1. 沈彩万 湖州师范学院 8 月 11 日 ▪ 兰州大学 准裂变与融合过程的两步模型描述 合作者： Y. Abe, D. Boilley, 沈军杰

2. p.2 Content  Introduction of the model  Quasi-fission stage  Fusion stage  Summary

3. p.3 Binary Processes (DIC) Reseparation (Quasi-Fission) C. N. SHE Spontaneous decays ( , fission) n Sketch map of the process

4. p.4 Theories to describe the fusion stage Fluctuation-Dissipation theory DNS (di-nuclear system) model ImQMD model …

5. p.5 Two-step Model (1) Coulomb barrier; (2) Liquid drop barrier 48 Ca+ 238 U R CB = 14.14fm R C = 11.86fm R LB = 9.5fm R V Coulomb Energy Liquid-drop Energy R LB RCRC R CB including two-consecutive steps overcoming the barriers P fusion = P sticking * P form

6. p.6 (1)Sticking probability P sticking (a) Surface friction model (b) Empirical formula by Swiatecki [Swiatecki et al., PRC 71, 014602(2005)] (c) Quantum tunneling (d) …

7. p.7 (2) Formation Probability: P form Using liquid drop model R V VBVB RcRc Contact Point = R p + R t E c.m. Coulomb Potential Liquid Drop Potential P Sticking P form

8. p.8 Parameters for the description of formation A1A1 A2A2 q 1 = R/R 0 q 2 =  p 1 = p R/R0 p 2 = p  R  : asymmetric parameter ， R 0 : spherical radius of the compound nucleus

9. p.9 Average value of the neck parameter

10. p.10 Criteria for fusion hindrance in radial evolution If system evolves to spherical case: without fusion hindrance. If system evolves to two fragments: with fusion hindrance. (F.H) (no F.H.)

11. p.11 Equation of motion for R and  Langevin equaiton:

12. p.12 Tracks of motion with random force E k =50MeV

13. p.13 Formation and fragment mass-distribution E k =50MeV formation quasi-fission initial point with p k

14. p.14 According to the friction model ， the relative momentums are distributed in Gaussian form ： For the fusion of heavy systems,  0 Initial radial momentum distribution at contact point

15. p.15 (A) Fragment mass distribution of Quasi-fission

16. p.16 Probability distribution of fragment after sticking: E k =50MeV quasi-fission

17. p.17 The cross section for mass distribution of quasi-fission

18. p.18 Mass-distribution probability in the formation stage 238 U + 26 Mg

19. p.19 Exp: W.Q. Shen, PRC (1987) 238 U+ 16 O 238 U+ 26 Mg 238 U+ 32 S

20. p.20 238 U+ 35 Cl 238 U+ 40 Ca 238 U+ 65 Zn Properties: the larger E lab and heavier target, the wider fragment mass-distribution of quasi-fission.

21. p.21 Heavier target, wider mass distribution Difference in the formation stage Difference in the sticking stage

22. p.22 Larger E lab, wider mass distribution Lighter target Heavier target

23. p.23 23 (B) Fusion process

24. p.24 (1) Formation probability Then we get formation probability ： E k =50MeV formation

25. p.25  Survival Probability (statistical evaporation model) [HIVAP program] (2) Fusion cross section  Residue cross section

26. p.26 Key parameters: (i)re-adjust the parameters in Swiatecki’s formula in the calculation of P sticking (  B, C) (ii) Shell correction factor f shell = 0.48  Application to the 50 Ti induced reaction to synthesize SHN

27. p.27 Adjusting  B and C to fit experimental data The two reactions are not hindered [Gaggerler et al., Z. Phys. A 316, 291(1984)] and thus the fusion cross sections are used to adjust the parameter  B and C.

28. p.28 Z = 120  : ~fb Comparison with others: (a) Feng, Adamin, Nasirov, Liu, Nan Wang, Zagrebaev: ~0.1pb (b) Ning Wang et al.: ~20 fb

29. p.29 1. The experimental data of quasi-fission is reproduced by two-step model. However more detailed aspects still should still be considered. 2. The residue cross section for 50 Ti+ 250 Cf is calculated. The predicted cross section is still far away from the current facilities. 3. Different method to calculate the capture cross section should be considered in near future. Summary

30. p.30 Thank you !