J. Su( 苏军 ) and F.S. Zhang( 张丰收 ) College of Nuclear Science and Technology

1. 第十四届全国核结构大会 ，2012.4.12-16，湖州 Nuclear temperature in heavy ion collisions J. Su(苏军)and F.S. Zhang(张丰收) College of Nuclear Science and Technology Beijing Normal University, Beijing, China Tel: 010-6220 5602，6220 8252-806 Fax: 010-6223 1765 E-mail: fszhang@bnu.edu.cn http://lenp.bnu.edu.cn/hkxyweb/zhangfengshou.htm

4. Outline  Introduction  Thermometer determination  Theoretical model  Results and discussion  Conclusions and perspectives

5. Introduction Definition of Temperature 1.Thermodynamics and Statistical mechanics: with fixed number of particles N at an energy E 2.The kinetic theory of gases : T in a classical ideal gas is related to its average kinetic energy <Ek>=number of degree of freedom * 1/2kBT

6. v=0.1-0.5c Projectile Target Nuclear dynamics at intermediate and high energies by a transport model ? Dense and hot nuclear matter Detectors R =? Equation of State Of Nuclear Matter E(r,T,p)=？ Liquid-to-Gas Phase transition? T=? What happened? Shape? Size? Lifetime?

7. From compound nuclei (  0, T1-2 MeV,) hot nuclei(  0,T>5 MeV), highly excited nuclei (  30,T>5 MeV) asymmetrical highly excited nuclei (  30,T>5 MeV, >0) Physical indications IEOS  0, T > 0,  >0 E(, T, ) = ?, How to determine T in theory ?

8. 张丰收等，IMP， HEPNP16(1992)666

9. Pochodzalla et al., ALADIN, PRL75(1995)1040 李文飞等，IMP， HEPNP25(2001)538

10. BUUBLE Zhang and Eric, PLB319(1993)35

11. Zhang and Suraud, Phys. Rev. C51,1995,3201 40Ca+40Ca, 90 MeV/u

13. v=0.1-0.5c Projectile Target Nuclear dynamics at intermediate and high energies by a transport model How to determine T From experiments? ? Dense and hot nuclear matter R =? T=? Detectors What happened? Equation of State Of Nuclear Matter E(r,T,p)=？ Liquid-to-Gas Phase transition? Shape? Size? Lifetime?

14. Thermometer determination 1. Kinetic approaches Based on the concept of a canonical ensemble. The temperature is extracted from the particle kinetic-energy spectra. 2. Population approaches Based on the grand-canonical concept. The temperature is extracted from the yields of the productions. 3. Double ratios of isotopic yields

15.  Kinetic approaches Originally proposed by Weisskopf in 1937in case of n-induced reactions (Maxwell-Boltzmann distribution) Slope thermometer G. D. Westfall, Phys. Lett. B 116, 118 (1982). B. V. Jacak et al., Phys. Rev. Lett. 51, 1846 (1983). Momentum fluctuation thermometer S. Wuenschel et al., Nuclear Physics A 843 (2010) 1–13

16. Slope thermometer The spectra shape can be Influenced by collective Dynamical effects • G. D. Westfall, Phys. Lett. B 116, 118 (1982) • B. V. Jacak et al., Phys. Rev. Lett. 51, 1846 (1983)

17. Momentum fluctuation thermometer S. Wuenschel et al., Nuclear Physics A 843 (2010) 1–13

18.  Population of excited states The ration of the populations of 2 states Correction: decay, final-state interaction,… • D.J. Morrissey et al., Phys. Lett. B 148, 423 (1984).

19.  Double ratios of isotopic yields density Ratio between the 2 different emitted fragments Temperature S. Albergo et al., Nuovo Cimento A 89, 1 (1985)

20. Theoretical Model (IQMD+Gemini) excited pre-fragments final products hot nuclear system t deexcitation Multifragmentation 50 fm/c 200 fm/c Isospin-dependent Quantum Molecular Dynamics model statistical decay model (GEMINI)

21. Isospin dependent quantum molecular dynamics model • Quantum molecular dynamics model (QMD) • The QMD model represents the many body state of the system and thus contains correlation effects to all orders. In QMD, nucleon i is represented by a Gaussian form of wave function. • After performing Wigner transformations, the density distribution of nucleon i is:

22. Uloc : density dependent potential UYuk: Yukawa (surface) potential UCoul: Coulomb energy USym: symmetry energy UMD: momentum dependent interaction From QMD model to IQMD model • mean field (corresponds to interactions) • two-body collisions • Pauli blocking • initialization • coalescence model

23. Fragment cross sections Two features (1) a minimum at Z=4 (2) Clear odd-even effect from Z=6-9 Good agreement between IQMD + GEMINI calculations and experimental data J. Su, B. A. Bian, and F. S. Zhang, PRC 83, 014608 (2011)

24. Odd-Even effect for 3 reaction systems at different energies--------Charge distributions

25. Odd-Even effect for 2 reaction systems at 400 MeV/nucleon------Neutron distributions

26. odd-even effect J. Su, B. A. Bian, and F. S. Zhang, PRC 83, 014608 (2011)

27. Results and Discussion Charge and Zbound distributions <MIMF> and Zmax/Zp ~ Zbound/Zp J. Su and F. S. Zhang, PRC 84 037601 (2011)

28. J. Su, B. A. Bian, and F. S. Zhang, PRC 84, 037601 (2011) Tz and mass dependence of THeLi The isotope temperatures show a smooth fall with increasing Zbound /Zp for the reactionsThe temperatures for the neutron-rich projectiles are larger than those for the neutron-poor projectilesThe mass effect of the isotope temperatures is found Ca, Zr, Sn, Pb (600MeV/u)+40Ca

29. 20天发表 !

30. Conclusions and perspectives 1. To verify different methods for determination of T Kinetic method, Population of excited states, Double ratios of isotopic yields 2. In each method, to know the reliability for different conditions 3. New methods are welcome for determination of T and it is still very far to get a proper definition of liquid-gas phase transitions in nuclear system

31. Recommend a book by TAMÁS SÁNDORBIRÓ,

32. HINP-BG in BNU2011-05-01 Thank youfor your attention !