1. Mauro BrunoBologna UniversityINFN-Bologna (Italy) H.Jaqaman et al. PRC27(1983)2782 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) (finite, charged, 2 components) observables to identify phase transition observables to identify phase transition Study: systems at different excitation energies peripheral reactions – excitation function peripheral reactions – excitation function central reactions – well defined excitation energy central reactions – well defined excitation energy Starting from measured reaction products get information on:  primary partitions  equilibrium  critical behaviour  thermodynamical signals

3. Heavy Ion collisions at intermediate energies Vacuum (10 -6 mb) ~100 fm/c DETECTOR ~20 fm/c (10 -22 sec) ~100 ÷ 1000 fm/c ~10 14 fm/c Expansion The decaying system can be identified and its calorimetric excitation energy results from the energy balance: 4device 4device

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

5. Sources at same  * : liquid, vapor & droplets Multics: Central from Z 0 =85 to Z 0 =100 (lines) Multics: Au peripheral Z 0 =79 (symbols) Isis: π+Au 8 GeV/c NPA734(2004)487 Fasa: p,α+Au 4-14 GeV NPA709(2002)392 A.Bonasera, Phys.World Feb.1999 Au nuclei: Multics-NPA650(1999)329 H clusters: B.Farizon, PRL81(1999)4108 Is the multifragmentation a thermal critical phenomenon? Z -2.1

6. Au Liquid-Gas         c  eV IsIs PRL2002 J.Finn et al PRL1982 p+Xe 80-350 GeV A -2.64 n A =q 0 A -  exp(- c 0  A  ) T Fisher 1967 Multics NPA724 (2003) 455 Power-laws are free of scales All the information falls on a single curve Scaled yield: n A /(q 0 A -   Scaled temperature:  A  / T EoS PRC2003 Critical exponents from moment analysis m 1 = ∑n s s ~ |ε| -β m 2 = ∑n s s 2 ~ |ε| -γ m k = ∑n s s k ~ |ε| (τ-1-k)/σ σ= (τ-2)/β Self similarity and scaling NO: The system is finite: power-laws are found at all densities inside the coexistence region (Lattice-gas) Can we conclude that the system reached the critical point?

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

8. Microcanonical thermodynamics of finite systems We can back-trace from data the average volume (ρ) of the system E*= E config + E kin E*= E coul (V)+Q v + E int (T)+E tr (T) Events sorted as a function of E* (calorimetry) the temperature T under the constraint of energy conservation Multics-Nucl.Phys.A699(2002)795

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

10. Early information from measured observables : Temperature Isotope thermometer P.M.Milazzo,PRC58(1998) 953 Indra correlation data N.Marie,PRC58(1998)256 =(3/2) T+ T 2 Multics-NPA699(2002)795 T, E int from independent measurements/methods Liquid-drop Aladin PRL1995

11. Microcanonical heat capacity from fluctuations E*=E config +E kin (  2 config =  2 kin ) Ph.Chomaz, F.Gulminelli, NPA 647(1999) 153 E kin = E trasl (T)+E internal (T) E config =Q v +E coul (V) The system being thermodynamically characterized: Multics-PLB473 (2000) 219;NPA699 (2002) 795;NPA734 (2004) 512 Microcanonical fluctuations larger than the canonical expectation? C kin /C = 1-  2 kin /  2 can where:  2 can =T 2 C kin =T 2 dE kin /dT

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

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

14. What is left for future measurements? COINCIDENT EXPERIMENTAL INFORMATION Multics E 1 =2  0.3 E 2 =6.5  0.7 Isis E 1 =2.5 E 2 =7. Indra E 2 =6.  0.5  Coincident experimental 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 !! Multics NPA 2004 E * /A (A.MeV)  A better quantitative nuclear metrology of hot nuclei

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

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

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

18. Experiments with n-rich/poor systems 32 S+ 58 Ni and 32 S+ 64 Ni 14.5 AMeV 3-IMF events T iso ≈ 3.5 MeV 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) α-α p-Li 7 d-α nucl-ex collaboration&garfield

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