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Neutrons correlations viewed through nuclear break-up

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).

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Neutrons correlations viewed through nuclear break-up

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

  2. Our tool : Nuclear break-up (« Towing Mode ») • Mechanism : “Towing Mode” • Time Dependent Schrödinger Eq. • small impact parameter • energies ~10 to 100 MeV/A • 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 57Ni 58Ni 40Ar • important cross section (~1 barn) • important at large angle  coulomb • sensitive to angular momentum of nucleon Probability density of a nucleon WF (44 MeV/A,b= 8 fm) J.A. Scarpaci et al PLB(1998) D. Lacroix et al, NPA(1999)

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

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

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

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

  7. Going beyond the mean field : Time dependent density matrix • Beyond the mean field : Evolutionof 2 body density : TDDM ih C12 = [h, C12] + P + B + H pairing dissipation higher order champ moyen • SKIII, SLy4, SkM* • code 3D S. Wang, W. Cassing, Annals of Physics 159 (1985)

  8. Going beyond the mean field : Time dependent density matrix • Beyond the mean field : Evolutionof 2 body density : TDDM ih C12 = [h, C12] + P + B + H pairingdissipation higher order champ moyen • SKIII, SLy4, SkM* • code 3D C12=* separable formally same equations as TDHFB S. Wang, W. Cassing, Annals of Physics 159 (1985)

  9. p1 p3 p2 p4 Going beyond the mean field : Time dependent density matrix • Beyond the mean field : Evolutionof 2 body density : TDDM ih C12 = [h, C12] + P + B + H pairingdissipation higher order champ moyen • SKIII, SLy4, SkM* • code 3D  collision 2p-2t (ETDHF) S. Wang, W. Cassing, Annals of Physics 159 (1985)

  10. Going beyond the mean field : Time dependent density matrix • Beyond the mean field : Evolutionof 2 body density : TDDMP TDDM ih C12 = [h, C12] + P + B + H pairing dissipation higher order champ moyen • SKIII, SLy4, SkM* • code 3D • Hypothesis guided by BCS : • pairing terms dominant •  restrict to pair of • time reversed states S. Wang, W. Cassing, Annals of Physics 159 (1985)

  11. Going beyond the mean field : Time dependent density matrix • Beyond the mean field : Evolutionof 2 body density : TDDMP ih C12 = [h, C12] + P + B • Numerical methods (for 3D) • Residual interaction • Adiabatic method for convergence - HF g.s. 0 correlated g.s. v12(1-e-t/) v12   branching of residual interaction  300 fm/c dynamics +

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

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

  14. Static properties : adiabatic method = 300 fm/c • 16O (spd) 1p3/2 1p1/2 f 1d5/2 t/ 1d5/2 Mean field 1p1/2 1p3/2 t/ Ecor TDDM coeur EHF Etotale t/

  15. Static properties : adiabatic method <|C12|> • 22O with 16O inert core f Matrice de Correlation  Mean field  10 • Convergence if gap important • Convergence in average if small gap • , no oscillation • Influence on 2 body observables ? 1 and C12 stable TDDM coeur

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

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

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

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

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

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

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

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

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

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

  26. Nuclear break-up of 6He

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

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

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

  30. Experimental set-up at GANIL = 3% of 4 = 1 (Spiral) 106-7 pps

  31. Experimental set-up at GANIL = 3% of 4 = 1 Stripped Si: - 500 m - from 8° à 18° - 9mm  41 mm - 4*16 rings (2mm) - 4*24 sectors (3,4°) (Spiral) 106-7 pps SiLi - 3,4 mm - 15 mm46 mm

  32. Experimental set-up at GANIL

  33. Experimental set-up at GANIL = 3% of 4 = 1 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° (Spiral) 106-7 pps

  34. Experimental set-up at GANIL = 3% of 4 = 1 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° (Spiral) 106-7 pps

  35. Experimental set-up at GANIL = 3% of 4 = 1 (Spiral) 106-7 pps

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

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

  38. Experimental set-up at GANIL • Distribution of relative angle between the neutrons for +n+n • 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)

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

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

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

  42. 1>30° ou 2>30° E> 5 MeV experiment di-neutron mixing cigar Corrélation rel (degrés) 1>50° ou 2>50° E> 5 MeV di-neutron Corrélation cigar rel (degrés) Correlation function

  43. di-neutron cigare Corrélation rel (degrés) di-neutron Corrélation cigare rel (degrés) Correlation function • 6He 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) 6He 6He

  44. Conclusions & Perspectives • TDDMP • 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 6He • 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

  45. 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

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