F. A. Ivanyuk

Fission dynamics at low excitation energy

The mass asymmetry in the fission of U-236 at low excitation energy is clarified by the analysis of the trajectories obtained by solving the Langevin equations for the shape degrees of freedom. It is demonstrated that the position of the peaks in the mass distribution of fission fragments is determined mainly by the saddle point configuration originating from the shell correction energy. The width of the peaks, on the other hand, results from the shape fluctuations close to the scission point caused by the random force in the Langevin equation. We have found out that the fluctuations between elongated and compact shapes are essential for the fission process. According to our results the fission does not occur with continuous stretching in the prolate direction, similarly to that observed in starch syrup, but is accompanied by the fluctuations between elongated and compact shapes. This picture presents a new viewpoint of fission dynamics and the splitting mechanism.

Scission-point configuration within the two-center shell model shape parameterization

Within the two-center shell model parameterization we have defined the optimal shape which fissioning nuclei attain just before the scission and calculated the total deformation energy (liquid drop part plus the shell correction) as function of the mass asymmetry and elongation at the scission point. The three minima corresponding to mass symmetric and two mass asymmetric peaks in the mass distribution of fission fragments are found in the deformation energy at the scission point. The calculated deformation energy is used in quasi-static approximation for the estimation of the total kinetic and excitation energy of fission fragments and the total number of emitted prompt neutrons. The calculated results reproduce rather well the experimental data on the position of the peaks in the mass distribution of fission fragments, the total kinetic and excitation energy of fission fragments. The calculated value of neutron multiplicity is somewhat larger than experimental results.

PAIRING CORRELATIONS AND FISSION BARRIER HEIGHTS

The influence of a pairing strength proportional to the surface of the deformed nucleus, on the fission barrier heights evaluated within the macroscopic-microscopic model which does not contain the average pairing energy in its macroscopic part is investigated. The calculations were carried out with the Lublin-Strasbourg drop model and the folded-Yukawa single-particle potential.

Allowance for the shell structure of colliding nuclei in the fusion-fission process

The motion of two nuclei toward each other in fusion-fission reactions is considered. The state of the system of interacting nuclei is specified in terms of three collective coordinates (parameters). These are the distance between the centers of mass of the nuclei and the deformation parameter for each of them (the nose-to-nose orientation of the nuclei is assumed). The evolution of collective degrees of freedom of the system is described by Langevin equations. The energies of the Coulomb and nuclear (Gross-Kalinovsky potential) interactions of nuclei are taken into account in the potential energy of the system along with the deformation energy of each nucleus with allowance for shell effects. The motion of nuclei toward each other are calculated for two reaction types: reactions involving nuclei that are deformed (42100Mo + 42100Mo → 84200Po) and those that are spherical (82208Pb + 818O → 90226Th) in the ground state. It is shown that the shell structure of interacting nuclei affects not only the fusion process as a whole (fusionbarrier height and initial-reaction-energy dependence of the probability that the nuclei involved touch each other) but also the processes occurring in each nucleus individually (shape of the nuclei and their excitation energies at the point of touching).

THE SHAPES OF CONDITIONAL EQUILIBRIUM IN THE LIQUID-DROP MODEL

The shape of the nuclear surface is defined looking for the minimum of liquid drop energy under the constraint of fixed volume, elongation and mass asymmetry. The method does not rely on any shape parameterization and leads to the shapes with the lowest energy. The results obtained with several deformation constraints are compared. The numerical methods used here for solving the variational problem allow for the straightforward generalizations which could include the surface diffusenes, nuclear interaction, separated shapes, eventually shell effects.

Multidimensional Langevin approach to describing the 18O + 208Pb fusion-fission reaction

The fusion-fission reaction is treated as a multistep process. Langevin equations are used to describe the evolution of the system at each reaction stage. The parameters of the fusion process are calculated at the first stage. The results obtained in the input channel are employed as initial conditions in calculating the features of the fission process. The cross sections for fusion and fission are successfully described, and the cross sections for the formation of evaporation residues are estimated. In addition, the procedure used makes it possible to describe the mass distribution of fission fragments and the fragment-mass dependence of the multiplicity of prefission neutrons and to determine the mass-energy distribution of fission fragments. From the calculations, it follows that all the fission features of the reaction in question can be reproduced without considering the formation of a classical compound nucleus. The reaction times are so long that it is impossible to separate experimentally such events from the case of true fission through a compound nucleus.

Analysis of the total kinetic energy of fission fragments with the Langevin equation

We analyzed the total kinetic energy (TKE) of fission fragments with three-dimensional Langevin calculations for a series of actinides and Fm isotopes at various excitation energies. This allowed us to establish systematic trends of TKE with

Allowance for the orientation of colliding ions in describing the synthesis of heavy nuclei

Z^2/A^{1/3}

Four-dimensional Langevin approach to low-energy nuclear fission of

of the fissioning system and as a function of excitation energy. In the mass-energy distributions of fission fragments we see the contributions from the standard, super-long, and super-short (in the case of

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