1、北京大学物理学院 School of Physics/Peking University兰州重离子加速器国家实验室 HIRFL/Lanzhou中国科学院理论物理研究所 Institute for Theor.Phys./AS,孟 杰 Jie Meng,Time reversal symmetry broken triaxial relativistic mean field approach for magnetic moment and nuclear current in odd mass nuclei,IntroductionTriaxial RMF with time-odd comp
2、onentNumerical detailsResults and discussionSummary,Contents,Single particle energydensity distributionMagnetic momentNuclear current,Magnetic moments are measured with high precision. Traditionally it provided a sensitive test for nuclear models.Because the single particle state can couple to more
3、complicated 2p-1h configurations and there are mesons exchange corrections caused by the nuclear medium effect, the configuration mixing provide a better foundation to describe the observed values . The mean field may not be expected to describe the magnetic moment well.,Introduction,Blin-Stoyle R J
4、 1957 Theories of Nuclear Moments (Oxford: Oxford University Press). Wilkinson D H and Rho M (Eds.) 1979 Mesons in Nuclei vol I1 (Amsterdam: North-Holland ). Arima A 1984 Prog. Part. Nucl. Phys. 11 53,Arima A Horie H 1954 Prog. Theor. Phys. 11 509Arima A, Shimizu K, Bentz W and Hyuga H 1988 Adu. Nuc
5、l. Phys. 18 1.,However, it should be appropriate for the isao-scalar magnetic moment in LS closed shell nuclei plus or minus one nucleon, asAlthough relativistic mean field approach has achieved great success during the last two decades:Straightforward application of the single-particle relativistic
6、 model does not agree with the experimental magnetic moments,Serot & Walecka, Adv. Nucl. Phys. 16 (86) 1Reinhard, Rep. Prog. Phys. 52 (89) 439Ring, Prog. Part. Nucl. Phys. 37 (96) 193Meng, Toki, Zhou, Zhang, Long & Geng, Prog. Part. Nucl. Phys. 2006, in press,LS-closure, no spin-orbit partners on bo
7、th sides of the Fermi surface, therefore the magnetic moment operator can not couple to magnetic resonance.Pion-exchange current contribution turned to be very small to iso-scalar current, as well as others processes.,Introduction,The Sigma and the time-component vector mesons of Omega fails to repr
8、oduce the corresponding Schmidt values:Taking into account the contribution of the back-flow to the current operator can solve this problem. This back-flow is caused by the polarization of the core by the external particle.,H.Ohtsubo, et. al., Prog. Theor. Phys. 49(1973 ) 877Miller L D, Ann. Phys.,
9、NY 91 (1975) 40. Bawin M, Hughes C A and Strobel G L Phys. Reu. C 28 (1983) 456. Bouyssy A, Marcos S and Mathiot J F Nucl. Phys. A 415 (1984) 497. Kurasawa H., et. al., Phys.Lett.B165 (1985) 234,H. Kurasawa, et. al., Phys.Lett.B165(1985)234J. A. McNeil, et. Al., Phys. Rev. C34(1986)746S. Ichii, W. B
10、entz and A. Arima, Phys. Lett. B 192(1987)11.J. R. Shepard, et al., Phys.Rev.C37(1988)1130P. G. Blunden, Nucl. Phys. A 464 (1987)525,Introduction,In these the widely investigated mean field theories there are only the time-even fields which are most sensitive to physical observables. The time-odd fi
11、elds, which appear only in the nuclear systems with time-reversal symmetry broken, are very important for the description of the magnetic moments, rotating nuclei, N=Z nuclei, and pairing correlations. The broken time reversal symmetry a non-vanishing vector part of the -field a magnetic potential a
12、nd changes the nuclear wave function and the resulting magnetic moments. The magnetic field created by magnetic potential will influence the magnetic moment, single-particle spin and angular momentum.,U. Hofmann and P. Ring, Phys. Lett. B 214, 307(1988) . J. Koenig, and P. Ring, Phys. Rev. Lett. 71,
13、 3079 (1993). W. Satua, in Nuclear Structure 98, edited by C. Baktash, AIP Conf. Proc. No. 481 AIP, Woodbury, NY, 1999!, p. 114. K. Rutz, M. Bender, P.-G. Reinhard, and J. A. Maruhn, Phys.Lett. B 468, 1 (1999),Introduction,The core polarization is always neglected in Spherical cases, For the axial d
14、eformed case, the RMF with time-odd components are developed and the isoscalar magnetic moment are well reproduced: Time-even triaxial RMF have been developed to investigate the triaxial deformation and MDPurpose: developing the time reversal symmetry broken triaxial RMF approach, investigating the
15、non-vanishing vector part of the -field, nuclear current, magnetic potential and magnetic moments,D. Hirata, et al., Nucl. Phys. A609, 131 (1996).J. Meng, et al., Phys. Rev. C 2006,Introduction,U. Hofmann and P. Ring, Phys. Lett. B 214, 307(1988) . R. J. Furnstahl, C. E. Price, Phys. Rev. C40 (1989)
16、 1398.,Starting point of RMF theory,(Jp T)=(0+0),(Jp T)=(1-0),(Jp T)=(1-1),Sigma-meson:attractive scalar field,Omega-meson:Short-range repulsive,Rho-meson:Isovector field,Nucleons are coupled by exchange of mesons via an effective Lagrangian,Serot & Walecka, Adv. Nucl. Phys. 16 (86) 1,Reinhard, Rep.
17、 Prog. Phys. 52 (89) 439,Ring, Prog. Part. Nucl. Phys. 37 (96) 193,Meng, Toki, Zhou, Zhang, Long & Geng, Prog. Part. Nucl. Phys. 2005, in press,Lagrangian of RMF theory,Same footing forDeformationRotationPairing (RHB,BCS,SLAP),Equations of Motion,Magnetic potential,space-like components of vector me
18、sonsbehaves in Dirac equation like a magnetic field,Nuclear magnetism,Magnetic field,Nucleon,Numerical techniques for time reversal invariance violation,Expanded on 3D HO Basis,Coulomb field: the standard Green function method,Nuclear Magnetic potential: vector part of the -field,Magnetic field B =
19、at y=z=1.29 fm,Nuclear Magnetic Fields due to the vector part of the -field,Single nucleon levels with time reversal invariance violation,Single nucleon levels with time reversal invariance violation,The other degree of freedom was integrated.,Density distribution of the last odd nucleon,Density dis
20、tribution for proton, neutron and matter,Magnetic Moment in Relativistic approach,Magnetic moment,nucleon wave function,Dirac current,Anomalous current,Spherical and axial RMF results with NL1 taken from Hofmann 1989Triaxial RMF with PK1,magnetic moments of light nuclei near closed shells (N),Magnet
21、ic Moment,Iso-scalar magnetic moment (N),Landau: taking into account the current by linear response theory,Magnetic Moment,Iso-vector magnetic moment (N),- including config. mixing: Y Nedjadi and J R Rook, J. Phys. G: Nucl. Part. Phys. 15 (1989) 589U. Hofmann, P. Ring, Phys. Lett. B214 (1988) 307,Ma
22、gnetic Moment,Dirac and Anomalous parts of Magnetic Moment (N),Nuclear current in 17F and 17O in y-z plane,Dirac current,Anomalous nuclear current in 17F and 17O in y-z plane,Dirac and anomalous current in 17F,Dirac current,Anomalous current,Summary and perspective,Triaxial RMF without time reversal
23、 symmetry is developedGround-state properties of light odd mass nuclei near double-closed shells, i.e., E/A, single-particle energy, density distribution, etc., are calculated self-consistentlyThe broken time reversal symmetry leads to a non-vanishing vector part of the -field, which creates a magne
24、tic potential and changes the nuclear wave function and the resulting magnetic moments. The first calculated nuclear magnetic moments of light LS-closed shells nuclei plus or minus one nucleon agree well with the Schmidt values and the data.,奇核子系统问题-时间反演对称性破缺,正确确定激态及价核子组态-绝热与非绝热约束计算,MD,constraints,s
25、.p. levels in 106Rh,奇核子系统问题-时间反演对称性破缺,奇核子系统问题-时间反演对称性破缺,41Ca 和 40Ca 的中子（左）和质子（右）的单粒子能级,考虑磁势后41Ca 中互为时间反演态的能级劈裂,Laudau and Migdal answer:,Relativistic extension of Landaus Fermi-liquid theory based on sigma-omega model,The responds of the system as a whole when a quasi-particle is removed.,Thus, the
26、single quasi-particle current is defined as the difference in the total baryon current when the particle is removed.,J. A. McNeil, et. Al., Phys. Rev. C34(1986)746,How to define the single-particle property in dense, strongly interacting many-body system?,model,Nucleon:,Meson fields:,Self-consistent
27、 Dirac equation:,Total current,Landau quasi-particle current:,Backflow effect,Renormalization of current,Enhancement is reduced,Especially T=0 K:,Remark: The cancellation of the scalar enhancement due to the vector meson,Spin particle One-body matrix element of current,Vertex correction,Renormalized
28、 current,Electric form factor,magnetic form factor,Transfer momentum,Vector fields,g,g,-ig,Remark: Dirac current is related to the electric form factor!,J. A. McNeil, et. Al., Phys. Rev. C34(1986)746,The relativistic wave functions are obtained from a relativistic Woods-Saxon well with parameters ad
29、justed to give the separation energy and elastic electron scattering form factor.,The interaction vertex is renormalized by consideration of backflow effect in nuclear medium, namely,Relativistic extension of Landaus Fermi-liquid theory,Effective (renormalized) Dirac current,Remark2: The anomalous c
30、urrent is not renormalized in this paper.,Remark1: the wave function and the interaction vertex are not consistent!,Remark3: The renormalization are considered without the consideration of iso-vector meson fields, i.e., rho and pi, thus the iso-vector current and magnetic moment are still enhanced.
31、Even if rho meson is considered, the enhancement of iso-vector current still can not be reduced significantly because of the small rho-N coupling constant.,P. G. Blunden, Nucl. Phys. A 464 (1987)525,Remark4: In additional, the anomalous iso-vector moment, which is much larger that the Dirac moment,
32、does not get affected by the scalar field, so that the total iso-vector spin moment will not be enhanced much.,Comment:,Iso-scalar and iso-vector magnetic moment,Dirac current,can be decomposed into an orbital current and a spin current,Anomalous current,Magnetic Moment in Relativistic approach,Exte
33、nsive shell model calculations within the full Ohw shell-model space show good agreement between theoretical and observed values. The remaining deviations arising from higher order corrections, i.e. meson exchange currents, isobar currents and higher-order configuration mixing, are removed through t
34、he use of effective operators to be determined empirically: Arima A, Shimizu K, Bentz W and Hyuga H 1988 Adu. Nucl. Phys. 18 1. Brown B A and Wildenthal B H 1983 Phys. Reu. C 28 2397. Relativistic - model + the configuration mixing within one major shell for the mirror pairs, 150-15N, 170-17F, 39K-3
35、9Ca and 41Ca-41S, removes most of the discrepancies for isovector moments while leaving the isoscalar moments unaltered, i.e. also in agreement with experiment when vertex corrections are included. For isovector moments, this agreement is better than in similar non-relativistic calculations: Y Nedja
36、di and J R Rook, J. Phys. G: Nucl. Part. Phys. 15 (1989) 589-600.,Introduction,奇核子系统: 未配对核子破坏时间反演对称性, 从而导致矢量介子场的空间部分不为零, Dirac 方程中出现磁势球对称: 奇A核处理成偶偶核额外加入一个核子, 体系核子波函数仍具有球对称性. 无法考虑时间反演对称性破缺对整个原子核的影响轴对称: Hofmann等人(88) 和 Furnstahl等人(89)自洽地考虑了磁势, 研究了核芯极化效应对整个原子核性质的影响. 这种核芯极化效应能抵消标量场引起的相对论效应对同位旋标量磁矩的增强, 给出与 Scnmidt 值一致的原子核磁矩.本工作: 三轴形变框架下研究时间反演对称性破缺,奇核子系统问题-时间反演对称性破缺,
