Skip to main content

Advertisement

SpringerLink
Log in

Stability analysis of the solution of the Dirac equation for the vibrational energies of the SiF+ molecule

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

Analytical solutions of the Dirac equation with the spin symmetry in higher spatial dimensions have been explored for the improved Manning-Rosen potential energy model. We present the bound-state energy equation and the corresponding upper and lower radial wave functions. It has been found that the behavior of the higher-dimensional relativistic vibrational energies remains similar to that of the three-dimensional molecular system for the \( X^{1}\Sigma^{+}\) state of the SiF+ molecule. This symmetry phenomenon will break upon the critical point through which the system undergoes a phase transition from a stable to an unstable state.

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. D.R. Herschbach, J. Chem. Phys. 84, 838 (1986)

    Article  ADS  Google Scholar 

  2. P. Serra, S. Kais, Phys. Rev. Lett. 77, 466 (1996)

    Article  ADS  Google Scholar 

  3. S. Kais, Q. Shi, Phys. Rev. A 62, 060502 (2000)

    Article  ADS  Google Scholar 

  4. S. Kais, P. Serra, Adv. Chem. Phys. 125, 1 (2003)

    Google Scholar 

  5. Q. Shi, S. Kais, Chem. Phys. 309, 127 (2005)

    Article  ADS  Google Scholar 

  6. X.T. Hu, L.H. Zhang, C.S. Jia, J. Mol. Spectrosc. 297, 21 (2014)

    Article  ADS  Google Scholar 

  7. X.T. Hu, L.H. Zhang, C.S. Jia, Can. J. Chem. 92, 386 (2014)

    Article  Google Scholar 

  8. G.D. Zhang, W. Zhou, J.Y. Liu, L.H. Zhang, C.S. Jia, Chem. Phys. 439, 79 (2014)

    Article  ADS  Google Scholar 

  9. J.F. Du, P. Guo, C.S. Jia, J. Math. Chem. 52, 2559 (2014)

    Article  MathSciNet  Google Scholar 

  10. C.S. Jia, L.H. Zhang, X.T. Hu, H.M. Tang, G.C. Liang, J. Mol. Spectrosc. 311, 69 (2015)

    Article  ADS  Google Scholar 

  11. P.Q. Wang, L.H. Zhang, C.S. Jia, J.Y. Liu, J. Mol. Spectrosc. 274, 5 (2012)

    Article  ADS  Google Scholar 

  12. M.F. Manning, N. Rosen, Phys. Rev. 44, 953 (1933)

    Google Scholar 

  13. R. Rydberg, Z. Phys. 80, 514 (1933)

    Article  ADS  Google Scholar 

  14. O. Klein, Z. Phys. 76, 226 (1932)

    Article  MATH  ADS  Google Scholar 

  15. A.L.G. Rees, Proc. Phys. Soc. 59, 998 (1947)

    Article  MATH  ADS  Google Scholar 

  16. J.Y. Liu, G.D. Zhang, C.S. Jia, Phys. Lett. A 377, 1444 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. C.S. Jia, G.C. Liang, X.L. Peng, H.M. Tang, L.H. Zhang, Few-Body Syst. 55, 1159 (2014)

    Article  Google Scholar 

  18. C.S. Jia, J.W. Dai, L.H. Zhang, J.Y. Liu, X.L. Peng, Phys. Lett. A 379, 137 (2015)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. H. Hassanabadi, B.H. Yazarloo, L.L. Lu, Chin. Phys. Lett. 29, 020303 (2012)

    Article  ADS  Google Scholar 

  20. H. Hassanabadi, L.L. Lu, S. Zarrinkamar, G.H. Liu, H. Rahimov, Act. Phys. Pol. A 122, 650 (2012)

    Google Scholar 

  21. S.H. Dong, J. Phys. A: Math. Gen. 36, 1 (2003)

    Article  Google Scholar 

  22. H. Hassanabadi, S. Zarrinkamar, H. Rahimov, Commun. Theor. Phys. 56, 423 (2011)

    Article  MATH  ADS  Google Scholar 

  23. A.N. Ikot, H.P. Obong, H. Hassanabadi, Few-Body Syst. 56, 185 (2015)

    Article  ADS  Google Scholar 

  24. T.T. Ibrahim, K.J. Oyewumi, S.M. Wyngaardt, Eur. Phys. J. Plus 127, 100 (2012)

    Article  Google Scholar 

  25. Y. Sun, G.D. Zhang, C.S. Jia, Chem. Phys. Lett. 636, 197 (2015)

    Article  Google Scholar 

  26. S.H. Dong, Wave Equation in Higher Dimensions (Springer, Berlin, 2011)

  27. J.N. Ginocchio, Phys. Rev. C 69, 034318 (2004)

    Article  ADS  Google Scholar 

  28. L.H. Zhang, X.P. Li, C.S. Jia, Phys. Lett. A 372, 2201 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. C.S. Jia, T. Chen, L.G. Cui, Phys. Lett. A 373, 1621 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. R.R. Reddy, T.V.R. Rao, R. Viswanath, Astrophys. Space Sci. 189, 29 (1992)

    Article  ADS  Google Scholar 

  31. M. Singh, P. Chaturvedi, Astrophys. Space Sci. 135, 1 (1987)

    Article  ADS  Google Scholar 

  32. Y. Akiyama, K. Tanaka, T. Tanaka, Chem. Phys. Lett. 155, 15 (1989)

    Article  ADS  Google Scholar 

  33. C.J. Reid, Chem. Phys. 210, 501 (1996)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 610500, Chengdu, PRC

    Chun-Sheng Jia, Lie-Hui Zhang & Jian-Yi Liu

Authors
  1. Chun-Sheng Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lie-Hui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian-Yi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chun-Sheng Jia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jia, CS., Zhang, LH. & Liu, JY. Stability analysis of the solution of the Dirac equation for the vibrational energies of the SiF+ molecule. Eur. Phys. J. Plus 131, 2 (2016). https://doi.org/10.1140/epjp/i2016-16002-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2016-16002-2

Keywords

Search

Navigation