包含非中心电耦极矩的环状非谐振子势场赝自旋对称性的三对角化表示

高洁; 张民仓

doi:10.7498/aps.65.020301

摘要

提出了一个包含非中心电耦极矩分量的环状非谐振子势模型, 在能够负载Dirac波动算子三对角化表示的完全平方可积L2空间讨论了这一势场的赝自旋对称性.利用三对角化矩阵方案,使得求解Dirac方程转换为寻求波函数展开系数满足的三项递推关系式.角向波函数和径向波函数分别以Jacobi多项式和Laguerre多项式表示. 由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱,显示出这一势模型具有严格的赝自旋对称性

关键词:

Abstract

The concepts of pseudospin symmetry in atomic nuclei and spin symmetry in anti-nucleon are reviewed. The exploration for understanding the origin of pseudospin symmetry and its breaking mechanism, and the empirical data supporting the pseudospin symmetry are introduced. A noncentral anharmonic oscillatory potential model is proposed, in which a noncentral electric dipole and a double ring-shaped component are included. The pseudospin symmetry for this potential model is investigated by working on a complete square integrable basis that supports a tridiagonal matrix representation of the Dirac wave operator. Then, solving the Dirac equation is translated into finding solutions of the recursion relation for the expansion coefficients of the wavefunction. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation, and the property of energy equation is discussed for showing the exact pseudospin symmetry. Several particular cases obtained by setting the parameters of the potential model to appropriate values are analyzed, and the energy equations are reduced to that of the anharmonic oscillator and that of the ring-shaped non-spherical harmonic oscillator, respectively. Finally, it is pointed out that the exact spin symmetry exists also in this potential model.

Keywords:

作者及机构信息

高洁,
张民仓

1.
陕西师范大学物理学与信息技术学院, 西安 710119

通信作者: 张民仓, mincangzhang@snnu.edu.cn

基金项目: 国家自然科学基金(批准号: 14101020155)和中央高校基本科研业务费(批准号: GK201402012)资助的课题.

Authors and contacts

1.
College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China

Corresponding author: Zhang Min-Cang, mincangzhang@snnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 14101020155) and the Fundamental Research Funds for the Central Universities, China (Grant No. GK201402012).

参考文献

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[25]	Dong S H, Sun G H, Lozada-Cassou M 2005 Phys. Lett. A 340 94
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[27]	Luban M, Luscome J H, Reed M A, Pursey D L 1989 Appl. Phys.Lett. 54 1997
[28]	Sutherland B 2008 Phys. Rev. Lett. 80 3678
[29]	Goudarzi H, Sohbati M, Zarrin S 2011 J. Math. Phys. 52 013506
[30]	Hautot A 1973 J. Math. Phys. 14 1320
[31]	Berkdemir C 2009 J. Math. Chem. 46 139
[32]	Zhang M C, Sun G H, Dong S H 2010 Phys. Lett. A 374 704
[33]	Eshghi M, Mehraban H, Arbabi M S 2014 Phys. Scr. 89 095202
[34]	Sun D S, You Y, Lu F L, Chen C Y, Dong S H 2014 Phys. Scr. 89 045002
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[36]	Wightman A S 1950 Phys. Rev. 77 521
[37]	Fox K, Turner J E 1966 J. Chem. Phys. 45 1142
[38]	Brown W B, Robers R E 1967 J. Chem. Phys. 46 2006
[39]	Alhaidari A D 2005 J. Phys. A: Math. Gen. 38 3409
[40]	Alhaidari A D 2008 Ann. Phys. 323 1709
[41]	Alhaidari A D, Bahlouli H 2008 Phys. Rev. Lett. 100 110401
[42]	Zhang M C, Huang-Fu G Q 2012 Ann. Phys. 327 841
[43]	Zhang M C 2012 Acta Phys. Sin. 61 240301 (in Chinese) [张民仓 2012 61 240301]
[44]	Alhaidari A D 2007 J .Phys. A: Math. Theor. 40 14843
[45]	Bahlouli H, Alhaidari A D 2010 Phys. Scr. 81 025008
[46]	Alhaidari A D 2005 Ann. Phys. 317 152
[47]	Zeng J Y 2000 Quantum Mechanics (Vol. 2) (Beijing: Science Press) (in Chinese) [曾谨言 2000 量子力学 (卷II) (北京: 科学出版社)]
[48]	Ginocchio J N, Leviatan A, Meng J, Zhou S G 2004 Phys. Rev. C 69 034303
[49]	Lisboa R, Malheiro M, de Castro A S, Alberto P, Fiolhais M 2004 Phys. Rev. C 69 024319
[50]	Guo J Y, Han J C, Wang R D 2006 Phys. Lett. A 353 378

施引文献

[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]	Ginocchio J N 1997 Phys. Rev. Lett. 78 436
[5]	Ginocchio J N, Leviatan A 1998 Phys. Lett. B 425 1
[6]	Meng J 1998 Nucl.Phys. A 635 3
[7]	Meng J, Sugawara-Tanabe K, Yamaji S, Ring P, Arima A 1998 Phys. Rev. C 58 R628
[8]	Meng J, Sugawara-Tanabe K, Yamaji S, Arima A 1999 Phys. Rev. C 59 154
[9]	Zhou S G, Meng J, Ring P 2003 Phys. Rev. Lett. 91 262501
[10]	Liang H Z, Shen S H, Zhao P W, Meng J 2013 Phys. Rev. C 87 014334
[11]	Shen S H, Liang H Z, Zhao P W, Zhang S Q, Meng J 2013 Phys. Rev. C 88 024311
[12]	Dudek J, Nazarewicz W, Szymanski Z, Leander G A 1987 Phys. Rev. Lett. 59 1405
[13]	Nazarewicz W, Twin P J, Fallon P, Garrett J D 1990 Phys. Rev. Lett. 64 1654
[14]	Zeng J Y, Meng J, Wu C S, Zhao E G, Xing Z, Chen X Q 1991 Phys. Rev. C 44 R1745
[15]	Xu Q, Zhu S J, Hamilton J H, Ramayya A V, Hwang J K, Qi B, Meng J, Peng J, Luo Y X, Rasmussen J O, Lee I Y, Liu S H, Li K, Wang J G, Jing H B, Gu L, Yeoh E Y, Ma W C 2008 Phys. Rev. C 78 064301
[16]	Hua W, Zhou X H, Zhang Y H, Zheng Y, Liu M L, Ma F, Guo S, Ma L, Wang S T, Zhang N T, Fang Y D, Lei X G, Guo Y X, Oshima M, Toh Y, Koizumi M, Hatsukawa Y, Qi B, Zhang S Q, Meng J, Sugawara M 2009 Phys. Rev. C 80 034303
[17]	Liang H Z, Zhou S G, Meng J 2015 Phys. Rep. 570 1
[18]	Schiff L I 1955 Quantum Mechanics (3rd Ed.) (New York: McGraw-Hill)
[19]	Mayer M G 1950 Phys. Rev. 78 16
[20]	Nilsson S G 1955 Dan. Mat. Fys. Medd. 29 16
[21]	Chen T S, L H F, Meng J, Zhang S Q, Zhou S G 2003 Chin. Phys. Lett. 20 358
[22]	Ginocchio J N 2004 Phys. Rev. C 69 034318
[23]	Quesne C 1988 J. Phys. A: Math. Gen. 21 3093
[24]	Zhang M C 2009 Int. J. Theor. Phys. 48 2625
[25]	Dong S H, Sun G H, Lozada-Cassou M 2005 Phys. Lett. A 340 94
[26]	Calogero F 1969 J. Math. Phys. 10 2191
[27]	Luban M, Luscome J H, Reed M A, Pursey D L 1989 Appl. Phys.Lett. 54 1997
[28]	Sutherland B 2008 Phys. Rev. Lett. 80 3678
[29]	Goudarzi H, Sohbati M, Zarrin S 2011 J. Math. Phys. 52 013506
[30]	Hautot A 1973 J. Math. Phys. 14 1320
[31]	Berkdemir C 2009 J. Math. Chem. 46 139
[32]	Zhang M C, Sun G H, Dong S H 2010 Phys. Lett. A 374 704
[33]	Eshghi M, Mehraban H, Arbabi M S 2014 Phys. Scr. 89 095202
[34]	Sun D S, You Y, Lu F L, Chen C Y, Dong S H 2014 Phys. Scr. 89 045002
[35]	Fermi E, Teller E 1947 Phys. Rev. 72 399
[36]	Wightman A S 1950 Phys. Rev. 77 521
[37]	Fox K, Turner J E 1966 J. Chem. Phys. 45 1142
[38]	Brown W B, Robers R E 1967 J. Chem. Phys. 46 2006
[39]	Alhaidari A D 2005 J. Phys. A: Math. Gen. 38 3409
[40]	Alhaidari A D 2008 Ann. Phys. 323 1709
[41]	Alhaidari A D, Bahlouli H 2008 Phys. Rev. Lett. 100 110401
[42]	Zhang M C, Huang-Fu G Q 2012 Ann. Phys. 327 841
[43]	Zhang M C 2012 Acta Phys. Sin. 61 240301 (in Chinese) [张民仓 2012 61 240301]
[44]	Alhaidari A D 2007 J .Phys. A: Math. Theor. 40 14843
[45]	Bahlouli H, Alhaidari A D 2010 Phys. Scr. 81 025008
[46]	Alhaidari A D 2005 Ann. Phys. 317 152
[47]	Zeng J Y 2000 Quantum Mechanics (Vol. 2) (Beijing: Science Press) (in Chinese) [曾谨言 2000 量子力学 (卷II) (北京: 科学出版社)]
[48]	Ginocchio J N, Leviatan A, Meng J, Zhou S G 2004 Phys. Rev. C 69 034303
[49]	Lisboa R, Malheiro M, de Castro A S, Alberto P, Fiolhais M 2004 Phys. Rev. C 69 024319
[50]	Guo J Y, Han J C, Wang R D 2006 Phys. Lett. A 353 378

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