Relativistic interpretation of the nature of the nuclear tensor force

Yao-Yao Zong; Bao-Yuan Sun

doi:10.1088/1674-1137/42/2/024101

Chinese Physics C> 2018, Vol. 42> Issue(2) : 024101 DOI: 10.1088/1674-1137/42/2/024101

Relativistic interpretation of the nature of the nuclear tensor force

Yao-Yao Zong ,
Bao-Yuan Sun ^,

1.
School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China

Abstract
HTML
Reference
Related

PDF

Abstract：
The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force.
- nuclear tensor force ,
- sum rule ,
- covariant density functional theory ,
- relativistic Hartree-Fock theory

References

[1]	H. Yukawa, Proc. Phys. Math. Soc. Japan, 17:48 (1935)
[2]	T. Otsuka, T. Suzuki, R. Fujimoto, H. Grawe, and Y. Akaishi, Phys. Rev. Lett., 95:232502 (2005)
[3]	T. Otsuka, T. Matsuo, and D. Abe, Phys. Rev. Lett., 97:162501 (2006)
[4]	B. A. Brown, T. Duguet, T. Otsuka, D. Abe, and T. Suzuki, Phys. Rev. C, 74:061303 (2006)
[5]	G. Col, H. Sagawa, S. Fracasso, and P. Bortignon, Phys. Lett. B, 646:227 (2007)
[6]	T. Lesinski, M. Bender, K. Bennaceur, T. Duguet, and J. Meyer, Phys. Rev. C, 76:014312 (2007)
[7]	W. Zou, G. Col, Z. Y. Ma, H. Sagawa, and P. F. Bortignon, Phys. Rev. C, 77:014314 (2008)
[8]	W. H. Long, H. Sagawa, J. Meng, and N. Van Giai, Euro. Phys. Lett., 82:12001 (2008)
[9]	W. H. Long, T. Nakatsukasa, H. Sagawa, J. Meng, H. Nakada, and Y. Zhang, Phys. Lett. B, 680:428 (2009)
[10]	M. Bender, K. Bennaceur, T. Duguet, P. H. Heenen, T. Lesinski, and J. Meyer, Phys. Rev. C, 80:064302 (2009)
[11]	T. Otsuka, T. Suzuki, M. Honma, Y. Utsuno, N. Tsunoda, K. Tsukiyama, and M. Hjorth-Jensen, Phys. Rev. Lett., 104:012501 (2010)
[12]	M. Moreno-Torres, M. Grasso, H. Z. Liang, V. De Donno, M. Anguiano, and N. Van Giai, Phys. Rev. C, 81:064327 (2010)
[13]	Y. Z. Wang, J. Z. Gu, J. M. Dong, and X. Z. Zhang, Phys. Rev. C, 83:054305 (2011)
[14]	Y. Z. Wang, J. Z. Gu, X. Z. Zhang, and J. M. Dong, Phys. Rev. C, 84:044333 (2011)
[15]	J. M. Dong, W. Zuo, J. Z. Gu, Y. Z. Wang, L. G. Cao, and X. Z. Zhang, Phys. Rev. C, 84:014303 (2011)
[16]	L. J. Wang, J. M. Dong, and W. H. Long, Phys. Rev. C, 87:047301 (2013)
[17]	S. H. Shen, H. Z. Liang, J. Meng, P. Ring, and S. Q. Zhang, arXiv:1709.06289[nucl-th]
[18]	C. L. Bai, H. Sagawa, H. Q. Zhang, X. Z. Zhang, G. Col, and F. R. Xu, Phys. Lett. B, 675:28 (2009)
[19]	C. L. Bai, H. Q. Zhang, H. Sagawa, X. Z. Zhang, G. Col, and F. R. Xu, Phys. Rev. Lett., 105:072501 (2010)
[20]	L. G. Cao, G. Col, H. Sagawa, P. F. Bortignon, and L. Sciacchitano, Phys. Rev. C, 80:064304. (2009)
[21]	M. Anguiano, G. Co', V. De Donno, and A. M. Lallena, Phys. Rev. C, 83:064306 (2011)
[22]	G. Co', V. De Donno, M. Anguiano, and A. M. Lallena, Phys. Rev. C, 85:034323 (2012)
[23]	F. Minato and C. L. Bai, Phys. Rev. Lett., 110:122501 (2013)
[24]	L. J. Jiang, S. Yang, J. M. Dong, and W. H. Long, Phys. Rev. C, 91:025802 (2015)
[25]	J. Meng, Relativistic Density Functional for Nuclear Structure, Vol. 10 of International review of nuclear physics, (Singapore, World Scientific, 2016) 596224
[26]	B. D. Serot and J. D. Walecka, Adv. Nucl. Phys., 16:1 (1986)
[27]	P. G. Reinhard, Rep. Prog. Phys., 52:439 (1989)
[28]	P. Ring, Prog. Part. Nucl. Phys., 37:193 (1996)
[29]	G. A. Lalazissis, J. Knig, and P. Ring, Phys. Rev. C, 55:540-543 (1997)
[30]	B. D. Serot and J. D. Walecka, Int. J. Mod. Phys. E, 06:515 (1997)
[31]	M. Bender, P. H. Heenen, and P. G. Reinhard, Rev. Mod. Phys., 75:121 (2003)
[32]	S. G. Zhou, J. Meng, and P. Ring, Phys. Rev. Lett., 91:262501 (2003)
[33]	W. H. Long, J. Meng, N. Van Giai, and S. G. Zhou, Phys. Rev. C, 69:034319 (2004)
[34]	J. Meng, H. Toki, S. G. Zhou, S. Q. Zhang, W. H. Long, and L. S. Geng, Prog. Part. Nucl. Phys, 57:470 (2006)
[35]	J. Meng, J. Peng, S. Q. Zhang, and S. G. Zhou, Phys. Rev. C, 73:037303 (2006)
[36]	J. Meng and S. G. Zhou, J. Phys. G, 42:093101 (2015)
[37]	P. W. Zhao, Z. P. Li, J. M. Yao, and J. Meng, Phys. Rev. C, 82:054319 (2010)
[38]	A. Bouyssy, J. F. Mathiot, N. Van Giai, and S. Marcos, Phys. Rev. C, 36:380-401 (1987)
[39]	P. Bernardos, V. N. Fomenko, N. Van Giai, M. L. Quelle, S. Marcos, R. Niembro, and L. N. Savushkin, Phys. Rev. C, 48:2665-2672 (1993)
[40]	H. L. Shi, B. Q. Chen, and Z. Y. Ma, Phys. Rev. C, 52:144-156 (1995)
[41]	S. Marcos, L. N. Savushkin, V. N. Fomenko, M. Lpez-Quelle, and R. Niembro, J. Phys. G, 30:703 (2004)
[42]	S. H. Shen, J. N. Hu, H. Z. Liang, J. Meng, P. Ring, and S. Q. Zhang, Chin. Phys. Lett., 33:102103 (2016)
[43]	W. H. Long, N. Van Giai, and J. Meng, Phys. Lett. B, 640:150 (2006)
[44]	W. H. Long, H. Sagawa, N. Van Giai, and J. Meng, Phys. Rev. C, 76:034314 (2007)
[45]	W. H. Long, P. Ring, N. Van Giai, and J. Meng, Phys. Rev. C, 81:024308 (2010)
[46]	J. J. Li, W. H. Long, J. Margueron, and N. Van Giai, Phys. Lett. B, 732:169-173 (2014)
[47]	J. J. Li, J. Margueron, W. H. Long, and N. Van Giai, Phys. Lett. B, 753:97-102 (2016)
[48]	W. H. Long, H. Sagawa, J. Meng, and N. Van Giai, Phys. Lett. B, 639:242-247 (2006)
[49]	W. H. Long, P. Ring, J. Meng, N. Van Giai, and C. A. Bertulani, Phys. Rev. C, 81:031302 (2010)
[50]	H. Z. Liang, W. H. Long, J. Meng, and N. Van Giai, Eur. Phys. J. A, 44:119-124 (2010)
[51]	J. J. Li, W. H. Long, J. L. Song, Q. Zhao, Phys. Rev. C, 93:054312 (2016)
[52]	H. Z. Liang, N. Van Giai, and J. Meng, Phys. Rev. Lett., 101:122502 (2008)
[53]	H. Z. Liang, N. Van Giai, and J. Meng, Phys. Rev. C, 79:064316 (2009)
[54]	H. Z. Liang, P. W. Zhao, and J. Meng, Phys. Rev. C, 85:064302 (2012)
[55]	Z. M. Niu, Y. F. Niu, H. Z. Liang, W. H. Long, T. Niksic, D. Vretenar, and J. Meng, Phys. Lett. B, 723:172-176 (2013)
[56]	Z. M. Niu, Y. F. Niu, H. Z. Liang, W. H. Long, and J. Meng, Phys. Rev. C, 95:044031 (2017)
[57]	B. Y. Sun, W. H. Long, J. Meng, and U. Lombardo, Phys. Rev. C, 78:065805 (2008)
[58]	W. H. Long, B. Y. Sun, K. Hagino, and H. Sagawa, Phys. Rev. C, 85:025806 (2012)
[59]	Q. Zhao, B. Y. Sun, and W. H. Long, J. Phys. G, 42:095101 (2015)
[60]	L. J. Jiang, S. Yang, B. Y. Sun, W. H. Long, and H. Q. Gu, Phys. Rev. C, 91:034326 (2015)
[61]	A. Arima, M. Harvey, and K. Shimizu, Phys. Lett. B, 30:517 (1969)
[62]	K. Hecht and A. Adler, Nucl. Phys. A, 137:129 (1969)
[63]	J. N. Ginocchio, Phys. Rev. Lett., 78:436 (1997)
[64]	J. Meng, K. Sugawara-Tanabe, S. Yamaji, P. Ring, and A. Arima, Phys. Rev. C, 58:R628-R631 (1998)
[65]	J. Meng, K. Sugawara-Tanabe, S. Yamaji, and A. Arima, Phys. Rev. C, 59:154-163 (1999)
[66]	J. N. Ginocchio, A. Leviatan, J. Meng, and S. G. Zhou, Phys. Rev. C, 69:034303 (2004)
[67]	H. Z. Liang, J. Meng, and S. G. Zhou, Phys. Rep., 570:1 (2015)
[68]	H. Z. Liang, S. H. Shen, P. W. Zhao, and J. Meng, Phys. Rev. C, 87:014334 (2013)
[69]	S. H. Shen, H. Z. Liang, P. W. Zhao, S. Q. Zhang, and J. Meng, Phys. Rev. C, 88:024311 (2013)
[70]	T. S. Chen, H. F. L, J. Meng, S. Q. Zhang, and S. G. Zhou, Chin. Phys. Lett., 20:358 (2003)
[71]	B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. Lett., 109:072501 (2012)
[72]	S. W. Chen and J. Y. Guo, Phys. Rev. C, 85:054312 (2012)
[73]	J. Y. Guo, S. W. Chen, Z. M. Niu, D. P. Li, and Q. Liu, Phys. Rev. Lett., 112:062502 (2014)
[74]	J. Y. Guo, R. D. Wang, and X. Z. Fang, Phys. Rev. C, 72:054319 (2005)
[75]	J. Y. Guo and X. Z. Fang, Phys. Rev. C, 74:024320 (2006)

[1]	Shi-Yuan Ding , Wei Yang , Bao-Yuan Sun . Density-dependent relativistic mean field approach and its application to single-Λ hypernuclei in oxygen hyperisotopes. Chinese Physics C, 2023, 47(12): 124103. doi: 10.1088/1674-1137/acf91e
[2]	Ming-Hui Zhou , Ze-Yu Li , Sheng-Yuan Chen , Yong-Jing Chen , Zhi-Pan Li . Three-dimensional potential energy surface for fission of ²³⁶U within covariant density functional theory. Chinese Physics C, 2023, 47(6): 064106. doi: 10.1088/1674-1137/acc4ac
[3]	Wei Sun , Kai-Yuan Zhang , Cong Pan , Xiao-Hua Fan , Shuang-Quan Zhang , Zhi-Pan Li . Beyond-mean-field dynamical correlations for nuclear mass table in deformed relativistic Hartree-Bogoliubov theory in continuum. Chinese Physics C, 2022, 46(6): 064103. doi: 10.1088/1674-1137/ac53fa
[4]	Zheng-Zheng Li , Shi-Yao Chang , Qiang Zhao , Wen-Hui Long , Yi-Fei Niu . Restoration of pseudo-spin symmetry in N = 32 and N = 34 isotonesdescribed by relativistic Hartree-Fock theory. Chinese Physics C, 2019, 43(7): 074107. doi: 10.1088/1674-1137/43/7/074107
[5]	Wei Zhang , Yi-Fei Niu . Shape evolution of ^{72, 74}Kr with temperature in covariant density functional theory. Chinese Physics C, 2017, 41(9): 094102. doi: 10.1088/1674-1137/41/9/094102
[6]	Xue-Wei Xia . Evolution of N=28 shell closure in relativistic continuum Hartree-Bogoliubov theory. Chinese Physics C, 2016, 40(7): 074101. doi: 10.1088/1674-1137/40/7/074101
[7]	WANG Pei , ZUO Wei . Effect of tensor force on the density dependence of symmetryenergy within the BHF framework. Chinese Physics C, 2015, 39(1): 014101. doi: 10.1088/1674-1137/39/1/014101
[8]	LI Zhao-Xi , LI Zhi-Pan . Center-of-mass correction and rotational correction in covariant density functional theory. Chinese Physics C, 2015, 39(11): 114101. doi: 10.1088/1674-1137/39/11/114101
[9]	LIU Lang , ZHAO Peng-Wei . Exact treatment of pairing correlations in Yb isotopes with covariant density functional theory. Chinese Physics C, 2014, 38(7): 074103. doi: 10.1088/1674-1137/38/7/074103
[10]	JI Juan-Xia , LI Jia-Xing , HAN Rui , WANG Jian-Song , HU Qiang . The neutron halo structure of ¹⁷B studied with the relativistic Hartree-Bogoliubov theory. Chinese Physics C, 2012, 36(1): 43-47. doi: 10.1088/1674-1137/36/1/007
[11]	LIU Lang , ZHAO Peng-Wei . α-cluster structure of ¹²C and ¹⁶O in the covariant density functional theory with a shell-model-like approach. Chinese Physics C, 2012, 36(9): 818-822. doi: 10.1088/1674-1137/36/9/004
[12]	HAN Rui , JI Juan-Xia , LI Jia-Xing . A relativistic continuum Hartree-Bogoliubov theory description of N=3 isotones. Chinese Physics C, 2011, 35(9): 821-824. doi: 10.1088/1674-1137/35/9/006
[13]	ZHANG Ai-Lin . Light four-quark states and QCD sum rule. Chinese Physics C, 2009, 33(6): 494-496. doi: 10.1088/1674-1137/33/6/017
[14]	SUN Bao-Yuan , MENG Jie . Neutron star equation of state in density dependent relativistic Hartree-Fock theory. Chinese Physics C, 2009, 33(S1): 73-75. doi: 10.1088/1674-1137/33/S1/024
[15]	CHEN Bao-Qiu , MA Zhong-Yu . Investigation of Properties of Exotic Nuclei in Relativistic Hartree-Fock Theory. Chinese Physics C, 2001, 25(4): 309-314.
[16]	Lu Wentao , Liu Jueping . Quantum Chromodynamics Sum Rules for the 0⁺⁺ Three-Gluon Scalar Glueball. Chinese Physics C, 1996, 20(S3): 261-268.
[17]	JING Xiaogong , ZHAO Guoquan , YAO Yujie , YANG Shande , WU Shishu . Study of Multiplicity of Hartree-Fock Solutions. Chinese Physics C, 1993, 17(11): 1026-1031.
[18]	Jing Xiaogong , Zhao Guoquan , Yao Yujie , Yang Shande , Wu Shishu . Study of Multiplicity of Hartree-Fock Solution. Chinese Physics C, 1993, 17(S3): 303-309.
[19]	Zhu Wei . Valence Quark Mixing Contribution to the Gottfried Sum Rule. Chinese Physics C, 1993, 17(S2): 157-159.
[20]	Xu Xiaoming , Qiu Xijun . A Chiral Quark-Soliton Model Theory for Nuclear Force. Chinese Physics C, 1990, 14(S4): 381-389.

Access

Get Citation

Yao-Yao Zong and Bao-Yuan Sun. Relativistic interpretation of the nature of the nuclear tensor force[J]. Chinese Physics C, 2018, 42(2): 024101. doi: 10.1088/1674-1137/42/2/024101

Yao-Yao Zong and Bao-Yuan Sun. Relativistic interpretation of the nature of the nuclear tensor force[J]. Chinese Physics C, 2018, 42(2): 024101. doi: 10.1088/1674-1137/42/2/024101 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2017-08-18
Revised: 2017-11-01

Fund

Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

Article Metric

Article Views(1612)
PDF Downloads(70)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Relativistic interpretation of the nature of the nuclear tensor force

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Relativistic interpretation of the nature of the nuclear tensor force

Corresponding author: Bao-Yuan Sun,

HTML

目录