A Microscopic Theory Of Fission Dynamics Based On The Generator Coordinate Method

This book introduces a quantum-mechanical description of the nuclear fission process from an initial compound state to scission. Issues like the relevant degrees of freedom throughout the process, the way of coupling collective and intrinsic degrees during the fission process, and how a nucleus divides into two separate daughters in a quantum-mechanical description where its wave function can be non-local, are currently being investigated through a variety of theoretical, computational, and experimental techniques. The term “microscopic” in this context refers to an approach that starts from protons, neutrons, and an effective (i.e., in-medium) interaction between them. The form of this interaction is inspired by more fundamental theories of nuclear matter, but still contains parameters that have to be adjusted to data. Thus, this microscopic approach is far from complete, but sufficient progress has been made to warrant taking stock of what has been accomplished so far. The aim is to provide, in a pedagogical and comprehensive manner, one specific approach to the fission problem, originally developed at the CEA Bruyères-le-Châtel Laboratory in France. Intended as a reference for advanced graduate students and researchers in fission theory as well as for practitioners in the field, it includes illustrative examples throughout the text to make it easier for the reader to understand, implement, and verify the formalism presented.

This thesis is concerned with the application of the time-dependent density functional theory (TDDFT) to investigate the fission dynamics of atomic nucleus, which is still one of the most complicated problem in nuclear physics and a full microscopic interpretation is still missing. The establishment of the time-dependent superfluid local density approximation (TDSLDA) and the increasing power of computing resources make the three-dimensional symmetry unrestricted simulations of fission dynamics possible in recent years. In this work, a qualitative new nuclear energy density functional (NEDF) is developed, which contains only seven uncorrelated fitting parameters, and have excellent performance in describing various nuclear properties, e.g. nuclear mass, charge radii, neutron separation energy, shell structure, and deformation properties like the height of fission barriers and the excitation energy of fission isomer. Using such NEDF and another popular NEDF among fission practitioners, SkM*, a comprehensive study of fission dynamics with TDSLDA formalism is presented. The role of pairing correlations in fission dynamics is demonstrated quantitatively. It is also shown that independent TDSLDA trajectories with different initial conditions on the potential energy surface generate almost the same fission fragment (FF) configurations, e.g. the mass split, total kinetic energy, total excitation energies etc. An important aspect of this study is to provide a quantitative validation that the fission dynamics from saddle to scission is a non-adiabatic, overdamped one. To overcome the limitation of TDDFT that fails to produce the variances in the FF properties, a novel method in the spirit of the classical Langevin approach is promoted to include fluctuations and dissipations into the TDDFT framework. Promising results are obtained in a simpler nuclear hydrodynamics simulation, while its implementation in full TDSLDA calculation is still challenging.

Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in 238U. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn't seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in 238U and 239U for an excitation energy of 2.3 MeV above the barrier. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.

Fission-fragment properties have been calculated for thermal neutron-induced fission on a 239Pu target, using constrained Hartree-Fock-Bogoliubov calculations with a finite-range effective interaction. A quantitative criterion based on the interaction energy between the nascent fragments is introduced to define the scission configurations. The validity of this criterion is benchmarked against experimental measurements of the kinetic energies and of multiplicities of neutrons emitted by the fragments.

While a predictive, microscopic theory of nuclear fission has been elusive, advances in computational techniques and in our understanding of nuclear structure are allowing us to make significant progress. Through nuclear energy density functional theory, we study the fission of thorium and uranium isotopes in detail. These nuclides have been thought to possess hyperdeformed isomers in the third minima of their potential energy surfaces, but microscopic theories tend to estimate either shallow or non-existent third minima in these nuclei. We seek an explanation in terms of neutron shell effects. We study how the fission pathways, the symmetry, and the third minima of these nuclei evolve with increasing excitation energy. We then study the fission of mercury-180, in which a recent experiment unexpectedly discovered that this nucleus fissions asymmetrically. We find that the fission of mercury-180 and mercury-198 is driven by subtleties in shell effects on the approach to scission. We finally survey fission barrier heights and spontaneous fission half-lives of several actinide nuclei, from radium to californium. For a new energy density functional, we find good agreement between our calculations and available experimental data, lending confidence to the predictions of our theory beyond experimentally measured nuclei.

This book brings together various aspects of the nuclear fission phenomenon discovered by Hahn, Strassmann and Meitner almost 70 years ago. Beginning with an historical introduction the authors present various models to describe the fission process of hot nuclei as well as the spontaneous fission of cold nuclei and their isomers. The role of transport coefficients, like inertia and friction in fission dynamics is discussed. The effect of the nuclear shell structure on the fission probability and the mass and kinetic energy distributions of the fission fragments is presented. The fusion-fission process leading to the synthesis of new isotopes including super-heavy elements is described. The book will thus be useful for theoretical and experimental physicists, as well as for graduate and PhD students.