T-odd asymmetries for evaporation neutrons in nuclear fission

T-odd asymmetries in the angular distributions of evaporation neutrons emitted by thermalized fission fragments in the fission of axially symmetric deformed nuclei by cold polarized neutrons are investigated within the quantum theory of fission. The asymmetries in question are due to the anisotropy of angular distributions of evaporation neutrons in the center-of-mass systems of the fission fragments, and this anisotropy arises from the orientation of large-value fission fragment spins in the direction perpendicular to the direction K ₀ of the symmetry axis of the fissioning nucleus at the time of its scission, caused by zero wriggling vibrations of the fissioning nucleus. The angle of rotation of the vector k ₀ with respect to the asymptotic direction k ₀ of the fissioning nucleus symmetry axis is calculated with allowance for the interference of fission amplitudes of neutron resonances excited in a fissioning nucleus as it captures an incident neutron. It is shown that the T-odd asymmetry coefficient for evaporation neutrons is close in structure and value to the analogous coefficient for evaporation γ-rays.     

<Emphasis Type="Italic">T</Emphasis>-odd asymmetries for evaporation γ-rays in nuclear fission

T-odd asymmetries in angular distributions of evaporation γ-rays emitted by thermalized fragments resulting from the fission of axially symmetric deformed nuclei induced by cold polarized neutrons are investigated within the quantum theory of fission. The asymmetries in question are due to the anisotropy of the angular distributions of evaporation γ-rays, caused by zero wriggling vibrations of the fissioning nucleus and associated with the orientation of large fission fragment spins in the direction perpendicular to the direction n ₀ of the symmetry axis of the fissioning nucleus at the time of its separation into fragments. The angle of rotation of the vector n ₀ with respect to the asymptotic direction of the light fission fragment emission is calculated with allowance for the interference of fission amplitudes of neutron resonances excited in the fissioning nucleus as it captures the incident neutron. It is shown that the angular and energy characteristics of the T-odd asymmetry calculated for evaporation γ-rays agree with the characteristics of the experimentally investigated T-odd asymmetry in angular distributions of all γ-rays emitted by a fissioning ²³⁶U nucleus.     

T-odd asymmetries in the cold neutron-induced ternary fission of polarized target nuclei

T-odd asymmetries in the ternary fission of oriented target nuclei, induced by cold unpolarized neutrons and accompanied by emission of ?? particles, are described using quantum fission theory. The differential cross section for the reaction in question is obtained using the spin density matrix of the target nucleus by considering the Coriolis interaction of the spin of a fissioning compound nucleus with the orbital momentum of an ?? particle and interference from the fission amplitudes of various pairs of neutron resonances excited in the compound nucleus as the target nucleus captures a cold neutron. It is shown that in the case under consideration, T-odd asymmetries occur only at odd values of the target nucleus??s order of orientation. It is demonstrated that the concepts of TRI and ROT asymmetries are preserved while the absolute values of the coefficients for these asymmetries can change noticeably in comparison to the similar coefficients for the fission of unoriented target nuclei induced by cold polarized neutrons.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

P-odd, P-even, and T-odd asymmetries in true quaternary fission of nuclei

The coefficients of P-odd, P-even, and T -odd asymmetries for a third and a fourth prescission particle emitted in the true quaternary fission of nuclei that was induced by polarized cold neutrons were studied on the basis of quantum-mechanical fission theory. By using non-evaporation (nonadiabatic) mechanisms of light-particle emission, these coefficients were compared with the analogous coefficients for prescission third particles emitted in the ternary fission of nuclei.     

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.     

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.     

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.     

<Emphasis Type="Italic">T</Emphasis>-odd asymmetries in the angular distributions of fragments originating from the ternary fission of nuclei

A version of a theoretical explanation is proposed for the recently discovered effect of T-odd correlation in ternary nuclear fission induced by polarized neutrons. It is shown that the inclusion of the Coriolis interaction between a third particle and the fissile-nucleus spin within the quantum theory of fission makes it possible to explain the experimental features of the effect and provides a correct estimate of its magnitude.     

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.