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A status review on symmetry energy and nuclear structure

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A status review on symmetry energy and nuclear structure

蒋维洲

南京东南大学物理系

Collaborators：Bao-An Li，Lie-Wen Chen，Y. L. Zhao, et. al.

Mini-workshop @ 西安交大

Introduction

- Ground-state properties: s.p. energies, neutron skin, shape coexistence
- Excitations: Giant Resonances, Pigmy resonances, Superdeformation
- Tensor force: np interactions & exchange terms & symmetry energy
- Neutron star crust: transition density & non-Newtonian gravity & pastas & symmetry energy
- Neutron star core: hyperons, quarks, meson condensates & Modeling
- New forms of symmetry energy: higher order, I(I+1)
- Summary

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II. Ground state properties

Approaches: RMF, SHF, Macroscopic+Microscopic model +Shell correction, Shell model,… +BCS/Bogoliubov,

Lattice effective field theory calculations for A = 3,4,6,12 nuclei, PRL104:142501.

- Neutron skin thickness in 208Pb

Chen, et.al.

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Model Lagrangian:

with

Further the best fit: FSUGold, PRL95, 122501 (2005);

Other works: DDME1, Niksic, Vretenar, et.al., PRC 66, 024306 (2002);

DDME2: Lalazissis, et.al. PRC71, 024312 (2005);

Rho tensor coupling included: Jiang, Zhao, PLB617,33 (2005).

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Level inversion & Symmetry energy

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Shape coexistence: A=190 Pb spherical / Hg oblate

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III. Excitations: Giant Resonances, Pigmy resonances, Superdeformation

- SHF+RPA
- RMF+BCS+RPA
- RMF+RPA+Resonances +BCS
- RMF+RPA+Resonances +Bogoliubov
- TDRMF
- TDSHF
- Vlasov

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Giant: Vretenar, et.al. PRC 68, 024310 (2003).

- Pigmy: Paar, et.al., PRL94,182501(2005).
- Giant: Piekarewicz, PRC69, 041301(R) (2006).
- Pigmy: Liang, PRC 75, 054320 (2007).
- Pigmy: Piekarewicz, arXiv:1012.1803: 68Ni

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De-excitation from superdeformation

Jiang, et.al. EPJA 44, 465 (2010); Commun.Theor.Phys.54,715 (2010).

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IV. Tensor force: np interactions & exchange terms&symmetry energy

- Dirac equation
- np interaction
- Tensor force

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Revisit the tensor force

- Mainly from exchange terms.
- Pion & rho: the most important ingredients of the chiral perturbative theory.
- Rho meson becomes important in the tensor force due to the in-medium mass dropping associated with the partial restoration of the chiral symmetry.
- Vacuum effect on the symmetry energy: vacuum condensate
- Applications in superheavy nuclei, nuclei near drip lines, high-spin states…

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V. Neutron star crust: transition density & non-Newtonian gravity & pastas & symmetry energy

Negele & Vautherin, NPA 207, 298 (73)

Shen,et.al.,NPA637, 435 (98).

Than, Khan, Giai,. arXiv:1006.2916 [nucl-th]

Horowitz,et.al, PRC69:045804,2004

Newton, et.al.PRC79:055801,2009

Watanabe,et.al,PRL94:031101,2005

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Transition density

- Horowitz, Piekarenwicz, PRL86,5647(01): RRPA, namely small amplitude perturbation using the Dyson’s equation
- Xu, et.al., PRC79:035802,(09); APJ697:1549,(09) ; PRC81, 055805 (10): Dynamical and the thermodynamical methods.

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More concern:

Non-Newtonian Gravity on transition density

Strong Gravity at surface

Wen,Li,Chen: PRL 103, 211102 (2009)

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Neutron star core: hyperons, quarks, meson condensates?

- Kaon condensate:
- Miransky & Shovkovy, PRL88:111601,2002.
- Glendenning & Bielich, PRC60:025803,1999.
- Zhang, Luo, Li, PRD68:054015,2003.
- W. Zuo, A. Li, Z.H. Li, U. Lombardo, PRC70:055802,2004.
- A. Odrzywolek, M. Kutschera, Acta Phys.Polon.B40:195,2009.
- Li, Zhou, Burgio, & Schulze, PRC81, 025806 (2010)
- Guo-hua Wang, Wei-jie Fu, et.al., PRC78: 025801(2008)
- Guo-yun Shao, Yu-Xin Liu, PLB682:171(2009).

Phenomenological / Chiral model? Self-consistency

Effect of Symmetry energy

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Hyperons

Glendening, Phys.Rept. 342, 393 (2001);

Schaffner-Bielich, et.al., PRL89, 171101(2002).

Jiang, PLB642, 28 (2006).

Xu, Chen, Ko, Li, PRC81, 055803

(2010).

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Symmetry energy and Lambda hyperons

fY=ρY /ρB

Jiang, Nucl-th/0609024, PLB 642, 28(06)

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Density dependence from chirality

Constraining with the chiral symmetry in RMF models

- Properties of nucleons and mesons in medium should be constrained by the chiral symmetry and its breaking.
- Symmetry energy is dominated by the isovector mesons.
- A good candidate is the Walecka model with Brown-Rho scaling: Simple but with chiral limit

Brown,Rho, PRL66, 2720(91)

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P.Danielewicz, R.Lacey,W.G.Lynch, Science 298(2002)1592

Pressure of well constructed models

Collective flow data from high energy heavy-ion reactions

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Hyperons in nuclear medium with BR scaling

- Questions:

(1)How do the Y-N and Y-Y interactions depend on the density?

(2) How to justify the assumption that the density-dependence of YN interaction is similar to NN interaction?

Nonlinearity, interior degrees of freedom

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Universal case

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SU2 case

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Quarks in dense matter and hybrid stars

R.X. Xu, ApJ,596 L59 (2003).

M. Alford,et.al., Astrophys. J.629, 969 (2005).

W.-j.Fu, Wei, Liu, PRL101:181102(2008).

G.X.Peng, A. Li, Lombardo, PRC 77, 065807 (2008)

F. Yang, H. Shen, PRC77:025801 (2008).

Xu, Chen, Ko, Li, PRC81, 055803 (2010).

A.Li, R.X.Xu, J.F.Lu, MNRAS 402, 2715 (2010).

H. Li, X.L.Luo, H.S. Zong, Phys.Rev.D82,065017(2010).

SD equation, ChPT, NLJ, CS, BR scaling, QMC, Quark cluster & mass scaling, Hadron-Bag model, Bag+pQCD correction…

Meson condensate, chiral condensate, di-quark condensate, CFL, QSC…Beyond standard model?

Symmetry energy vanishes in new phases?

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VII. New forms of symmetry energy: higher order, I(I+1)

- High orders beyond parabolic approximation

Isospin Physics in Heavy-Ion Collisions at Intermediate Energies, Eds. Bao-An Li and W. Udo Schroder (Nova Science Publishers, Inc, New York, 2001).

Myers & Swiatechi, Ann. Phys. 55, 395(1969); ibid.84, 186 (1974).

Danielewicz, NPA727, 233 (2003).

Xu, et.al., PRC79:035802,(09); APJ697:1549,(09) ; PRC81, 055805 (10):Importance of high orders on the transition density of the crust

Chen, et.al. High-order effects on the incompressibility of isospin asymmetric nuclear matter,PRC80: 014322, 2009.

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Why not I(I+1)?

RMF study on finite nuclei suggests E ~T(T+1), Ban, et.al. Phys.Lett.B633:231-236,2006.

In nuclear matter, the parabolic approximation suggests E~T*T

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No quantum effect

- Radiation correction requires the quantization of Coulomb field
- In strong fields, the renormalization required
- Calculations of the RRPA with the ring energy is still in progress.

From vacuum polarization of mesons (Chin, AP108, 301 (1977).)

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Discussion:

- With phase transition to quarks and hyperons, what happens to the symmetry energy?
- Tensor force should be constrained by chiral symmetry, or ChPT?

Quantum effects & symmetry energy?

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No Summary:

- Ground-state properties: s.p. energies, neutron skin, shape coexistence
- Excitations: Giant Resonances, Pigmy resonances, Superdeformation
- Tensor force: np interactions & exchange terms & symmetry energy
- Neutron star crust: transition density & non-Newtonian gravity & pastas & symmetry energy
- Neutron star core: hyperons, quarks, meson condensates & Modeling
- New forms of symmetry energy: higher order, I(I+1)

Mini-workshop @ 西安交大

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