Bohr Hamiltonian for \(\gamma = 0^{\circ}\) with Davidson potential

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Abstract.

A \(\gamma\)-rigid solution of the Bohr Hamiltonian is derived for \(\gamma=0^{\circ}\) utilizing the Davidson potential in the \(\beta\) variable. This solution is going to be called X(3)-D. The energy eigenvalues and wave functions are obtained by using an analytic method which has been developed by Nikiforov and Uvarov. B(E2) transition rates are calculated. A variational procedure is applied to energy ratios to determine whether or not the X(3) model is located at the critical point between spherical and deformed nuclei. The agreement with the experiment is achieved.

References

  1. 1.
    F. Iachello, Phys. Rev. Lett. 85, 3580 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    F. Iachello, Phys. Rev. Lett. 87, 052502 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    A. Bohr, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 26, No. 14 (1952)Google Scholar
  4. 4.
    I. Boztosun, D. Bonatsos, I. Inci, Phys. Rev. C 77, 044302 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    L. Fortunato, S. De Baerdemacker, K. Heyde, Phys. Rev. C 74, 014310 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    L. Fortunato, A. Vitturi, J. Phys. G Nucl. Part. Phys. 30, 627 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    D. Bonatsos, P.E. Georgoudis, N. Minkov, Phys. Rev. C 88, 034316 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    L. Naderi, H. Hassanabadi, Eur. Phys. J. Plus 131, 5 (2016)CrossRefGoogle Scholar
  9. 9.
    M. Chabab, A. El Batoul, A. Lahbas, M. Oulne, Nucl. Phys. A 953, 158 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    H. Sobhani, H. Hassanabadi, Mod. Phys. Lett. A 31, 1650152 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    L. Fortunato, Eur. Phys. J. A 26, s01 1 (2005)ADSGoogle Scholar
  12. 12.
    J. Meng, W. Zhang, S.G. Zhou, H. Toki, L.S. Geng, Eur. Phys. J. A 25, 23 (2005)CrossRefGoogle Scholar
  13. 13.
    Z.Q. Sheng, J.Y. Guo, Mod. Phys. Lett. A 20, 2711 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    T. Niksic, D. Vretenar, G.A. Lalazissis, Phys. Rev. Lett. 99, 092502 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    Z.P. Li, T. Niksic, D. Vretenar, Phys. Rev. C 80, 061301 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    D. Bonatsos, D. Lenis, N. Minkov, P.P. Raychev, P.A. Terziev, Phys. Rev. C 69, 014302 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    D. Bonatsos, D. Lenis, N. Minkov, P.P. Raychev, P.A. Terziev, Phys. Rev. C 69, 044316 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    P.M. Davidson, Proc. R. Soc. London, Ser. A 135, 459 (1932)ADSCrossRefGoogle Scholar
  19. 19.
    D. Bonatsos, D. Lenis, N. Minkov, D. Petrellis, P.P. Raychev, P.A. Terziev, Phys. Lett. B 584, 40 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    A.S. Davydov, A.A. Chaban, Nucl. Phys. 20, 499 (1960)CrossRefGoogle Scholar
  21. 21.
    D. Bonatsos, D. Lenis, D. Petrellis, P.A. Terziev, I. Yigitoglu, Phys. Lett. B 632, 238 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    M. Alimohammadi, H. Hassanabadi, Nucl. Phys. A 957, 439 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    M. Alimohammadi, H. Hassanabadi, S. Zare, Nucl. Phys. A 960, 78 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    M. Chabab, A. El Batoul, A. Lahbas, M. Oulne, Phys. Lett. B 758, 212 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    P. Buganu, R. Budaca, J. Phys. G: Nucl. Part. Phys. 42, 105106 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    R. Budaca, Phys. Lett. B 739, 56 (2014)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    R. Budaca, A.I. Budaca, J. Phys. G: Nucl. Part. Phys. 42, 085103 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    M. Chabab, A. El Batoul, A. Lahbas, M. Oulne, J. Phys. G: Nucl. Part. Phys. 43, 125107 (2016)ADSCrossRefGoogle Scholar
  29. 29.
    A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics (Birkhaüser Basel, 1988)Google Scholar
  30. 30.
    J.P. Elliott, J.A. Evans, P. Park, Phys. Lett. B 169, 309 (1986)ADSCrossRefGoogle Scholar
  31. 31.
    D.J. Rowe, C. Bahri, J. Phys. A 31, 4947 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    W. Greiner, Quantum Mechanics -- An Introduction (Springer, Berlin 1989)Google Scholar
  33. 33.
    P.E. Garrett, J. Phys. G: Nucl. Part. Phys. 27, R1 (2001)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Arts and SciencesGaziosmanpasa UniversityTokatTurkey

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