Systematic study of fusion reactions leading to super-heavy nuclei

1. Systematic study of fusion reactions leading to super-heavy nuclei 1. Introduction 2. Capture cross section 3. Survival probablity Wsur 4. Fusion probabilty PCN 5. Summary Ning Wang (王宁) Guangxi Normal University www.ImQMD.com/wangning/ Workshop on Synthesis of Super-heavy nuclei, August 10-13, 2012, Lanzhou

2. 1) to study the three parts individually; 2) to estimate the model uncertainty

3. # Coulomb Barrier(Skyrme EDF) # Barrier Distribution # Deformation & Dynamics … (ImQMD) • I. Capture • II. Decay • III. Formation # Fission Barrier # Masses & Shell corrections (mass formula) # Fission Fragment Yields … (DNS) # Quasi-Fission Barrier # Potential Energy Surface # Dynamics …

4. I. Capture cross sections with the Skyrme energy-density functional Density distributions of the reaction partners Skyrme energy-density functional Entrance-channel Coulomb barrier Barrier penetration & empirical fusion barrier distribution D(B) Capture cross sections M. Liu, N. Wang, Z. Li, X. Wu and E. Zhao, Nucl. Phys. A 768 (2006) 80 Ning Wang, et al., Phys. Rev. C 74 (2006) 044604

5. 1. Determination of density distributions according to Hohenberg-Kohn theorem Woods-Saxon form for densities Search for the minimum of energy by varying densities (R0p, R0n, ap, an)

6. R 2. Entrance-channel inter-nucleus potential E2 E1 Sudden approximation for density V.Yu. Denisov and W. Noerenberg, Eur. Phys. J. A15, 375 (2002).

7. D(B) considers the coupling between the relative motion and other degrees of freedom such as dyn. deform. etc.壳效应，形变效应，动力学效应 with 16O+208Pb, E=80MeV, ImQMD 3. Fusion (capture) cross section

8. for reactions with nuclei near the beta-stability line but the neutron-shell is not closed

9. The fusion excitation functions for a series of reactions with 16O bombarding on medium mass targets. suppression Wang et al. Sci China G 52, 1554 (2009) enhancement

13. Deviations from exp. data for 120 reactions N. Wang et al., J. Phys. G: 34 (2007) 1935 rms deviation for (E>B0) For about 70% systems, the deviations are smaller than 0.005, estimated systematic error 18%.

14. II. Survival probability Wsur with HIVAP The sensitive parameters: 1. fission barriers (Liquid-drop barriers, Sierk’s barriers…) 2. level density parameters (Fermi gas model, angular-momentum and shape-dependent) 3. masses shell corrections and particle separation energies In the standard HIVAP code: ra=1.153fm

15. Fusion-fission：EDF＋HIVAP Wang, Zhao, Scheid, Wu, PRC 77 (2008) 014603

17. Deviations of calculated evaporation (and fission) cross sections from exp. data for 51 fusion-fission reactions For 68% reactions, the deviations are smaller than 0.0714, Estimated systematic errors of the HIVAP code: 1.85Wsur and Wsur /1.85

18. WS* 152 3). Masses of super-heavy nuclei A reliable nuclear mass formula is crucial for a description of the properties and production cross sections of super-heavy nuclei An improved nuclear mass formula WS : PRC 81 (2010) 044322 WS*: PRC 82 (2010) 044304 WS3: PRC 84 (2011) 014333

19. Alpha-decay energies of super-heavy nuclei have been predicted rms ~ 248 keV to 46 Qa ofSHN

20. N=178 WS* N=178 N=162 N=178 WS* WS* H.F. Zhang, et al., Phys. Rev. C 85, 014325 (2012)

21. III. Fusion probability B0 Bf 水坝 Bqf E* also influences the results

22. 1) quasi-fission barrier Yu. Oganessian Wang, et al, PRC77, 014603 (2008) Wang, Tian, Scheid, PRC84, 061601(R) (2011)

23. Fusion probability

24. Mean barrier height 2) Evaporation residual cross sections PRC84, 061601(R) (2011)

25. Uncertainty at E>Bm : 1.18 (capture) x 1.85 (Wsur) x 2 (PCN) = 4.4

26. exp. (GSI) < 70 fb < 200 fb (from talk of D. Ackermann)

27. Summary • Models for calculations of capture cross sections, survival probability of compound nucleus and the fusion probability in fusion reactions leading to SHN have been tested step by step. • Coulomb barrier, fission barrier and quasi-fission barrier play important roles for the calculations of three parts. • More precise calculations for masses, fission barriers, fission fragment yields and the study of fusion dynamics are still required.

28. China Institute of Atomic energy： Zhu-Xia Li、Xi-Zhen Wu、Kai Zhao （李祝霞） （吴锡真） （赵凯） Institute of Theoretical Physics (CAS)： En-Guang Zhao （赵恩广） Justus-Liebig-Univ. Giessen： Werner Scheid Guangxi Normal Univ. Min Liu （刘敏） Anyang Normal Univ. Jun-Long Tian （田俊龙）

29. Fission fragment yields with driving potential DNS: En-Guang ZhaoShan-Gui ZhouJun-Qing LiNan Wang Nuclear engineering Nuclear structure Fission cycle in nuclearastrophysics

30. Thanks for your attention Some codes and data are available at：www.ImQMD.com

32. Skyrme energy-density functional Skyrme force SkM* Kinetic Nuclear Coulomb M. Brack, C. Guet, H.-B. Hakanson, Phys. Rep. 123, 275 (1985).

36. Nuclei Cohen-Swiatecki Sierk Dahlinger MWS 244Pu 4.16 5.17 3.95 4.13 256No 1.74 1.44 1.02 1.19 1). Fission barrier

37. 2). Level density parameters In the standard HIVAP code: Ed=18.5MeV, ra=1.153fm

38. Large-angle quasi-elastic scattering Tail of the barrier distribution influences the large-angle quasi-elastic cross sections PRC78, 014607 (2008)

39. Tail of barrier distribution influences the large-angle quasi-elastic cross sections S. G. Zhou