Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator

XU Qiang; ZHU Sheng-Jiang

Chinese Physics C> 2007, Vol. 31> Issue(3) : 251-257

Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator

XU Qiang ^, ,
ZHU Sheng-Jiang

Department of Physics, Tsinghua University, Beijing 100084, China

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Abstract：
Pseudospin symmetry and spin symmetry in the relativistic harmonic oscillator are investigated systematically by solving the Dirac equation with scalar and vector potentials and are found to be a good approximation in realistic nuclei such as ²⁰⁸Pb. The pseudospin breaking and spin breaking are shown in correlation with nuclear mean field. The harmonic oscillator frequency and the distance of well-bottom deviation from the center of the potential play an important role in the splittings of energy and wavefunction. The energy-level crossing are found for all the pseudospin partners. The dependence of splittings with quantum numbers is also analyzed.

References

[1]

. Arima A, Harvey M, Shimizu K. Phys. Lett., 1969, B30:5172. Hecht K T, Adler A. Nucl. Phys., 1969, A137: 1293. Bohr A, Hamamoto I, Mottelson B R. Phys. Scr., 1982, 26:2674. Dudek J, Nazarewicz W, Szymanski Z et al. Phys. Rev.Lett., 1987, 59: 14055. Troltenier D, Nazarewicz W, Szymanski Z et al. Nucl.Phys., 1994, A567: 5916. Stuchbery A E. Nucl. Phys., 2002, A700: 837. Nazarewicz W, Twin P J, Fallon P et al. Phys. Rev. Lett.,1990, 64: 16548. Stephens F S et al. Phys. Rev. Lett., 1990, 65: 3019. ZENG J Y, MENG J, WU C S et al. Phys. Rev., 1991,C44: R174510. Blokhin A L, Bahri C, Draayer J P. Phys. Rev. Lett., 1995,74: 414911. Bahri C, Draayer J P, Moszkowski S A. Phys. Rev. Lett.,1992, 68: 213312. Ginocchio J N. Phys. Rev. Lett., 1997, 78: 436; GinocchioJ N. Phys. Rep., 1999, 315: 23113. MENG J, Sugawara-Tanabe K, Yamaji S et al. Phys. Rev.,1998, C58: R62814. MENG J, Sugawara-Tanabe K, Yamaji S et al. Phys. Rev.,1999, C59: 15415. Ginocchio J N, Leviatan A. Phys. Rev. Lett., 2001, 87:07250216. Ginocchio J N. Phys. Rev., 2002, C66: 06431217. Sugawara-Tanabe K, Arima A. Phys. Rev., 1998, C58:3065R18. Sugawara-Tanabe K, Yamaji S, Arima A. Phys. Rev., 2000,C62: 05430719. Sugawara-Tanabe K, Yamaji S, Arima A. Phys. Rev., 2002,C65: 05431320. Ginocchio J N, Leviatan A, MENG J et al. Phys. Rev.,2004, C69: 03430321. Marcos S, Savushkon L N, Lopez-Quelle M et al. Phys.Rev., 2000, C69: 05430922. Marcos S, Lopez-Quelle M, Niembro R et al. Phys. Lett.,2001, B513: 3023. Lopez-Quelle M, Savushkon L N, Marcos S et al. Nucl.Phys., 2003, A727: 26924. CHEN J S, ZHUANG P F, LI J R. Phys. Rev., 2003, C68:04520925. MENG J, Toki H, ZHOU S G et al. Prog. Part. Nucl. Phys.,2006, 57: 47026. Centelles M, Vinas X, Barranco M et al. Nucl. Phys., 1990,A519: 73c27. Kukulin V I, Loyola G, Moshinsky M. Phys. Lett., 1991,A66: 158 1928. CHAO Q W. Chin. Phys., 2002, 66: 11 75729. CHEN T S, LU H F, MENG J et al. Chin. Phys. Lett.,2003, 20: 35830. Ginocchio J N. Phys. Rev., 2004, C69: 03431831. Lisboa R, Malheiro M, de Castro A S et al. Phys. Rev.,2004, C69: 02431932. Lisboa R, Malheiro M, de Castro A S et al. Int. J. Mod.Phys., 2004, D7: 13 1447. nucl-th/041009633. Alberto P, Fiolhais M, Malheiro M et al. Phys. Rev. Lett.,2001, 86: 5015; Alberto P, Fiolhais M, Malheiro M et al.Phys. Rev., 2002, C65: 03430734. GUO J Y,WANG R D, FANG X Z. Phys. Rev., 2005, C72:05431935. GUO J Y, FANG X Z, XU F X. Nucl. Phys., 2005, A757:44136. GUO J Y, SHENG Z Q. Phys. Lett., 2005, A338: 9037. XU Q, ZHU S J. Nucl. Phys., 2006, A768: 16138. MENG J, Tanihata I. Nucl. Phys., 1999, A650: 176

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[14]	Wang Jisuo , Sun Changyong , Teng Aiping . Quantum Statistic Properties of Eigenstates of the Annihilation Operatora_{qs^k of Two Parameter Deformed Harmonic Oscillator}. Chinese Physics C, 1997, 21(9): 793-800.
[15]	Dong Yubing . Study on the Helicity Amplitudes of the Resonances Based on the Relativistic Harmonic Oscillator Model. Chinese Physics C, 1997, 21(11): 1035-1040.
[16]	Wang Jisuo , Sun Changyong , He Jinyu . Eigenstates of the Higher Power of the Annihilation Operator ofTwo-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1996, 20(8): 703-706.
[17]	Zhou Huanqiang , He Jingsong , Zhang Xinming . Eigenstates of the Second Power of the Annihilation Operator of Two-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1995, 19(3): 251-257.
[18]	Sun Huibin , Ma Yingjun , Liu Yunzuo , Zheng Hua , Wen Shuxian , Yang Chunxiang . Spin Determination of ¹⁶⁰Lu at High-Spin States. Chinese Physics C, 1995, 19(10): 929-935.
[19]	YANG Xian-Jun , FAN Xi-Pei . State Densities of Deformed Nuclei Based on Axisymmetric Harmonic Oscillator Potential. Chinese Physics C, 1992, 16(5): 431-438.
[20]	DUAN Yi-Wu , WU Wei-Ping , BAO Cheng-Guang , AN Wei-Ke . The Expansion Method of Mixed Basis Vectors of Lower-energy States and Harmonic Oscillators in Calculation of Bound States of Few-Body Systems. Chinese Physics C, 1991, 15(1): 42-45.

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XU Qiang and ZHU Sheng-Jiang. Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator[J]. Chinese Physics C, 2007, 31(3): 251-257.

XU Qiang and ZHU Sheng-Jiang. Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator[J]. Chinese Physics C, 2007, 31(3): 251-257. shu

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Received: 2006-07-01
Revised: 2006-08-04

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator

Corresponding author: XU Qiang,

Department of Physics, Tsinghua University, Beijing 100084, China

Received Date: 2006-07-01

Accepted Date: 2006-08-04

Available Online: 2007-03-05

Abstract: Pseudospin symmetry and spin symmetry in the relativistic harmonic oscillator are investigated systematically by solving the Dirac equation with scalar and vector potentials and are found to be a good approximation in realistic nuclei such as ²⁰⁸Pb. The pseudospin breaking and spin breaking are shown in correlation with nuclear mean field. The harmonic oscillator frequency and the distance of well-bottom deviation from the center of the potential play an important role in the splittings of energy and wavefunction. The energy-level crossing are found for all the pseudospin partners. The dependence of splittings with quantum numbers is also analyzed.

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Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator

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