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Thermodynamical aspects in heavy ion reactions

H.Jaqaman et al. PRC27(1983)2782. Mauro Bruno. Bologna University. INFN-Bologna (Italy). Thermodynamical aspects in heavy ion reactions. Experimental Investigation of a van der Waals nuclear fluid-H.I. Collisions. Aims: study thermodynamics of nuclear systems

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Thermodynamical aspects in heavy ion reactions

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  1. H.Jaqaman et al. PRC27(1983)2782 Mauro Bruno Bologna University INFN-Bologna (Italy) Thermodynamical aspects in heavy ion reactions

  2. Experimental Investigation of a van der Waals nuclear fluid-H.I. Collisions Aims: study thermodynamics of nuclear systems (finite, charged, 2 components) observables to identify phase transition Study: systems at different excitation energies peripheral reactions – excitation function central reactions – well defined excitation energy Starting from measured reaction products get information on: • primary partitions • equilibrium • critical behaviour • thermodynamical signals

  3. 4device D E T E C T O R ~100÷1000 fm/c ~100 fm/c ~1014 fm/c ~20 fm/c (10-22 sec) Heavy Ion collisions at intermediate energies Expansion Vacuum (10-6 mb) The decaying system can be identified and its calorimetric excitation energy results from the energy balance:

  4. How to assess the source equilibration ? • isotropy • uniform population of the phase space • independence on the entrance channel • scaling Multics-NPA650 (1999) 329 Multics-NPA724 (2003) 329 Sorting the events: multidimensional analysis Peripheral (binary) collisions: two sources Central collisions: one source

  5. A.Bonasera, Phys.World Feb.1999 Au nuclei: Multics-NPA650(1999)329 H clusters: B.Farizon, PRL81(1999)4108 Multics: Central from Z0=85 to Z0=100 (lines) Multics: Au peripheral Z0=79 (symbols) Isis: π+Au 8 GeV/c NPA734(2004)487 Fasa: p,α+Au 4-14 GeV NPA709(2002)392 Is the multifragmentation a thermal critical phenomenon? Sources at same *: liquid, vapor & droplets Z-2.1

  6. p+Xe 80-350 GeV Multics NPA724 (2003) 455 Fisher 1967 nA=q0A-exp(- c0A) T Scaled yield:nA/(q0A- Scaled temperature: A/T IsIs PRL2002 Can we conclude that the system reached the critical point? EoS PRC2003 Au Liquid-Gas  •  εceV m1 = ∑nss ~ |ε|-β m2 = ∑nss2 ~|ε|-γ mk = ∑nssk ~ |ε| (τ-1-k)/σ σ=(τ-2)/β NO: The system is finite: power-laws are found at all densities inside the coexistence region (Lattice-gas) J.Finn et al PRL1982 Self similarity and scaling Power-laws are free of scales All the information falls on a single curve A-2.64 Critical exponents from moment analysis

  7. Experimentally 100 The transition is smoothed 10 probability 1 two states populated at the same temperature 0.1 energy 100 10 probability 1 0.1 energy Canonical thermodynamicsLattice-gas theory F.Gulminelli et al. PRL91(2003)202701 Liquid Gas Infinite System Liquid Gas Finite System

  8. Microcanonical thermodynamics of finite systems Events sorted as a function of E*(calorimetry) E*= Econfig + Ekin E*= Ecoul(V)+Qv+ Eint(T)+Etr(T) We can back-trace from data • the average volume (ρ) of the system • the temperature T under the constraint of energy conservation Multics-Nucl.Phys.A699(2002)795

  9. Circles=Multics data Squares=Coulomb trajectories Early information from measured observables: average volume

  10. Liquid-drop <Ekin>=(3/2) <m-1>T+<aAIMF>T2Multics-NPA699(2002)795 Isotope thermometerP.M.Milazzo,PRC58(1998) 953 Indra correlation data N.Marie,PRC58(1998)256 T, Eint from independent measurements/methods Early information from measured observables : Temperature Aladin PRL1995

  11. Econfig=Qv+Ecoul(V) Ekin= Etrasl(T)+Einternal(T) Microcanonical heat capacity from fluctuations E*=Econfig+Ekin (2config= 2kin) The system being thermodynamically characterized: Ph.Chomaz , F.Gulminelli, NPA 647(1999) 153 Ckin/C = 1-2kin/2can where: 2can=T2Ckin=T2dEkin/dT Microcanonical fluctuations larger than the canonical expectation? Multics-PLB473(2000) 219;NPA699 (2002) 795;NPA734 (2004) 512

  12. Indra: NPA699(2002)795 Au+C Au+Cu Au+Au Heat capacity from fluctuations Multics: PLB473 (2000) 219 NPA699 (2002) 795 NPA734 (2004) 512 Grey area: peripheral collisions Points: central collisions: 1-st order phase transition

  13. Au Liquid-Gas  •  εceV Liquid-drop Z B I G Asym 12 Critical behavior inside the coexistence region Liquid-gas phase transition: is the game over?

  14. Multics NPA 2004 E*/A (A.MeV) Multics E1=20.3 E2=6.50.7 Isis E1=2.5 E2 =7. Indra E2=6.0.5 What is left for future measurements? COINCIDENT EXPERIMENTAL INFORMATION • A better quantitative nuclear metrology of hot nuclei • Coincidentexperimental information are needed on: • critical partitioning of the system, fluctuations • calorimetric excitation energy • isotopic temperature • proximity of the decay products 4π mass and charge detection !!

  15. J.Besprosvany and S.Levit - PLB 217 (1989) 1 N=Z 2-nd generation devices and exotic beams are needed, to fully investigate the phase transition What is left for future measurements?an extra dimension of the EoS by changing: • the Coulomb properties • the isospin content (N/Z) of the fragmenting source T reaches a saturation at multifragmentation Protonrich nuclei (A≈100): vanishing limiting temperature The saturation value decreases for increasing size

  16. Starting from the liquid side EP/AP < 25 A MeVAP+T~100 (Laboratori Nazionali di Legnaro-INFN-Italy) Side Isotope Array nucl-ex collaboration: garfield apparatus • Low energy thresholds (ionization chambers as ΔE) • High granularity: 400 ΔE-E telescopes 4o-150o • A identification (1<=Z<=8) up to 90o • Digital electronics for CsI pulse-shape discrimination (A identification Z<=4)

  17. Experiments with n-rich/poor systems32S+58Ni and 32S+64Ni 14.5 AMeV nucl-ex collaboration&garfield

  18. α-α p-Li7 d-α Tiso ≈ 3.5 MeV Experiments with n-rich/poor systems32S+58Ni and 32S+64Ni 14.5 AMeV 3-IMF events Before concluding about the temperature: • thermodynamical characterization of the source is needed • isotope emission time scales have to be checked through correlation functions (intensity interferometry) nucl-ex collaboration&garfield

  19. Multics NPA 2004 E*/A (A.MeV) Multics E1=20.3 E2=6.50.7 Isis E1=2.5 E2 =7. Indra E2=6.0.5 1+R(q) 1+R(q) Conclusions • The physics of hot nuclei: a unique laboratory • for the thermodynamics of finite, charged, 2-component systems • fora quantitative nuclear metrology • for interdisciplinary connections • We need: • 4 mass and charge detection • 20-50 A.MeV radioactive beams nucl-ex collaboration&garfield

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