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

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

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

Compound Nucleus Theory Commonly used model: Compound Nucleus Theory

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

Parameters for the description of formation q1 = R/R0 q2 = a p1 = pR/R0 p2 = pa a: asymmetric parameter， R0: spherical radius of the compound nucleus

100Mo+100Mo

110Pd + 110Pd

Average value of the neck parameter

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:

(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.

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

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

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

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

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 )

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).

Extrapolation of parameter DB

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

Equation of motion for R and a Langevin equaiton:

Tracks of motion with random force Ek=50MeV

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：

Example 48Ca + 247Bk

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

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

(2) 48Ca + Bk isotopes ( Z = 117)

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

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$

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

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

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

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。

Thanks !