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Two-step Model

Two-step Model. in the synthesis of superheavy elements. 沈彩万. 浙江 · 湖州师范学院. 第十三届全国核结构研讨会 · 赤峰 2010 年 7 月 27 日. Collaborators. Y. Abe (RCNP, Japan) D. Boilley (GANIL, France) E. G. Zhao (ITP, CAS) G. Kosenko (Omsk Univ., Russia). Outlook. Introduction Fusion hindrance

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Two-step Model

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  1. Two-step Model in the synthesis of superheavy elements 沈彩万 浙江 ·湖州师范学院 第十三届全国核结构研讨会 · 赤峰 2010年7月27日

  2. Collaborators Y. Abe (RCNP, Japan) D. Boilley (GANIL, France) E. G. Zhao (ITP, CAS) G. Kosenko (Omsk Univ., Russia)

  3. Outlook • Introduction • Fusion hindrance • Two-step model in the fusion:Sticking processFormation process • Calculations • Conclusion

  4. Commonly used model: Compound Nucleus Theory

  5. Sketch map of the process n C. N. Reseparation (Quasi-Fission) Binary Processes (DIC) Spontaneous decays (a, fission) SHE

  6. Parameters for the description of formation A2 A1 R q1 = R/R0 q2 = a p1 = pR/R0p2 = pa a: asymmetric parameter，R0:spherical radius of the compound nucleus

  7. 100Mo+100Mo

  8. 110Pd + 110Pd

  9. Average value of the neck parameter

  10. 数值计算 For fixed a and R/R0, After equilibrium, the distribution probability of e : Approximately: where:

  11. Criteria for fusion hindrance in radial evolution (F.H) (no F.H.) If system evolves to spherical case: without fusion hindrance. If system evolves to two fragments: with fusion hindrance.

  12. Fusion hindrance area: (radial evolution) 110Pd+110Pd 100Mo+100Mo

  13. Features in the synthesis of SHE 1. Double barrier penetrations Coulomb barrier; Liquid drop barrier V Liquid-dropEnergy CoulombEnergy 48Ca+238U RCB = 14.14fm RC = 11.86fm RLB = 9.5fm RC R RCB RLB

  14. Features of the SHE synthesis R DE(shell) Bf (LD) 2. Shell correction takes very important role Fission barrier: Bf = Bf(LD)-DE(shell) Bf(liquid-drop fission barrier) : 0.1 ～ 2 MeV DE(shell) (shell correction energy): -1 到- 9 MeV

  15. Fusion Probability = Psticking* Pform • Sticking probability:Psticking V Ec.m. VB Coulomb Potential Liquid Drop Potential Contact Point = Rp+Rt R PSticking

  16. Sticking probability: (1) Surface friction model (2) Empirical formula by Swiatecki [Swiatecki et al., PRC 71, 014602(2005)] (parameters are slightly changed to fit the experimental capture cross section for 48Ca+238U, 244Pu, 248Cm )

  17. 在超重核区对 B0和 C进行重新拟合 B0 = Bswiat + DB experimental capture cross section: M. G. Itkis et al., Nuovo Cimento A111, 783 (1998).

  18. Extrapolation of parameter DB

  19. Formation Probability • Formation probability:Pform(Using LD model) V Ec.m. VB Coulomb Potential Liquid Drop Potential Contact Point = Rp + Rt Rc R PSticking Pform

  20. Equation of motion for R and a Langevin equaiton:

  21. Ek=50MeV Tracks of motion with random force

  22. For the fusion of heavy systems,  0 Formation probability According to the friction model，the relative momentums are distributed in Gaussian form： Then we get formation probability：

  23. Example 48Ca + 247Bk

  24. Evaporation probability (HIVAP) Statistical evaporation model ! (factor: fit to the experimental data for 48Ca+248Cm ) Yu. Ts. Oganessian et al., PRC70, (2004)064609

  25. 4n 3n 5n 2n Application (1) Repeat 48Ca+249Cf Experimental data: Yu. Ts. Oganessian, PRC70, (2004)064609

  26. (2) 48Ca + Bk isotopes ( Z = 117)

  27. 3n 4n 2n 5n 48Ca + 249Bk 2009年7月27-10月23 (70天) 2.4×1019 dose

  28. 22 mg 249Bk transport Bk(NO3)3 Prices per 1 mg 197Au ≈ 0.03 US$ 239Pu ≈ 4 US$ 48Ca ≈ 80 US$ 249Cf ≈ 60,000 US$

  29. (3) 48Ca +Es Z = 119, A = 300 T1/2=472d 3n 4n 2n 5n

  30. T1/2=276d Z = 119, A = 302

  31. Z = 120, A = 305 T1/2 = 100.5d Last chance for 48Ca to synthesize SHE

  32. 小结 • 根据重核融合的特点，融合过程分为两步 ： 粘连过程和形成过程。 • 融合阻止 (fusion hindrance) 起源于重核融合过程中的液滴能位垒。形成过程的郎之万模拟自动考虑了这一影响。 • 计算了48Ca引起的系列反应，与实验较好符合。计算的48Ca+249Bk被实验所证实。 • 剩余截面(通过裂变位垒)对壳修正严重依赖。后者需要更好的理论计算。

  33. Thanks !

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