Analytical approximation to the solution of the Dirac equation with the Eckart potential including the spin-orbit coupling term. (English) Zbl 1220.81101

Zhang, Lie-Hui; Li, Xiao-Ping; Jia, Chun-Sheng

Phys. Lett., A 372, No. 13, 2201-2207 (2008).

Summary: By using the supersymmetric WKB approximation approach and the functional analysis method, we solve approximately the Dirac equation with the Eckart potential for the arbitrary spin-orbit quantum number \(\kappa \). The bound state energy eigenvalues and the associated two-component spinors of the Dirac particles are obtained approximately.

MSC:

81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q60	Supersymmetry and quantum mechanics
81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory

Keywords:

Dirac equation; Eckart potential; pseudospin symmetry

References:

[1]	Arima, A.; Harvey, M.; Shimizu, K., Phys. lett. B, 30, 517, (1969)
[2]	Hecht, 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.; Bahri, C.; Draayer, J.P., Nucl. phys. A, 586, 53, (1995)
[6]	Ginocchio, J.N., Phys. rev. lett., 78, 436, (1997)
[7]	Ginocchio, J.N., Phys. rev. C, 57, 1167, (1998)
[8]	Ginocchio, J.N., Phys. rep., 414, 165, (2005)
[9]	Lisboa, R.; Malheiro, M.; De Castro, A.S.; Alberto, P.; Fiolhais, M., Phys. rev. C, 69, 024319, (2004)
[10]	Ginocchio, J.N., Phys. rev. lett., 95, 252501, (2005)
[11]	Gou, J.Y.; Fang, X.Z.; Xu, F.X., Nucl. phys. A, 757, 411, (2005)
[12]	de Castro, A.S.; Alberto, P.; Lisboa, R.; Malheiro, M., Phys. rev. C, 73, 054309, (2006)
[13]	Gou, J.Y.; Sheng, Z.Q., Phys. lett. A, 338, 90, (2005)
[14]	Gou, J.Y.; Han, J.C.; Wang, R.D., Phys. lett. A, 353, 378, (2006)
[15]	Berkdemir, C., Nucl. phys. A, 770, 32, (2006)
[16]	Qiang, W.C.; Zhou, R.S.; Gao, Y., J. phys. A: math. theor., 40, 1677, (2007)
[17]	Bayrak, O.; Boztosun, I., J. phys. A: math. theor., 40, 11119, (2007)
[18]	Jia, C.S.; Guo, P.; Peng, X.L., J. phys. A: math. gen., 39, 7737, (2006)
[19]	Jia, C.S.; Liu, J.Y.; He, L.; Sun, L.T., Phys. scr., 75, 388, (2007)
[20]	Jia, C.S.; Guo, P.; Diao, Y.F.; Yi, L.Z.; Xie, X.J., Eur. phys. J. A, 34, 41, (2007)
[21]	Eckart, C., Phys. rev., 35, 1303, (1930)
[22]	Cooper, F.; Khare, A.; Sukhatme, U., Phys. rep., 251, 267, (1995)
[23]	Weiss, J.J., J. chem. phys., 41, 1120, (1964)
[24]	Cimas, A.; Aschi, M.; Barrientos, C.; Rayón, V.M.; Sordo, J.A.; Largo, A., Chem. phys. lett., 374, 594, (2003)
[25]	Jia, C.S.; Zeng, X.L.; Sun, L.T., Phys. lett. A, 294, 185, (2002)
[26]	Jia, C.S.; Li, Y.; Sun, Y.; Liu, J.Y.; Sun, L.T., Phys. lett. A, 311, 115, (2003)
[27]	Zou, X.; Yi, L.Z.; Jia, C.S., Phys. lett. A, 346, 54, (2005)
[28]	Dong, S.H.; Qiang, W.C.; Sun, G.H.; Bezerra, V.B., J. phys. A: math. theor., 40, 10535, (2007)
[29]	Gonül, B.; Özer, O.; Cancelik, Y.; Kocak, M., Phys. lett. A, 275, 238, (2000)
[30]	Bayrak, O.; Kocak, G.; Boztosun, I., J. phys. A: math. theor., 40, 11521, (2007)
[31]	Qiang, W.C.; Dong, S.H., Phys. lett. A, 368, 13, (2007)
[32]	Gendenshtein, L.E., Sov. phys. JETP lett., 38, 356, (1983)
[33]	Comtet, A.; Bandrank, A.; Campbell, D.K., Phys. lett. B, 150, 159, (1985)
[34]	Dong, S.H., Factorization method in quantum mechanics, (2007), Springer/Kluwer Academic Press
[35]	Hruska, M.; Keung, W.Y.; Sukhatme, U., Phys. rev. A, 55, 3345, (1997)