1. Relativistic description of Exotic Nuclei and Magnetic rotation  北京大学物理学院 School of Physics/Peking U  兰州重离子加速器国家实验室核理论中心 HIRFL/Lanzhou  中国科学院理论物理研究所 Institute for Theor.Phys./AS 孟 杰 Jie Meng

2. Contents ① New Effective Interactions in RMF ② Nuclear matter and neutron star ③ Finite Nuclei and halos ④ SRHWS: replacement of HO basis ⑤ New Magic number in Super-heavy nuclei ⑥ Magnetic rotation and Chiral bands

3. Effective interaction for RMF Start: simple  models Incompressibility requires the self-coupling of  : NL1 and NLSH etc. Follow the Dirac-Brueckner Theory / Instability at high density a) the self-coupling of  : TM1 b) correct incompressibility: NL3 c) DD effective interactions (TW99,DD-ME1,  ) The problem for the correction of CM a) Phenomenological ( -3/4 41 A -1/3, -17.2 A -0.2  ) b) Microscopically ( - 1/2MA  ) So far, only in TM2 and DDME1, the correction of CM are better treated. Effective interaction with the microscopically correction of CM are needed. Extrapolation for low and high nuclear matter

4. Microscopic & Phenomenological ECM

5. Nonlinear & DD RMF Lagrangian density: Nonlinear RMF DD RMF Five constraints

6. Equations of Motion for DD RMF : Rearrangement terms:

7. Parameter sets PK1, PK1r and PKdd

8. DD for PKDD, TW99 and DD-ME1

9. E for PKDD, PK1 and PK1r

10. r ch for PKDD, PK1 and PK1r

11. Nuclear matter The density dependencies of various effective interaction strengths in relativistic mean field are studied and carefully compared for nuclear matter. The corresponding influences of those different density dependencies are presented and discussed on mean field potentials, saturation properties of nuclear matter.

12. Properties for nuclear matter TM2, TM1, NL2,NLSH

13. Nuclear matter

14. Density dependence of Interaction strengths in Nuclear Matter

15. Potentials in nuclear matter

16. Neutron Star The density dependencies of various effective interaction strengths in relativistic mean field are studied and carefully compared for neutron star. The corresponding influences of those different density dependencies are presented and discussed on mean field potentials, equations of state, maximum mass and corresponding radius in neutron star.

17. Density dependence of Interaction strengths in Neutron Star

18. Potentials in Neutron Star

19. Binding energy per baryon in Neutron Star

20. Particle n, p, e - and  - densities in Neutron Star

21. EOS for Neutron Star

22. Neutron Star Radius vs. masses Center density vs. masses

23. Finite Nuclei in DD RMF New parameter sets for Lagrangian density, PK1, PK1r, PKDD are able to provide an excellent description not only for the properties of nuclear matter but also for the nuclei in and far from the valley of beta- stability with the center-of-mass correction included in a microscopic way.

24. Pb isotopes in RCHB

25. Isotope shift in Pb isotopes

26. Single particle energy in RCHB

27. Sn isotopes in RCHB

28. Single particle energy in RCHB

29. Ni isotopes in RCHB

30. Single particle energy in RCHB

32. Recent work on the existence of giant halo and hyperon halo in relativistic continuum Hartree- Bogoliubov (RCHB) theory is reviewed. Experimental support of giant halos in Na and Ca isotopes near the neutron drip line is discussed and the progress on deformed halo is presented. Halos and Giant halos

33. J.Meng and P. Ring, 《 Physical Review Letters 》 80 (1998)460

34. The Exp. and calculated S 2n by RCHB for Ca, Ni, Zr, Sn and Pb isotopes J.Meng, et al. ，《 Physical Review 》 C 65 (2002 ) 41302(R)

35. Two neutron Separation Energy

36. Development of neutron skin

37. Neutron halos in hyper Ca isotopes Lu, et al., Euro. Phys. J. A17 ， 19-24 (2003)

38. Hyper Nuclei 13 C Λ 13 C 2Λ Hyperon halo nuclei ： 13 C 3Λ Lu HF, and Meng J Chin. Phys. Lett. 19 (12): 1775-1778 DEC 2002.

39. Existence of deformed halo ?  Otsuka et al. have studied the structure of 11 Be and 8 B with a deformed Woods-Saxon potential considered quadrupole deformation as a free parameter adjusted to the data. T.Otsuka,A.Muta,M.Yokoyama,N.Fukunishi,and T.Suzuki,Nucl.Phys.A588, 113c(1995).  Based on a spherical one-body potential: the positions of experimental drip lines are consistent with the spherical picture; I.Tanihata,D.Hirata,and H.Toki, Nucl.Phys.A583,769 (1995).  Using the deformed single-particle model ， the existence of the deformed halo is doubted ? T. Misu, W. Nazarewicz, S. Aberg, Nucl.Phys. A614 (1997) 44-70. nucl-th/9612016 : Deformed nuclear halos

40.  Deformation and Continuum: (DRCHB)  Coupled channel equations in coordinate space  The formalism and code for DRCHB  For given pairing potential DRCHB works well  Full self-consistence is under construction… Progress and Challenge

41. Limits of present methods RMF in H.O. basis: unsuitable for exotic nuclei In coordinate space: difficult for deformed nuclei RMF in Woods-Saxon basis

42. RMF Theory - Shan-Gui Zhou, Jie Meng, Peter Ring, Phys.Rev.C Lagrangian where Development of SRHWS

43. RMF Theory: field equations Dirac equations for nucleons K-G equations for mesons

44. Relativistic Hartree theory for spherical nuclei

45. SRHSWS

46. SRHDWS

47. Convergence with energy cutoff

48. Convergence with Dirac Sea

49. Convergence of SRHWS theory

50. Convergence of density distribution

51. SRHH O SRHWS

52. Convergence for 72 Ca.  r = 0.1 fm for SRHR and SRHWS ( E cut = 75 MeV )

53. Test of Pseudospin Symmetry in Deformed Nuclei J.N. Ginocchio, A. Leviatan, J. Meng, Shan-Gui Zhou Spin symmetry in the anti-nucleon spectrum Shan-Gui Zhou, J. Meng, P.Ring

54. Super heavy Element island Structure and synthesis Magic Number in S 2p and S 2N in RCHB Magic Number in Shell Correction Magic Number in pairing Synthesis of super heavy element

55. Superheavy Element island in RCHB

56. Magic Number in S 2n

58. Magic Number in S 2p

59. 120

60. Magic Number from difference in S 2n

61. Magic Number from difference in S 2p

62. Magic Number from Shell Correction

64. Magic Number in Neutron Effective Pairing Gap

65. Magic Number in Proton Effective Pairing Gap

66. Magic Number in Neutron Pairing Energy

67. Magic Number in Proton Pairing Energy

68. Magnetic Rotation: Self-consistent solution of the cranked RMF equations

69. Numerical details for RMF with NL3 Symmetry: parity Dirac equations solved in 3D HO basis With N F = N B =10 Configuration:  (pf) 7 (1g9/2) 2 (1g9/2) -3 For frequency  =0.1 MeV, search for energy minimum in  -  plane

70. CRMF 计算的两类转动惯量 H.Madokoro, J. Meng, M. Matsuzaki, S. Yamaji, 《 Physical Review 》 C62 (2000) Rapid Communication

71. B(M1) and B(E2) for magnetic rotation in RMF H.Madokoro, J. Meng, M. Matsuzaki, S. Yamaji, 《 Physical Review 》 C62 (2000) Rapid Communication

72. 倾斜角随角动量的变化 H.Madokoro, J. Meng, M. Matsuzaki, S. Yamaji, 《 Physical Review 》 C62 (2000) Rapid Communication Total Neutron Proton

73. Chiral bands for A~130 and 100 mass region in PRM Jie Meng, Jing Peng, Shuang-quan Zhang Peking University 2003 ECT  Trento

74. ＋ — particle － — hole Hamiltonian in triaxial deformed nuclei Formulation where Eigenvector of PRM Hamiltonian D2 symmetry:

75. The moments of inertia for irrotational flow The relationship between moments of inertia and gamma  Ｒ  =-30 

76. BM1 transition BE2 transition

77. A~170A~100A~130 Numerical details Particle and hole configurations ： Input parameters ： S. Frauendorf and J. Meng, Z. Phys. A365, 263(1996) 

78. Results and Discussion -27 -32 -39  [2] 0.195 0.175 0.16  [2] 0.21 0.19 0.175 C [MeV] １.Comparison between the calculated and the experimental results Reproduced the experimental bands in A  130 [2] [2] K. Starosta, et al., Phys. Rev. Lett. 86, 971(2001).  Input parameter (, )

79.  comparisons in ， ， ， Good agreement between the experimental and the calculated results

80. Reproduced the experimental bands in A  100 [10] [10] Porquet M G, et al., Eur. Phys. J. A. 15, 463(2002). Chiral doublets bands may exist in these four nuclei

81. Future development Magnetic rotation and rotation in neutron- rich nuclei Dirac equations solved in WS basis Axial symmetric  triaxial system Alternative options: 1.Triaxial RMF: Adiabatic calculations 2.Output as input for chiral bands

82. 谢谢 大家！ Thank you