Relativistic description of Exotic Relativistic description of Exotic Nuclei and Magnetic rotationNuclei and Magnetic rotation

北京大学物理学院北京大学物理学院 School of Physics/Peking USchool of Physics/Peking U 兰州重离子加速器国家实验室核理论中心 兰州重离子加速器国家实验室核理论中心 HIRFL/LanzhoHIRFL/Lanzho

uu 中国科学院理论物理研究所 中国科学院理论物理研究所 Institute for Theor.Phys.Institute for Theor.Phys.

/AS/AS

孟 杰孟 杰 Jie MengJie 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 RMFStart: simple models Incompressibility requires the self-coupling of : NL1 and NLSH e

tc. 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 < PCM

2 > )So far, only in TM2 and DDME1, the correction of CM are bette

r treated.Effective interaction with the microscopically correction of C

M 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 fo

r PK

DD

, PK

1 and

PK

1r

rch fo

r PK

DD

, PK

1 and

PK

1r

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

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 ReviewLetters 》 80 (1998)460

The Exp. and calculated S2n by RCHB for Ca, Ni, Zr, Sn and Pb isotopesJ.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， 19-24 (2003)

Hyper Nuclei 1

3CΛ 13C 2Λ

Hyperon halo nuclei ： 13C3Λ

Lu HF, and Meng JChin. Phys. Lett.

19 (12): 1775-1778 DEC 2002.

Existence of deformed halo ?Otsuka et al. have studied the structure of 11Be an

d 8B 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

① Deformation and Continuum: (DRCHB)

② Coupled channel equations in coordinate space

③ The formalism and code for DRCHB ④ For given pairing potential DRCHB

works well⑤ Full self-consistence is under

construction…

Progress and ChallengeProgress 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

SRHSWSSRHSWS

SRHDWSSRHDWS

Convergence with energy cutoff

Convergence with Dirac Sea

Convergence of SRHWS theory

Convergence of density distribution

Convergence of density distribution

SRHHSRHHOO SRHWSSRHWS

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

Test of Pseudospin Symmetry in Deformed NucleiJ.N. Ginocchio, A. Leviatan, J. Meng, Shan-Gui Zhou

Spin symmetry in the anti-nucleon spectrumShan-Gui Zhou, J. Meng, P.Ring

Super heavy Element islandStructure and synthesis

Magic Number in S2p and S2N in RCHB

Magic Number in Shell Correction

Magic Number in pairing Synthesis of super heavy

element

Superheavy Element island in RCHB

Magic Number in S2n

Magic Number in S2n

Magic Number in S2p

Magic Number in S2p

120

Magic Number from difference in S2n

Magic Number from difference in S2p

Magic Number from Shell Correction

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 NF = NB=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 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 nucleiHamiltonian in triaxial deformed nuclei

i ntr col lH=H +H

23

i icol l

i=1 i

(I - j )H =

2

2 2 2intr 3 + -

1 j (j +1) 1H =± C{(j - )cosγ + [j +j ]sinγ }

2 3 2 3

FormulationFormulation

wherewhere

Eigenvector of PRM HamiltonianEigenvector of PRM Hamiltonian

p n- j j p n

p n

IIKαk k p n p n

K,k kK0

1IMα = C [ IMKk kα +(-1) IM- K- k - kα ]

2(1+δ )

i i

p n p n

p n p

K I,k j (i =n,p);

(K- k - k )→ even, k +k >0;

when k +k =0,k 0

D2 symmetry:

2 2πsin(γ - ν )

3 ν = 1,2,3 The moments of inerti

a for irrotational flowThe moments of inertia for irrotational flow

The relationship between

moments of inertia and

gamma

(1)s (2)i

(3)l

Ｒ

pj

hj =-30

1 2 3R <R <R

1 3 2

1

4

BM1 transitionBM1 transition

' ' '' '

'

-j -j

' '

' ' ' '

' ' ' '

p n p n' '

p n p n

p n

IKα I Kαk k k k

μ ,k k k k K0 K0

p n p R pμ n R nμ p n

2Ip n p R pμ n R nμ p n

B(M1,Iα → I α )

3 1 1= C C

16π 1+δ 1+δ

[ IK1μ I K k k (g - g )j +(g - g )j k k

+(-1) I - K1μ I K k k (g - g )j +(g - g )j -k - k ]+sign.

BE2 transitionBE2 transition

' ' '

'

' '

' ' ' ' ' 'p n

p n p n

k ,kIKα I Kα 2k k k k

K,K

B(E2,Iα → I α )

5 sinγ= C C [cosγ IK20I K - ( IK22I K +IK2- 2I K )]|

16π 2

1 2μ 0 3 ± 1

(j ±j )j =(j =j ,j = )

2

' '

' '

' 'p p

n n

K→ -K

k → -k

k → -k

A~170

A~100

A~130

1 1 1 19 / 2 9 / 2 9 / 2 11/ 2 11/ 2 11/ 2 11/ 2 13/ 2g g g h h h h i | ｜｜

Numerical detailsNumerical details Particle and hole configurations ： Particle and hole configurations ：

Input parameters ： Input parameters ：

0.1,0.2,0.25MeVC

~ 30

S. Frauendorf and J. Meng, Z. Phys. A365, 263(1996)

-115 ~ 40MeV

Results and Discussion Results and Discussion

-27 -27 -32 -39 [2]

0.195 0.175 0.175 0.16 [2]

0.21 0.19 0.19 0.175C[MeV]

13075Cs

13275La

13475Pr

13675Pm

１ .Comparison between the calculated and the experimental results

Reproduced the experimental bands in A130 [2]

[2] K. Starosta, et al., Phys. Rev. Lett. 86, 971(2001).

Input parameter ( , )

-1=25MeV 0.95

13075Cs

13275La

13475Pr

13675Pm comparisons in ， ， ，

Good agreement between the experimentaland the calculated results

Reproduced the experimental bands in A100 [10]

[10] Porquet M G, et al., Eur. Phys. J. A. 15, 463(2002).

Chiral doublets bands may exist in these four nuc

lei

Future developmentMagnetic 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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