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.     

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.     

Asymmetries of various <Emphasis Type="Italic">P</Emphasis>- and <Emphasis Type="Italic">T</Emphasis>-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and <Emphasis Type="Italic">T</Emphasis>-invariance

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.     

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.     

<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.     

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 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.     

Investigations of fission characteristics and correlation effects

We review the experimental results on the P-even and P-odd angular correlations of fission fragments in the fission of the ²³⁵U and ²³⁹Pu nuclei induced by unpolarized and polarized resonance neutrons, and on the TRI and ROT effects in the ternary and binary fission of actinides induced by polarized thermal neutrons. Also reported are the measured yields of prompt and delayed neutrons per fission event. The experimental data are analyzed within a novel theoretical framework developed by the JINR—RNC KI Collaboration, whereby the reduction of the multidimensional phase space of fission fragments to the JπK-channel space is consistently validated and the role of resonance interference in the observed correlation effects is revealed.     

Application of <Emphasis Type="Italic">T</Emphasis>-Invariance Conditions in Selecting Mechanisms of Nuclear Reactions,Decays, and Fission

T-invariance conditions for the differential cross sections of multiparticle multistep nuclear reactions are found with allowance for spin orientations of particles in the initial channels of such reactions. It is shown that the asymmetry coefficients for different T-parities in the differential cross sections for original and time-reversed reactions are expressed in terms of unified scalar (pseudoscalar) functions that depend of the 3-momenta and spins of particles involved in the initial and final channels of the reactions under analysis. It is also shown that knowledge of the aforementioned functions for the asymmetries under analysis in the original reaction makes it possible to reconstruct the respective functions for the analogous asymmetries in the time-reversed reaction without studying it experimentally. By considering the example of T-even and T-odd asymmetries in reactions where oriented nuclei undergo binary and ternary fission induced by cold polarized neutrons, it is demonstrated that the T-invariance conditions in question can be used to select mechanisms behind the appearance of the above asymmetries—in particular, mechanisms associated with the presence of T-noninvariant interactions.     

<Emphasis Type="Italic">T</Emphasis>-odd angular asymmetry in nuclear reactions involving sequential particle emission

A triple T-odd angular correlation is considered in the kinematically similar reactions ¹⁰B(n, αγ) and ²³³U(n, αf) induced by cold polarized neutrons. It is shown that, in the former reaction, this correlation is suppressed by the double parity-conservation selection rule due to the two-step character of the process; however, T invariance does not impose any specific constraints on this correlation. The mechanism through which the T-odd correlation found in ternary-fission reactions is formed seems to be closely related to a nearly simultaneous disintegration of the nucleus involved into two fission fragments and an alpha particle.     

Search for <Emphasis Type="Italic">P</Emphasis>-odd asymmetry of prompt neutron emission in <Superscript>235</Superscript>U fission induced by cold polarized neutrons

The preliminary result of the P-odd asymmetry of prompt neutron emission in ²³⁵U fission induced by polarized cold neutrons is a=(2.7±0.8)×10^?5. Only scission neutrons can show such asymmetry, whereas neutrons emitted by excited fragments are the unavoidable background, which suppress the sought asymmetry. The P-odd asymmetry of light fragment emission for ²³⁵U is equal to (8.4±0.6)×10^?5. Assuming that the last figure defines the parity mixture of the fissile nucleus, then the suppression factor is equal approximately to 3.     

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.     

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 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 effects in nuclear fission

Various interference effects governing the character of angular distributions of binary and ternary nuclear fission products and P-odd, P-even, and T-odd asymmetries in these angular distributions have been studied within the quantum theory of spontaneous and low-energy induced nuclear fission.     

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.     

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.