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1、推广的液滴模型及其应用简介推广的液滴模型及其应用简介张鸿飞张鸿飞 兰州大学核科学与技术学院兰州大学核科学与技术学院2012超重核合成与性质研讨会（SHN2012），8月9-13, 2012, 兰州 内内 容容一一 物理目标物理目标二二 模型简介模型简介三三 模型应用模型应用四四 总结与展望总结与展望 采用改进的宏观模型定量描述：采用改进的宏观模型定量描述：1 原子核质量（结合能）与形变原子核质量（结合能）与形变2 alpha衰变衰变3 质子放射性质子放射性4 集团放射性集团放射性5 自发裂变自发裂变6 诱发裂变诱发裂变7 各种衰变模型竞争，较好确定原子核寿命各种衰变模型竞争，较好确定原子核寿命
2、8 熔合反应熔合反应一一 物理目标物理目标自发裂变与阿尔法衰变的竞争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 competitiv
3、e with alpha-decay.Phys. Rev. Lett. 104, 142502 (2010)The known heaviest odd-A and odd-odd nuclei are also detected by alpha decay. Forthe products, the decay mode is still alpha emission up to Rg and Db. It seems that theodd-even effect plays an important role on selecting the decay mode for SHN.Th
4、e decay mode of 114 isotopes is also isospin dependent.Confirm the odd-even effect is very important for determination of the decay mode.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
5、 fission.二二 模型简介模型简介(1) Potential barrier ( from GLDM)The spontaneous fission and alpha-decay potential barriers are constructedby 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
6、 separated spherical nuclei, The improvements were made for the conventional liquid drop model(a) Quasi-molecular shapesTwo parameters s1=a/c1, s2=a/c2are used to describe the shape evolutionThe most impressively feature of the quasi-molecular shapes is that it can describe the process of the shapes
7、 evolution from one body to two separated fragments in a unified way(b) Proximity energyThe nuclear energy EN has been introduced to take into account the finite-range effects of the nucleon-nucleon force between theclose surfaces . (Royer, NPA 444, (1985) 477)is surface parameter.The introduction o
8、f proximity force lowers the barrier of 7.3 MeV, and shift the peak 2.1 fm towards a more external position for 264Hs.(c) Shell correction energyW.D.Myers, Droplet Model of Atomic Nuclei (Plenum,New-York, 1977).The Strutinsky method was adopted to calculate Single particle levels ei are calculated i
9、n an axially Woods-Saxon potential.Wang Ning and Liu Min Phys Rev C 81,067302(2010).(d) Pairing energy(W.D. Myers and W.J. Swiatecki, Nucl. Phys. A601 (1996) 141)The pairing energy has been calculated with the following expressions used in a recent version of the ThomasFermi modelis the ratio of the
10、 surface area of the nucleus at the actual shapeto the surface area of the nucleus at the spherical shape.(2) Half-lifeJ.Randrup, S.E.Larsson, P.Moller, S.G.Nilsson,K.Pomorski and A.Sobiczewski, Phys.Rev.C 13229(1976).Where k is 14.8.Only several channels (in the bottom of every curve) play the key
11、role to determinethe spontaneous fission half-life. The decay constant of the mother nucleus is the summation of all possible spontaneous fission decay constant.三三 模型应用模型应用1 质子放射性质子放射性衰变常数衰变常数谱因子谱因子1 阿尔法衰变阿尔法衰变 Alpha decay process There are two different decay modes for alpha decay in the market, cl
12、uster-like and fission-like modes. Cluster-like modeFission-like modeThe experimental investigation can not unambiguously distinguish these two decay modes up to now. 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 clu
13、ster inside the mother nucleus can be extracted from Eq. (1).The penetration probabilityplays the most important roleto determine the life-time ofalpha decay.The preformation factor and assault frequency reflect thenuclear structure features ofthe mother nucleus.Clearly the closed shell structurespl
14、ay the key role for the preformationmechanism, and more the nucleonnumber is close to the magic nucleonnumbers, the more the preformationof alpha cluster is difficult inside themother nucleus. Zhang et al., PRC 80, (2009) 057301In the framework of fission-like mode (Wang,Zhang, Zuo and Li, CPL 27, (
15、2010), 062103)log10v0An approach to deal with the assault frequency Zhang,Royer and Li, PRC 84 (2011) 027303G is globle quantum number.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. Alpha d
16、ecay properties of SHNTo find out the reasonablealpha decay energy andthe features of SHN.MMM results formWang et al., PRC 81 (2010) 044322, PRC 82 (2010) 044304.Experimental data from Audi 2013.The RMS deviation with respectto 2149 measured nuclear massesIs 0.441 MeV ( the correspondingresults with
17、 FRDM is 0.566 MeV).Another impressed improvement isthe RMS deviation of 46 SHN is reduced 0.263 MeV ( 0.566 MeVfor FRDM )One proton separation energies and alpha decay energies of 162 isotones and 184 isotones.Potential energy surface of 270Hs and 298114 by Constrained Relativistic Mean Field theor
18、y with the parameters NL3The nucleus 270Hs is a double sub-magic nucleus and 298114 is a sphericaldouble magic nucleus.Alpha decay life-times of Hs and Z=114 isotopes with WKB penetration probability, and the potential barrier is constructed by the GLDM.The calculated alpha decay half-live of 264Hs
19、is 23.33 second with MMM Q, 15.14 second with experimental Q. For 298114, the calculated alpha decayhalf-live is 1537588.07 seconds ( about 18 days).3 Cluster radioactivity4 自发裂变自发裂变(1) Spontaneous fission of heavy and superheavy nuclei Spontaneous fission potential barrier for 235UIt is evident the
20、 ellipsoidal deformation will decrease the potential barrier, and theShell corrections of the fragment will produce the second and third humps.Comparison between theoretical (t) and experimental (e) barrier characteristics for actinide nuclei. Ea, Eb and Ec are the first, second and third peak heigh
21、ts 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 secondMinimum energy is a little too high. The still sparse but exciting data for the third bar
22、rier areCorrectly reproduced.The external barrier disappears since the attractive proximity forces can no morecompensate for the repulsive Coulomb forces.The spontaneous fission half-life is very sensitive with the nucleon number of the mother nucleus.The logarithm of average deviations of a total o
23、f 47 spontaneous fission nuclei is: The average deviation between theoretical spontaneous fission half-life and the experimental ones is less than 100 times.The trend of the theoretical results form 11 follows the experimental ones well, but the valuesare systematically larger than the experimental
24、data. Our calculated results can reproduce theexperimental spontaneous fission half-life better.It is evident, for many superheavy nuclei, the spontaneous fission half-lives arelong enough to be measured by the present experimental setups, if the spontaneous fission is the main decay mode.(2) Compet
25、ition between spontaneous fission and Alpha-decay for superheavy nuclei Our calculations can reasonably reproduce the experimental results, and the spontaneouscan compete with alpha-decay. The magic neutron number N=184 is clear, and the half-livesdecrease quickly after this neutron number.From neut
26、ron number N=174 to 186, the alpha-decay half-lives are shorter than spontaneousfission half-lives. These SHN can be identified by their alpha-decay properties. The neutronmagic number N=184 is confirmed.四四 总结与展望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
27、，并作了大量预言性以及自发裂变，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。CollaboratorsG. 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)Thank you !
