arXiv subjects

F. A. Ivanyuk

Publications and source records attributed to F. A. Ivanyuk.

At least 19 recordsLinked to original sources

arXiv2026

Shell effects and the neutron emission within the multi-dimensional Langevin model for nuclear fission

We solve the Langevin equations for the time evolution of parameters that describe the shape of fissioning system. On each integration step, we calculate the probability of neutron emission and estimate whether a neutron would be emitted or not. If yes, we decrease the excitation energy of the nucleus by the neutron separation energy plus the average energy of the emitted neutron, switch to the layer of potential energy surface with a smaller number of neutrons and continue the process of integration. If the trajectory reaches the scission point, we check how many neutrons were emitted along this trajectory. The pre-scission neutron multiplicity $M_{pre}$ is defined by the ratio of the total number of emitted neutrons to the total number of fission trajectories. Besides $M_{pre}$, the mass distribution of fission fragments, the distribution of emitted neutrons with respect to the fission stage (deformation of system) and the distribution of emitted neutrons with respect to their energies are calculated. The calculated quantities are compared with the available experimental data.

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arXiv2025

Shell effects and multi-chance fission in the sub-lead region

Within the recently developed five-dimensional Langevin approach for the description of fission of heavy nuclei, we have calculated the fission fragments mass and kinetic energy distributions for the fission of $^{180}$Hg and $^{190}$Hg formed in the reactions $^{36}$Ar +$^{144}$Sm $\Rightarrow$ $^{180}$Hg and $^{36}$Ar +$^{154}$Sm $\Rightarrow$ $^{190}$Hg at few excitation energies and found very good agreement between the calculated and experimental results. Special attention was paid to the accurate description of the dependence of shell effects on the excitation energy. It was shown that the effect of multi-chance fission on the mass distribution is noticeable only at small excitation energies. The kinetic energy distributions are more sensitive to pre-scission neutron emission.

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arXiv2024

Dumbbell shapes in the super-asymmetric fission of heavy nuclei

We have calculated the fission fragments' mass distributions for several isotopes of heavy and super-heavy nuclei from uranium to flerovium within an improved scission point model. For all considered nuclei, in addition to the standard mass-asymmetric fission mode we have found the mass super-asymmetric mode with the mass of heavy fragments equal 190. For the actinide nuclei, the probability of super-asymmetric fission is by 6 orders of magnitude smaller than for standard asymmetric fission. For the superheavy nuclei this probability is only by 2 orders of magnitude smaller. In all cases, the super-asymmetric scission shapes are dumbbells with the heavy fragment close to a sphere. We have estimated the stability of the light fragment concerning the variation of the neck and found out that sequential ternary fission is not favored energetically. The calculations were carried out with nuclear shape described by generalized Cassinian ovals with 6 deformation parameters, $α, α_1, α_2, α_3, α_4$ and $α_5$. The configuration at the moment of the neck rupture was defined by fixing $α=0.98$. This value corresponds to a neck radius $r_{neck}\approx$ 1.5 fm.

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arXiv2023

The 5-dimensional Langevin approach to fission of atomic nuclei

We have generalized the four-dimensional Langevin approach used in our previous works for the description of fission process to the five-dimensional by considering the neck parameter $\eps$ in the two-center shell model shape parametrization as an independent dynamical variable. The calculated results for the mass distribution of fission fragments are in better agreement with the available experimental data. In particular, the transition from the mass-symmetric to mass-asymmetric fission via the triple-humped distribution in fission of Thorium isotopes is well reproduced.

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arXiv2023

The Langevin approach for fission of heavy and super-heavy nuclei

In this contribution, we present the main relations of the Langevin approach to the description of fission or fusion-fission reactions. The results of Langevin calculations are shown for the mass distributions of fission fragments of super-heavy elements and used for the investigation of memory effects in nuclear fission.

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arXiv2021

Memory effects in Langevin approach to the nuclear fission process

We present the schematic calculations within the Langevin approach in order to investigate the dependence of fission width on the memory time and the excitation energy at low temperatures where the quantum fluctuations play an important role. For this we consider the simple one-dimensional case with the potential energy given by two parabolic potentials (Kramers potential). For friction and the mass parameters we use the deformation independent values fitted to the results obtained earlier within the microscopic linear response theory. We have found out that at small excitation energies (comparable with the fission barrier height) the memory effects in the friction and random force acts on the fission width in opposite direction. The total effect is not so large, but still quite noticeable (depending on the value of the relaxation time). The use of effective temperature in the diffusion coefficient turns out to be much more important compared with the memory effects. The calculated fission width at very low excitation energies is unrealistically too big.

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arXiv2020

Description of the reactions 36S + 238U and 64Ni + 238U within the two-stage fusion-fission model

We describe the capture, fusion, fission and evaporation residue formation cross sections of superheavy nuclei within the proposed earlier two stages dynamical model. The approaching of the projectile nucleus to the target nucleus is described in the first stage of the model. On the second stage, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by Langevin equations. The transport coefficients of these equations are calculated within the microscopic linear response theory. The mutual orientation of the colliding ions, the tunneling through the Coulomb barrier in the entrance channel and the shell effects in the potential energy on both stages of the calculations are taking into account. The obtained results are compared with the available experimental data and other theoretical predictions.

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arXiv2020

Fission of super-heavy elements: $^{132}$Sn-plus-the-rest, or $^{208}$Pb-plus-the-rest ?

In this work we try to settle down the controversial predictions on the effect of doubly magic nuclei $^{132}$Sn and $^{208}$Pb on the mass distributions of fission fragments of super-heavy nuclei. For this we have calculated the mass distribution of super-heavy nuclei from $^{286}$Cn to $^{306}$122 within the dynamical 4-dimensional Langevin approach. We have found that in "light" super-heavies the influence of $^{208}$Pb on the mass distributions is present but negligible small. In "heavy" super-heavies, Z=120-122, the (quasi)symmetric peaks and strongly asymmetric peaks at fragment mass $A_F$ close to $A_F$=208 are of comparable magnitude.

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arXiv2019

Description of the mass-asymmetric fission of the Pt isotopes, obtained in the reaction $^{36}$Ar + $^{142}$Nd within the two-stage fusion-fission model

The two stages dynamical stochastic model developed earlier for description of fusion-fission reactions is applied to the calculation of mass- and energy-distributions of fission fragments of platinum isotopes in reaction ${\rm ^{36}Ar + ^{142}Nd \to ^{178-x}Pt + xn}$. The first stage of this model is the calculation of the approaching of projectile nucleus to the target nucleus. On the second stage of the model, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by three-dimensional Langevin equations for the shape parameters of the system. The mutual orientation of the colliding ions and tunneling through the Coulomb barrier in the entrance channel are also taken into account. The potential energy of the system is calculated within the macroscopic-microscopic approach. The calculated mass-energy distributions of fission fragments are compared with the available experimental data. The impact of shell effects, rotation of the system and neutron evaporation on the calculated results is discussed.

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arXiv2019

Fission of super-heavy nuclei: Fragment mass distributions and their dependence on excitation energy

The mass and total kinetic energy distributions of the fission fragments in the fission of even-even isotopes of superheavy elements from Hs (Z=108) to Og (Z=118) are estimated using a pre-scission point model. We restrict to nuclei for which spontaneous fission has been experimentally observed. The potential energy surfaces are calculated with Strutinsky's shell correction procedure. The parametrization of the nuclear shapes is based on Cassini ovals. For the just before scission configuration we fix $α$=0.98, what corresponds to $r_{neck}\approx 2$ fm, and take into account another four deformation parameters: $α_1,α_3,α_4,α_6$. The fragment-mass distributions are estimated supposing they are due to thermal fluctuations in the mass asymmetry degree of freedom just before scission. The influence of the excitation energy of the fissioning system on these distributions is studied. The distributions of the total kinetic energy (TKE) of the fragments are also calculated (in the point-charge approximation). In Hs, Ds and Cn isotopes a transition from symmetric to asymmetric fission is predicted with increasing neutron number N (at N$\approx$168). Super-symmetric fission ocurs at N$\approx$160. When the excitation energy increases from 0 to 30 MeV, the peaks (one or two) of the mass distributions become only slightly wider. The first two moments of the TKE distributions are displayed as a function of the mass number A of the fissioning nucleus. A slow decrease of the average energy and a minimum of the width (at N$\approx$162) is found.

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arXiv2018

The temperature dependence of the shell corrections

We have examined the dependence of the shell correction to the nuclear liquid drop energy at finite excitations on the excitation energy (temperature). For this we have calculated the shell correction to the energy and free energy in very broad region of nuclei and deformations starting directly from their formal definitions. We have found out that the dependence of the shell corrections on the excitation energy differ substantially from the widely used approximation $δE(E^*)=δE(0)\exp(-E^*/E_d)$ both at small and large excitations. In particular, below the critical temperature at which the pairing effects vanish, the shell correction to the free energy is rather insensitive to the excitation energy. We suggest a more accurate approximation for the temperature dependence of the shell correction to the energy and free energy that is expressed in terms of the shell correction to the energy of independent particles and the shell correction to the pairing energy at T=0 and few fitted constants.

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arXiv2014

Fission dynamics at low excitation energy. 2

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.

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arXiv2014

The 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.

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arXiv2013

The shell effects in the scission-point configuration of fissioning nuclei

In the present work the formal definition of the scission point - the maximal elongation at which the nucleus splits into two fragments - is given. The shape and the deformation energy at the scission point are calculated within the macroscopic-microscopic model. Three minima in the scission point deformation energy are found corresponding to the "standard", "supershort" and "superlong" fission modes. The contribution of each fission mode to the mass distribution of the fission fragments and total kinetic energy is discussed and compared with the experimental results. On the example of the fission process of U-235 by thermal neutrons it is shown that the present approach reproduces correctly the position of the peaks of the mass distribution of the fission fragments, the value and the fine details of the total kinetic energy distribution and the magnitude of the total excitation energy of the fission fragments.

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arXiv2003

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' picture of fission no enhancement over that given by his rate formula need to be considered.

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arXiv2002

Time scales for fission at finite temperature

The concept of the "transient effect" is examined in respect of a "mean first passage time". It is demonstrated that the time the fissioning system stays inside the barrier is much larger than suggested by the transient time, and that no enhancement of emission of neutrons over that given by Kramers' rate formula ought to be considered.

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arXiv2001

Nuclear fission: The "onset of dissipation" from a microscopic point of view

Semi-analytical expressions are suggested for the temperature dependence of those combinations of transport coefficients which govern the fission process. This is based on experience with numerical calculations within the linear response approach and the locally harmonic approximation. A reduced version of the latter is seen to comply with Kramers' simplified picture of fission. It is argued that for variable inertia his formula has to be generalized, as already required by the need that for overdamped motion the inertia must not appear at all. This situation may already occur above T=2 MeV, where the rate is determined by the Smoluchowski equation. Consequently, comparison with experimental results do not give information on the effective damping rate, as often claimed, but on a special combination of local stiffnesses and the friction coefficient calculated at the barrier.

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arXiv2001

The Effect of Nuclear Rotation on the Collective Transport Coefficients

We have examined the influence of rotation on the potential energy and the transport coefficients of the collective motion (friction and mass coefficients). For axially symmetric deformation of nucleus Th-224 we have found that at excitations corresponding to temperatures T > 1 MeV the shell correction to the liquid drop energy practically does not depend on the angular rotation. The friction and mass coefficients obtained within the linear response theory for the same nucleus at temperatures larger than T=2 MeV are rather stable with respect to rotation provided that the contributions from spurious states arising due to the violation of rotation symmetry are removed. At smaller excitations both friction and mass parameters corresponding to the elongation mode are growing functions of rotational frequency.

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