Isospin observables Mechanisms sensitive to symmetry energy Observables

Isospin observables Mechanisms sensitive to symmetry energy Observables • Dilute asymmetric matter and related instabilities New features of the liquid-gas phase transition • N/Z of fragments, Isoscaling • Fragmentation in semiperipheral reactions at the Fermi energies and degree of equilibration • Isospin diffusion, Imbalance ratio • 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 • 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+/K 0

Isoscaling: experiments and comparison with statistical (hybrid) models (1) Xu et al. , PRL 85(2000) Tan et al. , PRC 64(2001) N Sn 124 -Sn 112 combinations @ 50 AMe. V Comparison with SMM-MSU (inputs from BUU, E*=4 -6 Me. V) Isoscaling in Lattice Gas Model: Y. G. Ma et al. , PRC 69 nearly linear relation with N/Z ρn = exp(α) Shetty et al. , PRC 70(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. PRC 64(2001) γ~19 Me. V (SMM-Mc. Gill, canonical)

Isoscaling analysis in dynamical models Stochastic BNV calculations T. X. Liu et al. , PRC 69(2004) AMD: Ono et al. , PRC 68(2003) 50 AMe. V 35 AMe. V 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. , NPA 732(2004) A. Botvina et al. , PRC 65(2002): H + Sn 112, 124 @ 6. 7 Ge. V He 4 + Sn 112, 124 @ 15. 3 Ge. V Shetty et al. , PRC 70(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 C 12 + Sn 112, 124 @ 300, 600 AMe. V Fragmentation of excited target residues Central collisions 18 O on 9 Be @ 60 AMe. V, Fang et al. , PRC 61(2000)

Isoscaling in Deep-Inelastic Collisions: PLF sources 25 AMe. V R 21 (N, Z) = Y 2/Y 1 • 86 Kr+124 Sn, 112 Sn (data inside gr=6. 2ο) R 21 = C exp ( α N ) • 86 Kr+64 Ni, 58 Ni (data outside gr=3. 5 o) G. Souliotis et al. PRC 68

Isoscaling Parameter α vs Charge Equilibration α =0. 43 α =0. 27 • 86 Kr+124 Sn, 112 Sn • 86 Kr+64 Ni, 58 Ni R 21 = C exp ( α N ) Cold α = 4 Csym/T ( (Z/A)12 – (Z/A)22 ) Quasi-projectiles 1: n-poor 2: nrich G. A. Souliotis et al. , Phys. Rev. C 68, 024605 (2003) Hot

86 Kr, 64 Ni, 136 Xe data: Isocaling parameter α vs Δ(Z/A)2: N/Z equilibrated ! negligible pre-eq. ! α = 4 Csym/T ( (Z/A)12 – (Z/A)22 ) Quasi-projectiles : E/A ~20 -25 Me. V Hot c = 19. 9 0. 2 c * 2. 0 Me. V/u 86 Kr+124 Sn, 112 Sn 86 Kr+64, 58 Ni c = 16. 5 0. 2 * 2. 4 Me. V/u No N/Z equil. Z=32 Z=33 64 Ni+124, 112 Sn 64 Ni+64, 58 Ni Cold 136 Xe+124, 112 Sn 136 Xe+64, 58 Ni 136 Xe+232 Th, 197 Au 64 Ni+232 Th, 208 Pb c = 13. 3 0. 4 * 2. 9 Me. V/u c = 13. 1 0. 6 * 2. 8 Me. V/u G. Souliotis et al.

Variation vs excitation energy Data : 86 Kr+124, 112 Sn 86 Kr+64, 58 Ni 64 Ni+ Ni, Sn, Th-Pb 136 Xe+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.

Isospin diffusion and imbalance ratio (1) Tsang et al. , PRL 92(2004) INDRA data: Galichet at al. (2005) • data QP Ni + Au @ 52 74 AMe. V Ni + Ni @ 52 74 AMe. V Imbalance ratio exp. deduced from α

Isospin diffusion and imbalance ratio (2) Stochastic BNV calculations (b=8 -10 fm) P T gas T P BUU calculations (b = 6 fm) Imbalance ratio constructed from I Tsang et al. , PRL 92(2004) Ternary events ? Baran et al. , (2005)

IMF properties in neutron-rich systems @600 AMe. V M. Veselsky et al. , PRC 62(2000) Breakup of projectile spectators C. Sfienti et al. , nucl-ex/0410044 From isoscaling analysis Veselsky et al. , PRC 69(2004)

Isotopic composition of sources (vs. centrality or rapidity) Cd 114 + Mo 98 @ 50 AMe. V (mid-rapidity source) H. Xu et al. , PRC 65(2002) Milazzo et al. , NPA 703(2002): Ni + Ni @30 AMe. V ! Neck Dynamics

Isotopic content of pre-equilibrium emission at Fermi energies Baran et al. , NPA 703(2002) AMD: Ono et al. , PRC 68(2003) 35 AMe. V Sn + Sn, 50 AMe. V b = 2 fm IQMD calculations: J-Y Liu et al. , PRC 70(2004) BUU calculations

Correlation functions and p. e. isotopic content L-W Chen et al. , PRL 90(2003) Isospin momentum dep. : m*n>m*p Symmetry pot. reduction at high momenta Sn 132+Sn 124 d. Nn/d. Np d. N/dy Asy-stiff Asy-soft B-A Li et al. , NPA 735(2004) Pt(Ge. V/c)

Gas asymmetry ( < 0/8) Asy-soft Asy-stiff Sn 124+Sn 124 @50 AMe. V, b=2 fm m*n>m*p m*n<m*p J. Rizzo et al. , (2005) Asy-soft t=60 fm/c t=80 fm/c t=100 fm/c Asy-stiff Asy-soft Asy-stiff

Pre-equilibrium dipole emission (1) O + Mo @ 4, 8, 14, 20 AMe. V Ca + Mo @ 4 AMe. V O 20 + Mg 20 @ 1 AMe. V, Simenel et al. , PRL 86(2001) Baran et al. , PRL 87(2001)

Pre-equilibrium dipole emission (2) Dk(t) D(t) S 32 + Mo 100 (6 AMe. V) Dk(t) D(t) time(fm/c) S 32 + Mo 100 (9 AMe. V) time(fm/c) D. Pierroutsakou et al. (2005) @25 AMe. V D(t) M. Papa et al. , PRC 68(2003) Cooling in hot fusion ?

Ru + Ru @ 400 AMe. V Comparison with IQMD calculations The isospin tracer Ru, Zr combinations |Rz| = 1 transparency Rz = 0 full stopping IQMD calculations Rami et al, PRL 84(2000), Hong et al. , PRC 66(2002) Q. Li and Z. Li, PRC 64(2001)

0. 4 AGev Hong et al. , PRC 66(2002) 1. 528 AGev Gaitanos et al, PLB 595(2004), RBUU calculations

IQMD calculations: Stopping and iso-fractionation n-p differential rapidity distribution information on stopping (Imbalance ratio constructed with t/He 3) @100 AMev (right panel) fractionation effects on top of semi-transparency Q. Li and Z. Li, PRC 64(2001)

Some considerations … üImprove 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) üCheck thermal equilibrium of sources (see Geraci et al. ) üIn hybrid calculations, the statistical model should have the same symmetry energy coefficient as the dynamical model at the moment of fragment formation üCompensative effects between variances (symmetry energy value) and isodistillation , 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 - b. N-c. Z} b = (4 (Zº/ Aº)² - 1) / σ ; c = (4 (Nº/ Aº)²- 1) / σ α = 4 [ (Zº/ Aº)² 1 - (Zº/ Aº)² 2 ] / σ The relation between σ and the symmetry energy coefficient depends on the fragmentation mechanism