Table of Contents
ISRN High Energy Physics
Volume 2012, Article ID 987196, 10 pages
http://dx.doi.org/10.5402/2012/987196
Research Article

Approximate Complete Solutions of DKP Equation under a Vector Exponential Interaction via a Pekeris-Type Approximation

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

Received 19 September 2012; Accepted 9 October 2012

Academic Editors: C. Ahn and W. Li

Copyright © 2012 S. Zarrinkamar 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 · View at Zentralblatt MATH
  2. R. J. Duffin, “On the characteristic matrices of covariant systems,” Physical Review, vol. 54, no. 12, p. 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 · View at Zentralblatt MATH
  4. G. Petiau, “University of Paris thesis,” Académie Royale De Belgique. Classe Des Sciences. Mémoires. Collection, vol. 16, p. 1114, 1936. View at Google Scholar
  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,” International Journal of Theoretical Physics, vol. 49, no. 1, pp. 10–17, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. T. R. Cardoso and A. S. de Castro, “On the threshold for the pair production and localization of spinless particles,” Revista Brasileira De Ensino De Fi'Sica, vol. 29, pp. 203–208, 2007. 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 Zentralblatt MATH
  8. L. Chetouani, M. Merad, T. Boudjedaa, and A. Lecheheb, “Solution of Duffin-Kemmer-Petiau equation for the step potential,” International Journal of Theoretical Physics, vol. 43, no. 4, pp. 1147–1159, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. T. R. Cardoso, L. B. Castro, and A. S. de Castro, “On the nonminimal vector coupling in the Duffin-Kemmer-Petiau theory and the confinement of massive bosons by a linear potential,” Journal of Physics A, vol. 43, no. 5, Article ID 055306, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  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 · View at Zentralblatt MATH
  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 · View at Zentralblatt MATH
  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 Zentralblatt MATH
  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, pp. 1760–1774, 1973. View at Publisher · View at Google Scholar
  15. B. C. Clark et al., “Relativistic impulse approximation for Meson-Nucleus scattering in the Kemmer-Duffin-Petiau formalism,” Physical Review Letters, vol. 55, 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, pp. 2240–2243, 1986. View at Publisher · View at Google Scholar
  17. R. E. Kozack, B. C. Clark, S. Hama et al., “Relativistic deuteron-nucleus scattering in the Kemmer-Duffin-Petiau formalism,” Physical Review C, vol. 37, pp. 2898–2901, 1988. View at Publisher · View at Google Scholar
  18. R. E. Kozack, B. C. Clark, S. Hama et al., “Spin-one Kemmer-Duffin-Petiau equations and intermediate-energy deuteron-nucleus scattering,” Physical Review C, vol. 40, pp. 2181–2194, 1989. View at Publisher · View at Google Scholar
  19. V. K. Mishra, B. C. Clark, S. Hama et al., “Implications of various spin-one relativistic wave equations for intermediate-energy deuteron-nucleus scattering,” Physical Review C, vol. 43, pp. 801–811, 1991. View at Publisher · View at Google Scholar
  20. B. C. Clarka, R. J. Furnstahla, L. K. Kerr et al., “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 distance,” The European Physical Journal C, vol. 10, pp. 71–90, 1999. 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 · View at Zentralblatt MATH
  23. 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 Zentralblatt MATH
  24. J. T. Lunardi, B. M. Pimentel, J. S. Valverde, and L. A. Manzoni, “Duffin-Kemmer-Petiau theory in the causal approach,” International Journal of Modern Physics A, vol. 17, no. 2, pp. 205–227, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  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 Zentralblatt MATH
  26. Y. Nedjadi and R. C. Barrett, “On the properties of the Duffin-Kemmer-Petiau equation,” Journal of Physics G, vol. 19, no. 1, article 006, pp. 87–98, 1993. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Nedjadi, S. Ait-Tahar, and R. C. Barrett, “An extended relativistic quantum oscillator for particles,” Journal of Physics A, vol. 31, no. 16, pp. 3867–3874, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. A. Boumali, “On the eigensolutions of the one-dimensional Duffin-Kemmer-Petiau oscillator,” Journal of Mathematical Physics, vol. 49, no. 2, Article ID 022302, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. I. Boztosun, M. Karakoc, F. Yasuk, 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, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. 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 Zentralblatt MATH
  31. M. Merad, “DKP equation with smooth ptential and position-dependent mass,” International Journal of Theoretical Physics, vol. 46, no. 8, pp. 2105–2118, 2007. View at Publisher · View at Google Scholar
  32. Y. Chargui, A. Trabelsi, and L. Chetouani, “Bound-states of the -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
  33. E. L. Hill, “The theory of vector spherical harmonics,” American Journal of Physics, vol. 22, pp. 211–214, 1954. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  34. G. Junker, Supersymmetric Methods in Quantum and Statistical Physics, Springer, 1996.
  35. F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Physics Reports A, vol. 251, no. 5-6, pp. 267–385, 1995. View at Publisher · View at Google Scholar
  36. B. K. Bagchi, Supersymmetry in quantum and classical mechanics, Chapman & Hall, 2000. View at Zentralblatt MATH
  37. E. J. Copeland et al., “Measuring the quantum state of a Bose-Einstein condensate,” Physical Review A, vol. 57, pp. 4686–4694, 1998. View at Publisher · View at Google Scholar
  38. Z. Guoa, Y. Piaoa, and Y. Zhang, “Cosmological scaling solutions and multiple exponential potentials,” Physics Letters B, vol. 568, no. 1-2, pp. 1–7, 2003. View at Google Scholar
  39. A. A. Coley, J. Ibáñez, and R. J. van den Hoogen, “Homogeneous scalar field cosmologies with an exponential potential,” Journal of Mathematical Physics, vol. 38, no. 10, pp. 5256–5271, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  40. L. Monchick, “Collision integrals for the exponential repulsive potential,” The Physics of Fluids, vol. 2, pp. 695–700, 1959. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  41. J. N. Ginocchio, “Pseudospin as a relativistic symmetry,” Physical Review Letters, vol. 78, pp. 436–439, 1997. View at Publisher · View at Google Scholar
  42. R. R. Betts and A. H. Wuosmaa, “Nuclear molecules,” Reports on Progress in Physics, vol. 60, no. 8, pp. 819–861, 1997. View at Publisher · View at Google Scholar · View at Scopus
  43. C. S. Lam and Y. P. Varshni, “Energies of s eigenstates in a static screened coulomb potential,” Physical Review A, vol. 4, no. 5, pp. 1875–1881, 1971. View at Publisher · View at Google Scholar · View at Scopus
  44. B. Durand and L. Durand, “Duality for heavy-quark systems,” Physical Review D, vol. 23, no. 5, pp. 1092–1102, 1981. View at Publisher · View at Google Scholar · View at Scopus
  45. R. L. Hall, “Envelope representations for screened Coulomb potentials,” Physical Review A, vol. 32, pp. 14–18, 1985. View at Publisher · View at Google Scholar
  46. A. A. Berezin, “Theory of positron trapping by F- and F′-colour centres in alkali halides,” Physica Status Solidi B, vol. 50, no. 1, pp. 71–75, 1972. View at Publisher · View at Google Scholar
  47. N. Hatano and D. R. Nelson, “Localization transitions in Non-Hermitian quantum mechanics,” Physical Review Letters, vol. 77, pp. 570–573, 1996. View at Publisher · View at Google Scholar
  48. N. Hatano and D. R. Nelson, “Vortex pinning and non-Hermitian quantum mechanics,” Physical Review B, vol. 56, pp. 8651–8673, 1997. View at Publisher · View at Google Scholar
  49. P. M. Morse, “Diatomic molecules according to the wave mechanics. II. Vibrational levels,” Physical Review, vol. 34, pp. 57–64, 1929. View at Publisher · View at Google Scholar
  50. S.-H. Dong, R. Lemus, and A. Frank, “Ladder operators for the Morse potential,” International Journal of Quantum Chemistry, vol. 86, no. 5, pp. 433–439, 2002. View at Publisher · View at Google Scholar
  51. R. Dutt, K. Chowdhury, and Y. P. Varshni, “An improved calculation for screened Coulomb potentials in Rayleigh-Schrodinger perturbation theory,” Journal of Physics A, vol. 18, no. 9, p. 1379, 1985. View at Publisher · View at Google Scholar
  52. T. Xu, Z.-Q Cao, Y.-C Ou et al., “Critical radius and dipole polarizability for a confined system,” Chinese Physics, vol. 15, no. 6, p. 1172, 2006. View at Publisher · View at Google Scholar
  53. T. Tietz, “Negative hydrogen ion,” Journal of Chemical Physics, vol. 35, p. 1917, 1961. View at Publisher · View at Google Scholar
  54. K. Szalewicz and H. J. Monkhorst, “On application of 0s orbitals in SCF calculations,” The Journal of Chemical Physics, vol. 75, no. 12, pp. 5785–5788, 1981. View at Publisher · View at Google Scholar · View at Scopus
  55. G. Malli, “Molecular integrals involving hulthén-type functions (n=1STO) in relativistic quantum chemistry,” Chemical Physics Letters, vol. 78, no. 3, pp. 578–580, 1981. View at Publisher · View at Google Scholar
  56. J. Lindhard and P. G. Hansen, “Atomic effects in low-energy beta decay: the case of tritium,” Physical Review Letters, vol. 57, pp. 965–967, 1986. View at Publisher · View at Google Scholar
  57. I. S. Bitenskya, V. Kh. Ferlegerb, I. A. Wojciechowski et al., “Distortion of H2 potentials by embedding into an electron gas at molecule scattering by a metal surface,” Nuclear Instruments and Methods in Physics Research Section B, vol. 125, no. 1–4, pp. 201–206, 1997. View at Publisher · View at Google Scholar
  58. C.-S. Jia, J.-Y. Wang, S. He, and L.-T. Sun, “Shape invariance and the supersymmetry WKB approximation for a diatomic molecule potential,” Journal of Physics A, vol. 33, no. 39, pp. 6993–6998, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  59. P. Pyykko and J. Jokisaari, “Spectral density analysis of nuclear spin-spin coupling: I. A Hulthén potential LCAO model for JX-H in hydrides XH4,” Chemical Physics, vol. 10, no. 2-3, pp. 293–301, 1975. View at Publisher · View at Google Scholar
  60. J. A. Olson and D. A. Micha, “Transition operators for atom-atom potentials—the Hilbert-Schmidt expansion,” Journal of Chemical Physics, vol. 68, pp. 4352–4356, 1978. View at Publisher · View at Google Scholar
  61. C. Berkdemir, “Pseudospin symmetry in the relativistic Morse potential including the spin-orbit coupling term,” Nuclear Physics A, vol. 770, no. 1-2, pp. 32–39, 2006. View at Publisher · View at Google Scholar
  62. O. Bayrak and I. Boztosun, “Application of the asymptotic iteration method to the exponential cosine screened Coulomb potential,” International Journal of Quantum Chemistry, vol. 107, no. 5, pp. 1040–1045, 2007. View at Publisher · View at Google Scholar
  63. C. Berkdemir and H. Jiaguang, “Any l-state solutions of the Morse potential through the Pekeris approximation and Nikiforov-Uvarov method,” Chemical Physics Letters, vol. 409, no. 4–6, pp. 203–207, 2005. View at Publisher · View at Google Scholar
  64. O. Bayrak and I. Boztosun, “The pseudospin symmetric solution of the Morse potential for any κ state,” Journal of Physics A, vol. 40, no. 36, pp. 11119–11127, 2007. View at Publisher · View at Google Scholar
  65. G. Wei and Sh. Dong, “Pseudospin symmetry in the relativistic Manning-Rosen potential including a Pekeris-type approximation to the pseudo-centrifugal term,” Physics Letters B, vol. 686, no. 4-5, pp. 288–292, 2010. View at Publisher · View at Google Scholar
  66. W. Chen and G. Wei, “Spin symmetry in the relativistic modified Rosen-Morse potential with the approximate centrifugal term,” Chinese Physics B, vol. 20, Article ID 062101, 2011. View at Publisher · View at Google Scholar
  67. A. Soylu, O. Bayrak, and I. Boztosun, “ state solutions of the Dirac equation for the Eckart potential with pseudospin and spin symmetry,” Journal of Physics A Mathematical and Theoretical, vol. 41, no. 6, Article ID 065308, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  68. A. Soylu, O. Bayrak, and I. Boztosun, “An approximate solution of Dirac-Hulthén problem with pseudospin and spin symmetry for any κ state,” Journal of Mathematical Physics, vol. 48, Article ID 082302, 2009. View at Publisher · View at Google Scholar
  69. H. Egrifes and R. Sever, “Bound-state solutions of the Klein-Gordon equation for the generalized -symmetric Hulthén potential,” International Journal of Theoretical Physics, vol. 46, no. 4, pp. 935–950, 2007. View at Publisher · View at Google Scholar
  70. A. Okninski, “Supersymmetric content of the Dirac and Duffin-Kemmer-Petiau equations,” International Journal of Theoretical Physics, vol. 50, no. 3, pp. 729–736, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  71. A. Lahiri, P. K. Roy, and B. Bagchi, “Supersymmetry and the three-dimensional isotropic oscillator problem,” Journal of Physics, vol. 20, p. 5403, 1987. View at Publisher · View at Google Scholar
  72. A. Lahiri, P. K. Roy, and B. Bagchi, “Supersymmetry in atomic physics and the radial problem,” Journal of Physics A, vol. 20, no. 12, pp. 3825–3832, 1987. View at Publisher · View at Google Scholar
  73. V. A. Kostelecky and M. M. Nieto, “Evidence from alkali-metal-atom transition probabilities for a phenomenological atomic supersymmetry,” Physical Review A, vol. 32, pp. 1293–1298, 1985. View at Publisher · View at Google Scholar
  74. R. W. Haymaker and A. R. P. Rau, “Supersymmetry in quantum mechanics,” American Journal of Physics, vol. 54, p. 928, 1986. View at Publisher · View at Google Scholar
  75. V. A. Kostelecky and M. M. Nieto, “Evidence for a phenomenological supersymmetry in atomic physics,” Physical Review Letters, vol. 53, pp. 2285–2288, 1984. View at Publisher · View at Google Scholar
  76. V. A. Kostelecký and M. M. Nieto, “Evidence from alkali-metal-atom transition probabilities for a phenomenological atomic supersymmetry,” Physical Review A, vol. 32, no. 3, pp. 1293–1298, 1985. View at Google Scholar