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.     

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.     

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.     

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.     

Study of pre-scission particle emissions and fission probability of the ~(178)W produced in fusion reactions

A dynamical model based on one-dimensional Langevin equations was used to calculate the average pre-fission multiplicities of neutrons, light charged particles, and the fission probability for compound nucleus178 W produced in fusion reactions. The pre-scission multiplicities of particles and fission probability are calculated and compared with the experimental data over a wide range of excitation energy. A modified wall and window dissipation with a reduction coefficient, ks, has been used in the Langevin equations for reproducing experimental data. It was shown that the results of the calculations are in good agreement with the experimental data by using values of ks in the range 0.24 ks 0.47.     

Angular momentum effect in prescission particle multiplicities for a light system by diffusion model

The effect of angular momentum on the competition between fission and particle emission during light system fission process was studied via fission diffusion model. The prescission particle multiplicities were found to increase with decreasing angular momentum. The experimental prescission proton and α particle multiplicities can be fitted for 10.6 MeV/nucleon ⁸⁴Kr(²⁷Al,binary fission) reaction with this model. Entrance channel effect found in [1] is proved to be angular momentum effect.     

Effect of pre-equilibrium emission on probing postsaddle nuclear dissipation with neutrons

Using the stochastic Langevin model coupled with a statistical decay model, we study the influence of pre-equilibrium(PE) emission on probing postsaddle friction(β) with neutrons. A postsaddle friction value of(14-16.5) ×10~(21)s~(-1) and(11-13) ×10~(21)s~(-1) is obtained from comparing calculated and measured prescission neutron multiplicities of heavy fissioning systems248 Fm and256Fm in the absence and presence of the deformation factor.Moreover, it is found that a larger β is required to fit multiplicity data after the PE effect is accounted for, and that the effect becomes stronger when more energy is removed by PE particles. Our findings suggest that, to more accurately determine the postsaddle friction strength through the measurement of prescission neutrons, in addition to incorporating the contribution of PE evaporation source into the experimental multi-source analysis for particle energy spectra in coincidence with fission fragments, on the theoretical side, it is very important to make a precise evaluation of the energy that PE emission carries away from excited compound systems produced in heavy-ion fusion reactions.     

Dissipative dynamics of fission in the framework of asymptotic expansion of Fokker-Planck equation

The dynamics of fission has been formulated by generalising the asymptotic expansion of the Fokker-Planck equation in terms of the strength of the fluctuations where the diffusion coefficients depend on the stochastic variables explicitly. The prescission neutron multiplicities and mean kinetic energies of the evaporated neutrons have been calculated and compared with the respective experimental data over a wide range of excitation energy and compound nuclear mass. The mean and the variance of the total kinetic energies of the fission fragments have been calculated and compared with the experimental values. Received: 8 September 1999 / Revised version: 22 November 1999     

基于路径分析方法探究核耗散的形变关系

利用动力学加统计模型对200Pb 系统的断前中子的发射进行了模拟。计算结果表明,在核耗散的形变关系(DDND) 确定的情况下,断前中子多重性会随着能级密度坐标关系(DDLDP) 的增强而减少,且该规律主要由第一阶段内断前中子的发射决定。此外,选定DDLDP 而采用核耗散的不同形变关系也都很好地重现了实验数据。为了解释上述现象,提出了研究热核退激的路径分析方法,其主要内容是把核耗散看成是实验粒子在拉伸维度上的阻尼力,而核裂变的动力学过程是该阻尼力和自由能产生的驱动力之间相互竞争的结果。利用该方法对200Pb 系统的断前中子多重性进行了分析,并指出在确定DDND时应考虑DDLDP。Within a certain deformation dependence of nuclear dissipation (DDND), the simulation results about the deexcitation process of 200Pb show that the prescission neutron multiplicities decrease with increasing deformation dependence of level density parameter (DDLDP). Moreover, this pattern is determined by the emission of prescission neutron in the first period of nuclear fission. On the other hand, all of the results from two kinds of different DDNDs can reproduce the experiment data perfectly with a certain DDLDP. In order to illustrate those phenomena, the pathwise analysis method (PAM) is presented in this paper. In the PAM, nuclear dissipation is treated as the damping force on the elongation dimension, whereas the fission dynamics process results from the competition between damping force and the driving force stemming from the nuclear free energy. The prescission neutron multiplicity in the deexcitation process of 200Pb is analyzed, and the results point out that the DDLDP needs to be taken into account in studying the DDND.     

Influence of pre-saddle neutrons on the fission fragment angular distribution

In the present note it is shown that distinguishing between pre-saddle and saddle-to-scission neutrons removes a discrepancy previously found [2–4] between data for the fission fragment anisotropy and an analysis in the framework of the transition state theory in which it has been assumed that all pre-scission neutrons influence the temperature at the saddle point. The analysis of the present paper requires a fairly weak (=2 * 10²¹ s ^–1) friction at compact shapes, in agreement with a previous [9,10] analysis of prescission neutron multiplicities and fission probabilities.     

Combining a langevin description of heavy-ion induced fission including neutron evaporation with the statistical model

A model is developed which combines dynamical (Langevin-) calculations with the Kramers modified statistical model in order to describe heavy-ion induced fission including neutron evaporation. In the example of the¹⁹F+¹⁸¹Ta collision, the energy dependence of fission probabilities, neutron multiplicities and (H.I.,xn)-cross sections is calculated and a fair agreement with the data is achieved with a reduced friction parameter ofβ=3^*10²¹sec^?1. We pay particular attention to the angular momentum dependence of the fusion-fission process.     

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).     

Stochastic model of angular distributions of fragments originating from the fission of excited compound nuclei

The anisotropy of angular distributions of fission fragments and the average multiplicity of prescission neutrons were calculated within a stochastic approach to fission dynamics on the basis of three-dimensional Langevin equations. This approach was combined with a Monte Carlo algorithm for the degree of freedom K (projection of the total angular momentum I onto the fission axis). The relaxation time τ _K in the coordinate K was considered as a free parameter of the model; it was estimated on the basis of a fit to experimental data on the anisotropy of angular distributions. Specifically, the relaxation time τ _K was estimated at 2 × 10^?21 s for the compound nuclei ²²⁴Th and ²²⁵Pa and at 4 × 10^?21 s for the heavier nuclei ²⁴⁸Cf, ²⁵⁴Fm, and ²⁶⁴Rf. The potential energy was calculated on the basis of the liquid-drop model with allowance for finiteness of the range of nuclear forces and for the diffuseness of the nuclear surface. A modified one-body viscosity mechanism featuring a coefficient k _s that takes into account the reduction of the contribution from the wall formula was used to describe collective-energy dissipation. The coefficient k _s was also treated as a free parameter and was estimated at 0.5 on the basis of a fit to experimental data on the average prescission multiplicity of neutrons.     

曲率能及压缩能对缺中子裂变系统断前中子发射的影响

用改进了的动力学与统计相结合的模型, 研究了曲率能及压缩能对\,4\,个缺中子裂变系统: ¹⁸⁸Pt, ²⁰⁰Pb, ²¹³Fr和²²⁴Th的断前中子发射的影响. 计算结果显示用改进模型得到的断前中子多重性相比原来模型的低估要更靠近实验数据. 对于目前工作考虑压缩能的原因进行了讨论.     

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.     

Prescission neutrons in the fission of 235U and 252Cf nuclei

Experimental data obtained previously for the energy-angular distribution of neutrons originating from the fission of ²⁵²Cf (spontaneous fission) and ²³⁵U (thermal-neutron-induced fission) nuclei are analyzed, the angle being measured with respect to the direction of fission-fragment motion. A regularity common to all independent experiments is revealed: at an angle of about 90°, there exists an excess of neutrons (30% for ²⁵²Cf and 60% for ²³⁵U) that does not admit explanation within the model of neutron emission from fully accelerated fragments. Two possible explanations of this experimental fact—neutron emission during the acceleration process and the existence of an additional source of neutrons (predominantly, prescission neutrons)—are considered. It is shown that the latter conjecture describes the observed features for both nuclei more adequately. The total yield of prescission neutrons and their energy and angular distributions are determined.     

Dynamical approach to calculating angular distributions of fission fragments

A dynamical approach is proposed for calculating the angular distributions of fission fragments. The relaxation time for the degree of freedom associated with the projection of the total angular momentum of the nuclear system onto the symmetry axis and the coefficient of damping of the fission mode are the basic parameters of this approach. Experimental data on the anisotropy of the angular distributions of fission fragments and on the multiplicities of prescission neutrons are analyzed within the proposed model for ¹⁶O+²⁰⁸Pb (E _lab=110–148 MeV), ¹⁶O+²³²Th (120–160 MeV), ¹⁶O+²⁴⁸Cm (110–148 MeV), and ¹⁶O+²³⁸U (96–148 MeV). The relaxation time and the damping coefficient are estimated at τ_K=(5–6)×10^?21 s and β=4×10²¹ s^?1, respectively.     

Nuclear dissipation,fission probability and neutron multiplicity prior to fission

We discuss the effects of nuclear dissipation on fission probabilities that are characteristic of a diffusion model of the fission process. Reproducing the experimental fission probabilities at low excitation energies fixes the ratioa _f/a_n of the level density parameters for a given strength of the reduced dissipation coefficientβ. These low energy constraints ona _f/a_n andβ balance the effects of transients on neutron multiplicities prior to fission at higher excitation energies. For the competitive decay of¹⁵⁸Er formed in the reaction¹⁶O+¹⁴²Nd at 207 MeV we show that dueto transients only the multiplicity of pre-fission neutrons is enhanced with respect to the prediction of the statistical model in a manner consistent with our earlier general analysis.