1. Isovector reorientation of deuteron in the field of heavy target nuclei The 9th Japan-China Joint Nuclear Physics Symposium (JCNP 2015) Osaka, Japan, Nov. 7-12, 2015 Zhigang Xiao ( 肖志刚 ) Tsinghua University, Beijing, China （清华大学） Li Ou （欧立） Guangxi Normal University, China （广西师范大学）

2. Contents 1 Introduction to the nuclear Symmetry Energy 2 Orientation of Deuteron in nuclear reactions 3 Isovector reorientation of d on heavy target nuclei 4 Summary

3. Symmetry Energy Energy cost to convert protons to neutrons in nuclear medium  :Compressibility E sym L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007).

4. Relevance of E sym (  ) in astrophysics and nuclear physics Proton fraction M-R relation  c for D-Urca Transition density …… Phy. Rep. 442(2007) 109; NPA777(2006)479 PRC76(2007),015801; PRC75(2007) 015801 PRC74 (2006),035802; Astro. J. 676 (2008) 1170 Phy. Rep. 411(2005) 325; PLB 642, 436 (2006)......  :Compressibility E sym Astrophysical Connection

5. A shopping list for sub-saturation density At sub-saturation densities  Isospin scalaring and isospin fractionaiton (MSU…)  Isospin diffusion (MSU …)  n/p ratio of fast and pre- equilibrium nucleons (MSU …)  N/Z of the emitted fragments (LNS, TAMU, MSU, HIRFL …)  GMR strength (ND/RCNP …)  HBT correlation function (KVI, MSU, HIRFL …)  Pb Polarizability(RCNP)…. ….  /0 /0 1 E sym (  ) 0.5 30 S0S0 Slope=L S 0 = 32±3 MeV L = 55±25 MeV

6. Topical issue on the Symmetry Energy EPJA 50(2014) 29 EPJA 50(2014) 37

7. Is there any other probes? Nucleon induced reaction:  For proton, isovector potential being attractive, the scattering angle  will be larger with a stronger symmetry energy.  Angular distribution in peripheral n/p-induced scattering carries the information of symmetry energy.

8. Nucleon induced scattering --- a new probe Shall it work well? How do you have the neutron beam? What about to bind n and p?  Deuteron!

9. Polarization Effect in d-induced reaction Oppenheimer proposed first J. R. Oppenheimer et al., Phys. Rev. 48, 500 (1935) E. O. Lawrence et al., Phys. Rev. 48, 493(1935) Favored p n Target Un-favored p n Target Coulomb polarization (Reorientation)

10. Polarization effect in breakup reactions 17 F polarization on target: PLB 681 (2009) 22–25 Dynamical Polarization p 16 O Target

11. A nature question arises now…… Coulomb force,1 for proton and 0 for neutron, leads to Coulomb polarization (reorientation), characterized by the moving away of proton. Isovector force, attractive for proton and repulsive for neutron, shall leads to isovector reorientation, characterized by the modification of the direction of the relative motion. If this effect is detectable, it should be sensitive to the isovector potential (  symmetry energy!) Isovector force act on p and n like a torque  Reorientation effect p n Target

12. Calculation framework IQMD

13. Initialization of Deuteron Initialization: d np =3  r (  r<0.25) p n, p p randomly sampled Bounded longer than 100 fm/c 1/2 = 2.1  0.2 fm

14. Define the observable in breakup events How can we find an observable?  Break up kinetics Correlation angle

15. First attempt: not that successful Isospin Effect is shown up, but not as sufficient as one would expect. What else?

16. Initial polarization of Deuteron Random orientation of the incident deuteron smears the isovector reorientation effect!  We need initial polarized deuteron beam! （ P V  1, P T  1 ） V. Baryshevsky, A. Rouba Physics Letters B 683 (2010) 229–234

17. A surprise When the incident deuteron is polarized, the isovector re-orientation effect is significant! Effect is sensitive to the impact parameter.

18. Figure out an observable The angular distribution is an observable. Fit the slope at cos  =0

19. Last question: How do we select the nucleons? Collision contribution is a contamination Kinetic feature characterizes the direct breakup events Only one 2-D cut is used in the data analysis. The sensitivity is kept!

20. Density range of sensitivity What density region is this observable sensitive on? Density range < 0.5  0 Just as what we expect! b=6 fmb=7 fm b=7.5 fm

21. Summary A novel reorientation effect of deuteron attributed to isovector interaction in the nuclear field of heavy target nuclei has been investigated for the first time. The correlation angle of nucleons from the breakup of polarized deuteron, depends sensitively on the isovector potential but insensitively on the isoscaler potential. In terms of sensitivity and cleanness, the breakup reactions induced by polarized deuteron beam at about 100 MeV/u provide a more stringent constraint to the symmetry energy at subsaturation densities. For details, Please refer to PRL 115, 2015, to be published Nov. 20

22. Welcome to 6 th international symposium on nuclear symmetry energy (NuSym2016) Tsinghua University, Beijing, Jun. 13-17, 2016 Thank you for your attention!