World Consensus Initiative 2005 WCI3 Texas A & M University

1. World Consensus Initiative 2005 WCI3 Texas A & M University Fe. 12-16, 2005 Rolf Scharenberg & Brijesh Srivastava Department of Physics, Purdue University West Lafayette, Indiana USA

2. Scharenberg and Srivastava Separation of collision stage from remnant stage EOS Experiment 1 A GeV Au on Carbon The shaded region indicates the events with a reconstructed charge of 75-82. If all charges from the gold projectile and carbon target were collected in each event , the reconstructed charge would be 79+6=85. Distribution of the total reconstructed charge in each event. The shaded region marks the event selected for further analysis WCI 3 Ref: Phys. Rev. C57,764(1998)

3. Scharenberg and Srivastava Evidence for two reaction stages : prompt ejectiles and remnant 1. Strong component centered near ybeam and at low pt suggestive of thermal emission from the remnant In reverse kinematics, the excited remnant moves nearly beam rapidity in the lab. frame 2. The ejectile component extending to lower rapidity and high pt is indicative of prompt emission. ybeam Linear contours of transverse momentum of protons vs rapidity. The dashed curve corresponds to quasielastic scattering. Ref: Phys. Rev. C57,764(1998) WCI3

4. Scharenberg and Srivastava Laboratory rapidity distribution of light particles and heavy fragments The heavy lines correspond to ybeam The proton distribution shows a Gaussian peak centered near ybeam and a tail extending to low rapidities. The peak near ybeam represents second stage protons + some first stage. The tail at low y indicates the emission of prompt protons. The distribution of fragments heavier than He is symmetric about ybeam, implying that that these fragments are emitted only from the decaying remnant. Conclusion: Clear data sorting possible in high energy asymmetric collisions Ref: Phys. Rev. C57,764(1998) WCI3

5. Scharenberg and Srivastava Fitting data with Statistical multifragmentation model (SMM) 1. Freezeout volume and remnant mass determined on an event by event basis 2. Input energy to SMM is the excitation energy less the flow energy SMM free volume Vf = c Vrem and experimental initial free volume : SMM breakup volume Vb= (1+k )Vrem and the experimental freezeout volume from p-p correlations. p-p correlation experiments for the MF of 1A GeV Au on Au show thatthe freeze-out Volume is ~ 2VAu WCI3 Ref: Phys.Rev. C64,054602(2001)

6. Scharenberg and Srivastava Au+C @ 1AGeV Average yield of fragments as a function of multiplicity from data and SMM WCI3 Ref: Phys.Rev. C64,054602(2001)

7. Scharenberg and Srivastava Au+C at 1AGeV Charge of the largest fragment as a function of multiplicity. Average yield of intermediate mass fragments for Z=3-30 as a function of multiplicity. SMM results are shown for e0=8 and e0=16. Conclusion: SMM fits the data for all three systems with the same parameters WCI3 Ref: Phys.Rev. C64,054602(2001)

8. Scharenberg and Srivastava The EOS collaboration has studied the MF of 1A Gev Au, La and Kr on carbon. One of the important results was the possible observation of critical behavior in Au and La and the extraction of associated critical exponents. The values of these exponents are very close to those ordinary fluids indicating that MF may arise from a continuous phase transition and may belong to the same universality class as ordinary fluids. Critical Parameters from Au+C 1AGeV data mc = 22 ±1 = 4.5±0.5 MeV/nucleon Ec t = 2.19 ±0.02 g = 1.4±0.3 s = 0.54±0.11 WCI3 Ref: Phys.Rev. C 64,054602(2001)

9. Scharenberg and Srivastava Data Determination of t and mc from data (a). cn values from the power law fit to fragment mass yield distribution obtained for different m. (b). Values of t as a function of m. (c). Power law fit to data point at m = mc 2 These values of mc ,t , g, and s are used in the data scaling WCI3 Ref: Phys.Rev. C 64,054602(2001)

10. Scharenberg and Srivastava The scaling functions for data. The intersection of solid lines marks the critical point. Au+C at 1A GeV Unscaled fragment yields for 2 £ Z £ 16 Scaling Function: Ref: Phys.Rev. C 64,054602(2001) Phys.Lett. B418,34(1998) WCI3

11. Scharenberg & Srivastava Data and SMM comparison SMM Data WCI3

12. Scharenberg and Srivastava The nature of the phase transition in MF has been explored using three systems of different sizes. The experimental results validate the variable volume version of the statistical multifragmentation model (SMM). The nature of the phase transition from SMM without cooling (SMMhot) gives values of the critical exponents t, b, and g, which are close to the values for liquid-gas system. Using SMMhot with fixed size remnant the back bending in the caloric curve for Kr suggests the presence of latent heat, which is consistent with a first order phase transition. The latent heat vanishes for A ~ 160. We conclude that the larger Coulomb energy in Au reduces the latent heat required for MF and indicates critical phase transition. Ref: Phys.Rev.C 65,054617(2002) WCI3

13. Scharenberg and Srivastava Fixed remnant A = 160, Z=64 SMM hot and SMM cold Multiplicity of Z=8,10, and 12 fragments Multiplicity of Z=1 and 2 particles Second stage multiplicity WCI3

14. Scharenberg and Srivastava SMMhot A=160, Z=64 Scaling function A=160, Z=64 A=70 ,Z=30 Unscaled 1 2 3 4 5 6 7 8 Ei (MeV/nucleon) Caloric curve from SMMhot for A=70 and 160. Scaled WCI3

15. Scharenberg and Srivastava Energy and temperature at critical point as a function of system size WCI3

16. Scharenberg and Srivastava A=160 A=100 WCI3

17. CONCLUSIONS • EOS is the first work in which the nature of the phase transition in MF has been explored using three systems of different size. • The experimental results in conjunction with SMM provide the order of phase transition in Au, La and Kr. • The values of critical exponents τ, β, and , which are close to the values for liquid-gas system, along with nearly zero latent heat suggest a continuous phase transition in Au and La. • The back bending in caloric curve for Kr suggest the presence of latent heat, which is consistent with a first order phase transition. • This change in transition from Au to Kr is attributed to the Coulomb expansion energy. The Coulomb energy plays a major role in nuclear MF.