G. I. Kosenko

ISOSPIN DEPENDENCE OF REACTIONS 48Ca+243-251Bk

The fusion process of 48Ca induced reactions is studied with the two-step model. In this model, the fusion process is devided into two stages: first, the sticking stage where projectile and target come to the touching point over the Coulomb barrier from infinite distance, and second, the formation stage where the di-nucleus formed with projectile and target evolve to form the spherical compound nucleus from the touching point. By the use of the statistical evaporation model, the residue cross sections for different neutron evaporation channels are analyzed. From the results, optimum reactions are given to synthesize Z=117 element with 48Ca induced reactions.

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).

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

The dynamical model proposed earlier for describing fusion-fission reactions was modified in order to take into account an arbitrary orientation of colliding ions. In this model, the evolution of collective coordinates of the system under study is treated as a two-stage process. The motion of the projectile nucleus toward the target nucleus is considered at the first stage, and the evolution of a continuous dinuclear system formed as soon as the projectile and target nuclei touch each other is calculated at the second stage. At either stage of the calculation, the dynamical evolution of the system is described in terms of Langevin equations. The shell structure of the nuclei involved is taken into account at both stages. The difference between the results obtained for the first stage with allowance for an arbitrary orientation of colliding ions and the respective results for the case where their symmetry axes are aligned are discussed. The cross sections for the touching of primary nuclei and for their fusion are calculated, along with the cross sections for evaporation-residue formation in reactions involving nuclei that are prolate and spherical in the ground state. The results are compared with available theoretical and experimental data.

Allowance for the shell structure of the 42 100 Mo and 46 110 Pd nuclei in the synthesis of 84 200 Po, 88 210 Ra, and 92 220 U

The effect of the shell structure of colliding nuclei in calculating the entrance channel on the ensuing evolution of the product system is investigated. The entrance channel is calculated under the assumption of the nose-to-nose orientation of colliding nuclei. The following three reactions involving nuclei that are deformed in the ground state are considered: 42100Mo + 42100Mo → 84100Po, 42100Mo + 46100Pd → 88210Ra, and 46110Pd + 46110Pd → 92220U. The state of the system at the point of touching is determined by the results obtained by calculating the entrance reaction channel. The shape of the system is specified by three collective coordinates (deformation parameters). The evolution of collective coordinates of the system is described in terms of Langevin equations. The potential energy of the system of colliding nuclei is calculated with allowance for their shell structure. It is shown that allowance for individual features of interacting nuclei in the entrance channel of the fusion-fission reactions makes it possible to obtain, for the reactions being considered, cross sections for evaporation-residue formation that are closer to available experimental data than their liquid-drop counterparts.

Di-nucleus dynamics towards fusion of heavy nuclei

The Two-Step Model for fusion of massive systems is briefly recapitulated, which clarifies the mechanism of so-called fusion hindrance. Since the neck changes the potential landscape, especially the height of the conditional saddle point, time evolution of the neck degree of freedom plays a crucial role in fusion. We analytically solve time-evolution of nuclear shape of the composite system from di-nucleus to mono-nucleus. The time-dependent distribution function of the neck is obtained, which elucidates dynamics of fusion processes in general, and thus, is useful for theoretical predictions on synthesis of the superheavy elements with various combinations of incident heavy ions.

Fusion hindrance and synthesis of superheavy elements

A mechanism for fusion hindrance is clarified, based on the observation that the sticking configuration of projectile and target is located outside of the conditional saddle point. Accordingly, the fusion process is described by two sequential steps of passing over the Coulomb barrier and shape evolution toward the spherical compound nucleus. The latter one is indispensable in massive systems. With the use of a two-step model, excitation functions of fusion reaction are calculated for various combinations of projectiles and targets which lead to superheavy elements. The hindered fusion excitation measured is reproduced precisely without any adjustable parameter. Combined with survival probabilities calculated by the statistical theory of decay, excitation functions for residues of superheavy elements are calculated to compare with the systematic data measured for the cold fusion path. The peak positions and the widths are correctly reproduced, though it is necessary to reduce the shell correction energies of the compound nuclei predicted by the structure calculations in order to reproduce their absolute values. Predictions are made for a few unknown heavier elements. Furthermore, a preliminary attempt toward the shell closure N = 184 is also presented using a neutron-rich secondary beam.

Theory of fusion for superheavy elements

A new model is proposed for fusion mechanisms of massive nuclear systems, where so-called fusion hindrance exists. The model describes the whole process in two steps: two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to 48Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. A schematic case is solved in an analytic way, the results of which shed light on fusion mechanisms. Combined with statistical decay theory, residue cross sections for superheavy elements can be readily calculated. Examples are given.

Allowance for the tunnel effect in the entrance channel of fusion–fission reactions

A two-stage model is developed in order to describe fusion–fission reactions. The process in the course of which colliding ions approach each other is simulated at the first stage, the deformations and relative orientations of the ions being taken into account. The first stage of the calculation is completed as soon as colliding nuclei touch each other. A continuous nuclear system (monosystem) is formed at this instant. The emerging distributions of the angular momenta of this system and of its potential and internal energies at the point of touching are used as input data that are necessary for triggering the second stage of the calculation. The evolution of collective coordinates that describe the shape of the monosystem is calculated at the second stage. The description of this evolution is terminated either at the instant of its fission or upon the release of a major part of its excess energy via particle and photon emission. In the latter case, the probability for the fission of the monosystem or a further decrease in its excitation energy becomes extremely small. The ion-collision process and the evolution of the monosystem formed after primary nuclei come into contact are simulated on the basis of stochastic Langevin equations. The quantities appearing in them (which include the potential energy and inertial and friction parameters) are determined with allowance for the shell structure of nuclei. The tunneling of colliding nuclei through the Coulomb barrier is taken into account, and the effect of this phenomenon on model predictions is studied.

Description of the two-humped mass distribution of fission fragments of mercury isotopes on the basis of the multidimensional stochastic model

The dynamical model proposed earlier for describing fusion-fission reactions is applied to describing the two-humped mass distribution of fission fragments of mercury isotopes. In this model, the calculation of the time evolution of collective coordinates of the system is broken down into two stages. The first stage is that within which the projectile approaches the target nucleus, while the second is that of the evolution of the system formed after the touching of the projectile and target nuclei. The dynamical evolution of the system within both stages of the calculation is described on the basis of Langevin equations. The shell structure of colliding nuclei is taken into account at either stage of the calculation. Mass distributions are calculated for fragments originating from the fission of the mercury isotopes 190, 184Hg formed in the fusion-fission reactions 48Ca + 142Nd → 190Hg and 40Ar + 144Sm → 184Hg. The process in which the isotope 180Hg undergoes fission from the ground state is also calculated. The results obtained in this way are compared with the results of previous theoretical calculations and with available experimental data.

Dynamical calculations of the cross section for heavy-ion fusion with allowance for tunneling

The surface-friction model was proposed for describing reactions induced by deep-inelastic heavy-ion interactions. Its use in describing heavy-ion fusion was restricted to the case of energies above the fusion barrier. An attempt is made here to extend the use of the model to subbarrier energies via the inclusion of the tunneling effect. A method for taking into account the tunneling effect in dynamical calculations on the basis of Langevin’s equations is proposed. It is shown that, at energies in the barrier region and at high angular momenta, this effect leads to an increase in the cross section for touching of ions.