1. Jul. 17 th, 2015, HaPhy in collaboration with Youngman Kim (RISP/IBS) Kang Seog Lee (Chonnam Nat’l Univ.)

2. RAON 2

3. 3 A few ~ tens MeV/n Rare Isotope beam from ISOL Hundreds MeV/n beam from IF Or Combination, ISOL + IF  Exotic beam at low and intermediate energies Effects of nuclear structure is important in these energies. Some transport model codes (AMD, CoMD, …) are available, but they are still not good enough to describe rare isotope beam. Good event generator for RAON is needed for both theoretical and experimental purposes.

4. Transport Model ? 4 Transport model : Model to treat non-equilibrium aspects of the temporal evolution of a collision. Many-body problem with nucleons Numerical simulation (event generator) Early time region in a collision Different methods with different energies

5. Nuclear Reactions at Low Energy 5 Direct Reactions Compound Nuclear Reactions Time ~10 -20 sec ~10 -16 sec Non-equilibrium aspects Equilibrated (decay statistically) n p α Transport model QMD BUU Other model HIPSE DIT … Statistical Model GEMINI SIMON EMPIRE …

6. Transport Model 6 Low and intermediate energy regime : < 100 MeV/n - fusion, quasi-fission (multinucleon transfer), fragmentation Relativistic regime : 100 MeV/n ~ a few GeV/n - production of hadrons, collective flow phenomena Kinetic Energy λ=h/p 1 MeV3 x 10 -14 m 10 MeV9 x 10 -15 m 100 MeV3 x 10 -15 m 1 GeV7 x 10 -16 m

7. Transport Model 7 Open square : experimental data from NSCL 40 Ca(140MeV/n) + 9 Be Blue line : Simulation data from HIPSE Red line : Simulation data from AMD Ref.) M.Mocko, et al. PRC 78, 024612

8. Transport Model 8 Ref.) F. Amorini, et al. PRL 102, 112701 Mass differences between two largest fragments at 40 Ca(25MeV/n) + 48 Ca Three different parametrizations of symmetry interaction give different results.

9. Transport Model 9 Ref.) L. Mao, et al. PRC 91, 044604

10. Transport Model 10 Ref.) T. Furuta, et al. PRC 82, 034307 (a)Ground state (b)E=0.1 MeV (c)E=5 MeV Frequency of monopole oscillations

11. Transport Model 11 Ref.) M. Papa PRC 87, 014001 F1 = Stiff1 F2 = Stiff2 F3 = Soft Total energy per nucleon and symmetry energy related value of nuclear matter

12. BUU vs. QMD 12 BUU-type Moving in the mean field One-body observables (1~100 test particles) Easy to modify E.O.S BUU, VUU, IBUU, RBUU, … QMD-type Two-body interaction Many-body dynamics Event generator QMD, IQMD, CoMD, AMD, ImQMD, …

13. Initialization 13 - Wood-Saxon function d > 1.5 fm

14. Initialization 14 Ref.) Moller, et al. Atomic Data and Nuclear Data Tables 59,185

15. Stability 15 9 Be 40 Ca 181 Ta

16. Propagation 16 Skyrme parametrization for NN potential Ref.) M. Papa PRC 64(2010)024612

17. Propagation 17 Volkov interaction Gogny interaction … ex) Gogny interaction Ref.) Prog.Part.Nucl.Phys.58:587

18. Propagation 18

19. N-N Collision 19 b r1r1 r2r2 In classical scattering, Two particles are always scattered. In our model, If a distance, d, between two nucleons is smaller than b, d<b, a collision is always tried.

20. N-N Collision 20 Ref.) J.Cugnon NIM B111(1996)215 Cross section at free space We need to correct in-medium effect. Divergence at very low momentum We need to cut at some value. 30% decrease 40mb cut

21. N-N Collision 21 Ref.) G.Li and R.Machleidt PRC 48, 1702, PRC 49, 566

22. Scattering Angle 22 Random number Ref.) J.Cugnon NIM B111(1996)215 Ref.) G.Li and R.Machleidt PRC 48, 1702, PRC 49, 566 pp and nn scatterings are roughly isotropic. np scattering has a peak at backward angles.

23. Pauli blocking 23 After a nucleon-nucleon collision, we calculate the 6-dim. phase space density for each nucleon. If this condition for any nucleon is not satisfied, that collision will be blocked by the Pauli principle. Occupation number

24. Cluster Recognition 24 Disconnected if a length is larger than 5 fm. from liquid drop model Ref.) Moller, et al. Atomic Data and Nuclear Data Tables 59,185

25. Fragmentation 25 Preliminary 40 Ca + 9 Be Elab = 140 MeV/n Total : 2000 events Impact parameter: 1~4 fm

26. De-excitation 26 Fission n p α Evaporation

27. Impact Parameter 27 R(Ca) = 4.30 fm, R(Be) = 3.27 fm, each 500 events

28. Impact Parameter 28 R(Ca) = 4.30 fm, R(Be) = 3.27 fm, each 500 events

29. Impact Parameter(Central) 29

30. Impact Parameter(Peri.) 30

31. Central and Peripheral Collisions 31

32. Central Collision 32 Preliminary 40 Ca + 9 Be Elab = 140 MeV/n Total : 2000 events Impact parameter: 1~4 fm

33. Peripheral Collision 33 Preliminary 40 Ca + 9 Be Elab = 140 MeV/n Total : 1500 events Impact parameter: 5~7 fm

34. 48 Ca + 9 Be 34 48 Ca + 9 Be Elab = 140 MeV/n Total : 2000 events Impact parameter: 1~4 fm Preliminary

35. 35 Preliminary 40 Ca + 9 Be 48 Ca + 9 Be

36. Summary and Outlook 36  Transport model is important to simulate heavy-ion collisions.  A QMD-type model is appropriate for event generator.  We complete the main frame of RAQMD(tentative). The stability of an initialized nucleus is acceptable and the cluster recognition module seems to work well. We expect that this code is enough to simulate heavy-ion collisions with stable nuclei.  We start to test our code at 100~200 MeV/n region with experimental data. After testing, we will test our code at tens MeV/n, also.  To simulate and to predict experimental data at RAON, we need to implement more precise fermionic nature of nucleons in the code. Also, many exotic structures of neutron-rich nuclei need to be considered.

37. Thank you for your attention!!

38. Backup Slides

39. Various Codes 39 BUU Type QMD Type Transport Model Boltzmann : Collision term Uehling & Uhlenbeck, Nordheim : Pauli blocking Vlasov : Mean field w/o collision Landau : Averaged collisions Many names,  Boltzmann-Uehling-Uhlenbeck : BUU  BNL, VUU, LV, …  Isospin dependent BUU : IBUU  Relativistic BUU : RBUU  …  Classical Molecular Dynamics : CMD  Quantum Molecular Dynamics : QMD  Antisymmetrized MD : AMD  Fermionic MD : FMD  Constrained MD : CoMD  Improved QMD : ImQMD  Ultra-relativistic QMD : UrQMD  …

40. Super Heavy Element 40

41. Super Heavy Element 41

42. Impact parameter 42