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Systematic study of fusion reactions leading to super-heavy nuclei Ning Wang Guangxi Normal University www.ImQMD.com/wangning/ BLTP/JINR-KLFTP/CAS Joint.

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Presentation on theme: "Systematic study of fusion reactions leading to super-heavy nuclei Ning Wang Guangxi Normal University www.ImQMD.com/wangning/ BLTP/JINR-KLFTP/CAS Joint."— Presentation transcript:

1 Systematic study of fusion reactions leading to super-heavy nuclei Ning Wang Guangxi Normal University BLTP/JINR-KLFTP/CAS Joint Workshop on Nuclear Physics, Aug. 2-6, 2012, Dubna 1. Introduction 2. capture cross sections 3. Survival probablity W sur 4. Fusion probabilty P CN 5. Conclusion

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3 I. Capture cross sections with the Skyrme energy-density functional Density distributions of the reaction partners Entrance-channel fusion barrier Fusion cross sections Skyrme energy-density functional Barrier penetration & empirical fusion barrier distribution D(B) 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)

4 Woods-Saxon form for densities Search for the minimum of energy by varying densities (R 0p, R 0n, a p, a n ) according to Hohenberg-Kohn theorem 1. Determination of density distributions

5 E1E1 E2E2 Sudden approximation for density R V.Yu. Denisov and W. Noerenberg, Eur. Phys. J. A15, 375 (2002). 2. Entrance-channel fusion barrier

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

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

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

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12 Deviations from exp. data for 120 reactions About 70% systems are less than 0.005, which gives the system error 18%. N. Wang et al., J. Phys. G: 34 (2007) 1935 rms deviation for (E>B)

13 II. Survival probability W sur with HIVAP The sensitive parameters: 1. fission barriers (Liquid-drop barriers, Sierks 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: r a =1.153fm

14 Wang, Zhao, Scheid, Wu, PRC 77 (2008) Fusion-fission EDF HIVAP

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

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

18 Alpha decay energies of super-heavy nuclei have been predicted rms ~ 248 keV to 46 Q a of SHN

19 Zhang, et al., Phys. Rev. C 85, (2012) N=178 WS* N=178 WS* N=162N=178 WS*

20 1) quasi-fission barrier Wang, Tian, Scheid, PRC84, (R) (2011) III. Fusion probability Yu. Oganessian

21 Fusion probability

22 2) Evaporation residual cross sections Mean barrier height PRC84, (R) (2011)

23 Uncertainty at E>B m : 1.18 (capture) x 1.85 (W sur ) x 2 (P CN ) = 4.4

24 Opt. 50 Ti+ 249 Bk 50 Ti+ 249 Cf 54 Cr+ 248 Cm 58 Fe+ 244 Pu Zagrebaev PRC(2008) ~ 50 fb ~ 40 fb ~ 20 fb~ 5 fb Liu-Bao PRC(2011) ~ 600 fb ~ 100 fb Nasirov PRC(2011) ~ 100 fb~ 70 fb Ning Wang PRC(2011) ~ 35 fb ~ 20 fb ~ 5 fb~ 3 fb Nan Wang PRC(2012) ~ 110 fb ~ 50 fb ~ 6 fb~ 4 fb Siwek- Wilczynska PRC(2012) ~ 30 fb ~ 6 fb ~ 1 fb~ 0.1 fb

25 Conclusion and discussion Methods for calculations of capture cross sections, survival probability of compound nucleus and the fusion probability in fusion reactions leading to super-heavy nuclei have been established and checked 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.

26 China Institute of Atomic energy Zhu-Xia Li Xi-Zhen Wu Kai Zhao Institute of Theoretical Physics (CAS) En-Guang Zhao Justus-Liebig-Univ. Giessen Werner Scheid Guangxi Normal Univ. Min Liu Anyang Normal Univ. Jun-Long Tian

27 Thanks for your attention Codes and data are available at

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

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33 I. Capture II. Decay III. Formation # Coulomb Barrier (Skyrme EDF) # Barrier Distribution # Deformation & Dynamics … (ImQMD) # Fission Barrier # Masses & Shell corrections (mass formula) # Fission Fragment Yields … (DNS) # Quasi-fission barrier # Potential energy surface # Dynamics …

34 1). Fission barrier Nuclei Cohen-Swiatecki Sierk Dahlinger MWS 244 Pu No

35 2). Level density parameters In the standard HIVAP code: E d =18.5MeV, r a =1.153fm

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

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


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