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**Systematic study of fusion reactions leading to super-heavy nuclei**

1. Introduction 2. capture cross sections 3. Survival probablity Wsur 4. Fusion probabilty PCN 5. Conclusion Ning Wang Guangxi Normal University BLTP/JINR-KLFTP/CAS Joint Workshop on Nuclear Physics, Aug. 2-6, 2012, Dubna

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**I. Capture cross sections with the Skyrme energy-density functional**

Density distributions of the reaction partners Skyrme energy-density functional Entrance-channel fusion barrier Barrier penetration & empirical fusion barrier distribution D(B) Fusion 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)

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**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)

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**2. Entrance-channel fusion barrier**

Sudden approximation for density V.Yu. Denisov and W. Noerenberg, Eur. Phys. J. A15, 375 (2002).

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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. 16O+208Pb, 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 16O 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**

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

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**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

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**Fusion-fission：EDF＋HIVAP**

Wang, Zhao, Scheid, Wu, PRC 77 (2008)

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

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WS* 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 WS : PRC 81 (2010) WS*: PRC 82 (2010) WS3: PRC 84 (2011)

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**Alpha decay energies of super-heavy nuclei have been predicted**

rms ~ 248 keV to 46 Qa of SHN

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

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**III. Fusion probability**

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

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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>Bm : 1.18 (capture) x 1.85 (Wsur) x 2 (PCN) = 4.4**

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**Opt. ~ 50 fb ~ 40 fb ~ 20 fb ~ 5 fb ~ 600 fb ~ 100 fb ~ 70 fb ~ 35 fb**

50Ti+249Bk 50Ti+249Cf 54Cr+248Cm 58Fe+244Pu Zagrebaev PRC(2008) ~ 50 fb ~ 40 fb ~ 20 fb ~ 5 fb Liu-Bao PRC(2011) ~ 600 fb ~ 100 fb Nasirov PRC(2011) ~ 70 fb Ning Wang PRC(2011) ~ 35 fb ~ 3 fb Nan Wang PRC(2012) ~ 110 fb ~ 6 fb ~ 4 fb Siwek-Wilczynska PRC(2012) ~ 30 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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**Zhu-Xia Li、Xi-Zhen Wu、Kai Zhao （李祝霞） （吴锡真） （赵凯）**

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）

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**Thanks for your attention**

Codes and data are available at：www.ImQMD.com

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**Skyrme energy-density functional**

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

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**I. Capture II. Decay III. Formation # 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 …

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**1). Fission barrier Nuclei Cohen-Swiatecki Sierk Dahlinger MWS**

244Pu 256No

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**2). Level density parameters**

In the standard HIVAP code: Ed=18.5MeV, ra=1.153fm

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**Large-angle quasi-elastic scattering**

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

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**Tail of barrier distribution influences the large-angle quasi-elastic cross sections**

S. G. Zhou

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