1. In-medium properties of nuclear fragments at the liquid-gas phase coexistence International Nuclear Physics Conference INPC2007 Tokyo, Japan, June 3-8, 2007 A.S. Botvina 1,2,3 1 Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia 2 Frankfurt Institute for Advanced Studies, J.W.Göthe University, Frankfurt am Main, Germany 3 Gesellschaft für Schwerionenforschung, Darmstadt, Germany ( In collaboration with W.Trautmann, I.Mishustin, N.Buyukcizmeci, R.Ogul )

2. Experimentally established: 1) few stages of reactions leading to multifragmentation, 2) short time ~100fm/c for primary fragment production, 3) freeze-out density is around 0.1ρ 0, 4) high degree of equilibration at the freeze-out. Multifragmentation of nuclei takes place in reactions initiated by all high energy particles (hadrons, heavy-ions, photons), where high excitation energy of residual nuclei is reached.

3. Thermal multifragmentation of nuclei: Production of hot fragments at temperature T ~ 3---8 MeV and density ρ ~ 0.1 ρ 0 (ρ 0 ≈0.15 fm -3 ) Interpretation: liquid-gas phase transition in finite nuclei. Investigation of properties of fragments surrounded by nuclear species.

4. Statistical Multifragmentation Model (SMM) IMF HR a Ensemble of nucleons and fragments in thermal equilibrium characterized by neutron number N 0 proton number Z 0, N 0 +Z 0 =A 0 excitation energy E * =E 0 -E CN break-up volume V=(1+ k )V 0 All break-up channels are enumerated by the sets of fragment multiplicities or partitions, f={N AZ } J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Phys. Rep. 257 (1995) 133 n p Statistical distribution of probabilities: W f ~ exp {S f (A 0, Z 0, E *,V)} under conditions of baryon number (A), electric charge (Z) and energy (E*) conservation

5. Fragments obey Boltzmann statistics, liquid-drop description of individual fragments, Coulomb interaction in the Wigner-Seitz approximation free energy of channel: individual fragments: Probability of channel: mass and charge conservation Energy conservation entropy of channel

6. ALADIN data multifragmentation of relativistic projectiles GSI A.S.Botvina et al., Nucl.Phys. A584(1995)737 H.Xi et al., Z.Phys. A359(1997)397 comparison with SMM (statistical multifragmentation model) Statistical equilibrium has been reached in these reactions

7. The surface ( B 0 ) and symmetry (γ) energy coefficients in the multifragmentation scenario F sym = γ·(N-Z) 2 /A F suf = B 0 f(T)A 2/3

8. Isoscaling and the symmetry coefficient γ α·T ≈ -4γ (Z 1 2 /A 1 2 -Z 2 2 /A 2 2 ) S(N)=Y( 124 Sn)/Y( 112 Sn)=C∙exp(N∙ α +Z∙ β ) ALADIN: 12 C+ 112,124 Sn A.Le Fevre et al., Phys.Rev.Lett 94(2005)162701

9. 1AGeV A 25AMeV γ=25 γ=15 Z/A The symmetry energy coefficient γ and isospin of fragments G.Souliotis et al., PRC75(2007)011601A.S.Botvina et al., PRC72(2005)048801

10. F suf = B 0 ((T c 2 -T 2 )/(T c 2 +T 2 )) 5/4 A 2/3 F sym = γ·(N-Z) 2 /A One can distinguish effects of the surface and symmetry energies since the charge yield of fragments is very sensitive to the surface: A.S.Botvina et al., PRC74(2006)044609

11. Properties of hot fragments: the surface energy term B 0 Z -τ analysis of IMF yields A.S.Botvina et al., PRC74(2006)044609 projectiles with different isospin ALADIN SMM

12. We obtain an evolution of the surface energy of hot fragments toward region of full multifragmentation We analyze all previous observables: distributions of IMF, Z max, T,... vs Z bound, and involve additionally new τ - observables for each projectile (Xe, Au, U) for single isolated nuclei: C -- Cameron mass formula (1957) MS -- Myers-Swiatecki mass formula (1966) (include separate volume and surface contributions to the symmetry energy)

13. Conclusions Multifragmentation reactions can be interpreted as a manifestation of the liquid-gas type phase transition in finite nuclei, and allow for investigating the phase diagram of nuclear matter. One can investigate properties of hot nuclei/fragments surrounded by other nuclear species. By analyzing experimental data it was found: -- decreasing the symmetry energy of primary hot fragments by ~ 40% when the systems evolve toward full multifragmentation (with increasing excitation energy and decreasing the freeze-out density): ALADIN, FRS, MARS; -- as a result of the same process the surface energy of these fragments becomes independent on their isospin, this means that the difference between surface and volume symmetry energies (as adopted in some mass formulas for isolated nuclei) disappears also: ALADIN. Important applications in astrophysics: since mass distributions of fragments in stellar matter, and electro-weak reactions are very sensitive to the symmetry energy A.Botvina and I.Mishustin, PRC72(2005)048801