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A noncentral harmonic oscillatory ring-shaped potential is proposed, in which the noncentral electric dipole is included. The pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relations for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound state is obtained by diagonalizing the radial recursion relation. The algebraic property of energy equation is also discussed, showing the exact pseudospin symmetry
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Keywords:
- noncentral electric dipole /
- tridiagonal representation /
- Dirac equation /
- pseudospin symmetry
[1] Arima A, Harvey M, Shimizu K 1969 Phys. Lett. B 30 517
[2] Hecht K T, Adler A 1969 Nucl. Phys. A 137 129
[3] Ginocchio J N 1999 Phys. Rep. 315 231
[4] Dudek J, Nazarewicz W, Szymanski Z, Leander G A 1987 Phys. Rev. Lett. 59 1405
[5] Nazarewicz W, Twin P J, Fallon P, Garrett J D 1990 Phys. Rev. Lett. 64 1654
[6] Zeng J Y, Meng J, Wu C S, Zhao E G, Xing Z, Chen X Q 1991 Phys. Rev. C 44 R1745
[7] Schiff L I 1955 Quantum mechanics 3rd ed. (McGraw-Hill, New York)
[8] Mayer M G 1950 Phys. Rev. 78 16
[9] Nilsson S G 1955 Dan. Mat. Fys. Medd. 29 16
[10] Chen T S, Lu H F, Meng J 2003 Chin.Phys. Lett. 20 358
[11] Kukulin V I, Loyola G, Moshinsky M 1991 Phys. Lett. A 158 19
[12] Ginocchio J N 2004 Phys. Rev. C 69 034318
[13] Quesne C 1988 J. Phys. A: Math. Gen. 21 3093
[14] Guo J Y, Han J C, Wang R D 2006 Phys. Lett. A 353 378
[15] Berkdemir C, Cheng Y F 2009 Phys. Scr. 79 1
[16] Lisboa R, Malheiro M, de Castro A S, Alberto P , Fiolhais M 2004 Phys. Rev. C 69 024319
[17] Fermi E, Teller E 1947 Phys. Rev. 72 399
[18] Wightman A S 1950 Phys. Rev. 77 521
[19] Fox K, Turner J E 1966 J. Chem. Phys. 45 1142
[20] Brown W B, Robers R E 1967 J. Chem. Phys. 46 2006
[21] Coon S A, Holstein B R 2002 Am. J. Phys. 70 513
[22] Jaramillo B, Núñez-Yépez H N, Salas-Brito A L 2010 Phys. Lett. A 374 2707
[23] Alhaidari A D 2005 J. Phys. A: Math. Gen. 38 3409
[24] Zhang M C, Huang-Fu G Q 2012 Ann. Phys. 374 841
[25] Alhaidari A D 2008 Ann. Phys. 323 1709
[26] Alhaidari A D, Bahlouli H 2008 Phys. Rev. Lett. 100 110401
[27] Alhaidari A D 2007J. Phys. A: Math. Theor. 40 14843
[28] Bahlouli H, Alhaidari A D 2010 Phys. Scr. 81 025008
[29] Bahlouli H, Abdelmonem M S, Nasser I M 2010 Phys. Scr. 82 065005
[30] Alhaidari A D 2005 Ann. Phys. 317 152
[31] Zeng J Y 2000 Quantum Mechanics Vol Ⅱ 3rd (Beijing: Science Press) (in Chinese) [曾谨言 2000 量子力学 (卷Ⅱ) 第三版(北京: 科学出版社)]
[32] Ginocchio J N, Leviatan A, Meng J, Zhou S G 2004 Phys. Rev. C 69 034303
-
[1] Arima A, Harvey M, Shimizu K 1969 Phys. Lett. B 30 517
[2] Hecht K T, Adler A 1969 Nucl. Phys. A 137 129
[3] Ginocchio J N 1999 Phys. Rep. 315 231
[4] Dudek J, Nazarewicz W, Szymanski Z, Leander G A 1987 Phys. Rev. Lett. 59 1405
[5] Nazarewicz W, Twin P J, Fallon P, Garrett J D 1990 Phys. Rev. Lett. 64 1654
[6] Zeng J Y, Meng J, Wu C S, Zhao E G, Xing Z, Chen X Q 1991 Phys. Rev. C 44 R1745
[7] Schiff L I 1955 Quantum mechanics 3rd ed. (McGraw-Hill, New York)
[8] Mayer M G 1950 Phys. Rev. 78 16
[9] Nilsson S G 1955 Dan. Mat. Fys. Medd. 29 16
[10] Chen T S, Lu H F, Meng J 2003 Chin.Phys. Lett. 20 358
[11] Kukulin V I, Loyola G, Moshinsky M 1991 Phys. Lett. A 158 19
[12] Ginocchio J N 2004 Phys. Rev. C 69 034318
[13] Quesne C 1988 J. Phys. A: Math. Gen. 21 3093
[14] Guo J Y, Han J C, Wang R D 2006 Phys. Lett. A 353 378
[15] Berkdemir C, Cheng Y F 2009 Phys. Scr. 79 1
[16] Lisboa R, Malheiro M, de Castro A S, Alberto P , Fiolhais M 2004 Phys. Rev. C 69 024319
[17] Fermi E, Teller E 1947 Phys. Rev. 72 399
[18] Wightman A S 1950 Phys. Rev. 77 521
[19] Fox K, Turner J E 1966 J. Chem. Phys. 45 1142
[20] Brown W B, Robers R E 1967 J. Chem. Phys. 46 2006
[21] Coon S A, Holstein B R 2002 Am. J. Phys. 70 513
[22] Jaramillo B, Núñez-Yépez H N, Salas-Brito A L 2010 Phys. Lett. A 374 2707
[23] Alhaidari A D 2005 J. Phys. A: Math. Gen. 38 3409
[24] Zhang M C, Huang-Fu G Q 2012 Ann. Phys. 374 841
[25] Alhaidari A D 2008 Ann. Phys. 323 1709
[26] Alhaidari A D, Bahlouli H 2008 Phys. Rev. Lett. 100 110401
[27] Alhaidari A D 2007J. Phys. A: Math. Theor. 40 14843
[28] Bahlouli H, Alhaidari A D 2010 Phys. Scr. 81 025008
[29] Bahlouli H, Abdelmonem M S, Nasser I M 2010 Phys. Scr. 82 065005
[30] Alhaidari A D 2005 Ann. Phys. 317 152
[31] Zeng J Y 2000 Quantum Mechanics Vol Ⅱ 3rd (Beijing: Science Press) (in Chinese) [曾谨言 2000 量子力学 (卷Ⅱ) 第三版(北京: 科学出版社)]
[32] Ginocchio J N, Leviatan A, Meng J, Zhou S G 2004 Phys. Rev. C 69 034303
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