1. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Nucleon-Nucleon momentum correlation functions induced by the radioactive beams Yu-Gang Ma Shanghai Institute of Applied Physics (SINAP, CAS) Introduction Our results: nn, np, pp vs Ebind, Esep? Halo nuclei? conclusions

2. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil  weak correlation function 11Li (+ 208Pb) -> 9Li + n + n (+208Pb) Ieki et al., PRL70, 730 (1993) Our work will focus on the systematic studies on nucleon-nucleon correlation function for light nuclei!

3. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Two-Proton correlation functions q (MeV/c) 1+R(q) p-p correlation function R(q) sensitive to the space-time properties of emitting sources Emitting Source Target Proj Detector Arrays Final State Interaction (Coulomb + Nuclear: s-wave peak) + Pauli

4. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Intensity interferometry: from large scales... Star R d << R Static systems: exploring the geometry (size, R) HBT: R. Hanbury Brown, R.Q. Twiss, Phil. Mag., Ser. 7 45 (1954) 663 … to subatomic physic scales ( , K-K, , p-p, n-n, IMF-IMF, …) Fast evolving systems: 10 -23 -10 -15 sec: geometry changing in time Detectors Nuclear reaction d >> R R+V  G. Goldhaber et al., PR 120 (1960) 300

5. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Theoretical Calculation formula of two particles correlation In particular, the geometry of a collision is not a scale model of imaging a star. But for HBT ……

6. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Source-sizes from angle-averaged correlations extracted from C(20 MeV/c) Gaussian sources extensively used One-parameter approach (r 0 )

7. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil HI collisions at intermediate energies Need probes of the space-time properties of the emission Transport theory is a tool to treat space-time evolution of nucleonic system, it is a good method to exlore the nucleon-nucleon correlation function. Use transport theory to relate dynamics to EOS,  NN, … NN collisions, compression, pre-equilibrium Breakup, expansion Secondary decays Short time scalesLong time scales

8. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil S. Pratt, Physical Review Letters. 53 (1984) 1219

9. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Our results  stability check  Fits to the data (n-n correl. function)  Cp-n vs Ebinding  Cp-h vs Esep  Cp-p vs proton halo?  EOS, Sigma_nn etc Y.B. Wei, YGM et al., Phys Lett B 586, 225 (2004) Y.B. Wei, YGM et al., J Phys G 30, 2019 (2004) YGM et al., Phys. Rev. C 73, 014604 (2006)

10. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil QMD Isospin-dependent Quantum Molecular Dynamics Model: N-body transportation theory model Including the most important parts for nuclear reaction at intermediate energy Nuclear mean field:.Fragment Recognition, a naive coalescence model ΔR  3.5fm; ΔP  300MeV/c Nucleon-nucleon collision and Pauli blocking etc are considered

11. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Check of stability of IQMD

12. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Firstly we reproduce the experimental results of two halo neutrons for 14 Be + 12 C @ 35MeV/n: The reaction channel: 14Be(+12C)-> 12Be + n + n (+12C) It is obviously that the cal. results reproduce the exp. data very well. Y.B. Wei, YGM et al., Phys. Lett. B 586, 225 (2004) Data: Marques et al., PLB 476, 219 (2000)

13. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil 11Li (+ 208Pb) -> 9Li + n + n (+208Pb) @ 28MeV/u The obvious different results were obtained between 2 halo neutrons (solid line) and 2 core neutrons (dash line).  Large space extension  low C(q) Data: Ieki et al., PRL70, 730 (1993)

14. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Systematical study: n-p correlation  Ebinding 11-14B (N,C,Li) + C  xn + xp + … @ 800MeV/u

15. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Just like that of binding energy per nucleon, the relationship between the HBT strength Cph and the separation energy still exits monotonic character. How about the separation energy ? In model, we can also explore the correltaion between proton and the most outside neutron (Cph), see what happens? This correlation should reveal the extent of single-neutron separation.

16. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil A new criterion of halo nuclei? Z. Ren et al., PRC (96)

17. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Density distribution and pp HBT

18. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil The similar behavior is expected for double-neutron halo nuclei. A new criterion of halo nuclei? If two-proton halo structure is assumed no halo nuclei

19. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Conclusions  Experimental two halo neutrons correlation function (11Li, 14 Be) can be well fitted by the transport model: QMD  n-p correlation function depends on the binding energy of the system. More close binding system, the stronger np correlation.  P-halo n correlation function depends on the single neutron separation energy. However, difficult accessible in the experiment.  p-p correlation function is useful to search for proton- halo nuclei. Weak correlation is expected for 2p halo nuclei.  Systematic experiment should be done in near future.

20. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil The influences of nuclear transport property on HBT total pair momentum nuclear EOS in-medium n-n cross section impact parameter incident energy emission time YGM et al., Phys. Rev. C 73, 014604 (2005)

21. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Total pair momentum dependence

22. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil In-medium cross section dependence

23. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Impact parameter dependence

24. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil

25. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Emission time & evolution time in low Ptot, neutron and proton has a similar emission rate; in higher Ptot, neutron has earlier emission time; Higher Ptot. Earlier Temission nucleon-nucleon correlation function is stronger in earlier evolution time

26. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Conclusions  Experimental two halo neutrons correlation function (11Li, 14 Be) can be well fitted by the transport model: QMD  n-p correlation function depends on the binding energy of the system. More close binding system, the stronger np correlation.  P-halo n correlation function depends on the single neutron separation energy. However, difficult accessible in the experiment.  p-p correlation function is useful to search for proton- halo nuclei. Weak correlation is expected for 2p halo nuclei.  Systematic experiment should be done in near future.

27. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Thanks for your attention!

28. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Systems with different binding character leads to different HBT strength and shape.

29. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil Sensitivity to space-time extent Final State Interactions (Coulomb+Nuclear) + Pauli Directional information: Shape, Lifetime Pauli exclusion principle Coulomb: Dip at q ~ 0 1+R(q) q (MeV/c) 050100 Large source Small source q (MeV/c) Nuclear: Peak at Size (S wave)

30. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil In the QMD model, we can choose the random initialization or a fixed Stable Initialization. What is the difference on the HBT results?

31. Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil