Tensor force induced short-range correlation and high density behavior of nuclear symmetry energy

Chang Xu ( 许 昌 )

Department of Physics, Nanjing Univerisity

NN2012

Collaborators: Bao-An Li (Texas A&M Univeristy-Commerce)Zhongzhou Ren (Nanjing Univeristy)Liewen Chen (Shanghai Jiaotong Univerity)

Outline

1. Brief introduction to symmetry energy

2. Theoretical framework and results

Esym and L at saturation density

Esym at supra-saturation densities

3. Short summary

The density dependence of nuclear symmetry energy ------ a key issue in both nuclear physics and astrophysics

18

18

12

12

12

3

0 )) (, (( ) sn ymp

nn

p pE E E

symmetry energy

Energy per nucleon in symmetric nuclear matter

Energy per nucleon in asymmetric nuclear matter

Isospin asymmetry

1. Introduction

Recent progress on the symmetry energy:

1 Sub-saturation densities: some constraints have been obtained from analyzing nuclear reaction data…

2 Saturation density: around 30 MeV from analyzing nuclear masses and other data.

3 Supra-saturation densities : the situation is much less clear because of very limited data available.

2. Theoretical Formulism

• Starting from the Hugenholtz–Van Hove theorem (HVH) that is a fundamental relation among the Fermi energy, the average energy per particle E and the pressure of the system P at the absolute temperature of zero.

The nucleon single-particle potentials can be expanded as a power series

isoscalar isovector

Lane potential:

Theoretical Formulism

Comparing the coefficient of each term then gives the symmetry energy of any order

Xu et. al, Phys. Rev. C 82, 054607 (2010); Xu et. al, Nucl.Phys. A 865, 1 (2011)

BUU: The Momentum dependent Interaction (MDI)

which is important for determining several critical quantities, such as the size of the neutron skin in heavy nuclei location of the neutron drip line core-crust transition density and gravitational binding energy of neutron stars……

The slope parameter L

Symmetry energy and its slope at saturation density

Systematics based on world data accumulated since 1969:(1) Single particle energy levels from pick-up and stripping reaction(2) Neutron and proton scattering on the same target at about the same energy(3) Proton scattering on isotopes of the same element(4) (p,n) charge exchange reactions

Constraining the symmetry energy near saturation density using global nucleon optical potentials

C. Xu, B.A. Li and L.W. Chen, PRC 82, 054606 (2010).

Iso Diff. (IBUU04, 2005),Iso Diff. (IBUU04, 2005),L.W. Chen et al., PRL94, 32701 (2005)L.W. Chen et al., PRL94, 32701 (2005)

IAS+LDM (2009),IAS+LDM (2009),Danielewicz and J. Lee, NPA818, 36 (2009)Danielewicz and J. Lee, NPA818, 36 (2009)

PDR (2007) in 208Pb Land/GSI, PRC76, 051603 (2007)

Constraints extracted from data using various modelsIso. Diff & double n/p (ImQMD, 2009), M. B. Tsang et al., PRL92, 122701 (2009).

GOP: global optical potentials (Lane potentials)C. Xu, B.A. Li and L.W. Chen, PRC 82, 054606 (2010)

PDR (2010) of 68Ni and 132Sn, A. Carbone et al., PRC81, 041301 (2010).

SHF+N-skin of Sn isotopes, L.W. Chen et al., PRC 82, 024301 (2010)

Isoscaling (2007), D.Shetty et al. PRC76, 024606 (2007)

DM+N-Skin (2009): M. Centelles et al., PRL102, 122502 (2009)

TF+Nucl. Mass (1996), Myers and Swiatecki, NPA601, 141 (1996)

Symmetry energy at supra-saturation densities

• Some indications of a supersoft Esym at high densities have been obtained from analyzing the π+/π− ratio data.

• Experiments have now been planned to investigate the high-density behavior of the Esym at the CSR in China, GSI in Germany, MSU in the United States, and RIKEN in Japan.

• Possible physical origins of the very uncertain Esym at supra-saturation densities?

0 1 0

sym 1 0

3 1U

2 4 41 1

U2 4 4

n pT T

n pT T

U Uu u

U Uu u

Effect of the spin-isospin dependent three-body force

Effects of the short range tensor force and nucleon correlation

U0: relatively well determined

Usym is very poorly known especially at high momenta.

Xu et. al, Phys. Rev. C 81, 064612 (2010)

Effect of the spin-isospin dependent three-body force

The symmetry energy obtained with different spin dependence x0 and density dependence α in the three-body force (Gogny force)

Effect of the in-medium short-range tensor force

The pion and rho

meson exchanges

tensor forces

We use the Brown-Rho Scaling (BRS)

for the in-medium rho meson mass

The tensor force leads to appreciable depletion/population of nucleons below/above the Fermi surface in the single nucleon momentum distribution in SNM.

Ekin(sym) is significantly below the Fermi gas model prediction that is widely used in both nuclear physics and astrophysics

Microscopic calculations:

I. Vidana, A. Polls, C. Providencia, PRC 84, 062801 (2011).

A. Carbone, A. Polls, A. Rios, arXiv:1111.0797 (2011)

A. Lovato, private communications (2011)

The symmetry energy with different values of the BRS parameter αBR= 0, 0.05, 0.10, 0.15, 0.20 using different values for the tensor correlation parameter.

3. Summary1. General expressions are derived for Esym and L by using the

HVH theorem.

2. Esym and L at normal density: extracted values from the global optical potential

3. The reason why the Esym and L at supra saturation density so uncertain: isospin-dependence of the three-body force, tensor force and nucleon-nucleon correlation.

The three-body force and the tensor force induced SRC will affects significantly the high-density behavior of symmetry energy.

Thanks!

References

• N. M. Hugenholtz and L. Van Hove, Physica 24, 363 (1958)

• C. Xu, B. A. Li, L. W. Chen, and C. M. Ko, ArXiv:1004.4403.

• K. A. Brueckner and J. Dabrowski, Phys. Rev. 134, B722 (1964).

• J. Decharge and D. Gogny, Phys. Rev. C 21, 1568 (1980).

• M. L. Ristig, W. J. Louw, and J. W. Clark, Phys. Rev.C 3, 1504 (1971).