Mechanisms of formation of P-odd,P-even and T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons

The experimentally measured P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons are classified, and the mechanisms of their appearance are studied. Basic asymmetries in the angular distributions of binary-fission fragments are found theoretically and are used to construct induced asymmetries in the angular distributions of prescission and evaporated third particles emitted in true and delayed ternary fission. If effects associated with the collective rotation of the polarized fissile system are disregarded, P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of prescission and evaporated photons are proven to be absent, and the coefficients of the analogous asymmetries in the angular distributions of prescission and evaporated neutrons are calculated for this case. The features of the coefficients of induced P-even, T-odd asymmetries are studied for evaporated photons and neutrons associated with taking into account the quantum rotation of the polarized fissile system.     

P-odd,T-odd asymmetries in the binary and ternary fissioning of oriented target nuclei by cold polarized neutrons

Since P-odd and T-odd asymmetries are generally not observed during the fissioning of unoriented target nuclei by polarized neutrons and oriented target nuclei by unpolarized neutrons, analogous asymmetries in angular distributions of products from binary and ternary fissioning of oriented target nuclei by cold polarized neutrons are thoroughly analyzed within the quantum theory of fission for finding these correlations. It is demonstrated that these correlations occur only when interference of the compound fissioning nucleus states with different spins is considered. Contributions from target nucleus orientations of different orders to coefficients of the asymmetries in question for fission fragments are estimated. Characteristics of analogous asymmetries for prescission and evaporation third particles are analyzed.     

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.     

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.     

P-odd and P-even correlations for third particles in ternary fission

Within quantum-mechanical fission theory, P-odd and P-even correlations in angular distributions of products of the ternary fission of nuclei that is induced by polarized cold and thermal neutrons are investigated on the basis of a nonevaporative mechanism of third-particle emission and under the assumption that a two-humped fission barrier exists. It is shown that these correlations for third particles are induced by the analogous correlations for ternary-fission fragments, the latter being transferred to the third particle because of the kinematical conditions of third-particle emission that are associated with the charge and mass asymmetry of fragments. Optimum methods for observing the above correlations for third particles are discussed. The possibility of discovering the emission of prescission neutrons in the fission process against the background of evaporated neutrons by means of studying P-odd and P-even correlations is explored.     

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.     

Description of true and delayed ternary nuclear fission accompanied by the emission of various third particles

The mechanisms and the features of the main types of nuclear ternary fission (that is, true ternary fission, in which a third particle is emitted before the rupture of the fissioning nucleus into fragments, and delayed ternary fission, in which a third particle is emitted from fission fragments going apart) are investigated within quantum-mechanical fission theory. The features of T-odd asymmetry in true ternary nuclear fission induced by cold polarized neutrons are investigated for the cases where alpha particles, prescission neutrons, and photons appear as third particles emitted by fissioning nuclei, the Coriolis interaction of the spin of the polarized fissioning nucleus with the spin of the third particle and the interference between the fission amplitudes for neutron resonances excited in the fissioning nucleus in the case of projectile-neutron capture being taken into account. For the cases where third particles emitted by fission fragments are evaporated neutrons or photons, T-odd asymmetries in delayed ternary nuclear fission induced by cold polarized neutrons are analyzed with allowance for the mechanism of pumping of large fission-fragment spins oriented orthogonally to the fragment-emission direction and with allowance for the interference between the fission amplitudes for neutron resonances.     

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.     

Interference of fission amplitudes of neutron resonances and <Emphasis Type="Italic">T</Emphasis>-odd asymmetry for various prescission third particles in the ternary fission of nuclei

Differential cross sections for reactions of the true ternary fission of nuclei that was induced by cold polarized neutrons were constructed with allowance of the effect that Coriolis interaction and the interference between fission amplitudes of neutron resonances excited in fissile nuclei upon incidentneutron capture by target nuclei exerted on angular distributions of prescission third particles (alpha particles, neutrons, or photons). It is shown that T -odd TRI- and ROT-type asymmetries for prescission alpha particles are associated with, respectively, the odd and even components of the Coriolis interaction-perturbed amplitude of angular distributions of particles belonging to the types indicated above. These asymmetries have angular distributions differing from each other and stemming from a nontrivial dependence of these components on the neutron-resonance spins J _s and their projections K _s onto the symmetry axis of the nucleus involved. It is shown that angular distributions of prescission photons and neutrons from reactions of the ternary fission of nuclei that is induced by cold polarized neutrons are determined by the effect of Coriolis forces exclusively. Therefore, the emerging T-odd asymmetries have a character of a ROT-type asymmetry and are universal for all target nuclei.     

Parity nonconservation in binary and ternary nuclear fission induced by polarized neutrons

Within the quantum-mechanical theory of the nuclear-fission process, the conditions of the emergence of coherent effects in the angular distributions of fragments originating from the binary and ternary fission of polarized nuclei are analyzed with allowance for the properties of transition fission states. In the case of ternary fission, the coefficients of P-odd asymmetry in the angular distributions of a light particle and a third particle, which is taken here to be an alpha particle, are calculated under the assumption that the third particle and two fragments are produced through a one-step mechanism. In order to confirm the ideas developed here, it is proposed to repeat, at a higher level of statistical accuracy, experiments devoted to seeking P-odd asymmetries for alpha particles in the ternary fission of nuclei.     

P-odd asymmetries for the binary fission of oriented target nuclei, induced by cold polarized neutrons

P-odd asymmetries in binary fission of oriented target nuclei induced by cold polarized neutrons are described for the first time using methods of the quantum theory of fission. A spin matrix of the compound nucleus density is constructed with allowance for the interference of the fission amplitudes of various pairs of neutron resonances excited in the given nucleus during the capture of a cold polarized neutron by the oriented target nucleus. In the differential cross sections for this reaction we obtain not only P-odd T-even correlations with the angular dependence different from that of the earlier investigated correlations in the fission of unoriented target nuclei by polarized neutrons but also P-odd T-odd correlations that do not occur in the fission of unoriented target nuclei by polarized neutrons and oriented target nuclei by unpolarized neutrons.     

T-odd asymmetries for products from the spontaneous fission of oriented nuclei

The problem of describing T-odd asymmetries in ternary fission reactions of oriented nuclei is solved for the first time on the basis of quantum theory. Estimates of the T-odd asymmetry coefficients in the angular distributions of the reaction products are obtained using the spin density matrix of the oriented fissioning nucleus. It is demonstrated that experiments on observing T-odd asymmetries in the spontaneous fission of oriented nuclei are of interest because the T-odd asymmetry coefficients can be around an order of magnitude greater than similar coefficients in the fission of unoriented target nuclei induced by polarized neutrons.     

Coriolis interaction as a source of the effect of quantum rotation on a deformed nucleus in collective modes of its internal motion

Interaction between the rotation of a decaying axially symmetric deformed nucleus and its internal motions corresponding to both the discrete and the continuous energy spectrum of the nucleus is studied within a generalized model of the nucleus using the Hamiltonian of the Coriolis and centrifugal forces. The particle + rotator model is generalized to the case where any groups of N nuclear nucleons, including N = A, participate in the internal motions under study. The results are used to describe T-odd asymmetries in true and delayed ternary fission of polarized nuclei with α particles, prescission and evaporation neutrons, and γ rays emitted as third particles.     

Even and odd amplitudes of distributions of third particles in nuclear fission

The principal values for the even and odd components of the amplitudes of the angular distributions of α particles emitted as the third particles in true low-energy ternary fission of nuclei are calculated within the quantum theory of fission using natural approximations for the dependence of the potential scattering phases of the α particle on its orbital momenta and experimental angular distributions, unperturbed by the fissioning nucleus rotation, of these third α particles. Knowing the angular dependences of these components, we can estimate the angular dependences of the T-odd ROT and TRI asymmetry coefficients for the ternary fission of actinide nuclei induced by cold polarized neutrons.     

<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.     

Relation of Experimental Features of P-Even,T-Odd Asymmetries in Ternary Nuclear Fission Induced by Cold Polarized Neutrons to Triple and Quintuple Scalar Correlations

In employing the concept of the isotropy of space, the coefficients D of P-even, T-odd asymmetry in the angular distributions of prescission alpha particles emitted as third particles in the ternary fission of nonoriented target nuclei that is induced by polarized cold neutrons are expressed in the lowest orders of perturbation theory in the neutron polarization vector in terms of two P-even scalar coefficients D₃ and D₅ associated with, respectively, triple and quintuple correlations depending on the unit vectors k_α, k_LF, and σ_n, which determine the features of the coefficients being studied. On the basis of the above representation, the experimental values of the coefficients D₃ and D₅ are determined by using the experimental values of D and the angular distributions of alpha particles emitted in the analogous reaction induced by unpolarized neutrons. The resulting coefficients D₃ and D₅ are compared with the analogous coefficients found by means of the classical method of trajectory calculations and by means of quantum-mechanical fission theory relying on the concept that it is the rotational mechanism that is responsible for the appearance of the asymmetries being studied. It turns out that the classical method, which disregards the interference between fission amplitudes for different S-wave neutron resonances, leads to an irremovable contradiction between the calculated coefficient D₃ and the analogous experimental coefficient for the ²³³U target nucleus. In the case of employing the quantum-mechanical approach, it is concluded that three-body calculations of the Coriolis interaction—perturbed amplitude of the angular distributions of alpha particles moving in the Coulomb fields of fission fragments are required for the ²³³U target nucleus.

     

Experimental studies of nuclear fission dynamics near the scission point

Conditions for formation of angular and energy distributions of light particles emitted in ternary fission of ^{233, 235}U, ²³⁹Pu, and ²⁴⁵Cm nuclei induced by cold polarized neutrons have been studied in the course of investigating T-odd asymmetry in emission of these particles with respect to the plane formed by the fission axis and the polarization axis of the fissioning nucleus. The results obtained lead to the conclusion that in ternary fission charged particles are emitted by the fissioning nuclear system rotating around the polarization direction.     

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.     

Search for scission neutrons using specific angular correlations in 235U fission induced by slow polarized neutrons

The experimental data concerning scission (or prescission) neutrons are very contradictory—the relative part of these neutrons in the prompt fission neutrons varies from 1 to 35% owing to arbitrary assumptions made in different analyses. To solve this problem, we have used a new alternative method to search for the scission neutrons. We have found the left-right asymmetry of prompt-fission-neutron (PFN) emission caused by sp-wave interference in the entrance channel of the reaction and the P-odd asymmetry of the PFN emission caused by parity nonconservation at the exit channel of the fission process. Both effects cannot reside in PFN evaporated by excited fission fragments. The scission (or prescission) neutrons are responsible for these effects. The text was submitted by the authors in English.