国家杰出青年科学基金申请书课件.ppt

1、pIntroductionpTriaxial RMF with time-odd componentpNumerical detailspResults and discussionpSummaryContents1.Single particle energy2.density distribution3.Magnetic moment4.Nuclear current Magnetic moments are measured with high precision.Traditionally it provided a sensitive test for nuclear models.

2、Because the single particle state can couple to more 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

3、magnetic moment well.IntroductionBlin-Stoyle R J 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 53Arima A Horie H 1954 Prog.Theor.Phys.11 509Arima A,Shimizu K,Bent

4、z W and Hyuga H 1988 Adu.Nucl.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 has achieved great success during the last two decades:Straightforward application of the single-particle relativistic model doe

5、s not agree with the experimental magnetic momentsSerot&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 press1.LS-closure,no spin-orbit partners on both sides of the Fermi surface,therefore the

6、magnetic moment operator can not couple to magnetic resonance.2.Pion-exchange current contribution turned to be very small to iso-scalar current,as well as others processes.IntroductionThe Sigma and the time-component vector mesons of Omega fails to reproduce the corresponding Schmidt values:Taking

7、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.,NY 91(1975)40.Bawin M,Hughes C A and Strobel G L Phys.Reu.C

8、 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)234H.Kurasawa,et.al.,Phys.Lett.B165(1985)234J.A.McNeil,et.Al.,Phys.Rev.C34(1986)746S.Ichii,W.Bentz and A.Arima,Phys.Lett.B 192(1987)11.J.R.Shepard,et al.,Phys.Rev.C37(1988)1130P.G.Blunden,

9、Nucl.Phys.A 464(1987)525IntroductionIn these the widely investigated mean field theories there are only the time-even fields which are most sensitive to physical observables.The time-odd fields,which appear only in the nuclear systems with time-reversal symmetry broken,are very important for the des

10、cription 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 and changes the nuclear wave function and the resulting magnetic moments.The magnetic field created by magnetic potenti

11、al 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.71,3079(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.Rei

12、nhard,and J.A.Maruhn,Phys.Lett.B 468,1(1999)IntroductionThe core polarization is always neglected in Spherical cases,For the axial deformed 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 investig

13、ate the triaxial deformation and MDPurpose:developing the ,investigating the non-vanishing vector part of the-field,magnetic potential and magnetic momentsD.Hirata,et al.,Nucl.Phys.A609,131(1996).J.Meng,et al.,Phys.Rev.C 2006IntroductionU.Hofmann and P.Ring,Phys.Lett.B 214,307(1988).R.J.Furnstahl,C.

14、E.Price,Phys.Rev.C40(1989)1398.Starting point of RMF theory(Jp T)=(0+0)swr(Jp T)=(1-0)(Jp T)=(1-1)(g)r(Srss)(Ae)(g)(g)(Vrrrr0303021-+r+wrwSigma-meson:attractive scalar fieldOmega-meson:Short-range repulsiveRho-meson:Isovector fieldNucleons are coupled by exchange of mesons via an effective Lagrangia

15、nSerot&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.2005,in pressLagrangian of RMF theoryrws-r+-w+-s-ss+-r-w-s-FF)(URR)(U)(UAegggMiLii41414121213(-rr-r-rw-wrAAFgRmesonJpTp0-1s0+0w1-0r1-1(223423223232

16、11123411241142UmggUmcUmdswrssssww ww wrrrrr+Same footing for Deformation Rotation Pairing(RHB,BCS,SLAP)Equations of Motion(iii)(SM)(V)(+-rr rV ps-+-+r+wsrwrw)(g)r(S)(Ae)(g)(g)()(Ae)(g)(g)(Vrrrrrrrrr21V213303030-r+AiicAiiRAiivAiiis)()()(j)()()(j)()()(j)()()(iii1311121rrrrrrrrrrrr+-+-r-s+rrwwssrwwwwss

17、PRvsej)(jg)m(cjg)m(ggg)m(Ar23233222yTiKs-(,)(,)(,)(,)Tr sr sTr sr s-NucleonNumerical techniques for time reversal invariance violation111(,)()()()(1)21(,)()()()(1)2(1)yxyzxyxyxyzxnnnnnnnnnnnnir sxyzir sxyz+-Expanded on 3D HO Basis(,)(,)()(,)(,)(,)()(,)fgfgnjtnntjnjjjjr sr s ttir sr sr s ttfgfigr s(,

18、)(,)(,)(,)jjjjr s tr s trr sTsTtt-Dirac equation()()()()xyznnnxxyz,s w rwheremesonCoulomb field:the standard Green function methodNuclear Magnetic potential:vector part of the-fieldMagnetic field B=ww at y=z=1.29 fmNuclear Magnetic Fields due to the vector part of the-fieldSingle nucleon levels with

19、 time reversal invariance violationSingle nucleon levels with time reversal invariance violationThe other degree of freedom was integrated.Density distribution of the last odd nucleonDensity distribution for proton,neutron and matter221()2Mcmrc+Magnetic Moment in Relativistic approach(,)(,)()(,)tf r

20、 sr s ttig r s Relativistic effect Magnetic momentnucleon wave functioniiAi1+)r()r()r(r)r(hcMcrdiiii21223+)r(j)r(jrhcMcrdAiAiAiDi1123212Dirac current()()()Dj+rrrAnomalous current()()()Aj+rrrSpherical and axial RMF results with NL1 taken from Hofmann 1989Triaxial RMF with PK1 magnetic moments of ligh

21、t nuclei near closed shells(N)15O17O39Ca41Ca15N17F39K41SExp.0.72-1.891.02-1.60-0.284.720.395.43Schmidt0.64-1.911.15-1.91-0.264.790.125.79Spher.0.66-1.911.17-1.91-0.035.05 0.726.32Axial0.65-2.030.96-2.13-0.294.990.336.07Triaxial0.57-2.000.982.130.194.890.376.04Magnetic MomentIso-scalar magnetic momen

22、t(N)A Schmidt LandauSpher.AxialRHATriaxialExp.150.190.190.320.180.200.190.22171.441.411.571.481.441.451.41390.640.640.940.640.660.670.71411.941.912.211.971.951.961.92(211/N,ZN,Zs-+Landau:taking into account the current by linear response theoryMagnetic MomentIso-vector magnetic moment(N)A Schmidt s

23、s-w w+config.mixingSpherTriaxialExp.150.4510.3570.3450.3760.50117-3.353-3.487-3.480-3.446-3.303390.5120.2170.2250.3050.31241-3.853-4.141-4.115-4.086-3.513(211/N,ZN,ZV-+-s s-w w 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)307M

24、agnetic Moment D15O17O39Ca41Ca15N17F39K41SSchmidt-0.333.001.204.00Spher.-0.593.261.814.54Axial-0.13-0.13-0.30-0.220.443.211.504.29Triaxial-0.11-0.13-0.16-0.280.463.150.644.31 A15O17O39Ca41Ca15N17F39K41SSchmidt0.64-1.911.15-1.91-0.601.79-1.081.79Spher.0.66-1.911.17-1.91-0.621.79-1.091.79Axial0.78-1.9

25、01.26-1.87-0.731.78-1.171.79Triaxial0.68-1.861.13-1.85-0.641.75-1.001.73Dirac and Anomalous parts of Magnetic Moment(N)Nuclear current in 17F and 17O in y-z planeDirac currentAnomalous nuclear current in 17F and 17O in y-z planeDirac and anomalous current in 17FDirac currentAnomalous currentSummary

26、and perspectiveoTriaxial RMF without time reversal symmetry is developedoGround-state properties of light odd mass nuclei near double-closed shells,i.e.,E/A,single-particle energy,density distribution,etc.,are calculated self-consistentlyoThe broken time reversal symmetry leads to a non-vanishing ve

27、ctor part of the-field,which creates a magnetic potential and changes the nuclear wave function and the resulting magnetic moments.oThe 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

28、破缺正确确定激态及价核子组态正确确定激态及价核子组态-绝热与非绝热约束计算绝热与非绝热约束计算M Dconstraintss.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 和和 40Ca 的中子（左）和的中子（左）和质子（右）的单粒子能级质子（右）的单粒子能级考虑磁势后考虑磁势后41Ca 中互为时中互为时间反演态的能级劈裂间反演态的能级劈裂l Laudau and Migdal answer:Relativistic extension of Landaus Fermi-liquid theory based on sigma-

29、omega modelThe responds of the system as a whole when a quasi-particle is removed.Thus,the single quasi-particle current is defined as the difference in the total baryon current when the particle is removed.,()BiijBjBjjjjjjJjnnJnkg JEw-J.A.McNeil,et.Al.,Phys.Rev.C34(1986)746How to define the single-

30、particle property in dense,strongly interacting many-body system?sw-modelNucleon:Meson fields:Self-consistent Dirac equation:Total currentLandau quasi-particle current:Backflow effectRenormalization of currentEnhancement is reducedEspecially T=0 K:2100|2iiTsikjk mmws r r-+-+0,sr r+Remark:The cancell

31、ation of the scalar enhancement due to the vector meson*0.6mm22/gmwwwSpin particle One-body matrix element of currentVertex correction Renormalized currentElectric form factormagnetic form factor0qpp-Transfer momentumVector fieldsgg-igRemark:Dirac current is related to the electric form factor!J.A.M

32、cNeil,et.Al.,Phys.Rev.C34(1986)746The relativistic wave functions are obtained from a relativistic Woods-Saxon well with parameters adjusted to give the separation energy and elastic electron scattering form factor.The interaction vertex is renormalized by consideration of backflow effect in nuclear

33、 medium,namely,23/221/210031()(*)2Rmw rp r-+Relativistic extension of Landaus Fermi-liquid theoryEffective(renormalized)Dirac current()()()DRRjrrrRemark2:The anomalous current is not renormalized in this paper.Remark1:the wave function and the interaction vertex are not consistent!Remark3:The renorm

34、alization 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.Even if rho meson is considered,the enhancement of iso-vector current still can not be reduced significantly because of the small rho-N cou

35、pling constant.P.G.Blunden,Nucl.Phys.A 464(1987)525Remark4:In additional,the anomalous iso-vector moment,which is much larger that the Dirac moment,does not get affected by the scalar field,so that the total iso-vector spin moment will not be enhanced much./1/4 1/9rw-mmwrComment:Iso-scalar and iso-v

36、ector magnetic moment331,1,np+-(0)(1)0.123.706NN-2(0)1()2sMcrc+2(1)3()2vMcrc-+Dirac current()()()Dj+rrrcan be decomposed into an orbital current and a spin current*1()()()()()2ppiqm s+-rrrrconvectionspinAnomalous current()()()Aj+rrrMagnetic Moment in Relativistic approachExtensive shell model calcul

37、ations 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 the use of effective operators

38、 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 s-w model+the configuration mixing within one major shell for the mirror pairs,150-15N,170-17F,39K-39Ca and 41Ca-41S,removes most of the discr

39、epancies 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 Nedjadi and J R Rook,J.Phys.G:Nucl.Part.Phys.15(1989)

40、589-600.Introductionp 奇核子系统奇核子系统:未配对核子破坏时间反演对称性未配对核子破坏时间反演对称性,从而导致矢量介从而导致矢量介子场的空间部分不为零子场的空间部分不为零,Dirac 方程中出现磁势方程中出现磁势p 球对称球对称:奇奇A核处理成偶偶核额外加入一个核子核处理成偶偶核额外加入一个核子,体系核子波函体系核子波函数仍具有球对称性数仍具有球对称性.无法考虑时间反演对称性破缺对整个原子核无法考虑时间反演对称性破缺对整个原子核的影响的影响p 轴对称轴对称:Hofmann等人等人(88)和和 Furnstahl等人等人(89)自洽地考虑了自洽地考虑了磁势磁势,研究了核芯极化效应对整个原子核性质的影响研究了核芯极化效应对整个原子核性质的影响.这种核芯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增强,给出与给出与 Scnmidt 值一致的原子核磁矩值一致的原子核磁矩.p 本工作本工作:三轴形变框架下研究时间反演对称性破缺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