Leading order relativistic chiral nucleon-nucleon interaction

Xiu-Lei Ren; Kai-Wen Li; Li-Sheng Geng; Bingwei Long; Peter Ring; Jie Meng

doi:10.1088/1674-1137/42/1/014103

Chinese Physics C> 2018, Vol. 42> Issue(1) : 014103 DOI: 10.1088/1674-1137/42/1/014103

Leading order relativistic chiral nucleon-nucleon interaction

Xiu-Lei Ren ^1,2 ,
Kai-Wen Li ³ ,
Li-Sheng Geng ^3,4,, ,
Bingwei Long ⁵ ,
Peter Ring ^1,6 ,
Jie Meng ^1,3,,

1.
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
2.
Institut fü
3.
School of Physics and Nuclear Energy Engineering &
4.
School of Physics and Nuclear Energy Engineering &
5.
Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 100191, China
6.
Center for Theoretical Physics, Department of Physics, Sichuan University, Chengdu, Sichuan 610064, China
7.
Physik Department, Technische Universitä
8.
School of Physics and Nuclear Energy Engineering &

Abstract
HTML
Reference
Related

PDF

Abstract：
Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian. We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the ¹S₀ and ³P₀ phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta J ≥ 1, the relativistic results are almost the same as their leading order non-relativistic counterparts.
- covariant chiral perturbation theory ,
- nucleon-nucleon interaction ,
- relativistic scattering equation

References

[1]	P. Schwerdtfeger, ed., Relativistic Electronic Structure Theory, Part I. Fundamentals, Theoretical and Computational Chemistry Vol. 11 (Elsevier Science B.V., 2002)
[2]	J. Meng, ed., In Relativistic Density Functional for Nuclear Structure, International Review of Nuclear Physics Vol. 10 (Singapore:World Scientific, 2016)
[3]	M. Mayer and J. Jensen, Elementary Theory of Nuclear Shell Structure, Structure of matter series (John Wiley Sons, 1955)
[4]	M. Karplus, M. Levitt, and A. Warshel, The Nobel Prize in Chemistry (2013)
[5]	S. Elhatisari, D. Lee, G. Rupak, E. Epelbaum, H. Krebs, T. A. Lhde, T. Luu, and U.-G. Meiner, Nature, 528:111 (2015)
[6]	V. Lapoux, V. Som, C. Barbieri, H. Hergert, J. D. Holt, and S. Stroberg, Phys. Rev. Lett., 117:052501 (2016)
[7]	T. D. Cohen, R. J. Furnstahl, and D. K. Griegel, Phys. Rev. Lett., 67:961 (1991)
[8]	T. D. Cohen, R. J. Furnstahl, and D. K. Griegel, Phys. Rev. C, 45:1881 (1992)
[9]	T. D. Cohen, R. J. Furnstahl, K. Griegel, and S. Jin, Prog. Part. Nucl. Phys., 35:221 (1995)
[10]	H. Yukawa, Proc. Phys. Math. Soc. Jap., 17:48 (1935),[Prog. Theor. Phys. Suppl.1,1(1935)]
[11]	V. G. J. Stoks, R. A. M. Klomp, C. P. F. Terheggen, and J. J. de Swart, Phys. Rev. C, 49:2950 (1994)
[12]	R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C, 51:38 (1995)
[13]	E. Epelbaum, H. Krebs, and U.-G. Meiner, Phys. Rev. Lett., 115:122301 (2015)
[14]	D. R. Entem, R. Machleidt, and Y. Nosyk (2017), 1703.05454
[15]	R. Machleidt, Adv. Nucl. Phys., 19:189 (1989)
[16]	R. Machleidt, Phys. Rev. C, 63:024001 (2001)
[17]	F. Gross, J. W. Van Orden, and K. Holinde, Phys. Rev. C, 45:2094 (1992)
[18]	F. Gross and A. Stadler, Phys. Rev. C, 78:014005 (2008)
[19]	R. Higa and M. R. Robilotta, Phys. Rev. C, 68:024004 (2003)
[20]	R. Higa, M. Pavon Valderrama, and E. Ruiz Arriola, Phys. Rev. C, 77:034003 (2008)
[21]	T. Becher and H. Leutwyler, Eur. Phys. J. C, 9:643 (1999)
[22]	B. Ter Haar and R. Malfliet, Phys. Rept., 149:207 (1987)
[23]	R. Brockmann and R. Machleidt, Phys. Rev. C, 42:1965 (1990)
[24]	S. Shen, J. Hu, H. Liang, J. Meng, P. Ring, and S. Zhang, Chin. Phys. Lett., 33:102103 (2016)
[25]	S. Shen, H. Liang, J. Meng, P. Ring, and S. Zhang, Phys. Rev. C, 96:014316 (2017)
[26]	S. Weinberg, Physica A, 96:327 (1979)
[27]	E. E. Jenkins and A. V. Manohar, Phys. Lett. B, 255:558 (1991)
[28]	S. Weinberg, Phys. Lett. B, 251:288 (1990)
[29]	S. Weinberg, Nucl. Phys. B, 363:3 (1991)
[30]	C. Ordonez and U. van Kolck, Phys. Lett. B, 291:459 (1992)
[31]	C. Ordonez, L. Ray, and U. van Kolck, Phys. Rev. Lett., 72:1982 (1994)
[32]	U. van Kolck, Phys. Rev. C, 49:2932 (1994)
[33]	N. Kaiser, R. Brockmann, and W. Weise, Nucl. Phys. A, 625:758 (1997)
[34]	N. Kaiser, Phys. Rev. C, 61:014003 (2000)
[35]	N. Kaiser, Phys. Rev. C, 65:017001 (2002)
[36]	N. Kaiser, Phys. Rev. C, 64:057001 (2001)
[37]	E. Epelbaum, W. Gloeckle, and U.-G. Meiner, Nucl. Phys. A, 637:107 (1998)
[38]	E. Epelbaum, W. Gloeckle, and U.-G. Meiner, Nucl. Phys. A, 671:295 (2000)
[39]	D. R. Entem and R. Machleidt, Phys. Lett. B, 524:93 (2002)
[40]	D. R. Entem and R. Machleidt, Phys. Rev. C, 66:014002 (2002)
[41]	D. R. Entem and R. Machleidt, Phys. Rev. C, 68:041001 (2003)
[42]	E. Epelbaum, W. Glockle, and U.-G. Meiner, Nucl. Phys. A, 747:362 (2005)
[43]	E. Epelbaum, H. Krebs, and U. G. Meiner, Eur. Phys. J. A, 51:53 (2015)
[44]	P. F. Bedaque and U. van Kolck, Ann. Rev. Nucl. Part. Sci., 52:339 (2002)
[45]	E. Epelbaum, H.-W. Hammer, and U.-G. Meiner, Rev. Mod. Phys., 81:1773 (2009)
[46]	R. Machleidt and D. R. Entem, Phys. Rept., 503:1 (2011)
[47]	D. R. Entem, N. Kaiser, R. Machleidt, and Y. Nosyk, Phys. Rev. C, 91:014002 (2015)
[48]	D. R. Entem, N. Kaiser, R. Machleidt, and Y. Nosyk, Phys. Rev. C, 92:064001 (2015)
[49]	M. J. Savage, in Nuclear physics with effective field theory. Proceedings, Joint Caltech/INT Workshop, Pasadena, USA, February 26-27, 1998 (1998), pp. 247-267, nucl-th/9804034
[50]	D. B. Kaplan, M. J. Savage, and M. B. Wise, Phys. Lett. B, 424:390 (1998)
[51]	D. B. Kaplan, M. J. Savage, and M. B. Wise, Nucl. Phys. B, 534:329 (1998)
[52]	J. Gegelia (1998), nucl-th/9806028
[53]	T. D. Cohen and J. M. Hansen, Phys. Rev. C, 59:13 (1999)
[54]	J. Gegelia, Phys. Lett. B, 463:133 (1999)
[55]	S. Fleming, T. Mehen, and I. W. Stewart, Nucl. Phys. A, 677:313 (2000)
[56]	T. Frederico, V. S. Timoteo, and L. Tomio, Nucl. Phys. A, 653:209 (1999)
[57]	S. R. Beane, P. F. Bedaque, L. Childress, A. Kryjevski, J. McGuire, and U. van Kolck, Phys. Rev. A, 64:042103 (2001)
[58]	S. R. Beane, P. F. Bedaque, M. J. Savage, and U. van Kolck, Nucl. Phys. A, 700:377 (2002)
[59]	A. Nogga, R. G. E. Timmermans, and U. van Kolck, Phys. Rev. C, 72:054006 (2005)
[60]	M. C. Birse, Phys. Rev. C, 74:014003 (2006)
[61]	V. S. Timoteo, T. Frederico, A. Delfino, and L. Tomio, Phys. Lett. B, 621:109 (2005)
[62]	M. C. Birse, Phys. Rev. C, 76:034002 (2007), 0706.0984
[63]	C. J. Yang, C. Elster, and D. R. Phillips, Phys. Rev. C, 77:014002 (2008), 0706.1242
[64]	C. J. Yang, C. Elster, and D. R. Phillips, Phys. Rev. C, 80:034002 (2009)
[65]	C. J. Yang, C. Elster, and D. R. Phillips, Phys. Rev. C, 80:044002 (2009), 0905.4943.
[66]	M. P. Valderrama, Phys. Rev. C, 83:024003 (2011)
[67]	M. P. Valderrama, Phys. Rev. C, 84:064002 (2011)
[68]	B. Long and C. J. Yang, Phys. Rev. C, 84:057001 (2011)
[69]	B. Long and C. J. Yang, Phys. Rev. C, 86:024001 (2012)
[70]	E. Epelbaum and J. Gegelia, Phys. Lett. B, 716:338 (2012)
[71]	E. Epelbaum, A. M. Gasparyan, J. Gegelia, and H. Krebs, Eur. Phys. J. A, 51:71 (2015)
[72]	L.-S. Geng, J. Martin Camalich, L. Alvarez-Ruso, and M. J. Vicente Vacas, Phys. Rev. Lett., 101:222002 (2008)
[73]	X.-L. Ren, L.-S. Geng, J. Martin Camalich, J. Meng, and H. Toki, JHEP, 12:073 (2012)
[74]	X.-L. Ren, L.-S. Geng, and J. Meng, Phys. Rev. D, 91:051502 (2015), 1404.4799
[75]	A. H. Blin, T. Gutsche, T. Ledwig, and V. E. Lyubovitskij, Phys. Rev. D, 92:096004 (2015)
[76]	D.-L. Yao, D. Siemens, V. Bernard, E. Epelbaum, A. M. Gasparyan, J. Gegelia, H. Krebs, and U.-G. Meiner, JHEP, 05:038 (2016)
[77]	M. Altenbuchinger, L.-S. Geng, and W. Weise, Phys. Rev. D, 89:014026 (2014)
[78]	L.-S. Geng, Front. Phys., (Beijing) 8:328 (2013), 1301.6815
[79]	M. H. Partovi and E. L. Lomon, Phys. Rev. D, 2:1999 (1970)
[80]	K. Erkelenz, Phys. Rept., 13:191 (1974)
[81]	R. J. Yaes, Phys. Rev. D 3:3086 (1971)
[82]	R. H. Thompson, Phys. Rev. D, 1:110 (1970)
[83]	R. Blankenbecler and R. Sugar, Phys. Rev., 142:1051 (1966)
[84]	V. G. Kadyshevsky, Nucl. Phys. B, 6:125 (1968)
[85]	F. Gross, Phys. Rev., 186:1448 (1969)
[86]	R. M. Woloshyn and A. D. Jackson, Nucl. Phys. B, 64:269 (1973)
[87]	K.-W. Li, X.-L. Ren, L.-S. Geng, and B. Long, Phys. Rev. D, 94:014029 (2016)
[88]	D. Djukanovic, J. Gegelia, S. Scherer, and M. R. Schindler, Few Body Syst., 41:141 (2007)
[89]	L. Girlanda, S. Pastore, R. Schiavilla, and M. Viviani, Phys. Rev. C, 81:034005 (2010)
[90]	K. A. Olive, Chin. Phys. C, 40:100001 (2016)
[91]	H. Polinder, J. Haidenbauer, and U.-G. Meiner, Nucl. Phys. A, 779:244 (2006)
[92]	S. Petschauer and N. Kaiser, Nucl. Phys. A, 916:1 (2013)
[93]	J. Goto and S. Machida, Progr. Theor. Phys., 25, 64 (1961)
[94]	E. Epelbaum, Ph.D. thesis, Julich, Forschungszentrum (2000)
[95]	H. P. Stapp, T. J. Ypsilantis, and N. Metropolis, Phys. Rev., 105:302 (1957)
[96]	V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester, and J. J. de Swart, Phys. Rev. C, 48:792 (1993)
[97]	R. A. Arndt, I. I. Strakovsky, and R. L. Workman, Phys. Rev. C, 50:2731 (1994)
[98]	J. Soto and J. Tarrus, Phys. Rev. C, 78:024003 (2008)
[99]	B. Long, Phys. Rev. C, 88:014002 (2013)
[100]	H. Kamada, W. Gloeckle, J. Golak, and C. Elster, Phys. Rev. C, 66:044010 (2002)

[1]	Chun-Xuan Wang , Li-Sheng Geng , Bingwei Long . Renormalizability of leading order covariant chiral nucleon-nucleon interaction. Chinese Physics C, 2021, 45(5): 054101. doi: 10.1088/1674-1137/abe368
[2]	Kai-Wen Li , Xiu-Lei Ren , Li-Sheng Geng , Bing-Wei Long . Leading order relativistic hyperon-nucleon interactions in chiral effective field theory. Chinese Physics C, 2018, 42(1): 014105. doi: 10.1088/1674-1137/42/1/014105
[3]	D. S. Martyanov , E. Sh. Soukhovitskí , R. Capote , J. M. Quesada , S. Chiba . Predicting the optical observables for nucleon scattering on even-even actinides. Chinese Physics C, 2017, 41(9): 094105. doi: 10.1088/1674-1137/41/9/094105
[4]	Li-Sheng Geng , Raquel Molina , Eulogio Oset . On the chiral covariant approach to ρρ scattering. Chinese Physics C, 2017, 41(12): 124101. doi: 10.1088/1674-1137/41/12/124101
[5]	Hong-na Li , P. Wang . Chiral extrapolation of nucleon axial charge g_A in effective field theory. Chinese Physics C, 2016, 40(12): 123106. doi: 10.1088/1674-1137/40/12/123106
[6]	ZHANG Ao , GUO Wen-Jun , HUANG Jiang-Wei , YANG Lin-Meng . Isospin effect of the in-medium nucleon-nucleon cross section in excited nuclear reactions. Chinese Physics C, 2014, 38(5): 054103. doi: 10.1088/1674-1137/38/5/054103
[7]	LI Cheng , TIAN Jun-Long , QIN Yu-Jiao , LI Jing-Jing , WANG Ning . Determination of the nucleon-nucleon interaction in the ImQMD model by nuclear reactions at the Fermi energy region. Chinese Physics C, 2013, 37(11): 114101. doi: 10.1088/1674-1137/37/11/114101
[8]	Eberhard Klempt . Nucleon excitations. Chinese Physics C, 2010, 34(9): 1241-1246. doi: 10.1088/1674-1137/34/9/017
[9]	. Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory. Chinese Physics C, 2010, 34(9): 1307-1311. doi: 10.1088/1674-1137/34/9/030
[10]	HE Jun . Study of nucleon resonances in a chiral quark model via η productions. Chinese Physics C, 2009, 33(12): 1389-1392. doi: 10.1088/1674-1137/33/12/062
[11]	DONG Hong-Fei , MA Yin-Qun , MA Zhong-Yu . Elastic scattering of ⁶He from ¹²C at 38.3 MeV/nucleon. Chinese Physics C, 2009, 33(7): 532-537. doi: 10.1088/1674-1137/33/7/006
[12]	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
[13]	YAO Jiang-Ming , . Towards Lambda-nucleon coupling constants in relativistic mean field theory. Chinese Physics C, 2009, 33(S1): 64-66. doi: 10.1088/1674-1137/33/S1/021
[14]	LUO Pei-Yan , ZUO Wei . Influence of two different representations of the G-matrix to the in-medium nucleon-nucleon cross sections. Chinese Physics C, 2008, 32(S2): 70-72.
[15]	LIU Yan-Rui , ZHU Shi-Lin . Δ contribution to the parity-violating nucleon-nucleon force. Chinese Physics C, 2008, 32(9): 700-704. doi: 10.1088/1674-1137/32/9/005
[16]	Ge Lingxiao , Zeng Xianghua . In-Medium Nucleon-Nucleon Cross Sections in the Nonrelativistic Energy Region. Chinese Physics C, 1995, 19(S4): 389-396.
[17]	Shen Xiaoyan , Shen Pengnian , Yu Youwen , Zhang Zongye . Color Screening Effect and Nucleon-Nucleon Interaction. Chinese Physics C, 1993, 17(S2): 207-213.
[18]	Luo Zhenfei , Qiu Xijun . Relativistic Two-Body Wave Equation and Short-range Interaction of Quarkonium. Chinese Physics C, 1991, 15(S4): 427-429.
[19]	Wei Chunlin , Fu Deji , Xu Gongou . Variation of Nuclear Deformation with Z, N and Charge Independence of Nucleon-Nucleon Interactions. Chinese Physics C, 1990, 14(S3): 309-317.
[20]	Cao Zhijun , Shen Jianping , Li Guanglie . The Role of Nucleon-Nucleon Short-Range Correlations in the Nuclear Structure Function in the x > 1 Region. Chinese Physics C, 1989, 13(S3): 281-288.

Access

Get Citation

Xiu-Lei Ren, Kai-Wen Li, Li-Sheng Geng, Bingwei Long, Peter Ring and Jie Meng. Leading order relativistic chiral nucleon-nucleon interaction[J]. Chinese Physics C, 2018, 42(1): 014103. doi: 10.1088/1674-1137/42/1/014103

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2017-07-12
Revised: 2017-09-08

Fund

Supported by National Natural Science Foundation of China (11375024, 11522539, 11335002, 11375120), DFG and NSFC through funds provided to the Sino-German CRC 110 Symmetries and the Emergence of Structure in QCD (NSFC Grant No. 11621131001, DFG Grant No. TRR110), the Major State 973 Program of China (2013CB834400), the China Postdoctoral Science Foundation (2016M600845, 2017T100008), the Fundamental Research Funds for the Central Universities, and by the DFG cluster of excellence Origin and Structure of the Universe (www.universe-cluster.de)

Article Metric

Article Views(1685)
PDF Downloads(56)
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

Leading order relativistic chiral nucleon-nucleon interaction

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Leading order relativistic chiral nucleon-nucleon interaction

Corresponding author: Li-Sheng Geng,

Corresponding author: Jie Meng,

HTML

目录