1. 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)

2. 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

3. The density dependence of nuclear symmetry energy ------ a key issue in both nuclear physics and astrophysics 1818 1818 1212 1212 1212 3 symmetry energy Energy per nucleon in symmetric nuclear matter Energy per nucleon in asymmetric nuclear matter Isospin asymmetry 1. Introduction

4. Recent progress on the symmetry energy: 1Sub-saturation densities: some constraints have been obtained from analyzing nuclear reaction data… 2Saturation 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.

5. 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

6. Lane potential:

7. 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)

8. BUU: The Momentum dependent Interaction (MDI)

9. 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

10. 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

11. 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).

12. Iso Diff. (IBUU04, 2005), L.W. Chen et al., PRL94, 32701 (2005) IAS+LDM (2009), Danielewicz and J. Lee, NPA818, 36 (2009) PDR (2007) in 208 Pb Land/GSI, PRC76, 051603 (2007) Constraints extracted from data using various models Iso. 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 68 Ni and 132 Sn, 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)

13. Symmetry energy at supra-saturation densities Some indications of a supersoft E sym 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 E sym at the CSR in China, GSI in Germany, MSU in the United States, and RIKEN in Japan. Possible physical origins of the very uncertain E sym at supra- saturation densities?

14. Effect of the spin- isospin dependent three-body force Effects of the short range tensor force and nucleon correlation U 0 : relatively well determined U sym is very poorly known especially at high momenta. Xu et. al, Phys. Rev. C 81, 064612 (2010)

15. Effect of the spin-isospin dependent three-body force The symmetry energy obtained with different spin dependence x 0 and density dependence α in the three-body force (Gogny force)

16. 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

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

18. E kin (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)

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

20. 3. Summary 1.General expressions are derived for E sym and L by using the HVH theorem. 2.E sym and L at normal density: extracted values from the global optical potential 3.The reason why the E sym 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.

21. Thanks!

22. 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).