J. Su( 苏军 ) and F.S. Zhang( 张丰收 ) College of Nuclear Science and Technology Beijing Normal University, Beijing, China Tel: ， Fax: 第十四届全国核结构大会 ， ，湖州 Nuclear temperature in heavy ion collisions

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

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 =number of degree of freedom * 1/2k B T Introduction

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

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 ?

张丰收等， IMP ， HEPNP16(1992)666

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

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

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

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

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

 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

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)

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

 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).

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

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

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: Isospin dependent quantum Isospin dependent quantum molecular dynamics model molecular dynamics model

From QMD model to IQMD model lmean field (corresponds to interactions)  two-body collisions  Pauli blocking  initialization  coalescence model U loc : density dependent potential U Yuk : Yukawa (surface) potential U Coul : Coulomb energy U Sym : symmetry energy U MD : momentum dependent interaction

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, (2011)

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

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

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

J. Su and F. S. Zhang, PRC (2011) Results and Discussion Charge and Z bound distributions and Z max /Z p ~ Z bound /Z p

T z and mass dependence of T HeLi  The isotope temperatures show a smooth fall with increasing Z bound /Z p 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)+ 40 Ca J. Su, B. A. Bian, and F. S. Zhang, PRC 84, (2011)

20 天发表 !

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

Recommend a book by TAMÁS SÁNDOR BIRÓ,

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