1. Neutrons correlations viewed through nuclear break-up  Theory beyond mean field to describe influence of correlations on dynamics  Nuclear break-up of 6 He ( 208 Pb, 208 Pb) 4 He +n+n (GANIL) Assié Marlène (GANIL), J.-A. Scarpaci (IPNO), D. Lacroix (GANIL)

2. Our tool : Nuclear break-up (« Towing Mode ») 57 Ni 40 Ar 58 Ni Mechanism : “Towing Mode” J.A. Scarpaci et al PLB(1998 )  emission of nucleons : - with large angle with respect to the beam axis - in the same plane and on the same side as the perturbative potential - with a velocity lower than the beam  small impact parameter  energies ~10 to 100 MeV/A Probability density of a nucleon WF (44 MeV/A,b= 8 fm) Time Dependent Schrödinger Eq. D. Lacroix et al, NPA(1999)  important cross section (~1 barn)  important at large angle  coulomb  sensitive to angular momentum of nucleon

3.  Small impact parameters  rel Intuitive view from the nuclear break-up of correlated nuclei anticorrelated

4.  Small impact parameters  rel  Probe intrinsic correlations of nuclei through nuclear break-up  theoretical description with a beyond mean-field description  nuclear break-up of 6 He on 208 Pb  Large impact parameters Intuitive view from the nuclear break-up of correlated nuclei anticorrelated

5. Theoretical description of nuclear break-up of correlated nuclei

6.  Mean field Evolution of 2 body density : SKIII, SLy4, SkM* code 3D champ moyen Kim et al, JPG (1997) / Vautherin & Brink PRC (1972) Going beyond the mean field : Time dependent density matrix

7. ih C 12 = [h, C 12 ] + P + B + H  Beyond the mean field : Evolution of 2 body density : SKIII, SLy4, SkM* code 3D champ moyen Going beyond the mean field : Time dependent density matrix pairing dissipation higher order S. Wang, W. Cassing, Annals of Physics 159 (1985) TDDM

8. ih C 12 = [h, C 12 ] + P + B + H  Beyond the mean field : Evolution of 2 body density : SKIII, SLy4, SkM* code 3D champ moyen Going beyond the mean field : Time dependent density matrix pairing dissipation higher order S. Wang, W. Cassing, Annals of Physics 159 (1985) TDDM C 12 =  * separable formally same equations as TDHFB

9. ih C 12 = [h, C 12 ] + P + B + H  Beyond the mean field : Evolution of 2 body density : SKIII, SLy4, SkM* code 3D champ moyen Going beyond the mean field : Time dependent density matrix pairing dissipation higher order S. Wang, W. Cassing, Annals of Physics 159 (1985) TDDM  collision 2p-2t (ETDHF) p1 p2 p4 p3

10. TDDM P ih C 12 = [h, C 12 ] + P + B + H  Beyond the mean field : Evolution of 2 body density : SKIII, SLy4, SkM* code 3D champ moyen Going beyond the mean field : Time dependent density matrix pairing dissipation higher order S. Wang, W. Cassing, Annals of Physics 159 (1985) TDDM Hypothesis guided by BCS : pairing terms dominant  restrict to pair of time reversed states

11.  Numerical methods (for 3D) Residual interaction Adiabatic method for convergence TDDM P ih C 12 = [h, C 12 ] + P + B  Beyond the mean field : Evolution of 2 body density : Going beyond the mean field : Time dependent density matrix v 12  (1-e -t/  ) v 12   branching of residual interaction  300 fm/c HF g.s. correlated g.s. dynamics -- 0 ++

12. Static properties Mean field ff Mean field empty and occupied states 1 body observables

13. Mean field TDDM coeur ff TDDM P choice of inert core choice of valence space occupation numbers  [0,1] 2 body observables Static properties

14. Mean field TDDM coeur ff Static properties : adiabatic method 16 O (spd) 1d 5/2 1p 1/2 1p 3/2 E totale E HF E cor  = 300 fm/c t/ 

15. Mean field TDDM coeur ff Static properties : adiabatic method 22 O with 16 O inert core Matrice de Correlation  Convergence if gap important  Convergence in average if small gap  , no oscillation  Influence on 2 body observables ?  1 and C 12 stable 10  

16. Mean field TDDM coeur ff  TDDM P close to HFB calculations  pairing correlations dominant (1) M. Matsuo NPA 696 (2001) (2) M. Tohyama PLB 548 (2002) TDDM (2) our calculation HFB (1) 22 O-3,1 MeV -3,5 MeV-3,3 MeV 24 O-2,5 MeV -3,1 MeV-3,4 MeV  Pairing Gap Static properties of oxygen isotopic chain L. Lapikas NPA 553 (1993)

17. Influence of correlations on dynamics 16 O 6 He p wave

18.  Initialization of correlated 16 O 16 O 6 He p wave attractive force repulsive force Correlation Influence of correlations on dynamics

19. 16 O b=11 fm 208 Pb  Dynamics : Influence of correlations on dynamics  Dynamics (inverse kinematics for experiment) :

20. 16 O b=11 fm 208 Pb projectile target  Dynamics (inverse kinematics for experiment) : Influence of correlations on dynamics

21. 16 O b=11 fm 208 Pb Nuclear Break-up Transfer Dynamical evolution o transfer o emission to continuum o in the core Influence of correlations on dynamics  Dynamics (inverse kinematics for experiment) :

22. 16 O b=11 fm 208 Pb Absorption of transferred part Influence of correlations on dynamics Dynamical evolution o transfer o emission to continuum o in the core Absorption of o transferred WF o inert core  Dynamics (inverse kinematics for experiment) : Absorption of inert core

23. 16 O b=11 fm 208 Pb  Dynamics : Absorption of transferred part Absorption of inert core Influence of correlations on dynamics Dynamical evolution o transfer o emission to continuum o in the core Absorption of o transferred WF o inert core

24. 16 O b=11 fm 208 Pb  Dynamics : Influence of correlations on dynamics  Final correlations very different from initial correlations

25. 16 O b=11 fm 208 Pb  Dynamics : Influence of correlations on dynamics  Final correlations very different from initial correlations Energy Correlation

26. 16 O b=11 fm 208 Pb  Dynamics : Influence of correlations on dynamics 1n >40°  Final correlations very different from initial correlations  Confirms our intuitive vision of nuclear break-up

27. Nuclear break-up of 6 He

28. The case of 6 He M.V. Zhukov et al, Phys. Rep. 231, 151 (1993) cigar 4 He di-neutron 4 He R nn-core R n-n

29. The case of 6 He M.V. Zhukov et al, Phys. Rep. 231, 151 (1993) cigar 4 He di-neutron 4 He R nn-core R n-n  2n-transfer : Y. Oganessian et al, PRL82 (1999) D.T. Khoa et al, PLB 595 (2004) A. Chatterjee et al, to be published 2n-transfer dominant  di-neutron configuration G.Normand PhD thesis F.M. Marquès et al, PLB 476 (2000)  Coulomb break-up & interferometry :  cigar configuration + t-transfer : 6 He (p,t) 4 He S  -2n =1 S t-t =0,08 L. Giot et al, PRC71 (2005)  Radiative capture : 6 He(p,  )x @ 40 MeV/A no  + t decay  cigar configuration E. Sauvan et al, PRL 87 (2001)

30. Nuclear break-up of 6 He  Intuitive view of nuclear break-up of 6 He :  distributions of relative angle very different for the two configurations  confirmed by the theoretical description  probe neutron correlations

31. Experimental set-up at GANIL = 3% of 4  = 1  (Spiral) 10 6-7 pps

32. Experimental set-up at GANIL = 3% of 4  = 1  (Spiral) 10 6-7 pps Stripped Si: - 500  m - from 8° à 18° - 9mm  41 mm - 4*16 rings (2mm) - 4*24 sectors (3,4°) SiLi - 3,4 mm - 15 mm  46 mm

33. Experimental set-up at GANIL 

34. = 3% of 4  = 1  (Spiral) 10 6-7 pps Neutron Wall - 45 modules (liquid scintillator) - 51cm from target - 14 cm thick - Energy resolution : 50% - Detection efficiency at 20 MeV  30% - 1  - angle between detectors : 13°  18°

35. Experimental set-up at GANIL = 3% of 4  = 1  (Spiral) 10 6-7 pps EDEN - 39 modules (liquid scintillator) - 1,8 m from target - 5 cm thick, diameter 20 cm - Energy resolution : 4% - Detection efficiency at 20 MeV  15% - 3% de 4  - angle between 2 detectors  9°

36. Experimental set-up at GANIL = 3% of 4  = 1  (Spiral) 10 6-7 pps

37. Experimental set-up at GANIL Energie (MeV)

38. Experimental set-up at GANIL Energie (MeV)

39. Experimental set-up at GANIL  large relative angle coverage of the experimental set-up  corrected from crosstalk contribution  angle between the centres of the detectors ( 9° EDEN - 13 -18° Neutron Wall for closed detectors)  Distribution of relative angle between the neutrons for  +n+n

40. Correlation function  Correlation function experimental distribution emission of correlated neutrons independant emission: obtained by mixing events independant emission {1,1’} {2,2’} {1,2 } {1’,2’} {1,2’} {2,1’}  Test of the method : neutron E< 5 MeV  Several iterations F.M. Marquès PLB (2000) d  /d  12

41. Correlation function  Correlation function experimental distribution emission of correlated neutrons independant emission: obtained by mixing events independant emission {1,1’} {2,2’} {1,2 } {1’,2’} {1,2’} {2,1’}  Test of the method : neutron E< 5 MeV  Several iterations F.M. Marquès PLB (2000) d  /d  12

42. Correlation function  Correlation function experimental distribution emission of correlated neutrons independant emission: obtained by mixing events independant emission {1,1’} {2,2’} {1,2 } {1’,2’} {1,2’} {2,1’}  Test of the method : neutron E< 5 MeV  distribution of relative angle from GEANT4 simulation for an isotropic distribution  Several iterations F.M. Marquès PLB (2000) d  /d  12

43. cigar di-neutron Corrélation  rel (degrés) Correlation function  1 >30° ou  2 >30° E> 5 MeV experiment mixing  1 >50° ou  2 >50° E> 5 MeV di-neutron cigar Corrélation  rel (degrés)

44. Correlation function  6 He g.s. seems to be a superposition of di-neutron and cigare configurations  4 body CDCC calculations under development by M. Rodriguez-Gallardo to estimate configuration mixing (PRC 72 2008) cigare di-neutron Corrélation  rel (degrés) di-neutron cigare Corrélation  rel (degrés) 6 He

45. Conclusions & Perspectives  TDDM P  static properties of correlated nuclei  dynamical evolution of correlated nuclei and correlation functions Extension to transfer and fusion reactions Giant resonances  Nuclear break-up of 6 He  triple coïncidences  + n + n  correlation in relative angle estimate configuration mixing with 4 body CDCC calculations improvement of experimental set-up systematic study of borromean nucleus, clusters in nuclei, pp correlations

46. Collaboration : IPNO D.Beaumel, Y.Blumenfeld, M. Chabot, H. Iwasaki, C. Monrozeau, C. Petrache, J.-A. Scarpaci F.Skaza, T.Tuna GANIL D. Lacroix, A. Chatterjee LPC J.C. Angélique NSCL Cyclotron Laboratory, MSU D.Bazin SUBATECH Nantes M. Fallot University of Surrey W.Catford University of Camerino D.Mengoni Uppsala university J.Nyberg