Isospin observables Observables Mechanisms sensitive to symmetry energy Dilute asymmetric matter and related instabilities New features of the liquid-gas phase transition Fragmentation in semiperipheral reactions at the Fermi energies and degree of equilibration Early stage of the reaction dynamics between neutron-rich nuclei: pre-equilibrium emission and collective flows   Competition between different dissipative reaction mechanisms, like fusion vs. deep-inelastic vs. fragmentation    Fusion dynamics in low-energy reactions: the role of the dynamical prompt dipole radiation (also in DIC) Isospin effects on energetic particle production Observables N/Z of fragments, Isoscaling Isospin diffusion, Imbalance ratio Distributions of pre-equilibrium particles: energy, angular, time,transverse momentum, isotopic content Correlations among light particles and/or fragments Differential flows (n/p, light isobars)      Fusion cross section vs. deep-inelastic cross section vs. fragmentation cross section Measure of pre-equilibrium GDR Isospin tracer, N/Z of IMF’s in central relativistic collisions, ratios: p+ / p- , K+/K0

Isoscaling: experiments and comparison with statistical (hybrid) models (1) Xu et al., PRL85(2000) Tan et al., PRC64(2001) N Sn124-Sn112 combinations @ 50 AMeV Comparison with SMM-MSU (inputs from BUU, E*=4-6 MeV) ρn = exp(α) Isoscaling in Lattice Gas Model: Y.G.Ma et al., PRC69 nearly linear relation with N/Z Shetty et al., PRC70(2004)

Isoscaling: experiments and comparison with statistical (hybrid) models (2) SMM Hot Cold A, fragment mass D.Shetty et al., nucl-ex/0409019 Tsang et al. PRC64(2001) γ~19 MeV (SMM-McGill, canonical)

Isoscaling analysis in dynamical models Stochastic BNV calculations T.X.Liu et al., PRC69(2004) AMD: Ono et al., PRC68(2003) 50 AMeV 35 AMeV Isoscaling in IQMD calculations: W.D.Tian et al., Chin.Phys.Lett.22 (2005)

Extraction of symmetry energy (1) Asy-soft Asy-stiff E.Geraci et al.,NPA732(2004) A.Botvina et al., PRC65(2002): H + Sn112,124 @ 6.7 GeV He4 + Sn112,124 @ 15.3 GeV Shetty et al., PRC70(2004) Isoscaling parameters depend on N/Z of systems and value of symmetry energy: effects in opposite directions… In SMM-MSU Csym is fixed … Δ(Z/A)²

Extraction of symmetry energy (2) Le Fevre et al., nucl-ex/0409026 C12 + Sn112,124 @ 300,600 AMeV Fragmentation of excited target residues Central collisions 18O on 9Be @ 60 AMeV, Fang et al., PRC61(2000)

Isoscaling in Deep-Inelastic Collisions: PLF sources R21 (N,Z) = Y2/Y1 25 AMeV •86Kr+124Sn,112Sn (data inside gr=6.2ο) R21 = C exp ( α N ) •86Kr+64Ni,58Ni (data outside gr=3.5o) G.Souliotis et al. PRC68

Isoscaling Parameter α vs Charge Equilibration • 86Kr+124Sn,112Sn • 86Kr+64Ni,58Ni α =0.43 α =0.27 R21 = C exp ( α N ) Cold α = 4 Csym/T ( (Z/A)12 – (Z/A)22 ) Hot Quasi-projectiles 1: n-poor 2:nrich G.A. Souliotis et al., Phys. Rev. C 68, 024605 (2003)

86Kr, 64Ni, 136Xe data: Isocaling parameter α vs Δ(Z/A)2:  N/Z equilibrated !  negligible pre-eq. ! c = 19.9 0.2 *  2.0 MeV/u 86Kr+64,58Ni c = 16.5 0.2 *  2.4 MeV/u 64Ni+124,112Sn 64Ni+64,58Ni 64Ni+232Th,208Pb c = 13.30.4 *  2.9 MeV/u Quasi-projectiles : E/A ~20-25 MeV α = 4Csym/T ( (Z/A)12 – (Z/A)22 ) Hot c 86Kr+124Sn,112Sn No N/Z equil. Z=32 Z=33 Cold 136Xe+124,112Sn 136Xe+64,58Ni 136Xe+232Th,197Au c = 13.10.6 *  2.8 MeV/u G.Souliotis et al.

Variation vs excitation energy Data : 86Kr+124,112Sn 86Kr+64,58Ni 64Ni+ Ni,Sn,Th-Pb 136Xe+Ni,Sn,Th-Au Calculation: Mononucleus expansion model (L. Sobotka, J. Toke) Csym = c T / 4 Very asy-stiff below saturation G.Souliotis et al.

data QP Isospin diffusion and imbalance ratio (1) Tsang et al., PRL92(2004) Ni + Ni @ 52 74 AMeV Ni + Au @ 52 74 AMeV INDRA data: Galichet at al. (2005) data QP Imbalance ratio exp.deduced from α

Isospin diffusion and imbalance ratio (2) Stochastic BNV calculations (b=8-10 fm) gas P T T P BUU calculations (b = 6 fm) Imbalance ratio constructed from I Tsang et al., PRL92(2004) Ternary events ? Baran et al., (2005)

IMF properties in neutron-rich systems @600 AMeV M.Veselsky et al., PRC62(2000) Breakup of projectile spectators C.Sfienti et al., nucl-ex/0410044 From isoscaling analysis Veselsky et al., PRC69(2004)

Isotopic composition of sources (vs. centrality or rapidity) Cd114 + Mo98 @ 50 AMeV (mid-rapidity source) H.Xu et al., PRC65(2002) Milazzo et al., NPA703(2002): Ni + Ni @30 AMeV ! Neck Dynamics

Isotopic content of pre-equilibrium emission at Fermi energies Baran et al., NPA703(2002) AMD: Ono et al., PRC68(2003) 35 AMeV Sn + Sn, 50 AMeV b = 2 fm IQMD calculations: J-Y Liu et al., PRC70(2004) BUU calculations

Correlation functions and p.e. isotopic content L-W Chen et al., PRL90(2003) Isospin momentum dep.: m*n>m*p Symmetry pot. reduction at high momenta Sn132+Sn124 Asy-stiff Asy-soft dN/dy dNn/dNp B-A Li et al., NPA735(2004) Pt(GeV/c)

Gas asymmetry J.Rizzo et al., (2005) Asy-soft Asy-stiff (<0/8) Sn124+Sn124 @50 AMeV, b=2 fm m*n>m*p m*n<m*p J.Rizzo et al., (2005) Asy-soft Asy-stiff Asy-soft Asy-stiff t=60 fm/c t=80 fm/c t=100 fm/c

Pre-equilibrium dipole emission (1) O + Mo @ 4,8,14,20 AMeV Ca + Mo @ 4 AMeV O20 + Mg20 @ 1 AMeV, Simenel et al., PRL86(2001) Baran et al., PRL87(2001)

Pre-equilibrium dipole emission (2) S32 + Mo100 (6 AMeV) S32 + Mo100 (9 AMeV) D(t) Dk(t) time(fm/c) Pre-equilibrium dipole emission (2) @25 AMeV M.Papa et al., PRC68(2003) D.Pierroutsakou et al. (2005) Cooling in hot fusion ?

The isospin tracer Ru,Zr combinations |Rz| = 1 transparency Ru + Ru @ 400 AMeV Comparison with IQMD calculations The isospin tracer Ru,Zr combinations |Rz| = 1 transparency Rz = 0 full stopping IQMD calculations Rami et al, PRL84(2000), Hong et al., PRC66(2002) Q.Li and Z.Li, PRC64(2001)

Gaitanos et al, PLB595(2004), RBUU calculations 0.4 AGev 1.528 AGev Hong et al., PRC66(2002) Gaitanos et al, PLB595(2004), RBUU calculations

IQMD calculations: Stopping and iso-fractionation n-p differential rapidity distribution information on stopping (Imbalance ratio constructed with t/He3) @100 AMev (right panel) fractionation effects on top of semi-transparency Q.Li and Z.Li, PRC64(2001)

Some considerations … Improve identification of sources: contamination from pre-equilibrium emission,… (also in dynamical calculations) Study emission time of all products, not only of nucleons (vd. neck emission) Check thermal equilibrium of sources (see Geraci et al.) In hybrid calculations, the statistical model should have the same symmetry energy coefficient as the dynamical model at the moment of fragment formation Compensative effects between variances (symmetry energy value) and iso-distillation ,Δ(Z/A)², in isoscaling parameters. Check directly isotopic distributions.

Some considerations… Isoscaling is expected on a very general basis, just assuming that isovector fluctuations have a gaussian shape: P(δρn – δρp) ~ exp – [(δρn – δρp)² / (σ´(ρ,T)/V)] P(N,Z) ~ exp –{ [(N-Z) - (Nº-Zº)]² / (A σ(ρ,T)) } = exp –{ a(N-Z)²/A - bN-cZ} b = (4 (Zº/ Aº)² - 1) / σ ; c = (4 (Nº/ Aº)²- 1) / σ α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ] / σ The relation between σ and the symmetry energy coefficient depends on the fragmentation mechanism