The statistical properties of q-deformed Morse potential for some diatomic molecules via Euler–MacLaurin method in one dimension

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Abstract

In this paper, we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function, the related thermodynamic functions are derived and studied in terms of the parameters of the model. Especially, we plotted the q-deformed vibrational partition function and vibrational specific heat for some diatomic molecule systems such as \(\text {H}_{2}\), HCl, LiH, and CO. The idea of a critical temperature \(T_{C}\) is introduced in relation to the specific heat.

Keywords

Morse potential Partition function Euler–MacLaurin method 

References

  1. 1.
    D. Bonatsost, L. Britot, D. Menezes, J. Phys. A: Math. Gen. 26, 895–904 (1993)CrossRefGoogle Scholar
  2. 2.
    L.C. Biedenharn, J. Phys. A: Math. Gen. 22, L873 (1989)CrossRefGoogle Scholar
  3. 3.
    A.J. Macfarlane, J. Phys. A: Math. Gen. 22, 4581 (1989)CrossRefGoogle Scholar
  4. 4.
    P.P. Kulish, E.V. Damaskinsky, J. Phys. A: Math. Gen. 23, L415 (1990)CrossRefGoogle Scholar
  5. 5.
    Y. Ng, J. Phys. A: Math. Gen. 23, 1023 (1990)CrossRefGoogle Scholar
  6. 6.
    H. Ui, N. Aizawa, Mod. Phys. Lett. A 5, 237 (1990)CrossRefGoogle Scholar
  7. 7.
    A. Lorek, A. Ruffing, J. Wess, Z. Phys. C 74, 369–377 (1997)CrossRefGoogle Scholar
  8. 8.
    I.L. Cooper, R.K. Gupta, Phys. Rev. A 52, 941 (1995)CrossRefGoogle Scholar
  9. 9.
    A. Lavagno, A.M. Scarfone, P.N. Swamy, Eur. Phys. J. C. 47, 253–261 (2006)CrossRefGoogle Scholar
  10. 10.
    J. Črnugelj, M. Martinis, V. Mikuta-Martinis, Phys. Lett. A 188, 347–354 (1994)CrossRefGoogle Scholar
  11. 11.
    A.M. Gavrilik, I.I. Kachurik, A.V. Lukash, Ukr. J. Phys. 58, 1025–1032 (2013)CrossRefGoogle Scholar
  12. 12.
    M.S. Abdalla, H. Eleuch, J. Appl. Phys 115, 234906 (2014)CrossRefGoogle Scholar
  13. 13.
    S. Cai, G. Su, J. Chen, J. Phys. A: Math. Theor. 40, 11245–11254 (2007)CrossRefGoogle Scholar
  14. 14.
    W.S. Chung, Int. J. Mod. Phys B. 29, 1550177 (2015)CrossRefGoogle Scholar
  15. 15.
    S.W. Chung, J. Adv. Phys. 4, 1–4 (2015)Google Scholar
  16. 16.
    M. Angelova, A. Frank, Phys. At. Nucl. 68, 1625–1633 (2005)CrossRefGoogle Scholar
  17. 17.
    M. Angelova, A. Franck, Phys. At. Nucl. 68, 1689–1697 (2005)CrossRefGoogle Scholar
  18. 18.
    A. Algin, M. Senay, Phys. A. 447, 232–246 (2016)CrossRefGoogle Scholar
  19. 19.
    M.L. Strekalov, Chem. Phys. Lett. 439, 209–212 (2007)CrossRefGoogle Scholar
  20. 20.
    C.-S. Jia, L.-H. Zhang, C.-W. Wang, Chem. Phys. Lett. 667, 211–215 (2017)CrossRefGoogle Scholar
  21. 21.
    X.-Q. Song, C.-W. Wang, C.-S. Jia, Chem. Phys. Lett. 673, 50–55 (2017)CrossRefGoogle Scholar
  22. 22.
    C.-S. Jia, C.-W. Wang, L.-H. Zhang, X.-L. Peng, Ran Zenga, X.-T. You, Chem. Phys. Lett. 676, 150–153 (2017)CrossRefGoogle Scholar
  23. 23.
    G. Arfken, Mathematical Methods for Physicists, 3rd edn. (Academic Press, Orlando, 1985), pp. 327–338Google Scholar
  24. 24.
    M.R. Setare, O. Hatam, Mod. Phys. Lett. A. 24, 361–367 (2009)CrossRefGoogle Scholar
  25. 25.
    S.-H. Dong, F. Lara-Rosana, G.-H. Sun, Phys. Lett. A. 325, 218 (2004)CrossRefGoogle Scholar
  26. 26.
    I. Nasser, M.S. Abdelmonem, H. Bahlouli, A.D. Alhaidar, J. Phys. B. 40, 4245 (2007)CrossRefGoogle Scholar
  27. 27.
    A.K. Roy, Result Phys. 3, 103–108 (2013)CrossRefGoogle Scholar
  28. 28.
    G. Valencia-Ortega, L.A. Arias-Hernandez, (2017). arxiv:1708.00926v1
  29. 29.
    J.-F. Wang, X.-L. Peng, L.-H. Zhang, C.-W. Wang, C.-S. Jia, Chem. Phys. Lett. 686, 131–133 (2017)CrossRefGoogle Scholar
  30. 30.
    C.-S. Jia, C.-W. Wang, L.-H. Zhanh, X.-L. Peng, H.-M. Tang, J-Yi Liu, Yu. Xiong, R. Zeng, Chem. Phys. Lett. 692, 57–60 (2018)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Physique Appliquée et ThéoriqueUniversité Larbi Tébessi -TébessaW. TébessaAlgeria

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