Determination of freeze-out temperatures Excellent consistency with thermal equilibrium for central collisions near the multi-fragmentation threshold Deduced.

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Determination of freeze-out temperatures Excellent consistency with thermal equilibrium for central collisions near the multi-fragmentation threshold Deduced temperatures are close to SMM+MSUdecay predictions. M.J. Huang et al, (1996)  MeV 0.0  MeV 4 He p+ 3 H  g.s. Exited state populations: Isotope double ratios: Au+Au, E/A = 35 MeV Central collisions PRL, 78, 1648 (1997)

Comparison of He excited state T( 4 He * ) and isotope ratio T iso (He) Sequential decays should affect T( 4 He * ) and T iso (He) the same Experimentally, T( 4 He * ) behaves very differently than T iso (He). PLB, 431, 8 (1998)PRC, 58, 2636 (1998)

Grand canonical temperature vs. canonical temperature PRC, 64, (2001)

Summary– How well can we measure temperature Q: What is temperature A: Due to lack of consistency in temperature measurements at high energy (E/A>40 MeV), temperature can be measured well only in systems with low excitation (E/A<35 MeV, T~4 MeV). Reality constraints including sequential decays may put a limit on the temperature measurement. System studied: Au+Au, E/A=35 MeV, PRL, 78, 1648 (1997) Ar+Sc, Kr+Ni E/A= MeV, PRC, 58, 2636 (1998) MSU Sequential decay calc, PLB, 431, 8 (1998) Grand canonical and canonical calculations, PRC, 64, (2001)

Summary Q: What is equilibrium? Q: How far from equilibrium are the reactions? Q: How can one determine kinetic, chemical or isospin equilibrium? Q: What is the meaning of temperature? Q: What values of temperatures are observed or calculated? Systems studied: Models used in the calc’s: