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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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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)

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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

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

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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

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

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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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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)

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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

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

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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

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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

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

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

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

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Fusion probability

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

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

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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

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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.

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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

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Thanks for your attention Codes and data are available at

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

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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 …

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

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

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

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

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