Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2012, Article ID 804652, 13 pages
http://dx.doi.org/10.1155/2012/804652
Research Article

Quasi-Analytical Solutions of DKP Equation under the Deng-Fan Interaction

Physics Department, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran

Received 4 April 2012; Revised 6 June 2012; Accepted 8 June 2012

Academic Editor: S. H. Dong

Copyright © 2012 S. Hassanabadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Kemmer, “Quantum theory of Einstein-Bose particles and nuclear interaction,” Proceedings of the Royal Society A, vol. 166, no. 924, pp. 127–153, 1938. View at Publisher · View at Google Scholar
  2. R. J. Duffin, “On the characteristic matrices of covariant systems,” Physical Review, vol. 54, no. 12, article 1114, 1938. View at Publisher · View at Google Scholar · View at Scopus
  3. N. Kemmer, “The particle aspect of Meson theory,” Proceedings of the Royal Society A, vol. 173, no. 952, pp. 91–116, 1939. View at Publisher · View at Google Scholar
  4. G. Petiau, [Ph.D. thesis], University of Paris, Académie Royale de Belgique. Classe des. Sciences. Mémoires. Collection in-8o 16, no. 2, 1936.
  5. T. R. Cardoso, 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,” The International Journal of Theoretical Physics, vol. 49, no. 1, pp. 10–17, 2010. View at Publisher · View at Google Scholar
  6. H. Hassanabadi, B. Yazarloo, S. Zarrinkamar, and A. A. Rajabi, “Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction,” Physical Review C, vol. 84, no. 6, Article ID 064003, 4 pages, 2011. View at Publisher · View at Google Scholar
  7. T. R. Cardoso, L. B. Castro, and A. S. de Castro, “Inconsistencies of a purported probability current in the Duffin-Kemmer-Petiau theory,” Physics Letters A, vol. 372, no. 38, pp. 5964–5967, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Chetouani, M. Merad, T. Boudjedaa, and A. Lecheheb, “Solution of Duffin-Kemmer-Petiau equation for the step potential,” The International Journal of Theoretical Physics, vol. 43, no. 4, pp. 1147–1159, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Oudi S. Hassanabadi, A.A. Rajabi, and H. Hasanabadi, “Approximate bound state solutions of DKP equation for any J state in the presence of Woods-Saxon potential,” Communications in Theoretical Physics, vol. 57, no. 1, pp. 15–18, 2012. View at Publisher · View at Google Scholar
  10. A. S. de Castro, “Bound states of the Duffin-Kemmer-Petiau equation with a mixed minimal-nonminimal vector cusp potential,” Journal of Physics A, vol. 44, no. 3, Article ID 035201, 2011. View at Publisher · View at Google Scholar
  11. M. Nowakowski, “The electromagnetic coupling in Kemmer-Duffin-Petiau theory,” Physics Letters A, vol. 244, no. 5, pp. 329–337, 1998. View at Publisher · View at Google Scholar
  12. J. T. Lunardi, B. M. Pimentel, R. G. Teixeira, and J. S. Valverde, “Remarks on Duffin-Kemmer-Petiau theory and gauge invariance,” Physics Letters A, vol. 268, no. 3, pp. 165–173, 2000. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Riedel, Relativistische Gleichungen Fuer Spin-1-Teilchen, Diplomarbeit, Institute for Theoretical Physics, Johann Wolfgang Goethe-University, Frankfurt, Germany, 1979.
  14. E. Fischbach, M. M. Nieto, and C. K. Scott, “Duffin-Kemmer-Petiau subalgebras: representations and applications,” Journal of Mathematical Physics, vol. 14, no. 12, pp. 1760–1774, 1973. View at Google Scholar · View at Scopus
  15. B. C. Clark, S. Hama, and G. R. Kalbermann, “Relativistic impulse approximation for Meson-nucleus scattering in the Kemmer-Duffin-Petiau formalism,” Physics Review Letters, vol. 55, no. 6, pp. 592–595, 1985. View at Publisher · View at Google Scholar
  16. G. Kalbermann, “Kemmer-Duffin-Petiau equation approach to pionic atoms,” Physical Review C, vol. 34, no. 6, pp. 2240–2243, 1986. View at Publisher · View at Google Scholar
  17. R. E. Kozack, B. C. Clark, S. Hama, and V. K. Mishra, “Relativistic deuteron-nucleus scattering in the Kemmer-Duffin-Petiau formalism,” Physical Review C, vol. 37, no. 6, pp. 2898–2901, 1988. View at Publisher · View at Google Scholar
  18. R. E. Kozack, “Spin-one Kemmer-Duffin-Petiau equations and intermediate-energy deuteron-nucleus scattering,” Physical Review C, vol. 40, no. 5, pp. 2181–2194, 1989. View at Publisher · View at Google Scholar
  19. V. K. Mishra, S. Hama, and B. C. Clark, “Implications of various spin-one relativistic wave equations for intermediate-energy deuteron-nucleus scattering,” Physical Review C, vol. 43, no. 2, pp. 801–811, 1991. View at Publisher · View at Google Scholar
  20. B. C. Clark, R.J. Furnstahl, L. K. Kerr, J. Rusnak, and S. Hama, “Pion-nucleus scattering at medium energies with densities from chiral effective field theories,” Physics Letters B, vol. 427, no. 3-4, pp. 231–234, 1998. View at Publisher · View at Google Scholar
  21. V. Gribov, “QCD at large and short distances (annotated version),” The European Physical Journal C, vol. 10, no. 1, pp. 71–90, 1999. View at Publisher · View at Google Scholar
  22. I. V. Kanatchikov, “On the Duffin-Kemmer-Petiau formulation of the covariant Hamiltonian dynamics in field theory,” Reports on Mathematical Physics, vol. 46, no. 1-2, pp. 107–112, 2000. View at Publisher · View at Google Scholar
  23. H. Hassanabadi, S. F. Forouhandeh, H. Rahimov, S. Zarrinkamar, and B. H. Yazarloo, “Duffin-Kemmer-Petiau equation under a scalar and vector Hulthen potential; an ansatz solution to the corresponding Heun equation,” Canadian Journal of Physics, vol. 90, no. 3, pp. 299–304, 2012. View at Publisher · View at Google Scholar
  24. J. T. Lunardi, L.A. Manzoni, B.M. Pimentel, and J.S. Valverde, “Duffin-Kemmer-Petiau theory in the causal approach,” International Journal of Modern Physics A, vol. 17, no. 2, pp. 205–227, 2000. View at Publisher · View at Google Scholar
  25. 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,” Journal of Physics A, vol. 33, no. 31, pp. L273–L278, 2000. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Zarrinkamar, A. A. Rajabi, and H. Hassanabadi, “Dirac equation for the harmonic scalar and vector potentials and linear plus coulomb-like tensor potential; the SUSY approach,” Annals of Physics, vol. 325, no. 11, pp. 2522–2528, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. H. Hassanabadi, H. Rahimov, and S. Zarrinkamar, “Cornell and Coulomb interactions for the D-dimensional Klein-Gordon equation,” Annalen der Physik, vol. 523, no. 7, pp. 566–575, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. A. D. Alhaidari, H. Bahlouli, and A. Al-Hasan, “Dirac and Klein-Gordon equations with equal scalar and vector potentials,” Physics Letters A, vol. 349, no. 1–4, pp. 87–97, 2008. View at Publisher · View at Google Scholar
  29. R. L. Hall, N. Saad, and K. D. Sen, “Soft-core Coulomb potentials and Heun's differential equation,” Journal of Mathematical Physics, vol. 51, no. 2, Article ID 022107, 2010. View at Google Scholar
  30. Y. Nedjadi and R. C. Barrett, “On the properties of the Duffin-Kemmer-Petiau equation,” Journal of Physics G, vol. 19, no. 1, pp. 87–98, 1993. View at Publisher · View at Google Scholar
  31. Y. Nedjadi, S. Ait-Tahar, and R. C. Barrett, “An extended relativistic quantum oscillator for S=1 particles,” Journal of Physics A, vol. 31, no. 16, pp. 3867–3874, 1998. View at Publisher · View at Google Scholar · View at Scopus
  32. A. Boumali, “On the eigensolutions of the one-dimensional Duffin-Kemmer-Petiau oscillator,” Journal of Mathematical Physics, vol. 49, no. 2, Article ID 022302, 10 pages, 2008. View at Publisher · View at Google Scholar
  33. I. Boztosun, M. Karakoc, and A. Durmus, “Asymptotic iteration method solutions to the relativistic Duffin-Kemmer-Petiau equation,” Journal of Mathematical Physics, vol. 47, no. 6, Article ID 062301, 11 pages, 2006. View at Publisher · View at Google Scholar
  34. B. Boutabia-Chéraitia and T. Boudjedaa, “Solution of DKP equation in Woods-Saxon potential,” Physics Letters A, vol. 338, no. 2, pp. 97–107, 2005. View at Publisher · View at Google Scholar · View at Scopus
  35. M. Merad, “DKP equation with smooth potential and position-dependent mass,” The International Journal of Theoretical Physics, vol. 46, no. 8, pp. 2105–2118, 2007. View at Publisher · View at Google Scholar
  36. Y. Chargui, A. Trabelsi, and L. Chetouani, “Bound-states of the (1+1)-dimensional DKP equation with a pseudoscalar linear plus Coulomb-like potential,” Physics Letters A, vol. 374, no. 29, pp. 2907–2913, 2010. View at Publisher · View at Google Scholar · View at Scopus
  37. K. Sogut and A. Havare, “Scattering of vector bosons by an asymmetric Hulthen potential,” Journal of Physics A, vol. 43, no. 22, Article ID 225204, 14 pages, 2010. View at Publisher · View at Google Scholar
  38. F. Yaşuk, C. Berkdemir, A. Berkdemir, and C. Önem, “Exact solutions of the Duffin-Kemmer-Petiau equation for the deformed hulthen potential,” Physica Scripta, vol. 71, no. 4, pp. 340–343, 2005. View at Google Scholar · View at Scopus
  39. A. Okninski, “Supersymmetric content of the Dirac and Duffin-Kemmer-Petiau equations,” The International Journal of Theoretical Physics, vol. 50, no. 3, pp. 729–736, 2011. View at Publisher · View at Google Scholar
  40. S. Zarrinkamar, A. A. Rajabi, H. Rahimov, and H. Hassanabadi, “DKP equation under a vector Hulthén-type potential: an approximate solution,” Modern Physics Letters A, vol. 26, no. 22, pp. 1621–1629, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. H. Deng and Y. P. Fan, Shandong University Journal, vol. 7, article 162, 1957.
  42. S. H. Dong and X. Y. Gu, “Arbitrary l state solutions of the Schrödinger equation with the Deng-Fan molecular potential,” Journal of Physics: Conference Series, vol. 96, no. 1, Article ID 012109, 2008. View at Google Scholar
  43. S. H. Dong, “Relativistic treatment of spinless particles subject to a rotating Deng-Fan oscillator,” Communications in Theoretical Physics, vol. 55, no. 6, article 969, 2011. View at Publisher · View at Google Scholar
  44. A. D. S. Mesa, C. Quesne, and Yu. F. Smirnov, “Generalized Morse potential: symmetry and satellite potentials,” Journal of Physics A, vol. 31, no. 1, pp. 321–335, 1998. View at Publisher · View at Google Scholar
  45. Z. M. Rong, H. G. Kjaergaard, and M. L. Sage, “Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules,” Molecular Physics, vol. 101, no. 14, pp. 2285–2294, 2003. View at Publisher · View at Google Scholar
  46. H. Hassanabadi, B. Yazarloo, S. Zarrinkamar, and H. Rahimov, “Deng-Fan potential for relativistic spinless particles—an Ansatz solution,” Communications in Theoretical Physics, vol. 57, no. 3, pp. 339–342, 2012. View at Publisher · View at Google Scholar
  47. H. Hassanabadi, S. Zarrinkamar, and H. Rahimov, “Approximate solution of D-dimensional Klein-Gordon equation with Hulthén-type potential via SUSYQM,” Communications in Theoretical Physics, vol. 56, no. 3, pp. 423–428, 2011. View at Publisher · View at Google Scholar