It is shown that all the features of fast alpha particles with energies close to the two-body kinematic limit emerging in heavy-ion collisions are well explained by the direct theory of stripping and knock-on reactions. Recently found particles with energies exceeding this limit are interpreted as a result of the newly discovered reaction process, namely, the direct quasi-fission reaction.

It is shown that when the Liouville–Arnold theorem is applied to quantum systems, the purely quantum first integrals of motion of the parity type should not be considered when comparing the number of the first integrals to that of the degrees of freedom.

It is shown that the distribution of energy levels in a system is a fairly weak sign of a system’s chaoticity and cannot serve as a quantitative measure of it. A brief description is presented of a better criterion of quantum chaos and its quantitative measure that was proposed in the author’s earlier works.

A detailed analysis of T-odd asymmetries in the reactions of true ternary fission of nuclei that involves the emission of prescission alpha particles is performed within quantum-mechanical fission theory. This analysis is based on taking into account the effect of quantum rotation of a fissile compound nucleus formed upon the capture of a polarized cold neutron by an nonoriented target nucleus on angular distributions of both alpha particles and fission fragments. It is shown that the asymmetries in question cannot be described within the approach relying on the use of the classic method of trajectory calculations without taking into account the interference between the fission amplitudes for different neutron resonance states of a fissile compound nucleus that are formed at the initial stage of the reactions being studied.

A comparison is made of two theoretical approaches to describing the coefficients of T-odd asymmetries in the angular distributions of prompt γ-quanta and neutrons evaporated from thermalized fragments of the binary fission of non-oriented target nuclei by cold polarized neutrons, and in angular distributions of pre-scission α particles emitted in the same ternary nuclear fission: the classical approach, which is based on trajectory calculations, and the quantum approach, which is based on quantum fission theory. It is shown that the coefficients for all of the considered nuclei are of a quantum nature and vanish in the classical approach when there is no interference from the fission amplitudes of the different neutron resonances of a compound nucleus. The advantages of the quantum approach versus the classical one are demonstrated.

The possibility of semiclassical description of ROT and TRI effects in the asymmetry of the angular distribution of products originating from the ternary fission of nuclei that is induced by polarized cold neutrons is considered. It is shown that, in the semiclassical approximation, respective experimental results can be explained qualitatively by taking into account Coriolis effects in the emission of a light third particle from a rotating nucleus that undergoes fission.

The possibility is investigated of observing deviations in the angular distributions of fragments from the low-energy binary fission of aligned actinide nuclei by resonant neutrons, calculated within the theory of quantum fission with allowance for the wriggling vibrations of fissile nuclei using angular distributions determined with Bohr’s formula. The relative errors of the experimental anisotropy coefficients of these distributions are compared to deviations of the theoretical anisotropy coefficients, calculated with allowance for wriggling vibrations of fissile nuclei, from those calculated using Bohr’s formula. Estimates are obtained on this basis for the wriggling vibration parameters: Open image in new window and Open image in new window for 233U and 235U nuclei, respectively, for which deviations from Bohr’s formula can be detected.

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 sJs 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.

The probability estimates for the emission of scission neutrons (those emitted in the vicinity of the scission point) were done several times. The main method used in these estimates was the comparison of the experimental and theoretical energy and angular distributions of neutrons accompanying fission. The basic assumption of the method was the isotropic emission of neutrons in the c.m. system of each fission fragment. The present work takes into account the anisotropy of such an emission, which results from the large fragments spins appeared at scission and are perpendicular to the line of the fragment’s relative motion. Contrary to the majority of previous works the sequential emission of neutrons was calculated in the framework of the standard evaporation model by Monte-Carlo method.

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.

It is shown that A. Bohr’s classic theory of angular distributions of fragments originating from low-energy fission should be supplemented with quantum corrections based on the involvement of a superposition of a very large number of angular momenta L m in the description of the relative motion of fragments flying apart along the straight line coincidentwith the symmetry axis. It is revealed that quantum zero-point wriggling-type vibrations of the fissile system in the vicinity of its scission point are a source of these angular momenta and of high fragment spins observed experimentally.

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.

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.