The energy eigenvalues of Dirac equation with the modified Eckart and modified deformed Hylleraas potential by shape invariance approach

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• 作者：S. Arbabi Moghadam ; H. Mehraban…
• 关键词：Dirac equation ; spin and pseudospin symmetry ; SUSY ; Coulomb ; like tensor potential ; modified Eckart ; modified deformed Hylleraas
• 刊名：Physics of Particles and Nuclei Letters
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：12
• 期：5
• 页码：667-679
• 全文大小：752 KB
• 参考文献：1.R. Lisboa, M. Malheiro, A. S. de Castro, P. Alberto, and M. Fiolhais, 鈥淧seudospin symmetry and the relativistic harmonic oscillator,鈥?Phys. Rev. C 69, 024319 (2004).CrossRef ADS
  2.S. Zarrinkamar, A. A. Rajabi, and H. Hassanabadi, 鈥淒irac equation for the harmonic scalar and vector potentials and linear plus Coulomb-like tensor potential the SUSY approach,鈥?Ann. Phys. (N.Y.) 325, 2522 (2010).MATH MathSciNet CrossRef ADS
  3.J. N. Ginocchio, 鈥淯(3) and pseudo-U(3) symmetry of the relativistic harmonic oscillator,鈥?Phys. Rev. Lett. 95, 252501 (2005).CrossRef ADS
  4.S. Arbabi Moghadam, H. Mehraban, and M. Eshghi, 鈥淓igen-spectra in the Dirac-attractive radial problem plus a tensor interaction under pseudospin and spin symmetry with the SUSY approach,鈥?Chin. Phys. B 22, 100305 (2013).CrossRef
  5.J. Y. Gou, X. Z. Fang, and F. X. Xu, 鈥淧seudospin symmetry in the relativistic harmonic oscillator,鈥?Nucl. Phys. A 757, 411 (2005).CrossRef ADS
  6.M. Eshghi, 鈥淢akarov potential in relativistic equation via Laplace transformation approach,鈥?Can. J. Phys. 91, 71 (2013).CrossRef
  7.A. S. de Castro, P. Alberto, R. Lisboa, and M. Malheiro, 鈥淩elating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator,鈥?Phys. Rev. C 73, 054309 (2006).CrossRef ADS
  8.M. Eshghi and H. Mehraban, 鈥淪olution of the Dirac equation with position-dependent mass for Q-parameter modified P枚schl鈥揟eller and Coulomb-like tensor potential,鈥?Few-Body Syst. 52, 41 (2012).CrossRef ADS
  9.M. C. Zhang, G. H. Sun, and S. H. Dong, 鈥淓xactly complete solutions of the Schr枚dinger equation with a spherically harmonic oscillatory ring-shaped potential,鈥?Phys. Lett. A 374, 704 (2010).MATH MathSciNet CrossRef ADS
  10.M. Eshghi, 鈥淧seudo-harmonic oscillatory ring-shaped potential in a relativistic equation,鈥?Chin. Phys. Lett. 29, 110304 (2012).CrossRef ADS
  11.H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, and H. Rahimov, 鈥淎n approximate solution of the Dirac equation for hyperbolic scalar and vector potentials and a Coulomb tensor interaction by SUSYQM,鈥?Mod. Phys. Lett. A 26, 2703 (2011).MATH MathSciNet CrossRef ADS
  12.S. H. Dong, 鈥淎 new quantization rule to the energy spectra for modified hyperbolic-type potentials,鈥?Int. J. Quantum. Chem. 109, 701 (2009).CrossRef ADS
  13.J. Y. Gou and Z. Q. Sheng, 鈥淪olution of the Dirac equation for the Woods鈥揝axon potential with spin and pseudospin symmetry,鈥?Phys. Lett. A 338, 90 (2005).MathSciNet CrossRef ADS
  14.G. F. Wei and S. H. Dong, 鈥淪pin symmetry in the relativistic symmetrical well potential including a proper approximation to the spin鈥搊rbit coupling term,鈥?Phys. Scr. 81, 035009 (2010).CrossRef ADS
  15.J. Y. Gou, J. C. Han, and R. D. Wang, 鈥淧seudospin symmetry and the relativistic ring-shaped non-spherical harmonic oscillator,鈥?Phys. Lett. A 353, 378 (2006).MathSciNet CrossRef ADS
  16.C. S. Jia, T. Chen, and L. G. Gui, 鈥淎pproximate analytical solutions of the Dirac equation with the generalized P枚schl鈥揟eller potential including the pseudo-centrifugal term,鈥?Phys. Lett. A 373, 1621 (2009).MATH MathSciNet CrossRef ADS
  17.C. Berkdemir, 鈥淧seudospin symmetry in the relativistic Morse potential including the spin鈥搊rbit coupling term,鈥?Nucl. Phys. A 770, 32 (2006).CrossRef ADS
  18.M. Eshghi and M. Hamzavi, 鈥淪pin symmetry in Diracattractive radial problem and tensor potential,鈥?Commun. Theor. Phys. 57, 355 (2012).MATH MathSciNet CrossRef ADS
  19.W. C. Qiang, R. S. Zhou, and Y. Gao, 鈥淎pplication of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry,鈥?J. Phys. A: Math. Theor. 40, 11119 (2007)MathSciNet CrossRef
  19a.W. C. Qiang, R. S. Zhou, and Y. Gao, J. Phys. A: Math. Theor. 40, 1677 (2007).MATH MathSciNet CrossRef ADS
  20.S. M. Ikhdair and R. Sever, 鈥淎pplication?of the inversion method to the heavy quarkonium systems,鈥?Appl. Math. Commun. 216, 545 (2010).MATH MathSciNet CrossRef
  21.O. Bayrak and I. Boztosun, 鈥淭he pseudospin symmetric solution of the Morse potential for any 魏 State,鈥?J. Phys. A: Math. Theor. 40, 11119 (2007).MATH MathSciNet CrossRef ADS
  22.G. F. Wei and S. H. Dong, 鈥淎pproximately analytical solutions of the Manning鈥揜osen potential with the spin鈥搊rbit coupling term and spin symmetry,鈥?Phys. Lett. A 373, 49 (2008).MATH MathSciNet CrossRef ADS
  23.C. S. Jia, P. Guo, and X. L. Peng, 鈥淓xact solution of the Dirac鈥揈ckart problem with spin and pseudospin symmetry,鈥?J. Phys. A: Math. Gen. 39, 7737 (2006).MATH MathSciNet CrossRef ADS
  24.C. S. Jia, J. Y. Liu, L. He, and L. T. Sun, 鈥淧seudospin symmetry in the relativistic empirical potential as a diatomic molecular model,鈥?Phys. Scr. 75, 388 (2007).MATH CrossRef ADS
  25.C. S. Jia, P. Guo, Y. F. Diao, L. Z. Yi, and X. J. Xie, 鈥淪olutions of Dirac equations with the P枚schl-Teller potential,鈥?Eur. Phys. J. A 34, 41 (2007).CrossRef ADS
  26.Y. P. Varshni, 鈥淐omparative study of potential energy functions for diatomic molecules,鈥?Rev. Mod. Phys. 29, 664 (1957).CrossRef ADS
  27.E. A. Hilleraas, 鈥淓nergy formula and potential distribution of diatomic molecules,鈥?J. Chem. Phys. 3, 595 (1935).CrossRef ADS
  28.A. N. Ikot, O. A. Awoga, and A. D. Antia, 鈥淏ound state solutions of d-dimensional Schr枚dinger equation with Eckart potential plus modified deformed Hylleraas potential,鈥?Chin. Phys. B 22, 020304 (2013).CrossRef
  29.S. H. Dong, W. C. Qiang, G. H. Sun, and V. B. Bezerra, 鈥淎nalytical approximations to the l-wave solutions of the Schr枚dinger equation with the Eckart potential,鈥?J. Phys. A 40, 10535 (2007).MATH MathSciNet CrossRef ADS
  30.H. Hassanabadi, E. Maghsoodi, N. Ikot Akpan, and S. Zarrinkamar, 鈥淎pproximate arbitrary-state solutions of Dirac equation for modified deformed Hylleraas and modified Eckart potentials by the NU method,鈥?Appl. Math. Comput. 219, 9388 (2013).MATH MathSciNet CrossRef
  31.M. Hamzavi, A. A. Rajabi, and H. Hassanabadi, 鈥淓xact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method,鈥?Phys. Lett. A 374, 4303 (2010).MATH MathSciNet CrossRef ADS
  32.H. Ak莽ay and C. Tezcan, 鈥淓xact solutions of the Dirac equation with harmonic oscillator potential including a Coulomb-like tensor potential,鈥?Int. J. Mod. Phys. C 20, 931 (2009).MATH CrossRef ADS
  33.S. M. Ikhdair and R. Sever, 鈥淎pproximate bound state solutions of Dirac equation with Hulth茅n potential including Coulomb-like tensor potential,鈥?Appl. Math. Commun. 216, 911 (2010).MATH MathSciNet CrossRef
  34.W. Greiner, Relativistic Quantum Mechanics-Wave Equation, 3rd ed. (Springer, Berlin, 2000).CrossRef
  35.J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964).
  36.J. N. Ginocchio, 鈥淭he relativistic foundations of pseudospin symmetry in nuclei,鈥?Nucl. Phys. A 654, 663 (1999).CrossRef ADS
  37.J. N. Ginocchio, 鈥淎 relativistic symmetry in nuclei,鈥?Phys. Rep. 315, 231 (1999).CrossRef ADS
  38.L. E. Gendenshtein, 鈥淒erivation of exact spectra of the Schr枚dinger equation by means of supersymmetry,鈥?JETP Lett. 38, 356 (1983).ADS
  39.F. Cooper, A. Khare, and U. Sukhatme, 鈥淪upersymmetry and quantum mechanics,鈥?Phys. Rep. 251, 276 (1995).MathSciNet CrossRef ADS
  
• 作者单位：S. Arbabi Moghadam (1)
  H. Mehraban (2)
  H. Habibi Khoshmehr (3)
  
  1. Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
  2. Physics Department, Faculty of Sciences, Semnan University, Semnan, Iran
  3. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Elementary Particles and Nuclei
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8567

文摘

By using the supersymmetry quantum mechanics method, we approximately solve the Dirac equation for the modified Eckart potential and the modified deformed Hylleraas including Coulomb-like tensor potential under spin and pseudospin symmetry. We obtained approximate energy eigenvalues and the corresponding wave functions in terms of the Jacobi polynomial under the spin and pseudospin symmetries limit. In order to test the accuracy of our work, we compared our numerical results with that Nikiforov-Uvarov (NU) method. This shows that our results are consistent with those found in the literature. Keywords Dirac equation spin and pseudospin symmetry SUSY Coulomb-like tensor potential modified Eckart modified deformed Hylleraas