https://doi.org/10.1140/epjp/s13360-024-05284-y
Regular Article
Ro-vibrational relativistic states for the q-deformed hyperbolic barrier potential
1
National Higher School of Mathematics, P.O. Box 75, Scientific and Technology Hub of Sidi Abdellah, 16093, Algiers, Algeria
2
Laboratory of Energy and Intelligent Systems, University of Khemis Miliana, 44225, Khemis Miliana, Algeria
Received:
5
March
2024
Accepted:
16
May
2024
Published online:
8
June
2024
Approximate solutions of the Dirac equation under spin and pseudo-spin symmetries are derived for a q-deformed hyperbolic barrier potential in the presence of a Coulomb-like tensor potential. The relativistic rotation-vibrational energies of the general potential in addition to two diatomic molecules 
and 
are determined. Additionally, numerical solutions of the Dirac equation are presented. The obtained approximate solutions are compared to previous ones, the RKR data, and the numerical solutions of the Dirac equation. It is observed that relativistic effects, subject to the relative motion of the ions, yield a slight increase in the vibrational energies, which is consistent with that obtained in the literature. This yields better precision when compared to the RKR data. Additionally, degeneracy between the two states of the spin doublet for the nucleus motions is theoretically identified and numerically observed.
Mohammed Hachama and Ahmed Diaf contributed equally to this work.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
