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Advances in High Energy Physics
Volume 2015, Article ID 915796, 17 pages
http://dx.doi.org/10.1155/2015/915796
Research Article

Spin and Pseudospin Symmetry in Generalized Manning-Rosen Potential

Department of Physics, Mersin University, 33143 Mersin, Turkey

Received 8 May 2015; Accepted 18 June 2015

Academic Editor: Shi-Hai Dong

Copyright © 2015 Hilmi Yanar and Ali Havare. 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. The publication of this article was funded by SCOAP3.

Linked References

  1. J. N. Ginocchio, “Relativistic symmetries in nuclei and hadrons,” Physics Reports, vol. 414, no. 4-5, pp. 165–261, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. J. N. Ginocchio, “Relativistic harmonic oscillator with spin symmetry,” Physical Review —Nuclear Physics, vol. 69, no. 3, Article ID 034318, 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. S. G. Zhou, J. Meng, and P. Ring, “Spin symmetry in the antinucleon spectrum,” Physical Review Letters, vol. 91, no. 26, Article ID 262501, 4 pages, 2003. View at Publisher · View at Google Scholar
  4. J. N. Ginocchio, “A relativistic symmetry in nuclei,” Physics Report, vol. 315, no. 1–4, pp. 231–240, 1999. View at Publisher · View at Google Scholar · View at Scopus
  5. P. R. Page, T. Goldman, and J. N. Ginocchio, “Relativistic symmetry suppresses quark spin-orbit splitting,” Physical Review Letters, vol. 86, article 204, 2001. View at Publisher · View at Google Scholar · View at Scopus
  6. K. T. Hecht and A. Adler, “Generalized seniority for favored J0 pairs in mixed configurations,” Nuclear Physics A, vol. 137, no. 1, pp. 129–143, 1969. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Arima, M. Harvey, and K. Shimizu, “Pseudo LS coupling and pseudo SU3 coupling schemes,” Physics Letters B, vol. 30, no. 8, pp. 517–522, 1969. View at Google Scholar · View at Scopus
  8. A. Bohr, I. Hamamoto, and B. R. Mottelson, “Pseudospin in rotating nuclear potentials,” Physica Scripta, vol. 26, no. 4, pp. 267–272, 1982. View at Publisher · View at Google Scholar
  9. W. Nazarewicz, P. J. Twin, P. Fallon, and J. D. Garrett, “Natural-parity states in superdeformed bands and pseudo SU(3) symmetry at extreme conditions,” Physical Review Letters, vol. 64, no. 14, pp. 1654–1657, 1990. View at Publisher · View at Google Scholar · View at Scopus
  10. F. S. Stephens, M. A. Deleplanque, J. E. Draper et al., “Pseudospin symmetry and quantized alignment in nuclei,” Physical Review Letters, vol. 65, article 301, 1990. View at Publisher · View at Google Scholar · View at Scopus
  11. B. Mottelson, “Some themes in the study of very deformed rotating nuclei,” Nuclear Physics, Section A, vol. 522, no. 1-2, pp. 1–12, 1991. View at Publisher · View at Google Scholar · View at Scopus
  12. D. Troltenier, W. Nazarewicz, Z. Szymański, and J. P. Draayer, “On the validity of the pseudo-spin concept for axially symmetric deformed nuclei,” Nuclear Physics, Section A, vol. 567, no. 3, pp. 591–610, 1994. View at Publisher · View at Google Scholar · View at Scopus
  13. A. E. Stuchbery, “Magnetic behaviour in the pseudo-Nilsson model,” Journal of Physics G: Nuclear and Particle Physics, vol. 25, no. 4, pp. 611–615, 1999. View at Publisher · View at Google Scholar
  14. A. E. Stuchbery, “Magnetic properties of rotational states in the pseudo-Nilsson model,” Nuclear Physics A, vol. 700, no. 1-2, pp. 83–116, 2002. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Troltenier, C. Bahri, and J. P. Draayer, “Generalized pseudo-SU(3) model and pairing,” Nuclear Physics A, vol. 586, no. 1, pp. 53–72, 1995. View at Publisher · View at Google Scholar · View at Scopus
  16. C. Bahri, J. P. Draayer, and S. A. Moszkowski, “Pseudospin symmetry in nuclear physics,” Physical Review Letters, vol. 68, article 2133, 1992. View at Publisher · View at Google Scholar · View at Scopus
  17. A. L. Blokhin, C. Bahri, and J. P. Draayer, “Origin of pseudospin symmetry,” Physical Review Letters, vol. 74, no. 21, pp. 4149–4152, 1995. View at Publisher · View at Google Scholar · View at Scopus
  18. A. L. Blokhin, C. Bahri, and J. P. Draayer, “Pseudospin transformation of physical operators,” Journal of Physics A, vol. 29, no. 9, pp. 2039–2052, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. J. N. Ginocchio, “Pseudospin as a relativistic symmetry,” Physical Review Letters, vol. 78, no. 3, pp. 436–439, 1997. View at Publisher · View at Google Scholar
  20. J. N. Ginocchio and A. Leviatan, “On the relativistic foundations of pseudospin symmetry in nuclei,” Physics Letters B, vol. 425, no. 1-2, pp. 1–5, 1998. View at Publisher · View at Google Scholar
  21. J. N. Ginocchio, “On the relativisitic origins of pseudo-spin symmetry in nuclei,” Journal of Physics G: Nuclear and Particle Physics, vol. 25, no. 4, article 617, 1999. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Leviatan and J. N. Ginocchio, “Consequences of a relativistic pseudospin symmetry for radial nodes and intruder levels in nuclei,” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 518, no. 1-2, pp. 214–220, 2001. View at Publisher · View at Google Scholar · View at Scopus
  23. J. Meng, K. Sugawara-Tanabe, S. Yamaji, P. Ring, and A. Arima, “Pseudospin symmetry in relativistic mean field theory,” Physical Review C - Nuclear Physics, vol. 58, no. 2, pp. R628–R631, 1998. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Meng, K. Sugawara-Tanabe, S. Yamaji, and A. Arima, “Pseudospin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line,” Physical Review C: Nuclear Physics, vol. 59, no. 1, pp. 154–163, 1999. View at Publisher · View at Google Scholar · View at Scopus
  25. J. S. Bell and H. Ruegg, “Dirac equations with an exact higher symmetry,” Nuclear Physics B, vol. 98, no. 1, pp. 151–153, 1975. View at Publisher · View at Google Scholar
  26. G.-F. Wei and S.-H. Dong, “Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry,” Physics Letters A, vol. 373, no. 1, pp. 49–53, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  27. G.-F. Wei and S.-H. 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
  28. T. Chen, J.-Y. Liu, and C.-S. Jia, “Approximate analytical solutions of the Dirac-Manning-Rosen problem with the spin symmetry and pseudo-spin symmetry,” Physica Scripta, vol. 79, no. 5, Article ID 055002, 2009. View at Publisher · View at Google Scholar · View at Scopus
  29. F. Taşkın, “Approximate solutions of the Dirac equation for the Manning-Rosen potential including the spin-orbit coupling term,” International Journal of Theoretical Physics, vol. 48, no. 4, pp. 1142–1149, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  30. H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, and H. Rahimov, “Actual and general manning-Rosen potentials under spin and pseudospin symmetries of the Dirac equation,” Canadian Journal of Physics, vol. 90, no. 7, pp. 633–646, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. S. Asgarifar and H. Goudarzi, “Exact solutions of the Manning-Rosen potential plus a ring-shaped like potential for the Dirac equation: spin and pseudospin symmetry,” Physica Scripta, vol. 87, no. 2, Article ID 025703, 2013. View at Publisher · View at Google Scholar · View at Scopus
  32. H. Feizi and A. H. Ranjbar, “Relativistic symmetries of the Manning-Rosen potential in the frame of supersymmetry,” The European Physical Journal Plus, vol. 128, article 3, 2013. View at Publisher · View at Google Scholar
  33. H. Tokmehdashi, A. A. Rajabi, and M. Hamzavi, “Hulthén and coulomb-like potentials as a tensor interaction within the relativistic symmetries of the manning-rosen potential,” Advances in High Energy Physics, vol. 2014, Article ID 870523, 14 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  34. S. Ortakaya, H. Hassanabadi, and E. Maghsoodi, “Scattering phase shifts of Dirac equation with Manning-Rosen potential and Yukawa tensor interaction,” Indian Journal of Physics, vol. 89, no. 4, pp. 307–316, 2015. View at Publisher · View at Google Scholar
  35. O. Aydoğdu and R. Sever, “Pseudospin and spin symmetry in the Dirac equation with Woods-Saxon potential and tensor potential,” The European Physical Journal A, vol. 43, no. 1, pp. 73–81, 2010. View at Publisher · View at Google Scholar
  36. E. Maghsoodi, H. Hassanabadi, S. Zarrinkamar, and H. Rahimov, “Relativistic symmetries of the Dirac equation under the nuclear WoodsSaxon potential,” Physica Scripta, vol. 85, no. 5, Article ID 055007, 2012. View at Publisher · View at Google Scholar · View at Scopus
  37. S. M. Ikhdair and R. Sever, “Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry,” Central European Journal of Physics, vol. 8, no. 4, pp. 652–666, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. J.-Y. Guo and Z.-Q. Sheng, “Solution of the Dirac equation for the Woods-Saxon potential with spin and pseudospin symmetry,” Physics Letters A, vol. 338, no. 2, pp. 90–96, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  39. H. Feizi, M. R. Shojaei, and A. A. Rajabi, “Raising and lowering operators for the Dirac-Woods-Saxon potential in the presence of spin and pseudospin symmetry,” The European Physical Journal Plus, vol. 127, article 41, 2012. View at Publisher · View at Google Scholar · View at Scopus
  40. O. Aydoğdu, E. Maghsoodi, and H. Hassanabadi, “Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction,” Chinese Physics B, vol. 22, no. 1, Article ID 010302, 2013. View at Publisher · View at Google Scholar · View at Scopus
  41. S. M. Ikhdair, C. Berkdemir, and R. Sever, “Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthén problem,” Applied Mathematics and Computation, vol. 217, no. 22, pp. 9019–9032, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. 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, 2007. View at Publisher · View at Google Scholar
  43. A. N. Ikot, H. Hassanabadi, E. Maghsoodi, and S. Zarrinkamar, “Relativistic symmetries of Hulthén potential incorporated with generalized tensor interactions,” Advances in High Energy Physics, vol. 2013, Article ID 910419, 10 pages, 2013. View at Publisher · View at Google Scholar
  44. S. M. Ikhdair and R. Sever, “Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential,” Applied Mathematics and Computation, vol. 216, no. 3, pp. 911–923, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  45. O. Aydoğdu and R. Sever, “Pseudospin and spin symmetry for the ring-shaped generalized Hulthén potential,” International Journal of Modern Physics A: Particles and Fields. Gravitation; Cosmology, vol. 25, no. 21, pp. 4067–4079, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  46. O. Aydoğdu and R. Sever, “Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit,” Annals of Physics, vol. 325, no. 2, pp. 373–383, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  47. M. Hamzavi, A. A. Rajabi, and H. Hassanabadi, “Exact spin and pseudospin symmetry solutions of the Dirac equation for Mie-type potential including a Coulomb-like tensor potential,” Few-Body Systems, vol. 48, no. 2–4, pp. 171–182, 2010. View at Publisher · View at Google Scholar
  48. M. Eshghi and S. M. Ikhdair, “Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method,” Chinese Physics B, vol. 23, no. 12, article 120304, 2014. View at Publisher · View at Google Scholar
  49. O. Aydoğdu and R. Sever, “Pseudospin and spin symmetry in Dirac–Morse problem with a tensor potential,” Physics Letters B, vol. 703, no. 3, pp. 379–385, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  50. O. Bayrak and I. Boztosun, “The pseudospin symmetric solution of the Morse potential for any κ state,” Journal of Physics A: Mathematical and Theoretical, vol. 40, no. 36, pp. 11119–11127, 2007. View at Publisher · View at Google Scholar
  51. 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
  52. W.-C. Qiang, R.-S. Zhou, and Y. Gao, “Application of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry,” Journal of Physics A. Mathematical and Theoretical, vol. 40, no. 7, pp. 1677–1685, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  53. L.-H. Zhang, X.-P. Li, and C.-S. Jia, “Approximate analytical solutions of the Dirac equation with the generalized Morse potential model in the presence of the spin symmetry and pseudo-spin symmetry,” Physica Scripta, vol. 80, no. 3, Article ID 035003, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  54. S. M. Ikhdair, “An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry,” Journal of Mathematical Physics, vol. 52, Article ID 052303, 2011. View at Publisher · View at Google Scholar
  55. O. Aydoğdu and R. Sever, “The Dirac–Yukawa problem in view of pseudospin symmetry,” Physica Scripta, vol. 84, no. 2, Article ID 025005, 2011. View at Publisher · View at Google Scholar
  56. E. Maghsoodi, H. Hassanabadi, and O. Aydoğdu, “Dirac particles in the presence of the Yukawa potential plus a tensor interaction in SUSYQM framework,” Physica Scripta, vol. 86, no. 1, Article ID 015005, 2012. View at Publisher · View at Google Scholar
  57. S. M. Ikhdair, “Approximate κ-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry,” Central European Journal of Physics, vol. 10, no. 2, pp. 361–381, 2012. View at Publisher · View at Google Scholar
  58. M. R. Setare and S. Haidari, “Spin symmetry of the Dirac equation with the Yukawa potential,” Physica Scripta, vol. 81, no. 6, Article ID 065201, 2010. View at Publisher · View at Google Scholar
  59. A. Arda and R. Sever, “Approximate analytical solutions of the Dirac equation for Yukawa potential plus tensor interaction with any κ-value,” Few-Body Systems, vol. 54, no. 11, pp. 1829–1837, 2013. View at Publisher · View at Google Scholar
  60. X.-Y. Liu, G.-F. Wei, X.-W. Cao, and H.-G. Bai, “Spin symmetry for Dirac equation with the trigonometric Pöschl-Teller potential,” International Journal of Theoretical Physics, vol. 49, no. 2, pp. 343–348, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  61. C.-S. Jia, P. Guo, Y.-F. Diao, L.-Z. Yi, and X.-J. Xie, “Solutions of Dirac equations with the Pöschl-Teller potential,” European Physical Journal A, vol. 34, no. 1, pp. 41–48, 2007. View at Publisher · View at Google Scholar · View at Scopus
  62. Y. Xu, S. He, and C.-S. Jia, “Approximate analytical solutions of the Dirac equation with the Pöschl–Teller potential including the spin–orbit coupling term,” Journal of Physics A: Mathematical and Theoretical, vol. 41, no. 25, Article ID 255302, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  63. C.-S. Jia, T. Chen, and L.-G. Cui, “Approximate analytical solutions of the Dirac equation with the generalized Pöschl-Teller potential including the pseudo-centrifugal term,” Physics Letters A, vol. 373, no. 18-19, pp. 1621–1626, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  64. G.-F. Wei and S.-H. Dong, “The spin symmetry for deformed generalized Pöschl-Teller potential,” Physics Letters A, vol. 373, no. 29, pp. 2428–2431, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  65. G. F. Wei and S. H. Dong, “Algebraic approach to pseudospin symmetry for the Dirac equation with scalar and vector modified Pöschl-Teller potentials,” EPL (Europhysics Letters), vol. 87, Article ID 40004, 2009. View at Publisher · View at Google Scholar
  66. G.-F. Wei and S.-H. Dong, “A novel algebraic approach to spin symmetry for Dirac equation with scalar and vector second Pöschl-Teller potentials,” The European Physical Journal A, vol. 43, no. 2, pp. 185–190, 2010. View at Publisher · View at Google Scholar
  67. A. Taş, S. Alpdoğan, and A. Havare, “The scattering and bound states of the Schrödinger particle in generalized asymmetric manning-rosen type potential,” Advances in High Energy Physics, vol. 2014, Article ID 619241, 10 pages, 2014. View at Publisher · View at Google Scholar
  68. M. F. Manning and N. Rosen, “A potential function for the vibrations of diatomic molecules,” Physical Review, vol. 44, no. 11, pp. 953–954, 1933. View at Publisher · View at Google Scholar
  69. W.-C. Qiang and S.-H. Dong, “Analytical approximations to the solutions of the Manning-Rosen potential with centrifugal term,” Physics Letters A, vol. 368, no. 1-2, pp. 13–17, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  70. W.-C. Qiang and S.-H. Dong, “The Manning–Rosen potential studied by a new approximate scheme to the centrifugal term,” Physica Scripta, vol. 79, no. 4, Article ID 045004, 2009. View at Publisher · View at Google Scholar
  71. S.-H. Dong and J. García-Ravelo, “Exact solutions of the s-wave Schrödinger equation with Manning–Rosen potential,” Physica Scripta, vol. 75, no. 3, pp. 307–309, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  72. G.-F. Wei, C.-Y. Long, and S.-H. Dong, “The scattering of the Manning-Rosen potential with centrifugal term,” Physics Letters A, vol. 372, no. 15, pp. 2592–2596, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  73. X.-Y. Gu and S.-H. Dong, “Energy spectrum of the Manning-Rosen potential including centrifugal term solved by exact and proper quantization rules,” Journal of Mathematical Chemistry, vol. 49, no. 9, pp. 2053–2062, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  74. P. M. Morse, “Diatomic molecules according to the wave mechanics. II. Vibrational levels,” Physical Review, vol. 34, no. 1, pp. 57–64, 1929. View at Publisher · View at Google Scholar · View at Scopus
  75. S.-H. Dong and G.-H. Sun, “The series solutions of the non-relativistic equation with the Morse potential,” Physics Letters. A, vol. 314, no. 4, pp. 261–266, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  76. W.-C. Qiang and S.-H. Dong, “Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method,” Physics Letters A, vol. 363, no. 3, pp. 169–176, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  77. J. Yu, S.-H. Dong, and G.-H. Sun, “Series solutions of the Schrödinger equation with position-dependent mass for the Morse potential,” Physics Letters A, vol. 322, no. 5-6, pp. 290–297, 2004. View at Publisher · View at Google Scholar
  78. G. Pöschl and E. Teller, “Bemerkungen zur Quantenmechanik des anharmonischen Oszillators,” Zeitschrift für Physik, vol. 83, no. 3-4, pp. 143–151, 1933. View at Publisher · View at Google Scholar · View at Scopus
  79. H. Yanar, A. Havare, and K. Sogut, “Scattering and bound states of Duffin-Kemmer-Petiau particles for q-parameter hyperbolic Pöschl-Teller potential,” Advances in High Energy Physics, vol. 2014, Article ID 840907, 9 pages, 2014. View at Publisher · View at Google Scholar
  80. A. Kratzer, “Die ultraroten Rotationsspektren der Halogenwasserstoffe,” Zeitschrift für Physik, vol. 3, no. 5, pp. 289–307, 1920. View at Publisher · View at Google Scholar · View at Scopus
  81. E. Fues, “Das Eigenschwingungsspektrum zweiatomiger Moleküle in der Undulationsmechanik,” Annalen der Physik, vol. 385, no. 12, pp. 367–396, 1926. View at Publisher · View at Google Scholar
  82. O. Bayrak, I. Boztosun, and H. Ciftci, “Exact analytical solutions to the kratzer potential by the asymptotic iteration method,” International Journal of Quantum Chemistry, vol. 107, no. 3, pp. 540–544, 2007. View at Publisher · View at Google Scholar · View at Scopus
  83. R. D. Woods and D. S. Saxon, “Diffuse surface optical model for nucleon-nuclei scattering,” Physical Review, vol. 95, no. 2, pp. 577–578, 1954. View at Publisher · View at Google Scholar · View at Scopus
  84. L. Hulthen, “Uber die Eigenlösungen der Schrödinger chung des Deutrons,” Arkiv för Matematik, Astronomi och Fysik, vol. 28A, no. 5, 1942. View at Google Scholar
  85. H. Yukawa, “The prediction and discovery of pions and muons,” Proceedings of the Physico-Mathematical Society of Japan, vol. 17, p. 48, 1935. View at Google Scholar
  86. A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics, Birkhäuser, Basel, Switzerland, 1988.
  87. W. Greiner, Relativistic Quantum Mechanics, Springer, Berlin, Germany, 2nd edition, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  88. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, Addison-Wesley, Boston, Mass, USA, 2nd edition, 2010.
  89. C. L. Pekeris, “The rotation-vibration coupling in diatomic molecules,” Physical Review, vol. 45, article 98, 1934. View at Publisher · View at Google Scholar · View at Scopus
  90. K. Sogut and A. Havare, “Transmission resonances in the Duffin-Kemmer-Petiau equation in (1+1) dimensions for an asymmetric cusp potential,” Physica Scripta, vol. 82, no. 4, Article ID 045013, 2010. View at Publisher · View at Google Scholar · View at Scopus
  91. R. L. Greene and C. Aldrich, “Variational wave functions for a screened Coulomb potential,” Physical Review A, vol. 14, no. 6, pp. 2363–2366, 1976. View at Publisher · View at Google Scholar · View at Scopus