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Investigation on the Origin of Spin and Pseudospin Symmetries in Atomic Nuclei

Afaf A. Alsulaimi

Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia

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Zuheir El-bayyari

https://orcid.org/0000-0003-2525-259X

Department of Basic Sciences and Mathematics, Faculty of Science, Philadelphia University, Aein Albasha 19392, Jordan

E-mail Address: zbayyari@rocketmail.com

Corresponding author.

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H. A. Alhendi

Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia

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, and

T. Barakat

Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia

E-mail Address: tbarakat@ksu.edu.sa

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https://doi.org/10.1142/S2010324721500053Cited by:1 (Source: Crossref)

Abstract

The spin and pseudo-spin symmetries are analytically investigated by solving the three-dimensional Dirac equation for the Kratzer potential plus a ring-shaped potential. Relativistic Schrödinger-like wave equations coupled in energy are derived from Dirac equation. The energy eigenvalues and eigenfunctions are calculated by solving the coupled relativistic radial, and angular wave equations in the framework of asymptotic iteration method. Our numerical results revealed that the spin and pseudo-spin symmetries are relativistic symmetries of the Dirac Hamiltonian. Effects of the angle-dependent potential on the relativistic energy spectra are also investigated. In addition, we include illustrative tables to examine the solutions in detail.

Keywords:

PACS: 03.65.Fd, 03.65.Pm, 03.65.Ge

References

1. J. Ginocchio, Phys. Rep. 414, 165 (2005). Crossref, Google Scholar
2. P. Alberto, A. Castro, M. Fiolhais, R. Lisboa and M. Malheiro, J. Phys. Conf. Ser. 490, 012069 (2014). Crossref, Google Scholar
3. S. G. Zhou, J. Meng and P. Ring, Phys. Rev. Lett. 91, 262501 (2003). Crossref, Google Scholar
4. M. G. Mayer and J. H. D. Jensen, Elementary Theory of Nuclear Shell Structure (John Wiley & Sons, 1955). Google Scholar
5. S. Chun-Yan, Y. Jiang-Ming and M. Jie, Chin. Phys. Lett. 26, 122102 (2009). Crossref, Google Scholar
6. P. R. Page, T. Goldman and J. N. Ginocchio, Phys. Rev. Lett. 86, 204 (2001). Crossref, Google Scholar
7. Å. Bohr, I. Hamamoto and B. R. Mottelson, Phys. Script. 26, 267 (1982). Crossref, Google Scholar
8. J. Dudek, W. Nazarewicz, Z. Szymanski and G. A. Leander, Phys. Rev. Lett. 59, 1405 (1987). Crossref, Google Scholar
9. D. Troltenier, C. Bahri and J. Draayer, Nucl. Phys. A 586, 53 (1995). Crossref, Google Scholar
10. J. N. Ginocchio, Phys. Rev. C 69 (2004). Google Scholar
11. J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997). Crossref, Google Scholar
12. R. Lisboa, M. Malheiro, P. Alberto, M. Fiolhais and A. S. de Castro, Phys. Rev. C 81, 064324 (2010). Crossref, Google Scholar
13. K. Hecht and A. Adler, Nucl. Phys. A 137, 129 (1969). Crossref, Google Scholar
14. A. Arima, M. Harvey and K. Shimizu, Phys. Lett. B 30, 517 (1969). Crossref, Google Scholar
15. C. Ti-Sheng, L. Hong-Feng, M. Jie, Z. Shuang-Quan and Z. Shan-Gui, Chin. Phys. Lett. 20, 358 (2003). Crossref, Google Scholar
16. A. Alhaidari, H. Bahlouli and A. Al-Hasan, Phys. Lett. A 349, 87 (2006). Crossref, Google Scholar
17. Q. Xu and S.-J. Zhu, Nucl. Phys. A 768, 161 (2006). Crossref, Google Scholar
18. T. Barakat, Phys. Lett. A 344, 411 (2005). Crossref, Google Scholar
19. T. Barakat and H. A. Alhendi, Found. Phys. 43, 1171 (2013). Crossref, Google Scholar
20. O. Bayrak, I. Boztosun and H. Ciftci, Int. J. Quantum Chem. 107, 540 (2007). Crossref, Google Scholar
21. H. Hassanabadi, A. N. Ikot and S. Zarrinkamar, Acta Phys. Polonica A 126, 647 (2014). Crossref, Google Scholar
22. C. Berkdemir and R. Sever, J. Phys. A Math. Theo. 41, 045302 (2008). Crossref, Google Scholar
23. C. Y. Chen and S.-H. Dong, Phys. Lett. A 335, 374 (2005). Crossref, Google Scholar
24. D. Agboola, Commun. Theo. Phys. 55, 972 (2011). Crossref, Google Scholar
25. Y. F. Cheng and T.-Q. Dai, Phys. Scripta 75, 274 (2007). Crossref, Google Scholar
26. C. Gang, Chin. Phys. 13, 144 (2004). Crossref, Google Scholar
27. W. Greiner, Relativistic Quantum Mechanics (Springer, 1990). Crossref, Google Scholar
28. J. Y. Guo, J. C. Han and R.-D. Wang, Phys. Lett. A 353, 378 (2006). Crossref, Google Scholar
29. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 2007). Google Scholar
30. H. Ciftci, R. L. Hall and N. Saad, J. Phys. A Math. Gen. 36, 11807 (2003). Crossref, Google Scholar
31. W. W. Bell, Special Functions for Scientists and Engineers (D. Van Nostrand Company Ltd., London, 1968). Google Scholar
32. T. Barakat, Phys. Script. 87, 065005 (2012). Crossref, Google Scholar
33. O. Aydoğdu and R. Sever, Ann. Phys. 325, 373 (2010). Crossref, Google Scholar