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In-medium properties of nuclear fragments at the liquid-gas phase coexistence

International Nuclear Physics Conference INPC2007 Tokyo, Japan, June 3-8, 2007. In-medium properties of nuclear fragments at the liquid-gas phase coexistence. A.S. Botvina 1,2,3. ( In collaboration with W.Trautmann, I.Mishustin, N.Buyukcizmeci, R.Ogul ).

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In-medium properties of nuclear fragments at the liquid-gas phase coexistence

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  1. International Nuclear Physics Conference INPC2007 Tokyo, Japan, June 3-8, 2007 In-medium properties of nuclear fragments at the liquid-gas phase coexistence A.S. Botvina1,2,3 (In collaboration with W.Trautmann, I.Mishustin, N.Buyukcizmeci, R.Ogul) 1Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia 2Frankfurt Institute for Advanced Studies, J.W.Göthe University, Frankfurt am Main, Germany 3Gesellschaft für Schwerionenforschung, Darmstadt, Germany

  2. 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. 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 0.1ρ0 , 4) high degree of equilibration at the freeze-out.

  3. Thermal multifragmentation of nuclei: Production of hot fragments at temperature T ~ 3---8 MeV and density ρ ~ 0.1 ρ0 (ρ0≈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) J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Phys. Rep. 257 (1995) 133 Ensemble of nucleons and fragments in thermal equilibrium characterized by n IMF p neutron number N0 proton number Z0 , N0+Z0=A0 excitation energy E*=E0-ECN break-up volume V=(1+k)V0 HR IMF a IMF All break-up channels are enumerated by the sets of fragment multiplicities or partitions, f={NAZ} Statistical distribution of probabilities: Wf ~ exp {Sf (A0, Z0, E*,V)} under conditions of baryon number (A), electric charge (Z) and energy (E*) conservation

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

  6. ALADINdata GSI multifragmentation of relativistic projectiles 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 (B0) and symmetry (γ) energy coefficients in the multifragmentation scenario Fsym = γ·(N-Z)2/A Fsuf = B0f(T)A2/3

  8. Isoscaling and the symmetry coefficient γ ALADIN: 12C+ 112,124Sn A.Le Fevre et al., Phys.Rev.Lett 94(2005)162701 S(N)=Y(124Sn)/Y(112Sn)=C∙exp(N∙α+Z∙β) α·T≈ -4γ (Z12/A12-Z22/A22)

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

  10. 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 Fsuf = B0((Tc2-T2)/(Tc2+T2))5/4A2/3 Fsym = γ·(N-Z)2/A

  11. Properties of hot fragments: the surface energy termB0Z-τ analysis of IMF yields projectiles with different isospin SMM ALADIN A.S.Botvina et al., PRC74(2006)044609

  12. We analyze all previous observables: distributions of IMF , Zmax , T , ... vs Zbound , 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) We obtain an evolution of the surface energy of hot fragments toward region of full multifragmentation

  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

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