1. M.Di Toro, ECT*/Eurisol Jan.06, ditoro@lns.infn.it Isospin Dynamics in Heavy Ion Collisions at Fermi Energies: EOS-sensitive Observables Dissipative Collisions Isospin Distillation Neck Fragmentation Isospin Transport n,p collective flows Lane Potential, E-slope Mean Field Effective Masses Transport Dynamics In-medium cross sections HIC probing: - different densities - high momenta - covariant structure Why EOS?

2. EOS of Symmetric and Neutron Matter Dirac-Brueckner Variational+3-body(non-rel.) RMF(NL3) Density-Dependent couplings Chiral Perturbative Ch.Fuchs, WCI Final Report 2006

3. Gas Liquid Density   Temperature 20200 MeV Plasma of Quarks and Gluons Crab nebula July 5, 1054 Collisions Heavy Ion 1: nuclei 5? Phases of Nuclear Matter Philippe Chomaz artistic view

4. Symmetry Energy E sym    MeV)     1 230 Expansion around   Pressure & compressibility Asy-stiff Asy-soft Pressure gradient Phys.Rep.410(2005)335-466 Asy-superstiff

5. SLOPE OF THE SYMMETRY TERM SYMMETRY PRESSURE SHIFT of SYMMETRIC NUCLEAR MATTER P sym Central density of Heavy Nuclei ? Compressibility shift Exotic Monopole?

6. 124 Sn “asymmetry”  = 0.2 Symmetry part of the mean field neutron proton Nucleon emission; Flows…. Asy-superstiff Asy-stiff Asy-soft Lane Potentials

7. 124 Sn “asymmetry”  = 0.2 neutron-proton chemical potentials neutron proton bulk neck at equilibrium… Isospin Transport and Chemical Potentials currents diffusion coeffs. DiffusionDrift Asy-superstiff Asy-soft -Isospin Distillation -Isospin Equilibration

8. EFFECTIVE MASS SPLITTING: SKYRME FORCES n-rich matter

9. SKYRME LANE POTENTIAL E-slope same sign of Phys.Rep.410(2005), nucl-th/0505013 (MSU-RIA) low energy crossing

10. Spinodal instabilities are directly connected to first-order phase transitions and phase co-existence: a good candidate as fragmentation mechanism Nuclear matter phase diagram: Liquid-Gas Transition V A way to test the low-density behaviour of the symmetry energy

11. F =  Free energy density Instability Condition Mechanical Chemical X u 2 +Y v 2 < 0 X<0 isoscalar-like Y<0 isovector-like u= cos   p +sen   n v= cos   p -sen   n  n =  p  X Y=X Y= F F Chemical effect F =  Free energy density Instability Condition Mechanical Chemical X u 2 +Y v 2 < 0 X<0 isoscalar-like Y<0 isovector-like u= cos   p +sen   n v= cos   p -sen   n  n =  p  X Y=X Y= F F Chemical effect PRL86 (2001) 4492 Multifragmentation: Instabilities of binary systems y: proton fraction

12. X<0 Y>0 X = 1+F s, Y= 1+F a attractiveint. 0F np 0  X<0 In Symmetric NM   chemical UNIQUE INSTABILITY: isoscalar-like PRL86 (2001) 4492 Instability Region: just from!!

13. Isospin Distillation Mechanism: “direction” of the spinodal unstable mode ! y = proton fraction =Z/A

14. STOCHASTIC MEAN-FIELD TRANSPORT APPROACH VLASOV + COLLISION and PAULI CORRELATIONS FLUCTUATIONS Equilibrium in a phase space cell OK if tot. number of collisions Initial: any time FLUCT.-DISS. THEOREM gainloss Markov NPA 642 (1998)

15. Fusion - Deep Inelastic Competition E= 30 AMeV, b=0.45 b max 46 Ar + 64 Ni (1.55) (1.29) n-rich 46 V + 64 Ge n-poor M. Colonna et al., PRC57 (1998) Asy-soft Asy-stiff Asy-soft Asy-stiff More fast proton emission Asy-soft more attractive Asy-stiff more attractive

16. Isospin Effect on Dissipation at lower energies Asy-soft Asy-stiff t fm/c Neutron-rich system: 124Sn+64Ni semicentral E=10AMeV Asy-soft more repulsive Interaction region below normal density: Sensitive to E_sym(ρ) at ρ<ρ_0 and not to cross sections Opposite with respect to the Fermi Energies M.Colonna for Spiral2 proposals 2005

17. b = 2 fm b = 4 fm b = 6 fm 124Sn+ 124Sn, E/A = 50 MeV/A Stochastic mean field (SMF) “fragmentation events” Freeze-out configurations Time-scale matching: Instability growth vs Interaction time t fm/c

18. 124 Sn+ 124 Sn 50 AMeV: average asymmetry Asy-stiff: neutron enrichment of neck IMFs Asy-soft Semi-peripheral collisions Isospin migration V.Baran et al., NPA703(2002)603 NPA730(2004)329 gas liquid

19. VELOCITY CORRELATIONS: DEVIATIONS FROM VIOLA SYSTEMATICS r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocity; r1- the same ratio for the pair TLF-IMF The IMF is weakly correlated with both PLF and TLF Wilczynski-2 plot ! V.Baran et al. NPA 730 (2004) Fragment clock

20. REDUCED VELOCITY PLOTS: BNV V. Baran et al. Nucl. Phys A730 (2004) 329 Note: stochastic BNV model accounts only for the “prompt” component of IMF’s E.De Filippo et al. (Chimera Coll.) PRC71(2005)044602 and 064604 Chimera 124Sn+64Ni 35AMeV data, same E_loss selections

21. Gating the reduced plot for light IMFs: E.De Filippo et al. (Chimera Coll.) PRC71(2005)044602 and 064604

22. Alignement

23. Angular distributions: alignment characteristics  plane is the angle, projected into the reaction plane, between the direction defined by the relative velocity of the CM of the system PLF- IMF to TLF and the direction defined by the relative velocity of PLF to IMF Out-of-plane angular distributions for the “dynamical” (gate II) and “statistical” (gate I) components E.De Filippo et al. (Chimera Coll.) PRC71(2005)044602 and 064604 Relatively large alignement even for the “statistical” cut

24. N  = 0.95 Z=1 Z=3 Z=2 Z=5 Z=7 Z=6 Z=8 Z=4 Z=9 lnR 21 NECK ISOSCALING at 35 MeV/n (b=6,7,8fm) asysoft asystiff superasystiff  0.69 0.95 1.10 V. Baran, M. Colonna, M. Di Toro : NPA 370 (2004) 329 Increasing slope with Z? Neck-frag. Iso-migration: heavier fragments more neutron rich! Fine structure of mid-rapidity fragments

25. Fe + Fe, Ni + Ni @ 47 AMeV IMF’s properties vs. alignement ~ N/Z Mass-alignement correlation: reaction mechanism, not Iso-EOS dependent N/Z-alignement correlation: iso-migration, Iso-EOS dependent even for Ni+Ni ! R.Lionti et al., PLB625 (2005) 33

26. Counts asy-stiff asy-soft 0<A<10 IMF hierarchy effects in v_tra : asymmetry small I middle I large I v_tra (x 100) 02 4 0246 Larger v_tra: smaller alignement Smaller masses and asymmetries Continous transition from multi- to neck-fragmentation up to PLF dynamical fission Isospin migration Isospin distillation Natura non facit saltus 124Sn+124Sn 50AMeV semicentral

27. b=8fm b=10fm ISOSPIN TRANSPORT AT FERMI ENERGIES 124 Sn + 112 Sn at 50 AMeV a) the neck region – low density interface b) pre-equilibrium particle emission BNV - transport model b=8fm b=9 fm b=10fm 120fm/c 100fm/c 80fm/c contact time Concentration (diffusion) and Density (drift) Gradients V.Baran et al., nucl-th/0506078, PRC in press

28. Rami imbalance ratio: ISOSPIN EFFECTS IN REACTIONS Mass(A)=Mass(B) ; N/Z(A) = N/Z(B) A dominance mixing B dominance +1 0 isoscaling vs. Centrality (fixed y) vs. Rapidity (fixed centrality) vs. Transverse momentum (fixed y, centrality) ?

29. ISOSPIN IMBALANCE RATIO asysoft eos superasystiff eos ASYSOFT EOS – FASTER EQUILIBRATION experimental data ( B. Tsang et al. PRL 92 (2004) ) Asysoft: more efficient for concentration gradients + larger fast neutron emission Asystiff: more efficient for density gradients + larger n-enrichement of the neck IMFs -Momentum Dependence: faster dynamics and smaller isodiffusion -In medium cross-sections: just scaling with the effective masses?

30. Collective flows In-plane Out-of-plane  1 < V 2 < +1 X Z y = rapidity p t = transverse momentum =  1 full out V 2 = 0 spherical = + 1 full in

31. ASY-STIFF ASY-SOFT Isospin effects on Transverse Flows:Fermi Energies Fe-Fe (1.24) vs Ni-Ni (1.07) p-Fe n-Fe p-Ni Light isobar flow 3H3H 3 He below balance : opposite to Coulomb p T selection Scalone et al., PLB (1999)

32. GBD extension Correspondence to Skyrme parameters NPA732(2004)202, nucl-th/0505013, nucl-th/0508008 PRC in press I=0.2 Lane Potential Momentum Dependence and Effective Masses: Fast Nucleon Emission Skyrme-like parametrization

33. 132 Sn+ 124 Sn, 50 AMeV, b=2 fm, y (0)  0.3 m * n >m * p m * n <m * p No mass splitting ! High p_t “gas” asymmetry: Observable very sensitive to the mass splitting and not to the asy-stiffness Pre-equilibrium emission: 132Sn projectile Gas asymmetry vs. p_t different times: end of pre-eq., freeze out Light isobar (3H vs. 3He) measurements ? : equil.asymmetry

34. 132 Sn+ 124 Sn, 100 AMeV, b=2 fm, y (0)  0.3 m * n >m * p m * n <m * p Pre-equilibrium emission (2) Enhanced effects at higher energy J.Rizzo et al., nucl-th/0508008, PRC in press Gas asymmetry vs. p_t

35. t=50 fm/c t=80 fm/c 132 Sn+ 124 Sn, b=2 fm, y (0)  0.3 50 AMeV 100 AMeV t=60 fm/c t=100 fm/c m * n >m * p m * n <m * p Pre-equilibrium emission (3) Asy-softAsy-stiff Asy-soft Asy-stiff Gas asymmetry vs. rapidity

36. Au+Au 250 AMeV, b=7 fm Z=1 data M3 centrality 6<b<7.5fm Difference of n/p flows Larger effects at high momenta Triton vs. 3 He Flows? Differential Transverse Flows nucl-th/0505013

37. Au+Au 250 AMeV, b=7 fm protons neutrons m*n<m*p : larger neutron squeeze out at mid-rapidity Z=1 data, M3 centrality, 6<b<7.5fm Differential Elliptic Flows

38.  Global fit to experimental charge distributions E.Santini et al., NPA756(2005)468 Fragment Formation in Central Collisions at Intermediate Energies Au+Au, Zr+Zr, Ni+Ni at 400 AMeV Central Stochastic RBUU + Phase Space Coalescence Size dependence: the lightest is the hotter? No but Fast clusterization in the high density phase

39. In-medium effects of  NN on stopping (E. Santini et al., NPA756(2005)468) C.Fuchs at al.,PRC64(2001)024003 Fragment z- and x- rapidity distributions

40. Transparency properties of protons & clusters (E. Santini et al., NPA756(2005)468) Opposite trend for protons vs clusters: correlation between fragment multiplicity and stopping Deuteron coalescence problem: protons overestimated (but not Z=1-6)

41. System size behaviour of clusters (E. Santini et al., NPA756(2005)468) Li-stopping correlation Z=1-10 cluster directed flow Size (Z_sys^2)-dependence of heavy cluster multiplicity Seeds: two-body correlations

42. Time-evolution of fragment formation (E. Santini et al., NPA756(2005)468) Au+Au 0.4 AGeV Central Z=3,4 Heavier fragments: “relics” of the high density phase Isospin Content vs. Symmetry Term ?

43. 1. N/Z of fast particle emission, hard photons 2. Fusion-Deep Inelastic Competition 3. E-slope Lane Potential 4.Isospin distillation (from Fermi to Intermediate En.) 5. Isospin transport * 6. Neck fragments: N/Z, alignement, size… * 7. n – p collective flows light isobar flows * * Asy-stiff indications (around saturation) but low asymmetries so far Isospin in Reactions at Fermi Energies: Iso-EOS Sensitive Observables People: V.Baran, M.Colonna, M.Di Toro, R.Lionti, M.Pfabe, J.Rizzo, E.Santini, and H.H.Wolter RIB up to 100AMeV & 4πDetectors, low threshold and high mass resolution

44. NECK FRAGMENTATION: CM V z -V x CORRELATIONS PLF IMF TLF Large dispersion also along transversal, x, direction 124 Sn + 64 Ni 35 AMeV  <0  >0 Alignement + Centroid at Clear Dynamical Signatures !

45. 58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV: Freeze-out Asymmetry distributions Fe Ni Fe Ni White circles: asy-stiff Black circles: asy-soft Asy-soft: smaller isospin migration Fe: fast neutron emission Ni: fast proton emission R.Lionti et al., PLB625 (2005) 33