沈彩万 重离子反应中 碎片质量分布的计算 浙江 · 湖州师范学院 湖州 2012.4.12-16 Y. Abe, D. Boilley, J. J. Shen

Outlook Introduction Two-step model in the fusion stage Fragment mass distribution 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

Theories to describe the fusion state Fluctuation-Dissipation theory (Abe,Bao,Shen,…) DNS (di-nuclear system) model (Schide, Li, Zhou, …) imQMD model …

Pfusion = Psticking* Pform Two-step Model including two-consecutive steps overcoming the barriers (1) Coulomb barrier; (2) Liquid drop barrier V Liquid-drop Energy Coulomb Energy 48Ca+238U RCB = 14.14fm RC = 11.86fm RLB = 9.5fm RC R RLB RCB Pfusion = Psticking* Pform

Sticking probability: (1) Surface friction model (2) Empirical formula by Swiatecki [Swiatecki et al., PRC 71, 014602(2005)]

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

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

Average value of the neck parameter

(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.

对称反应中液滴能随 z 的变化

Fusion hindrance area: (radial evolution)

Equation of motion for R and a Langevin equaiton:

Tracks of motion with random force Ek=50MeV

Formation and mass-fragment distribution initial point with pk Ek=50MeV quasi-fission formation

Formation and mass-distribution probability According to the friction model，the relative momentums are distributed in Gaussian form： For the fusion of heavy systems,  0 Probability for mass-fragment distribution

在质量分布中，通常以单位质量数的相关量表示：

238U + 26Mg Mass-distribution probability in the formation stage

Exp: W.Q. Shen, PRC (1987) 238U+16O 238U+26Mg 238U+32S

238U+35Cl 238U+40Ca 238U+65Zn

结果分析 1、理论计算较好符合实验。 2、中心偏移: 理论仅包含了两分裂情况，三分裂等多碎片分裂会分布中心左移。 2、中心偏移: 理论仅包含了两分裂情况，三分裂等多碎片分裂会分布中心左移。 3、两端差异：理论仅含准裂变，实验应含有散射等其他成分。 4、仅在复合阶段仅考虑液滴 能时无法给出细致结果。

进一步改进 1、考虑壳修正影响； 2、自洽考虑颈部自由度； 3、要与实验结果更好复合，还需 考虑其它形式引起的质量分布。

小结 1、两步模型不但能较好地计算重离子反应的熔合截面，还能给出准裂变的质量碎片分布。 2、若要更好地计算准裂变碎片分布，还需要将两步扩展至更多的自由度。 3、壳效应应该考虑在熔合过程中。

Thanks !