Abstract
In this paper, we consider the relativistic Dirac equation with Tietz and general Manning-Rosen potential. By using appropriate approximation, we obtained the approximate analytical solutions of the Dirac equation for the combined potential via the supersymmetric quantum mechanics (SUSYQM). Within the framework of spin and pseudospin symmetry limits, we obtained the relativistic energy eigenvalus and the corresponding components of the wave functions for Tietz and Manning-Rosen potential using the SUSYQM. We have also reported some numerical results and figures to show the effect of the tensor interactions.
Similar content being viewed by others
References
A. N. Ikot, E. Maghsoodi, S. Zarrinkamar, and H. Hassanabadi, “Relativistic spin and pseudospin symmetries of inversely quadratic Yukawa-like plus Mobius square potentials including a Coulomb-like tensor interaction, Few-Body Syst., doi:10.1007/s00601-013-0701-6.
J. N. Ginocchio, A. Leviatan, J. Meng, and S. G. Zhou, “Test of pseudospin symmetry in deformed nuclei,” Phys. Rev. C 69, 034303 (2004).
J. N. Ginocchio, “Pseudospin as a relativistic symmetry,” Phys. Rev. Lett. 78, 436 (1997).
H. Hassanabadi, E. Maghsoodi, and S. Zarrinkamar, “Spin and pseudospin symmetries of Dirac equation and the Yukawa potential as the tensor interaction,” Commun. Theor. Phys. 58, 807 (2012).
P. R. Page, T. Goldman, and J. N. Ginocchio, “Relativistic symmetry suppresses quark spin-orbit splitting,” Phys. Rev. Lett. 66, 204 (2001).
D. Troltenier, C. Bahri, and J. P. Draayer, “Generalized pseudo-SU(3) model and pairing,” Nucl. Phys. A 586, 53 (1995).
J. N. Ginocchio, “Relativistic symmetries in nuclei and hadrons,” Phys. Rep. 414, 165 (2005).
H. Hassanbadi and Z. Molaee, “Approximate solution of the spin-one Duffin-Kemmer-Petiau (DKP) equation under a non-minimal vector Yukawa potential in (1+1)-dimensions,” Chin. Phys B 21, 120304 (2012).
E. Maghsoodi, H. Hassanabadi, and O. Aydogdu, “Dirac particles in the presence of the Yukawa potential plus a tensor interaction in SUSYQM framework,” Phys. Scr. 86, 015005 (2012).
O. Aydogdu, E. Maghsoodi, and H. Hassanabadi, “Dirac equation for the Hulth’en potential within the Yukawa-type tensor interaction,” Chin. Phys. B 22, 010302 (2013).
M. Hamzavi, S. M. Ikhdair, and B. I. Ita, “Approximate spin and pseudospin solutions to the Dirac equation for the inversely quadratic Yukawa potential and tensor interaction,” Phys. Scr. 85, 04500 9 (2012).
A. N. Ikot, E. Maghsoodi, S. Zarrinkamar, et al., “Solutions of Dirac equation in the presence of modified Tietz and modified Poschl-Teller potentials plus a Coulomb-like tensor interaction using SUSYQM,” Few-Body Syst., doi:10.1007/S00601-013-0716-z.
F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep. 251, 267 (1995).
A. N. Ikot, E. Maghsoodi, A. D. Antia, et al., “Approximate κ-state solutions to the Dirac Mobius square-Yukawa and Mobius square-quasi Yukawa problems under pseudospin and spin symmetry limits with Coulomb-like tensor interaction,” Can. J. Phys. 91, 1–16 (2013).
H. Hassanabadi, E. Maghsoodi, and S. Zarrinkamar, “Relativistic symmetries of Dirac equation and the Tietz potential,” Eur. Phys. J. Plus. 127, 31 (2012).
S. M. Ikhdair and M. Hamzavi, “Approximate relativistic bound state solutions of the Tietz-Hua rotating oscillator for any kappa-state,” Few-Body Syst. 53, 461–471 (2012).
H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, and H. Rahimov, “An approximate solution of the Dirac equation for hyperbolic scalar and vector potentials and a Coulomb tensor interaction by SUSYQM,” Mod. Phys. Lett. A 26, 2703 (2011).
H. Hassanbadi, E. Maghsoodi, A. N. Ikot, and S. Zarrinkmar, “Approximate arbitrary-state solutions of Dirac equation for modified deformed hylleraas and modified Eckart potentials by the NU method,” Appl. Math. Comput. 219, 9388 (2013).
P. Boonserm and M. Visser, “Quasi-normal frequencies: key analytic results,” JHEP 1103, 073 (2011).
H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, and H. Rahimov, “Dirac equation for generalized Pöschl-Teller scalar and vector potentials and a Coulomb tensor interaction by Nikiforov-Uvarov method,” J. Math. Phys. 53, 022104 (2012).
E. Maghsoodi, H. Hassanabadi, and S. Zarrinkamar, “Spectrum of Dirac equation under Deng-Fan scalar and vector potentials and a Coulomb tensor Interaction by SUSYQM,” Few-Body Syst. 53, 525 (2012).
B. J. Falaye and S. M. Ikhdair, “Relativistic symmetries with the trigonometric Pöschl-Teller potential plus Coulomb-like tensor interaction,” Chin. Phys. B 22, 060305 (2013).
G. F. Wei and S. H. Dong, “Algebraic approach to pseudospin symmetry for Dirac equation with scalar and vector modified Pöschl-Teller potential,” Europhys. Lett. 87, 4004 (2009).
G. Junker, Supersymmetric Methods in Quantum and Statistical Physics (Springer-Verlag, Berlin, 1996).
H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, and H. Rahimov, “Actual and general Manning-Rosen potentials under spin and pseudospin symmetries of the Dirac equation,” Can. J. Phys. 90, 633 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Ikot, A.N., Hassanabadi, H., Maghsoodi, E. et al. Approximate solutions of Dirac equation for Tietz and general Manning-Rosen potentials using SUSYQM. Phys. Part. Nuclei Lett. 11, 432–442 (2014). https://doi.org/10.1134/S1547477114040189
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477114040189