基于傅里叶级数展开的裂变位能曲面与碎片质量分布计算

裂变位能曲面是裂变核结构性质和裂变动力学研究的基础。本文使用傅里叶级数展开方法描述裂变过程中原子核的形状,采用基于Lublin Strasbourg Drop(LSD)宏观模型和Yukawa Folded微观模型计算了236U多维裂变位能曲面,研究了位能曲面随不同集体自由度(原子核拉长形变、左右碎片质量不对称度以及颈部宽度)的变化情况以及温度对位能曲面的影响。在位能曲面基础上采用基于Born Oppenheimer近似的三维集体模型描述原子核裂变过程,计算了236U裂变碎片质量分布,计算结果与实验数据符合较好,特别是质量分布的峰位,同时分析了核温度、零点能和颈部断裂概率半宽度对裂变碎片质量分布计算结果的影响。     

基于协变密度泛函理论的258Fm诱发裂变动力学研究

采用基于协变密度泛函理论的含时生成坐标方法研究了258Fm低能诱发裂变动力学性质,重点探讨了裂变位能曲面、裂变碎片总动能分布和碎片质量分布等。研究表明,258Fm位能曲面中存在显著的对称裂变谷,因而其低能裂变碎片总动能分布与质量分布均呈单峰结构,且随剪裂线判据Qn（脖子处粒子数）从4减至1,碎片总动能分布变窄,碎片质量分布的峰值从988%增至1028%。此外,随初态激发能从83 MeV增至173 MeV,碎片质量分布峰值从988%降至855%。     

十年来核裂变电荷分布研究的新进展

近十年来电荷分布研究取得了显著进展。独立产额测量技术的进步加快了实验数据积累,得到了较为丰富的信息。在分析总结现有效据基础上提出并建立了某些新的电荷分布经验模型。新模型为低能核裂变电荷分布系统学研究、独立产额实验数据评价和预报提供了一个更为有效的方法。     

Nuclear fission in heavy elements by high-energy particles

The results of a radiochemical investigation of nuclear fission in uranium, thorium, and bismuth by protons with an energy of 680 Mev are presented. Using an interpolation method a complete chart of the fission residue products is obtained. It is noted that there is a predominance in the production of nuclei with excess neutrons (58–64%); it is also shown that isotopes with maximum yield lie mainly in the neutron-ex cess region. The probability for symmetric fission is largest in bismuth. The cross sections for fission in uranium and thorium are 55–60% of the geometric cross section; in bismuth it is 5%. The charge distribution of fragments in fission induced by high energy protons is constant and independent of the mass number of the fission fragments and the atomic number of the fissioning nucleus. An analysis of the main features of the fission process seems to indicate that fission in uranium and thorium is due to a combined barrier-emission mechanism.     

Investigation of the statistical distribution of spontaneous U238 fission acts according to the energies of the two fragments

Using an apparatus consisting of a double pulse ionization chamber, two amplifying channels, a coincidence circuit and a two-beam pulsed oscillograph, we measured the kinetic energy of each of the two fragments formed during nuclear fission. 780 cases of spontaneous U²³⁸ fission and about 4500 cases of U²³⁵ fission by slow neutrons were recorded. Using these data we plotted the statistical distributions of acts of spontaneous fission and fission with slow neutrons according to the energies of the two fragments. These distributions gave the following curves for the two fission methods: a) the energy spectrum of all fragments and that of light and heavy fragments separately; b) the distribution of acts according to the total kinetic energy of the two nuclear fragments; c) the distribution of fission fragments according to mass; d) the relation of the average total kinetic energy of the two fragments to the ratio of their masses; and e) the relation of the average kinetic energy of light and heavy fragments to their total kinetic energy. The results of the two methods of fission are quite similar. It was found that the total kinetic energy of the two fragments in spontaneous U²³⁸ fission was, on the average, 4 Mev less than the energy in U²³⁵ fission by slow neutrons.     

热中子诱发239Pu裂变初级裂变产物质量分布测量

原子核裂变是最复杂的物理过程之一,至今仍缺乏可以统一描述裂变前和裂变后过程的理论。中子诱发239Pu裂变产额数据是重要的核数据,完整的初级裂变产物质量分布数据有助于完善裂变理论模型并提高产额评价数据的质量。本文研制了初级裂变产物鉴别谱仪（FFIS）,通过屏栅电离室和微通道板时间探测器分别测量裂变碎片的动能和飞行时间,基于动能 速度关联的方法直接获得碎片放中子后的质量分布,在BNCT医院中子照射器（IHNI 1）上开展了热中子诱发239Pu裂变初级裂变产物的质量分布测量。测量结果表明,对轻峰碎片质量分辨约为1 amu,对重峰碎片质量分辨约为15 amu。239Pu(nth,f)初级裂变产物质量分布的精确测量可为裂变产额理论计算和评价提供重要的实验数据。     

234U裂变的五维势能曲面计算

本工作基于连接二次曲面的形状描述+LSD(Lublin Strasbourg drop)公式+折叠汤川势建立了宏观 微观模型。对234U裂变,计算了具有5 906 250个格点的五维势能曲面,然后通过搜索势能曲面得到了对称裂变和非对称裂变两个裂变通道,给出了裂变势垒高度以及鞍点和断点等特殊位置的原子核形状。     

The excitation energy of fragments in nuclear fission

The multiplication factor for chain reactions in a nuclear reactor depends essentially on the number of secondary neutrons emitted during fission, and this is determined completely by the excitation energy of the fragments. Therefore, calculation of the excitation energy of the fragments as a function of the atomic number Z and the atomic weight A of the fissioning nucleus is of considerable interest in atomic energy.In the work it was shown that the excitation energy of the fragments may be found by solving a system of equations for the deformation parameters of the fragments and the distance between them. The basic excitation energies of the fragments were found for some nuclei. An investigation was made of the dependence of the excitation energy on Z and A of the fissioning nucleus.In conclusion, the author would like to thank V. M. Galitskii and V. M. Strutinskii for an interesting discussion and I. G. Krutikova for carrying out the numerical calculations.     

A New Insight into Energy Distribution of Electrons in Fuel-Rod Gap in VVER-1000 Nuclear Reactor

In order to calculate the electron energy distribution in the fuel rod gap of a VVER-1000 nuclear reactor,the Fokker-Planck equation(FPE)governing the non-equilibrium behavior of electrons passing through the fuel-rod gap as an absorber has been solved in this paper.Besides,the Monte Carlo Geant4 code was employed to simulate the electron migration in the fuel-rod gap and the energy distribution of electrons was found.As for the results,the accuracy of the FPE was compared to the Geant4 code outcomes and a satisfactory agreement was found.Also,different percentage of the volatile and noble gas fission fragments produced in fission reactions in fuel rod,i.e.Krypton,Xenon,Iodine,Bromine,Rubidium and Cesium were employed so as to investigate their effects on the electrons' energy distribution.The present results show that most of the electrons in the fuel rod's gap were within the thermal energy limitation and the tail of the electron energy distribution was far from a Maxwellian distribution.The interesting outcome was that the electron energy distribution is slightly increased due to the accumulation of fission fragments in the gap.It should be noted that solving the FPE for the energy straggling electrons that are penetrating into the fuel-rod gap in the VVER-1000 nuclear reactor has been carried out for the first time using an analytical approach.     

基于能量-速度关联技术的裂变产物质量分布测量方法研究

采用能量E-速度v关联技术测量裂变产物碎片的动能和飞行速度能精确测定裂变产物核的质量。本工作主要研究能量-速度关联技术的可行性并解决相关关键技术。实验测量系统由飞行时间测量单元、能量探测器和真空靶室系统组成。实验中用1对微通道板探测器测量粒子飞行时间来确定粒子速度,金硅面垒探测器测量粒子能量。对于~(241) Am放射源5.48 MeVα粒子,飞行时间测量系统时间分辨(FWHM)为186ps,金硅面垒探测器能量分辨(FWHM)为44keV。实验完成了~(252) Cf自发裂变源产物质量分布试测量。初步实验结果显示,裂变产物质量分布在110amu(amu为原子质量单位)的位置时,其质量分辨为1.6amu。     

Calcul du profil d'endommagement par une source isotrope de fragments de fission: Application aux gaines d'acier inoxydable du combustible UO2

The damage distribution produced by an isotropie fission fragments source in contact with a metallic target has been investigated. More precisely, the density of energy transferred by such a source to the target lattice has been computed as a function of the depth in the target. The basis of these calculations is Lindhard's theory which gives for each fission fragment emitted by the source the energy lost in atomic collisions. The results can be applied to the fission fragments damage produced by the fuel of a nuclear reactor in the clad which contains it.     

Diffraction Effects in Nuclear Cross Sections

Some of the most noticeable resonance structures in the energy dependence of nuclear cross sections and other reaction characteristics, for example, the kinetic energy and angular anisotropy, of fission fragments are correlated for different nuclei irrespective of the parity of their atomic number and mass number. The resonance structures in the neutron cross sections can also correlate with the structure of the cross sections of photonuclear reactions with equal wave length of the neutron and radiation. These correlations could be due to the diffraction of waves by the spatial structures of a nucleus, for example, isolated nuclear shells.     

宏观-微观模型和朗之万方法在低能核裂变研究中的应用

基于三维朗之万模型对低能核裂变动力学过程和断点构型进行了研究,其中位能曲面采用基于双中心壳模型和有限程液滴模型的宏观 微观模型计算得到,质量张量和黏滞张量分别采用Werner Wheeler方法和墙加窗一体模型得到。以14 MeV中子诱发235U裂变为例,分别研究了拉长形变空间和壳衰减因子对裂变碎片质量分布、总动能分布及断点处核拉长与质量非对称度关联的影响,确定了模型计算中拉长形变空间边界至少应为35R0（R0为球形核半径）,以及壳衰减因子的合理取值为60 MeV。基于该模型,计算得到了14 MeV中子诱发233,235U裂变碎片质量分布,与ENDF/B Ⅷ0评价数据符合较好,说明该模型具有定量计算裂变碎片质量分布的能力。     

Improvements in the description of the multiplicities of the prompt neutrons emitted in fission

Various parameterizations of the multiplicity distribution of prompt neutrons from nuclear fission are investigated. The currently accepted formalism is found to fail for those fission processes which release on average a low number of neutrons. Based on realistic assumptions regarding binary fission, an improved multiplicity distribution formula gives much better agreement with the experimental data. Explicit details of the practical usage of the new formalism are presented. Finally, it is shown that for spontaneously fissioning isotopes, it is possible to calculate the variance of the neutron multiplicity distribution from a knowledge of the mass yield and the variances of the neutron multiplicity distributions of the individual fission fragments.     

Distribution of fragments by mass in fission of U235. U238 and Pu239 by neutrons of 14.6 Mev energy

A study of the mass distribution of fission fragments provides a better understanding of the fission process for heavy nuclei. In addition, a knowledge of the relative yield of various fragments is necessary in some practical uses of radioactive isotopes.In this paper the method and results of measurements of the relative production of several fragments, formed in the fission of U²³⁵, U²³⁸ and Pu²³⁹ by neutrons with energy of 14.6 Mev, are given. By experimental and reflected points, curves are obtained for the distribution of fragments by masses. Some special features of this distribution are interpreted.     

Systematic behaviour of the average parameters required for the Los Alamos model of prompt neutron emission

A large number of fissioning systems have been studied in the frame of the Los Alamos model which showed interesting regular behaviours of the average model parameters (the energy release in fission 〈E_r〉, the total kinetic energy of the fission fragments 〈TKE〉, the average neutron separation energy 〈S_n〉 from the fission fragments, the prompt gamma-ray energy 〈E_γ〉 and the level density parameter 〈a〉 parameterized as 〈C〉 = A/〈a〉, where A is the mass number of the fissioning nucleus)) as well as of other quantities in connection with the prompt fission neutron emission (such as the total average prompt neutron multiplicity at thermal incident energy, the total average fission fragment excitation energy leading to prompt neutron emission, the total average prompt fission energy deposition, the average excitation energy given to the fragments, and the average center-of-mass energy of prompt neutrons and so on) and to elaborate systematics of model parameters.     

Angle and energy distributions of fission neutrons

Using the statistical model of the nucleus the angle distribution of fission neutrons is determined taking into account the anisotropy in the angle distribution of the fission fragments. The latter quantity is approximated by a simple expression of the form 1 + kcos² α. It is assumed that the neutrons are emitted isotropically in the coordinate system in which the fragment is at rest. Using U²³⁸, a calculation is carried out to determine the values of P — the ratio of the intensity of fission neutrons emitted in the direction of the incident neutrons to that of neutrons emitted perpendicularly to the incident beam — at various energy values of the primary and secondary neutrons (in the region from 1 to 10 Mev). The mean value of P in fission in U²³⁸ by neutrons characteristic of a fission spectrum is found to be approximately 1.13. The energy spectra for fission neutrons at various primary-neutron energies are also obtained. The method of calculation can also be employed in investigations of the anisotropy of neutrons produced in fission of other nuclei.     

Neutron Repulsion Confirmed as Energy Source

Systematic properties of heavy nuclides reveal a fine structure in Coulomb energy that parallels variations in mass arising from n-n interactions between neutrons. These results confirm an earlier suggestion that n-n interactions in the nucleus are repulsive. Neutron emission may release up to 1.1%–2.4% of the nuclear rest mass as energy. By comparison, 0.8% of the rest mass is converted to energy in hydrogen fusion and 0.1% is converted to energy in fission. Neutron emission in the core of the Sun may trigger a series of reactions that collectively produce the Sun's luminosity and an outpouring of protons and neutrinos from its surface.     

基于贝叶斯机器学习对中子诱发235U裂变的产额-能量关系的研究

核裂变碎片产额是核能发展和核技术应用领域的重要基础数据,但在实验和理论上获得精确且完整的能量依赖的裂变产额到目前为止都非常困难。本文提出采用贝叶斯机器学习方法对所有收集到的中子诱发235U裂变产额实验数据进行了数据融合学习和评价。基于该评价方法对关键裂变碎片的产额 能量关系进行推断,并得到了二维的碎片累积产额分布随入射中子能量的变化关系。所得的二维产额分布能合理地反映裂变模式随能量增加的演化,但目前结果的不确定度较大,有待进一步改进。