A modified Kramers approach to describing the fission of excited atomic nuclei

We present a detailed comparison of the analytical Kramers fission rate (KFR) and the dynamic quasi-stationary rate (QSFR) obtained by numerical simulation. It turns out that for the polynomial potential, the KFR regularly exceeds the QSFR by more than 5%. We obtain KFR corrections that allow us to reduce this disparity to 1%.     

The fission width of excited nuclei

An interpolation formula for the fission width is obtained valid for small and large values of the viscosity parameter and assumptions concerning the shape of the potential energy barrier. Some inaccuracy in the commonly used statistical model expression for Γ_f is discussed.     

Nucleon-content effect on the fission lifetime of excited nuclei

It was shown previously that the fission lifetime of a nucleus excited to about 100 MeV depends strongly and nonmonotonically on the initial value of its angular momentum L ₀. This result was obtained on the basis of a refined version of the combined dynamical and statistical model. The present study is devoted to a theoretical analysis of the dependence of the fission time on the nucleonic composition of the nucleus involved. The respective calculations were performed within the same model. The dependence of the average fission time 〈t _f 〉 on the initial fissility parameter (Z ²/A)₀ appears to be of a resonance type and is similar to its dependence on L ₀. This dependence of the average fission time on (Z ²/A)₀ stems both from statistical calculations and from a dynamical simulation of the fission mode with allowance for friction. The conditions under which the average fission time reaches a maximum are specified. The dependence of the average fission time on (Z ²/A)₀ remains nonmonotonic in the fusion-fission reaction as well, in which case the distribution of compound nuclei with respect to the initial angular momentum is broad.     

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.     

Mass distributions of fission fragments emitted by highly excited nuclei

The mass distributions of fission fragments emitted by highly excited nuclei have been investigated for the determination of some peculiarities of fission process. It has been shown that the fragment mass distributions obtained by the time-of-flight method change their character in the region of Ag, as expected in the liquid drop model (LDM). The cascade-evaporation model and the statistical method of Fong describe the experimental data with a good accuracy.     

Combined dynamical and statistical approach to describing induced fission of heavy nuclei

A combined dynamical and statistical approach to describing induced fission of heavy nuclei is proposed. This approach takes into account the nuclear-dissipation phenomenon and the double-humped structure of the fission barrier. A method that is intended for calculating the angular distribution of fission fragments and which is applicable over a broad range of excitation energies is discussed. The potential of the approach is demonstrated by addressing the problems of self-consistently describing experimental data on fission probabilities for plutonium and americium isotopes, the yields of shape isomers in the α+²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV and the d+^242,240Pu reactions at deuteron energies in the range E _d = 20–30 MeV, fission times in the α + ²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV, and angular distributions of fission fragments in the α + ²³⁸U, ²³⁷Np reactions at alpha-particle energies in the range E _α = 20–100 MeV.     

Theoretical investigation of the angular-momentum dependence of the mean fission lifetime of excited nuclei

Physics of Atomic Nuclei - Mean fission lifetimes of nuclei excited to energies of 80 to 400 MeV were recently measured at the GANIL accelerator by the crystal-blocking technique. Those experiments...     

Determination of the lifetime of excited compound nuclei in fission using the shadow effect

The results of three experiments on the observation of the shadow effect in the fission of ²³⁸U nuclei in a UO₂ single crystal induced by 1.7 and 3.3 MeV neutrons and 25 MeV α-particles are discussed. Comparison is made of the shapes of the fission-fragment angular distributions in the vicinity of two 〈111〉 crystallographic axes directed along and normal to the incident beam. It was found that the displacement of a fissionable nucleus from a lattice site in response to the momentum of the incident particle affects the shape of the shadow. The values of the lifetime of the ²³⁹U compound nucleus were found to be (3.5±1.0) × 10⁻¹⁶sec at an excitation energy of 6.5 MeV and (2.0±0.8) × 10⁻¹⁶sec at 8.1 MeV.     

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 excited nuclei within the liquid-drop model

We evaluate the temperature T_scis at the scission point and the saddle-to-scission time τ_scis for the fission of heated nuclei. We use classical Lagrange-like equations of motion within the liquid-drop model. The nuclear surface is parameterized by a two-parameter family of the Lawrence shapes. Conservative forces are defined through the free energy of the nucleus at finite temperatures. We use the friction tensor that is derived from the Navier-Stokes momentum-flux tensor and which takes into account the boundary conditions at the nuclear surface. The scission line is determined from the instability condition of the nuclear shape with respect to variations of the neck radius. A numerical solution to the dynamical equations is obtained for the ²³⁶U nucleus. The viscosity coefficient μ is deduced from a comparison of experimental data on the kinetic energy of fission fragments with the computed one. It is found that μ obtained by using our approach deviates significantly from μ of the standard hydrodynamic model.     

Langevin description of the charge distribution of fragments originating from the fission of excited nuclei

The charge distribution of fragments originatingfrom the fission of the ²³⁶U compound nucleus is calculated within a stochastic approach based on Langevin equations. The elongation coordinate, the neck-thickness coordinate, and the charge-asymmetry coordinate are chosen as collective variables. The friction parameter of the charge mode is calculated on the basis of two nuclear-viscosity mechanisms, that of one-body and that of two-body dissipation. It is shown that the Langevin approach is applicable to studying isobaric distributions. In addition, the charge distribution in question is studied as a function of the excitation energy of the compound nucleus and as a function of the coefficient of two-body viscosity.     

Dynamic and statistical simulation of the fission of highly excited atomic nuclei with allowance for the relaxation stage

Statistical and combined dynamic-statistical approaches to simulating the fission of excited nuclei are compared. It is shown that in the statistical approach, the complete suppression of the fission pro cess during time τ _s does not result in double consideration of the emission of light particles. The importance of dynamic simulation of fission at the stage of relaxation of fission rate R _f (t) to its quasistationary value is demonstrated.     

A dumbbell model with five parameters describing nuclear fusion or fission

We propose a five-parameter dumbbell model to describe the fusion and fission processes of massive nuclei, where the collective variables are: the distance ρ between the center-of-mass of two fusing nuclei, the neck parameter ν, asymmetry D, two deformation variables β₁ and β₂ . The present model has macroscopic qualitative expression of polarization and nuclear collision of head to head, sphere to sphere, waist to waist and so on. The conception of the "projectile eating target" based on open mouth and swallow is proposed to describe the nuclear fusion process, and our understanding of the probability of fusion and quasi-fission is in agreement with some previous work. The calculated fission barriers of a lot of compound nuclei are compared with the experimental data.     

A statistical model for simulating the emission of light particles from excited nuclei

The algorithms and basic equations of a novel evaporation model that have been implemented in the program package EVAP15 are detailed. The level density of an excited nucleus is described by the composite Gilbert–Cameron formula with parameter values as suggested by the IAEA working group RIPL-3. Special attention is paid to the cross sections of inverse reactions and, in particular, to those for the interactions of low-energy neutrons with nuclei and for crossing of the Coulomb barrier by low-energy charged particles. The model predictions are compared with a large volume of experimental data on the spectra of particles emitted in the reactions (n, xn), (n, xp), and (n, xα) induced by neutrons with energy near 14 MeV and on the four spectra for the reaction (p, xp) induced by 62-MeV protons.     

Potential for describing single nucleon states during fission

A potential is suggested for describing single nucleon states encountered during both symmetric and asymmetric nuclear fission. The equipotential surfaces for this potential will correspond to quite arbitrary nuclear shapes; intersecting spheres and ellipsoids of various shapes, Cassini ovaloids, and more general figures which are not symmetric about the z axis. Methods are considered for solving the Schrödinger equation for those parts of the potential which depend on z, and energy levels are found in this potential for some different deformations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 23–31, July 1971.