Abstract
We solve the Dirac equation for Mie-type potential including a Coulomb-like tensor potential under spin and pseudospin symmetry limits with arbitrary spin–orbit coupling quantum number κ. The Nikiforov–Uvarov method is used to obtain analytical solutions of the Dirac equation. Since it is only the wave functions which are obtained in a closed exact form; as for the eigenvalues, only the eigenvalue equations have been given and they have been solved numerically. It is also shown that the degeneracy between spin doublets and pseudospin doublets is removed by tensor interaction.
Similar content being viewed by others
References
Mesa A.D.S., Quesne C., Smirnov Y.F.: Generalized Morse potential: symmetry and satellite potentials. J. Phys. A: Math. Gen. 31, 321 (1998)
Codriansky S., Cordero P., Salamo S.: On the generalized Morse potential. J. Phys. A: Math. Gen. 32, 6287 (1999)
Jia C.S., Zeng L.X., Sun L.T.: PT symmetry and shape invariance for a potential well with a barrier. Phys. Lett. A 294, 185 (2002)
Rong Z., Kjaergaard H.G., Sage M.L.: Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules. Mol. Phys. 101, 2285 (2003)
Dong S.H.: The realization of dynamic group for the pseudoharmonic oscillator. Appl. Math. Lett. 16, 199 (2003)
Jia C.S., Li Y., Sun Y., Liu J.Y., Sun L.T.: Bound states of the five-parameter exponential-type potential model. Phys. Lett. A 311, 115 (2003)
Haouat S., Chetouani L.: Approximate solutions of Klein–Gordon and Dirac equations in the presence of the Hulthén potential. Phys. Scr. 77, 025005 (2008)
Wei G.F., Liu X.Y.: The relativistic bound states of the hyperbolical potential with the centrifugal term. Phys. Scr. 78, 065009 (2008)
Zhang L.H., Li X.P., Jia C.S.: Analytical approximation to the solution of the Dirac equation with the Eckart potential including the spin–orbit coupling term. Phys. Lett. A 372, 2201 (2008)
Xu Y., He S., Jia C.S.: Approximate analytical solutions of the Dirac equation with the Pöschl–Teller potential including the spin–orbit coupling term. J. Phys. A: Math. Theor. 41, 255302 (2008)
Dong S.H., Gu X.Y.: Arbitrary l state solutions of the Schrödinger equation with the Deng-Fan molecular potential. J. Phys.: Conf. Ser. 96, 012109 (2008)
Soylu A., Bayrak O., Boztosun I.: κ state solutions of the Dirac equation for the Eckart potential with pseudospin and spin symmetry. J. Phys. A: Math. Theor. 41, 065308 (2008)
Chen T., Diao Y.F., Jia C.S.: Bound state solutions of the Klein–Gordon equation with the generalized Pöschl–Teller potential. Phys. Scr. 79, 065014 (2009)
Chen T., Liu J.Y., Jia C.S.: Approximate analytical solutions of the Dirac–Manning–Rosen problem with the spin symmetry and pseudo-spin symmetry. Phys. Scr. 79, 055002 (2009)
Jia C.S., Chen T., Cui L.G.: Approximate analytical solutions of the Dirac equation with the generalized Pöschl–Teller potential including the pseudo-centrifugal term. Phys. Lett. A 373, 1621 (2009)
Xu Y., He S., Jia C.S.: Reply to ‘comment on’ approximate analytical solutions of the Dirac equation with the Pöschl–Teller potential including spin–orbit coupling. J. Phys. A: Math. Theor. 42, 198002 (2009)
Taskin F.: Approximate solutions of the Dirac equation for the Manning-Rosen potential including the Spin-Orbit coupling term. Int. J. Theor. Phys. 48, 1142 (2009)
Liu X.Y., Wei G.F., Long C.Y.: Arbitrary wave relativistic bound state solutions for the Eckart potential. Int. J. Theor. Phys. 48, 463 (2009)
Bohr A., Hamamoto I., Mottelson B.R.: Pseudospin in rotating nuclear potentials. Phys. Scr. 26, 267 (1982)
Dudek J., Nazarewicz W., Szymanski Z., Leander G.A.: Abundance and systematics of nuclear superdeformed states; relation to the pseudospin and pseudo-SU(3) symmetries. Phys. Rev. Lett. 59, 1405 (1987)
Troltenier D., Bahri C., Draayer J.P.: Generalized pseudo-SU(3) model and pairing. Nucl. Phys. A 586, 53 (1995)
Page P.R., Goldman T., Ginocchio J.N.: Relativistic symmetry suppresses Quark spin-orbit splitting. Phys. Rev. Lett. 86, 204 (2001)
Ginocchio J.N., Leviatan A., Meng J., Zhou S.G.: Test of pseudospin symmetry in deformed nuclei. Phys. Rev. C 69, 034303 (2004)
Ginocchio J.N.: Pseudospin as a relativistic symmetry. Phys. Rev. Lett. 78(3), 436 (1997)
Ginocchio J.N.: Relativistic symmetries in nuclei and hadrons. Phys. Rep. 414(4-5), 165 (2005)
Hect K.T., Adler A.: Generalized seniority for favored J ≠ 0 pairs in mixed configurations. Nucl. Phys. A 137, 129 (1969)
Arima A., Harvey M., Shimizu K.: Pseudo LS coupling and pseudo SU3 coupling schemes. Phys. Lett. B 30, 517 (1969)
Ikhdair S.M., Sever R.: Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential. Appl. Math. Com. 216, 911 (2010)
Moshinsky M., Szczepanika A.: The Dirac oscillator. J. Phys. A: Math. Gen. 22, L817 (1989)
Kukulin V.I., Loyla G., Moshinsky M.: A Dirac equation with an oscillator potential and spin-orbit coupling. Phys. Lett. A 158, 19 (1991)
Akcay H.: Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential. Phys. Lett. A 373, 616 (2009)
Akcay H.: The Dirac oscillator with a Coulomb-like tensor potential. J. Phys. A: Math. Theor. 40, 6427 (2007)
Aydoğdu O., Sever R.: Exact Pseudospin symmetric solution of the Dirac equation for pseudoharmonic potential in the presence of tensor potential. Few-Body Syst. 47, 193 (2010)
Berkdemir C.: Pseudospin symmetry in the relativistic Morse potential including the spin–orbit coupling term. Nucl. Phys. A 770, 32 (2006)
Chen T.S., Lü H.F., Meng J., Zhang S.Q., Zhou S.G.: Pseudospin symmetry in relativistic framework with harmonic oscillator potential and Woods-Saxon potential. Chin. Phys. Lett. 20, 358 (2003)
Alhaidari A.D., Bahlouli H., Al-Hasan A.: Dirac and Klein–Gordon equations with equal scalar and vector potentials. Phys. Lett. A. 349, 87 (2006)
Guo J.Y., Zhou F., Guo F.L., Zhou J.H.: Exact solution of the continuous states for generalized asymmetrical Hartmann potentials under the condition of pseudospin symmetry. Int. J. Mod. Phys. A 22, 4825 (2007)
Guo J.Y., Sheng Z.Q.: Solution of the Dirac equation for the Woods–Saxon potential with spin and pseudospin symmetry. Phys. Lett. A 338, 90 (2005)
Qiang W.C., Zhou R.S., Gao Y.: Application of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry. J. Phys. A: Math. Theor. 40, 1677 (2007)
Xu Q., Zhu S.J.: Pseudospin symmetry and spin symmetry in the relativistic Woods–Saxon. Nucl. Phys. A 768, 161 (2006)
Aydoğdu O., Sever R.: Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit. Ann. Phys. 325, 373 (2010)
Ikhdair S.M., Sever R.: Approximate eigenvalue and eigenfunction solutions for the generalized Hulthén Potential with any angular momentum. J. Math. Chem. 42, 461 (2007)
Erkoc S., Sever R.: Path-integral solution for a Mie-type potential. Phys. Rev. D 30, 2117 (1984)
Morse P.M.: Diatomic molecules according to the wave Mechanics. II. Vibrational levels. Phys. Rev. 34, 57 (1929)
Ikhdair S.M., Sever R.: On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz. Cent. Eur. J. Phys. 6, 697 (2008)
Ikhdair S.M., Sever R.: Polynomial solutions of the Mie-type potential in the D-dimensional Schrödinger equation. J. Mol. Struc. (Theochem) 13, 855 (2008)
Berkdemir C., Berkdemir A., Han J.: Bound state solutions of the Schrödinger equation for modified Kratzer’s molecular potential. Chem. Phys. Lett 417, 326 (2006)
Bjorken J.D., Drell S.D.: “Relativistic Quantum Mechanics”. McGraw-Hill, NY (1964)
Meng J., Sugawara-Tanabe K., Yamaji S., Arima A.: Pseudospin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line. Phys. Rev. C 59, 154 (1999)
Meng J. et al.: Pseudospin symmetry in relativistic mean field theory. Phys. Rev. C 58, R628 (1998)
Satchler G.R.: “Direct Nuclear Reactions”. Oxford University Press, London (1983)
Nikiforov A.F., Uvarov V.B.: “Special Functions of Mathematical Physics”. Birkhausr, Berlin (1988)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hamzavi, M., Rajabi, A.A. & Hassanabadi, H. Exact Spin and Pseudospin Symmetry Solutions of the Dirac Equation for Mie-Type Potential Including a Coulomb-like Tensor Potential. Few-Body Syst 48, 171–182 (2010). https://doi.org/10.1007/s00601-010-0095-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-010-0095-7