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

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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)

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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

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

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

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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

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Relativistic interpretation of the nature of the nuclear tensor force

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