中子诱发锕系核裂变初始碎片质量分布的研究
摘要
尽管核裂变机制的研究自其发现至今已经发展了70多年,但是到目前为止,理论上还没有一套可以很好描述核裂变机制的基本理论。由于锕系核在核能应用中占据着非常重要的地位,中子诱发锕系核裂变机制的研究是最多,同时也是最为详细的。核裂变生成的初始碎片质量分布是核裂变研究的重点内容之一,它与核裂变机制、产物产额、中子多重数、裂变碎片平均总动能等关键核数据密切相关。因此,本文致力于研究中子诱发锕系核裂变初始碎片的质量分布,为核裂变机制及其裂变后现象的研究奠定基础。
对中低能中子诱发锕系核裂变的调研表明,初始碎片质量分布具有双峰分布特征,质量分布的峰谷位置及其高度与入射中子能量具有一定的依赖关系。基于实验数据的特点以及现有理论模型的优点,本文提出了一个新的唯象裂变势理论,以计算中低能中子诱发锕系核裂变初始碎片质量分布。该裂变势理论中包含的各物理参量都可以写成与质量分布的峰谷位置及其高度的函数依赖关系。因此,质量分布的峰谷位置及其高度是整个唯象裂变势理论研究的重点内容。(1)对于低能中子诱发锕系核裂变(En(?)7MeV),初始碎片质量分布的双峰位置是利用基于Skyrme能量密度泛函和Thomas-Fermi近似条件下的核-核驱动势计算得到,计算结果表明重峰位置A2基本保持在140附近,这与实验数据及P. Moller等人的研究结论一致。同时我们给出了核裂变碎片质量分布的峰谷高度与入射中子能量线性关系的表示形式。(2)在中子入射能量较高的情况(7MeV(?)En(?)60MeV,有最新的测量数据),锕系核裂变机制更为复杂,表现为需要考虑裂变前发射中子的可能性,而且随着中子入射能量不同而有所不同。对入射中子能量小于60MeV的中子诱发238U裂变初始碎片质量分布的实验数据调研表明,分布的轻峰位置基本保持恒定A1=99,而重峰位置则随入射中子能量的增大而减小,并与裂变道理论密切相关。同时,我们给出了碎片质量分布的峰谷高度与入射中子能量的指数依赖关系。根据以上两点研究结果,我们利用唯象裂变势理论计算了能量不同的中子诱发锕系核裂变初始碎片质量分布。计算结果表明,唯象裂变势理论不仅可以较好地重现已有的实验数据,而且还能对没有实验数据的能点给出合理的预言。为进一步开展对裂变后现象的研究积累了一定的理论基础。
Though the nuclear fission mechanism has been studied since it was discovered more than70years, there are not any theories or models which can well reproduce or predict the experimental data. Due to the actinide is the most important nucleus in the nuclear energy applications, the research of the neutron induced actinide nucleus fission is the most detailed. The pre-neutron-emission fragments mass distribution of the nuclear fission is one of the most important fission characteristics, which closely relative with the fission mechanism, the product yields, the neutron multiplicity, and the average total kinetic energy of the fragments. Therefore, this article focuses on studying the pre-neutron-emission fragments mass distributions of neutron induced actinide nucleus fission, which can lay foundation of the fission mechanism and the fission phenomenon.
From the investigation of the neutron induced actinide nucleus fission can be found that, the pre-neutron-emission fragments mass distributions have double-peaks characteristics, and the positions and heights of the distributions dependent on the incident neutron energies. Therefore, based on the experimental data and the advantages of the available theory models, this paper proposed a new phenomenological fission potential theory for calculating the pre-neutron-emission fragments mass distributions of the middle-low energies neutron induced actinides fission. In this phenomenological fission potential theory, there are two important physical quantities, the positions and the heights of the peaks and the valley of the mass distributions. All of the coefficients of our theory can be written as the function of the positions and heights.(1) For the low energies (En≦7MeV) neutron induced actinide fission, the positions of the double-peaks can be calculated by the nucleus-nucleus potential which based on the the Shyme energy-density functional together with the extended Thomas-Fermi approximation. The positions of the heavy peak of the mass distributions A2≈140, which is good agreement with the measured result and the calculative result of the P. Moller. The heights of the peak and valley of the pre-neutron-emission fragments mass distributions are linear with the incident neutron energies in this paper.(2) Compared with low-energy fission, the intermediate energies (7MeV≦En≦60MeV, based on the new measured data) neutron induced actinide fission is more complicated. In this process, it must be considered the effect of neutron evaporation before the compound nuclear fission. For the neutron induced238U fission with incident energy less than60MeV, the investigation of the new experimental data found that the position of the light peak of the mass distributions A1=99, and the position of the heavy peak is closely relative with the multichannel. The heights of the double-peaks are index with the incident neutron energy. Based on the above conclusion, the pre-neutron-emission fragments mass distributions of different energies neutron induced actinide fission are calculated. The results of the calculations shown that, the phenomenological fission potential theory can not only well reproduce the measured data, but also can reasonably predict the unmeasured incident energies. The phenomenological fission potential theory is good for further study the fission phenomenon.
对中低能中子诱发锕系核裂变的调研表明,初始碎片质量分布具有双峰分布特征,质量分布的峰谷位置及其高度与入射中子能量具有一定的依赖关系。基于实验数据的特点以及现有理论模型的优点,本文提出了一个新的唯象裂变势理论,以计算中低能中子诱发锕系核裂变初始碎片质量分布。该裂变势理论中包含的各物理参量都可以写成与质量分布的峰谷位置及其高度的函数依赖关系。因此,质量分布的峰谷位置及其高度是整个唯象裂变势理论研究的重点内容。(1)对于低能中子诱发锕系核裂变(En(?)7MeV),初始碎片质量分布的双峰位置是利用基于Skyrme能量密度泛函和Thomas-Fermi近似条件下的核-核驱动势计算得到,计算结果表明重峰位置A2基本保持在140附近,这与实验数据及P. Moller等人的研究结论一致。同时我们给出了核裂变碎片质量分布的峰谷高度与入射中子能量线性关系的表示形式。(2)在中子入射能量较高的情况(7MeV(?)En(?)60MeV,有最新的测量数据),锕系核裂变机制更为复杂,表现为需要考虑裂变前发射中子的可能性,而且随着中子入射能量不同而有所不同。对入射中子能量小于60MeV的中子诱发238U裂变初始碎片质量分布的实验数据调研表明,分布的轻峰位置基本保持恒定A1=99,而重峰位置则随入射中子能量的增大而减小,并与裂变道理论密切相关。同时,我们给出了碎片质量分布的峰谷高度与入射中子能量的指数依赖关系。根据以上两点研究结果,我们利用唯象裂变势理论计算了能量不同的中子诱发锕系核裂变初始碎片质量分布。计算结果表明,唯象裂变势理论不仅可以较好地重现已有的实验数据,而且还能对没有实验数据的能点给出合理的预言。为进一步开展对裂变后现象的研究积累了一定的理论基础。
Though the nuclear fission mechanism has been studied since it was discovered more than70years, there are not any theories or models which can well reproduce or predict the experimental data. Due to the actinide is the most important nucleus in the nuclear energy applications, the research of the neutron induced actinide nucleus fission is the most detailed. The pre-neutron-emission fragments mass distribution of the nuclear fission is one of the most important fission characteristics, which closely relative with the fission mechanism, the product yields, the neutron multiplicity, and the average total kinetic energy of the fragments. Therefore, this article focuses on studying the pre-neutron-emission fragments mass distributions of neutron induced actinide nucleus fission, which can lay foundation of the fission mechanism and the fission phenomenon.
From the investigation of the neutron induced actinide nucleus fission can be found that, the pre-neutron-emission fragments mass distributions have double-peaks characteristics, and the positions and heights of the distributions dependent on the incident neutron energies. Therefore, based on the experimental data and the advantages of the available theory models, this paper proposed a new phenomenological fission potential theory for calculating the pre-neutron-emission fragments mass distributions of the middle-low energies neutron induced actinides fission. In this phenomenological fission potential theory, there are two important physical quantities, the positions and the heights of the peaks and the valley of the mass distributions. All of the coefficients of our theory can be written as the function of the positions and heights.(1) For the low energies (En≦7MeV) neutron induced actinide fission, the positions of the double-peaks can be calculated by the nucleus-nucleus potential which based on the the Shyme energy-density functional together with the extended Thomas-Fermi approximation. The positions of the heavy peak of the mass distributions A2≈140, which is good agreement with the measured result and the calculative result of the P. Moller. The heights of the peak and valley of the pre-neutron-emission fragments mass distributions are linear with the incident neutron energies in this paper.(2) Compared with low-energy fission, the intermediate energies (7MeV≦En≦60MeV, based on the new measured data) neutron induced actinide fission is more complicated. In this process, it must be considered the effect of neutron evaporation before the compound nuclear fission. For the neutron induced238U fission with incident energy less than60MeV, the investigation of the new experimental data found that the position of the light peak of the mass distributions A1=99, and the position of the heavy peak is closely relative with the multichannel. The heights of the double-peaks are index with the incident neutron energy. Based on the above conclusion, the pre-neutron-emission fragments mass distributions of different energies neutron induced actinide fission are calculated. The results of the calculations shown that, the phenomenological fission potential theory can not only well reproduce the measured data, but also can reasonably predict the unmeasured incident energies. The phenomenological fission potential theory is good for further study the fission phenomenon.
引文
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[3]胡济民.核裂变物理[M].北京大学出版社,1999.
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[7]王书暖.核反应理论[M].北京：原子能出版社,2007.
[8]杨毅.235U裂变产额随入射中子能量变化的实验研究[D].中国原子能科学院,2007.
[9]张竞上.核裂变和裂变机制的模型理论[J].现代物理知识,2003,1：22-27.
[10]孙小军.预平衡裂变动力学研究及n+12C反应的理论分析与中子核数据库的建立[D].中国原子能科学院,2007.
[11]D.G. Madland. Total prompt energy release in the neutron-induced Fission of 235U,238U, and 239Pu [J], Nuclear Physics A 772,113-137,2006.
[12]吴锡真.2011年核数据大会：裂变产物产额理论研究的一些进展.北京,2011.
[13]N. Bohr. J. A. Wheeler. The mechanism of fission [J]. Phys. Rev.56,426-450,1939.
[14]Peter Moller, Arnold J. Sierk, Takatoshi Ichikawa, et al. Heavy-element fission barriers [J]. Phys. Rev. C 79,064304,2009.
[15]S. Frankel and N. Metropolis. Calculations in the liquid-drop model of fission [J]. Phys. Rev. 72,914,1947.
[16]A. Bohr. On the theory of nuclear fission. In:IAEA. Proceedings of the international conference on the peaceful uses of atomic energy (Vol 2). Geneva:IAEA,1955.151-154.
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[19]P. Moller and J. R. Nix. In Proceedings of the Third IAEA Symposium on the Physics and Chemistry of Fission, Rochester, NY,1973 (IAEA, Vienna,1974), Vol. I, p.103.
[20]P. Moller, D. G. Madland. A. J. Sierk & A. Iwamoto. Nuclear fission modes and fragment mass asymmetries in a five-dimensional deformation space [J]. Nature (London) 409, 785-790,2001.
[21]孙小军,余呈刚.核裂变现象及其研究现状[J].广西物理,2010,31(2)：14-19.
[22]J. Decharge and D. Gogny. Hartree-Fock-Bogolyubov calculations with the D1 effective interaction on spherical nuclei [J]. Phys. Rev. C 21,1568-1593,1980.
[23]H. Goutte, J. F. Berger, P. Casoli, and D. Gogny. Microscopic approach of fission dynamics applied to fragment kinetic energy and mass distributions in 238U. Phys. Rev. C 71,024316, 2005.
[24]W. Younes and D. Gogny. Microscopic calculation of 240Pu scission with a finite-range effective force [J]. Phys. Rev. C 80,054313,2009.
[25]Wahl A. C. "Systematics of Fission-Product Yields", a paper Presented on 3rd Research Co-ordination Meeting on "Fission Product Yield Data Required for Transmutation of Minor Actinide Nuclear Waste" IAEA, Vienna,29 October-02 November,2001.
[26]D. V. Vanin, G. I. Kosenko, and G. D. Adeev. Langevin calculations of fission fragment mass distribution in fission of excited nuclei [J]. Phys. Rev. C 59,2114-2121,1999.
[27]A.V. Karpov, P. N. Nadtochy, D. V. Vanin, and G. D. Adeev. Three-dimensional Langevin calculations of fission fragment mass-energy distribution from excited compound nuclei [J]. Phys. Rev. C 63,054610,2001.
[28]P. N.Nadtochy, G. D.Adeev, A.V.Karpov. More detailed study of fission dynamics in fusion-fission reactions within a stochastic approach [J]. Phys. Rev. C 65,064615,2002.
[29]E.GRyabov, A.V. Karpov, P. N. Nadtochy, and G. D. Adeev. Application of a temperature-dependent liquid-drop model to dynamical Langevin calculations of fission-fragment distributions of excited nuclei [J]. Phys. Rev. C 78,044614,2008.
[30]P. Moller, Arnold J. Sierk, and Akira Iwamoto. Five-Dimensional Fission-Barrier Calculations from 70Se to 252Cf [J]. Phys. Rev. Lett 92,072501,2004.
[31]J. Randrup and P. Moller. Brownian Shape Motion on Five-Dimensional Potential-Energy Surfaces:Nuclear Fission-Fragment Mass Distributions [J]. Phys. Rev. Lett 106,132503, 2011.
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