Study of fission dynamics with the three-dimensional Langevin equations

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei ²¹⁰Po and ²²⁴Th formed in the fusion-fission reactions ⁴He + ²⁰⁶Pb , ¹⁶O + ²⁰⁸Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data.     

Fission dynamics of the compound nucleus 213Fr formed in heavy-ion-induced reactions

A stochastic approach based on one-dimensional Langevin equations was used to calculate the average pre-fission multiplicities of neutrons, light charged particles and the fission probabilities for the compound nucleus ²¹³Fr and the results are compared with the experimental data. In these calculations, a modified wall and window dissipation with a reduction coefficient, k _s , has been used in the Langevin equations. It was shown that the results of the calculations are in good agreement with the experimental data by using values of k _s in the range 0.3?≤?k _s ?≤?0.5.     

Influence of nuclear dissipation on fission dynamics of the excited nucleus <Superscript>248</Superscript>Cf within a stochastic approach

A stochastic approach to fission dynamics based on two-dimensional Langevin equations was applied to calculate the anisotropy of the fission fragments angular distribution and average pre-scission neutron multiplicities for the compound nucleus ²⁴⁸Cf formed in the ¹⁶O+²³²Th reactions. Postsaddle nuclear dissipation strength of (12–14) × 10²¹ s^?1 was extracted for Cf nucleus by fitting the results of calculations with the experimental data. Furthermore, it was found that the results of calculations for the anisotropy of the fission fragments angular distribution and pre-scission neutron multiplicities are very sensitive to the magnitude of post-saddle nuclear dissipation.     

中子诱发233,235,238U裂变机制的多通道理论研究

用改进的多通道和无规颈断裂模型,计算了能量E_n=0—6MeV的中子诱发²³³U、²³⁵U裂变和E_n=1.3—5.3MeV中子诱发²³⁸U裂变的碎片的质量分布、动能分布和瞬发中子数分布,理论计算在定量上与实验符合较好.     

Research on the prompt neutron multiplicity of fission fragments for 235U(n,f)

According to some experimental and evaluated data, the total excitation energy partitioning way between both of the fission fragments was given with a semi-empirical method. With the calculated energy partitioning way, the prompt neutron multiplicity as a function of fragment mass, (-v)(A), for neutron-induced fission of 235U at En=0.0253 eV, 3 MeV, and 5 MeV was calculated. The results are checked with the total average prompt neutron multiplicities (-v) and compared with the experimental and evaluated data.     

Potential energy surfaces and fission fragment mass yields of even-even superheavy nuclei

Potential energy surfaces and fission barriers of superheavy nuclei are analyzed in a macroscopic-microscopic model. The Lublin-Strasbourg Drop (LSD) model is used to obtain the macroscopic part of the energy, whereas the shell and pairing energy corrections are evaluated using the Yukawa-folded potential; a standard flooding technique is utilized to determine barrier heights. A Fourier shape parametrization containing only three deformation parameters is shown to effectively reproduce the nuclear shapes of nuclei approaching fission. In addition, a non-axial degree of freedom is taken into account to better describe the structure of nuclei around the ground state and in the saddle region. In addition to the symmetric fission valley, a new highly asymmetric fission mode is predicted in most superheavy nuclei. The fission fragment mass distributions of the considered nuclei are obtained by solving 3D Langevin equations.     

Temperature dependent fission fragment distribution in the Langevin equation

The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.     

Temperature dependent fission fragment distribution in the Langevin equation

The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.     

Prompt neutron multiplicity distribution for 235U(n,f) at incident energies up to 20 MeV

For the n+<'235>U fission reaction, the total excitation energy partition of the fission fragments, the average neutron kinetic energy <ε>(A) and the total average energies E<,γ>(A) removed by γ rays as a function of fission fragment mass are given at incident energies up to 20 MeV. The prompt neutron multiplicity as a function of the fragment mass, ν(A), for neutron-induced fission of <'235>U at different incident neutron energies is calculated. The calculated results are checked with the total average prompt neutron multiplicities ν and compared with the experimental and evaluated data. Some prompt neutron and γ emission mechanisms are discussed.     

高温下复合核的热裂变速率

在核裂变的动力学描述中,考虑到质量随坐标的连续变化,提出了自由能有效势,导出了一个新的裂变速率公式.改进后的公式对于核温度与势能位垒高度相当的热核裂变同样适用,其结果比Kramers公式更接近于断点裂变速率的朗之万模拟值.     

Langevin fission dynamics of hot rotating nuclei: Systematic application to Z 2/A=34–42 heavy nuclei

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations is used to calculate the mass-energy distributions of fragments originating from the fission of compound nuclei whose fissility parameter lies in the range Z ²/A=34–42. In these calculations, use was made of the liquid-drop model allowing for finite-range nuclear forces and the diffuseness of the nuclear surface in calculating the potential energy and a modified one-body mechanism of viscosity in describing dissipation. The emission of light prescission particles is taken into account on the basis of the statistical model. The calculations performed within three-dimensional Langevin dynamics reproduce well all parameters of the experimental mass-energy distributions of fission fragments and all parameters of the prefission-neutron multiplicity for various parameters of the compound nucleus. The inclusion of the third collective coordinate in the Langevin equations leads to a considerable increase (by up to 40–50%) in the variances of mass-energy distributions in relation to what was previously obtained from two-dimensional Langevin calculations. For the parameters of the mass-energy distributions of fission fragments and the parameters of the prefission-neutron multiplicity to be reproduced simultaneously, the reduction coefficient K _s must be diminished at least by a factor of 2(0.2≤K _s ≤0.5) in relation to that in the case of total one-body viscosity (K _s =1).     

同位旋对用裂变截面探测鞍点前摩擦的影响

耦合了轻粒子发射的随机Langevin模型被用于计算三个Bi裂变系统因核耗散效应引起的相对于标准统计模型预计的裂变截面值的变化,σ_fdrop作为激发能的函数。发现209Bi的σ_fdrop要大于202Bi和195Bi的σ_fdrop,这表明高同位旋系统209Bi的裂变截面对摩擦强度有更大的敏感性。该结果建议,当实验上使用裂变激发函数来更精确地提取鞍点前摩擦强度时,应产生具有高同位旋的复合核。进而,通过Langevin计算拟合p+206Pb和p+209Bi反应的裂变激发函数数据,提取的鞍点前摩擦强度为（3~5）×1021 s-1。Langevin models that are coupled with particle emission are applied to calculate the drop of fission cross section caused by friction over its standard statistical-model value, σ_fdrop, as a function of excitation energy for three Bi nuclei with different isospins. We find that σ_fdrop become larger for 209Bi than for 202Bi and 195Bi, indicating a greater sensitivity of fission cross section to friction for high-isospin 209Bi. These results suggest that, to more accurately determine the presaddle dissipation strength by measuring fission excitation functions, it is best to populate those compound systems with a high isospin. Furthermore, we analyze the data of fission excitation functions measured in p + 209Bi and p + 208Pb reactions, which yield high-isospin 210Po and 209Bi systems, and extract a presaddle friction strength of (3-5)×1021 s-1 by comparing Langevin simulations with these experimental data.     

基于裂变γ标识技术的瞬发裂变中子谱测量新方法

瞬发裂变中子谱（prompt fission neutron spectrum,PFNS）是用于核实验诊断过程中十分重要的参数数据,传统的测量主锕系核素（U,Pu）PFNS的技术手段是采用裂变室,利用裂变碎片标识裂变中子,通过中子飞行时间技术获得裂变中子谱.目前出现了一种新的用于PFNS测量的技术,其原理是基于如下的物理事实：在一次裂变过程中,释放中子的同时伴随着释放7–8个γ射线光子,而非弹性散射效应产生的γ射线光子只有1–2个.据此,可以通过裂变γ射线的多重性将裂变中子和其他杂散中子甄选出来,达到测量PFNS的目的.本文建立了基于裂变γ标识技术的PFNS测量实验系统.利用该系统对²⁵²Cf中子源的PFNS进行了实验测量,测量结果与传统的裂变碎片标识法及ENDF/B-VⅡ数据库的标准谱进行了比较,对新方法的裂变标识率以及实验不确定度也一并进行了分析.     

Calculation of prompt fission neutron spectra for 235U(n,f)

The prompt fission neutron spectra for the neutron-induced fission of ²³⁵U at E_n < 5 MeV are calculated using nuclear evaporation theory with a semi-empirical model, in which the nonconstant and constant temperatures related to the Fermi gas model are taken into account. The calculated prompt fission neutron spectra reproduce the experimental data well. For the n(thermal)+²³⁵U reaction, the average nuclear temperature of the fission fragment, and the probability distribution of the nuclear temperature, are discussed and compared with the Los Alamos model. The energy carried away by γ rays emitted from each fragment is also obtained and the results are in good agreement with the existing experimental data.     

Multiparameter studies of polar emission in 236U fission

The energy distributions and relative intensities of protons, deutrons, tritons and α-particles emitted along the fission axis during thermal neutron fission of ²³⁵U were measured simultaneously with both fission fragment energies. The mass distributions of fragments, the total kinetic energy (TKE), the dependence of the mean TKE on the fragment mass, as well as the mean kinetic energy dependence of polar particles on the fragment mass and energy were subsequently deduced from these data. Although some experimental results agree remarkably well with the hypothesis that polar particles are evaporated in flight from fission fragments, the general conclusion is that these particles are emitted according to some other mechanism.     

Study of different features offission dynamics of ~(224)Th produced in fusion reactions within a stochastic approach

The evaporation residue cross section anisotropy of the fission fragment angular distribution, pre-scission neutron multiplicity and the pre-saddle and post-saddle contributions of the pre-scission neutron multiplicity were analyzed within a stochastic approach based on one-, two- and three-dimensional Langevin equations for the compound nucleus224 Th formed via a complete fusion. In these calculations, dissipation was generated through the chaos weighted wall and window friction formula. Comparison of the theoretical results with the experimental data showed that three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula make it possible to reproduce satisfactorily the above-mentioned experimental data.     

Angular distributions of light charged particles from 252Cf fission in the ranges 0–46° and 134–180°

Alpha particles, tritons, deuterons and protons accompanying ²⁵²Cf fission were registered in coincidence with both fission fragments by means of a system containing two-dimensional position-sensitive silicon detectors. Angular distributions, kinetic energy spectra of light charged particles as well as mass distributions of fission fragments in coincidence with light charged particles were measured. The experimental results are compared with some theoretical models.     

Mass-energy distribution of fragments from the fission of excited nuclei within three-dimensional Langevin dynamics

Two-dimensional mass-energy distributions of fission fragments are calculated for the first time on the basis of three-dimensional stochastic Langevin equations. In these calculations, the emission of light prescission particles is taken into account within the statistical model. The results demonstrate that calculations within three-dimensional Langevin dynamics make it possible to describe most compre-hensively the properties of the mass-energy distribution of fission fragments and the mean multiplicity of prescission neutrons.