1. 沈彩万 Two-step Model in the synthesis of superheavy elements 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. Compound Nucleus Theory
Commonly used model:
Compound Nucleus Theory

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

6. Parameters for the description of formation
q1 = R/R q2 = a
p1 = pR/R p2 = 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. After equilibrium, the distribution probability of e :
数值计算
For fixed a and R/R0,
After equilibrium, the distribution probability of e :
Approximately:
where:

11. (F.H) (no F.H.) Criteria for fusion hindrance in radial evolution
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-drop Energy
Coulomb Energy
48Ca+238U
RCB = 14.14fm
RC = 11.86fm
RLB = 9.5fm RC R
RLB
RCB

14. Features of the SHE synthesis
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
DE(shell)
Bf (LD) R

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, (2005)]
(parameters are slightly changed to fit the experimental capture cross section for 48Ca+238U, 244Pu, 248Cm )

17. B0 = Bswiat + DB 在超重核区对 B0 和 C 进行重新拟合
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
Pform
PSticking

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

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

22. Formation probability
According to the friction model，the relative momentums are distributed in Gaussian form：
For the fusion of heavy systems,  0
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. Application (1) Repeat 48Ca+249Cf 3n 4n 5n 2n
Experimental data: Yu. Ts. Oganessian, PRC70, (2004)064609

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

28. 48Ca + 249Bk 2n 3n 4n 5n
2009年7月27-10月23
(70天)
2.4×1019 dose

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

30. (3) 48Ca +Es
Z = 119, A = 300
T1/2=472d 3n 4n 2n 5n

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

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

33. 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。

34. Thanks !