Symmetry energy and pion production in the Boltzmann-Langevin approach

1. Symmetry energy and pion production in the Boltzmann-Langevin approach Wen-Jie Xie and Feng-Shou Zhang 谢文杰 张丰收 Supervisor: Prof. Feng-Shou Zhang College of Nuclear Science and Technology, Beijing Normal University, Beijing, China E-mail: wjxie@mail.bnu.edu.cn

2. Contents Introduction 2. The improved isospin- and momentum- dependent Boltzmann-Langevin model (ImIBL) 3. The calculated results on the pion production using the ImIBL model 4. Conclusions and questions

3. Contents Introduction 2. The improved isospin- and momentum- dependent Boltzmann-Langevin model (ImIBL) 3. The calculated results on the pion production using the ImIBL model 4. Conclusions and questions

4. Symmetry energy at subnormal densities The trend is almost confirmed. The quantitative results are not obtained. Soft:ImQMD, M.B. Tsang, et al., PRL102,122701(2009) By analyzing the isospin diffusion data, a soft symmetry energy was suggested. Experimental data: M. A. Famiano et al., Phys. Rev. Lett. 97, 052701 (2006).

5. By using the same symmetry energy, the same experimental data, a more soft symmetry energy was suggested Soft:IQMD, S. Kumar, et al., PRC 84, 044620 (2011) Experimental data: M. A. Famiano et al., Phys. Rev. Lett. 97, 052701 (2006).

6. Stiff:IBUU04, L.W. Chen, et al., PRL94,032701(2005) Using the isospin diffusion as a probe, a stiff symmetry energy was suggested Experimental data: M.B. Tsang et al., Phys. Rev. Lett. 92, 062701 (2004).

7. Stiff: CoMD-II, F. Amorini, et al., PRL102, 112701(2009) By calculating the mass distribution of heaviest fragments, a stiff symmetry energy was suggested

8. Symmetry energy at supranormal densities Even the trend of the symmetry energy with increasing density is not constrained. Soft : IBUU04, Z.G. Xiao, et al., PRL102, 062502 (2009) By calculating the excitation function of pion ratio, a very soft symmetry energy was obtained. Experimental data: W. Reisdorf, et al., Nucl. Phys. A 781, 459 (2007).

9. Soft:ImIBL, W.J. Xie, F.S. Zhang, et al., PLB 2012,(in press) Experimental data: W. Reisdorf, et al., Nucl. Phys. A 781, 459 (2007).

10. Stiff:ImIQMD, Z.Q. Feng, et al., PLB 683, 140 (2010) Experimental data: W. Reisdorf, et al., Nucl. Phys. A 781, 459 (2007).

11. By calculating the transverse momentum distributions of pion ratio, a soft symmetry energy was obtained Soft:UrQMD, Q. Li, et al., PRC72,034613 (2005)

12. Stiff:RBUU, G. Ferini, et al. PRL97, 202301(2006) By calculating the excitation function of pion ratio, a stiffer symmetry energy was obtained. Due to the inclusion of delta meson field. stiffer

13. Symmetry energy at low-temperature, low-density limit Experimental data: S. Kowalski, et al., Phys. Rev. C75, 014601(2007).Theoretical model: Quantum-statistical model

14. Pion production • Experimental data: (FOPI and EoS Collaborations) FOPI : • Multiplicity; transverse mass, rapidity, transverse momentum distributions; pion flow and so on. NPA610(1996)49c; PRC71(2005)034902; ZPA357(1997)207; NPA781(2007)459 EoS : Pion Antiflow PRL78(1997)4165

15. Coulomb ? Multiplicity: The results calculated by theories are very close to the experimental data. • IBUU04, Z.G. Xiao, et al., PRL102, 062502 (2009) • ImIQMD, Z.Q. Feng, et al., PLB 683, 140 (2010) • ImIBL, W.J. Xie, et al. PLB2012(in press) Pion ratio: Model-dependent Pion antiflow: uncertain

16. Contents Introduction 2. The improved isospin- and momentum- dependent Boltzmann-Langevin model (ImIBL) 3. The calculated results on the pion production using the ImIBL model 4. Conclusions and questions

17. outline 1. The framework of the ImIBL model 2. The differences between the BL and usual BUU models 3.The fluctuations 4.The single-nucleon potential and the inelastic channels and cross sections

18. The framework of the ImIBL model Inputs Initialization Single-nucleon potential Mean field Elastic and inelastic collisions Pauli blocking Collisions Fluctuations The next step Outputs

19. The differences between the BL and BUU models BUU：The quadrupole moment is almost fixed. BL：For the existence of fluctuations, the range of variation of quadrupole moment is larger. The is the standard deviation function.

20. The differences among the Vlasov, BUU and BL models Vlasov: BUU： BL： A. Ono, J. Randrup, Eur. Phys. J. A 30 (2006) 109

21. The fluctuation term The fluctuating collision term can be interpreted as a stochastic force acting on density and is characterized by a correlation function, • A projection method is used in the BL model. The fluctuations are projected on a set of low-order multipole moments of the momentum distribution, F.S. Zhang et al. Phys. Rev. C 51(1995) 3201; Y. Abe, S. Ayik, et, al. Phys. Rep. 275 (1996)49

22. The scaling procedure The scaling procedure used to rescale the local momentum distribution is given in the following The are solved in terms of the following equations: F. S. Zhang et al. Phys. Rev. C 51(1995) 3201

23. The evolution process of ImIBL model 1.Starting with a definite density at time , the first step is to determine the local average evolution from to , which yields and the elements of the diffusion matrix . 2. The fluctuations are calculated. 3. The fluctuations are inserted into the single-particle density. The above three steps are repeated at each time step.

24. The single-nucleon potential J. Aichelin, Phys. Rep. 202 (1991) 233;Z.Q. Feng, et al., Phys. Lett. B 683 (2010) 140; J. Aichelin, et al., Phys. Rev. Lett. 58 (1987) 1926

25. The inelastic channels and cross sections The parameterized cross sections for each channel to produce resonances are obtained in terms of the one-boson exchange model. The resonance lifetime are calculated according to the following figure. Z.Q. Feng, Phys. Rev. C 82 (2010) 057901; S. Huber, et al. Nucl. Phys. A573, (1994) 587; A.B. Larionov, et al., Phys. Rev. C66,(2002)054604

26. Developing processes from BL,IBL to ImIBL No isospineffects,no inelastic channels • BL: • IBL: • ImIBL: F.S. Zhang, Phys. Rev. C51,3201(1995) No inelastic channels B.A. Bian, et al., Nucl. Phys. A807,71(2008) Inelastic channels and MDI W.J. Xie, et al., Phys. Lett. B 2012 (in press)

27. Contents Introduction 2. The improved isospin- and momentum- dependent Boltzmann-Langevin model (ImIBL) 3. The calculated results on the pion production using the ImIBL model 4. Conclusions and questions

28. Pion multiplicity W. Reisdorf, et, al., Nucl. Phys. A 781(2007) 459 Z.G. Xiao, et, al. ,Phys. Rev. Lett. 102 (2009) 062502

29. The dependence of the ratio on the N/Z at 400A MeV W. Reisdorf, et, al, Nucl. Phys. A 781(2007) 459 R. Stock, Phys. Rep. 135 (1986) 259

30. The excitation function of from central Au+Au collisions

31. Contents Introduction 2. The improved isospin- and momentum- dependent Boltzmann-Langevin model (ImIBL) 3. The calculated results on the pion production using the ImIBL model 4. Conclusions and questions

32. Conclusions • The pion multiplicity is dependent on the EoS and independent on the symmetry energy. • The pion multiplicity is very sensitive to the fluctuations at pion subthreshold energies. 3. Calculations with a supersoft symmetry energy describe well the experimental data.

33. Questions • The threshold effects are not included. • The isospin effect in MDI is not included. • The pion potential is not included. • The symmetry energy at low-temperature, low-density limit is not included. We need further improve our model !!!

35. Acknowledgement Dr. Zhao-Qing Feng (IMP) Prof. Zhi-Gang Xiao (Tsinghua) Prof. Lie-Wen Chen (SJTU) Prof. Zhuxia Li (CIAE)

36. Thank you for your attention！