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Systematics of fusion probability in reactions leading to super-heavy nuclei

Systematics of fusion probability in reactions leading to super-heavy nuclei. Ning Wang ( 王宁 ). Guangxi Normal University www.imqmd.com. 2011 Dec., Beijing. Introduction Calcualtions of capture cross sections Survival probablity W sur Fusion probabilty P CN. 6 new superheavy elements.

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Systematics of fusion probability in reactions leading to super-heavy nuclei

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  1. Systematics of fusion probability in reactions leading to super-heavy nuclei Ning Wang (王宁) Guangxi Normal University www.imqmd.com 2011 Dec., Beijing

  2. Introduction • Calcualtions of capture cross sections • Survival probablity Wsur • Fusion probabilty PCN

  3. 6 new superheavy elements 118 117 116 2010 115 114 Yu. Oganessian 2010 113 112 249Bk +48Ca 111 T1/2= 320d 110 109 48 new isotopes 108 107 106 105 ??? 104 Yu. Oganessian “SHE in JINR” 109-th Session of the SC of JINR, Feb. 17-18, 2011, Dubna

  4. 2003-2008, 7477hours /312days, 2 events Theoretical support for these very time-consuming and extremely-expensive experimentsis vital in choosing the optimum target-projectile-energy combinations, and for the estimation of cross sections. 50Ti, 54Cr, 58Fe, 64Ni, 70Zn + 208Pb 48Ca：1克20万美金 Cf：1克10亿美元 S.Hofmann, GSI

  5. # Coulomb barrier # Barrier distribution (~2005 -- 2007) # Deformation & dynamics … (~2000 -- present) • I. Capture • II. Decay • III. Formation # Fission barrier # Masses & shell corrections (~2009 -- present) # Mass distributions … # Quasi-fission barrier # Potential energy surface (~2005、2011…) # Dynamics …

  6. 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) 044604

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

  8. 1. Determination of density distributions according to Hohenburg-Kohn theorem Spherical symmetric Fermi functions Search for the minimum of energy by varying densities (R0p, R0n, ap, an)

  9. R 2. Entrance-channel fusion barrier E2 E1 Sudden approximation for density V.Yu. Denisov and W. Noerenberg, Eur. Phys. J. A15, 375 (2002).

  10. 3. Fusion (capture) cross section D(B) to empirically take into account the coupling between the relative motion and other degrees of freedom such as deformation etc. Determination of D(B) is the key of this approach with Min Liu, Ning Wang, et al., Nucl. Phys. A 768 (2006) 80

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

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

  13. The fusion excitation functions of a series of reactions with 16O bombarding on medium mass targets.

  14. Large-angle quasi-elastic scattering PRC 78, 014607 (2008)

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

  16. 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

  17. 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

  18. Obtained deviations with different models for 51 fusion-fission reactions N. Wang, M. Liu and Y. Yang, Sci. China G 52, 1554 (2009)

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

  20. Radius parameter ra in the level density parameter

  21. Optimal value of the radius parameter ra 68% reactions have a value smaller than 0.0714, Estimated systematic errors of the HIVAP code: 1.85Wsur and Wsur /1.85

  22. WS* 3). Masses of super-heavy nuclei A reliable nuclear mass model is needed for studies on synthesis of super-heavy, nuclear astrophysics and nuclear symmetry energy, etc. WS : PRC 81 (2010) 044322 WS*: PRC 82 (2010) 044304 WS3: PRC 84 (2011) 014333 “Mass Olympics” Trento 2008

  23. Fusion-fission：EDF＋HIVAP Ning Wang, et al., Phys. Rev. C 77 (2008) 014603

  24. M. Itkis，Dubna III. Fusion probability PCN (preliminary) • 1) Driving potential • 2) Quasi-fission • 3) Calculations of evaporation residual cross sections

  25. Y. Oganessian, 109th Session of the JINR Scientific Council, 2010, Dubna. Esh Bqf 2) quasi-fission barrier

  26. Mean barrier height 3) Evaporation residual cross sections

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

  28. Collected by Junlong Tian

  29. A. K. Nasirov, et al., Phys. Rev. C 84, 044612 (2011)

  30. Results fromNan Wang (王楠) http://www.phys-hutc.net/conference/2011-09-trans/pdf/王楠.pdf

  31. For 4n channel Zagrebaev, et al., arXiv:1105.1659v1

  32. 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 are established step by step. • Coulomb barrier, fission barrier and quasi-fission barrier play important role for the calculations of three parts. • More precise calculations for masses, fission barrier and the study on dynamics of fusion and fission processes are still required.

  33. 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）

  34. Thanks for your attention I am very grateful to Prof. Shan-Gui Zhou (周善贵) for many discussions and valuable suggestions This work was supported by Alexander von Humboldt Foundation and National Natural Science Foundation of China

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