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Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit. (English) Zbl 1186.81049

Summary: We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term \(\kappa \). We also investigate the energy eigenvalues of the Dirac particles for the well-known Kratzer-Fues and modified Kratzer potentials which are Mie-type potentials.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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[1] Arima, A.; Harvey, M.; Shimizu, K., Phys. Lett. B, 30, 517 (1969)
[2] Hect, K. T.; Adler, A., Nucl. Phys. A, 137, 129 (1969)
[3] Bohr, A.; Hamamoto, I.; Mottelson, B. R., Phys. Scr., 26, 267 (1982)
[4] Dudek, J.; Nazarewicz, W.; Szymanski, Z.; Leander, G. A., Phys. Rev. Lett., 59, 1405 (1987)
[5] Troltenier, D.; Nazarewicz, W.; Szymanski, Z.; Draayer, J. P., Nucl. Phys. A, 567, 591 (1994)
[6] Stuchbery, A. E., Nucl. Phys. A, 700, 83 (2002)
[7] Nazarewicz, W.; Twin, P. J.; Fallon, P.; Garrett, J. D., Phys. Rev. Lett., 64, 1654 (1990)
[8] Stephens, F. S.; Deleplanque, M. A.; Draper, J. E., Phys. Rev. Lett., 65, 301 (1990)
[9] Ginocchio, J. N., Phys. Rev. Lett., 78, 436 (1997)
[10] Ginocchio, J. N., Phys. Rep., 414, 165 (2005)
[11] Chen, T.-S.; LÜ, H.-F.; Meng, J.; Zhang, S.-Q.; Zhou, S.-G., Chin. Phys. Lett., 20, 358 (2003)
[12] Wei, G.-F.; Dong, S.-H., Phys. Lett. A, 373, 45 (2008)
[13] Kratzer, A., Z. Phys., 3, 289 (1920)
[14] Fues, E., Ann. Physik, 80, 367 (1926)
[15] Berkdemir, C.; Berkdemir, A.; Han, J., Chem. Phys. Lett., 417, 326 (2006)
[16] van Hooydonk, G., J. Mol. Struc.-Theochem., 109, 84 (1984)
[17] Secrest, D., J. Chem. Phys., 89, 1017 (1988)
[18] Requena, A.; Zuniga, J.; Fuentes, L. M.; Hidolgo, A., J. Chem. Phys., 85, 3939 (1986)
[19] Frances, J. M.; Zuifga, J.; Alacid, M.; Requena, A., J. Appl. Phys., 90, 5536 (1989)
[20] Le Roy, R. J.; Bernstein, R. B., J. Chem. Phys., 52, 3869 (1970)
[21] IKhdair, S. M.; Sever, R., J. Math. Chem. (2008), doi:10.1007/s10910-008-9438-8
[22] Oyewumi, K. J., Found. Phys. Lett., 18, 75 (2005)
[23] Xu, Y.; He, S.; Jia, C.-S., J. Phys. A: Math. Theor., 41, 255302 (2008)
[24] Ciftci, H.; Hall, R. L.; Saad, N., J. Phys. A, 36, 11807 (2003)
[25] Soylu, A.; Bayrak, O.; Boztosun, I., J. Phys. A: Math. Theor., 41, 065308 (2008)
[26] Bayrak, O.; Boztosun, I., J. Phys. A: Math. Theor., 40, 11119 (2007)
[27] Berkdemir, C.; Sever, R., J. Phys. A: Math. Theor., 41, 045302 (2008)
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