1. Z.Q. Feng( 冯兆庆 ), W.F. Li( 李文飞 ), Z.Y. Ming( 明照宇 ), L.W. Chen( 陈列文 ), F. S. Zhang ( 张丰收 ) Institute of Low Energy Nuclear Physics Beijing Normal University Tel: 010-6220 8252 Fax: 010-6223 1765 E-mail: fszhang@bnu.edu.cn Chemical instability in heavy ion collisions at high and intermediate energies

2. Outline 1 Introduction 2 Isospin dependent quantum molecular dynamics model 3 Isospin effects in nuclear multifragmentation 4 Chemical and mechanical instabilities 5 Conclusions and perspectives

3. 1 Introduction Experimental status  p(1GeV)+Kr, Xe, Ag, 1984  excited nuclei(4  detector)  Aladin, Au (600 MeV/nucl.) +X  Z bound  Miniball, Xe (30 MeV/nucl.)+X  N C, N LC, N N  Indra, Ar(32-95 MeV/nucl.)+X Xe(25-50 MeV/nucl.)+X  etc. Nuclear Multifragmentation, Zhang and Ge, Science Press, 1998

4. Au (600 MeV/nucl.) +X  Z bound (Aladin, GSI)

5. Xe (30 MeV/nucl.)+X  N C, N LC, N N (Miniball, MSU)

6. Ar(32-95 MeV/nucl.)+X Xe(25-50MeV/nucl.)+X (Indra, Ganil)

7.  Isospin effects in nuclear multifragmentation  induced by radioactive ion beams (RIB facilities) GANIL, GSI, MSU, Riken, IMP,   induced by stable nuclei with large neutron excesses (Accelerator with ECR source)

8. MSU, 1996-1998  112,124 Sn(40MeV/nucl.)+ 112,124 Sn isospin effects in multifragmentation  58 Fe(45-105 MeV/nucl.)+ 58 Fe, 58 Ni(45-105 MeV/nucl.)+ 58 Ni, disappearance of isospin effects in multifragmentation  Physical indications and challenges   0, T > 0,  >0 E( , T,  ) = ? Important to production of RIB &Neutron Stars !!!

9. G. J. Kunde et al., 112,124 Sn(40MeV/nucl.)+ 112,124 Sn isospin effects in multifragmentation, ~N C, ~N C, ~N N

10. G. J. Kunde et al., isospin effects in multifragmentation 224,248 100 X(  *=1.3-10 MeV), ~N N, ~N C, ~N LC, EES model

11. G. Kortemeyer et al. Percolation model just regenerate the isospin effects in the relationship of ~N N, but not for ~ N C

12. M. L. Miller et al. Disappearance of isospin dependence of multifragmentation prooduction 58 Fe(Ni)+ 58 Fe(Ni), at 45-105 MeV/n

13. 2 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:

14. From QMD model & IQMD model mean field (corresponds to interactions) U loc : density dependent potential U Yuk : Yukawa (surface) potential U Coul : Coulomb energy U Sym : symmetry energy U MD : momentum dependent interaction

15.  two-body collisions  Cugnon’s parameterization:  np =  nn =  pp  Experimental data:  NN is isospin dependent, for E beam < 300 MeV/nucl.,  np  3  nn =3  pp

16.  Pauli blocking: the Pauli blocking of n and p is treated separately  Initialization:  in real space: the radial position of n and p are sampled by using MC method according to the n and p radial density distribution calculated from SHF (or RMF) theory  in momentum space: local Fermi momentum is given by

17. Proton, neutron, and total density distributions in 58 Fe and 58 Ni

18.  Coalescence model:  physics: r i -r j  R 0, p i -p j  P 0 R 0 =3.5 fm, P 0 =300 MeV/c  geometry: R rms  1.14 A 1/3  reality: comparing the isotope calculated with the nuclear data sheets

19. 3 Isospin effects in nuclear multifragmentation 4  analyzing  b=1, 2, 3, 4, 5, 6, 7, 8, 9, 10 fm  the number events is proportional to b statistics: t  200 fm/c, the charge distribution have been stable. One selects fragments over t=200-400 fm/c

20. Charge distributions at t=200, 400 fm/c, and the average over t=200-400 fm/c

21. Average n multiplicity, as a function of charged-particle multiplicity N C

22. Averaged number of IMF as a function of N C, N LC, and N N (4  analyzing)

23. Averaged number of IMF as a function of N C, N LC,and N N (4   pre equilibrium emissions)

24. Averaged number of MF as a function of Z bound (4  and 4   pre-equilibrium emissions) Chapter 10: “ Isospin-Dependent Quantum Molecular Dynamics Model and Its Applications in Heavy Ion Collisions, ” Isospin Physics in Heavy Ion Collisions at Intermediate Energies, ed. By Li and Schrode, Nova Science Publishers Inc. ， New York,2001

25. Averaged number of MF as a function of Z bound (4  and 4   pre-equilibrium emissions) Chapter 10: “ Isospin-Dependent Quantum Molecular Dynamics Model and Its Applications in Heavy Ion Collisions, ” Isospin Physics in Heavy Ion Collisions at Intermediate Energies, ed. by Li and Schrode, Nova Science Publishers Inc ， New York,2001

26. 4 Chemical and mechanical instabilities (  E/  T) ,   0 thermodynamical instability (  P/  ) T,  <0 mechanical instability (volume, surface, Coulomb instabilities) (   n /  ) P,T <0(   n /  ) P,T <0 chemical instability

27. Averaged number of IMF as a function of N C and Z bound (4   pre-equilibrium emissions)

28. Isotopic distributions of Li, Be, Ne and Na for central collisions at 40 and 100 MeV/nucl.

29. Isotopic distributions of Ne (A=17 ~32) for central collisions at 40 and 100 MeV/nucl. ---------- 112 Sn+ 112 Sn _______ 124 Sn+ 124 Sn

30. Origin of multifragmentation: mechanical or/and chemical instabilities ?

33. Origin of multifragmentation: mechanical or/and chemical instabilities ?

34. 61 MeV 50.6 MeV Li and Schroder, book in 2001

35. -69 MeV

36. 5 Conclusions and perspectives Theoratical Models phenomenological :  expanding evaporating model  percolation model  statistical multifragmentation model microscopic:  isospin dependent quantum molecular dynamics model  Boltzmann-like model, such as IBL  isospin dependent far from equilibrium model

37. Experimental signals of chemical instability  isospin effects in multifragmentation  propose more physical observable sensitive to chemical instability ? nuclear reactions induced byradioactive ion beams  neutron-rich  neutron-poor  n-halo nuclei