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.     

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.     

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.     

<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.     

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 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.     

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.     

Neutron-neutron angular correlations in spontaneous fission of <Superscript>252</Superscript>Cf

An experiment has been carried out to study neutron-neutron angular correlations in spontaneous fission of ²⁵²Cf. Angular dependences of the number of neutron-neutron coincidences obtained in the experiment were compared with the results of the Monte Carlo calculations for various neutron detection thresholds in the range 425–1600 keV. It was inferred that 10–11% of the total number of prompt neutrons from ²⁵²Cf (s.f.) in the laboratory system were emitted isotropically and may probably be interpreted as neutrons directly associated with the instant of scission of the nucleus. The analysis allowed their energy distribution to be determined as well. A similar method was also used to describe the angular correlation of prompt neutrons that accompanied the reaction ²³⁵U(n _th ,f).     

Prompt-fission-neutrons spectra of <Superscript>238</Superscript>U

The spectra of prompt fission neutrons from the reaction ²³⁸U(n, F) for neutrons of energy in the range E _n ≤ 20 MeV are interpreted within the statistical model. It is shown that exclusive spectra of prefission neutrons emitted in (n, xnf) reactions play a decisive role in describing the observed promptfission-neutron spectra and determine the average energies of prompt-fission neutrons. The dependence of the effect of prefission neutrons on the fissility of a target nucleus is demonstrated for the reactions ²³²Th(n, F), ²³⁵U(n, F), and ²³⁹Pu(n, F).     

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.     

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.     

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.     

Unified quantum description of TRI and ROT effects in ternary fission

It is shown that consideration of the Coriolis interaction makes it possible to explain both T-odd effects observed in ternary fission induced by polarized neutrons. A possible reason for the difference in the effects observed for ²³³U and ²³⁵U targets is discussed.     

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.     

<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.     

<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.     

Compton polarimetry detection of small circularly and linearly polarized impurities in Mössbauer 8.4 keV (3/2-1/2) M1 γ-transition of 169Tm

The arrangement of an experiment to detect the P?odd and P, T?odd polarized part of the Mössbauer (⁺3/2– ⁺1/2) gamma transition of a deformed ¹⁶⁹Tm nucleus with an energy of 8.4 keV by Compton polarimetry is discussed. Tm ₂O₃ single crystal with a quadrupolarly split Mössbauer spectrum is proposed as a resonance polarizer. A Be-scatterer-based Compton polarimeter and a synchronously detecting system will be used to measure the P-odd circular polarization P_Cand P, T-odd linear polarization P_L.The expected accuracy of measuring the relative magnitude of the P, T-odd contribution is about 1% of the magnitude of usual weak nucleon–nucleon interaction.     

Spectra and mean energies of prompt neutrons from <Superscript>238</Superscript>U fission induced by primary neutrons of energy in the region <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><20 MeV

The time-of-flight technique is used to measure the ratios R(E, E _n )=N(E, E _n )/N_Cf(E) of the normalized (to unity) spectra N(E, E _n ) of neutrons accompanying the neutron-induced fission of ²³⁸U at primary-neutron energies of E _n =6.0 and 7.0 MeV to the spectrum N_Cf(E) neutrons from the spontaneous fission of ²⁵²Cf. These experimental data and the results of their analysis are discussed together with data that were previously obtained for the neutron-induced fission of ²³⁸U at the primary energies of E _n =2.9, 5.0, 13.2, 14.7, 16.0, and 17.7 MeV.