推广的液滴模型及其应用简介

1. 2012超重核合成与性质研讨会（SHN2012），8月9-13, 2012, 兰州 推广的液滴模型及其应用简介 张鸿飞 兰州大学核科学与技术学院

2. 内 容 一 物理目标 二 模型简介 三 模型应用 四 总结与展望

3. 一 物理目标 采用改进的宏观模型定量描述： • 1 原子核质量（结合能）与形变 • 2 alpha衰变 • 3 质子放射性 • 4 集团放射性 • 5 自发裂变 • 6 诱发裂变 • 7 各种衰变模型竞争，较好确定原子核寿命 • 8 熔合反应

4. 自发裂变与阿尔法衰变的竞争 Alpha deacy is the main decay mode for SHN, spontaneous fission is also competitive decay for some heavy nuclei. The known heaviest even-even nucleus decays by alpha emission. For the products Z=114, Z=112, 106,104, spontaneous fission will be competitive with alpha-decay.

5. Phys. Rev. Lett. 104, 142502 (2010) The known heaviest odd-A and odd-odd nuclei are also detected by alpha decay. For the products, the decay mode is still alpha emission up to Rg and Db. It seems that the odd-even effect plays an important role on selecting the decay mode for SHN.

6. The decay mode of 114 isotopes is also isospin dependent.

7. Confirm the odd-even effect is very important for determination of the decay mode.

8. An experimental indication that Z=114 shell closure predicted around N=184. It is an interesting topic to study the competition between alpha-decay and spontaneous fission.

9. 二 模型简介 (1) Potential barrier ( from GLDM) The spontaneous fission and alpha-decay potential barriers are constructed by a generalized liquid drop model (GLDM). For one body shapes, assuming volume conservation and constant density, the volume and surface energies in this model read: For two separated spherical nuclei,

10. The improvements were made for the conventional liquid drop model (a) Quasi-molecular shapes Two parameters s1=a/c1, s2=a/c2 are used to describe the shape evolution The most impressively feature of the quasi-molecular shapes is that it can describe the process of the shapes evolution from one body to two separated fragments in a unified way

11. (b) Proximity energy The nuclear energy EN has been introduced to take into account the finite-range effects of the nucleon-nucleon force between the close surfaces . (Royer, NPA 444, (1985) 477) is surface parameter. The introduction of proximity force lowers the barrier of 7.3 MeV, and shift the peak 2.1 fm towards a more external position for 264Hs.

12. (c) Shell correction energy W.D.Myers, Droplet Model of Atomic Nuclei (Plenum,New-York, 1977). The Strutinsky method was adopted to calculate Single particle levels ei are calculated in an axially Woods-Saxon potential. Wang Ning and Liu Min Phys Rev C 81,067302(2010).

13. (d) Pairing energy The pairing energy has been calculated with the following expressions used in a recent version of the Thomas–Fermi model (W.D. Myers and W.J. Swiatecki, Nucl. Phys. A601 (1996) 141) is the ratio of the surface area of the nucleus at the actual shape to the surface area of the nucleus at the spherical shape.

14. (2) Half-life J.Randrup, S.E.Larsson, P.Moller, S.G.Nilsson,K.Pomorski and A.Sobiczewski, Phys.Rev.C 13 229(1976). Where k is 14.8. Only several channels (in the bottom of every curve) play the key roleto determine the spontaneous fission half-life. The decay constant of the mother nucleus is the summation of all possible spontaneous fission decay constant.

15. 三 模型应用 1 质子放射性 衰变常数 谱因子

17. 1 阿尔法衰变

21. Alpha decay process There are two different decay modes for alpha decay in the market, cluster-like and fission-like modes. Cluster-like mode Fission-like mode The experimental investigation can not unambiguously distinguish these two decay modes up to now.

22. In the framework of cluster-like mode(Zhang and Royer, PRC 77, (2008), 054318) (1) (2) (3) (4) The preformation factor P0 of an alpha cluster inside the mother nucleus can be extracted from Eq. (1).

23. The penetration probability plays the most important role to determine the life-time of alpha decay. The preformation factor and assault frequency reflect the nuclear structure features of the mother nucleus.

24. Clearly the closed shell structures play the key role for the preformation mechanism, and more the nucleon number is close to the magic nucleon numbers, the more the preformation of alpha cluster is difficult inside the mother nucleus. Zhang et al., PRC 80, (2009) 057301

25. In the framework of fission-like mode(Wang,Zhang, Zuo and Li, CPL 27, (2010), 062103) log10v0

26. An approach to deal with the assault frequencyZhang,Royer and Li, PRC 84 (2011) 027303 G is globle quantum number.

27. The alpha decay process is rather a radioactivity emission process of a cluster preformed on the surface of the nucleus but before the potential penetration.

28. Alpha decay properties of SHN To find out the reasonable alpha decay energy and the features of SHN. MMM results form Wang et al., PRC 81 (2010) 044322, PRC 82 (2010) 044304. Experimental data from Audi 2013. The RMS deviation with respect to 2149 measured nuclear masses Is 0.441 MeV ( the corresponding results with FRDM is 0.566 MeV). Another impressed improvement is the RMS deviation of 46 SHN is reduced 0.263 MeV ( 0.566 MeV for FRDM )

29. One proton separation energies and alpha decay energies of 162 isotones and 184 isotones.

30. Potential energy surface of 270Hs and 298114 by Constrained Relativistic Mean Field theory with the parameters NL3 The nucleus 270Hs is a double sub-magic nucleus and 298114 is a spherical double magic nucleus.

31. Alpha decay life-times of Hs andZ=114 isotopes with WKB penetration probability, and the potential barrier is constructed by the GLDM. The calculated alpha decay half-live of 264Hs is 23.33 second with MMM Q, 15.14 second with experimental Q. For 298114, the calculated alpha decay half-live is 1537588.07 seconds ( about 18 days).

32. 3Cluster radioactivity

36. 4 自发裂变 (1) Spontaneous fission of heavy and superheavy nuclei Spontaneous fission potential barrier for 235U It is evident the ellipsoidal deformation will decrease the potential barrier, and the Shell corrections of the fragment will produce the second and third humps.

37. Comparison between theoretical (t) and experimental (e) barrier characteristics for actinide nuclei. Ea, Eb and Ecare the first, second and third peak heights while E2 and E3 are the energies of the second and third potential minima relatively to the ground state energy (in MeV). Ea and Eb are consistent with the experimental data. The predicted values of the second Minimum energy is a little too high. The still sparse but exciting data for the third barrier are Correctly reproduced.

38. The external barrier disappears since the attractive proximity forces can no more compensate for the repulsive Coulomb forces.

39. The spontaneous fission half-life is very sensitive with the nucleon number of the mother nucleus.

40. The logarithm of average deviations of a total of 47 spontaneous fission nuclei is: The average deviation between theoretical spontaneous fission half-life and the experimental ones is less than 100 times.

41. The trend of the theoretical results form [11] follows the experimental ones well, but the values are systematically larger than the experimental data. Our calculated results can reproduce the experimental spontaneous fission half-life better.

43. It is evident, for many superheavy nuclei, the spontaneous fission half-lives are long enough to be measured by the present experimental setups, if the spontaneous fission is the main decay mode.

44. (2) Competition between spontaneous fission and Alpha-decay for superheavy nuclei Our calculations can reasonably reproduce the experimental results, and the spontaneous can compete with alpha-decay. The magic neutron number N=184 is clear, and the half-lives decrease quickly after this neutron number.

45. From neutron number N=174 to 186, the alpha-decay half-lives are shorter than spontaneous fission half-lives. These SHN can be identified by their alpha-decay properties. The neutron magic number N=184 is confirmed.

46. 四 总结与展望 • 采用推广的液滴模型计算了原子核的质子放射性、阿尔法衰变、重离子放射性以及自发裂变，结果与实验符合很好，并作了大量预言. • 推广的液滴模型的计算结果表明，原子核的阿尔法衰变具有预形成过程. • 超重核的自发裂变与阿尔法衰变具有竞争性. • 下一步的研究将考虑对重核和超重核，质子放射性、阿尔法衰变、重离子放射性以及自发裂变的竞争，较好预言原子核的半寿命. • 采用推广的液滴模型研究熔合反应，并将准分子形状机制引入到与双核模型。

47. Collaborators G. Royer (Nantes University/IN2P3,France) 李君清, 左维 (兰州近物所) 马中玉、陈宝秋（中国原子能科学研究院） 赵恩广、周善贵(中科院理论物理研究所) 王宁 (广西师范大学) 高远 (兰州大学/杭州电子科技大学) 董建敏、包小军、王永佳、王佳眉、黄银、王莎 (兰州大学)

48. Thank you !