搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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

Tridiagonal representation with pseudospin symmetry for a noncentral electric dipole and a ring-shaped anharmonic oscillator potential

Gao Jie, Zhang Min-Cang
PDF
导出引用
  • 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
    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.
      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.
      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).
    [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 物理学报 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

  • [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 物理学报 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

  • [1] 张民仓. 环状非有心球谐振子势场赝自旋对称性的三对角化表示. 物理学报, 2012, 61(24): 240301. doi: 10.7498/aps.61.240301
    [2] 林恺, 杨树政. 高维de Sitter时空中宇宙视界处的Fermi子隧穿. 物理学报, 2010, 59(4): 2223-2227. doi: 10.7498/aps.59.2223
    [3] 胥建卫, 王顺金. 电子的相对论平均场理论与一阶、二阶Rashba效应. 物理学报, 2009, 58(7): 4878-4882. doi: 10.7498/aps.58.4878
    [4] 林恺, 杨树政. Vaidya-Bonner黑洞的费米子隧穿. 物理学报, 2009, 58(2): 744-748. doi: 10.7498/aps.58.744
    [5] 张民仓. 类Quesne环状球谐振子势场中的赝自旋对称性. 物理学报, 2009, 58(2): 712-716. doi: 10.7498/aps.58.712
    [6] 张民仓. 相对论性非球谐振子势场中的赝自旋对称性. 物理学报, 2009, 58(1): 61-65. doi: 10.7498/aps.58.61
    [7] 杨 波. 直线加速Kinnersley黑洞中Dirac粒子的热辐射. 物理学报, 2008, 57(2): 1278-1284. doi: 10.7498/aps.57.1278
    [8] 梁麦林, 张福林, 袁 兵. 无穷深势阱中相对论粒子的矩阵元及其经典近似. 物理学报, 2007, 56(7): 3683-3687. doi: 10.7498/aps.56.3683
    [9] 张民仓, 王振邦. 一类环状非球谐振子势场中相对论粒子的束缚态解. 物理学报, 2007, 56(7): 3688-3692. doi: 10.7498/aps.56.3688
    [10] 张民仓, 王振邦. 第二类P?schl-Teller势场中相对论粒子的束缚态. 物理学报, 2006, 55(2): 525-528. doi: 10.7498/aps.55.525
    [11] 曹江陵. 任意加速带电动态黑洞中Dirac粒子的Hawking辐射. 物理学报, 2006, 55(6): 2682-2686. doi: 10.7498/aps.55.2682
    [12] 张民仓, 王振邦. Manning-Rosen标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态. 物理学报, 2006, 55(2): 521-524. doi: 10.7498/aps.55.521
    [13] 张民仓, 王振邦. Makarov势的Dirac方程的束缚态解. 物理学报, 2006, 55(12): 6229-6233. doi: 10.7498/aps.55.6229
    [14] 李 宁, 鞠国兴, 任中洲. 一类相对论性非球谐振子系统的束缚态. 物理学报, 2005, 54(6): 2520-2523. doi: 10.7498/aps.54.2520
    [15] 陈 刚. 具有Wood-Saxon势的Dirac方程的束缚态. 物理学报, 2004, 53(3): 680-683. doi: 10.7498/aps.53.680
    [16] 张靖仪, 赵 峥. 电磁直线加速动态黑洞时空中Dirac粒子的Hawking辐射. 物理学报, 2003, 52(8): 2096-2101. doi: 10.7498/aps.52.2096
    [17] 张靖仪. 一般球对称带电蒸发黑洞Dirac场的熵. 物理学报, 2003, 52(9): 2354-2358. doi: 10.7498/aps.52.2354
    [18] 张靖仪, 赵峥. 直线加速动态黑洞Dirac场的熵. 物理学报, 2002, 51(10): 2399-2406. doi: 10.7498/aps.51.2399
    [19] 冉扬强, 薛立徽, 胡嗣柱. 具有一维Coulomb型对称势Dirac方程的精确解. 物理学报, 2002, 51(11): 2435-2439. doi: 10.7498/aps.51.2435
    [20] 陈刚. 具有P?schl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态. 物理学报, 2001, 50(9): 1651-1653. doi: 10.7498/aps.50.1651
计量
  • 文章访问数:  4420
  • PDF下载量:  353
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-07-31
  • 修回日期:  2015-09-28
  • 刊出日期:  2016-01-20

/

返回文章
返回