. Rev. C 40, 2181 (1989).

    Article  ADS  Google Scholar 

  18. V. K. Mishra, S. Hama, B. C. Clark, R. E. Kozack, R. L. Mercer, and L. Ray, “Implications of various spin-one relativistic wave equations for intermediateenergy deuteron-nucleus scattering,” Phys. Rev. C 43, 801 (1991).

    Article  ADS  Google Scholar 

  19. B. C. Clark, R. J. Furnstahl, K. L. Kurth, J. Rusnak, and S. Hama, “Pion-nucleus scattering at medium energies with densities from chiral effective field theories,” Phys. Lett. B 427, 231 (1998).

    Article  ADS  Google Scholar 

  20. V. Gribov, “QCD at large and short distances (annotated version),” Eur. Phys. J. C 10, 71 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  21. I. V. Kanatchikov, “On the Duffin–Kemmer–Petiau formulation of the covariant Hamiltonian dynamics in field theory,” Rep. Math. Phys. 46, 107 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. J. T. Lunardi, B. M. Pimentel, R. G. Teixeiri, and J. S. Valverde, “Remarks on Duffin–Kemmer–Petiau theory and gauge invariance,” Phys. Lett. A 268, 165 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. M. de Montigny, F. C. Khanna, A. E. Santana, E. S. Santos, and J. D. M. Vianna, “Galilean covariance and the Duffin–Kemmer–Petiau equation,” J. Phys. A 33, L273 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. E. Fischbach, M. M. Nieto, and C. K. Scott, “Structure of the Duffin–Kemmer–Petiau matrix element for k(l3) decay,” Prog. Theor. Phys. 51, 1585–1597 (1974).

    Article  ADS  Google Scholar 

  25. R. A. Krajcik and M. M. Nieto, “Bhabha first order wave equations. 2. Mass and spin composition, Hamiltonians, and general Sakata–Taketani reductions,” Phys. Rev. D: Part. Fields 11, 1442–1458 (1975).

  26. E. S. Cheb-Terrab, “Solutions for the general, confluent and biconfluent heun equations and their connection with Abel equations,” J. Phys. A: Math. Gen. 37, 9923 (2004).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. D. Singh, Y. P. Varshni, and R. Dutt, “Boundeigenstates for two truncated Coulomb potentials,” Phys. Rev. A 32, 619 (1985).

    Article  ADS  Google Scholar 

  28. H. de Meyer and G. Vandenberghe, “Exact boundstate solutions of the potential V(r) =–Ze2/ (r + ß),” J. Phys. A: Math. Gen. 23, 1323 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  29. A. Sinha and R. Roychoudhury, “Exact analytical solutions for the cut-off Coulomb potential V(r) = γZe2/(r + ß),” J. Phys. A: Math. Gen. 23, 3869 (1990).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. R. N. Chaudhuri and M. Mondal, “Exact bound-state solutions of the cut-off Coulomb potential in Ndimensional space,” Pramana J. Phys. 39, 493 (1992).

    Article  ADS  Google Scholar 

  31. C. W. Clark, “Closed-form solutions of the Schrödinger equation for a class of smoothed Coulomb potentials,” J. Phys. B 30, 2517 (1997).

    Article  ADS  Google Scholar 

  32. Y. I. Salamin, S. H. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, “Relativistic high-power laser-matter interactions,” Phys. Rep. 427, 41 (2006).

    Article  ADS  Google Scholar 

  33. C. A. S. Lima and L. C. M. Miranda, “Atoms in superintense laser fields,” Phys. Rev. A 23, 3335 (1981).

    Article  ADS  Google Scholar 

  34. J. H. Eberly, Q. Su, and J. Javanainen, “Nonlinear light scattering accompanying multiphoton ionization,” Phys. Rev. Lett. 62, 881 (1989).

    Article  ADS  Google Scholar 

  35. Q. Su and J. H. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A 44, 5997 (1991).

    Article  ADS  Google Scholar 

  36. J. von Stecher and C. Greene, “Correlated Gaussian hyperspherical method for few-body systems,” Phys. Rev. A 80, 022504 (2009).

    Article  ADS  Google Scholar 

  37. A. Kievsky, E. Garrido, C. Romero-Redondo, and P. Barletta, “The helium trimer with soft-core potentials,” Few-Body Syst. 51, 259 (2011).

    Article  ADS  Google Scholar 

  38. G. S. Bali, “QCD forces and heavy quark bound states,” Phys. Rep. 343, 1 (2001).

    Article  ADS  MATH  Google Scholar 

  39. J. L. Richardson, “The heavy quark potential and the γ, J/ systems,” Phys. Lett. B 82, 272 (1976).

    Article  ADS  Google Scholar 

  40. Sh. Banerjee, “Cosmological dark energy from the cosmic QCD phase transition and colour entanglement,” Phys. Lett. B 611, 27 (2005).

    Article  ADS  Google Scholar 

  41. O. Andreev and V. I. Zakharov, “Heavy-quark potentials and AdS/QCD,” Phys. Rev. D: Part. Fields 74, 025023 (2006).

    Article  ADS  Google Scholar 

  42. C. D. White, “The cornell potential from general geometries in AdS/QCD,” Phys. Lett. B 652, 79 (2007).

    Article  ADS  Google Scholar 

  43. X. Song and H. Lin, “A new potential model for heavy quarkonium,” Zeit. Phys. C 34, 223 (1987).

    Article  Google Scholar 

  44. L. P. Fulcher, “Phenomenological predictions of the properties of the Bc system,” Phys. Rev. D: Part. Fields 60, 074006 (1999).

    Article  ADS  Google Scholar 

  45. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Dover, Mineola, N.Y., 2008).

    MATH  Google Scholar 

  46. H. W. Crater and P. van Alstine, “Two-body Dirac equations,” Ann. Phys. (N.Y.) 148, 57 (1983).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. H. W. Crater and J. Schiermeyer, “Applications of twobody Dirac equations to the meson spectrum with three versus two covariant interactions, SU(3) mixing, and comparison to a quasipotential approach,” Phys. Rev. D: Part. Fields 82, 094020 (2010).

    Article  ADS  Google Scholar 

  48. S. H. Dong, “A new approach to the relativistic Schrödinger equation with central potential: ansatz method,” Int. J. Theor. Phys. 40, 569 (2001).

    Article  Google Scholar 

  49. H. Hassanabadi, B. H. Yazarloo, S. Zarrinkamar, and A. A. Rajabi, “Dirac equation under the Deng-Fan potential and the Hulthén potential as a tensor interaction via SUSYQM,” Phys. Part. Nucl. Lett. 10, 132 (2013).

    Article  Google Scholar 

  50. H. Hassanabadi, Z. Molaee, S. Zarrinkamar, and M. Ghominejad, “Exact solutions of spin-one DKP equation under Kratzer potential in (1 + 2) dimensions,” Phys. Part. Nucl. Lett. 10, 699 (2013).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

    S. Zarrinkamar

  2. Department of Physics, University of Guilan, Rasht, 41635-1914, Iran

    H. Panahi & M. Rezaei

Authors
  1. S. Zarrinkamar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Panahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Rezaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Zarrinkamar.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zarrinkamar, S., Panahi, H. & Rezaei, M. The generalized Coulomb interactions for relativistic scalar bosons. Phys. Part. Nuclei Lett. 13, 436–441 (2016). https://doi.org/10.1134/S1547477116040142

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477116040142

Search

Navigation