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

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

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, 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

Microscopic & Phenomenological ECM

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

Equations of Motion for DD RMF : Rearrangement terms:

Parameter sets PK1, PK1r and PKdd

DD for PKDD, TW99 and DD-ME1

E for PKDD, PK1 and PK1r

r ch for PKDD, PK1 and PK1r

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.

Properties for nuclear matter TM2, TM1, NL2,NLSH

Nuclear matter

Density dependence of Interaction strengths in Nuclear Matter

Potentials in nuclear matter

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.

Density dependence of Interaction strengths in Neutron Star

Potentials in Neutron Star

Binding energy per baryon in Neutron Star

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

EOS for Neutron Star

Neutron Star Radius vs. masses Center density vs. masses

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.

Pb isotopes in RCHB

Isotope shift in Pb isotopes

Single particle energy in RCHB

Sn isotopes in RCHB

Single particle energy in RCHB

Ni isotopes in RCHB

Single particle energy in RCHB

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

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

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)

Two neutron Separation Energy

Development of neutron skin

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

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

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) nucl-th/ : Deformed nuclear halos

 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

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

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

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

Relativistic Hartree theory for spherical nuclei

SRHSWS

SRHDWS

Convergence with energy cutoff

Convergence with Dirac Sea

Convergence of SRHWS theory

Convergence of density distribution

SRHH O SRHWS

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

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

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

Superheavy Element island in RCHB

Magic Number in S 2n

Magic Number in S 2p

120

Magic Number from difference in S 2n

Magic Number from difference in S 2p

Magic Number from Shell Correction

Magic Number in Neutron Effective Pairing Gap

Magic Number in Proton Effective Pairing Gap

Magic Number in Neutron Pairing Energy

Magic Number in Proton Pairing Energy

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

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

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

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

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

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

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

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

BM1 transition BE2 transition

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

Results and Discussion  [2]  [2] 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 (, )

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

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

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

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