Statistical Mechanics. — A Set of Lectures

General Description of Fission Observables: GEF Model Code

In the last two decades, through technological, experimental and theoretical advances, the situation in experimental fission studies has changed dramatically. With the use of advanced production and detection techniques both much more detailed and precise information can now be obtained for the traditional regions of fission research and, crucially, new regions of nuclei have become routinely accessible for fission studies. This work first of all reviews the recent developments in experimental fission techniques, in particular the resurgence of transfer-induced fission reactions with light and heavy ions, the emerging use of inverse-kinematic approaches, both at Coulomb and relativistic energies, and of fission studies with radioactive beams. The emphasis on the fission-fragment mass and charge distributions will be made in this work, though some of the other fission observables, such as prompt neutron and γ-ray emission will also be reviewed. A particular attention will be given to the low-energy fission in the so far scarcely explored nuclei in the very neutron-deficient lead region. They recently became the focus for several complementary experimental studies, such as β-delayed fission with radioactive beams at ISOLDE(CERN), Coulex-induced fission of relativistic secondary beams at FRS(GSI), and several prompt fusion-fission studies. The synergy of these approaches allows a unique insight in the new region of asymmetric fission around 180Hg, recently discovered at ISOLDE. Recent extensive theoretical efforts in this region will also be outlined. The unprecedented high-quality data for fission fragments, completely identified in Z and A, by means of reactions in inverse kinematics at FRS(GSI) and VAMOS(GANIL) will be also reviewed. These experiments explored an extended range of mercury-to-californium elements, spanning from the neutron-deficient to neutron-rich nuclides, and covering both asymmetric, symmetric and transitional fission regions. Some aspects of heavy-ion induced fusion-fission and quasifission reactions will be also discussed, which reveal their dynamical features, such as the fission time scale. The crucial role of the multi-chance fission, probed by means of multinucleon-transfer induced fission reactions, will be highlighted. The review will conclude with the discussion of the new experimental fission facilities which are presently being brought into operation, along with promising 'next-generation' fission approaches, which might become available within the next decade.

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Nuclear fission: a review of experimental advances and phenomenology.

An overview is given on some of the main advances in the experimental methods, experimental results, theoretical models and ideas of the last few years in the field of nuclear fission. New approaches have considerably extended the availability of fissioning systems for the experimental study of nuclear fission, and have provided a full identification of all fission products in A and Z for the first time. In particular, the transition from symmetric to asymmetric fission around 226Th, some unexpected structures in the mass distributions in the fission of systems around Z  =  80-84, and an extended systematics of the odd-even effect in the fission fragment Z distributions have all been measured (Andreyev et al 2018 Rep. Prog. Phys. 81 016301). Three classes of model descriptions of fission presently appear to be the most promising or the most successful. Self-consistent quantum-mechanical models fully consider the quantum-mechanical features of the fission process. Intense efforts are presently being made to develop suitable theoretical tools (Schunck and Robledo 2016 Rep. Prog. Phys. 79 116301) for modeling the non-equilibrium, large-amplitude collective motion leading to fission. Stochastic models provide a fully developed technical framework. The main features of the fission-fragment mass distribution have been well reproduced from mercury to fermium and beyond (Moller and Randrup 2015 Phys. Rev. C 91 044316). However, limited computer resources still impose restrictions, for example, on the number of collective coordinates and on an elaborate description of the fission dynamics. In an alternative semi-empirical approach (Schmidt et al 2016 Nucl. Data Sheets 131 107), considerable progress in describing the fission observables has been achieved by combining several theoretical ideas, which are essentially well known. This approach exploits (i) the topological properties of a continuous function in multidimensional space, (ii) the separability of the influence of fragment shells and the macroscopic properties of the compound nucleus, (iii) the properties of a quantum oscillator coupled to a heat bath of other nuclear degrees of freedom, (iv) an early freeze-out of collective motion, and (v) the application of statistical mechanics for describing the thermalization of intrinsic excitations in the nascent fragments. This new approach reveals a high degree of regularity and allows the calculation of high-quality data that is relevant to nuclear technology without specifically adjusting the empirical data of individual systems.

https://iopscience.iop.org/article/10.1088/1361-6633/aacfa7/pdf

Review on the progress in nuclear fission-experimental methods and theoretical descriptions.

Direct Interactions and Nuclear Reaction Mechanisms

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.

T-odd asymmetries in the angular distributions of fragments originating from the ternary fission of nuclei

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.

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

The angular distributions of fragments originating from the binary decay of oriented spherical and deformed nuclei are investigated with allowance for correct transformation properties of wave functions under time inversion. It is shown that, as in the case of protonic decay, the adiabatic approximation for collective rotational degrees of freedom of the systems under investigation is inapplicable in describing the angular distributions of fragments of the deep-subbarrier alpha and cluster decays of nuclei. It is demonstrated that this approximation is justified in describing spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of intrinsic axes, spins, and projections of spins and relative orbital angular momenta of fission fragments is analyzed by using the formalism of the unified theory of nuclear reactions and the theory of open Fermi systems. It is shown that the adiabatic approximation leads to the coherent interference between the wave functions for the relative motion of fragments, whereby the universal angular distributions of fission fragments of oriented nuclei is formed. Deviations from the A. Bohr formula are investigated for these distributions.

Decay and Fission of Oriented Nuclei

Within quantum fission theory, angular distributions of products originating from 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 a consistent description of fission-channel coupling. It is shown that the inclusion of Coriolis interaction both in the region of the discrete and in the region of the continuous spectrum of states of the system undergoing fission leads to T-odd correlations in the aforementioned angular distributions. The properties of the TRI and ROT effects discovered recently, which are due to the interference between the fission amplitudes of neutron resonances, are explored. The results obtained here are compared with their counterparts from classic calculations based on the trajectory method.

Angular distribution of products of ternary nuclear fission induced by cold polarized neutrons

The angular distributions of fragments originating from the binary fission of odd and odd-odd nuclei capable of undergoing spontaneous fission that are polarized by a strong magnetic field at ultralow temperatures and from the low-energy photofission of even-even nuclei that is induced by dipole and quadrupole photons are investigated. It is shown that the deviations of these angular distributions from those that are obtained on the basis of the A. Bohr formula make it possible to estimate the maximum relative orbital angular momentum of fission fragments, this estimate providing important information about the relative orientation of the fragment spins. The angular distributions of fragments originating from subthreshold fission are analyzed for the case of the 238U nucleus. A comparison of the resulting angular distributions with their experimental counterparts leads to the conclusion that the maximum relative orbital angular momentum of binary-fission fragments exceeds 20, the fragment spins having predominantly a parallel orientation. The possibility is considered for performing an experiment aimed at measuring the angular distributions of fragments of the spontaneous fission of polarized nuclei in order to determine both the spins of such nuclei and the maximum values of the relative orbital angular momenta of fission fragments.

S. G. Kadmensky

Papers

T-odd asymmetries in the angular distributions of fragments originating from the ternary fission of nuclei

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

Decay and Fission of Oriented Nuclei

Angular distribution of products of ternary nuclear fission induced by cold polarized neutrons

Angular distributions, relative orbital angular momenta, and spins of fragments originating from the binary fission of polarized nuclei