Sequential character of low-energy ternary and quaternary nuclear fission

An analysis of low-energy true ternary (quaternary) nuclear fission leads to the conclusion that these fission modes have a sequential two-step (three-step) character such that the emission of a third particle (third and fourth particles) and the separation of fission fragments occur at distinctly different instants, in contrast to the simultaneous emergence of all fission products in the case of onestep ternary (quaternary) fission. This conclusion relies on the following arguments. First, the emission of a third particle (third and fourth particles) from a fissile nucleus is due to a nonevaporative mechanism associated with a nonadiabatic character of the collective deformation motion of this nucleus at the stages preceding its scission. Second, the axial symmetry of the deformed fissile compound nucleus and the direction of its symmetry axis both remain unchanged at all stages of ternary (quaternary) fission. This circumstancemakes it possible to explain themechanism of the appearance of observed anisotropies and T — odd asymmeries in the angular distributions of products of ternary (quaternary) nuclear fission. Third, the T —odd asymmetry discovered experimentally in ternary nuclear fission induced by cold polarized neutrons obeys the T —invariance condition only in the case of a sequential two-step (three-step) character of true ternary (quaternary) nuclear fission. At the same time, this asymmetry is not a T —invariant quantity in the case of the simultaneous emission of products of true ternary (quaternary) nuclear fission from the fissile compound nucleus.     

The quantum and thermodynamical characteristics of fission taking into account adiabatic and nonadiabatic modes of motion

In the framework of the quantum theory of spontaneous and low-energy induced fission, the nature of quantum and thermodynamical properties of a fissioning system is analyzed taking into account adiabatic and nonadiabatic modes of motion for different fission stages. It is shown that, owing to the influence of the Coriolis interaction, the states of the fissile nucleus and of primary fission products are cold and strongly nonequilibrium. The important role of superfluid and pairing nucleon-nucleon correlations for binary and ternary fission is demonstrated. The mechanism of pumping of high values of relative orbital momenta and spins of fission fragments for binary and ternary fission and the nonevaporation mechanism of formation of third particles for ternary fission are investigated. The anisotropies and P-odd, P-even, and T-odd asymmetries for angular distributions of fission products are analyzed. The text was submitted by the author in English.     

Mechanisms of excitation of <Emphasis Type="Italic">T</Emphasis>-odd correlations for prescission gamma rays and structure of these correlations

Conditions for the appearance and observation of prescission gamma rays emitted by a fissioning nucleus prior to its separation into fission fragments were investigated within quantum-mechanical fission theory. It is shown that these conditions are realizable in the gamma decay of isovector electric giant dipole resonances in a fissile nucleus that are excited because of nonadiabaticity of the collective deformation motion of the nucleus at the ultimate stages of its prefission evolution. Angular and energy distributions of prescission gamma rays emitted by unpolarized fissioning nuclei are analyzed. Features of T-odd correlations in angular distributions of gamma rays arising in the fission of unpolarized target nuclei that is induced by polarized cold neutrons are investigated, and it is shown that these correlations are similar in nature to T-odd ROT correlations discovered earlier for alpha particles emitted in the ternary fission of nuclei.     

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.     

<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.     

Unified Mechanism behind the Appearance of <Emphasis Type="Italic">T</Emphasis>-Odd TRI and ROT Asymmetries in Actinide Fission Induced by Cold Polarized Neutrons

Some shortcomings of the approaches that are used to describe T-odd ROT and TRI asymmetries in true ternary fission via reactions involving the emission of prescission alpha particles and which are based on employing the classical method of trajectory calculations are analyzed. These shortcomings are caused by the disregard of the interference between the fission widths of different sJ_s neutron resonance states formed in the first well of the deformation potential of fissile compound nuclei. It is shown that the method used in some studies to determine T-odd TRI-asymmetries for prescission alpha particles is at odds with basic concepts of the generalizedmodel of the nucleus and approaches to constructing collective (for example, bending) vibrations of a fissile compound nucleus. Quantum-mechanical fission theory is generalized via employing a unified mechanism of formation of T-odd TRI and ROT asymmetries for prescission alpha particles and evaporated photons (neutrons). The proposed mechanism takes correctly into account the effect of quantum rotation of a fissile compound nucleus on the angular distributions of fission fragments and alpha particles for true ternary fission, as well as on the angular distribution of prompt photons (neutrons) emitted by fragments originating from the delayed fission of the aforementioned nuclei.     

Angular distributions of fragments originating from the spontaneous fission of oriented nuclei and problem of the conservation of the spin projection onto the symmetry axis of a fissile nucleus

The concept of transition fission states, which was successfully used to describe the angular distributions of fragments for the spontaneous and low-energy induced fission of axisymmetric nuclei, proves to be correct if the spin projection onto the symmetry axis of a fissile nucleus is an integral of the motion for the external region from the descent of the fissile nucleus from the external fission barrier to the scission point. Upon heating a fissile nucleus in this region to temperatures of T ≈ 1 MeV (this is predicted by many theoretical models of the fission process), the Coriolis interaction uniformly mixes the possible projections of the fissile-nucleus spin for the case of low spin values, this leading to the loss of memory about transition fission states in the asymptotic region where the angular distributions of fragments are formed. Within quantum-mechanical fission theory, which takes into account deviations from A. Bohr’s formula, the angular distributions of fragments are calculated for spontaneously fissile nuclei aligned by an external magnetic field at ultralow temperatures, and it is shown that an analysis of experimental angular distributions of fragments would make it possible to solve the problem of spin-projection conservation for fissile nuclei in the external region.     

Probabilities for the emission of light particles and their energy and angular distributions for true quaternary nuclear fission

On the basis of quantum-mechanical fission theory, the features of true quaternary nuclear fission are studied by treating this fission process as a sequence of three processes following one another in the course of time. The first two processes are the escape of the first and then the second of the two light particles emitted from the neck of a fissioning nucleus because of a nonadiabatic character of the collective deformation motion of this nucleus. Finally, the third process is the separation of the fissioning nucleus into two rather heavy fission fragments. The differences that arise in the emission probabilities and in the angular and energy distributions upon going over from the first emitted to the second emitted prescission third and fourth particles are analyzed by invoking experimental data on the spontaneous and thermalneutron-induced fission of nuclei, and it is shown that these differences are caused by the changes both in the geometric configuration of the fissioning nucleus and in the shell structure of its neck after the first prescission particle is emitted from it.     

Mechanisms for the appearance of prescission γ-rays and their related T-odd asymmetries

Conditions for the appearance and observation of prescission γ-rays emitted by a fissioning nucleus before its separation into fission fragments were investigated within the quantum theory of fission. It was demonstrated that these conditions can be fulfilled in the γ-decay of giant electric isovector dipole resonances in a fissioning nucleus that become excited due to the nonadiabaticity of the collective deformation motion of the nucleus at the final stages of its prefission evolution. Angular and energy distributions of prescission γ-rays emitted by unpolarized fissioning nuclei were analyzed. Characteristics of T-odd asymmetries in angular distributions of prescission γ-rays were investigated for fission of unpolarized target nuclei induced by polarized cold neutrons, and these correlations were shown to be similar in nature to the T-odd ROT correlations earlier found for α-particles emitted in ternary nuclear fission.     

Angular and spin distributions of primary fission fragments

It is demonstrated that the formation of the fissile nucleus prescission configuration with two fission prefragments connected by a neck is possible only with the simultaneous appearance of high values of relative orbital moments [(L)\vec]\vec L of the abovementioned prefragments, independently of their form. It is found that conservation of the fissile nucleus spin when its values are low leads to the formation of high values of prefragment spins [(J)\vec]₁\vec J_1, [(J)\vec]₂\vec J_2 that are oriented antiparallel to the moment [(L)\vec]\vec L and perpendicular to the fissile nucleus symmetry axis. It is shown that for two deformed fission prefragments, the pumping mechanism of high values of their relative moments [(L)\vec]\vec L and spins [(J)\vec]₁\vec J_1, [(J)\vec]₂\vec J_2 is due to the combined influence of bending- and wriggling- vibrations, the latter predominating. It is found that the high values of spherical fission prefragments are not related to thermal excitations but is determined by the excitation of the initial high-spin double quasiparticle states, due to the nonadiabatic collective deformation motion of the fissile nucleus in the vicinity of its rupture point.     

Decisive role of wriggling vibrations in the formation of angular and spin distributions of products originating from binary and ternary fission of oriented nuclei

It is shown that the multiplicities and angular and energy distributions of neutrons and photons evaporated from thermalized fragments originating from the spontaneous and low-energy induced fission of nuclei, the relative yields of ground and isomeric states of final fragments, and the features of delayed neutrons emitted upon the beta decay of the above fragments can successfully be described by employing nonequilibrium distributions of spins and relative orbital angular momenta of fission fragments formed in the vicinity of the scission point for the fissile nucleus being studied. It is also shown that these distributions, which are characterized by large mean values of the spins and orbital angular momenta directed orthogonally to the symmetry axis of the fissioning nucleus are successfully constructed upon simultaneously taking into account zero-mode transverse wriggling and bending vibrations of a fissile compound nucleus in the vicinity of its scission point, the wriggling vibrations being dominant. It is confirmed that the zero-mode wriggling vibrations considered immediately above are directly involved in the formation of the angular distributions of fragments originating from the spontaneous and low-energy fission of nuclei. This makes it possible to describe successfully such distributions for photofission fragments.     

Mechanisms of binary and ternary low-energy fission of nuclei with allowance for nonsphericity effects

Within the quantum-mechanical theory of fission, wave functions for fragments of binary nuclear fission and amplitudes of partial fission widths are constructed with allowance for a strong nonsphericity of fragment-interaction potentials. It is shown that, in the strong-coupling approximation, the symmetry axes of fission fragments are oriented along the symmetry axis of a fissile nucleus. The structure of the fragment-interaction potentials is analyzed, and the mechanism that is responsible for the alignment of the spins and relative orbital angular momenta of fission fragments and which explains the emergence of high fragment-spin values in experiments is substantiated. The mechanisms in question are generalized to the case of ternary nuclear fission. The fragment-interaction potentials and fragment wave functions are investigated, along with the partial fission widths with respect to the ternary fission of nuclei.     

Coriolis interaction in the second well of deformation potential and low-energy fission

It is shown that, because of sufficiently large energy spacing between neutron resonance states (NRS-II) in the second well of the deformation potential for actinide nuclei, the Coriolis interaction, mixing the states of an axially symmetric deformed nuclei with different values of the projection K of the nuclear spin J onto the symmetry axis, is week, and the K value in the wave functions of NRS-II is a good quantum number. It is concluded that the K distribution for the states of fissile actinide nuclei in the vicinity of their scission point into fission fragments is determined by simultaneous influence of the internal and external fission barriers, which allows to coordinate the experimental data on subbarrier photofission with the P-odd and P-even correlations in the angular distributions of fission fragments.     

Recent studies in heavy ion induced fission reactions

Nuclear fission process involves large scale shape changes of the nucleus, while it evolves from a nearly spherical configuration to two separated fission fragments. The dynamics of these shape changes in the nuclear many body system is governed by a strong interplay of the collective and single particle degrees of freedom. With the availability of heavy ion accelerators, there has been an impetus to study the nuclear dynamics through the investigations of nucleus-nucleus collisions involving fusion and fission process. From the various investigations carried out in the past years, it is now well recognized that there is large scale damping of collective modes in heavy ion induced fission reactions, which in other words implies that nuclear motion is highly viscous. In recent years, there have been many experimental observations in heavy ion induced fission reactions at medium bombarding energies, which suggest possible occurrence of various non-equilibrium modes of fission such as quasi-fission, fast fission and pre-equilibrium fission, where some of the internal degrees of freedom of the nucleus is not fully equilibrated. We have carried out extensive investigations on the fission fragment angular distributions at near barrier bombarding energies using heavy fissile targets. The measured fragment anisotropies when compared with the standard saddle point model (SSPM) calculations show that for projectile-target systems having zero or low ground state spins, the angular anisotropy exhibits a peak-like behaviour at the sub barrier energies, which cannot be explained by the SSPM calculations. For projectiles or targets with large ground state spins, the anomalous peaking gets washed out due to smearing of the K-distribution by the intrinsic entrance channel spins. Recently studies have been carried out on the spin distributions of fission fragments through the gamma ray multiplicity measurements. The fission fragments acquire spin mainly from two sources: (i) due to rigid rotation of the nascent fragments at scission and (ii) due to statistical excitation of the spin bearing collective modes in the fissioning nucleus. One of the collective modes — the tilting mode depends on the K quantum number and is responsible for the emission angle dependence of fragment spin. In our studies, we have shown conclusively that the collective statistical spin modes get strongly suppressed for high K values corresponding to large rotational frequencies along the fission axis. These results bring out the importance of the dynamical effects in the heavy ion induced fusion-fission reactions. The present article will review the work carried out on the above aspects in heavy ion fission reactions as well as on the fission time scales, and some of the recent studies on the mass-energy correlations of fission fragments at near-barrier bombarding energies.     

Nonadiabatic excitation of nucleons in a fissile system

The probabilities for nonadiabatic transitions of nucleons in a fissile system are analyzed. Nearly all the excitation energy is expended in exciting single-particle degrees of freedom. The occupation numbers of the nucleon states and the potential energies of the collective motion are calculated for U²³⁸ for various values of the deformation parameter.Translated from Izvestiya VUZ. Fizika, No. 5, pp. 16–22, May, 1971.     

Decay and fission of oriented nuclei

The angular distributions of fragments originating from the binary decay of oriented spherical and deformed nuclei are investigated with allowance for correct transformation properties of wave functions under time inversion. It is shown that, as in the case of protonic decay, the adiabatic approximation for collective rotational degrees of freedom of the systems under investigation is inapplicable in describing the angular distributions of fragments of the deep-subbarrier alpha and cluster decays of nuclei. It is demonstrated that this approximation is justified in describing spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of intrinsic axes, spins, and projections of spins and relative orbital angular momenta of fission fragments is analyzed by using the formalism of the unified theory of nuclear reactions and the theory of open Fermi systems. It is shown that the adiabatic approximation leads to the coherent interference between the wave functions for the relative motion of fragments, whereby the universal angular distributions of fission fragments of oriented nuclei is formed. Deviations from the A. Bohr formula are investigated for these distributions.     

Classification of <Emphasis Type="Italic">T</Emphasis>-odd asymmetries for prescission and evaporated light particles in ternary and quaternary nuclear fission induced by cold polarized neutrons

A unified mechanism of the emergence of T-odd ROT- and TRI-asymmetries is proposed for describing experimental T-odd asymmetry coefficients D(θ) in the angular distributions of prescission alphaparticles that are emitted in true ternary and quaternary nuclear fission reactions induced by cold polarized neutrons. The mechanism is related to the different ways in which the Coriolis interaction of the total spin of a polarized compound fissile nucleus with the orbital moment of alpha-particles affects even (for ROT-asymmetries) and odd (for TRI-asymmetries) components of the amplitude of an undisturbed angular distribution of emitted alpha-particles. Coefficients D_ROT(θ) and D_TRI(θ) derived with this mechanism for T-odd ROT- and TRI-asymmetries successfully describe the dependences of corresponding experimental coefficients for ²³⁵U and ²³⁹Pu nuclei over the range of angles θ, and for the ²³³U nucleus in the angular range of 60° < θ < 110°. It is explained why only ROT-type T-odd asymmetries emerge for evaporated neutrons and γ-quanta emitted by fission fragments in similar reactions if we allows for the Coriolis interaction of the total spin of the compound fissile nucleus with the orbital moments of the fission fragments and the wriggling vibrations of the above nucleus near its scission point.     

Investigation of the reaction 208Pb(18O, f): Fragment spins and phenomenological analysis of the angular anisotropy of fission fragments

The average multiplicity of gamma rays emitted by fragments originating from the fission of ²²⁶Th nuclei formed via a complete fusion of ¹⁸O and ²⁰⁸Pb nuclei at laboratory energies of ¹⁸O projectile ions in the range E _lab = 78–198.5 MeV is measured and analyzed. The total spins of fission fragments are found and used in an empirical analysis of the energy dependence of the anisotropy of these fragments under the assumption that their angular distributions are formed in the vicinity of the scission point. The average temperature of compound nuclei at the scission point and their average angular momenta in the entrance channel are found for this analysis. Also, the moments of inertia are calculated for this purpose for the chain of fissile thorium nuclei at the scission point. All of these parameters are determined at the scission point by means of three-dimensional dynamical calculations based on Langevin equations. A strong alignment of fragment spins is assumed in analyzing the anisotropy in question. In that case, the energy dependence of the anisotropy of fission fragments is faithfully reproduced at energies in excess of the Coulomb barrier (E _c.m. ? E _B ≥ 30 MeV). It is assumed that, as the excitation energy and the angular momentum of a fissile nucleus are increased, the region where the angular distributions of fragments are formed is gradually shifted from the region of nuclear deformations in the vicinity of the saddle point to the region of nuclear deformations in the vicinity of the scission point, the total angular momentum of the nucleus undergoing fission being split into the orbital component, which is responsible for the anisotropy of fragments, and the spin component. This conclusion can be qualitatively explained on the basis of linear-response theory.     

On Ternary Fission Induced by Neutrons

Experiments on measuring the rotational effect of the ²³⁴U fissile nucleus at the scission point showed that the fissile nucleus rotates as a right screw with respect to the longitudinally polarized neutron beam direction in the ternary fission of the ²³³U target nucleus induced by polarized s-neutrons; in the binary fission of the same nuclei it rotates in the opposite direction. Moreover, it was found that ternary fission “prefers” the spin state of J = I +1/2. This phenomenon cannot be explained within the existing concepts of ternary fission as one of the two “final” states after neck rupture. The same “parent” ²³⁴U nucleus cannot rotate in opposite directions in the two different final states. It should be assumed that ternary fission is a special branch of descent from the saddle point to the point of neck rupture. It can also be assumed that this branch is formed at the saddle point in a configuration favorable for cluster formation. Why does it prefer the spin state of J = I + 1/2? This is an interesting question for further studies.