重核熔合与裂变位垒的动力学回流现象

用实验粒子多次通过位垒的方法计算重核熔合与裂变过程中的熔合几率和裂变速率,结果发现位垒附近存在着一种强烈的回流现象.研究还表明当鞍点后势变得平滑,则回流变大.这种效应降低了以往所用的实验粒子首次通过位垒方法得到的熔合几率和裂变速率,从而给出这两种量的正确描述     

Fokker-Planck方程的数值解

采用扩散模型研究核裂变,需要求解Fokker-Planck方程。本文提出一个数值计算方法-平均隐式差分方法。对具有粘滞性的核体系的有关裂变动力学量,如几率分布、裂变率、断点处的平均动能以及鞍点到断点的平均扩散时间等一系列物理量做了计算,并与适合大粘滞性的Kramers的解析解做了比较。通过与解析解的比较及对归一常数的检验,证明计算结果精确可靠。     

<Emphasis Type="Italic">P</Emphasis>-even correlations in binary and ternary nuclear fission induced by polarized neutrons

The evolution of a fissile nucleus from transition fission states specified at the saddle point of the deformation potential to fission states associated with prescission configurations of this nucleus and characterized by a pearlike shape of the nucleus is studied within the quantum-mechanical theory of fission processes that is based on the time-independent formalism. The coefficients of P-even asymmetries in the angular distributions of a light fragment and a third particle are calculated on the basis of the idea of the one-step mechanism of the production of a third particle and two fragments from the ternary fission of nuclei that is induced by polarized thermal neutrons. In order to confirm the developed concepts, it is proposed to repeat, at a higher level of statistical accuracy, experiments devoted to observing left-right asymmetries in the angular distributions of alpha particles from the ternary fission of nuclei.     

Mean first passage time for nuclear fission and the emission of light particles

The concept of a mean first passage time is used to study the time lapse over which a fissioning system may emit light particles. The influence of the "transient" and "saddle to scission times" on this emission are critically examined. It is argued that within the limits of Kramers's picture of fission no enhancement over that given by his rate formula needs to be considered.     

Stationary Fokker-Planck equation applied to fission dynamics

By use of both analytical and numerical techniques, we study the relaxation of time-dependent solutions of the Fokker-Planck equation for an inverted oscillator to Kramers' stationary solution. This is done by integrating over all time the time-dependent solutions for given initial conditions at the saddle point to obtain stationary solutions, whose densities and higher velocity moments are compared as functions of the coordinate with the corresponding quantities calculated from Kramers' stationary solution. For large values of the coordinate an a symptotic expansion of the density is obtained, but for general values of the coordinate and for higher velocity moments the time integration must be done numerically. With increasing dissipation the relaxation to Kramers' stationary solution occurs at successively smaller values of the coordinate. By use of Kramers' stationary solution, we derive analytical expressions as functions of nuclear temperature and dissipation strength for several quantities of interest in fission dynamics, including the mean time from the saddle point to scission, the mean fission-fragment kinetic energy at the scission point and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom. We apply these results to some examples that have been studied experimentally, including the mean saddle-to-scission time for the heavy-ion-induced fission of the compound nucleus ¹⁶⁸Yb and the mean fission-fragment kinetic energy at scission and the contribution to its variance for the α-particle-induced fission of the compound nucleus ²¹³At.     

Light-charged particle emission in fission

The emission of light charged particles in the fission process is of interest as they are believed to emerge from the neck region of the deformed fissioning nucleus at a time close to the scission point and may thus prove a useful probe to investigate the last stages of fission close to the rupture point. Experimental results on light charged particle emission and the efforts made to obtain information about the scission point parameters therefrom are reviewed.     

裂变路径对断点前粒子发射的影响

用扩散模型研究了裂变系统从鞍点到断点的时间演化, 以及在此间的粒子发射与鞍点前粒子发射的比随着裂变系统质量的变化. 解释了实验上发现的断点前粒子多重性随裂变碎片质量不对称性的变化趋势. 结果表明上述两种变化趋势都可以归因于裂变演化路程长短的影响.     

EFFECT OF NUCLEAR VISCOSITY ON FISSION PROCESS

According to the fission diffusion model,the deformation motion of fission nucleues is regarded as a diffusion process of quasi-Brownian particles under fission potential,Through simulating such Brownian motion in two dimensional phase space by Monte-Carlo method,the effect of nuclear viscosity on Brownian particle diffusion is studied,Dynamical quantities,suchas fission rate,kinetic energy distribution on scission,and so on are numerally calculated for various viscosity coefficients,The results are reasonable in physics,This method can be easily extended to deal with multi-dimensional diffusion problems.     

THE MICROSCOPIC CALCULATION OF THE STATISTICAL THEORY OF NUCLEAR FISSION

Based on the statistical fission theory, we have calculated the mass and kinetic energy distributions as well as other physical quantities of ²³⁵U fission induced by thermal neutron using microscopical method. That is, the quantum state densities of the fragments at scission point are calculated by means of BCS hamiltonian. The contribution of the collective deformation of fragments to the quantum state density has been taken into consideration. The potential energy of fragment is calculated by means of Strutinski procedure, and the shelling effect, pairing correlation as well as collective deformation have been taken into consideration in calculating the excitation energy at scission point. The scission point distance is treated as an adjustable parameter.Comparing with other statistical fission theories, our results give better agreement with existing experiments.     

多维Kramers公式的研究

本文研究了鞍点附近多维的位能曲面及鞍点所在位置;并用Werner Wheeler及无旋液体等两种方法计算了多维的质量系数与粘滞系数,然后用多维Kramers公式计算了裂变速率.发现裂变速率随着维数的增加而适当增大.不同的形变参量以及不同的计算质量和粘滞系数方法对计算核裂变速率影响不大.从结果看,采用三维计算裂变几率已足够准确.     

平均最后通过时间和热核裂变速率

提出利用平均最后通过鞍点时间计算热核裂变速率,结果表明平均最后通过鞍点时间的倒数比平均首次通过断点时间的倒数更接近朗之万数值模拟值. The mean last passage time is introduced to instead of the mean first passage time for studying the decay of an induced-fissioning system. The stationary fission rate determined by the inverse of mean last passage time across the saddle point is agreement with the resulting rate of Langevin simulation and better than that of mean first passage time arriving at the scission point.     

Quantum and thermodynamical aspects of binary and ternary fission

A short review is given of the recent developments in the quantum theory of low-energy fission. It is emphasized that angular anisotropy and various angular correlations of fission products are possible only if the fissioning nucleus remains nonthermalized during all the stages of fission from the saddle point to scission. The text was submitted by the authors in English.     

Deformation parameter changes in fission mass yields within the systematic statistical scission-point model

The fission fragment mass-yields are evaluated for pre-actinide and actinide isotopes using a systematic statistical scission point model. The total potential energy of the fissioning systems at the scission point is presented in approximate relations as functions of mass numbers,deformation parameters and the temperature of complementary fission fragments. The collective temperature, Tcoll, and the temperature of fission fragments, Ti, are separated and the effect of collective temperature on mass yields results is investigated. The fragment temperature has been calculated with the generalized superfluid model. The sum of deformation parameters of complementary fission fragments has been obtained by fitting the calculated results with the experimental data. To investigate the transitions between symmetric and asymmetric modes mass yields for pre-actinide and heavy actinides are calculated with this model. The transition from asymmetric to symmetric fission is well reproduced using this systematic statistical scission point model. The calculated results are in good agreement with the experimental data with Tcoll= 2 Me V at intermediate excitation energy and with T_(coll)= 1MeV for spontaneous fission.Despite the Langevin model, in the scission point model, a constraint on the deformation parameters of fission fragments has little effect on the results of the mass yield.     

Analysis of fragment mass distribution in asymmetric area at fission of <Superscript>235</Superscript>U induced by thermal neutrons

The fragment mass yields in fission of ²³⁵U induced by thermal neutrons for A = 145–160 and E_K = 50–75 MeV were measured using a mass spectrometer. The fine structure is observed at A = 153, 154 and E_K = 50–60 MeV. The obtained results were described in the framework of a model based on the dinuclear system concept. The analyzed correlation between the total kinetic energy and mass distribution of fission fragments is connected with the shell structure of the formed fragments of fission. From this correlation and the time dependence of the calculated mass distribution of the binary reaction products, one can conclude that the descent time from a saddle point to a scission point for the more deformed fragments is longer than that for fragments of more compact shape.     

Nonuniform character of the population of spin projections K for a fissile nucleus at the scission point and anisotropies in the angular distributions of fragments originating from the induced fission of nuclei

It is shown that the emergence of anisotropies in the angular distributions of fragments originating from the spontaneous and induced fission of oriented actinide nuclei is possible only if nonuniformities in the population of the projectionsM (K) of the fissile-nucleus spin onto the z axis of the laboratory frame (fissile-nucleus symmetry axis) appear simultaneously in the vicinity of the scission point but not in the vicinity of the outer saddle point of the deformation potential. The possibilities for creating the orientation of fissile nuclei for spontaneous and induced fission and the effect of these orientations on the anisotropies under analysis are considered. The role of Coriolis interaction as a unique source of the mixing of different-K fissile-nucleus states at all stages of the fission process is studied with allowance for the dynamical enhancement of this interaction for excited thermalized states of the nucleus involved that is characterized by a high energy density. It is shown that the absence of thermalization of excited states of the fissile nucleus that appear because of the effect of nonadiabaticity of its collective deformation motion in the vicinity of the scission point is a condition of conservation of the influence that transition fission states formed at the inner and outer fission barriers exerts on the distribution of the spin projections K for lowenergy spontaneous nuclear fission. It is confirmed that anisotropies observed in the angular distributions of fragments originating from the fission of nuclei that is induced by fast light particles (multiply charged ions) are due to the appearance of strongly excited equilibrium(nonequilibrium) states of the fissile nucleus in the vicinity of its scission point that have a Gibbs (non-Gibbs) distribution of projections K.     

Energy partition in nuclear fission

A scission point model (two spheroid model TSM) including semi-empirical, temperature-dependent shell correction energies for deformed fragments at scission is presented. It has been used to describe the mass-asymmetry-dependent partition of the total energy release on both fragments from spontaneous and induced fission. Characteristic trends of experimental fragment energy and neutron multiplicity data as function of incidence energy in the Th — Cf region of fissioning nuclei are well reproduced. Based on model applications, information on the energy dissipated during the descent from second saddle of fission barrier to scission point have been deduced.     

Lattice formulation of general relativity

It is shown that almost the entire excitation energy acquired by the fission fragments during the descent from the saddle to the scission point comes from Landau-Zener transitions. The states tractable in the first order adiabatic approximation carry an excitation energy of a few hundred keV.     

Quantum and thermodynamic properties of spontaneous and low-energy induced fission of nuclei

It is shown that A. Bohr’s concept of transition fission states can be matched with the properties of Coriolis interaction if an axisymmetric fissile nucleus near the scission point remains cold despite a nonadiabatic character of nuclear collective deformation motion. The quantum and thermodynamic properties of various stages of binary and ternary fission after the descent of a fissile nucleus fromt he outer saddle point are studied within quantum-mechanical fission theory. It is shown that two-particle nucleon-nucleon correlations—in particular, superfluid correlations— play an important role in the formation of fission products and in the classification of fission transitions. The distributions of thermalized primary fission fragments with respect to spins and their projections onto the symmetry axis of the fissile nucleus and fission fragments are constructed, these distributions determining the properties of prompt neutrons and gamma rays emitted by these fragments. A new nonevaporation mechanism of third-particle production in ternary fission is proposed. This mechanism involves transitions of third particles from the cluster states of the fissile-nucleus neck to high-energy states under effects of the shake-off type that are due to the nonadiabatic character of nuclear collective deformation motion.     

Study of Fission Barrier Heights of Uranium Isotopes by the Macroscopic-Microscopic Method

Potential energy surfaces of uranium nuclei in the range of mass numbers 229 through 244 are investigated in the framework of the macroscopic-microscopic model and the heights of static fission barriers are obtained in terms of a double-humped structure. The macroscopic part of the nuclear energy is calculated according to Lublin-Strasbourg-drop (LSD) model. Shell and pairing corrections as the microscopic part are calculated with a folded-Yukawa single-particle potential. The calculation is carried out in a five-dimensional parameter space of the generalized Lawrence shapes. In order to extract saddle points on the potential energy surface, a new algorithm which can effectively find an optimal fission path leading from the ground state to the scission point is developed. The comparison of our results with available experimental data and others' theoretical results confirms the reliability of our calculations.     

Study of Pre-equilibrium Fission Based on Diffusion Model

In terms of numerical method of Smoluchowski equation the behavior of fission process in diffusion model has been described and analyzed, including the reliance upon time, as well as the deformation parameters at several nuclear temperatures in this paper. The fission rates and the residual probabilities inside the saddle point are calculated for fissile nucleus n+²³⁸U reaction and un-fissile nucleus p+²⁰⁸Pb reaction. The results indicate that there really exists a transient fission process, which means that the pre-equilibrium fission should be taken into account for the fissile nucleus at the high temperature. Oppositely, the pre-equilibrium fission could be neglected for the un-fissile nucleus. In the certain case the overshooting phenomenon of the fission rates will occur, which is mainly determined by the diffusive current at the saddle point. The higher the temperature is, the more obvious the overshooting phenomenon is. However, the emissions of the light particles accompanying the diffusion process may weaken or vanish the overshooting phenomenon.